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Application of seismic cone for characterization of ground improved by vibro-replacement Asalemi, Ali Amini 2006

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A P P L I C A T I O N O F SEISMIC C O N E FOR CHARACTERIZATION OF GROUND IMPROVED BY VIBRO-REPLACEMENT  by  ALI AMINI ASALEMI  M . A . S c , University o f Science and Technology, Tehran, Iran B . S c , University o f Science and Technology, Tehran, Iran  A THESIS S U B M I T T E D IN P A R T I A L F U L F I L L M E N T OF T H E REQUIREMENTS F O R T H E D E G R E E OF  D O C T O R OF PHILOSOPHY in .THE F A C U L T Y OF G R A D U A T E STUDIES ( C i v i l Engineering)  T H E UNIVERSITY OF BRITISH C O L U M B I A December 2006 © A L I A M I N I A S A L E M I , 2006  ABSTRACT The objective of this thesis was to gain a better understanding of the physical process o f ground improvement by vibro-replacement and o f how the induced changes in ground conditions affect the interpretation o f seismic cone penetration testing used to assess its effectiveness. This was achieved by a combination o f field testing and monitoring supported by numerical modelling o f both the vibro-replacement process and o f in situ testing. Field measurements were made o f the input motions created by the vibrator and the induced response of the ground. The measured vibrator motions were input to a numerical model of the soil mass and the results of the analysis were compared to the measured data. The results o f seismic cone testing before and after treatment at 15 sites and existing chamber test data were analyzed and additional numerical modelling o f seismic cone testing in the post-treatment ground conditions was carried out. The study showed that the ground response to the vibrator attenuated with distance due to geometrical spreading and material damping. The direction o f the principal horizontal acceleration changed with distance from the vibrator. It was shown that vibro-replacement creates a young, heterogeneous deposit comprising the native soil with increases in density and horizontal stress varying with distance from stiffer stone columns. heterogeneity  If the induced  is neglected when interpreting in situ test results, there w i l l be  some  over-estimation o f the soil properties close to the cone hole and considerable under-estimation of the average properties o f the composite mass. The stiffer stone columns also change the wave propagation regime during down-hole testing and prevent reliable interpretation of the shear wave velocity o f the improved native soil. Analysis o f field test data showed that vibro-replacement causes an apparent shift in soil behaviour type classification. The combined effects o f changes in density, horizontal stress and time dependent soil stiffness were shown to be important when interpreting seismic cone results. Friction ratio was found not diagnostic o f changes in soil conditions. For the soils studied, a correlation was derived between achievable tip resistance and pre-treatment soil behaviour type for several stone column spacings.  ii  TABLE OF CONTENTS  ABSTRACT T A B L E OF CONTENTS LIST OF T A B L E S LIST OF FIGURES GLOSSARY ACKNOWLEDGEMENTS DEDICATION  ii iii viii ix xxi xxv xxvi  CHAPTER 1 INTRODUCTION 1.1 Background 1.2 Focus o f this research ; 1.3 Methodology and organization o f the thesis  1 1 2 3  CHAPTER 2 CURRENT APPROACHES TO GROUND IMPROVEMENT A N D C H A R A C T E R I Z A T I O N O F ITS E F F E C T S 2.1 Introduction 2.2 Soil behaviour during monotonic and cyclic shearing 2.3 Characterization o f granular soils 2.3.1 Introduction 2.3.2 Piezo-cone testing, C P T U 2.3.3 Soil classification by C P T 2.3.4 Engineering properties o f soil 2.4 Mechanism o f compaction o f granular soil 2.5 Ground improvement methods for liquefaction mitigation o f granular soils 2.5.1 Introduction 2.5.2 Vibro-compaction 2.5.3 Wet vibro-replacement 2.5.4 Vibrators 2.5.5 Quality control during vibro-replacement 2.5.6 Previous works on vibration measurement and the mechanism o f compaction by vibro-compaction methods 2.6 Discussion and need for further research 2.7 Summary and conclusions  18 21 22  CHAPTER 3 M E C H A N I S M OF V I B R O - R E P L A C E M E N T 3.1 Introduction 3.2 In situ ground response to vibro-replacement 3.2.1 Field vibration measurement 3.2.2 Vibration measurement equipment 3.2.3 Results o f vibration measurement 3.2.4 Analysis o f results 3.2.4.1 Frequency analysis o f the time histories 3.2.4.2 Attenuation o f vibration 3.2.4.3 Horizontal motion paths o f the vibroflot and soil particles  45 45 45 45 46 48 49 49 49 55  iii  .4 4 4 7 7 7 8 10 11 12 12 13 15 16 17  3.2.4.4 Optimal frequency o f vibration 3.2.4.5 Densification phase 3.2.4.6 Pore pressure response during penetration 3.3 Mechanism o f penetration o f the vibroflot 3.4 Numerical modelling o f vibro-compaction 3.4.1 Introduction 3.4.2 Numerical model 3.4.3 Results o f numerical modelling 3.4.4 Mechanism o f compaction during vibro-replacement 3.4.4.1 Shear-volume coupling model 3.4.4.1.1 Drained condition 3.4.4.1.2 Undrained condition 3.4.4.2 Proposed mechanism of compaction vibro-replacement 3.4.5 Other mechanisms o f the effects o f vibro-replacement 3.4.5.1 Increase in lateral stress 3.4.5.2 Geological ageing effects 3.5 Summary and conclusions  55 56 58 59 60 60 61 64 65 65 65 67 during 67 70 70 72 72  C H A P T E R 4 E F F E C T O N C O N E TIP R E S I S T A N C E O F H E T E R O G E N E I T Y CAUSED B YVIBRO-REPLACEMENT 120 4.1 Introduction 120 4.2 Field evidence 120 4.3 Relation between cone tip resistance and cavity expansion theory 122 4.4 Numerical modelling o f cavity expansion theory 122 4.4.1 Soil model and selection o f parameters 123 4.4.2 Verification o f the numerical analysis 125 4.4.3 Effect o f soil stress dependency on limit pressure 125 4.4.4 Effect o f presence o f stone columns on limit pressure 126 4.4.5 Effect on limit pressure o f variation o f soil parameters in the grid zone between the stone columns 126 4.5 Discussion o f the results o f numerical analyses 128 4.5.1 Effect o f G / G 129 4.5.2 Assumption o f Plane strain condition 129 4.6 Implications for interpretation o f post-densification C P T testing 130 4.7 Effect o f the heterogeneity on ground performance during earthquake shaking. 131 4.8 Summary and conclusions 132 m a x  CHAPTER 5 EFFECT OF HETEROGENEITY C A U S E D B Y V I B R O - R E P L A C E M E N T O N SEISMIC C O N E TESTING RESULTS 147 5.1 Introduction 147 5.2 Interpretation o f S C P T signals for shear wave velocity 147 5.3 Observed effects o f vibro-replacement on seismic cone testing 150 5.3.1 Field evidence on the effect o f stiffer inclusions on seismic test results ..151 5.4 Numerical modelling for investigation o f the effect o f stone columns on V 153 5.4.1 Numerical modelling o f the down-hole seismic test without stone columns 153 s  iv  5.4.1.1 5.4.1.2 5.4.1.3 5.4.1.4  Soil model and conditions analyzed 153 Loading condition 154 Results o f numerical analysis 155 Characteristics o f the simulated signals compared to field data 155 5.4.1.4.1 Shape o f the waveforms 156 5.4.1.4.2 Attenuation o f signals with depth 156 5.4.1.4.3 Widening o f the signals with depth 156 5.4.1.4.4 Compression wave arrival (near field effect) 157 5.4.1.5 Calculation o f V from field data 159 5.4.1.6 Calculation o f V from simulated signals ; 160 5.4.1.7 Summary and conclusions o f the numerical analysis o f S C P T without stone columns 161 5.4.2 Numerical modelling o f the down-hole seismic test with stone columns. 162 5.4.2.1 Wave propagation 162 5.4.2.2 Simulated signals 163 5.4.2.3 Calculation o f the V s from simulated signals 163 5.4.2.4 Discussion 163 5.4.2.5 Summary o f the numerical analysis o f seismic cone testing in presence o f stone columns 165 5.5 Implication on Q C / Q A o f densified soil by shear wave velocity 165 5.6 Summary and conclusions 166 s  s  C H A P T E R 6 EFFECTS OF V I B R O - R E P L A C E M E N T O N T H E G R O U N D RESPONSE TO CONE PENETRATION TESTING 200 6.1 Introduction 200 6.2 Observation o f the changes in ground response to C P T U 200 6.2.1 Database o f vibro-replacement projects in the L o w e r Mainland, B C 200 6.2.2 Geological history o f Richmond 201 6.2.3 Pre- and post-compaction database on C P T classification chart 201 6.2.3.1 Effect o f compaction on soil classification by C P T 203 6.2.3.2 Effect o f compaction on estimation o f apparent fines content ...204 6.2.4 Effect o f changes in soil conditions on classification by C P T in Calibration chamber tests 204 6.2.4.1 Normally consolidated zone 206 6.2.4.2 Effect o f changes in ground conditions on the direction o f movement on the classification chart 206 6.2.4.3 Effect o f changes o f D and lateral stress on I value 208 6.2.4.4 Conclusions 208 6.3 Achievable penetration resistance after vibro-replacement 209 6.4 Summary and conclusions 211 r  c  C H A P T E R 7 EFFECT OF A G E I N G O N INTERPRETATION OF SCPT D A T A 7.1 Background 7.1.1 Mechanism o f ageing 7.1.2 Effect o f ageing on small strain soil properties 7.1.3 Effect o f ageing on stress-strain behaviour o f sand 7.1.4 Effect o f ageing on cone tip resistance v  229 229 230 230 231 232  7.1.5 7.1.6 7.1.7 7.2 Case 7.2.1  Mechanism o f the effect o f ageing on S C P T 232 Effect o f ageing on liquefaction resistance 232 Evidence o f the geological ageing. 233 studies 234 Arthur Laing Bridge site, vibro-replacement 234 7.2.1.1 Introduction 234 7.2.1.2 S C P T results 235 7.2.1.3 Conclusions 236 7.2.2 Massey Tunnel site, blast liquefaction test '. 236 7.2.2.1 Introduction 236 7.2.2.2 S C P T results before and after the blast experiment 237 7.2.2.3 Evidence o f ageing/destructuring 237 7.2.2.4 Implication o f ageing/destructuring in estimation o f soil properties 239 7.2.2.5 Effect o f blasting on G /q, 240 7.2.2.6 Conclusions 240 7.2.3 Kidd2 site, time effect on seismic testing 241 7.2.3.1 Introduction 241 7.2.3.2 Test procedure 242 7.2.3.3 Test results 242 7.2.3.4 Summary and Conclusions 243 7.3 Ageing effects and ground improvement 244 7.4 Effect o f ageing/destructuring on interpretation o f post-densification S C P T for soil properties 245 7.4.1 Interpretation o f relative density and friction angle 245 7.4.2 Interpretation o f soil stiffness 245 7.4.3 Effect o f destructuring on liquefaction cyclic resistance ratio ( C R R ) o f improved ground 246 7.5 Conclusions 247 m a x  C H A P T E R 8 EFFECT OF INCREASE IN H O R I Z O N T A L STRESS O N INTERPRETATION OF CPTD A T A 270 8.1 Introduction 270 8.2 Field evidence o f increase in horizontal stress 270 8.3 Effect o f increase in horizontal stress on interpretation o f soil properties 271 8.3.1 Effect o f increase in horizontal stress on interpretation o f D 271 8.3.2 Effect o f increase in horizontal stress on shear modulus and footing settlement 273 8.3.3 Effect o f increase in horizontal stress on interpreted friction angle from C P T results 277 8.3.4 Effect o f increase in horizontal stress on interpreted cyclic resistance from C P T results 277 8.3.5 Effect o f the increase horizontal stress on estimation o f earthquake induced settlement 278 8.4 Summary and conclusions 279 r  CHAPTER 9 S U M M A R Y A N D CONCLUSIONS 9.1 Research focus and objectives vi  289 289  9.2 Methodology... 9.3 Summary o f major findings 9.4 Recommendations for future research  :  REFERENCES  290 290 295 297  A P P E N D I X O N E : Database o f C P T s carried out before and after vibro-replacement ....313  vii  LIST O F T A B L E S  Table 2-1  Factors affecting mechanical behaviour o f granular soils  Table 2-2  Commonly  used  vibrators  and  their  24  specifications  (from  www.vibroflotation.com) Table 2-3  24  Comparison o f some o f ground improvement methods for liquefaction mitigation (adapted from Mitchell and Gallagher 1998)  Table 2-4  25  M a i n components o f design o f ground improvement for liquefaction mitigation  26  Table 3-1  Distance o f monitored stone columns from the ground sensor...  76  Table 3-2  Calibration o f accelerometers in the ground vibration package  76  Table 3-3  Soil parameters used in the numerical model  76  Table 4-1  Assumed density zonation within compaction grid zones  Table 4-2  Cases of numerical modelling of plane strain analysis o f cavity expansion  :  134  at the centroid o f stone column grid  134  Table 5-1  Input soil parameters in numerical model, homogeneous soil condition  168  Table 5-2  Comparison o f the V obtained from different methods, Richmond, B . C  168  Table 5-3  Material properties used in numerical model  168  Table 5-4  Interpretation o f V (m/s) from simulated signals, depth interval o f 5m- 6m  s  s  168 Table 7-1  Values o f N G for various soils (After Baxter 1999- based on studies by A f i f i and Woods 1971 and Anderson and Stokoe 1978)  Table 7-2  249  Examples o f ageing effects on cone penetration resistance and their main findings (after Baxter 1999)  250  viii  LIST O F F I G U R E S  Figure 2-1  Typical behaviour of sand under monotonic loading in drained condition (after Bolton 1979)  Figure 2-2  Typical behaviour  27 of sand under monotonic  loading in  undrained  condition (after Robertson and Wride 1998)  28  Figure 2-3  Schematic illustration o f the seismic piezo-cone, S C P T U  :  29  Figure 2-4  A typical C P T U profde, K i d d 2 site, Richmond, B C  30  Figure 2-5  Schematic illustration o f seismic cone testing  31  Figure 2-6  C P T classification chart (after Robertson et al. 1986)  32  Figure 2-7  Normalized C P T classification charts (after Robertson 1990)  33  Figure 2-8  C R R curve from C P T (after Robertson and Wride 1998)  34  Figure 2-9  Dependence o f compaction of sands on shear strain magnitude and the number of cycles (a) after Y o u d 1972, (b) air pluviated Fraser River Sand under drained cyclic simple shear testing (adapted from Sriskandakumar 2004)  Figure 2-10  35  Suitability o f ground  improvement  methods based on grain  size  distribution of soils (after Mitchell and Gallagher 1998)  36  Figure 2-11 Wet vibro-replacement process (adapted from www.haywardbaker.com) Figure 2-12  Cross-section  of  a  vibroflot  (adapted  from  website  www.vibroflotation.com) Figure 2-13  Soil  vibroflot  37  interaction-  horizontal  section-  (originally  from  Greenwood 1991, annotated by Green 2001) Figure 2-14  37  38  Schematic illustration o f the effect o f fins to prevent rotation of the vibroflot about its vertical axis  39  Figure 2-15  A typical vibro-replacement set up  39  Figure 2-16  Variation of relative density or SPT blow counts after vibro-compaction as a function of tributary area per compaction point (after Dobson and Slocombe 1982)  '.  40  ix  Figure 2-17 Achievable relative Density vs. Probe Spacing for Soil Densification (From N A V F A C 1997) Figure 2-18  Figure 2-19  41  A n example o f record o f the drawn amperage and depth versus time during vibro-replacement (adapted from www.vibroflotation.com)  42  CPT-based zonation for compactability (adapted from Massarsch 1991)  42  Figure 2-20 Comparative  profdes  of  the  amplitude  of  the  vibroflot  and  post-compaction penetration resistance (after Morgan and Thomson 1983) Figure 2-21  43  Densification zones as a function o f acceleration around a compaction point proposed by Greenwood and Kirsch (1983)  44  Figure 2-22 Vibration history recorded during vibro-stone column. Depth o f monitoring points 4.2m. Distance from the compaction point= 1.5m (adapted from Baez and Martin 1992)  44  Figure 3-1  Pre-compaction C P T profile  77  Figure 3-2  Site plan- location o f the instrumentation and monitored stone columns and ground. The production stone columns around the monitored stone columns were constructed after the test  78  Figure 3-3  Sensor package for ground vibration measurement  79  Figure 3-4  Sensor package for vibroflot vibration measurement  80  Figure 3-5  A view o f the site during vibration measurement  81  Figure 3-6  C P T profile and interpreted soil profile. Relative density curves are based on Baldi (1986) and normally consolidated condition  82  Figure 3-7  Recorded time histories during construction o f stone column #3  83  Figure 3-8  Recorded time histories during stone column #3, enlarged scale during densification. Note that scales are not consistent  Figure 3-9  84  Frequency spectra o f acceleration time histories o f the vibroflot and the ground during densification  85  Figure 3-10 Frequency spectra o f acceleration time histories- enlarged scale  85  Figure 3-11  86  Energy loss due to damping in a visco-elastic material  Figure 3-12 Partial transmission and conversion at the interface (after Santamarina et al. 2001)  86  x  Figure 3-13  Attenuation o f radial and tangential acceleration with distance from vibroflot  Figure 3-14  Attenuation  87 of the resultant horizontal acceleration.  The #number  indicates the order of installation of monitored stone columns. The theoretical  attenuations only include geometric spreading and  not  material damping  ....87  Figure 3-15  Attenuation o f the resultant horizontal acceleration  88  Figure 3-16  Attenuation o f the resultant horizontal acceleration  88  Figure 3-17  Attenuation of radial displacement in the ground around vibrators (after Morgan and Thomson 1983)  Figure 3-18  89  Interpretation of Green (2001) for attenuation o f radial  acceleration  around Keller S-type vibrator based on Baez (1995) data Figure 3-19  90  Variation of damping and modulus ratio with shear strains in sands (after Seed and Idriss 1970, graphs are taken from Shake 2000 manual)  91  Figure 3-20  Attenuation of vertical vibration around the vibroflot  92  Figure 3-21  Horizontal motion paths (acceleration paths) of vibroflot  93  Figure 3-22  Soil particle horizontal motion path (acceleration  paths) for stone  columns # 1 to 3- vertical axis is tangential and horizontal axis is radial to the vibroflot Figure 3-23  94  Soil particle horizontal motion (acceleration paths) at grid centroid (r=1.8m) for stone columns #4 and 5. Vertical axis is tangential and horizontal axis is radial to the vibroflot  Figure 3-24  95  Time history of ground response at 3.5 m from a vertically oscillating vibratory probe during switch on (adapted from Massarsch and Heppel 1991)  Figure 3-25  96  Response of the vibroflot and ground during switch-on at 10m depthstone column #3, enlarged from Figure 3-7  Figure 3-26  97  Ratio of the responses of ground and vibroflot as a function o f frequency during switch-on  Figure 3-27  98  Comparison of the vibroflot motion and power consumption densification phase  during 99  xi  Figure 3-28  Pore pressure time history during stone column #3  100  Figure 3-29  Pore pressure response during penetration o f vibroflot  101  Figure 3-30  Schematic of the Original Vibratory Piezocone designed by Sasaki and Koga (1982) (taken from M c G i l l i v r a y et al. 2000)  Figure 3-31  102  Vibrocone tests (a) at site 1 which shows no apparent damage during seismic events and (b) at site 2 with historical liquefaction  evidence  following seismic events ( from Sasaki et al. 1984) Figure 3-32  (a) Schematic  illustration of soil-vibroflot interaction  102 in horizontal  section through the vibroflot, (b) Symmetric condition of the motion of the vibroflot  ...103  Figure 3-33  Mechanical model of the vibrator in the ground (after Fellin 2000)  104  Figure 3-34  Geometry o f the numerical model of soil-vibroflot interaction  104  Figure 3-35  Interface elements between soil and vibroflot (enlarged from figure 3-34).... 105  Figure 3-36  Motion o f the vibroflot during densification (stone column #3, depth of the vibroflot=9m, t=562-564 sec.)  106  Figure 3-37  Iteration of analysis for equivalent linear method  106  Figure 3-38  Magnified deformed shape of the model (vertical and horizontal axes are in metres)  Figure 3-39  Comparison  107 of  resultant  horizontal  accelerations  from  field  measurement and equivalent elastic analyses Figure 3-40  108  Motion paths of vibroflot and soil particles at different radial distances, (left) Field observation, (right) Numerical. model. Note figures have different scales  Figure 3-41  109  M i n i m u m required measurement points in the ground for calculation of the 3 components of shear strains  Figure 3-42  110  Distribution of shear strains in horizontal plane from equivalent linear analyses  Ill  Figure 3-43  Shear-volume coupling model for sands proposed by Byrne (1991)  112  Figure 3-44  Change in relative density due to cyclic shearing based on Byrne (1991)  Figure 3-45  model  112  Cone tip resistance before and after vibro-replacement  113  xii  Figure 3-46  Pore pressure generation at different  radial distance, r, around  the  vibroflot, based on the calculated shear strains and Byrne (1991) model for undrained conditions Figure 3-47  114  Radial displacement of grid point at different distances from the vibroflot versus vibration time  Figure 3-48  115  Increase of average horizontal stress with the number o f cycles at different radial distances, r from the vibroflot.  Figure 3-49  Radial stress vs. radial displacement at radial distance o f r=l .7m from the vibroflot. Negative sign indicates compression stress  Figure 3-50  117  Expanded cavity by the vibroflot. Note the formation of a gap between the vibroflot and soil  Figure 3-51  116  118  Stress path o f a soil element at radial distance o f r=l .7m from the vibrator obtained from numerical model  119  Figure 4-1  Schematic contours of vibration amplitude within a grid zone  135  Figure 4-2  Variation of D from the vibroflot (reproduced from D ' A p p o l o n i a 1953)  135  Figure 4-3  Variation of q with distance from the compaction points for two different  r  c  vibrators Vibroflot V 2 3 and V 3 2 ( after Degen and Hussin 2001)  136  Figure 4-4  Idealization of analysis for cone penetration (after Y u and Mitchell 1998).... 137  Figure 4-5  Ratio of cone tip resistance to cavity limit pressure from pfessuremeter vs. state parameter (after Ghionna et al. 1990)  138  Figure 4-6  Geometry o f plane strain numerical model  138  Figure 4-7  Geometry o f numerical model, enlarged from Figure 4-6  139  Figure 4-8  Back calculated G / G  m a x  from the pressuremeter tests in calibration  chamber Figure 4-9  140  Comparison of F L A C analyses with Carter et al. (1986) closed form solution  Figure 4-10  140  Effect of stress dependency of the soil model on limit pressure from F L A C analysis compared with non-stress-dependent soil model  141  Figure 4-11  Geometry of numerical model with the addition of three stone columns  141  Figure 4-12  Effect of inclusion of stone columns on cylindrical cavity limit pressure  142  Figure 4-13  Schematic illustration of lateral fixity of the stone columns in 3-d space  142  xiii  Figure 4-14  Effect o f fixity o f stone columns on cylindrical cavity limit pressure (G/G  Figure 4-15  max  =0.1)  ..  Variation o f cylindrical cavity limit pressure as a function o f D for r  homogeneous soil condition ( G / G Figure 4-16  143  = m a x  0.5)  Variation o f cylindrical cavity limit pressure as a function o f D for r  homogeneous soil condition for G / G  max  = 0 . 1 and 0.5. Note the assumption  of G/G ax does not affect the interpreted D m  Figure 4-17  143  144  r  Consideration o f heterogeneity o f soil within compaction grid on Q C after vibro-replacement  Figure 4-18  145  A n example o f interpretation o f C R R with and without consideration o f heterogeneity o f ground conditions within the compaction grid. Using and average q results in a greater interpreted C R R  120  t  Figure 5-1  Comparison o f S C P T seismic signals before (left) and after (right) vibro-replacement, Richmond, B C  Figure 5-2  169  V profile from cross-over and cross-correlation methods, (left) before s  vibro-Replacement, (right) after vibro-Replacement  170  Figure 5-3  Variation o f phase velocity, before: 7.9m & 8.9m, after: 7.7m & 8.7m  171  Figure 5-4  Frequency spectra before and after vibro-replacement, before: 7.9m & 8.9m, after: 7.7m & 8.7m  Figure 5-5  SCPT  profile before  and  171 after  vibro-replacement,  Laing  Bridge,  Richmond, B C Figure 5-6  172  Comparison o f S C P T and S A S W after vibro-stone column - Laing bridge, Richmond, B . C . (after Pidlisecky 2003)  173  Figure 5-7  Cross-hole test in presence o f stone columns (after Schneider et al. 2000)  174  Figure 5-8  Comparison o f cross-hole and down-hole seismic test in mudstone with interbedded thin limestone bands (after Pinches and Thompson 1990)  175  Figure 5-9  Schematic geometry o f the F L A C model  176  Figure 5-10  Modelling o f soil behaviour in compliance with strain  dependent  deformation characteristics (after Ishihara 1996) Figure 5-11  176  Input loading at the ground surface over the length o f the seismic source beam  177  xiv  Figure 5-12  Wave propagation in homogeneous soil, velocity vectors at 0.05 sec after the impact  Figure 5-13  177  Time histories of horizontal velocity in numerical model at 5 m, homogeneous soil  Figure 5-14  178  Time histories of horizontal acceleration in numerical model at 5 m, homogeneous soil  Figure 5-15  178  Simulated signals, acceleration time histories in homogeneous soil, damping=5%  179  Figure 5-16  A typical C P T profile at Kidd2, Richmond, B C  180  Figure 5-17  Typical S C P T accelerometer response, K i d d 2 , Richmond, B . C  181  Figure 5-18  Effect o f material damping on the number of cycles, homogeneous soil  182  Figure 5-19  Comparison o f F F T spectra of simulated and S C P T signals  183  Figure 5-20  Simulated signals, increasing stiffness with depth, damping ratio=2%  184  Figure 5-21  Typical bender element test signal with square pulse excitation (after Viggiani and Atkinson 1995)...  185  Figure 5-22  Near field effect in S C P T signals, enlarged from Figure 5-17  185  Figure 5-23  Near field effect in simulated signals, enlarged from Figure 5-20  186  Figure 5-24  Comparison o f different interval methods for calculation of the V , s  Richmond, B . C  187  Figure 5-25  Profile o f shear wave velocity, Kidd2, Richmond, B . C  188  Figure 5-26  The  V  s  profile  from  the  simulated  signal,  homogeneous  soil,  Damping=5% Figure 5-27  189  The V profile from the simulated signal- increasing stiffness with depth, s  Damping=2% Figure 5-28  190  Variation o f phase velocity, simulated  signals, homogeneous soil,  Damping=5%, 5m & 6m depth interval Figure 5-29  191  Schematic illustration of effects of inclusion of stone columns on wave propagation during S C P T  192  Figure 5-30  Plane strain model including two stone columns  193  Figure 5-31  Propagation o f body waves in presence o f two stone columns  194  Figure 5-32  Simulated signals in the presence of two stone column, G =5, D = l m  195  r  xv  Figure 5-33  S C P T signals after Vibro-Replacement - Richmond, B . C  196  Figure 5-34  Enlarged S C P T signals from Figure 5-33  197  Figure 5-35  Phase velocity of simulated signals, 5m & 6m  197  Figure 5-36  Frequency spectrum of simulated signals at 5m  198  Figure 5-37  Sensitivity of phase velocity to G and D , simulated signals  198  Figure 5-38  Comparison of change in V and q after vibro-replacement  199  Figure 6-1  History o f the  r  s  growth  t  of the  Fraser  River Delta (Source: C G S ,  http://sts.gsc.nrcan.gc.ca/geoscape/va^  213  Figure 6-2  Typical soil profde in Richmond, B C (not to scale)  213  Figure 6-3  Typical S C P T profdes before and after Vibro-Replacement (after Howie et al. 2000)  Figure 6-4  214  C P T test results before vibro-replacement (natural ground) from the local database plotted on classification charts (all sites). For C P T classification zones see Figures 2-6 & 2-7  Figure 6-5  215  C P T test results after vibro-replacement from the local database plotted on classification charts (all sites). For C P T classification zones see Figures 2-6 & 2-7  Figure 6-6  215  Path of movement of the position on the classification charts due to vibro-replacement  216  Figure 6-7- Comparison of pre-I and post-I values c  c  217  Figure 6-8  Comparison of pre- and post apparent fines content interpreted from C P T ....217  Figure 6-9  Calibration chamber data for Ticino sand plotted on C P T classification charts- (Left) N C Ticino sand, (Right) O C Ticino sand , (Top) Classification chart (Robertson  et al. 1986), (Bottom) Normalized  classification chart, (Robertson 1990) Figure 6-10  218  Results of calibration chamber data for N C Ticino sand on normalized classification chart using true normalization for stress level  Figure 6-11  CPT-based soil classification chart (1993)  219  proposed by Jefferies and Davies 220  xvi  Figure 6-12 Comparison o f normally consolidated zones by Robertson (1990) and by Jefferies and Davies (1993)- Data points from calibration chamber data for N C Ticino sand Figure 6-13  221  Effect o f changes in only D on C P T classification chart, data taken from r  calibration chamber testing on Ticino sand  222  Figure 6-14 Effect o f D on Rf, Ticino sand, data taken from calibration chamber r  testing on Ticino sand Figure 6-15  223  Effect o f the horizontal stress on Rf, data taken form calibration chamber testing on Ticino sand  Figure 6-16  223  Effect o f O C R on Rf, data taken from calibration chamber testing on Ticino sand  Figure 6-17  224  Effect o f the increase in D and/or a ' on I - from C C testing data on N C r  n  c  Ticino sand  224  Figure 6-18 Normalized tip resistance before and after vibro-replacement, triangular grid, Lower Mainland, B C Figure 6-19  Comparison o f the  225  normalized tip  resistance  before  and  after  vibro-replacement, Lower Mainland, B C with Baez (1995) correlation  226  Figure 6-20 Effect o f fines content on the achievable penetration resistance after compaction by vibro-rod method (from Saito 1977) Figure 6-21  227  Achievable normalized tip resistance as a function o f pre-compaction I . c  (triangular grid, Lower Mainland, B C , only Geopac sites)  228  Figure 7-1  Increase in shear modulus with time (after A f i f i and Woods 1971)  251  Figure 7-2  Comparison o f strain-dependent shear modulus o f dense sand from disturbed and undisturbed samples (taken from Ishihara 1996, data originally from Katayama et al. 1986)  Figure 7-3  Effect o f ageing on stress-strain curve, Fraser River sand (after Howie et al. 2001)  Figure 7-4  251 .  252  Comparison o f modulus reduction curve o f dense sand from disturbed and undisturbed samples (after Ishihara 1996- data originally from Katayama et al. 1986)  252  xvii  Figure 7-5  Comparison o f modulus reduction curve in the field and in the lab (after Ishihara 1996). Correction factor may be used to obtain the in situ modulus reduction curve  Figure 7-6  253  Normalized tip resistance in saturated sands versus time after disturbance (originally by Charles et al. 1992; updated by Jefferies and Rogers 1993)  254  Figure 7-7  Time effect on liquefaction resistance (after Seed 1979)  254  Figure 7-8  Field cyclic strengths o f aged sand deposits relative to the cyclic strength of Holocene sand, age < 10,000 years (after Arango and Migues 1996)  Figure 7-9  255  Comparison o f undrained simple shear response o f undisturbed sand and water-pluviated sand (after V a i d and Sivathayalan 2000)  255  Figure 7-10 Plot o f average q i and 14C age o f organic material in topset sand (after c  Monahan et al. 2000) Figure 7-11  256  Change in normalized shear wave velocity with age for uncemented sands (after Robertson et al. 1995)  256  Figure 7-12 Possible effects o f age o f deposit on C P T penetration resistance and shear wave velocity (after Wride et al. 2000) Figure 7-13  257  S C P T U profiles before and after Vibro-Replacement, Laing Bridge site, Richmond, B C  258  Figure 7-14 Massey Tunnel blast experiment, location o f S C P T holes Figure 7-15  259  Settlement as a function o f depth below the ground surface at the test area with no drains, (after Gohl 2002)  .....260  Figure 7-16 Result o f 10 cone penetration testing before and at 4 different times up to 10 months after the blast-liquefaction experiment at Massey Tunnel Site  261  Figure 7-17 Result o f seismic cone testing before and at 4 different times after blasting, Massey Tunnel Site  262  Figure 7-18 Variation o f the average values o f q and V with time after blasting, t  Massey Tunnel Site Figure 7-19 Variation o f average G  s  '. m a x  263  / q before and after blasting, Massey Tunnel t  Site  264  Figure 7-20 C P T U sounding, K i d d 2 site, Richmond, B . C  xviii  265  Figure 7-21  Windowed signals at 11.95m at wait times o f 1, 5, 10, 20, 40 and 60 minutes after the stoppage o f penetration- left hammer hit - low pass 250Hz- Kidd2 site, Richmond, B . C  Figure 7-22  266  The shift o f the signals relative to that at one minute for left and right hits at depth interval 10.95-11.95m  267  Figure 7-23  Variation o f V s with wait time at depth interval 10.95-11.95m  267  Figure 7-24  Schematic seismic wave travel path  268  Figure 7-25  Conceptual representation o f the effect o f densification on soil modulus, #1= natural aged deposit; #2=After destructuring; #3=Young densified deposit; #4=Aged densified deposit  Figure 8-1  229  K o measurement by Stepped Blade, conducted at 70 cm from Stone Column and 85 cm from Geopier Element. A l l tests oriented to measure radial stress (after Pitt et al. 2003)  Figure 8-2  Non-uniqueness  281  o f interpretation  o f cone tip resistance-  combinations o f D and ah results in the same q R  Figure 8-3  Application o f combination o f q  t  and V  s  different 281  t  for post-compaction site  investigation, Vibro-Replacement project, Richmond, B C Figure 8-4  282  Settlement versus foundation sizes for different K Q - D R combinations (Adapted from Jamiolkowski and Pasqualini 1992)  Figure 8-5  Effect o f variation o f K o on G  m a x  283  for constant q . Variation o f K o and D t  R  are such that the resulting q remains constant  283  t  Figure 8-6  Effect o f increase in coefficient o f lateral stress on the shape o f the modulus reduction curve  284  Figure 8-7  Effect o f increase in K o on the shear modulus (assume a' =100 kPa)  285  Figure 8-8  Effect o f increase in K o on G normalized to G at Ko=0.45 for shear strain  v  ofy=0.002 Figure 8-9  286  Effect o f increase in K o on the interpretation o f G  m a x  from measured V  s  (through the effect o f estimation o f soil density)  286  Figure 8-10  Effect o f increase in K o on the interpretation o f G from measured V  Figure 8-11  Effect o f increase in K o on the interpretation o f peak friction angle from post-densification tip resistance  s  287  287  xix  Figure 8-12  Comparison o f derived C R R correlation with the empirical correlation suggested by Robertson and Campanella (1985), (after Salgado et al. 1997)  288  xx  GLOSSARY  a: Net area ratio of the cone A : Single amplitude o f acceleration A i and A : Vibration amplitudes at distances ri and r 2  2  A C C , : Acceleration o f the vibroflot in x direction x  t  A C C , : Acceleration o f the vibroflot in y direction y  a  m a x  t  : M a x i m u m acceleration at ground surface  A : Area o f soil in stone column tributary area s  A : Cross section area o f stone column s c  A : Tributary area o f one stone column t r  A : Correlation parameter in empirical shear wave velocity equation v s  B : B u l k modulus B : Correlation parameter in empirical shear wave velocity equation v s  Ci and C : Regression parameters in shear volume coupling model 2  C S R : Cyclic stress ratio D : Damping ratio Dchambei-: Diameter o f calibration chamber Dcone: Diameter o f cone D : Relative density r  E : void ratio f: Frequency o f vibration F: Normalized friction ratio F C : Fines content fs : Sleeve friction g: Gravitational acceleration G  m a x  : Small strains shear modulus  G a (t): G m  X  m a x  at time t  G x(tp): Gmax at end o f primary consolidation ma  G : Ratio o f shear modulus o f stone column to soil. r  I : Soil Behaviour Type Parameter c  xxi  IR: A coefficient in Bolton empirical correlation K : A coefficient in empirical correlation for soil modulus m  K  o  and K<,  c  0  N C  : Coefficients of lateral stresses for over and normally consolidated soil  Koi coefficient of horizontal stress L and Li: Slant distances between sensor in cone and source beam at two intervals 2  m: a coefficient in empirical correlation for soil modulus M : Soil Modulus n: A coefficient in the geometric spreading equation; n=0, 0.5 and 1 for plane, cylindrical and spherical wave front, respectively N  C Y C  : Number of cycles  N Q : A parameter for ageing effect on small strain shear modulus n : A correlation parameter in shear wave velocity empirical equation vs  OCR: Over-consolidation ratio P : A reference pressure a  P : Atmospheric pressure a2  PI: Plasticity index post-q i: Normalized cone tip resistance before compaction c  pre-q i: Normalized cone tip resistance after compaction c  Q: Normalized cone tip resistance q : Measured cone tip resistance c  q i Cone tip resistance normalized to vertical effective stress c  :  : Cone tip resistance normalized to vertical effective stress (unitless)  q iN c  qc-me sured: a  Cone tip resistance measured during penetration in calibration chamber  Qa: Inverse of twice damping ratio q : Cone tip resistance corrected for water pressure behind the friction sleeve t  r: Radial distance between the vibration source and point of interest ri and r : Distances from the source of vibration 2  ra: Stress reduction factor Rf: Friction ratio Si(t) and S (t+x) : Two consecutive SCPT signals recorded in the time domain at upper and 2  lower interval depths  xxii  T : A coefficient representing the reduction o f amplitude due to partial transmission and mode r  conversion. T: Length o f the time record in seconds t: Time t2-ti: Travel times o f shear waves from the source to the sensor in the cone at at two successive depths intervals t : Time to the end o f primary compression p  V : Wave velocity V : Compression wave velocity p  V : Shear wave velocity. s  V i : Shear wave velocity normalized to vertical effective stress s  Wp: Hysteresis area under stress-strain curve Ws: The triangular area under stress-strain curve (Ymax-T ax/2) m  a : A n empirical coefficient for energy damped in vibration a i Attenuation coefficient associated with fj :  A s : Incremental volumetric strain in the current cycle v  A s : Cyclic elastic volumetric strain e  v  A s : Cyclic plastic volumetric strain p  v  A s : Cyclic accumulated volumetric strain v  A a ' : Vertical effective stress change per half a cycle v  At: Interval time equal to t -ti in S C P T 2  s : Accumulated volumetric strain from the previous cycles v  <j) : Friction angle at critical state or constant-volume cv  <j): Peak friction angle p  (j)(f): Phase difference y : Engineering shear strain in the current cycle y = shear strain threshold t  Y*: Net engineering shear strain in the current cycle X: wave length v: Poisson's ratio  xxiii  p : B u l k density r j ' : Mean normal stress m  o"' _B Mean normal stress at failure in Bolton (1986) equation m  :  a ' : Vertical effective stress v  a ' : In situ vertical effective stress vo  r j : In situ total vertical stress vo  rj : Radial stress r  GQ: Tangential stress v|/ : M a x i m u m dilation angle max  T : Time shift in cross-correlation method T : Shear stress o f the soil s  xxiv  ACKNOWLEDGEMENTS  First o f all, I would like to deeply thank my advisor, Dr. John Howie for his guidance, support, mentorship, patience and above all his friendship. The support o f my industrial collaborators, Dr. A l e x Sy from Klohn-Crippen, David Woeller from Conetec Investigations Ltd., Nelson Beaton from Geopac West Ltd., and Dennis Diggle from Foundex Explorations is also greatly appreciated. Special thanks goes to D r A l e x Sy for his mentorship and guidance. There are many other people who were also instrumental to this research. Professor Peter Byrne, Dr. Carlos Ventura, Ernest Naesgaard, Dr. P. Stewart for their technical guidance, Scott Jackson and Harald Schrempp and other staff o f the University o f British Columbia, Department o f C i v i l Engineering for their technical support, and long discussions with fellow student and office mate Chris Daniel are acknowledged. I also acknowledge the financial support o f the Natural Science and Engineering Research Council o f Canada, the G R E A T A w a r d Scholarship o f the Science Council o f B . C .  xxv  To my dearparents, fihmadandTah  To my Coving wife, fMitra  To my dear son, Mehrdad  And to many others that I dearly Love  XXVI  CHAPTER 1 INTRODUCTION  1.1  BACKGROUND Almost all construction works are done on, i n and/or with the soil. However, soil is a  natural material and its properties do not always suit the proposed construction. In particular, seismic loading may result in liquefaction, which can induce unacceptably large deformations, lateral spreading, slope failure, loss o f bearing capacity, etc. In such cases, one may choose to improve the in situ soils to withstand the design loads with acceptable performance. Design o f ground improvement for liquefaction mitigation requires answers to the following questions: • Is ground improvement necessary? • T o what level should the ground be improved (specification) and how should the improved ground be assessed ( Q C / Q A ) ? • W h i c h techniques are suitable to improve the ground? Ground improvement has a long history. V a n Impe (1989) noted that it is probably the oldest o f all common execution methods i n civil engineering but that while ground improvement methods are usually simple in concept, in most cases it is difficult to explain the scientific basis for their success. In the preface to the first Geotechnique Symposium i n Print, entitled "Ground Treatment by Deep Compaction", the editors, Burland et al. (1976) noted that there was a mystique surrounding ground treatment methods. Thirty eight years later, i n the Geotechnique Symposium in Print on "Ground and Soil Improvement", Raison (2004) noted: "Methods for  improving ground and soil have undergone significant  developments since the first Symposium particularly in terms of application and usage, and many innovative techniques have been introduced. However, it is of significance that in many areas the design process still lacks a theoretical framework. It is also clear that ground and soil improvement has received little input from the research community in the last two decades despite the immense practical importance of the subject. "  1  Charles (2002) indicated that the application o f ground treatment methods had remained mainly empirical and would benefit from the application o f better engineering science. H e suggested that this would ideally result i n the following: 1. A n improved understanding o f soil behaviour and diagnosis o f deficiencies, 2. A n improved understanding o f physical treatment processes through numerical analysis and testing o f physical models, 3. A clearer relationship between  field  performance  o f treated ground and  improvement indicated by i n situ testing before and after treatment, and 4. A more realistic appreciation o f what can be achieved by ground treatment through the study o f well documented case histories o f long-term performance.  This thesis is an attempt to achieve progress on each o f the above points.  1.2  F O C U S O F THIS R E S E A R C H In the Lower Mainland o f British Columbia, ground improvement is commonly required  to increase the resistance o f soil to liquefaction and large ground movements during seismic loading. From a survey o f ground improvement projects completed in B . C . between 1990 and 2000, the author found that vibro-replacement was the most common ground improvement technique in B C for liquefaction mitigation and that cone penetration testing ( C P T ) was the primary method o f both site characterization and o f assessment o f the degree o f improvement achieved. Consequently, this thesis focuses on achieving an improved understanding o f the vibro-replacement process and on how the most common in situ testing techniques used to characterize the ground conditions before and after ground treatment are affected by the changes in ground conditions caused by the treatment. The objectives o f the research were as follows: 1. To understand the physical process o f vibro-replacement and its effects on ground conditions; 2. To understand  the effects  o f changes  in ground conditions induced by  vibro-replacement on site characterization by the seismic cone penetration test.  2  1.3  M E T H O D O L O G Y A N D O R G A N I Z A T I O N O F T H E THESIS To approach the objectives o f this research, the following steps were taken: 1.  Investigation o f the physical process o f vibro-replacement method and its effects on ground conditions by vibration measurement  in the field followed by  numerical modelling (Chapter 3). 2.  Investigation o f the effect o f the heterogeneity induced by vibro-replacement, on seismic cone penetration testing by field observation and numerical modelling o f the seismic cone penetration test (Chapters 4 and 5).  3.  Development o f a database o f pre- and post-vibro-replacement C P T U results for 15 vibro-replacement sites to observe the trends o f changes in C P T response (Chapter 6).  4. Investigation o f the effect o f time on the S C P T results by monitoring the time effect in field case studies (Chapter 7). 5. Investigation o f the  effect  o f increase  in horizontal stress, caused  by  vibro-replacement, on interpretation o f S C P T using parametric studies (Chapter 8).  Chapter 9 summarizes the major findings and conclusions o f this study followed by recommendations for further research.  3  CHAPTER 2 CURRENT APPROACHES T O GROUND IMPROVEMENT AND C H A R A C T E R I Z A T I O N O F ITS E F F E C T S  2.1  INTRODUCTION This chapter presents an overview o f ground improvement as a remedial measure against  the effects o f seismic loading on sandy soils and reviews the current state o f understanding o f how densification is achieved and how its success is assessed. A brief review o f the stress strain behaviour o f sands under monotonic and cyclic loading is provided as a background to discussions on the mechanism o f densification and on the use o f site characterization to assess ground conditions before and after ground improvement.  2.2  SOIL B E H A V I O U R D U R I N G M O N O T O N I C A N D C Y C L I C S H E A R I N G The mechanical behaviour o f granular soils is a function o f many factors as summarized  in Table 2-1. For more details refer to Hight and Leroueil (2003). Typical drained behaviour o f sand under monotonic loading is shown in Figure 2-1. The behaviour can be divided into loose and dense behaviours relative to an ultimate or critical state. Theoretically, when the soil reaches the ultimate state, there is no further tendency for volume change and the mobilized shear strength and void ratio remain constant with increasing strain. The locus o f combinations o f mean normal effective stress and void ratio at ultimate limit or critical state is called the Ultimate State Line ( U S L ) or Critical State Line ( C S L ) . However, the shear strain required to reach this state is typically too large to be attainable during laboratory tests. In the following, we w i l l assume that the ultimate limit state exists and that it is identical to the critical state. In loose sands, the volume decreases (contraction) with increasing shear strain, until the ultimate limit state is reached. A t this state, the maximum shear strength is mobilized and no further volume change occurs with increasing shear strain. In dense behaviour, there is usually an initial contraction followed by dilation as the shear strain increases. The peak shear strength occurs at the maximum dilation rate. W i t h further increase o f shear strain, the dilation rate decreases towards the ultimate state and the soil displays brittle behaviour.  4  The tendency towards volume change under drained conditions, results i n a tendency for generation o f pore water pressure when shearing occurs under conditions o f restricted drainage, with typical behaviour for a fully undrained case shown in Figure 2-2. For contractive sand (loose o f critical - curve SS in Figure 2-2) positive excess pore pressure is generated, which decreases the effective stress and the shear resistance o f the soil. Under undrained conditions, contractive sand exhibits a peak strength at a shear stress much less than its drained strength at the current effective stress level and then goes into a strain softening phase. The envelope o f stress ratio or shear stress at which strain softening is initiated has been given a variety o f names.  T w o common names are the Critical Stress Ratio or Collapse  Surface. Because there is no tendency for volume change after reaching the ultimate state, the shear strength remains constant as the shear strain increases. The strain softening phase is called liquefaction (e.g. Castro 1969) or true liquefaction by V a i d and Chern (1985). This behaviour could result in a flow failure under static loading i f the i n situ driving stress exceeds the shear strength at U L S (q T in Figure 2-2). S  For sand that is dense o f critical (curve S H in Figure 2-2), the initial tendency for contraction under drained loading causes positive excess pore pressure under conditions o f restricted drainage but this is quickly followed by a tendency for dilation, causing a reduction o f excess pore pressure. The point where pore pressure generation changes from positive to negative is called the phase transformation. Thereafter, the soil remains strain hardening during the entire shearing until the soil reaches the C L S at a higher effective stress or cavitation o f the pore water occurs. It is seldom possible to reach the U L S in laboratory specimens. Generation o f positive pore pressure in the initial phase decreases the soil tangential stiffness to its minimum magnitude just before phase transformation. There is an intermediate state at which the soil shows a limited strain softening ( L S S curve in Figure 2-2) followed by strain hardening phase. This behaviour is called limited liquefaction by Castro (1969) and the shear stress at which the behaviour reverses from strain softening to strain hardening is termed the quasi-steady state (QSS) by Ishihara (1996). Whether a soil displays "loose" or "dense" behaviour depends on its current void ratio relative to the steady state line at its current effective stress level. In undrained conditions, the soil with loose behaviour lies to the right o f the U S L in (e-p') space. Therefore, to reach the U S L , positive pore pressure would be generated for failure at constant void ratio. The soil with  5  dense behaviour falls to the left side o f the U S L and hence generates negative pore pressure to reach the ultimate state at constant void ratio. Where volume change is possible, the same concept applies with the difference that the void ratio changes during shearing. Under field conditions, the soil stress-strain behaviour and generation o f excess pore pressure depend on the balance between the tendency towards volume change and the rate at which drainage is possible. V a i d and Eliadorani (2000) showed that a small injection o f water into a dense soil, which would be considered dilative under undrained conditions, could make the sample strongly contractive. This has important practical implications as a dense layer could liquefy due to water injection which could occur due to the flow resulting from liquefaction in an adjacent liquefied layer. Sand behaviour has also been noted to vary with soil fabric (spatial arrangement o f the soil particles), direction o f loading relative to the direction o f deposition and length o f time and stress history since deposition. Under repeated cycles o f shearing as occurs during seismic loading, there is a tendency towards accumulation o f volume changes where drainage is possible and for generation o f excess pore pressure under conditions o f restricted drainage. The net volume change is contractive for both loose and dense sand. The cyclic behaviour o f sand is a function o f the factors listed in Table 2-1 as well as o f the number o f cycles and the magnitude o f the cyclic strain. The reduction i n effective stress causes a drop in stiffness and results in accumulation o f shear strain as cyclic loading continues. W i t h sufficient cyclic loading, the soil may liquefy. Liquefaction is, by definition, the transformation o f granular soil from a solid state into a heavy fluid due to an extreme drop in strength and stiffness caused by increased pore water pressure and the resulting reduction in effective stress (Marcuson 1978). Laboratory tests have confirmed that the liquefaction resistance is primarily a function o f relative density but that confining stress, the lateral earth pressure coefficient KQ, ageing/fabric and number o f cycles (Ishihara 1996) among other factors listed in Table 2-1 also influence the susceptibility. A n increase in relative density o f sand, with other parameters constant, decreases the volume o f voids and thus decreases the potential to contract during shearing under drained conditions and reduces the generation o f positive pore pressure under undrained conditions. This can be accomplished by ground densification.  6  2.3  2.3.1  C H A R A C T E R I Z A T I O N O F G R A N U L A R SOILS  Introduction Once it has been determined that granular soils are present, it is necessary to determine  their initial state to assess whether they are liquefiable and require ground improvement. Characterization o f granular soils is normally carried out by in situ testing. It is possible to obtain undisturbed samples by ground freezing (e.g. Tatsuoka and Shibuya 1992, Hofmann et al. 2000) but this is generally done only for critical/important projects due to its difficulty and costs. In situ tests (e.g. cone penetration test, C P T ; standard penetration test, SPT; Dilatometer test, D M T : Pressuremeter test, P M T ; seismic tests) are the main tools for characterization o f granular soils. Most i n situ tests, including all penetration tests, are index tests and not a direct measurement o f soil properties. Only the soil response to a specific imposed perturbation is measured during the tests, e.g. the response to penetration o f a cone into the ground. The soil response, such as the penetration resistance, q , is a function o f the same parameters that affect c  the soil behaviour under monotonic or cyclic loading. This is the basis o f correlations to engineering soil properties. These correlations have been developed under certain conditions and for certain soils types and, therefore, are most relevant when the design conditions are similar to those used for developing the correlations. Seismic-piezo-cone testing ( S C P T U ) is the main tool used in this thesis and is described below. 2.3.2  Piezo-cone testing, C P T U The standard electric piezo-cone, as specified in A S T M D 5778, has a conical tip with a  60 degree apex angle, is 10 cm in cross section, has a 150 cm friction sleeve and pore pressure can be measured during penetration at one or more locations on or near the cone tip. Figure 2-3 shows a schematic diagram o f a standard piezo-cone. The cone is pushed into the ground at a standard rate o f 2 cm/sec. Cone tip resistance, q , c  sleeve friction, f , and pore pressure, u, are recorded. q is the total force acting on the cone s  c  divided by the projected area, and f is the total force acting on the friction sleeve divided by its s  surface area. The pore pressure is typically measured behind the shoulder o f the cone at the u  2  position. The pore pressure could also be measured at the tip (ui), or behind the friction sleeve  7  (113). T i p resistance should be corrected for unequal end area effects caused by the pore pressure acting on the back o f the cone tip using the following equation: Q =c  +u (l-a)  a  t  Equation 2-1  2  where q is the corrected tip resistance and " a " is the net area ratio o f the cone. In sands, t  where u is small relative to q , the above correction is small and thus q and q are almost 2  c  c  t  identical. The data are usually recorded at typical intervals o f 2.5 or 5 cm. This provides a detailed and practically continuous profile o f the soil response to penetration. A t the standard rate o f penetration, the soil response tends to be drained in sands, undrained in clays and clayey silts, and partially drained i n soils o f intermediate grain size. A typical C P T U profile for a well characterized site (Kidd2 research site, Richmond, B . C . ) is shown in Figure 2-4. The capability o f the C P T U can be enhanced by the inclusion o f accelerometers or geophones in a module mounted above the cone (Robertson et al. 1986). The combined tool is known as a seismic cone (SCPT) or seismic piezo-cone ( S C P T U ) . The vibration sensors can be used as receivers during down-hole or cross-hole seismic testing.  Seismic testing during  C P T U testing is commonly used as a down-hole test to determine shear wave velocity, V and, s  less frequently, the compression wave velocity and damping o f the soil. During pauses i n penetration, seismic waves are generated at ground surface as shown in Figure 2-5.  The  average seismic wave velocity for a given depth interval is calculated from the difference i n wave arrival time over that increment o f depth. Based on the theory o f wave propagation in an isotropic, linear elastic medium, measured shear wave velocities can be used to estimate the small strain shear modulus, G  m a x  o f the strata as shown by the following equation  G,max  Equation 2-2  where p is bulk density and V is shear wave velocity. s  2.3.3  Soil classification by CPT The C P T has a wide range o f application in geotechnical engineering in both  fine-grained and coarse-grained soil. Here, the application for granular soils, especially sands, w i l l be briefly described. Generally, the C P T results can be used in three different ways: •  For determining stratigraphy, and soil classification.  8  •  For direct correlation to ground or foundation performance such as liquefaction resistance, pile capacity, and compactability.  •  For correlation to engineering properties o f the soil, which are then used i n design calculations to predict the performance o f the ground or foundation.  The C P T U profile can be interpreted to allow determination o f soil stratigraphy, as shown in Figure 2-4. The near continuous profile allows identification o f thin layers in the range o f centimetres. For example, thin interbedding o f silty sand within the sand stratum from 7 to 12m, can be clearly observed by a decrease in q , an increase in Rf and sudden change o f u . t  2  Robertson et al. (1986) used the basic C P T parameters, q , f and u in two separate t  s  2  classification charts (Figure 2-6). The soil behaviour type, S B T , corresponding to each zone i n the classification chart is also included in the figure.  These have been found generally  applicable for classification o f alluvial deposits to depths o f up to about 30 m. Beyond that depth, it becomes necessary to account for the effect o f stress level. Attempts were made to normalize the classification charts for i n situ stress (e.g. Olsen 1984 & 1994, Olsen & Mitchell 1995; Robertson 1990). Robertson (1990) used a linear normalization for q that works best for t  clayey soils but is less suited for sandy soils (Figure 2-7). Jefferies and Davies (1993) introduced the concept o f a material index in development o f alternative C P T classification charts. Robertson and Fear (1995) amended the Jefferies and Davies material index. They defined a Soil Behaviour Type Parameter, I which is the radius c  o f concentric circles in Q versus F space and is given by the following equation: t  r  Equation 2-3  where  I  P«  Equation 2-4  A O *ioo  Equation 2-5  9  where all the parameters are as defined previously. A contour for I =2.25 is shown on Figure c  2-7 as an example. The top left hand corners o f the charts (small I ) typically represent coarser, c  cohesionless soils and the soil becomes finer i f it plots towards the bottom right o f the chart as I increases. c  Robertson and Fear (1995) used the following equation to correlate fines content (ratio o f the weight particles finer than 0.074mm to the total weight o f the soil) to I . c  FC(%)  = 1.75-  I  Equation 2-6  c  This was an attempt to account for the effect o f fines content when using the C P T in evaluation of liquefaction resistance, for which fines content (FC) is required.  Robertson and Wride  (1997) subsequently called the estimated fines content from the C P T the "apparent fines content". 2.3.4  Engineering properties of soil Soil response to penetration during C P T is a function o f the same factors that affect the  mechanical soil behaviour as noted in Table 2-1. The main factors for C P T response i n granular soils are: • State, including relative density and effective stress conditions ( a ' and a' ) n  v  • Composition (grain size distribution and mineralogy/compressibility) • Soil structure (fabric, ageing, cementation) The  engineering  properties  for  sands,  such  as  relative  density,  stress  state,  overconsolidation ratio ( O C R ) , modulus, unit weight, friction angle, dilation angle and state parameter are often obtained using empirical correlations. These correlations have been developed between the desired soil property and C P T results (mainly cone tip resistance) in controlled conditions such as in a calibration chamber (e.g. Parkin and Lunne 1982; Baldi et al. 1982 and 1986; Been et al. 1988; Houlsby and Hitchman 1988; Salgado 1993), or where the soil property is known from another test. Correlations have also been obtained to liquefaction resistance as shown in Figure 2-8. In Figure 2-8, a boundary has been defined between sites that have liquefied and those that did not. The chart is presented in terms o f the cyclic stress ratio ( C S R ) experienced at the site and  q iN, c  the normalized tip resistance given by the  expression:  10  Equation 2-7  Qc\N \ a2 P  J  where q is the cone tip resistance, P 2 is a reference pressure o f 1 atmosphere in the same units c  a  as q , P is a reference pressure o f 1 atmosphere in the same units as a' , and a ' c  a  v0  v 0  is the vertical  effective overburden stress, ' n ' varies with soil type and is typically taken to be 0.5 for clean sands. Shear wave velocity has also been used for screening the liquefaction susceptibility o f soils. Andrus and Stokoe (1997, 2000) developed a database for estimating liquefaction resistance from field measurements o f V . Thus, the seismic cone has the advantage o f s  providing data for two independent methods o f liquefaction assessment in one sounding. If the soil is determined to be liquefiable then it may be necessary to densify.  2.4  M E C H A N I S M O F C O M P A C T I O N O F G R A N U L A R SOIL Greenwood (1991) defined compaction (or densification) to be the instantaneous  rearrangement o f the soil particles into a more compact state. Compaction reduces the void ratio and requires concurrent expulsion o f pore fluid. This in turn requires a high permeability o f the soil and is the main reason why saturated fine grained soils, or sands with large fines content, are practically not compactable. V o i d ratio can be reduced statically or dynamically. Compaction o f granular soils by static loading is not efficient. Volume change o f granular soil is most efficiently achieved by inducing cyclic shear strains in the soil. This gives the grains the opportunity to either fall or slide past one another into a denser arrangement. This concept is supported by many cyclic tests i n the lab (e.g. Y o u d 1972; Silver and Seed 1971; Martin et al. 1975; Dobry et al. 1982). Figure 2-9a shows that the volumetric strains, s depends on the magnitude o f shear strains, y v  and the number o f cycles. Figure 2-9b shows the same concept for air pluviated Fraser River Sand in a cyclic simple shear test. The shear-volume coupling obtained from laboratory tests has been used to estimate the compaction o f granular soils by vertically vibrating probes and also to estimate the earthquake-induced settlement o f granular soils. 11  There have also been some attempts to relate the compaction o f granular soils to the magnitude o f acceleration during vibration instead o f to shear strains. D ' A p p o l o n i a et al. (1967) used a shaking table to subject unconfined damp sand to controlled vertical accelerations over a range o f frequencies (20-35 H z ) . They found that the maximum density was independent o f the displacement amplitude and frequency. The main factor influencing the degree o f compaction attained was found to be the peak acceleration (the product o f displacement amplitude and the square o f frequency). The increase in dry unit weight was small below an acceleration o f l g and the peak density was achieved at an acceleration o f about 2g. Higher accelerations loosened the soil. More recently, Bement and Selby (1997) conducted a laboratory test program to study the compaction o f granular soils by vibration under controlled stresses. They found that compaction was correlated best to the peak acceleration rather than to the peak velocity or displacement. In addition, compaction at accelerations smaller than l g was small and it increased significantly at 2g and above. However, Y o u d (1972) noted that approaches using acceleration, normal stress fluctuations and frequency had not led to a clear understanding o f the compaction process. Massarsch (2000), also basing his opinion on laboratory test results, emphasized that shear strain was the main factor for compaction o f granular soils and argued that acceleration cannot be a fundamental parameter for compaction. In this thesis, it is considered that volume change due to shear-volume coupling (shear strains and number o f cycles) is the fundamental mechanism for compaction o f granular soils. While acceleration can be used as an index o f compaction effectiveness, it cannot be uniquely related to effectiveness o f compaction because the relation between shear strains and acceleration is a function o f the frequency o f vibration.  2.5  GROUND IMPROVEMENT METHODS FOR LIQUEFACTION MITIGATION O F G R A N U L A R SOILS  2.5.1  Introduction Soils that are susceptible to liquefaction are typically saturated loose to medium dense  granular soils in which drainage may be restricted relative to the rate o f pore pressure  12  generation. Figure 2-10 shows the wide range o f available soil improvement methods. They can be categorized as follows: •  Densification;  •  Replacement  •  Drainage/dewatering  •  Reinforcement/mixing.  Ideally, the ground improvement technique selected should suit the soil type, should be economic, should have been proven effective in previous local projects and it should be implemented by a specialty contractor with successful previous experience. Figure 2-10 indicates the range o f soil grain size most susceptible to liquefaction and the ground improvement methods most applicable to these soils. Ferritto (1997) gives a list o f ground improvement methods typically used for mitigation o f liquefaction indicating that densification by vibratory probes (vibro-compaction including vibro-replacement), dynamic compaction, and compaction grouting (Hayden and Baez 1994) have been widely used. These methods have also demonstrated successful performance in past earthquakes as noted by Mitchell et al. (1995). Explosive compaction is also suitable but has not been as widely used. In general, vibro-replacement is the most widely used technique for liquefaction mitigation in North America (Hayden and Baez 1994). This is due to its applicability for a wide range o f soil types, economy o f the technique (Martin and L e w 1999) and also its applicability to urban areas. Further details can be found in Mitchell and Gallagher (1998), Schaefer et al. (1997) and Mitchell and Jardin (2002). 2.5.2  Vibro-compaction Vibro-compaction using a vibrator designed to induce horizontal vibrations, also called  vibroflotation, was developed by Steuermann and Degen i n 1934 in Germany and was introduced to the United States in the 1940's (Degen and Hussin 2001) and has been used for liquefaction mitigation since the 1970's (Dobson 1987). The main items o f equipment required are a vibrator, extension tubes, a crane, a water pump and an air compressor. The vibrator, which is also called a vibroflot, is jetted into the ground to the target depth and is then withdrawn slowly while backfill material is added to the hole (Figure 2-11). Withdrawal o f the vibroflot is stopped at intervals to allow maintained vibration to densify the surrounding soil.  13  The backfill compensates for the volume change induced in the native ground and provides coupling between the vibrator and the soil. The backfill gets pushed to the sides by the lateral impacts and forms a dense column. The end result is a denser soil, with elevated horizontal stress and reinforcement by stiffer columns. If coarse backfill is used, this column also has the potential to work as a vertical drain during seismic shaking. Vibro-compaction is assigned different names based on the methodology employed and the backfill material. Some common terms are: vibro-compaction; vibro-replacement; wet vibro-replacement; dry vibro-displacement; and vibro-stone columns. Vibro-compaction typically uses sand for backfill material. Where coarse material (gravel size) is used for the backfill, the technique is often called vibro-stone columns. If water jets are used for penetration and keeping the hole open, and coarse back fill is fed from the surface, then the method  is called vibro-replacement  or more  accurately wet vibro-replacement.  The  dry-displacement method does not use water jets during the process and backfill is fed to the bottom o f the hole through a separate tube mounted on the outside o f the vibrator with the help o f compressed air. This method is also called bottom-feed stone columns as opposed to top-feed vibro-replacement. Other deep vibratory methods for densification use vertical vibrations along the length o f the probe (vibro-rod methods). The source o f energy is attached to the top o f the rod (Mitchell 1981; Saito 1977; Massarsch and Broms 2001; V a n Impe et al. 1993; V a n Impe and Madhav 1995). Dynamic compaction uses repeated high energy impacts on the ground surface. Weights are typically in the range o f 10 to 30 tonnes and are dropped from heights o f typically 15 to 30 m (Lukas 1995). Dynamic compaction improves the soil by consolidation, vibration and increase i n horizontal stress. Compaction grouting involves injection o f a low slump and low-mobility soil-cement grout under pressure into the soil mass at spacing o f 0.9 to 4.5m (Mitchell and Gallagher 1998). This results in lateral displacement and hence consolidates and/or densities surrounding soils in-place. It also increases lateral stresses (Mace 1999) Blast-densification (also called explosive compaction) uses explosives to generate vibrations in the ground. A typical blast-densification program consists o f charges placed i n a grid pattern, in a pre-bored hole at one or more depths. (Mitchell and Gallagher 1998). They  14  are sequentially detonated to create a period o f vibratory shaking which encourages the soil grains to settle into a denser packing. This thesis w i l l concentrate on vibro-replacement. 2.5.3  Wet vibro-replacement Wet vibro-replacement uses a down-hole vibrator, with centrifugal vibration. The  vibrator is inserted into the ground with the help o f water and/or air jetted from its nose and side jets (Figure 2-11). Excess pore pressure caused by a combination o f the vibration and the jetting along with the dynamic instability due to high accelerations, reduce the soil resistance. This allows the vibrator to penetrate into the ground under its own weight. Vibrators are typically about 2 to 4 metres long. In order to reach greater depths, the vibrator is attached to follower tubes (extension tubes) by a coupling which includes a vibration isolator. Once the target depth is reached, and after typically one or two cycles o f flushing o f the hole, the backfilling process starts from the bottom up. The vibrator is withdrawn slowly, usually in half-metre intervals, while gravel size backfill is fed from the surface to the bottom o f the hole. It passes through the annulus opened up between the soil and vibrator unit by flushing cycles using the side jets. The vibrator is held at each interval for a predetermined amount o f time or until a specified power consumption is reached. These parameters are usually determined by the specialty contractor and/or are derived during a field trial.  Lateral movements o f the  vibrator, created by centrifugal forces due to rotation o f an eccentric mass, are transferred to the soil. Furthermore, the tendency o f the vibrator to spin about its vertical axis is resisted by 2 fins protruding from its sides.  This imparts torsional vibrations to the soil. The soil is  compacted primarily b y the large number o f cycles o f shearing as well as by increases in confinement due to increase o f lateral stress. Coupling between soil and vibrator is enhanced by the introduction o f stones to the annular zone around the vibrator. The overall ground improvement is achieved by a combination o f densification, increase in lateral stress, reinforcement by stiffer stone columns and probably an enhanced drainage condition. In order to treat a large area, vibro-replacement is carried out in a triangular or square pattern with centre to centre spacing in the range o f usually 2.5 to 3.5m. The choice o f spacing depends on the target performance, soil gradation, vibrator characteristics and methodology. A  15  stronger vibrator i n a free draining soil type and appropriate methodology helps to increase the spacing between the stone columns. For more details on design and equipment, numerous publications may be consulted such as Barksdale and Bachus 1983, Greenwood and Kirsch 1983, Mitchell and Huber 1985, Dobson 1987,, Greenwood 1991, Baez 1995 and 1997 and Slocombe et al. 2000. 2.5.4  Vibrators The vibrators used in vibro-compaction are also known as vibroflots, vibro probes or  vibrating pokers. In this chapter, the term vibroflot w i l l be used. The vibration is created by the rotation o f an eccentric mass about the vertical axis o f the vibroflot (Figure 2-12). This generates a centrifugal force, which excites the entire vibroflot and makes it move in a conical path in a manner similar to a rotating pendulum. When hanging in the air, the pivot point is close to the coupling o f the vibroflot and the extension tubes. In the ground, the pivot point moves down towards the tip o f the vibroflot (Greenwood 1991). The amplitude o f vibration depends on the soil resistance and confinement. Figure 2-13 is a schematic horizontal section through the vibroflot and shows the soil-vibroflot interaction. The actual interaction is more complex due to the presence o f water and introduction o f gravel around the vibroflot. The vibroflot imparts direct impacts and torsional forces to the ground. The torsional forces are generated by the friction between the soil and vibroflot. The frictional forces tend to twist the vibrator about its vertical axis opposite to the direction o f rotation o f the eccentric mass as shown in Figure 2-14. This tendency for twisting is resisted by two fins protruding from the sides o f the vibroflot. If the vibrator were allowed to twist, all the supply lines delivering power, water and air to the vibroflot would get tangled (Figure 2-15). The fins prevent the twisting by applying bearing pressure to the soil as shown schematically in Figure 2-14. The frictional force and the bearing pressures on the fins impart torsional forces and induce additional shear strains to the ground. Vibrators are made by different manufacturers. Table 2-2 lists some o f the well known vibrators and their main specifications. In this table, the vibrators by Bauer are powered hydraulically and the rest by electric motor.  16  2.5.5  Quality control during vibro-replacement Vibro-compaction design is largely empirical (e.g. Barksdale and Bachus 1983; Mitchell  and Huber 1985; Dobson 1987; Baez 1995 & 1997) and due to the great variety o f vibrators and construction methodologies, there is no universal vibro-compaction design method. Some design charts are available that relate the post-compaction soil condition (penetration resistance or relative density) to the spacing o f the compaction points or to the replacement ratio. Figure 2-16 and 2-17 are examples o f such charts and can be used only as guidelines. However, there is a need for a means o f assessing the improvement during the treatment process by monitoring the details o f construction. Electrical vibrators are designed to operate at a constant rate, so they draw more power as the constraint from the surrounding soil increases (Brown 1977). The power consumption is used as an indication o f the level o f compaction. The correlation between the power consumption and the post-compaction soil performance is usually established by experience or from a field trial. Power consumption is usually assessed by monitoring the current drawn for electrical vibrators or hydraulic pressure for hydraulic vibrators. For example, with an electric vibrator, the operator continuously monitors the ammeter during the compaction phase. If the amperage builds up to a pre-selected current, the holding period in the interval is terminated and the vibrator is moved to the next interval. For each compaction point, the ammeter reading and the depth o f the vibroflot are usually recorded, either manually or on a strip chart recorder for comparison to expectations which are based on experience or on the results o f a field trial carried out before the production phase. Figure 2-18 shows an example o f such a strip chart record. M o r e recently, Fellin (2000) proposed that measurement o f the vibrator motion in two horizontal directions at two points on the vibroflot (the tip and the shoulder) along with the phase angle between the eccentric mass and the vibrator would be necessary to define the motion o f vibroflot and could be used for online quality control o f the compaction. The post-compaction soil performance is conventionally assessed by measuring the change in penetration resistance achieved.  Figure 2-19 shows a C P T based zonation for  compactability o f soil using vibratory probes suggested by Massarsch and Heppel (1991). This figure suggests that soil is compactable, marginally compactable, or uncompactable for ranges o f Rf< 1%, 1.5% > Rf> 1% and Rf> 1.5% respectively. For comparison, the Robertson et al. (1986) classification chart is over-plotted. The Massarsch and Heppel zonation mainly falls on  17  to the silty sand and sandy silt (zone 7) and coarser S B T classifications. According to Mitchell (1981), a fines content o f about 20% is the limit for compactability o f silty sand. Using F C - I  C  correlation (Equation 2-6), a fines content o f 20% is approximately equivalent to I -2.25 c  (Figure 2-7). There are other factors involved in choosing the ground improvement technique. These factors are described i n terms o f advantages and disadvantages, and are compared in Table 2-3 for the more popular densification methods in B C , Canada. Note that the achievable performance is approximate and reproduced from Mitchell and Gallagher (1998) only for the purpose o f comparison. 2.5.6  Previous works on vibration measurement and the mechanism of compaction by vibro-compaction methods Although vibratory compaction is simple in concept, the actual interaction o f the vibrator  and soil is very complex. Despite the popularity o f the vibro-replacement method, very little attempt has been made to explain the compaction process analytically or by numerical modelling. V e r y few cases could be found i n the literature in which the vibrations o f the vibroflot and/or ground were measured and then used to explain the soil-vibroflot interaction and the mechanism o f compaction. It is likely that there have been some cases o f vibration measurement conducted by manufacturers/contractors for improvement o f the vibrator design, but these have not been published probably because they are considered proprietary. The only known case o f simultaneous vibration measurement o f both the vibrator and ground in the literature is the one reported by Morgan and Thomson (1983). Their main concern was to correlate the amplitude o f vibration to post-compaction penetration resistance as a method for quality control. They noted that the power consumption did not always match the achieved penetration resistance profile and was affected by factors other than soil density. They found that the amplitude o f horizontal displacement measured near the tip o f the vibroflot correlated well with penetration resistance after compaction and showed that the shape o f the variation o f the vibroflot amplitude and the variation o f post-compaction penetration resistance with depth were similar (Figure 2-20).  They only presented data on the amplitude o f the  vibroflot and the attenuation o f radial vibration in the ground. They also noted that the  18  recorded data should have been analyzed in an analytical framework but this was not pursued, likely due to the complexity o f the problem. Greenwood (1991) and Greenwood and Kirsch (1983) divided the ground around the vibrator into four radial zones based on the acceleration level, as shown in Figure 2-21. The range o f accelerations for different zones came from Rodger's (1979) work. H e had measured the accelerations at the ground surface. In Figure 2-21, a critical acceleration o f 0.5g is selected as a threshold at which the dynamic stresses start to destroy the soil structure and cause densification. The zone with accelerations in the range o f 1.5g represents the optimum compaction. Increasing acceleration beyond 1.5g reduces the compaction efficiency due to dilation o f the soil structure. A t accelerations greater than 3g, the soil is fluidized due to over-excitation, at which the soil particles lose contact with one another and continually bounce without compacting. Although accelerations could be used as an indication o f vibration intensity, and thus o f densification effort, it appears unlikely that they can fundamentally explain the mechanism o f densification o f granular soils (see Massarsch 2000, Massarsch and Broms 2001 for more discussion on this matter). In addition, the relation between ground surface accelerations and in-depth ground accelerations is site specific and depends on the soil condition above the layer being densified. Therefore, measurements o f the accelerations at ground surface cannot necessarily be correlated to the acceleration in the layer at depth being densified. Greenwood (1991) also mentioned some vibration measurement cases conducted by his company in uniform fine sand at 3 m below the surface. They used vibrators with equal power but differing frequencies. They measured accelerations o f about 8g to 15g at 0.5m and l g to 3g at 4m radial distance from the vibroflot. N o vibration time history was presented. Baez and Martin (1992) used geophones and a pore pressure transducer i n the seismic piezo-cone to measure the radial ground vibration, vertical ground vibration and pore water pressure during the dry vibro-displacement method at 3 different radial distances. The input vibration o f the vibroflot and the tangential vibration i n the ground were not measured. The effect o f the cone rods on the ground vibration measurement is not known. Figure 2-22 shows an example o f their vibration time histories which were collected at 4.2m depth and a horizontal distance o f 1.5m from the centre o f a stone column during construction. They identified the mechanism o f compaction as a "controlled vibrator-induced liquefaction". They  19  referred to liquefaction as the condition when the induced excess pore pressure ratio approached one ( A u / a '  = v o  l ) - Their interpretations o f liquefaction occurrences are annotated on  Figure 2-22. Note that the high pore pressures occurred only during penetration o f the vibrator. It is apparent that penetration o f the vibrator increases the pore pressure i n a manner similar to cavity expansion under an undrained/partially drained condition. While the shearing due to the cavity expansion during the vibroflot penetration does contribute to the densification o f the soil, it does not explain the densification mechanism by vibration during backfilling which is the main stage o f densification. In the case o f the wet vibro-replacement method, pore water pressure in the ground is also affected by the water jets used to facilitate the penetration. The only existing mathematical model applied to soil-vibrator interaction available in the literature was developed by Fellin (2000) who was only concerned with the motion o f the vibroflot. In his model, the ground was replaced with springs and dashpots. Therefore, this model does not give any insight into what happens in the ground. Green (2001) noted that the shear strains around the vibrator were responsible for compaction. These shear strains are induced by the horizontal impacts and friction between the soil and the vibrator (Figure 2-13). However, he acknowledged that the soil-vibroflot interaction was very complicated and thus made no attempt to analyze the shear strains around the vibrator. Fellin (2002) measured the acceleration o f the vibrator and the phase difference o f the eccentric mass relative to the vibrator and tried to use them for quality control o f compaction. N o measurement o f the ground response was carried out. Some other vibration measurement cases at the ground surface have also been published. Most o f them were concerned with the noise level and the possible destructive effect o f the induced vibration on the adjacent foundations (e.g. Woods and Jedele 1985). It appears that the main reason for the scarcity o f published vibration data is the level o f difficulty o f high quality measurement o f vibration and the complexity o f analysis o f data in a mathematical or numerical framework. In Chapter 3, the mechanism o f vibro-replacement w i l l be discussed in detail based on the result o f field vibration measurement and numerical modelling.  20  2.6  DISCUSSION A N D N E E D F O R F U R T H E R R E S E A R C H Ideally, design and implementation o f ground improvement for liquefaction mitigation  requires consideration o f the items listed in Table 2-4. Despite considerable advancement in the geotechnical and earthquake engineering field, we are still far from a full understanding o f these above items. For example i n item 1, the relative density or state o f the sand, which is a basic parameter o f sand, is at best a good estimate in the current state o f practice. Fundamental soil behaviour (item 2 above) is mainly obtained from the laboratory tests under controlled and idealized conditions. Considerable extrapolation is still required to predict in situ soil response. While there has been relatively good success in predicting/explaining the mechanism o f compaction and the ground response using analytical or numerical modelling for compaction by vibro-rod (e.g. Massarsch 2000, Green 2001), dynamic compaction (e.g. Scott and Pearce 1975, Mayne et al. 1984, Chow et al. 1992, K r o g h and Lindgren 1997, Pan and Selby 2001), compaction grouting (Mace 1999, Shuttle and Jefferies 2000) and blast-densification ( W u 1995, Gohl 2002). However, little research has been carried out into the fundamentals o f densification by vibrators where the induced vibrations are primarily horizontal. Ground improvement adds to complexity o f site characterization since it changes the ground conditions and consequently changes the soil parameters and response o f the ground to the i n situ testing, which is the main tool for site characterization o f granular soils. Generally the changes in ground conditions affect the soil parameters and response to in situ testing i n the same way, e.g. it increases the density o f sand and also the cone tip resistance. However, these changes may change the correlations between the soil parameters and in situ test results. Ignoring the changes in soil conditions could lead to misinterpretation o f in situ test results. It is important to understand how a certain ground improvement, technique changes the soil conditions and how these changes affect interpretation o f the in situ tests (items 6 and 7). Without this understanding,  it is hard to write a technical specification for ground  improvement, characterize, the post-treatment ground and/or predict the performance o f the improved ground under the design loads. These aspects o f ground improvement have not had sufficient attention from researchers as noted by Charles (2002) and Raison (2004). The lack o f attention is more pronounced for vibro-compaction technique including vibro-replacement (Items 6 and 7 in Table 2). 21  2.7  S U M M A R Y AND CONCLUSIONS The summary o f the main points in this chapter is as follows: •  Behaviour o f granular soils under monotonic loading is a function o f many factors including gradation, relative density, stress state, age, fabric and stress • path. The above factors plus magnitude and number o f cycles affect the granular soil response to dynamic loading.  •  In situ tests, primarily penetration tests such as C P T , are the main tools for characterization  o f granular  soils  and  also  for  QC/QA  after  ground  improvement. •  C P T is an index test and measures the soil response to penetration o f a cone. Its response is function o f the same parameters that affect the soil behaviour.  •  Shear-volume coupling is the main factor i n compaction o f granular soils. Compaction o f granular soils is mainly a function o f magnitude and number o f shear strain cycles.  •  The physical process and. mechanism o f compaction o f some widely used compaction methods  such as dynamic compaction, compaction grouting,  vibro-rod method and blast-densification have been explained in an analytical or numerical modelling framework. Despite the popularity o f vibro-compaction methods (including vibro-replacement), very little fundamental work such as analytical studies, experimental studies, small scale laboratory tests or numerical analysis has been published to allow understanding o f the physical process and its effects on ground conditions. •  Ground improvement changes the soil conditions and thus the soil response to cone penetration. Interpretation o f post-treatment cone penetration results needs to address the effect o f changes on ground conditions induced by ground improvement.  From the foregoing, it is apparent that despite considerable advancement o f our knowledge regarding ground improvement methods and mitigation o f liquefaction, there is a need for further research on all components listed in Table 2-4. The focus o f this thesis w i l l be  22  on improving our understanding  o f the physical process  characterization o f post-treatment ground by this method.  23  o f vibro-replacement  Table 2-1 Factors affecting mechanical behaviour of granular soils (adapted from Hight and Leroueil 2003) Factors  Sub-factors  State  void ratio /relative density, stress condition  Fabric  macro-fabric, micro-fabric, interbedding, discontinuities, distribution of void ratio, orientation of grains  Stress path  compression, extension, shear  Composition  gradation, silt and clay fraction, plasticity, mineralogy, organic content, pore water chemistry  Micro-fabric  ageing, creep, cementation  Stress-strain history Disturbance/destructuring Drainage conditions Formative history  sedimentary/residual, age  Table 2-2 Commonly used vibrators and their specifications (from www.vibroflotation.com)  Manufacturer  Bauer  Bauer Keller Keller Keller Keller  Vibro  Vibro  Machine name  TR13  TR85  M  S  A  L  V23  V32  Length [m] Diameter [mm]  3.13 300  4.20 420  3.30 290  3.00 400  4.35 290  3.10 320  3.57 350  3.57 350  Weight [kg]  1000  2090  1600  2450  1900  1815  2200  2200  Motor [kW]  105 3250  210 1800  50 3000  120+ 50 1800 2000  100 3600  130 1800  130 1800  6  22  7.2  18  13.8  5.3  23  32.  150  330  150  280  160  201  300  450  Speed [miiW] Ampl. [mm] Dyii.Force [kN]  " Y * Dynamic force for the S type Keller vibrator was reported as 200 kN by Baez and Martin (1992)  24  Table 2-3 Comparison of some of ground improvement methods for liquefaction mitigation (adapted from Mitchell and Gallagher 1998)  Ground Improvement Method  Achievable Penetration Resistance  Disadvantages  Advantages  Reinforcement • Vertical drainage • Overall homogeneity • Low noise level • Small chance of damagetothe adjacent structure • • Lots of previous experience •  High technology Elaborate equipment q = 10-15 MPa Needs high head room Management of the return water,(N,) =25 relatively expensive Difficulty in penetrating into coarse material Densification only for fines content less than 15-20%.  Dynamic Compaction  • • • •  High noise and vibrations Potential for damage to adjacent q i=10-l5 MPa, (Ni) =25 foundation Needs high head room Relatively small improvement depth  B last-Densification  • No depth limit • Relatively less expensive • Low technology  Vibro-Replacement (Vibro-Stone column)  Compaction Grouting  • • • • •  Low technology • Relatively less expensive • Works for a wide range of soil Works for large particle size • •  cl  m  • High noise and vibration • Relatively lower degree of uniformity  • Reinforcement, works for a • Relatively more expensive wide range of soil. • Monotonic loading • Good control on the volume of the column • Low head room • Low noise and vibration  25  c  M  q =10-12MPa, (N,kn=20-25 cl  q ,=10-15MPa (N,) =25 c  M  Table 2-4 M a i n components of design of ground improvement for liquefaction mitigation Ground Improvement Design Component  Objective  1. Site characterization  To obtain stratigraphy, site variation and engineering soil properties of natural ground.  2. Fundamental soil behaviour  To understand the soil response under design loads at soil element level.  3. Earthquake characteristics  To estimate the earthquake demand at the location of the project.  4. Performance of ground and/or foundation  To predict the ground response including the proposed structure under design loads. If the performance is not acceptable, ground improvement is required.  5. Specification of ground improvement  To specify the desired engineering soil properties of the improved ground.  6. Physical process of ground improvement techniques and their effect on ground conditions  To understand how a particular ground improvement technique works and how it changes the ground conditions and engineering soil properties.  7. Post-treatment site characterization  For QC/QA and to obtain the site variability and engineering soil properties after treatment  8. Performance of the ground and/or foundation after ground improvement  To predict the response of the improved ground under design loads.  26  27  V o i d ratio  Mean effective .stress, p  Figure 2-2  f  Typical behaviour of sand under monotonic loading in undrained condition (after Robertson and Wride 1998)  28  T o data acquisition system  o  Accelerometer/Geophone  •il  Sleeve friction, f  s  Pore pressure, u  2  /  1 Figure 2-3  Tip resistance, q  t  Schematic illustration of the seismic piezo-cone, SCPTTJ  29  Figure 2-4  A typical C P T U profile, Kidd2 site, Richmond, B C .  30  31  100  -0.2  100r  0  0.2  0.4  0.6  0.8  1.0  Pore pressure parameter B Zone:  Soil Behaviour Type:  1. 2. 3. 4.  Sensitive fine grained Organic material Clay Silty clay to clay  5. 6. 7. 8.  1.2  2  1.4  3  4  5  q  Friction ratio (%)  Clayey silt to silty clay Sandy silttoclayey silt Silty sand to sandy silt Sand to silty sand  9. 10. 11. 12.  6  Sand Gravelly sand to sand Very stiff fine grained* Sand to clayey sand*  Overconsolidated or cemented.  Figure 2-6  C P T classification chart (after Robertson et al. 1986)  32  1000  1000  1  r  ncreasing i . OCR, age • cementation' N  100  6  •% * \%  AH  -  10  \  ^  a -  -  %  N  \  4  ^ \  Increasing sensitivity  \  3  \  ^ ^ \ \  1 0.1  10  F (%) r  Q  Zone 1. 2. 3.  Soil behaviour type Sensitive, fine grained; Organic soils-peats; Clays-clay to silty clay;  Figure 2-7  =£r^ Zone 4. 5. 6.  x  Soil behaviour type Silt mixtures clayey silt to silty clay Sand mixtures; silty sand to sand silty Sands; clean sands to silty sands  100%  Zone 7. 8. 9.  Soil behaviour type Gravelly sand to sand; Very stiff sand to clayey sand Very stiff fine grained  Normalized C P T classification charts (after Robertson 1990)  33  0.6  0 2 5 < Dgjjmin) < 2.0 F C (%) < 5  M=7.5  o  OC  0.5 +  CPT Clean Sand Base Curve  o^ ~ <u  nj o  No Liquefaction  or  </) .S3 0) (0  co or  g g  o o >» >.  Q O  NCEER (1996)  0  Workshop 0  50  Field Performance Uq. Stwk& 0*0/1(1995) • Sujeufciet al (1S98b) *  -p  100  150  200  250  Corrected CPT Tip Resistance,  Figure 2-8  NtoUq. 0 A 300  q iN c  C R R curve from C P T (after Robertson and Wride 1998)  34  Figure 2-9  Dependence of compaction of sands on shear strain magnitude and the  number of cycles (a) after Youd 1972, (b) air pluviated Fraser River Sand under drained cyclic simple shear testing (adapted from Sriskandakumar 2004)  35  jcRAva. |  100  •  sawo  ,  SH.T  M O S T UOUEF1AJ3LE  PARTICULATE S « O U T 3  SOUS  " 1 ' JMfiTOflrtSttM  90  VISSATORT PROBES' :  80  CHEMICAL GROUTS i. BtpurenM COMPACTOR OEiP DYNAMIC COMPACTION?  sz CD *5  5 a  Hi  c ii ** c (!) O  a.  I  i > COMWICTlOW GROUT  60  ORANS  50  COMPACTION PILES JET GROUTING  40  ADMIXTURES 30  D E E P SOIL MIXING  SOlLRSaffORCEMENT  20  SUftCHARGgSUTTRESS FBXS ELECTROKJNETtC INJECTION  10  PRECOWREBSIOM  10  0.1  o.ot  0.001  00001  Particle Size (mm)  Figure 2-10 Suitability of ground improvement methods based on grain size distribution of soils (after Mitchell and Gallagher 1998)  36  Figure 2-11 Wet vibro-replacement process (adapted from www.haywardbaker.com)  Follow-up-Tubes  Vibration Damper  Electric Motor  Water jet pipe Eccentric Mass  Nose Figure 2-12 Cross-section of a vibroflot (adapted from website www.vibroflotation.com)  37  Locus of Gyration of Origin of Machine Axis  Impacting Forces  Origin of Machine Vibration W a l l of  Bore Hole Vibrator  Double Amplitude about Machine Axis Rotating Eccentric  Horizontal and Torsional forces  e  T  m  Soil element and induced strains and stresses  Err  Figure 2-13 Soil vibroflot interaction- horizontal section- (originally from Greenwood 1991, annotated by Green 2001)  38  Vibroflot  Fins bearing pressure resisting rotation  Eccentric mass  Frictional force from soil to the vibrator Figure 2-14 Schematic illustration of the effect of fins to prevent rotation of the vibroflot about its vertical axis  Figure 2-15 A typical vibro-replacement set up 39  20  •  60 100 Tributary A r e a per Compaction Point  Silty Sand i (5%- 15% Silt) I  1 Uniform. Fine to ' Medium Sand (clean i  i I  140 iff) j Well-Graded » Clean Sand  Figure 2-16 Variation of relative density or SPT blow counts after vibro-compaction as function of tributary area per compaction point (after Dobson and Slocombe 1982)  40  100  o o n c) o O H u -H hD c) O k  90  d  c  >  80  u  U 70  VIbroflo :atlon Terraprc ibe Upper L imit  10  60  Vlbro flotation -Lower Limit Corn}taction I lles -  5  3  Uppe r Limit  50  Terr aprobe - Lower  Lim t  ill 10  0  2  4  6  8  10  12  Dimensionless Spacing - D/d  Figure 2-17 Achievable relative Density vs. Probe Spacing for Soil Densification (From N A V F A C 1997)  41  Figure 2-18 A n example of record of the drawn amperage and depth versus time during vibro-replacement (adapted from www.vibroflotation.com)  Rr  (%)  Figure 2-19 CPT-based zonation for comparability (adapted from Massarsch 1991)  42  PENETROMETER RESULTS N°QF B L O W S / 3 0 0 m m V I B R A T I O N DiSPLACEM£NT.(Pk) 20 60 100 K O ISO I 5 „ 13 II 9 7 5 3  A  1  20  V^N X  S  rkFREQUENCY  MACHINE-;:  1—I  > . - I..,  .)...  1, v . . I  • • I  •  NOSECONE ACCEL EROMETER  V«  RESULTS  Q.  3-5h  PENETROMETER RESULTS RADIUS  Figure 2-20 Comparative profiles of the amplitude of the vibroflot and post-compaction  —i 1— 30 1 5 - 1 0  ^  T  ACCELERATION (q s)  RADIUS FROM VIBRATOR MCREASING  penetration resistance (after Morgan and Thomson 1983)  43  Figure 2-21 Densification zones as a function of acceleration around a compaction point proposed by Greenwood and Kirsch (1983)  TIME (seconds)  Figure 2-22 Vibration history recorded during vibro-stone column. Depth of monitoring point= 4.2m. Distance from the compaction point= 1.5m (adapted from Baez and Martin 1992)  44  CHAPTER 3 MECHANISM OF VIBRO-REPLACEMENT  3.1  INTRODUCTION A s noted in Chapter 2, very limited data are available documenting the interaction  between the vibrator and the soil during ground improvement. In this chapter, field vibration measurement and numerical analysis are used to provide insights into the physical process o f vibro-replacement, the mechanism o f soil-vibrator interaction and the resulting changes in ground conditions during the process. The chapter is organized into the following main sections: •  A case study o f vibration measurement during vibro-replacement in which vibration measurement was carried out for both input vibration on the vibroflot and ground response during vibro-replacement  •  Numerical analysis o f the soil-vibroflot interaction used to analyze the data obtained and explain the observed response.  •  3.2  3.2.1  Examination o f the mechanism o f ground improvement by vibro-replacement.  IN SITU G R O U N D R E S P O N S E T O V I B R O - R E P L A C E M E N T  Field vibration measurement Installation o f five stone columns was monitored during a vibro-replacement project  conducted to improve the foundation for construction o f a high rise building in Richmond, B C , Canada. The soil profile consisted o f about 5 m o f clayey silt underlain by 1.5 m o f sandy silt to silty sand which in turn was underlain by sand to silty sand up to about 12.3 m depth (Figure 3-1). The vibro-replacement method was selected to reinforce the top clayey silt layer with stone columns thus improving bearing capacity and reducing settlement. It would also density the loose pockets o f sand and silty sand to the target depth o f 9m. Stone columns were to be placed in a triangular pattern at 3m centres to a depth o f 9m. Another round o f stone columns was to be placed at the centroid o f each o f the 3-m triangles to a depth o f 6m. A s shown in Figure 3-1, the sandy layers were generally medium dense to dense with some loose pockets.  45  Correlation o f relative density obtained from Ticino Sand (Baldi et al. 1986) is also shown on the C P T profile for reference.. A loose uniform sandy deposit would have been more desirable for this experiment as the densification effect would have been more obvious. However, this site was the only available project at the time. The 5 stone columns in the research test section were installed to a depth o f 10m (one metre longer than the production columns). Figure 3-2 shows the location at which ground response and pore pressure time histories were monitored. The numbers beside the stone columns indicate the sequence o f construction. Table 3-2 shows the horizontal distance o f each stone column from the vibration sensor i n the ground. The following data were gathered versus time during monitoring o f construction o f the five stone columns: •  3-axis accelerations at 0.7 m above the nose on the vibroflot.  •  Current drawn by the electric motor o f the vibroflot.  •  Depth o f the vibroflot.  •  3-axis vibration o f the ground at 8.7m depth.  •  Pore water pressure o f the soil at 8.7m depth.  The vibrator used was a Vibroflot model V F A G - V 2 3 manufactured by Vibroflotation Ltd. This vibroflot operates at - 1 8 0 0 rpm (~30 Hz), has a 130 k W electric motor and produces 300 K N o f centrifugal force. Details o f the construction and operation o f vibrators and o f the vibro-replacement process were presented in Section 2.5. 3.2.2  Vibration measurement equipment T w o sensor packages, designed and built at the University o f British Columbia ( U B C ) ,  were used to monitor the vibration o f the vibroflot and ground. The sensor package for monitoring the ground vibration consisted o f 3 orthogonal accelerometers and one pore pressure transducer as shown in Figure 3-3. IC-Sensors model 3031 piezo-resistive accelerometers were used. These have a range o f +/- lOg, a frequency response range o f 0-600 H z and a mounted resonant frequency o f 1200Hz. They were mounted rigidly in a steel cone shaped housing, about 300mm long and 45 m m in diameter. The pore pressure transducer had a capacity o f 350 kPa and was manufactured by Sensym I C T . The motion o f the vibroflot was monitored using an accelerometer package as shown in Figure 3-4-a. The package consisted o f three orthogonal accelerometers and an amplifier  46  board. After installation o f all the parts, the housing was filled with epoxy to protect the electronic parts from damage due to high impacts and leakage o f water. Down-hole amplification o f signals was necessary to increase the signal to noise ratio as the cable carrying the signals passed through the strong electromagnetic field o f the electric motor in the vibroflot. The accelerometers used were the same brand as in the ground package but with higher capacity. They had a range o f ±50g, a frequency response range o f 0 to 1050 H z and a mounted resonant frequency o f 1800 H z . The steel package housing was 200mm long, 35 m m in diameter and was bolted on a plate which was then welded to the vibroflot wear jacket, 0.7 m above the nose (Figure 3-4-b). This is about the middle o f the eccentric mass. The electric cable was guided through a Vi" steel pipe all the way up to the top o f the extension tubes, over a pulley and then to the data acquisition computer in the U B C truck. Figure 3-5 is a view o f the site during vibration measurement. The steel pipe was replaced by a strong hydraulic hose passing over the vibration damper to prevent breakage o f the steel pipe. The package had to be very robust to be able to survive a very rough environment and high impacts. A l l the transducers were calibrated before and after the vibration measurement. N o change in calibration factor was observed. The piezo-resistive accelerometer is sensitive to both dynamic and static (gravitational) accelerations. This is an advantage as it allows calibration under static accelerations o f + l g , 0 and - l g . Table 3-2 shows an example o f calibration o f accelerometers i n the ground vibration sensor. A t the selected location for ground vibration measurement, a cone hole was pushed to a depth o f about 8.2m. Inclination during the cone pushing was monitored and was less than 1 degree. Figure 3-6 shows the measured q profile at the location o f ground instrumentation t  over-plotted on the previous pre-compaction C P T . After pulling out the cone, the ground sensor package was pushed to 8.7 m depth in the C P T hole. The objective was to install the sensor package in a loose sandy deposit. Rods o f 45 m m diameter were used to push the package. These rods were normally used for pushing the K B A T tool, which is the U B C ground water sampling system. The rods were then detached from the instrumentation housing and withdrawn. This was to eliminate any effect o f the rods on the measured vibration. Care was taken to prevent the sensor package from rotating during installation. A 10-mm steel cable attached to the package (Figure 3-3) allowed retrieval o f the package after completion o f monitoring.  47  The time histories o f vibration were recorded at a sampling rate o f 333 H z using E G A A data acquisition system developed by RC-Electronics Inc. This was the maximum sampling rate that could support simultaneous recording o f 7 channels. This rate was considered to be adequate as about 11 data points would be recorded for each cycle o f vibration at the predominant frequency o f about 30 H z . The ground vibration signals were amplified at the surface in the U B C cone penetration testing truck before recording. 3.2.3  Results of vibration measurement Figure 3-7 shows the time histories o f the measured parameters in the ground and on the  vibroflot along with the depth o f the vibroflot nose and its power consumption during construction o f stone column #3. The horizontal ground accelerations were measured in the direction o f the active axes o f the horizontal accelerometers. These are axes 1 and 2 in Figure 3-2. These horizontal accelerations were then transformed to the local coordinate system with axes radial and tangential (x and y respectively) to stone column #3. In Figure 3-2, the local coordinate system is shown only for stone column #3 for clarity. It may be observed from Figure 3-7 that the vibroflot was turned on at t=5 seconds while hanging in the air. A t t=30 second, the vibroflot started penetrating the ground. Once i n the ground, the amplitude o f vibration on the vibroflot dropped due to the ground constraint. The vibration sensors in the ground did not register much vibration until the vibroflot had almost passed through the 5-m thick upper fine-grained soil. This is partly due to the poor coupling between soil and vibroflot in fine-grained soil. The soil adjacent to the vibroflot would liquefy and due to its low permeability did not recover quickly enough to re-establish the coupling. A t this point, although the vibroflot is vibrating, only a small portion o f the energy gets transmitted to the ground due to the lack o f shear strength. It took about 90 seconds for the vibroflot to reach the target depth o f 10 m. A t this point, the vibroflot and water jets were turned off to allow the pore water pressure response o f the ground to be monitored. Note that this is not the conventional procedure and was done only for testing purposes. After a wait time o f about 200 sec, the water jets and the vibroflot were turned on again. This caused a sudden rise in the measured pore pressure. From the depth profile, it may be observed that the hole was flushed twice before the densification phase began at about 440 sec at 10 m depth. During the first flushing, the first load o f crushed rocks was  48  deposited into the hole by a wheel loader. From comparison o f ground vibration at 330 seconds and 440 seconds, from increased vibration in the soil, it may be observed that adding the backfill improved the vibroflot-soil coupling. The operator then worked his way up at 0.5 m depth increments with a minimum hold time o f 30 seconds per interval. Due to the small time scale, data presented in Figure 3-7 are compressed and only show the maximum and minimum envelopes. Figure 3-8 is a portion o f the time histories during densification showing the full signals. It may be observed that the motion o f the vibroflot is sinusoidal whereas the ground responses are irregular but still periodic. The radial acceleration (acc-x) signal is the most irregular. It is likely that the interaction between the vibrator and the stones around it generates higher frequency ground motions that contribute to this irregularity. 3.2.4  Analysis of results  3.2.4.1  Frequency analysis o f the time histories  Figure 3-9 shows that the predominant frequency o f the input and output vibration are both about 29 H z . A forced vibration system at steady state should theoretically vibrate at the frequency o f excitation. The predominant frequency remained constant throughout the process and was independent o f the ground condition around the vibroflot. Figure 3-10 shows the frequency spectra in a broader scale. It may be observed that besides the predominant frequency, there are some other frequencies which are multiples o f the predominant frequency. It is not known whether these frequencies are due to errors inherent i n Fast Fourier Transformation, or related to sampling rate and handling (aliasing or windowing). It is also possible that these frequencies physically exist. A t each cycle o f the vibroflot, there would be four smaller impacts generated by two fins and two water tubes (see Figure 3-4-b). Therefore, frequencies, which are multiples o f the predominant frequency such as 29, 58, 87 and 116 H z can be generated. 3.2.4.2  Attenuation o f vibration  The amplitude o f vibration attenuates in the ground due to geometric spreading and material  damping.  If  the  propagating  wave  encounters  an  interface,  partial  transmission/reflection o f energy and mode conversion also occurs (Santamarina et al 2001). Geometric spreading occurs because o f the increase o f the size o f the wave front with distance  49  from the source and thus the decrease o f energy per unit area. The amplitude o f vibration is a function o f the square root o f energy and also decreases with geometric spreading. If the soil is approximated by a visco-elastic model, the material damping causes energy loss i n each cycle as shown by the area o f the hysteresis loop in Figure 3-11. When a wave hits the interface o f two different media at an angle, some o f the energy reflects back into the first medium and the rest transmits into the second one. The interface may alter the particle motion too. For example an oblique incident P-wave, 9pi, in Figure 3-12 transforms into a P-wave and an S-wave in the second medium. Attenuation o f vibration can be expressed by the following equation:  g-«(<2-'-,)  Equation 3-1  1  T where A i and A2 are amplitudes at distances r  (  and r  2  from the source o f vibration,  respectively; n is a coefficient representing the geometric spreading (n=0 for rods and plane waves, n=0.5 for cylindrical wave fronts and n=l for spherical wave fronts); and a is an empirical coefficient which depends on the soil conditions, source o f the vibrator and frequency, a can be presented by the following equation:  a =  Equation 3-2  Q-V  where f is the frequency, V is the wave velocity and Qd is expressed by the following equation:  Equation 3-3  where D is the damping ratio and is defined as the ratio o f the hysteresis area (dotted area in Figure 3-11) to the area o f the shaded triangle, all divided by 4TC (Kramer 1996):  D =  W,D  Equation 3-4  AnW  s  50  and T is a coefficient representing the reduction o f amplitude due to partial transmission and r  mode conversion. W $ and W D are defined in Figure 3-11. Figure 3-13 illustrates the maximum radial and tangential accelerations measured at different distances from the vibroflot during backfilling (densification phase) where the vibroflot was at the same depth as the vibration sensor in the ground. It may be observed that the relative values o f tangential and radial accelerations change with distance. It indicates that the variation o f the ground acceleration with distance is not due only to attenuation but also due to the complex wave propagation regime. Therefore, a plot o f the resultant horizontal acceleration (the square root o f the sum o f square o f radial and tangential accelerations) versus distance is likely to give a better indication o f attenuation o f the energy o f the vibration. Figure 3-14 shows the attenuation o f the resultant horizontal acceleration with distance. A l s o shown for comparison are the theoretical geometric attenuations due to cylindrical and spherical spreading, which are obtained from Equation 3-1, ignoring partial transmission and mode conversion effects. It may be observed that the spherical spreading seems to fit the field data better. In Figures 3-15 and 3-16, the effect o f material damping is also considered. It is possible to fit the data with the theoretical curve assuming cylindrical spreading and a=0.3-0.6 m" and 1  with spherical spreading and a=0-0.1 m" . The effects o f partial transmission and mode 1  conversion are ignored. Woods and Jedele (1985) proposed the coefficient a=(0.03 to 0.1 m" ) for most sands, 1  sandy clays, etc. and for a vibration frequency o f 50Hz. This a can be corrected for the frequency o f 30 H z as follows :  Equation 3-5  :.a « 0.02 - 0 . 0 6 n i-i  Equation 3-6  where a i is the known attenuation coefficient associated with fi and f is the frequency o f the vibration at which a is to be obtained. The obtained a is close to that found from spherical attenuation in Figure 3-16.  51  Morgan and Thomson (1983) also found that the spherical spreading fitted their field data as shown in Figure 3-17. They obtained the amplitude of radial displacement from double integration o f radial acceleration. Figure 3-18 illustrates Green's (2001) interpretation o f the vibration data around an " S " type Keller vibrator as reported by Baez and Martin (1992). This vibrator generates a 200 k N centrifugal force operating at 30 H z . He concluded that attenuation was due to cylindrical spreading (note that n=0.5 is the best fitted line) and an attenuation coefficient o f a=0.2 fitted the data. This value for a is too large compared to the range (a=0.02-0.06) obtained from equation 3-5 above. In addition, it w i l l be shown below that the damping ratio obtained from the back-analyzed a is also larger than the expected value for cylindrical spreading. Therefore, spherical spreading would have been a better interpretation. It is possible to back-analyze the damping ratio from the a value obtained from the field vibration attenuation using the following equation:  D =  Equation 3-7  From Figures 3-15 and 3-16, the average a can be found from attenuation curves as follows: •  Assuming spherical spreading: a=0 to 0.1 m"  •  Assuming cylindrical spreading a=0.3 to 0.6 m"  1  1  Assuming a wave velocity o f V=180m/s and f=29hz gives a damping ratio as follows: •  Assuming spherical spreading: D ~ 0 to 10%  •  Assuming cylindrical spreading D ~ 30% to 60%  It may be observed i n Figure 3-19 that a damping ratio o f 30-50% is associated with shear strains o f more than 10% and thus is likely to be unreasonable. O n the other hand, a damping ratio o f 0-10% is likely to be the range for the horizontal vibration. Note that this is an average value and the actual damping ratio would be higher at closer distance to the vibroflot and lower at further distance. The effect o f material damping on attenuation is not likely to be significant in the vibroflotation. The energy attenuated by material damping is a function o f the material damping and the number o f cycles. The number o f cycles, N  c y c  is the number o f wavelengths  required to travel the distance and can be obtained by the following expression: 52  Equation 3-8  where r is the radial distance between the source and point o f interest, and X is the wavelength and can be obtained from  Equation 3-9  where V is the speed o f wave and f is the frequency of the wave. Using a shear wave velocity o f 180m/s and a frequency o f 30Hz results i n N c 0 . 2 8 at the centroid (r=1.7m) and N = 0 . 7 8 =  c y  cyc  for the furthest measuring point, r=7.6m. This means that only 28% o f the energy that attenuates in a full cycle w i l l be damped out o f the shear wave after travelling 1.7m. It may be observed from Figure 3-14 that the peak acceleration at r ~ l .7m increased with the order o f construction o f stone columns #3, 4 and 5 which are equidistant from the measuring point. This could be explained by the effect o f material damping. A s the soil compacts, its stiffness and wave velocity increases, which decreases N  c y c  and energy loss by  damping. For comparison, the radial steady state acceleration data reported by Baez and Martin (1992) is over-plotted on Figure 3-13. A s was mentioned before, these accelerations were not actually measured but obtained from differentiation o f velocity measurements. Moreover, the effect o f C P T rods on the measurement is not known. Despite these deficiencies and although the soil conditions, instrumentation depth and vibrators were different from those in this study, their radial accelerations seem to have similar trends. Figure 3-20 shows the attenuation o f vertical acceleration in the ground. It is assumed that the vertical acceleration o f the vibroflot is completely transmitted to the ground. This is a reasonable assumption, as the relatively large horizontal force should provide enough frictional force to transfer the vertical motion. It may be observed that the data points fall between the theoretical cylindrical and spherical spreading. This is partly because vertical excitation is transmitted to the ground through a longer length o f contact between the vibroflot and soil than that which transmits the horizontal vibrations. The source for vertical vibration is somewhere between a line source with cylindrical attenuation (such as a vertically vibrating long vibro-rod) and a point source. 53  The imposed acceleration and the number o f cycles imposed by vibro-replacement are significant as compared to those occurring during earthquakes. For example horizontal accelerations in the range o f 14g to 1.7 g were measured on the vibroflot and i n the ground at the centroid (~1.7m away from the vibroflot), respectively. Therefore, the soil within the densification grid w i l l experience a few thousand cycles o f vibration with horizontal accelerations larger than 1.7g. O n the other hand, during a 7.5 magnitude earthquake with 475 year return period in the Lower Mainland, B C , 15 cycles o f horizontal acceleration i n the range o f about 0.3g are expected. A simplified evaluation would indicate that such vibrations during densification should prepare a vulnerable soil to resist the design earthquake. There are other published attenuation data from vibration measurement at the ground surface, which were obtained from monitoring ground vibration adjacent to foundation structures. The objective o f such vibration monitoring was to ensure that the construction vibration would not exceed a certain level (usually in terms o f particle velocity) at the location o f the foundations or structures (e.g. Woods and Jedele, 1985). Lacy and Gould (1985) considered a peak particle velocity o f 2.5 mm/sec as a threshold for causing possible significant settlements at vulnerable sites due to pile driving vibrations. Dowding (1996) presented allowable peak particle velocity as a function o f frequency o f vibrations caused by blasting. For example, for a frequency o f 30Hz, a maximum allowable P P V o f 50 mm/sec is recommended. The horizontal peak particle velocity o f the ground during vibro-replacement may be obtained by integration o f measured accelerations. For horizontal acceleration o f 14g t o l . 7 g and frequency o f 29 H z , the peak particle velocity would be in the range o f 750mm/sec to 90mm/sec. Therefore, the vibration caused by vibro-replacement within the densification grid is equal or much greater than the maximum allowable particle velocity. This is a strong indication o f the effectiveness o f the vibro-replacement method. Despite the strong vibrations that vibro-replacement generates at depth i n the ground, the technique is a popular method in urban areas as the destructive radius o f vibro-compaction at the usual depth o f building foundations is usually less than 10m. Locally in the Lower Mainland, vibro-replacement has been carried out as close as about 3m from adjacent buildings.  54  3.2.4.3  Horizontal motion paths o f the vibroflot and soil particles  The displacement paths o f the soil particles and vibroflot could be obtained by double integration o f the acceleration time histories. Due to potential errors introduced by integration, the following discussion presents a demonstration o f the shape o f the motion paths in terms o f accelerations. Assuming a harmonic signal, which is the case for vibroflot motion, the shape o f the acceleration path and displacement path, should be the same. This may not be exact for the soil particle motion. However, it serves the purpose o f showing the relative significance o f motion i n the tangential and radial directions. In Figure 3-2la, it may be observed that the vibroflot has a circular horizontal motion while suspended in the air. The amplitude o f motion o f the vibroflot decreases in the ground but almost maintains its circular shape (Figure 3-2 lb). During installation o f the subsequent stone columns (#4 and #5), the shape o f the motion o f the vibroflot turns into an ellipse (Figure 3-2 l c ) . Morgan and Thomson (1983) also made a similar observation and attributed it to the larger ground resistance in the direction normal to the fins. Figure 3-22 illustrates the ground particle motion path in response to the vibrator during densification for stone columns #1 to #3. It may be observed that the shape and orientation o f the motion path is a function o f the distance o f the vibroflot from the monitoring point. A t a radius o f 1.7 m, the acceleration is greater in the tangential direction. The same observation was made for stone columns #4 and 5 at a horizontal distance o f about 1.8m from the measuring point as shown in Figure 3-23. It is counter-intuitive to get tangential acceleration greater than radial acceleration in the ground. One expects that the radial accelerations i n the ground would be greater due to direct radial impacts o f the vibroflot. It w i l l be shown that numerical modelling confirms the observed characteristics o f the field motion paths. 3.2.4.4  Optimal frequency o f vibration  Massarsch (1991) showed that the energy transfer from the vibrator to ground becomes the most efficient and results in larger vibration amplitude and better densification at input frequencies  close to the resonant frequency o f the ground. Massarsch and Heppel (1991)  suggested that this optimal frequency could be found by spectral analysis o f the system response during switch-off or switch-on o f the vibrator. During these periods, all the frequencies  below the operating frequency o f the vibrator are excited and the optimal  55  frequency is the one corresponding to the maximum ground response. Figure 3-24 shows the ground response after switching the vibrator on. The compaction method used was the vibro-rod method, which uses a vibrator with vertical vibration. The ground response peaks before reaching the steady state vibration and indicates that the optimal frequency is lower than the operating frequency at the steady state. This is despite the fact that the impact force is a function o f the square o f frequency. The technique used by Massarsch and Heppel (1991) w i l l be applied to the present data set for vibro-replacement. Figure 3-25 shows the time history o f vibration o f the vibroflot and the horizontal accelerations o f the ground after switch-on at t~322 sec (enlarged from Figure 3-7). The ground response peaks before reaching the maximum frequency at steady state. This is marked by small arrows in Figure 3-25. Figure 3-26 shows the ratio o f ground acceleration to vibroflot acceleration versus the frequency at three different times during the transient state. The optimal frequency, which is the frequency corresponding to the peak response ratio, is found to be about 26 H z . It should be noted that the optimal frequency depends on the soil conditions and should increase as the soil becomes denser during compaction. It may be concluded that the operating frequency o f 29 H z is close to the optimal frequency for this site. If the resonant frequency cannot be provided, a frequency slightly higher is more desirable. A t higher frequencies, the larger dynamic force may compensate for the less efficient energy absorption. The operating frequency o f vibroflots is usually either 30 or 50 H z . This historically originates from the early electrical vibroflots operating at a factor o f the frequency o f the alternating current, 50 H z in Europe and 60 H z in the U S . Some newly designed vibrators operate at 25 H z . 3.2.4.5  Densification phase  Figure 3-27 shows the vibroflot response, its depth and amperage drawn (electrical current consumption) during the densification phase. Due to symmetry, only the positive half of the acceleration time history is shown for more clarity. It is conventionally assumed that an increase in resistance o f the ground due to densification is indicated by increased amperage and decreased amplitude o f vibroflot motion. Amperage is conventionally used for field quality control during construction. It has also been suggested that the amplitude o f the  56  vibroflot vibration is a better indication o f densification. The data presented here suggests that these parameters may sometimes be contradictory. From 400 to 435 sec, the vibroflot was lifted up to the ground surface to flush the hole. The hole was kept open by the side and nose water jets and so the resistance o f the soil against the vibrator was small. This resulted i n low amperage and high vibroflot amplitude. Then the vibroflot re-penetrated at about 440 sec. During penetration, the weight o f the vibroflot is on its toe and restricts the lateral vibration. This results i n a low amplitude and high amperage. After re-penetration to 10 m depth, the nose jets were turned off and densification began at 440 sec. It may be observed that it took about 10 sec for the amplitude o f vibroflot to decrease to its steady state vibration. This is thought to be the time taken for the crushed stone to get down to the hole and around the vibroflot to build up resistance and decrease the amplitude o f the vibroflot. During this 10 sec, the amperage consumption decreased, which is opposite to the usual trend. B u i l d up o f resistance around the vibroflot should have increased the amperage. This apparent contradiction could be explained as follows. The amperage drawn by the motor depends on the motion o f the entire vibroflot and not only on the motion o f the tip. The pivot point o f the vibration moves further down from the vibration isolator when the vibroflot goes into the ground as noted by Greenwood (1991). This causes greater motion o f the vibroflot shoulder. Therefore, the resistance around the tip increased but because the level o f the crushed stone available i n the hole dropped, the motion of the shoulder was less restricted and so the overall power demand decreased. This contradiction suggests that for monitoring the vibroflot, vibrations sensors at the tip and shoulder o f vibroflot, are required to monitor the motion o f the entire vibroflot and not only the tip. A t 478 sec, the densification o f this depth interval was over and the vibroflot was lowered half a metre to penetrate the previously densified stone and was then lifted one metre to start densification o f the next depth interval. During re-penetration, the current peaked and the vibroflot amplitude decreased as a result o f the increased resistance around the vibroflot and increased tip fixity. From 480 to 520 sec, the vibroflot amplitude decreased indicating that the soil was being densified. However, the amperage did not appear to be sensitive to the effect o f densification. This indicates that the vibrator amplitude and amperage could show  57  opposite trends due to the complexity o f the phenomenon. Based on local experience, a diminished amperage increase occurs when fines contents are in the range o f 15-20% or more. The above suggests that basing the quality control o f densification on interpretation o f the amperage or vibroflot amplitude alone may not be sufficient as these factors are dependent on the methodology and the soil grain size distribution (i.e. fines content / drainage characteristics) o f the soils being treated. For example, i f the penetration into the crushed stone was greater, the observed drop in current from 440 to 460 sec may not have occurred. While Morgan and Thomson (1983) found good correlation between the post-compaction S P T blow counts and the vibroflot amplitude, Fellin (2000) suggested that measurement o f the acceleration at the tip and shoulder o f the vibroflot and the phase angle o f the eccentric mass relative to the motion o f the vibroflot could be used to determine an average stiffness and damping o f the ground. This requires further research. During densification, no residual pore pressure was observed at the location o f the ground sensor. This could be due to different reasons as follows: •  The rate o f dissipation was faster than generation o f pore pressure.  •  The soil was relatively dense and generated little residual pore pressure.  •  The shear strains at the location o f the ground sensor were not large enough to cause considerable shear induced pore pressure.  O n the other hand, there was a general decrease o f pore pressure from t=440sec to 700sec as shown i n Figure 3-7. This pore pressure had been generated by penetration o f the vibroflot and water jets. The general decrease i n pore water pressure is due to dissipation and increasing distance o f the side water jets from the measuring point in the ground. 3.2.4.6  Pore pressure response during penetration  Pore pressure response at a depth o f 8.7m and at a radial distance o f 1.7m from the compaction point is shown i n Figure 3-28. It may be observed that during the first penetration the pore pressure increases about 50 k P a which is almost a pore pressure ratio r = A u / a ' u  = vo  0.6.  The total excess pore pressure is the sum o f the cyclic pore pressure caused by cyclic impacts, pore pressure due to water jets and pore pressure generated from the cavity expansion by penetration o f the vibroflot. In the second and third penetrations, the pore pressure does not  58  increase as much as during the first penetration. It could be because there was a pre-existing hole and thus less increase i n the total stress. Figure 3-29a shows the distribution o f the pore pressure during the first penetration o f the vibroflot observed from stone columns #1 to 5 which are located at different radial distances from the measuring point. During construction o f stone columns #2 and #3, the vibroflot motor and water jets were turned off after penetration to the target depth. Then after partial dissipation, the vibroflot and water jets were switched back on. The sudden rise in pore pressure at this time (t - 3 2 0 in Figure 3-28) is caused by water jets and cyclic pore pressure. K n o w i n g the pore pressures from the water jets and cyclic impacts, the pore pressure caused by cavity expansion during penetration can be calculated, which is shown in Figure 3-29b. It may be observed that the main portion o f the total pore pressure measured at the centroid o f the triangle is from the water jets.  3.3  MECHANISM OF PENETRATION OF THE VIBROFLOT The pointed nose at the tip o f the vibroflot keeps the bearing pressure high, making it  easier to penetrate and to push the soil aside. In this case study, the vibroflot penetrated into the soil deposits under its own weight and the weight o f the follower tubes, a total weight o f about 50 k N . Assuming a diameter o f 0.35m for the vibrator, this weight can provide a bearing pressure o f up to about 0.5 M P a (5 bars). The vibroflot was able to penetrate into medium to dense sandy layers with a tip resistance in excess o f 20 M P a (200 bars). T w o main factors made the penetration o f vibroflot possible: vibrations and water jets. The large accelerations imposed by the vibroflot destabilize the soil particles and reduce the shear strength o f the soil. Vibration also causes some volume reduction in the surrounding soil, which helps to accommodate the vibroflot. Moreover, in loose to medium dense saturated sands, vibration liquefies the soil adjacent to the vibrator causing a further decrease in soil shear resistance. The effect o f vibration on penetration is similar to that in the vibrocone. The Japanese vibrocone (Sasaki and Koga, 1982) has the same gyratory motion as a vibroflot (Figure 3-30). Figure 3-31, compares the tip resistance o f a Japanese vibrocone and a static cone. It may be observed that in liquefiable loose sand, the tip resistance o f the vibrocone is much smaller than a standard static cone, but is not much different in a non-liquefiable soil.  59  Therefore the vibration itself has some benefit for penetration. In granular soils, the strength increases with depth and so the end bearing becomes critical for penetration o f the vibroflot after a few metres. This limits the dry vibro-displacement method to shallow depths. In this condition, the vibrator could even density the ground below the tip, making it harder to penetrate. Water jetting helps the penetration significantly. It scours the soil below the tip and then washes it up to the surface. It also increases the pore water pressure below and around the tip, which reduces the shear resistance.  In Figure 3-29, extrapolation o f measured excess pore  pressures caused by water jets alone to the radius o f the vibroflot gives a pore pressure o f about 350 kPa. This pressure can cause zero effective pressure around the tip o f vibroflot to about 35 m depth in a saturated granular soil. The above observations suggest that the main reason for penetration o f the vibroflot under relatively small tip bearing pressure is the pore water pressure generated b y water jets. The vibration also helps but to a lesser extent.  3.4  NUMERICAL MODELLING OF VIBRO-COMPACTION Due to the complex nature o f soil-vibroflot interaction and wave propagation during  vibro-replacement, a numerical modelling approach is used to simulate and gain insight into the soil-vibroflot interaction and ground response. 3.4.1  Introduction A vibroflot is a tube that gets excited by the centrifugal force, F , induced by the rotation  o f an eccentric mass. The soil-vibroflot interaction is schematically shown i n the horizontal plane in Figure 3-32a. The soil is substituted by a number o f springs and dashpots. The magnitude o f the cyclic force, F is constant but its direction changes with time as a function o f the speed o f rotation o f the eccentric mass. This gives the vibroflot a gyratory motion. Due to the symmetric condition, the excitation force can be defined in two perpendicular directions with a nil phase lag. The motion o f the vibroflot can be formulated independently in only one direction (Figure 3-32b). The motion i n the perpendicular direction is similar but with a TC/2 time lag.  60  Fellin (2000) used this concept and developed a mathematical model for the motion o f the vibroflot in the vertical plane as shown i n Figure 3-33. H e further simplified the problem by substituting the soil by one spring and one dashpot and formulated the motion o f the vibroflot by solving the differential equation o f motion. For more detail refer to Fellin (2000). This is the only published mathematical model o f soil-vibroflot interaction. Although this approach gives a framework to study the motion o f the vibroflot, it does not give any insight into the soil response such as the attenuation o f vibration, particle motion, shear strains, etc. Full modelling o f the soil-vibroflot interaction is very challenging. It is a 3-dimensional soil-structure interaction problem and needs a coupled flow-stress analysis with a soil model capable o f modelling liquefaction and densification. Addition o f stone backfill and changes i n soil properties during the process make the modelling even more complicated. A t this stage, the main objectives o f the numerical modelling are to explain the field response observed during the vibration measurement and to get a better understanding o f the soil-vibroflot interaction. 3.4.2  Numerical model The following simplifying assumptions are used to develop the numerical model o f  vibro-replacement. •  Plane strain condition (horizontal plane)  •  Visco-elastic soil model  •  Equivalent linear analysis  •  Constant properties during vibration  •  Effect o f pore pressure generation is ignored  •  The fins are not explicitly modelled  These simplifications make the numerical modelling most relevant to the vibrations towards the end o f the holding time at each depth interval when, after numerous cycles, the generation o f pore pressure, volume change and the change o f soil properties could be neglected. Being limited to a 2-dimensional analysis, the plane strain assumption is the best option. The main disadvantage o f the plane strain assumption is that the waves spread cylindrically in the model, whereas the data in Figure 3-16 suggests that the true behaviour is more similar to spherical spreading.  61  The finite difference program F L A C (Fast Lagrangian Analysis o f Continua) version 3.4 with the dynamics option was used for numerical modelling (Itasca 1998).  In F L A C the  equations o f motion for each lumped mass at each grid point are used to derive new velocities and displacements from stresses and forces. Then, strain rates are derived from velocities, and new stresses from strain rates. A circular block o f the ground 20m in diameter, represented by about 4200 quadrant elements, is used to model the ground and vibrator as shown in Figure 3-34. The maximum size o f the elements is limited to 1/10 o f the wavelength o f shear waves, which is about 6m for the assumed conditions, to ensure proper modelling o f wave propagation (Kuhlemeyer and Lysmer, 1973). The maximum aspect ratio o f the soil elements is limited to about 2. The soil and the vibroflot in the model are connected by a row o f interface elements as shown i n Figure 3-35. B y assigning zero tensile strength and a friction angle to the interface elements, the separation and slippage o f vibroflot and soil are automatically simulated. The friction between vibroflot and soil is simulated by assigning a friction angle to the interface elements. Note that in reality the fins prevent slippage at the soil-vibroflot contact and the slippage surface is pushed into the soil. Therefore, a fairly high friction angle o f 40° is assigned to this interface. The interface friction o f 40° is obtained by scaling up tan((p n) by so  the ratio o f (vibroflot radius + width o f fin) to the vibroflot radius. It was visually observed in the field that the vibroflot twisted about 10-30 degrees when it just entered the ground and then it stopped twisting. This indicates that initially, the resistance of the fins was smaller than the frictional forces resulting in twisting o f the vibroflot. However, at about l m depth into the ground, the resistance o f the fins became greater than the frictional forces and thus stopped the vibroflot from twisting. A "quiet boundary" (Itasca 1998) is used for the outer boundaries of the model to prevent the waves from reflecting back into the model. The quiet boundary setting in F L A C uses independent dashpots in the normal and shear directions at the model boundaries to absorb the energy o f the approaching waves (Itasca 1998). The measured motion of the vibroflot during the densification phase at 9m depth (Figure 3-36) is applied to all the nodes o f the vibroflot in the model as the input motion. This generates a rigid body motion for the vibroflot. The motion of the vibroflot is close to a circular motion and is defined as follows:  62  ACC =A-sm(2-x-f-t)  Equation 3-10  ACC  Equation 3-11  xl  = A • cos(2 -TT-f-t)  vl  where: A : Single amplitude o f acceleration^ 3.4 g (obtained from the field measurement) A C C : Acceleration o f the vibroflot in x direction x t  A C C , : Acceleration o f the vibroflot in y direction y  t  f : Frequency o f vibration (29 H z ) t: Time (sec) A visco-elastic model and an equivalent linear method are used (Ishihara, 1996). The Seed and Idriss (1970) modulus reduction curve for sand is used. Table 3-3 presents the soil parameters used in the numerical analyses. The small strain shear modulus, G  is calculated from the shear wave velocity, V obtained from seismic cone  m a x  s  testing using the following equation:  G  ,nax=P s F  Equation 3-12  2  where p is the density and V is about 180m/sec. A high Poisson's ratio is selected to account s  for the high bulk modulus o f a saturated soil equivalent to a V =1500 m/s and a V =180 m/s. p  s  Effective in situ stresses were calculated for a depth o f ~8.5 m and submerged unit weight o f 10kN/m . 3  The average material damping was found to be about 5% from the back analysis o f field vibration data, which was based on spherical spreading (Figure 3-16). However, the geometrical attenuation is cylindrical in the model. In order to be able to match the field data using the plane strain model, the material damping is increased to compensate for the difference in rates o f geometrical damping. This modified material damping is obtained from Figure 3-15, in which the cylindrical spreading was forced to fit the field data. This suggests a material damping o f 30-60%. However, it w i l l be shown that an average damping ratio in the range o f 18% to 35% matches the field data. The elastic analysis started with an arbitrary G / G  m a x  = 0.5. The maximum shear strains  that were obtained after the analysis were used to adjust the G / G x and the analysis was m a  63  repeated with the new stiffness values. This procedure was iterated a number o f times until the G/Gm 3.4.3  a x  converged. Figure 3-37 shows that the analyses converged after 4 iterations. Results of numerical modelling  Figure 3-38 illustrates the deformed shape o f the model during vibration at an arbitrary time. It may be observed that as the vibroflot moves away from the soil, separation occurs and leaves a gap behind. The effect o f soil-vibrator friction on the deformed shape is also clear. Figure 3-39 compares the resultant horizontal accelerations from the field and those predicted by the numerical analyses. It may be observed that a reasonable agreement between modelled and measured data is obtained. The measured data falls within the range obtained from simulations using two average damping ratios o f 18% and 35%. Figure 3-40-right shows the acceleration paths o f the vibroflot and soil at different radial distances from the vibroflot obtained from the numerical model. Note that the scales are different in each plot for more clarity. The alignment o f the motion paths and the relative significance o f the accelerations vary with the radial distance. Closer to the vibroflot, the particle motion is stronger in the radial direction and as the distance from the vibroflot increases, the tangential motion becomes relatively significant. A l s o repeated in Figure 3-40 for comparison, are the field acceleration paths, which show similar characteristics to the modelled ground response. Note that at a radial distance o f 1.7m, the tangential motion is dominant and the orientation o f the acceleration path is almost in the tangential axis i n both the field and numerical model. The normal and frictional impact o f the vibroflot to the wall o f the hole continuously changes its contact point and direction. These impacts create a complex wave propagation regime by sending body waves (shear and compression waves) into the ground. These waves travel at different speeds and wavelengths. The superposition o f these body waves generates a unique particle motion pattern as a function o f radial distance from the vibroflot. The results show that despite the simplifying assumptions, the numerical model is able to capture the characteristics o f the field data. A l s o it is able to obtain a reasonable match to the measured accelerations in the field (Figure 3-39). It is difficult to measure the field shear strains to check numerical analysis results. Field measurement o f shear strains requires simultaneous measurement o f vibration at 4 points, as  64  shown in Figure 3-41. To obtain shear strains in each plane, the displacements o f three points in that plane should be measured versus time. Based on numerical analyses, Figure 3-42 shows the distribution o f shear strains in the horizontal plane with radial distance from vibroflot. These values w i l l be used to explain the mechanism o f compaction during vibro-replacement in the next section. In order to evaluate the effect o f soil-vibroflot friction, the shear strains obtained from an interface friction angle o f 40° and 0° were compared. It was found that a friction angle o f 40  0  increases the shear strains at 0.5m and 1.7m by factors o f about 1.15 and 1.05 respectively. 3.4.4  Mechanism of compaction during vibro-replacement Densification o f granular soils is mainly due to shear-volume coupling and is mainly  dependent on the magnitude o f the induced shear strains and the number o f cycles o f shearing. In this study, a procedure based on cyclic shear strains, and a shear-volume coupling model w i l l be presented to estimate the densification effect o f vibro-replacement. Firstly, the shear-volume coupling model that is used here w i l l be introduced. 3.4.4.1  Shear-volume coupling model  Our understanding o f shear induced volume change is based on cyclic/monotonic behavior o f soil in the laboratory. Shear-volume coupling models have been formulated by many researchers. The model developed by Byrne (1991) w i l l be briefly presented below. 3.4.4.1.1 Drained  condition  Based on simple shear tests on sands, Martin et al. (1975) proposed a relation for incremental volume change at each cycle as a function o f the shear strain at that cycle and the accumulated volumetric strains from the previous cycles. Byrne (1991) normalized the data with respect to the shear strains and proposed the following expression for shear volume coupling o f sands:  -7- = C,.exp —C .  Equation 3-13  2  r  J  65  where A s is the incremental volumetric strain i n the current cycle i n percent, £ is the v  v  accumulated volumetric strain from the previous cycles i n percent, y* is the net engineering shear strain i n the current cycle and is obtained as follows:  Y  =Y ~7  Equation 3-14  t  where y is the engineering shear strain in the current cycle and y is the shear strain threshold. t  Byrne (1991) suggested that a y o f 0.005% fitted the laboratory data. C i and C are regression t  2  parameters. d controls the volume change and is defined as:  i^ v)cycle\ £  n  C, =  Equation 3-15  7  The data also shows that the accumulated volumetric strain after 15 cycles is 5 times greater than the first cycle. So C\ can also be defined as: (s ) Q  =  WZH  Equation 3-16  Equation 3-16 may be preferable because there are considerable data on volumetric strains after 15 cycles as a function o f D . The parameter C2 controls the shape o f the curve. r  Based on the available data (from Martin et al 1975; Tokimatsu and Seed 1987), Byrne (1991) noticed that the shape o f curve was the same for all densities and so C2 could be presented as a fraction o f C i as: C =0.4/C,  Equation3-17  2  C | can be obtained from the relative density as follows: C, = 7600 • (D )"  Equation 3-18  25  R  It may be observed that for this model, the shear-volume coupling o f sand depends on the relative density o f sand. However, Byrne (1991) suggested that C2 be kept as a parameter as it gives more flexibility to match the data in case a more complete cyclic history was available. Figure 3-43 shows the volumetric strain as a function o f y and number o f cycles obtained from Byrne (1991) model.  66  3.4.4.1.2 Undrained condition Pore pressure generation under the cyclic loading may be estimated based on Byrne (1991). The tendency towards volumetric change under drained conditions turns into the tendency for generation o f pore pressure under undrained condition as formulated below.  (A*r).21 '  -cycle  = 0 . 5 - 7 -C,.exp '  1  1  •c,  Equation 3-19  where all the parameters are defined above. In undrained conditions, the total volumetric strain is: As  = Asl +As\,  v  = 0  Equation 3-20  where p and e denote the plastic and elastic volumetric strains, respectively. The elastic volume change can be obtained as follows:  Asl where A a '  =•  ACT,, Equation 3-21  M  is the vertical effective stress change per half a cycle and M is the constrained  v  modulus o f the soil given by:  M =  K -P m  Equation 3-22  a  Values o f K = 1 6 0 0 and m=0.5 are in good agreement with the Martin et al. (1975) data. From m  Equation 3-21 we have: Au = -A<jy = M • As,  Equation 3-23  After each half cycle, the incremental A u is calculated and a ' and stiffness are updated. v  3.4.4.2  Proposed mechanism o f compaction during vibro-replacement  The shear strain field around the vibroflot may be estimated either by field measurement or by analytical/numerical modelling. Field measurement o f shear strains i n the field requires simultaneous measurement o f vibration at 4 points as shown in Figure 3-41. This method needs  67  further research and was not used as part o f this study. The other approach is to calibrate the numerical model to the field measurement and then estimate the shear strains from the results o f numerical analysis. This approach is taken here. It was shown that numerical modelling captured the mechanism o f soil-vibroflot interaction and obtained a reasonable match to the field measurements o f acceleration. However, it should be emphasized that more work is needed before the numerical analysis can be used i n a quantitative manner. Figure 3-42 shows the distribution o f shear strains in the horizontal plane with radial distance obtained from the numerical analyses. Average shear strains o f about 0.125%, 0.09% and 0.075% are obtained from this figure for radial distances o f 0.5m, l m and 1.7m respectively. Figure 3-44 shows the predicted changes in relative densities by the Byrne (1991) model.. After about 6000 cycles, this model predicts A D = 8 % at r=0.5m and A D = 5 % at r  r  r=1.7m, which is the centroid o f compaction grid. Based on the correlation between q and D r c  for Ticino sand (Baldi et al. 1986), a 5% increase i n relative density at the depth o f about 9m is equivalent to an increase o f less than 10 bars in tip resistance (note that geological ageing effects are ignored). Figure 3-45 compares pre- and post-q which were both carried out within a 3 m radius o f t  the location o f the ground vibration sensor. It may be observed that the pre- and post-q have t  similar profile and that the post-q has improved very little relative to pre-q . The reason for the t  t  limited improvement is likely to the high initial density o f the sand. The sand at the location o f the vibration sensor (depth o f 8.7m) is medium to dense and could have had an initial density greater than 60%. It should be noted that the actual tip resistance at 8.7m should be greater than that shown in the figure i f corrected for an adjacent silty layer at 8.5m depth. Therefore the initial density o f sand could be even higher. The approximate tip resistance correction factor for the thin layer ( N C E E R 1997) is about 1.2 which increases the pre-q value from about 100 t  bars to 120 bars and consequently the initial relative density could have been in the range o f 70 to 75%. This initial density is quite high and therefore little increase in tip resistance would be expected. Moreover, it should be noted that the monitored depth was confined by two dense to very dense sandy layers (at 7.5 and 8.5 m). These dense sands tend to confine the vibroflot movements and reduce its vibration amplitude at the location o f the sensor package leading to even lower densification effects.  68  In general the amount o f densification estimated from the procedure suggested here (using the shear strain method) is in agreement with the densification indicated by the post-densification C P T U .  Obviously this subsoil condition was not ideal for this research.  However, this site was the only vibro-replacement site available at the time o f this study. It would be good to confirm this procedure in a uniform loose sandy deposit. The procedure used here to estimate the change in density during vibration has some shortcomings as follows: •  Shear-strains in the 3-dimensional model are different from those in the plane strain model.  •  The soil close to the vibroflot may liquefy, soften and undergo larger shear strains. This is not considered.  •  Multi-directional vibration causes more densification, which was not considered.  The first item above could be investigated using 3-dimensional modelling and is beyond the framework o f this thesis. The second and third items are discussed below. Figure 3-46 shows the application o f the Byrne (1991) model assuming an undrained condition. The results suggest that the soil around the probe would liquefy i n less than 25 cycles which is less than 1 second worth o f vibration. However, the field measurement o f pore pressure during vibration did not show any significant pore pressure at a radial distance o f 1.7m. The actual condition in the field is not completely drained but partially drained. Considering the field drainage condition and the attenuation o f the shear strains with distance from the vibroflot, it is likely that the soil close to the vibroflot liquefies. The liquefaction zone may extend to a radial distance where the rate o f dissipation is less than the rate o f pore pressure generation. Addition o f gravel size backfill is likely to reduce the extent o f liquefaction during densification by providing better drainage to the sand. Addition o f stones also enhances the soil-vibroflot coupling since the stones around the vibroflot have better chance to drain the shear induced pore pressure.  A fully coupled analysis is required to  account for the effect o f the generated pore pressure during vibration. The input parameters for Byrne's shear-volume coupling model are obtained from simple shear testing, in which the shear strains are in a vertical plane. A l s o , the direction o f the net movement o f the particles is vertically downward. In the numerical model, the shear strains  69  are in the horizontal plane. Therefore, the estimated volume change is relevant to the volume change occurring in the horizontal plane. The plane strain numerical model cannot consider the volume change due to the shear strains in vertical planes and the resulting volume change under gravity. This could be related to the effect of multi-directional straining. Pyke et al. (1975) concluded that the settlements caused by combined horizontal motions were about equal to the sum of the each horizontal motion separately. They also found that vertical accelerations less than l g caused no significant settlement whereas vertical accelerations combined with horizontal accelerations caused a marked increase in the settlements. Martin and Lee (1999) recommend doubling the estimated settlement obtained from the method of Seed and Tokimatsu (1987) to account for the effect of multi-directional shaking. During vibro-replacement, where 3-dimensional vibrations are generated, it can be perceived that the superposition of the horizontal and vertical shear strains would be more effective in destabilizing the grain arrangement. Vertical vibrations cause temporary partial or complete reduction of effective overburden stress, which reduces the stiffness of the soil. At this time, horizontal shear cycling would be more effective for inducing large shear strains and rearranging the particles into a denser state. 3.4.5  Other mechanisms of the effects of vibro-replacement Besides increasing the density, vibro-replacement also induces other changes in the soil  such as an increase in lateral stress, removal of geological ageing effects and probably a change in soil fabric, as discussed in the following sections. 3.4.5.1  Increase in lateral stress  It is generally accepted that the lateral stress increases after vibro-compaction. This has important implications for the characterization of the compacted ground (e.g. Saito 1977; Jamiolkowski and Pasqualini 1992; Howie et al. 2001). However, the mechanism causing the increase in lateral stress during vibro-replacement has not been clearly explained. Numerical modelling with an elastic-plastic (Mohr-Coulomb) soil model is used here to give insight into this mechanism. The main parameters in this soil model are friction angle,(j), dilation angle,vj/, shear modulus, G , Poisson ratio, v and cohesion, c. The soil parameters assumed in this  70  analysis are G = G  m a x  / 3 , v=0.48, <p=41 °, \|/=10°, c=0. Note that the objective is only to capture  the mechanism o f increase o f lateral stress and no attempt is made to match the field data. Figure 3-47 shows the radial displacement time history o f some points at different radial distances from the vibroflot. It may be observed that the radial displacement is cyclic but accumulates with increasing number o f cycles. The rate o f the increase o f the radial displacement is greater at smaller radial distances. Figure 3-48 shows that the increase i n the average horizontal stress, (a +ae)/2 is greater closer to the vibroflot. This is similar to a cavity r  expansion problem. Here, instead o f a static internal pressure on the cavity wall, there is an impact whose contact area and direction rotate with time. The rapid rotation o f the impact maintains the cavity pressure. Figure 3-49 shows the radial stress versus radial displacement at r=1.7m from the vibroflot. Plastic radial displacement does not recover in unloading and accumulatively increases with the number o f cycles. This results in a gap forming between the vibroflot and the soil in the model as shown i n Figure 3-50. In the field condition, the gap formed between vibroflot and the soil gets continuously filled by the backfill gravels flowing down and around the vibroflot. This prevents full elastic rebound  and causes more  accumulation o f locked in stresses in each cycle (not modelled here). The backfill also maintains the locked in lateral stress after withdrawal o f the vibroflot. Figure 3-51 shows the predicted stress path o f a soil element at a radial distance o f r=1.7m (location o f centroid o f compaction grid) obtained from the numerical model. During the loading portion o f each cycle ( A B C ) , the vibroflot pushes the soil out. This increases the radial stress and decreases the tangential stress until the stress path reaches the failure line at point B . The stress path then moves along the failure line, where both the radial and tangential stress increase. This is similar to the loading stress path o f an element around an expanding cavity i n granular soil. A t point C , the vibroflot starts to retract from the wall o f the hole, which causes unloading ( C D A ) . The unloading along C D causes a reduction in radial stress and an increase in tangential stress similar to the elastic unloading portion o f a pressuremeter test. The portion D A is similar to plastic unloading in a pressuremeter test. It is believed that a failure criterion is reached in F L A C with the vertical stress (out o f plane stress) as one o f the principal stresses. A t point A , another cycle o f loading occurs similar to previous cycles but at a higher stress level. Eventually at the end o f densification at this depth interval, the ground would be at some higher mean normal stresses. A t this point, the vibroflot is pulled up, which leaves a gap  71  behind it (not modelled in the numerical analysis), which in turn causes some reduction in horizontal stresses. Conventionally, after the end o f densification at the next depth interval, the vibroflot is allowed to penetrate half a metre down, which is likely increases the lateral stress again. In the pressuremeter, the wall o f the cavity moves inward to reach a new equilibrium after deflation o f the membrane, In the case o f vibro-replacement, most o f the cavity created is kept expanded by backfill. This ensures that the increased lateral stresses get locked into the ground. This section gave a qualitative explanation o f the changes in horizontal stresses. It is encouraging that the numerical model also confirmed the increase in the horizontal stress. However, a quantitative evaluation o f the change in horizontal stresses would be very complicated and needs more research. 3.4.5.2  Geological ageing effects  Laboratory tests on Fraser River sand (Howie et al. 2002) showed that soil stiffness increases with time under a maintained shear stress. After completion o f this ageing period, a monotonic shear strain in the range o f 0.01% to 0.1% is enough to remove the stiffness due to the ageing effect. This is considered to be similar to the effects o f disturbance on soil structure that has developed over geological time, termed geological ageing. This effect would be more severe in the case o f cyclic loading (Thomann 1990) and thus even a smaller shear strain may be capable o f causing a loss o f geological ageing. Assuming that the shear strains obtained from the numerical analysis (Figure 3-39) are approximately in the right range, it may be concluded that the geological ageing effect would be significantly reduced to a distance o f about 4m from the vibroflot.  3.5  S U M M A R Y AND CONCLUSIONS In this chapter a case study o f field vibration measurement was presented. Vibrations and  pore pressures i n the ground, and vibration on the vibroflot were measured. The field data showed the details o f ground response to the vibro-replacement process. Numerical modelling was used to simulate the soil-vibroflot interaction and wave propagation i n the ground. The model was successful in simulating the field response. The model was also successful for simulation o f the increase i n lateral stress during vibro-compaction. 72  The main conclusions from field vibration measurement may be summarized as follows: •  A s expected in a forced vibration system, the ground vibration generated by vibro-replacement has the same frequency as the vibrator (-29 H z ) .  •  The optimal frequency (resonance) o f the site i n this case study, interpreted from the transient state o f vibration during switch-on, was found to be about 26 H z .  •  The vibroflot acceleration was measured to be about 20g when freely suspended in the air and reduced to about 14g during the backfilling and densification phase.  •  The horizontal acceleration o f ground within the densification grid (3 metre spacing in this case study) was i n the range o f 14 g (adjacent to the vibrator) to a minimum o f 1.7g (at the centroid o f compaction grid). These accelerations are significantly higher than the expected accelerations during a 475yr return period design earthquake (e.g. ~0.3g) for the Lower Mainland, B C . The number o f loading cycles during vibro-replacement is i n the range o f a few thousands, which is significantly higher than 15 major cycles expected from a 7.5 magnitude earthquake.  •  Peak particle velocities i n the ground within the densification grid in this study were inferred to be in the range o f 750mm/sec (adjacent to the vibrator) to 90mm/sec (at the centroid o f compaction grid), which is significantly higher than the range o f strains used as a damage threshold in conventional practice o f from 2.5mm/sec to 50 mm/sec.  •  The horizontal vibration around the probe appears to attenuate spherically, whereas the vertical motions appear to attenuate more slowly.  •  The relative magnitude o f the horizontal radial and the horizontal tangential acceleration in the ground was found to be dependent on the distance from the vibrator. A t 1.7m away from the vibroflot, the tangential accelerations were greater than the radial accelerations.  •  It was shown that measurements o f vibrator amplitude and power consumption could indicate contradictory trends and variable sensitivity to the  details o f the  densification process. This suggests that additional performance indicators may be required to improve quality control o f the densification process in the field. •  The mechanism o f the penetration o f the vibroflot was described based on the measured pore pressure and analogy to a vibro-cone. The increase in pore water 73  pressure caused by the water jets is believed to be the main reason for the penetration of the vibroflot.  Numerical simulation of soil-vibroflot interaction was carried out using the finite difference program F L A C with an equivalent linear elastic soil model and elastic-plastic Mohr-Coulomb soil model. The analyses were performed in plane strain condition. The summary o f the main conclusions from numerical analyses o f soil-vibroflot interaction is as follows: •  The numerical model proved very useful in providing insight into the soil-vibroflot interaction. It captured the mechanism o f wave propagation and confirmed the field observation o f soil particle motion paths. It showed that the orientation o f particle motion varies with distance from the vibroflot similar to observation i n the field.  •  The numerical model also showed that the motion o f the vibroflot causes accumulation o f radial expansion o f the cavity. This increases the horizontal stress in a manner similar to cavity expansion.  •  A large material damping ratio was required to match the numerical analysis result with the field accelerations. This was to compensate for the smaller geometrical attenuation i n the plane strain model (2-dimensional attenuation) as compared to the actual spherical attenuation (3-dimensional attenuation) i n the field. The damping ratios needed in the numerical model to match the field accelerations were close to material damping obtained from the back analysis of the field data with an assumption of cylindrical attenuation.  •  Based on shear-volume coupling of sand (using a model given in Byrne, 1991) and shear strains obtained from the numerical modelling, a procedure was developed to estimate the anticipated change in density during vibro-replacement. The procedure predicted little change in density for the case studied here. This agreed with the small improvement in tip resistance measured at the depth of vibration monitoring. The small improvement was likely due to high initial relative density of the sand in the range of 70%. W i t h improvement i n numerical modelling, it is hoped that this procedure could be used quantitatively to predict the magnitude of densification.  74  •  The magnitude o f vibrations and shear strains decrease with radial distance from the compaction points. Therefore, the post-compaction density should also change with the radial distance from the compaction point.  From the insight gained into the process and effect o f the vibro-replacement, it is concluded that the final product o f vibro-replacement is a young soil (i.e. after destruction o f the effects o f geological ageing) with increased density and horizontal stresses. The soil density and horizontal stress decrease with radial distance from the compaction point. The variation o f densification effect within the densification grid and also inclusion o f stone columns results in the ground improved by vibro-replacement being a heterogeneous mass. The heterogeneity induced by vibro-replacement can be anticipated to affect  the  response o f the ground to i n situ testing. The likely effects o f the observed changes induced by vibro-replacement on the measured cone tip resistance and shear wave velocity w i l l be studied separately in the next two chapters.  75  Table 3-1 Distance of monitored stone columns from the ground sensor  Stone column (#) Distance 0 1 7.6 2 4.7 3 1.7 4 1.8 5 1.8 Note 1: The sequence of construction of stone columns. Note 2: The horizontal distance of stone column to the vibration sensor in the ground.  Table 3-2 Calibration of accelerometers in the ground vibration package Sensor  Orientation  -lg (volt)  +lg (volt)  Calib. factor (g/volt)  Acc. 1. Acc. 2 Acc. 3  Horizontal Horizontal Vertical  -1.005 -1.002 -0,997  + 1.004 + 1.001 + 1.003  0.996 0.999 1.000  Table 3-3 Soil parameters used in the numerical model Soil parameter  Value  Shear wave velocity, V (m/s) Compression wave velocity, V (m/s) Density, p (kg/m ) Small strain shear modulus, G (MPa) Poisson's Ratio, v Initial horizontal effective stress, a' (kPa) Initial vertical effective stress, o' (kPa) Soil-Vibroflot interface friction angle, (p (degrees) Soil-Vibroflot interface tensile strength Material damping ratio (%) Frequency of vibration, f (Hz) s  p  3  max  h  v  76  180 1500 2000 66 0.48 85 38 40 0 18-35 29  Figure 3-1  Pre-compaction C P T profile  77  Stone column #1  O  #2  o Vibration and PP sensor package Depth=8.7m  'lire 3-2  Site plan- location of the instrumentation and monitored stone columns and  ground. The production stone columns around the monitored stone columns were constructed after the test.  78  Figure 3-3  Sensor package for ground vibration measurement  79  Figure 3-4  Sensor package for vibroflot vibration measurement  80  .  ......  Figure 3 - 5  .,  '  '  : ,  -  A view of the site during vibration measurement  81  q (bars) t  Figure 3-6  C P T profile and interpreted soil profile. Relative density curves are based on Baldi (1986) and normally consolidated condition,  (both CPTs are predensification- CPT04-pre is at the location of instrumentation)  82  Soil Radial Acceleration (g)  Soil Tangential Acceleration (g)  Soil Vertical Acceleration (g)  100  200  300  400  500  600  700  800  100  200  300  400  500  600  700  800  100  200  300  400  500  600  700  800  100  200  300  400  500  600  700  800  100  200  300  400  500  600  700  800  2  •a  U  ¥  0.5  1 S -0.5 "I  Ip  Pore Pressure (kPa)  Vibroflot Radial Acceleration (g)  Vibroflot Tangential Acceleration (g)  1 &  1  Vibroflot Vertical Acceleration (g)  Depth of Vibroflot Tip (m)  3  2  *  4  »  6  1 4  Vibroflot Power Consumption (amp)  0  10 12 200 180 160 140 120 100  J i  k 100  B 100  Figure 3-7  200  300  400  V|  f  [  L  200  i  *i—» 500  r-» 600  r  700  |  •P^l*"^^^^^^^^^^  400 time (sec)  500  600  700  Recorded time histories during construction of stone column #3 83  800  1  — k 300  /  800  0.5 0.3 0.1 i< -0.1 o -0.3 -0.5 520  r  V  \ / t  520.025  520.05  2 1.5 ""bo 1 y \ ^ 0.5 / \ S 0 / « -0.5 S -1.5 -2 '520 520.025 0.5 ® 0.3 ZZ\ 0 1  -I  I  -0.!  / s\  -0.5. 520 100 96 92 V  S _ 3$ ^ S  |  J T  84  -15 -20 "25, 520 3 25 ,s 20 £ 15 / 10 / •S 5  1 *  Figure 3-8  520.05  520.075  A.  .. / /  \  1 520.1  I  i  ,C\  t  A / I \ /  : -  1  W  \  j  V 520.05  V  \ \/  /  v  520.075  \ \  A  -  \  520.1  ^ \ _z w 520.05  520.075  \  520.15  520.1  520.125  /  / 520.025  \  i\ i i 520.075  520.05  /  \  /  •  s  520.1  520.125  .  i  \v/  ; f 520.02 520.04 520.06  %  \  / —' .  i 1  >  \  /  \  \  """  /  1 \  /  i  I \ -L  520.02 520.04 520.06 520.08  \  /  520.2  -  520.12 520.14 520.16 520.18  7  i  i i  /"\ v  520.2  520.175  \  /  \  \\  /  \  520.1  /  520.175  V  ; 520.08  520.2  \  / v.  •  520.2  \  520.15  •  \  ' \  Y  v_ ' V  \ ...  520.175  520.15  / ^?  l  !  '* i *• t \  \  /  / \  A,  520.15  X\ -  /  520.2  520.175  \/  I  /  j  /  i  \.  520.125  V\ \  520.175  \  /  \\  *. A  f..  „ !^.X „  /  520.125  J  /  n'T^  520.15 f 1  .. / * \  /  \  A -i -3 -5, 520  .  .-•-""v  -5° Q -10 f; -15 ^ -20 -25 520  1  .  520.125  /\  /!  1  520.025  F  --B ^  520.1  ! / \  1  \  520 25 20 15 10  -To  H  \  520.025  SO,  520.075  \  \  >v A, A .... \ V  V  Si  /  !  \Z.  \ I  ..  v  /  y  520.2  \  V  520.1 520.12 520.14 520.16 520.18 520.2 time (sec) Recorded time histories during stone column #3, enlarged scale during densification. Note that scales are not consistent.  84  -29 Hz i i stone Col #3- FFT of densification phase O  I  o 3  Vibroflot  0.5  T3  10  20  25  30  35  40  45  50  Frequency (Hz)  i»ure 3-9  Frequency spectra of acceleration time histories of the vibroflot and the ground during densification  stone Col #3- FFT of densification phase.  0  20  40  60  80  100  120  140  160  180 200  20  40  60  80  100  120  140  160  180 200  g 0.04 H-  a 0.02 it a 0  Frequency (Hz)  Figure 3-10 Frequency spectra of acceleration time histories- enlarged scale  85  i  Figure 3-11 Energy loss due to damping in a visco-elastic material  Figure 3-12 Partial transmission and conversion at the interface (after Santamarina et al.2001)  86  2.5 A radial accel., this study • tangential, accel., this study  2.0  + radial a c e , Baez & Martin (1992)  + •  3 c  o  $  CO 1.5  ji5  CD o o co  "co  1.0  c o  +  N  0  1  2  3  4  5  6  7  8  9  Radial d i s t a n c e from vibroflot, r (m)  Figure 3-13  Attenuation of radial and tangential acceleration with distance from vibroflot  100 radius of vibroflot  D)  c o  *•—»  C O 1_ JD  0  10 Cylindrical  O O CO  - ^attenuation  Spherical  ~s  c o  attenuation  #4  N  >*... —  o -C c ra "5 </> 0  #2  — #1  0.1 0.1  1  10  R a d i a l d i s t a n c e from vibroflot, r (m)  Figure 3-14  Attenuation of the resultant horizontal acceleration. The #number  indicates the order of installation of monitored stone columns. The theoretical attenuations only include geometric spreading and not material damping.  87  100 radius of vibroflot  -5 c o CO  1_ 0)  10  CD O O  Cylindrical attenuation  co  ~s  a=0  s  a=0.1 \  c  a=0.3 a=0.6  TO co  "5  CD  0.1  A 0.1  1  10  R a d i a l d i s t a n c e from vibroflot, r (m)  Figure 3-15  Attenuation of the resultant horizontal acceleration.  The theoretical attenuation includes cylindrical spreading and material damping.  100  Radial d i s t a n c e from vibroflot, r (m)  Figure 3-16  Attenuation of the resultant horizontal acceleration.  The theoretical attenuation includes spherical spreading and material damping.  88  10r  '  ilL  r  t—^llo—i-ali-  2  3 i 5 6 73 1 ,2 RAOIUS r (m)  H r  3 4" 5  Figure 3-17 Attenuation of radial displacement in the ground around vibrators (after Morgan and Thomson 1983)  89  4.0  •Appro*. Face of Vibraoii  * Max, Accel.  3.5  a  Steady-Stale Accel.  3.0 3  \_«,„=2.7-  "  Tl  a 2,0 < i.s  0.5 .0  1  K  - |  .cxp[-0.2-(r-3)].  \  a ,,,,,„ = 1.7- -i -exp[--0.2-(r 3)]" 1  1  0  1  2  3  i  : 4  • 5  ! 6  1  !  7  8  1  Horizontal Distance from Center Line of Stone. Col unut {ft)  1  9-10  »ure 3-18 Interpretation of Green (2001) for attenuation of radial acceleration around Keller S-type vibrator based on Baez (1995) data  90  1.0T 0.84  dt  44-  0.64  0.4 0.24  0.0 L0.00001  0.0001  0.001  0.01  0.1  10  0.1  10  S h e a r Strain I'M 30 25 20 15 E Q  10  0.00001  A  0.0001  0.001  0.01 S h e a r Strain (%)  Figure 3-19 Variation of damping and modulus ratio with shear strains in sands (after Seed and Idriss 1970, graphs are taken from Shake 2000 manual)  91  0  1  2  3  4  5  6  7  8  9  10  R a d i a l d i s t a n c e from vibroflot, r (m)  Figure 3-20 Attenuation of vertical vibration around the vibroflot  92  (a) Vibroflot In the air  "20 "15 -10 -5  0  5  10  15 20  vibroflot radial acceleration (g)  93  2 1.5 1  c _o  rt  0.5  _u u o o CU  0  i  >,  'o  St. col. #3 r=1.7m  "0.5 -1 "1.5 -2  "2 "1.5 " I "0.5 0 0.5 1 soil x-acceleration (g)  1.5  0.6 e  o  St.col. #2 r =4.7 m  0.2 "0.2 -0.6 "I  -1  -0.6  "0.2 0.2 0.6 soil x-acceleration (g)  0.6 e  o  ta  _u 13 o o C3 i  >>  0.2  St.col. #1 r=7.6 m  "0.2  \  '5  -0.6  -1  Figure 3-22  "0.6  -0.2 0.2 0.6 soil x-acceleration (g)  1  Soil particle horizontal motion path (acceleration paths) for stone  columns # 1 to 3- vertical axis is tangential and horizontal axis is radial to the vibroflot  94  2 1.5  ''I  1  1 S3 o  0.5  St. col. #4 r=1.8 m  j  0 -0.5  1  -1 -1.5 -2  -2 -1.5 -1 -0.5 0 0.5 1 soil x-acceleration (g)  1.5  2  St. col. #5 r=1.8 m  -1 -0.5 0 0.5 1 soil x-acceleiation (g)  Figure 3-23 Soil particle horizontal motion (acceleration paths) at grid centroid (r=1.8m) for stone columns #4 and 5. Vertical axis is tangential and horizontal axis is radial to the vibroflot  95  40  30  Transient state  Steady state  20 10 -a 3  "a,  B <  ,3  -10 h  >  -20 h -30 h -40 h  _i  i i_  Time (sec)  Figure 3-24 Time history of ground response at 3.5 m from a vertically oscillating vibratory probe during switch on (adapted from Massarsch and Heppel 1991)  96  Transient state, f < 29Hz  322  322.2  322.4  322(5  r  j  322.8  Steady state , f = 29 Hz  323  323.2  323.4  323.6  323.8  324  323.2  323.4  323.6  323.8  324  323 323.2 time (sec)  323.4  323.6  323.8  324  -Peak respo use j. , j. |J J  i l l fit m  322  322.2  322.4  322.6  322.8  322  322.2  322.4  322.6  322.8  323  Figure 3-25 Response of the vibroflot and ground during switch-on at 10m depth- stone column #3, enlarged from Figure 3-7  97  t=322.68 sec  > o  20  21  22  23  24  25  26  27  28  Frequency of vibration (Hz)  Figure 3-26 Ratio of the responses of ground and vibroflot as a function of frequency during switch-on  98  Hole flushing  Re-penetration Densification at 10 m  3 -J  a £  400  420  440  460  480  500  520  540  560  580  600  560  580  600  580  600  a. 140 E 128 116 -1  •9  S u  I  'J  104  v  Ii  -  92 80 400  420  0  s  2  ft  4  > o  6  ft u -a  10  !  440  \  m  A  460  480  500  520  540  /\  •  420  440  460  480  500  520  J  A  1\ j  8  12 "400  I  k  .^rf  540  560  time (sec)  Figure 3-27 Comparison of the vibroflot motion and power consumption during densification phase  99  Switch-on First penetration  Second penetration Third penetration PP response at 8.7m depth during densification from 10 to 8m  0  100  200  300  430  500  600  700  800  900  1000  100  200  300  400  500 time (sec)  600  700  300  900  1000  Figure 3-28 Pore pressure time history during stone column #3  100  1000 -Radius of vibroflot  CD  100  Total=Pressure induced by Cyclic+Watt  Water jets= Pressure induced by water j 3  (/) a) £ Q.  1"  10  CD  o  Q. E  A total X water Jets • cyclic  3 X CD  (a) 0.1 0.1  10 Radial distance from vibroflot, r(m)  1000  CD 0 _ j*:  100  a> CO CO  a. cu o  Q. E E 'x CD  10  0.1 Radial distance from vibroflot, r(m)  Figure 3-29 Pore pressure response during penetration of vibroflot (a) Observed pore pressure induced by water jets and cyclic vibration during installation o f stone columns #1 to 5. Total is the sum o f pressures caused by water jets, cyclic loading and penetration o f vibroflot (cavity expansion) (b) Calculated pore pressure induced by cavity expansion during installation o f stone columns #2 and 3 (Cavity expansion PP= Total-water jets-cyclic)  101  C otrifugal Motion  V ibl itot C omponent  41mm  (lj6in)  Lengh = 790 mm (31.1 in) Diameur= 41 mm (1.6 xi) Wei^fl. = 6.31«gf(13Pljf)  Certrifcgal Force = 32kgf (70.5 bf) Fr*qi«ncy=200Hs  Figure 3-30 Schematic of the Original Vibratory Piezocone designed by Sasaki and Koga (1982) (taken from McGillivray et al. 2000)  <5  I 0  •  i 40  i SO  I 130  •' i 100  I  ,  0  i 40  I 80  i  I 120  .  I 160  Cone Tip Resistance (kg/cm ) 2  Sitel  Site 2  Figure 3-31 Vibrocone tests (a) at site 1 which shows no apparent damage during seismic events and (b) at site 2 with historical liquefaction evidence following seismic events ( from Sasaki et al. 1984).  102  (»)  ure 3-32 (a) Schematic illustration of soil-vibroflot interaction in horizontal section through the vibroflot, (b) Symmetric condition of the motion of the vibroflot  103  Figure 3-33 Mechanical model o f the vibrator in the ground (after Fellin 2000)  Figure 3-34 Geometry of the numerical model of soil-vibroflot interaction  104  Figure 3-35 Interface elements between soil and vibroflot (enlarged from figure 3-34)  105  20  -20 -15 -10 -5 0 5 10 15 20 vibioflotradialacceleration (g)  Figure 3-36 Motion of the vibroflot during densification (stone column #3, depth of the vibroflot=9m, t=562-564 sec.)  106  Figure 3-38 Magnified deformed shape of the model (vertical and horizontal axes are in metres)  107  100 c g  - - Equiv. Linear. Damp=18%  " i_co  _co cu o o  Equiv. Linear. Damp=35%  10  O  CO  field measurement  c o  N  c CO  O"  X CO  •o  0.1 2  3  4  5  6  7  Radial distance from vibroflot (m)  Figure 3-39 Comparison of resultant horizontal accelerations from field measurement and equivalent elastic analyses  108  Field measurement  Soil acceleration (g)  r = 0.5 m  r = 1.0 m  r = 1.7 m  Soil acceleration (g)  r = 4.6 m  Soil acceleration (g)  r = 7.6 m  Vibroflot Numerical model  Figure 3-40  Motion paths of vibroflot and soil particles at different radial distances, (left) Field observation, (right) Numerical model. Note figures have different scales.  Stone column  Figure 3-41 Minimum required measurement points in the ground for calculation of the 3 components of shear strains  110  0.2 0.18 • 0.16 AEquiv. Linear. Damp=18% 0.14 • Equiv. Linear. Damp=35%  c 'ns 0.12  "35 »  </)  0.1  cu "§ 0.08  I  006  c 0.04 CO 0.02  A  3 4 5 Radial distance from vibroflot (m)  ;ure 3-42 Distribution of shear strains in horizontal plane from equivalent linear analyses  111  2  -  1.8  = C,.exp  1.6  -  -c . 2  1.4  c CO  o  £  1.2  -  y=0.3  •1  - - y=0.2  0.8  - -y=0.1  0.6 0.4 0.2 0 10  20  30  40  50  Number of cycles  Figure 3-43 Shear-volume coupling model for sands proposed by Byrne (1991)  70 -, 69 -  s  68 Q 67 66 to 65 c CD Q 64 a> 63 > 62 -  Y=0.125%  •jf r=0.5m r=1 m  7=0.09%  r=1.7m  s  7=0.075% -/*  V  or 61 60 0.1  T  ^  ' M M  1  10  100  1000  10000  number of cycles  Figure 3-44 Change in relative density due to cyclic shearing based on Byrne (1991) model  112  q (bars) t  0  50  100  150  200  Figure 3-45 Cone tip resistance before and after vibro-replacement  113  r = 1.0 m  r = 1.7 m  y  Yave= 0.07%  ave  = 0.09%  D =60% ro  10  15  N u m b e r of c y c l e s , N  20  25  30.  c y c  Figure 3-46 Pore pressure generation at different radial distance, r, around the vibroflot, based on the calculated shear strains and Byrne (1991) model for undrained conditions.  114  115  116  (1.0  + 0 5  )  -0.400 -0.600 -0.800  0> 3  Pi  -1.000 -1-200 -1.400 -1.600 -1.800  0  i  r~  2  4  i—  6  i 8  1  1  1—  10  12  14  Radial displacement (m)  (ID"  0 3  )  »ure 3-49 Radial stress vs. radial displacement at radial distance of r=1.7m from the vibroflot. Negative sign indicates compression stress.  117  Figure 3-50 Expanded cavity by the vibroflot. Note the formation of a gap between the vibroflot and soil  118  Figure 3-51  Stress path of a soil element at radial distance of r=1.7m from the vibrator obtained from numerical model.  119  C H A P T E R 4 E F F E C T O N C O N E TIP R E S I S T A N C E O F H E T E R O G E N E I T Y CAUSED BY VIBRO-REPLACEMENT  4.1  INTRODUCTION Vibration measurement and numerical modelling presented in Chapter 3 showed that the  amplitude o f vibration and thus the induced shear strains attenuate with horizontal distance from the vibrator. Consequently, the densification effects also vary with radial distance from the compaction points. Figure 4-1 shows a triangular grid pattern o f vibro-replacement. Each point within this grid is affected by compaction carried out at the location o f 3 stone columns. This makes the distribution o f soil properties within a grid area complicated. The presence o f stone columns, which are stiffer than the densified soil, creates a composite mass and makes the situation more complicated. Q C / Q A o f the improved ground in practice is usually based on penetration testing at the centroid o f the compaction grids. The centroids o f the grids have the largest distance from the compaction points and thus are expected to be the weakest points. Interpretation o f q for engineering properties o f soil is mainly based on correlations c  obtained from calibration chamber testing on ideally homogeneous samples. Therefore, the conventional interpretation procedures are not strictly applicable to the heterogeneous condition after vibro-replacement The objective o f this chapter is to explore the effect o f this induced heterogeneity on the interpretation of the C P T results. First, field evidence w i l l be presented to show that the ground after vibro-replacement is in fact heterogeneous.  Numerical modelling w i l l be used to  understand the mechanism o f the effect o f heterogeneity on the interpretation o f cone tip resistance.  4.2  FIELD EVIDENCE Probably the only published case o f measurement o f variation o f soil density around a  vibrator is the one reported by D ' A p p o l o n i a (1953). He measured the density o f a sandy  120  deposit (sand bottle test) at different horizontal distances around a single compaction point and within rectangular grids with different spacings. The variation o f density versus horizontal distance from a 23-kW vibroflot is shown in Figure 4-2. The data suggest an exponential variation o f density with distance. H e found similar variation o f density around a single compaction point and also within the grid area. Baez (1995) carried out C P T tests at different horizontal distance from an " S " type Keller vibrator and observed a decrease i n q with distance from the compaction point. More t  recently, Degen and Hussein (2001) reported the variation o f q with distance within a t  triangular grid for two different vibroflots as shown in Figure 4-3. It may be observed that q at t  the centroid is the lowest. Studies on cone penetration testing in calibration chambers indicate a significant boundary effect on the tip resistance. Salgado et al. (1997) suggested that for heavily dilative silica sand, the diameter ratio  (D h mber/D e) c  a  con  o f 25-120 could cause a chamber to  field  penetration resistance ratio in the range o f 0.5 to 0.9, respectively. This is for a constant lateral stress boundary type calibration chamber. In a calibration chamber with a rigid boundary, the boundary effect results in a higher tip resistance than that in the field. The zone o f influence is higher i n denser and more dilative sand. Assuming a diameter o f 35.7mm for the cone tip and an influence diameter ratio o f 100, the zone o f influence could be as big as 3.6 m, which is greater than the distance from grid centroid to stone columns. Therefore, q at the centroid is expected to be affected by the t  surrounding denser soil and stiffer stone columns. In order to investigate such effects, a numerical modelling approach was taken here. T w o dimensional numerical analysis o f a plane strain condition is used to check the effect o f heterogeneity on the cone results. Some simplifications are required to reduce the problem from an actual 3-dimensional condition to a 2-dimensional condition. These simplifications/assumptions are as follows: •  q and the limit pressure calculated from cylindrical cavity expansion theory are c  related. This assumption w i l l be evaluated in the next section. •  The effect o f heterogeneity on the cylindrical cavity limit pressure and cone tip resistance is similar.  121  Based on the above simplifications, it is assumed that cone penetration can be qualitatively modelled by cylindrical cavity expansion. This can be done by a 2-dimensional plane strain analysis. It should be noted that with the above assumptions, only a qualitative assessment is possible.  4.3  R E L A T I O N B E T W E E N C O N E TIP R E S I S T A N C E A N D C A V I T Y E X P A N S I O N THEORY Bishop et al. (1945) first noted the analogy between cavity expansion and cone  penetration. Since then many investigators have tried to simplify the mechanism o f cone penetration (Figure 4-4) and use cavity expansion theory to predict cone tip resistance. It should be noted that cone penetration is neither spherical nor cylindrical cavity expansion. However, they are functions o f the same parameters and thus could be correlated through empirical factors. Y u (2000) noted that the success o f cavity expansion theory to capture the characteristics o f cone tip resistance is because it can account for the soil stiffness, dilatancy and penetration-induced stress increase. Ghionna et al. (1990) found a good relation between state parameter, cavity limit pressure from pressuremeter testing in calibration chamber, P ' , and cone tip resistance i n u  calibration chamber, q . Figure 4-5 shows that P ' c  u  and q  c  are related through the state  parameter, which is the difference between the soil void ratio at the current state and that at critical state at the same stress level. This confirms that q and P ' , which is close to the c  u  cylindrical limit pressure, have a good correlation.  4.4  N U M E R I C A L M O D E L L I N G O F C A V I T Y EXPANSION T H E O R Y The finite difference program F L A C (Itasca 1998) is used to model the cylindrical cavity  expansion i n a heterogeneous soil condition in the presence o f stone columns. The plane strain condition (horizontal plane) is assumed here. This is equivalent to the cylindrical cavity expansion. A circular block o f ground with a radius o f 9.6 m , represented by about 4200 quadrant elements is used to model the cavity expansion (Figure 4-6). A previous model o f 3.2 m radius 122  was found to have a significant boundary effect for cases with high dilation angle and stiffness. The model has an initial circular cavity o f 0.01 m radius at the centre of the model (Figure 4-7). A smaller hole would be more desirable but would cause meshing problems. Firstly, the model is allowed to reach equilibrium under the assumed in situ stress condition, a'h=38.3 k P a and rj' =85 kPa. A constant stress boundary is used for both outer and inner boundaries. The cavity v  is then expanded in a strain controlled mode by applying a constant velocity o f 10" m/step to 7  the cavity wall. The cavity is expanded to strains o f A r / r o f about 180%, where A r is the 0  displacement o f the cavity wall and r is the initial radius o f the cavity. The final size o f the 0  hole after the expansion w i l l be about 0.036 m , close to the size o f a standard 10 c m cone tip. 2  A l s o , this amount o f strain is enough to get very close to the cavity limit pressure. 4.4.1  Soil model and selection of parameters The Mohr-Coulomb elasto-plastic model is used in this study. This model assumes a  linear elastic-perfectly plastic behaviour. The main parameters in this model are friction angle,((), dilation angle,  shear modulus, G and Poisson's ratio, v.  Relative density, D is selected as the main variable and all the other soil model r  parameters are obtained from the correlations to D . In all the cases, v is assumed 0.2. Friction r  angle and dilation angle are obtained from relationships recommended by Bolton (1986) as functions o f D and mean normal stress as follows: r  4> = ^cv + ° - • Vmax  Equation 4-1  8  P  0.8-(//  max  0.8 • y/  max  =3.1  R  = 5.1  R  (triaxial condition)  Equation 4-2  (plane strain condition)  Equation 4-3  where IR is defined as follows: I  R  =D  r  -(10-Lncr  m  )-\  Equation4-4  B  where ^ is the peak friction angle, \ | / x is the maximum dilation angle, <j) is the friction angle ma  cv  at critical state or constant-volume, and a' _B is the mean normal stress at failure (kPa). m  123  The small strain shear modulus can be obtained from the following equation proposed by Seed and Idriss (1970): x  Gmax  = 2 1 . 7 A " 2, max  K  = 0.6D +15  2. max  <7  0.5 Equation 4-5  Equation 4-6  r  where P A is the atmospheric pressure and a'  ltl  is the mean normal stress and D is the relative r  density in (%). The Mohr-Coulomb model is linear elastic-perfectly plastic. Selecting a value of G which can represent the overall response of the soil is not straightforward. The available closed-form solutions for cavity expansion with an elastic-perfectly plastic soil model, such as those by Carter et al. (1986) or Vesic (1972), offer no recommendation for the selection of G. Salgado et al (1997) proposed a G value between 0.67-0.7G . The range increased with max  confining stress but did not change much with relative density. Wilson (2003) used the Carter et al. (1986) closed-form solution and was able to match the self-boring pressuremeter test results in sand by using a G value in the range of 0.65 to 0.75 of the unload-reload shear modulus, G U R . Byrne et al. (1987) noted that to fit the lab data using an elasto-plastic model, an average G of about G x/10 would be appropriate. ma  It may be observed that there is a large discrepancy between the different suggestions for G/G  m a x  . A parametric analysis is performed here to estimate the equivalent G / G x in the ma  elastic-plastic model. Data reported by Ghionna et al. (1990) including the D and stress r  condition of the soil in the chamber, and the cylindrical limit pressure are used as the input data for this parametric analysis. Based on the soil conditions in the C C , the soil parameters required for the Carter et al. (1986) solution for cylindrical cavity expansion including (j), and G  m a x  are calculated. The ratio of G / G  m a x  is then varied until the calculated limit pressure  from the Carter et al. (1986) solution matches the limit pressure reported by Ghionna et al. (1990). Figure 4-8 shows the required G / G suggests that the applicable G / G variation of G / G  m a x  m a x  m a x  vs a function of D and stress level. This figure r  ratio is not constant and changes with soil conditions. The  for the available data is from 0.06 to 0.14. It may be inferred that an  average value of 0.1 can be used in conjunction with an elastic-plastic model to match the 124  observed limit pressures. This agrees with Byrne et al. (1987) but is very different from the Salgado et al. (1997) recommendation.  This is inconclusive. Therefore, the numerical  modelling w i l l be carried out for two values o f 0.1 and 0.5 and the sensitivity o f the results to this assumption w i l l be assessed. It w i l l be shown that the conclusions from these analyses w i l l not be sensitive to the selected value o f G / G 4.4.2  m a x  .  Verification of the numerical analysis Before modelling the cavity expansion in a heterogeneous condition, a series o f analyses  was performed with homogeneous conditions to verify the model against the Carter et al. (1986) closed-form solution. A s may be observed in Figure 4-9, the results from the numerical model and closed-form solution are in reasonable agreement. Numerical modelling exhibits a slightly softer initial response but eventually matches the closed form solution. However, they closely agree on the limit pressure, which is the main objective o f these analyses. One possible explanation for the softer response could be the different failure criteria used i n the closed-form solution and F L A C . In the closed-form solution, the vertical stress is ignored and failure occurs i n the horizontal plane. In other words, a i and 03 are always horizontal. O n the other hand, in the numerical model the vertical stress is also considered i n the Mohr-Coulomb criterion and could contribute to failure. Therefore, it is likely that some elements in the model reach failure in the vertical plane. The failure o f these elements in the numerical model results in an overall softer initial response. The numerical model result is spiky, which is due to the way F L A C handles plastic deformations. A slower rate o f cavity expansion would decrease the amplitude o f these spikes. To evaluate the boundary effect on the results, F L A C analyses were performed with two different boundary conditions: a fixed boundary; and constant stress boundary,. The results were identical which indicates that the model is large enough to simulate the free  field  condition. 4.4.3  Effect of soil stress dependency on limit pressure Figure 4-10 shows the effect o f the stress dependency on cavity expansion. During the  F L A C analysis, the soil properties including the dilation angle and shear modulus are updated every 1000 steps based on the current stress condition. This causes the spiky response o f the model. A more frequent update would result in a smoother curve. In the elastic zone, the 125  effective mean normal stress, (o +ae)/2 remains constant and so do the soil properties. In the r  plastic zone, the mean normal stress increases with the expansion o f the cavity. This decreases the dilation angle and consequently the cavity limit pressure. 4.4.4  Effect of presence of stone columns on limit pressure Three 1 -m-diameter stone columns, arranged in a triangular pattern at 3 m centres are  added to the model (Figure 4-11). The stiffness o f stone columns is assumed to be 5 times greater than the soil. This is based on shear wave velocities measured by others (see Section 5.4.2). Figure 4-12 shows that the effect o f the inclusion o f the stone columns on limit pressure is small (less than 3%). It seems that the stone columns move as a rigid body with the rest o f the expanding medium. In reality, the cavity generated by the cone is not infinitely long. The stone columns resist the movement in shear as shown by the arrows i n Figure 4-13. This provides some restriction to the movement o f stone column which cannot be modelled in the plane strain condition. Assuming stone columns fixed against lateral displacement provides an upper bound result. A s shown in Figure 4-14, even the effect o f fixed stone columns on the cavity limit pressure is still small (less than 5%). Note that the responses are identical at small strains. A s the cavity expands, the influence zone grows and reaches the stone columns. It is concluded that the effect o f the stone columns on the limit pressure and hence on q is negligible. t  4.4.5  Effect on limit pressure of variation of soil parameters in the grid zone between the stone columns Very little field measurement can be found in the literature as to how the soil properties  vary within the zone between the stone columns. D ' A p p o l o n i a (1953) is probably the only researcher who actually measured post-densification soil density at different distances from a compaction point (Figure 4-2). Note that the vibrator used at that time, a 23 k W vibroflot, was much weaker than the current models. For example, compare it with the 130 k W power o f the V F A G - V 2 3 used in the vibration measurement presented in Chapter 3. It is acknowledged by the author that the ground vibration and so the distribution o f density around the vibrator depends on the vibrator and the soil condition. However due to the lack o f actual measurements and the fact that this study is a parametric study, the variation o f D in Figure 4-2 r  is used here. Variation o f any other parameter such as locked-in lateral stress is ignored. The 126  soil around the centroid is divided into radial zones with different D (Table 4-1) and their soil r  properties are calculated accordingly. Table 4-2 shows the P L values obtained from numerical analyses for homogeneous (D =58%) and variable soil condition with stone columns. It may be observed that the addition r  of the soil variability and stone columns to the model increases the limit pressure, Pi_. The magnitude o f the increase depends on the choice o f G/Gmax- P L increases by 11 % and 21 % for cases with G / G x o f 1/10 and 1/2 respectively. The effect o f stress dependency on the increase m a  of limit pressure is negligible. The influence o f the far field (beyond the stone columns, distance more than 1.7m in this model) on limit pressure was studied by varying the D from 58% to 90%. This had very little r  effect on the limit pressure.  127  4.5  DISCUSSION O F T H E R E S U L T S O F N U M E R I C A L A N A L Y S E S Figure 4-15 shows the variation o f P L versus D for homogeneous soil condition obtained r  from the Carter et al. (1986) closed-form solution for the case G / G  max  = 0 . 5 . The observed slope  change in the trend is because the dilation angle was limited to a maximum o f 15 degrees. After a certain density, where the dilation angle reaches 15 degrees, additional increase i n density only increases the soil stiffness and not the soil strength (cp). The homogeneous soil condition at D =58% is associated with P L =1300 kPa. From the r  numerical modelling, it was observed that the variation o f D according to Table 4-1 (from r  58% at the centroid to 100% close to the stone columns) increased the P to 1580 k P a (Table L  4-2). If the homogenous curve o f Figure 4-15 is used to interpret this P L a D =66% is obtained. r  This interpretation ignores the heterogeneity o f the ground. This is similar to interpretation o f the post-compaction q , which uses the correlations developed for a homogeneous soil t  condition. The interpretation o f P L for relative density in this case (D =66%) is greater than the r  D at the centroid ( D =58%) and is considerably smaller than the average D =85%. The r  r  r  average D for the case analyzed here is obtained from the following equation: r  D  r  =  Y^A.  Equation 4-7  where Dg and Aj are relative density and area for each zone j as assumed in Table 4-1. It may be concluded that: •  Ignoring the heterogeneity in the case analyzed here overestimates the density at the centroid and significantly underestimates the average density o f the soil mass between the stone columns.  •  The interpreted D is closer to the D at the centroid and indicates the greater r  r  influence o f the near field soil on q . t  The above conclusions are based on a plane strain model and a G / G sensitivity o f the above conclusion on these assumptions is evaluated below:  128  m a x  o f 0.5. The  4.5.1  Effect of G / G  m a x  In order to assess the sensitivity o f the conclusions from the numerical analysis to the selected value o f G / G  m a x  , analyses with two different values o f G / G x o f 0 . 5 and 0.1 are m a  compared. Figure 4 - 1 6 shows the variation o f the P L versus D for a homogeneous soil condition for R  two values o f G / G  m a x  o f 0.5 and 0 . 1 . The figure shows that i f the heterogeneity is ignored, the  interpreted value o f D is 6 6 % for both assumptions o f G / G R  m a x  o f 0.1 and 0 . 5 . In other words,  the interpreted D from the limit pressure obtained in a heterogeneous condition is not sensitive R  to the assumed ratio o f G / G 4.5.2  m a x  .  Assumption of Plane strain condition Cone penetration is neither spherical nor cylindrical cavity expansion. However, it  seems to be closer to spherical cavity expansion. O n the other hand, the plane strain assumption used i n the numerical analysis here models the cylindrical cavity expansion. It should be noted that the cylindrical cavity expansion has a greater influence zone than spherical cavity expansion. The variation o f both tangential and radial stresses in the elastic region around the cavity depends on  (ro/r) , where r m+l  0  is the radius o f the cavity, r is the radial  distance from the centre o f the cavity to the point o f interest, and m = l for cylindrical and m = 2 for spherical cavity expansion ( Y u and Houlsby 1 9 9 1 ) . In the plastic region, the stress field is a function f r " [  0  m(ct  "  l)]/a  where a=(l+sin<|>)/(l-sin<|>) and m is already defined. It may be observed  that the stresses around the expanding cavity attenuate more slowly for the cylindrical cavity. This causes a greater influence zone for the cylindrical cavity which in turn results i n a greater influence from the far field. It may be concluded that the plane strain analysis gives an upper bound result for the influence o f the far field. In other words, the q at the centroid is expected t  to be less affected by denser far field soil and tends to be more affected by the soil properties at the centroid.  129  4.6  IMPLICATIONS F O R INTERPRETATION O F POST-DENSIFICATION CPT TESTING It has been shown that the cylindrical cavity limit pressure, P L is more affected by the  properties o f the soil close to the centroid and not the overall properties o f the composite mass. The influence zone o f the cone tip should be even smaller than that for a cylindrical cavity. Therefore, q should be even less affected by the far field than is suggested by this numerical t  modelling. It may be concluded that q slightly overestimates the density o f the soil in the t  weakest zone at the centroid but significantly underestimates the overall stiffness and strength o f the composite mass including the variable soil and the stone columns. For example, in the particular case shown i n Figure 4-3, treatment by V 2 3 failed to meet the specification o f q =15 M P a , whereas the V 3 2 could achieve the criterion. However, the t  average q in both cases is greater than the specification. In Figure 4-17, the zones with q t  t  greater and smaller than the specification are shown schematically. It may be seen that only a small area relative to the grid area fails the specification. From Figure 4-3, it may be observed that the V 3 2 vibroflot with higher dynamic force (see Table 2-2) resulted in less variable q than the V 2 3 vibrator. A stronger vibrator has a t  greater reach and the overlapping effects from the other compaction points should result i n a more uniform condition. A t the same spacing, a weaker vibrator cannot have as great an effect at the centroid and produces a more heterogeneous condition. The reason why the maximum q  t  for the V 2 3 is greater than that for the V 3 2 is not clear. This could be due to the site variability or due to over-excitation by too strong a vibrator. Greenwood (1991) suggested that over-excitation reduces the compaction efficiency. He defined over-excitation as the vibration at which the grains experience accelerations greater than 3g. It is understood that accelerations referred to by Greenwood (1991) are measured at the surface and may not directly relate to the acceleration measured at depth. For Q C / Q A purposes, the engineer should know what the main criterion is. For example, i f the settlement o f the building on a mat foundation is the main concern, then treatment by the V23 is still conservative despite the failed test result at the centroid as the settlement is a function o f the overall stiffness rather than the stiffness o f the weakest point.. For liquefaction mitigation purposes, the presence o f the denser soil and stiffer stone columns around the weaker centroid should increase the overall stiffness o f the ground, resulting in a smaller shear 130  strains and better overall performance. However, it is difficult to quantify the effect. This is because the performance o f such heterogeneous  ground with vertical layering during  earthquake shaking is not known. Further research is required to evaluate what governs the ground behaviour during shaking. Is it the loosest zone at the centroid or is it some average condition over the grid zone?  4.7  EFFECT  OF T H E HETEROGENEITY  ON  GROUND  PERFORMANCE  DURING E A R T H Q U A K E SHAKING Baez and Martin (1992) proposed that reinforcement by the stiffer stone columns reduces the shear stresses in the soil matrix. This reduces the demand and hence the liquefaction susceptibility. They distributed the shear stress between the soil and the stone columns proportional to their shear stiffness (the product o f the area b y the shear modulus). They proposed the following expression for the reduced shear stress in the soil:  Equation 4-8  where x is the shear stress o f the soil, x is the total shear stress, A s  stone column , A is the plan area o f the soil, A s  s c  t r  is the tributary area o f one  is the plan area o f stone column and G is the r  ratio o f shear modulus o f the stone column to that o f the soil. For a triangular grid pattern, A =0.87S where S is the spacing o f the stone columns. The reduction factor for shear stress or tr  C S R is:  S  Equation 4-9  i  r ~\ +  (G -l).A r  r  For example for a triangular pattern, 3m spacing and 0.75 m diameter stone columns, A =0.064 r  and G =5, a ratio xJx =80% is obtained. This suggests that stone columns reduce the C S R r  demand on sand by 20%. Goughnour and Pestana (1998) argued that stone columns were slender elements and work as flexural elements. This reduces their shear stiffness and their ability to reduce the shear stress in the soil suggested by Baez and Martin (1992). They also proposed an expression  131  for the stress reduction i n the soil similar to Baez and Martin (1992). In their expression, they considered the concentration o f the overburden pressure in the stone columns. Girsang et al. (2004) used dynamic numerical analysis and showed that indeed the stiffer columns reduced the shear stresses within the soil matrix. They also found good agreement with reduction factors suggested by Baez and Martin (1992). In all these, the effect o f reinforcement by stone columns was the core o f the discussion and the effect o f the heterogeneity within the grid zone has been entirely neglected. The effect o f the soil heterogeneity could be as significant, given the large area o f the zones denser than at the centroid. For example in Figure 4-17, it is assumed that the average q o f the hatched t  triangle is 20 M P a and the average at the centroid is 12 M P a . Using their respective areas, the total average o f the soil within the grid zone is about 19 M P a . A s shown in Figure 4-18, the C R R at the centroid is about 0.22 whereas the total average indicates a non-liquefiable condition with a C R R higher than 0.5. Consideration o f heterogeneity results in a cyclic resistance that differs by more than 200% than that calculated using the measured q at the t  centroid. Due to the empirical nature o f the ground improvement design for liquefaction mitigation, it may be premature to suggest any changes i n the state o f the practice for Q C / Q A . The good performance o f improved ground observed in earthquakes could be to some extent due to the conservatism involved in the procedure. A s shown above, one o f the sources o f conservatism is the ignorance o f the heterogeneity. More research into this subject could result in a more relaxed specification for quality control o f vibro-compaction. This potentially has some cost benefits.  4.8  S U M M A R Y AND CONCLUSIONS Based on vibration measurement, numerical modelling and field evidence, it was  concluded that densification effects decrease with radial distance from the compaction points. This variation and inclusion o f stiffer stone columns creates a heterogeneous ground condition. Conventionally, C P T s conducted for Q C / Q A o f densification contracts are carried out at the centroids o f the compaction grids, which are the weakest zones. Conventionally, interpretation  132  o f C P T is based on an assumption o f uniform soil conditions throughout the zone treated and ignores the horizontal heterogeneity o f the post-compaction ground. Cone tip resistance was shown to be related to cylindrical cavity expansion. This was used as a framework to study the effect o f heterogeneity caused by vibro-replacement using a 2-D plane strain numerical model. The main conclusions from this chapter are as follows: •  The numerical model showed that the presence o f stone columns with the assumed spacing o f 3m has minimal effect on the cylindrical limit pressure. Consequently, the numerical model showed that the cylindrical limit pressure at the centroid is mainly influenced by the soil at the centroid and to a lesser extent by the denser far field soil.  •  Ignoring the heterogeneous ground conditions caused by vibro-replacement results in some over-estimation o f the soil properties at the centroid and considerable under-estimation o f the average soil properties o f the composite soil-stone column mass.  •  The overall stiffness and strength o f the ground is greater than that interpreted from C P T at the centroid.  133  Table 4-1  Assumed density zonation within compaction grid zones Zone 1 2 3 4 5 6  Table 4-2  (%)  Radius around centroid (m)  58 63 72 87 100 58 or 90  0.01-0.1 0.1-0.35 0.35-0.7 0.7-0.9 0.9-2.4 2.4-9.6  D  r  Cases of numerical modelling of plane strain analysis of cavity expansion at the centroid of stone column grid  Input Filename  soil  stone column  Gl G  m a x  stress dependency  P (kPa) L  Increase in PL  (%)  CPT50 CPT54  uniform variable  N Y  1/10 1/10  No No  640 710  CPT60 CPT64  uniform variable  N Y  1/2 1/2  No No  1300 1580  21  CPT100 CPT121  uniform variable  N Y  1/10 1/10  Yes Yes  590 670  13  CPT 130 CPT131  uniform variable  N Y  1/2 1/2  Yes Yes  1100 1380  26  134  11  Stone column  Figure 4-1  Schematic contours of vibration amplitude within a grid zone  135  Compaction  Distance from compaction point 1 along A-A (ni)  Figure 4-3  Variation of q with distance from the compaction points for two different c  vibrators Vibroflot V23 and V32 ( after Degen and Hussin 2001)  136  (a). Ladanyi & Johniloa (1974)  0>).Vtsic(1977)  (c). SatRado (1993)  Figure 4-4  (d). Yasufulm & Hyde (1995)"  Idealization of analysis for cone penetration (after Y u and Mitchell 1998)  137  (  1  • "  •  "*  A  o c l  ^ A N C  A  •  > SPECIMEN J  \  A  § A  s  -  -  i  A A  C C  ' 46  -0.30  TESTS  < OR < 9 2 % ; I  -0.25  SAND  60  < <?M<  i  !  !  -0.20  -0.15  -0.10  STATE  Figure 4-5  IN T I C I N O  P A R A M E T E R  311i  kPa  f -0.05  0  *  Ratio of cone tip resistance to cavity limit pressure from pressuremeter vs. state parameter (after Ghionna et al. 1990)  Figure 4-6  Geometry of plane strain numerical model  138  JOB TfTLE : Cylind cavity exp.Mohr+dalitn i-Homog-constant stress bound-CFT20  /  FLAC (Version 3.40)  /X  16-Sep-3 23:55 step 26 -48 .15E-02 <x< 38 .18E-02 -41 .35E-02 <y< 44 .99E-02 Giici  /  plot  r„= Q.Qljpjr...  Civil Eng. Department UBC  ure 4-7  -0.400  -O300  -O 200  -0.100  0 000  0,100  0 2O0  0.300  (x 0.10 m)  Geometry of numerical model, enlarged from Figure 4-6  139  0.16 0.14 0.12 0.10 X CO  —  CD 0.08 0.06 0.04 0.02 0.00  4  6  8  10  relative density, D / ( a ) ° r  Figure 4-8  Back calculated G / G  m a x  m  12  5  from the pressuremeter tests in calibration  chamber  1600  G-G /2  1400  inax  G=G /10 max  (h40.5°, v=9.3°, v=0.2, G =79MPa llliU  0.2  0.4  0.6  0.8  1  1.2  1.4  1.6  1.8  Displacement for unit initial cavity radius (Ar/r ) Q  Figure 4-9  Comparison of F L A C analyses with Carter et al. (1986) closed form solution  140  1400  G=Gmax/2  0 0  0.5  1  1.5  2  Displacement for unit initial cavity radius (Ar/ro)  Figure 4-10 Effect of stress dependency of the soil model on limit pressure from F L A C analysis compared with non-stress-dependent soil model  (x10m)  Figure 4-11 Geometry of numerical model with the addition of three stone columns  141  1600 G=Gmax/2  1400  With 3 stone columns  1200 H  ,j,. •  " Without stone columns  1000 3  in in <o 800 u.  G=Gmax/10  a. •> 600 re o  With and without stone columns are  400  identical 200 0 0.2  0.4  0.6  0.8  1  1.2  1.4  1.6  1.8  Displacement for unit initial cavity radius (Ar/ro)  Figure 4-12  Effect of inclusion of stone columns on cylindrical cavity limit pressure  Ground surface  Stone column  Figure 4-13 Schematic illustration of lateral fixity of the stone columns in 3-d space 142  2500  Relative density, D (%) r  Figure 4-15  Variation of cylindrical cavity limit pressure as a function of D for r  homogeneous soil condition ( G / G x 0 . 5 ) =  ma  143  2500 G=Gmax/2  CL  -  2000  I  G/G »=0.5^------^  •  m  - G=Gmax/10  CU  (m/)  a> Q.  1500  E £  G/G =0.1 maj  1000  co o CO  o  500  O 20  30  40  50  60  70  Relative density, D  r  80  90  100  (%)  Figure 4-16 Variation of cylindrical cavity limit pressure as a function of D for r  homogeneous soil condition for G/Gmax 0.1 and 0.5. Note the assumption of G / G =  not affect the interpreted D . r  144  m a  x does  Compaction J ^ ^ " ! Points 3.70»i Passed zone (V23) q,~ 20 > 15 M P a  Failed zone (V23) q=12 < 15 M P a t  15 MPa (specification)  0 3.2 Distance from compaction point i along A*A (m) t  Figure 4-17  Consideration of heterogeneity of soil within compaction grid on Q C after vibro-replacement  145  06 CRR »  0.5  M=7.5  0.25 * Dsotmm) < 2.0 FC(%)<5  0.5 +  w2 o TO to o c  p P T Clean Sand Base Curve  0.4 +  I No Liquefaction  0.3 +  CO  (ft •*£ «) S2 0.2 + 0) (fi is O J (73 CC O  O  O  O  0.1 + Raid Perfcrmlfice Uq. No Uq. Stark &Qt9t»f!1S955 • O Suzuki e t aljJ9S5&) A A  NCEER (1998) Workshop  50  100|  150  =1=  ,200  250  300  Corrected C P t Tip Resistance, q i N c  I  I  q» at centroid  A v e r a g e q, over compaction g r i d  Figure 4-18  A n example of interpretation of C R R with and without consideration of  heterogeneity of ground conditions within the compaction grid. Using and average q results in a greater interpreted C R R  146  t  CHAPTER 5 EFFECT OF HETEROGENEITY CAUSED BY V I B R O - R E P L A C E M E N T O N SEISMIC C O N E T E S T I N G R E S U L T S  5.1  INTRODUCTION Direct measurement o f the ground stiffness is possible by measurement o f the seismic  shear wave, compression wave or surface wave velocity. Performance o f seismic tests during the C P T has little impact on the cost and/or the time o f testing. This makes the seismic cone test, S C P T , a feasible test for commercial applications in the quality control o f ground improvement. Conventional interpretation methods to obtain shear wave velocity o f soil from S C P T results are based on an assumption o f homogeneous soil or o f horizontal layering. This assumption simplifies the mathematical solution o f wave propagation and is a good approximation for natural deposits. However, i n more complicated situations with unusual boundary conditions and/or when irregular non-homogeneities exist in the ground, these methods may result in considerable error. For example, the vibro-stone column method introduces stiff vertical elements and produces vertical layering. The vertical layering changes the wave propagation regime and this should be considered in interpretation o f the shear wave velocity from seismic cone signals. In this chapter, numerical modelling w i l l be used to investigate the effect o f the presence of stone columns on the interpreted shear wave velocity and the implications for using shear wave velocity for Q C / Q A o f ground improvement w i l l be discussed.  5.2  INTERPRETATION O F SCPT SIGNALS F O R S H E A R W A V E V E L O C I T Y The procedure used in the seismic cone testing presented in this thesis was as follows. A t  selected depth intervals (usually l m ) , the penetration was stopped and the rod string was unloaded. Seismic waves were generated at the surface using a 12 k g swing hammer to strike either end o f the front steel pad supporting the 13-tonne U B C cone truck as shown in Figure 2-5. This pad was 2.45 m long, 0.5 m wide, 0.15 m thick and was offset at .0.8 m from the vertical axis o f the cone. The contact between the steel hammer and steel pad triggered the  147  data acquisition system which recorded the horizontal particle motion that arrived at the accelerometer i n the seismic module. The signal was displayed on the computer screen. The same procedure was repeated by hitting the other end o f the pad, which generated shear waves with inverse polarity and produced a mirror image response at the sensor as shown in Figure 2-5. T w o or more blows on each end o f the pad were recorded to ensure repeatability o f the signals. The cone was then advanced to the next depth interval and the procedure was repeated. The seismic module in the University o f British Columbia ( U B C ) cone contains two orthogonal horizontally mounted piezo-resistive accelerometers with a range o f ± 2g, a flat frequency response from 0 to 500 H z , a natural frequency o f about 600Hz and damping at 70% o f critical (Campanella and Stewart 1992). These accelerometers respond to both static and dynamic accelerations. This allows their use as inclinometers to indicate changes in inclination during penetration as well as for sensing the seismic waves during seismic testing. The average V over a given depth interval can be calculated by an interval technique s  using the following equation:  Equation 5-1  K = ~ — ~  where L 2 and L i are the slant distances between the sensor in the cone and the source beam taking account o f the offset between the vertical axis o f the cone string and the source beam (Figure 2-5). The time interval, At=t2-ti, is the difference between the arrival times o f shear waves at two successive depths intervals. Since it is hard to accurately pick out the initial arrival o f shear waves from the seismic signals, different approaches have been developed for definition o f the time interval. Three main methods are used by geotechnical engineers to interpret the S C P T signals to obtain time intervals. These methods are the cross-over, cross-correlation and phase o f cross-spectrum methods. Each is described below. For more detailed information refer to Stewart (1992). The simplest approach, termed the cross-over method, uses the mirror image wave traces plotted over one another to identify a consistent reference time or time marker. The difference in arrival time indicated by any chosen time marker at two successive depth intervals can be used as the time interval for calculation o f shear wave velocity. Usually the first cross-over or the next peak (shown in Figure 2-5) is the selected time marker.  148  A more elaborate approach uses cross-correlation o f signals at two successive depths by shifting one signal by small time steps relative to the other signal. A t each shift, the sum o f the product o f the signal amplitudes is calculated as shown in the following equation:  C C „ (r) = lim - f S, (t).S, (t + z).dt  Equation 5-2  T->co 7 JT 1  where Si(t) and S2(t+x) are two consecutive S C P T signals recorded in the time domain at upper and lower interval depths, respectively. T is the length o f the time record in seconds and x is the time shift in seconds. The time shift corresponding to the maximum cross-correlation is taken as the interval travel time between the two depths. The entire signal or only a part o f the signal may be used for this method. Gillespie (1990) noted that the first half cycle o f the shear wave between the first arrival and the first cross-over was the optimum window. Campanella and Stewart  (1992) used the entire  first  cycle o f the measured  shear wave arrival for  cross-correlation. They isolated the first shear wave cycle from the rest o f the signal by a process called windowing, a common technique i n signal processing (Bath 1974). Interval techniques assume no distortion and/or dispersion o f signals between two adjacent depths. In this condition, both interval techniques should give similar values for V . In s  a dispersive medium, the wave velocity is a function o f frequency and the velocity at any frequency is called a phase velocity. Sheriff (1984) defines the phase velocity as the velocity at which any given phase such as a trough or a wave o f a single frequency travels. In a dispersive medium, the above interval techniques may not give similar values o f V . s  A more comprehensive method o f determining V  s  is the phase o f cross-spectrum  method, which gives the phase velocity as a function o f frequency. For each frequency, f, the time interval is calculated as:  </>(/)  Equation 5-3  2Kf  where (j)(f) is the phase difference in radians, f is the frequency in H z and At is the time interval in seconds. The phase velocity is then calculated as:  149  Equation 5-4  where A L = L 2 - L i as defined i n Figure 2-5. The phase velocity associated with the predominant frequency o f the signal may be selected as the shear wave velocity o f the soil as suggested by Stewart (1992) or an average velocity associated with a range o f frequency o f interest may be selected as the group velocity (Bodare and Massarsch, 1984).  5.3  O B S E R V E D E F F E C T S O F V I B R O - R E P L A C E M E N T O N SEISMIC C O N E TESTING Figure 5-1 shows typical seismic signals before and after vibro-replacement in a sandy  deposit i n Richmond, B C . Plots such as Figure 5-1 give a general picture o f the variation o f the wave arrivals and allow identification o f any anomalies in the data. The increase in total travel time o f the seismic waves with depth is clear. A s depth increases, the signals shift to right on the time axis indicating a later arrival. Signals from before and after vibro-replacement have definitive differences. The general shape o f pre-compaction signals does not change with depth. Each characteristic point on the signal at each depth (a cross-over point or a peak) can be traced with depth. For example the broken line in Figure 5-1 (left) traces the first cross-over with depth. The slope o f this line (ADepth/At) is approximately equal to the shear wave velocity at each interval. A change in the slope at a depth o f 10 metres indicates a general increase in the stiffness o f the deposit below that depth. O n the other hand, the post-treatment signals are somewhat irregular compared to those of the ground before vibro-replacement, with some low amplitude cycles which have arrived before the arrival o f the main shear wave. The V  s  obtained from the first part o f the  post-compaction signal is about 450 m/s, which is too high for the native sand even after compaction. It is likely that this velocity is associated with the seismic wave which has travelled preferentially through the stiffer columns. Unlike the pre-compaction signals, a characteristic point on the post-compaction signals cannot be traced continuously with depth. For example, the broken line in Figure 5-1 (right) traces the first major cross-over. The positions o f the first cross-over and maximum peak, marked with triangles, shift with depth. It  150  may be observed that this point has a shift at depth 10.7m. Significant distortion occurs i n the signals with depth. The signals contain some inflections, which are marked with vertical arrows. These inflections move relative to the rest o f the signal with increasing depth and seem to disappear at depths below the tip o f the stone columns. Figure 5-2 compares the V profile obtained from cross-over and cross-correlation s  methods for pre- and post-compaction. For pre-compaction signals, the V profile obtained is s  relatively smooth with depth. In addition the results from cross-over and cross-correlation methods are close. This is consistent with past experience from seismic cone testing in natural deposits in Fraser Delta (Campanella and Stewart, 1992). The variation o f the post-compaction V profile with depth is not smooth and may vary s  significantly between adjacent intervals. The post- V profile obtained from the cross-over s  method is usually spiky. This is partly due to distortion o f the signals i n the vicinity o f the selected time markers. For example, the movement o f the first cross-over in Figure 5-1-right at depths 6.7m and 7.7m is due to the local distortion o f the wave trace. Figure 5-3 is an example o f a comparison o f the variation o f phase velocities with frequency before and after vibro-replacement obtained from the phase o f cross-spectrum method. Figure 5-4 compares their respective frequency spectra. Before vibro-replacement, the phase velocity is almost constant for a wide range o f frequency about the predominant frequency o f 70 H z . O n the contrary, the phase velocity becomes dependent on the frequency after vibro-replacement. This implies dispersion. Dispersion refers to the condition in which wave velocity is a function o f wave frequency. 5.3.1  Field evidence on the effect of stiffer inclusions on seismic test results In a site in Richmond, B C , seismic cone testing was carried out before and after  vibro-replacement (Howie et al. 2000). The S C P T profiles are shown in Figure 5-5. Pre- and post - S C P T were carried out at exactly the same location (centroid o f triangular grid). It may be observed that the ground has been improved considerably by comparing the pre- and post-treatment q and V . Spectral analysis o f surface waves, S A S W was also carried out t  s  sometime after the post-densification S C P T as an alternative method for evaluation o f bulk stiffness o f the improved ground (Pidlisecky 2002). S A S W was performed along two perpendicular lines passing through the location o f S C P T hole.  151  The S A S W method is used for determining the shear wave velocity profile and is based on the dispersive characteristic o f Rayleigh waves when travelling through a layered medium. The velocity o f Rayleigh waves depends on the ground stiffness, thickness o f the layers and wavelength. For more details refer to Nazarian and Stokoe (1984) or Stokoe (1994). Figure 5-6 compares the V profiles obtained from S C P T and S A S W methods after s  vibro-stone column. Note that the average post-compaction V from S C P T is about 210 m/s. s  On the other hand, the V from S A S W is about 177 m/s, which is close to the pre-compaction s  V . One explanation for this discrepancy is that the V from S C P T might have been affected by s  s  the stiffer stone column whereas the V from S A S W is more biased towards the bulk stiffness s  o f the ground. Schneider et al. (2000) carried out S C P T and cross-hole seismic tests to measure the V  s  o f a native silty clayey soil and stone columns respectively after construction o f stone columns. Due to the tight spacing o f stone columns, they had to use the cross-hole configuration shown in Figure 5-7 whose result would be some average o f V o f the stone column and the soil. The s  S C P T was also performed at the centroid o f the triangular grid. It had been expected that a higher V would be obtained from the cross-hole test due to the direct effect o f the stiffer stone s  column. However, both seismic tests resulted in approximately the same values for the V . s  They speculated that during S C P T tests, the shear waves must have travelled through the stiffer stone columns resulting i n a higher shear wave velocity. Pinches and Thompson (1990) carried out down-hole and cross-hole seismic tests to measure the V o f mudstone containing interbedded thin limestone bands. They found that s  where the limestone bands were closely spaced, the cross-hole V was as much as 4 5 % greater s  than the down-hole V (Figure 5-8). They noted that V from cross-hole testing in these zones s  s  was higher because shear waves refracted and preferred to travel through the stiffer limestone bands. The cases presented here suggest that the inclusion o f stiffer material parallel to the travel path o f shear waves may result in overestimation o f the V o f the native soil. This is s  important i f V is to be used for Q C / Q A o f densification or i f V is used to obtain the stiffness s  s  of the densified soil. The effect o f the inclusion o f stone columns w i l l be investigated using numerical modelling  152  5.4  NUMERICAL M O D E L L I N G FOR INVESTIGATION O F T H E E F F E C T O F STONE COLUMNS ON V  s  F L A C (Itasca 1998) version 3.4, with the dynamics option, was used for simulation o f the down-hole seismic test. Firstly, numerical modelling is carried out for the case o f natural ground without stone columns. This is to ensure that the numerical modelling can actually capture the characteristics of seismic cone testing. Then the more complicated condition with inclusion o f stone columns w i l l be modelled. 5.4.1  Numerical modelling of the down-hole seismic test without stone columns Figure 5-9 illustrates the configuration o f the model. A block o f ground 20 m x 20 m is  represented by a mesh o f 150 x 150 rectangular elements with dimensions o f 0.1m or 0.2m. "Quiet boundaries (see Section 3.4.2 for definition) are used on the bottom and vertical sides o f the model to minimize the wave reflections from the boundaries. 5.4.1.1  Soil model and conditions analyzed  During a down-hole seismic test by S C P T , Stewart and Campanella (1991) measured soil shear strains in the range o f 1.4 x 10" at 5 m to 1.0 x 10" at 25m. A s shown in Figure 5-10 5  6  from Ishihara (1996), the soil response at such small strain levels may be modelled using the theory o f linear elasticity.  In this study, a linear visco-elastic model is used to allow  consideration o f attenuation due to energy absorption. The numerical analysis was first conducted for homogeneous and isotropic soil conditions using the soil properties shown in Table 5-1. The assumed small strain modulus, G  m a x  is obtained from a shear wave velocity o f  182 m/s. A high bulk modulus is selected to give a compression wave velocity close to that o f a saturated soil. Based on field seismic test measurements, the damping ratio at small strains has been reported to be about 6% for sand (Kudo and Shima 1981) and 4-7 % for clays ( M o k et al. 1988). In his study o f S C P T signals, Stewart (1992) found lower damping ratios in the range o f about 0.5 to 2% for sand. This agrees with findings by Santamarina and Cascante (1996). For the analysis reported here, the damping ratio is firstly selected in the higher range as this assumption results i n a cleaner simulated signal with fewer cycles. In more complicated  153  conditions, such as where vertical inclusions are present in the ground, different kinds o f waves may be generated. Fewer numbers o f cycles simplifies identification o f different types o f waves in the simulated signal. Wave velocities are obtained from the assumed elastic properties using the following equations:  Equation 5-5  B+1.33G  max  Equation 5-6  A l l the above parameters are defined in Table 5-1. It is more realistic to increase the stiffness o f sandy deposits with depth. Based on several case studies in Richmond, B . C . , V o f the sandy deposits increases almost linearly with depth s  from 5 m to 20m. T o model this condition, V is assumed to vary as follows: s  Equation 5-7  V = \Q.d +100 s  where d is the depth in metres and V is in m/s. s  5.4.1.2  Loading condition  The impact o f the hammer on the truck pad was simulated by a horizontal initial velocity o f 1 m/s applied for 8x10~ seconds to the ground surface over the length o f the source beam. 5  This is the time required for a compression wave to travel twice the length o f the head o f the hammer (2x0.2m) and return to the impact point as a tension wave. This is approximately the contact time between the hammer and the source beam. Figure 5-11 shows the input velocity time history applied at the contact points between an imaginary source beam and the ground surface. The source beam itself is not modelled. The magnitude o f the velocity is o f no significance in this model as the main interest is in the waveform o f the seismic signals rather than their amplitudes.  154  5.4.1.3  Results o f numerical analysis  A horizontal impact at ground surface transmits body waves and surface waves into the ground. Figure 5-12 is a snapshot o f the velocity vectors at 0.05 sec after the impact for the case o f homogeneous soil. The shear wave and Rayleigh wave fronts are annotated. Note that the compression wave has already travelled beyond the boundary o f the model and hence cannot be observed in this figure. The shear wave, which is the main interest of this discussion, appears as two darker areas, which are a consequence o f the concentration o f velocity vectors in opposite directions. These are separated by a light coloured area which is the transition zone where the velocity vectors change direction. Time histories o f horizontal velocity and horizontal acceleration at a depth o f 5 m at the centreline o f the model are shown in Figures 5-13 and 5-14, respectively. These are the responses o f ideal, embedded  horizontal geophones  and accelerometers,  respectively,  assuming perfect coupling between soil and instrument. Note that the signals from the left and right impacts are plotted over each other. Signals from the left impact are obtained from the results o f the analysis and signals from the right impact are the mirror image o f the left signals using the symmetric condition o f the problem. The positive sign indicates the direction o f velocity or acceleration vectors to the right of the model. The first arrival o f the seismic energy can be attributed to compression waves and the second group o f cycles to the shear wave, as shown in Figure 5-14. In the remainder o f the chapter, the time histories o f the horizontal acceleration obtained from the numerical analysis at the centreline o f the model w i l l be referred to as the "simulated signals". Figure 5-15 shows the simulated signals between 5 and 10m depths for the case o f homogeneous soil and 5% damping. 5.4.1.4  Characteristics o f the simulated signals compared to field data  Figure 5-16 is a typical C P T profile from the well characterized U B C research site, Kidd2 at Richmond, B C . Figure 5-17 shows typical seismic signals (accelerometer response) from the same sounding at one metre intervals. The characteristics o f the field seismic signals w i l l be compared to those o f the simulated signals obtained by numerical modelling. The simulated signals shown in Figure 5-15 have the following characteristics: •  They contain a compression wave component as well as a shear wave component.  155  •  The shear wave comprises 1.5 cycles with the second peak displaying the maximum amplitude.  •  Signals attenuate with depth.  •  Signals appear to widen with depth.  •  The direction o f initial deflection o f the compression wave component is opposite to that o f the shear wave component.  When compared to the field data shown in Figure 5-17, certain similarities can be observed as discussed in the following sections.  5.4.1.4.1 Shape of the waveforms The general shape o f the simulated and actual S C P T signals is quite similar. In each field signal, there are at least 3 half-cycles with larger amplitudes than the cycles in the rest o f the signal. However, the number o f oscillations or cycles i n the simulated signal is smaller than i n the field data. The number o f oscillations in the simulated signals depends on the damping ratio as illustrated i n Figure 5-18 which compares simulated waveforms for damping values o f 1% and 5%. A reduction i n the assumed damping ratio results in more cycles i n the simulated signals.  5.4.1.4.2 Attenuation of signals with depth The signals reduce i n amplitude with depth. Attenuation o f the waves propagating in homogeneous ground is due to the geometric attenuation and material damping. In layered ground, interfaces cause effects such as partial transmission, mode conversion or diversion, which also contribute to signal attenuation (Santamarina et al. 2001). Stewart and Campanella (1991) used the attenuation o f the S C P T signals to determine the damping ratio o f the soil.  5.4.1.4.3 Widening of the signals with depth The signals appear to increase in length with increasing distance from the source. This results in the time difference between any two time markers on a signal increasing with depth. In the frequency domain, the widening effect appears as a shift o f the peak o f the spectrum towards lower frequencies with depth as shown in Figure 5-19a. According to Santamarina et al. (2001), material damping causes dispersion and signal widening. Signal widening takes  156  place because material damping attenuates higher frequencies faster than lower frequencies (Mancuso et al. 1989). Campanella and Stewart (1992) noted a similar shift o f the peak o f the frequency spectrum with depth in a sandy deposit as shown in Figure 5-19b. However, the rate o f the shift in their field data was much smaller than that in Figure 5-19a. Figure 5-19c shows the F F T o f full signals from three depths from the K i d d 2 site shown in Figure 5-16. Figure 5-19d is the F F T o f the first shear wave cycle o f the same depths for comparison. In each case, the peak o f the frequency spectrum remains constant with depth. Figure 5-19e shows the frequency spectra o f simulated signals obtained from the numerical model, i n which V increased linearly with depth and the damping ratio was 5%. It s  may be observed that the peak o f the spectrum and its rate o f decrease with depth have become more similar to the field data in Figure 5-19b. Figure 5-19f shows the results o f the same analysis repeated for a damping ratio o f 2%. The combination o f an increase i n V with depth s  and a smaller damping ratio resulted in a balanced condition in which the peak o f spectrum remained constant with depth. This is similar to the field data shown in Figures 5-19c and 5-19d. It may be concluded that for the field data analyzed, the increase i n stiffness with depth counterbalances the effect o f damping on the peak o f the spectrum. The peak frequency o f the S C P T signals is about 80 H z , which is smaller than peak frequency o f the simulated signals o f 97 H z . This is a result o f the field site being slightly less stiff (lower V ) than the simulated soil s  conditions. Better agreement could be achieved between simulated and field data by varying the input stiffness, density and damping ratio.  5.4.1.4.4 Compression wave arrival (near field effect) The simulated signals for the case o f increasing stiffness with depth and 2% damping are shown in Figure 5-20. The simulated signals shown in Figure 5-15 and 5-20 have two distinguishable components. The interval velocity o f the first component is consistent with the input compression velocity, V , o f 1500 m/s and the interval velocity o f the second component p  is consistent with the input V o f 182 m/s. Despite a purely horizontal excitation at the ground s  surface, a compression wave has also been generated. This phenomenon has been explained by wave propagation theory and has also been observed in laboratory experiments. The field S C P T data confirms the existence o f such a  157  compression wave component. Sanchez-Salinero et al. (1986) carried out theoretical studies o f the propagation o f waves generated b y a point source within a three-dimensional infinite isotropic elastic medium. They showed that the first deflection in a seismic signal at the receiver corresponds to the "near field" component o f the transmitted wave and not to the shear wave component. The near field component is actually a compression wave, which is generated when the shear wave source has finite dimensions. Its initial polarity is opposite to the initial polarity o f the shear wave component and causes the first particle motion to be opposite to the direction o f the excitation. This phenomenon is an important issue for interpretation o f dynamic measurements on small samples in laboratory tests since it makes it difficult to identify the arrival o f the shear waves. Figure 5-21 shows a typical signal from a bender element test reported by Viggiani and Atkinson (1995). They noted that the first arrival (point 0) significantly overestimated the V . They suggested that point 1 could be regarded as s  the arrival o f shear wave. Brignoli et al. (1996) noted that the polarization o f the near field component was opposite to the excitation pulse. Therefore point 1 is usually considered to be the arrival o f the shear wave because at this point the deflection o f the signal is in the same direction as the input excitation. The near field effect can also be observed i n field S C P T signals. Figure 5-22 shows field data at an enlarged scale from two successive depths in Figure 5-17. It may be observed that the signals have two components with different arrival times. The cross-over velocity o f the first component is about 1600m/s, which is close to the compression wave velocity o f a saturated soil. Figure 5-22a is for the left hammer strike, which gives a left to right excitation motion to the ground. However, the first deflection o f the signals at point " A " has an initial movement to the left, opposite to the excitation direction. A t point " B " which is the arrival o f the shear wave, the deflection o f the signal is in the same direction o f the excitation. The same trend exists in the signal at the subsequent depth. Figure 5-22b shows that the polarity o f the compression wave component reverses when the hammer hits the opposite side o f the shear source. The above effect is also present in the simulated signals. Figure 5-23 shows simulated signals in Figure 5-20 to an enlarged scale. Again, the first arrival travels at the compression wave velocity and its initial deflection is opposite to the excitation direction. The second arrival, which is the shear wave, displays an initial deflection in the same direction as the  158  excitation. A l s o note that the compression component is o f higher frequency than the shear wave component in both S C P T and simulated signals. The near field effect is not problematic i n interpretation o f S C P T signals mainly because the distance between the source and the receivers is sufficiently large for attenuation o f the compression component to occur and to provide enough time for the compression and shear components to separate.  A s the frequency o f the compression wave component is  considerably higher than that o f the shear wave component, it may be removed from the signal by low pass filtering. Gillespie (1990) used explosive sources (shotgun shells) to generate seismic waves i n conjunction with S C P T . He noticed that whenever the arrival o f the shear wave was known, the first departure due to the shear wave arrival had the opposite sign to the first departure due to the arrival o f the p-wave. He used this observation to interpret the arrival o f the shear waves. His observation is consistent with the modelling and field test results i n this study. 5.4.1.5  Calculation o f V  s  from field data  The cross-over method, cross-correlation method and phase o f cross-spectrum techniques are used on some o f the signals i n Figure 5-17. The interpreted shear wave velocities are shown in Figures 5-24. Values o f V obtained from the cross-over method for the s  time markers indicated in Figure 5-24a are shown for two depth intervals in Figure 5-24b. The V values tend to decrease for time markers later i n the trace. Figure 5-24c shows an example s  o f the use o f cross-correlation to obtain the time interval and the corresponding V , and Figure s  5-24d shows the variation o f phase velocity with frequency obtained from the phase o f cross-spectrum method. The variation o f V with frequency suggests a slight dispersion. In the s  frequency range o f interest, either side o f the predominant frequency o f about 80Hz, the phase velocity tends to increase slightly for the depth interval o f 3.6 and 4.6m and tends to decrease for the depth interval o f 7.6 to 8.6 m. Table 5-2 compares the results o f the values o f V  s  obtained from the three different methods. V varies by up to about 3%. This would result i n s  about a 6% variation in the calculated value o f small strain shear modulus (Equation 2-2). A l l the signals were first filtered using a low pass 200 H z filter. For calculation o f V  s  from the  cross-over technique, the first cross-over and the maximum peak were used. The first shear wave cycle o f the signal was separated from the rest o f the signal by rectangular windowing  159  and was used for the cross-correlation method. The V values from the first cross-over are s  within 2% o f the cross-correlation V . For most depths, the results from the maximum peak are s  also close to the cross-correlation V . However, for this data set, the first cross-over appears to s  give better agreement with the cross-correlation V . This may be due to the peak being more s  sensitive to local irregularities than the first cross-over. The closeness o f the results indicates that the dispersion does not strongly affect the calculation o f shear wave velocity for the case analyzed. Figure 5-25 compares the V profile s  from cross-over and cross-correlation methods. It may be observed that for the most part, the results are close. Campanella and Stewart (1992) noted that for the usual one metre intervals, the effect o f dispersion and/or distortion could be ignored provided a soil layer boundary was not intercepted. They recommended more caution and judgement for larger spacing. W h i l e Sheriff and Geldart (1995) noted that dispersion o f seismic body waves has not been definitively observed over a wide range o f frequencies, Mancuso et al. (1989) reported the results from a 3-borehole cross-hole seismic test in which a marked signal widening effect was observed. The effect was such that the time intervals obtained from different time markers varied by up to about 10%. 5.4.1.6  Calculation o f V from simulated signals s  The V values interpreted from the simulated signals in the numerical model can be s  compared with the input value o f shear wave velocity i n the model. Figure 5-26 presents a comparison o f the V profile calculated using the cross-over method for time markers 2, 3, C s  and D in Figure 5-15. The computed V varies with the location o f the time markers on the s  signal. The earlier time markers give greater V . The maximum peak and the first cross-over, s  time markers 3 and c, give V values within 0.8% and 2% o f the input value, respectively. This s  suggests that these may be the optimum time markers for estimating V by the cross-over s  method in field data. The V profile obtained by cross-correlation is also shown i n Figure 5-26 s  and is within 1% o f the input value o f V . s  Figure 5-27 shows the calculated values o f V by cross-over and cross-correlation s  approaches for the simulated case o f stiffness increasing with depth and damping o f 2%. The cross-over and cross-correlation V profiles are much closer to the input value o f V . The s  s  cross-correlation value o f V is within 0.2% o f the input value. s  160  The slopes o f the dashed lines connecting the time markers in Figure 5-15 represent the cross-over values o f V for the respective time markers. The slopes o f the lines change s  depending on the choice o f time marker. This is an indication o f the effect o f signal widening on the calculated velocity. A s mentioned earlier, material damping causes signal widening and variation o f cross-over velocity i n the time domain. The effect o f material damping appears as dispersion i n the frequency domain and causes a variation o f phase velocity with frequency. Figure 5-28 shows the variation o f the phase velocity for simulated signals over the depth interval 5 m to 6 m in homogeneous ground with 5% damping. In Figure 5-28, the trend line shows that, except for the first few data points, the phase velocity decreases slightly with increasing frequency. A t the predominant frequency o f about 97 H z , the phase velocity is about 183 m/s. This is almost identical to the cross-correlation V and is less than 1% different s  from the input V o f 182m/s. s  In a non-dispersive medium, all these methods would have given identical results. In a dispersive medium, the cross-spectrum method is the most comprehensive method. However, for practical purposes, it may be concluded that the results from the cross-correlation, maximum peak or the first cross-over are also acceptable for the simulated ground conditions. 5.4.1.7  Summary and conclusions o f the numerical analysis o f S C P T without stone columns  Plane strain dynamic analysis has been carried out using the finite difference program F L A C to model the wave propagation i n seismic cone testing and to simulate the signals received at down-hole accelerometers. Analyses were performed based on assumptions o f a homogeneous ground condition and for the case i n which the stiffness o f the ground increased with depth. The results o f the simulations were compared to field data.  This process has  provided insight into the factors affecting wave propagation and the determination o f V from s  field seismic testing. The shape o f waveforms, the near field effect (or compression wave arrival), attenuation of signal amplitude, frequency content, shift o f the peak frequency and signal widening observed in the field data were captured in the simulated traces. It is concluded here that the numerical modelling is capable o f simulation o f the seismic test. In the next section, the stone columns w i l l be added to the numerical model and their effects w i l l be discussed.  161  5.4.2  Numerical modelling of the down-hole seismic test with stone columns The wave propagation during down-hole seismic testing at the centroid o f the grid is a  three-dimensional problem as shown in Figure 5-29a. However, a two-dimensional model can be used to qualitatively simulate the wave propagation and the seismic signals. The main question is the effect o f stone columns on the propagation o f shear waves as shown schematically in Figure 5-29b. Two stone columns are added to the plane strain model as shown in Figure 5-30. The numerical analyses were carried out for different diameters o f the stone columns, D , o f 0.3 and lm. It is assumed that the soil and stone columns are homogeneous and isotropic materials. Table 5-3 presents the material properties assumed for the analyses. The shear stiffness ratio o f the stone columns to the soil, G  r  =G one.coi/ G oii st  S  is assumed to be 2.5 and 5 based on field  measurements (Baez 1995 and Martinez et al. 2001). In the analyses, a damping ratio o f 5% is used. A damping ratio i n the higher range, reduces the number o f oscillations i n simulated signals and helps in identification o f different types o f waves i n the signal.  5.4.2.1  Wave propagation  A horizontal impact is applied to the ground surface at the contact points with the shear beam. This transmits body waves and surface waves into the ground. Figure 5-31 is a snapshot of the velocity vectors at 0.02 seconds after the impact i n the presence o f two stone columns. The arrows show the direction o f the velocity vectors. Compared to Figure 5-12 for homogeneous conditions, the inclusion o f stone columns complicates the wave propagation regime and makes it difficult to identify different types o f waves. However, several patterns can be observed which are designated as waves " 2 " to " 4 " i n Figure 5-31. Wave " 1 " , the compression wave, has already reached the boundaries o f the model at 0.02 seconds. Wave " 2 " travels mainly through the stone columns. From the concentration o f the velocity vectors, it seems that this wave has little effect on the soil elements at the centreline. A t 0.02 sec, wave " 2 " has travelled about 8.5m which gives an approximate velocity o f about 425 m/sec. This is close to the input V o f the stone columns o f 406m/s. Wave " 3 " is thought to be an interface s  wave based on its limited lateral influence zone from the soil-stone column interface. Interface  162  waves decay exponentially away from the interface (Pao 1983). Wave "4" is thought to be the main shear wave with a wave front distorted by the stiffer stone columns. 5.4.2.2  Simulated signals  Time histories o f the horizontal acceleration at the centreline o f the model are shown i n Figure 5-32. The simulated signals are the responses o f imaginary horizontal accelerometers embedded at the centreline o f the model. A t each depth, one wave is simulated and is plotted along with its mirror image. This is to mimic the seismic signals from left and right impacts. The simulated signals become more complicated when stone columns are added to the model (compare with Figure 5-15). Different wave types identified i n Figure 5-31 are also annotated in Figure 5-32. Wave " 1 " is a compression wave and arrives first. Wave " 2 " appears as some small amplitude cycles. Wave 3 and 4 are mixed at the shallow depths but due to their different velocities, they separate with increasing depth. Their relative movement appears as inflections in the signal as indicated by vertical arrows. The inflections cause a shift in the time markers in the portion o f the signal where the two wave traces are still mixed. A s wave " 4 " has a lower velocity, it falls behind at greater depths. A t 10 m, the waves are almost separated into waves " 3 " and "4". In the simulations, the magnitude o f wave distortion and time marker shifting diminished as the diameter o f the stone columns and/or G were reduced. r  5.4.2.3  Calculation o f the V s from simulated signals  Table 5-4 presents V values obtained by various techniques from the simulated signals s  for the depth interval o f 5 to 6 m in homogenous ground and with stone columns. In each case, the input elastic V o f the soil is 182 m/s. A s shown earlier, for the case o f a uniform soil s  model, the V results obtained from different methods were consistent. The results were within s  ± 2% from the input elastic V . O n the contrary for the case with stone columns, the results s  from different methods are very different and also much larger from the input soil V in the s  model.  5.4.2.4  Discussion  In the case o f the homogeneous ground, for both field and simulated cases, the signals are regular, no apparent distortion occurs in the signal and a time marker can be followed with  163  depth without any shifting. The V values obtained from all three interpretation techniques are s  similar. The phase velocity is almost constant i n the frequency range o f interest. Figure 5-33 shows the post-vibro-replacement seismic signals (repeated from Figure 5-1). Comparison o f Figures 5-32 and 5-33 shows that the characteristics o f the field data are duplicated in the simulated signals. The inclusion o f stone columns changes the characteristics o f the signals. The signals are irregular and more difficult to interpret than in the untreated case. There is an apparent arrival o f some low energy waves ahead o f the main shear wave in Figure 5-33. This is similar to Wave " 2 " in the simulated signals which is represented by the low amplitude cycles in the signals before the arrival o f the main shear wave, as shown in Figure 5-32. The V obtained from this part o f the simulated signal is close to the input V o f s  s  the stone columns (406 m/s). Similarly, the interval velocity o f the same part o f the measured field signal is about 450 m/s, which is considered to be close to V o f the stone column (Figure s  5-34). Selection o f the time markers for the cross-over method is not straightforward. For example, in uniform ground, the first cross-over is usually followed by the maximum peak. This is not the case for the treated ground. In Figure 5-32, time markers A and B result i n very high values o f V . Time markers E and F result i n much lower V values but are still 20% s  s  higher than the input V for the soil. The time markers between B and E cannot be used, as they s  are located in the portion o f the signals with large distortion. For example, note that the maximum peak shifts half a cycle from 5m to 7m. Cross-correlation o f the two complete signals overestimates the soil V by about 13%. s  Figure 5-35 shows that the phase velocity in homogenous model is almost constant i n a wide range o f frequencies around the dominant frequency. Inclusion o f stone columns causes the phase velocity to be frequency dependent. The variation o f the phase velocity with frequency can be divided into two plateaux, m-n and u-v, with velocities o f about 235 and 200 m/s, respectively as illustrated in Figure 5-35. The plateaux straddle the peak o f the spectrum at 100 H z (Figure 5-36). This can be interpreted as dispersion which is brought about by the vertical layering. The velocity associated with each is less than the input V for the stone s  columns but greater than that for the soil. Although a similar pattern is observed in the field data (Figure 5-3), the plateau is not as well defined. This may be due to a more gradual variation o f shear stiffness from the centroid o f the grid towards the stone column in the field  164  case, as opposed to an abrupt change assumed i n the numerical model. Figure 5-37 shows how G and D affect the phase velocity spectrum. Small values o f G and D result in a phase velocity r  r  relatively unaffected by frequency, which is more similar to the untreated case but V is still s  overestimated. 5.4.2.5  Summary o f the numerical analysis o f seismic cone testing in presence o f stone columns  This section shows the results o f numerical modelling to explain the mechanism o f the effects o f the vertical stiffer stone columns on the wave propagation regime and the interpretation o f V from the S C P T signals. The inclusion o f stone columns creates vertical s  layering, which causes dispersion. This effect introduces irregularities into the signals compared to those in untreated ground. For example, smaller amplitude waves arrive before the main shear waves, signals contain inflections and there are shifts in the positions o f time markers within the signals with depth, due to superposition o f wave arrivals. These effects are observed i n field data and in the simulated signals. Conventional interpretation o f the seismic signals results in V greater than the V o f the soil between the stone columns. For any s  s  particular stone column spacing, the magnitude o f the overestimation depends mainly on the shear stiffness ratio and stone column diameter. From the similarities found between the field and simulated signals, it is thought that the mechanism o f the effect o f the stone column could be explained by the results o f the numerical model. However, more research is needed to develop a method to separate the effect o f stone columns and to determine the shear wave velocity o f the in situ soil between stone columns.  5.5  IMPLICATION  ON QC/QA  O F DENSIFIED SOIL B Y S H E A R  WAVE  VELOCITY Shear wave velocity has been used for Q C / Q A o f densified soil (e.g. Addo et al. 1993, Andrus et al. 1998, M o x h a y et al. 2000, Pidlisecky 2002). The shear wave velocity after vibro-replacement is usually greater than pre-compaction due to increases in density and lateral stress in the native soil and also due to the inclusion o f stiffer stone columns. Based on the results o f numerical modelling, the increase i n post-V due to inclusion o f stone columns s  could be in the range o f 15 to 20%. If the increase in the V due to inclusion o f stone columns s  165  is ignored, then the post-compaction V w i l l overestimate the degree o f improvement o f the s  native soil. Figure 5-38 compares the increase in q and V for a site in Richmond, B C . It may be t  s  observed that the tip resistance has improved by about 50 to 100% whereas V has improved by s  about 5 to 20%. For example in Figure 5-38 at 10m depth, consider an increase from 100 bars to 160 bars for q and an increase from 190m/s to 220 m/s for the V (15% increase). The following is t  s  assumed for the changes i n soil conditions based on changes i n the cone tip resistance. 1 ^ = 0 . 5 to Ko.  post  =0.75 and D - = 6 5 % to D . r  pre  r  post  =75%  The above changes in ground conditions should increase the V by only 8%. This is s  based on the following correlation proposed by Chillarige et al. (1997). This correlation was obtained from bender element testing on reconstituted samples o f Fraser River sand.  V ={AS  B.e).  (K f'  Equation 5-8  U5  0  where A = 2 9 5 , B =143 and n =0.26, e =void ratio, Ko=coefficient o f horizontal stress and vs  vs  vs  P =atmospheric pressure. a  The apparent increase o f V beyond about 8% could be attributed to the effect o f stone s  columns.  In this case the effect o f stone columns may have caused about 7% o f  over-estimation o f the shear wave velocity o f the in situ sand. Ignoring the effect o f stone columns would overestimate the degree o f improvement i n the native soil.  5.6  S U M M A R Y AND CONCLUSIONS Shear wave velocity and cone tip resistance are different functions o f the same  parameters o f granular soils. Therefore, an independent measurement o f shear wave velocity, V along with tip resistance helps in better characterization o f granular soils. The seismic cone s  penetrometer is a valuable tool that can measure both parameters in one hole. Conventional interpretation methods o f seismic tests to determine the interval V are mainly based on s  uniform or horizontally layered ground. O n the other hand, the improved ground after vibro-replacement includes stone columns, which result in vertical layering. The conventional 166  methods are not strictly applicable to interpretation o f seismic signal in vertical layering and may result in erroneous V . s  Plane strain numerical modelling was used to explore the effect o f stone columns on the wave propagation seismic waves and consequently on the results o f seismic tests. The numerical model was capable o f duplicating the field observations for pre-treatment ground and improved ground with stone columns. Numerical modelling showed that the vertical stiffer stone columns change the wave propagation regime. The velocity o f seismic waves is a function o f the properties o f i n situ soils as well as the properties o f stone columns. It also showed that in ground with stone columns, the V determined from the conventional techniques would be greater than that o f the s  native soil. In other words, the conventional methods over-estimate the V o f the native soil s  when stone columns are present. For the normal construction o f stone columns i n sand ( ~ l m diameter columns and 3m spacing), plane strain analyses showed the over-estimation in the V o f native soil could be up s  to 15 to 20%. O n the other hand, the increase in the V after vibro-replacement i n the sites s  studied during the course o f this research was usually less than 25%. Therefore, an overestimation in the range o f 15 to 20 % would be significant.. It is not currently possible to interpret the shear wave velocity obtained by interval techiniques from S C P T after vibro-replacement. Failing to acknowledge the effect o f stone columns leads to overestimation o f the degree o f improvement o f the native soil. Further research, including three-dimensional numerical modelling, is required for better quantitative conclusions.  167  Table 5-1 Input soil parameters in numerical model, homogeneous soil condition Soil parameters Small strain shear modulus, G  m a x  Soil (MPa)  66  B u l k modulus, B (MPa.)  4410  Poisson's ratio  -0.49 2000  B u l k density, p (kg/m ) 3  Damping ratio (%)  5  Elastic Shear wave velocity, V (m/s)  182  s  Elastic compression wave velocity, V  p  (m/s)  1500  Table 5-2 Comparison of the V obtained from different methods, Richmond, B.C. s  Shear wave velocity, Vs (m/s)  Depth interval (m)  1st cross-over  Max. peak  Cross-correlation  Cross-spectrum  3.6-4.6 7.6-8.6  157 169  153 166  153 171  157 170  Table 5-3  Material properties used in numerical model  Material properties Maximum shear modulus, G , (MPa) Bulk modulus, B (MPa.) Density, p (Mg/m3) Damping ratio (%) Elastic shear wave velocity (m/s), V Elastic compression wave velocity (m/s), V nax  s  p  Soil  Stone column  66 4410 2 5 182 1500  2.5x66 or 5.0x66 4410 2 5 287 or 406 1500  Table 5-4 Interpretation of V (m/s) from simulated signals, depth interval of 5m- 6m s  Interpretation method  Cross-over  Cross-correlation  Cross-spectrum  Homogeneous ground  181 - 186  183  183  With stone columns, Gr =5, D=lm  221 -297  206  200-235  Note: The input elastic V is 182 m/s for the soil and 406 m/s for the stone columns. s  168  time (sec) 0.00  0.02  0.04  0.06  time (sec)  0.08  0.10  maximum peak  0.12  0.14  0.00 3.7  0.02  0.04  1 st cross-over  ](-*  0.06  0.08  0.10  0.12  maximum peak  4.7 5.7 6.7 7.7 8.7 9.7 10.7 11.7 12.7  ^8-  13.7 f^-i Tip of stone column 14.7 15.7 16.7  Figure 5-1  Comparison of S C P T seismic signals before (left) and after (right) vibro-replacement, Richmond, B C  0.14  s h e a r wave velocity, V s (m/s) 100  150  200  250  shear wave velocity, V s (m/s) 300  100  150  250  max. peak —m— x-over - o •x-correlation  — m a x peak —«— x-over - o •x-correlation  Figure 5-2  200  V profile from cross-over and cross-correlation methods, (left) before s  vibro-Replacement, (right) after vibro-Replacement  170  300  240  before stone column  40  60  80  100  120  140  160  180  frequency (Hz)  Figure 5-3  Variation of phase velocity, before: 7.9m & 8.9m, after: 7.7m & 8.7m  - before stone col.  f r e q u e n c y (Hz)  Figure 5-4  Frequency spectra before and after vibro-replacement, before: 7.9m & 8.9m, after: 7.7m & 8.7m 171  Figure 5-5  S C P T profile before and after vibro-replacement, Laing Bridge, Richmond, BC  172  Shear Wave Velocity Profile for LB Line A Or  ;i  Shear Wave Velocity Profile for LB Line 2 0,  . ++; -j-  -----  t  •  -  4  !  +  -  -  -  •  o  .  o  C L  Q.  Q  Q  O  10  4"  10  o  SCPT SASW(d=4m) SASW(d=6m) SASW(d=4m) SASW(d=14m) SASW(d=8m)  12  14 50  Figure 5-6  - • '•  100 150 200 Velocity (m/s)  12  14 50  250  C + -f-,-  SCPT SASW(d=12) SASW(d=10) SASW(d=4)  100 • 150 200 Velocity (m/s)  250  Comparison of S C P T and S A S W after vibro-stone column - Laing bridge, Richmond, B . C . (after Pidlisecky 2003)  173  Figure 5-7  Cross-hole test in presence of stone columns (after Schneider et al. 2000)  174  Shear wave velocity: m/s  0  1000  2000 mmm Limestone band i Mudstone  **  10  h^j  Sillstone/limestone  US Fissile mudstone  20  Siltstone and gypsum  t'  Down-hole measurements  -1  30  Cross-hole measurements  a a 40  50  60  1>  i  «  Cross-hole V s affected by limestone bands  —v  70  Figure 5-8  Comparison of cross-hole and down-hole seismic test in mudstone with  interbedded thin limestone bands (after Pinches and Thompson 1990)  175  20mJ  20m  Figure 5-9  Shear strain  Schematic geometry of the F L A C model  10"  10"  6  Small strain i  s  10~  4  Medium strain 1  10 "  10~ 1  3  Large strain  2  10"' I  Failure strain  Elastic Elasto-plastic Failure  Effect of load repetition Effect of loading rate Model M e t h o d of response analysis  . ••  Linear elastic model Linear . ^ . method ttt  \ Visco\ elastic \ model \ Equivalent \ linear ^ method  !  \ Load history \ tracing type \ model \ \  \  Step-by-step integration method  Figure 5-10 Modelling of soil behaviour in compliance with strain dependent deformation characteristics (after Ishihara 1996)  176  Excitation velocity y cu in  g  Free vibration  4-*  o  o  cu >  -0.20 0.000  0.001  0.002  0.003  time (sec) Figure 5-11 Input loading at the ground surface over the length of the seismic source beam  Left  Time =0.05 sec  Figure 5-12  Wave propagation in homogeneous soil, velocity vectors at 0.05 sec after the impact  177  time (sec)  0.02  0.01 -0.03 ? -0.02  kight impact  /  $ -0.01 E  r8 o.oi0 v  "7 /  Left impact  0.04  0.03  A  0.05  \  \  \  \  •«•  /  > 0.02 0.03 Figure 5-13 Time histories of horizontal velocity in numerical model at 5 m,  Figure 5-14 Time histories of horizontal acceleration in numerical model at 5 homogeneous soil  178  time (sec) 0.00  0.01  •  0.02  0.03  0.04  0.05  0.06  0.07  3  4  / T " \ ^  2  time markers  f\j\ L  \OT« U T V / • — t \ jy i \ \ / 1 / V \ \ J\ j *\ 1  *\ J\\ / \  %  1 '  \  v  »  i i  * \  i  »  \ *  i *  *  11  ure 5-15 Simulated signals, acceleration time histories in homogeneous soil, damping=5%  179  180  time (sec) 0.00  0.02  0.04  0.06  0.08  0.10  0.12  11.6  Figure 5-17 Typical S C P T accelerometer response, Kidd2, Richmond, B . C .  85  -85  0.02  0.03  0.04  0.05  time (sec)  Figure 5-18 Effect of material damping on the number of cycles, homogeneous soil  182  £  0.020  depth increases 50  100  150  50  200  frequency (Hz) a) Simulated signals, homogeneous,  100  ISO  200  b) Full SCPT signals, 2.7 to 9.7m in a sandy deposit  damp=5%  50  10O  Frequency (Hz) (after Campanella and Stewart 1992)  150  200  50  frequency (Hz)  100  150  200  frequency (Hz)  c) Full SCPT signals Richmond, B.C.  d) First shear wave cycle of SCPT signals  (this study)  Richmond, B.C.(this study)  0.070  - •-  0.060  5 m  s - 7m —A™ 9 m  0.050  •S  0.040  3 'E  |  0.030  0.020 -I  0.010  0.000  » , V depth increases  if—r-  0.000  50  100  150  50  200  frequency (Hz) e) Simulated signals, increasing stiffness  100  frequency (Hz)  150  200  f) Simulated signals, increasing stiffness with  with depth, dainp=5%  depth, damp=2%  Figure 5-19 Comparison of FFT spectra of simulated and SCPT signals 183  184  Figure 5-21 Typical bender element test signal with square pulse excitation (after Viggiani and Atkinson 1995)  time (sec) 0.00 1.7  i  '  0.01  '  '  0.02  '  '  0.03  '  '  time (sec) 0.04  '  0.05  '  '  0.06 0.00  '  1  0.01  0.02  0.03  0.04  0.05  0.06  1.7-  Moves to right "B"  Moves to right  A  /  2.7  \ 2.7  "A" Moves to left  Moves to left  Q.  T3  /w /S  3.7 -J—J\ Compression wave  x  \  N  3.7  Figure 5-22  'viAA.  ' / N  \ i  \I  '  a) Left to right impact 4.7  -'VX/V——-  b) Right to left impact 4.7  Near field effect in S C P T signals, enlarged from Figure 5-17  185  time (sec)  0.00  0.02  0.04  i  i  Moves to left  5  -J%v—  E Moves to right  Q. <D  •a  Left to right impact  Figure 5-23 Near field effect in simulated signals, enlarged from Figure 5-20  186  time (sec)  0.04  0.02  0.06  0.08  180  160  I  3 6m - 4 6m 7.6m - 8.6m  X  a  Linear (3.6m - 4.6m) - - - Linear (7.6m -8.6m) | 120 number of time marker  b) Variation of cross-over Vs At= 0.0058 sec Vs=171 m/s  1 -0.01  0  0.01  0.(  time shift (sec)  c) Cross-correlation, depth interval 7.6m-8.6m  240 220  1 = 180 u o o > 160  0>  (A a  140 0 7.6-8.6m  120  X3.6-4.6m 100 25  50  75 100 frequency (Hz)  125  d) Variation of phase velocity ure 5-24 Comparison of different interval methods for calculation of the V Richmond, B.C.  187  s  100  200  2-r-  11  Figure 5-25 Profile of shear wave velocity, Kidd2, Richmond, B . C .  188  shear wave velocity, Vs (m/s) 160  180.  170  190  200  cross-correlation 5  Cross-over time markers  )  3  t>  /  C  T T  • /  1  6 1  i  _  2  +  7 k  '*?  •  I  9  \1 \i  +i */ •  10  Input Vs-182 m/s  *  Figure 5-26 The V profile from the simulated signal, homogeneous soil, Damping=5% s  189  shear wave velocity, Vs (m/s)  ii J  1  Figure 5-27 The V profile from the simulated signal- increasing stiffness with depth, s  Damping=2%  190  210 205 _  200  ~  195  2 190 a) >  8 5 re  from cross-correlation  J  185  180 175  Input V  S  170 50  100  150  200  250  Frequency (Hz)  Figure 5-28 Variation of phase velocity, simulated signals, homogeneous soil, Damping=5%, 5m & 6m depth interval  191  192  193  Left hit  Wave "4"  Wave "3  Wave "2"  Stone columns D=lm, G =5, L=12m r  time = 0.02 sec  Figure 5-31 Propagation of body waves in presence of two stone columns  194  Time (sec) 0 00  0.01  0.02  0.03  0.04  0.05  I  I  I  i  1—  Wave"1"  v^isoo  A  II  i  1J \ V  i  Wave "2" V ~400m/s \  \ \ \  1  \  \  \  VIV  > \  » M \  \  7  E  \  \  i  ^  i  v—*^  I U A f\\ / V J[\ A / \  \ \  2  0.07  A  ' vi'Av v  II'  0.06  /  ••v v  V *  \ t  \  \  -1 /  \  \ /  V  Y XJV \ i  >  \  \  \  <  Q. Q >  \ i  1  1  1  ....  10  »  J > "  Wave "3" Vs ~297 m/s 3  «  »  \  \  r  »  »  V  \ A-  v  »  \  l  > x-N»  1  > l  >  l  k  \ \  \ \  v  ^f> U  Wave 4" Vs ~221 m/s M  4  U  11  Figure 5-32 Simulated signals in the presence of two stone column, G =5, D=lr r  195  time (sec) 0.00  0.02  0.04  0.06  0.08  0.10  0.12  16.7  Figure 5-33 S C P T signals after Vibro-Replacement - Richmond, B . C  196  0.14  frequency (Hz)  Figure 5-35 Phase velocity of simulated signals, 5m & 6m  197  —•— Gr=5, D=1m  f r e q u e n c y (Hz)  Figure 5-36 Frequency spectrum of simulated signals at 5m  Increase in G r or  240 J  Input Vs  40  60  /  -®— - A — -*— H— -  80  Gr=5.0. D=1m Gr=2.5, D=1m Gr=5.0, D=0.3m Gr=2.5, D=0.3m Uniform (no stone column)  100  120  frequency (Hz)  140  160  Figure 5-37 Sensitivity of phase velocity to G and D , simulated signals r  198  Shear wave velocity (m/s) 100  + 0  100  300  200  Tip of stone columns!  200  300  cone tip resistance, qt (bars)  400  pre-Vs (x-correlation) + - post-Vs (cross-correlation) • post-Vs (cross-spectrum) pre-qt * post-qt  Figure 5-38 Comparison of change in V and q after vibro-replacement s  199  t  CHAPTER 6 EFFECTS OF VIBRO-REPLACEMENT ON T H E GROUND RESPONSE T O C O N E PENETRATION TESTING  6.1  INTRODUCTION The changes in ground condition caused by ground improvement also change the  response o f ground to C P T U . This chapter presents the results o f analysis o f a database o f C P T U data from vibro-replacement projects carried out in the Lower Mainland, B C . C P T U classification charts are then used as a platform to present the observed changes in ground response  to  CPTU  after  vibro-replacement.  The  effect  of  induced  changes  by  vibro-replacement on interpretation o f soil classification by C P T w i l l be discussed. A correlation for achievable cone tip resistance after vibro-replacement is presented.  6.2  6.2.1  O B S E R V A T I O N O F T H E C H A N G E S IN G R O U N D R E S P O N S E T O C P T U  Database of vibro-replacement projects in the Lower Mainland, B C A database consisting o f pre- and p o s t - C P T U was gathered from 13 vibro-replacement  projects in the Lower Mainland o f British Columbia. A total o f 40 post-compaction C P T U profiles have been compared to their corresponding pre-compaction C P T U profiles. The cone penetration testing was carried out either by U B C as part o f this research or by Conetec Investigations L t d . for commercial projects. Liquefaction mitigation was the main purpose o f vibro-replacement at these projects. In the majority o f these sites, the water table was at a depth o f about 1 m below surface. A l l the cone holes were pushed at the centroids o f the triangular grids. The distances between pre-CPT and post-CPT holes were usually a few metres to a maximum o f about 10 metres. Occasionally when pre- and post-CPT profiles did not match at some layers, it was interpreted as site variability and those layers were discarded. Only relatively thick well-defined layers were chosen for comparison to avoid the effects o f thin layering which has different effects on q and f . These data include projects completed by three different t  s  contractors using different vibrators.  200  6.2.2  Geological history of Richmond A l l the data presented are from vibro-replacement projects in Lower Mainland B C with  the majority o f them in Richmond, B C . A brief history o f the geology o f Greater Vancouver and Richmond is useful to understand the general setting o f the area. This section is mainly drawn from Clague and Luternauer (1982) and Blunden (1975). Greater Vancouver was below sea level until 14,000 years ago when the ice started to melt. About 11,000 years ago, great volumes o f ice melted and water flowed from the mountains carrying large volume o f sediments. The regime o f this deposition in the Lower Mainland has been mainly controlled by the Fraser River. In the Lower Mainland, the recent deposits could be as deep as 300 metres. They overlie Pleistocene glacial deposits, which in turn overlie Tertiary Freshwater sediments. 11,000 years ago, Richmond was about 40 k m out to sea. About 5000 years ago, the large volume o f sediments quickly expanded the delta. A n 11 m rise in the sea level slowed down the development o f the delta. A t this time Richmond was about 10 k m out to sea. In the past 5000 years, the sea level increased one more metre and the delta grew to its present condition. A s the delta front approached Richmond, the deposits became coarser, which resulted i n sandy layers being deposited over the deeper clays and silts. Near-surface fine-grained overbank clayey silt was deposited during annual flooding. The current rate o f growth o f the delta is about 2.5m to 8.5 m/y. Figure 6-1 illustrates the growth o f the Fraser River delta over the past 10,000 years. A s shown in Figure 6-2, the typical soil profile in Richmond, B C consists o f a few metres o f silt to clayey silt overlying interbedded silt and sand, overlying clean sand with some thin layers o f silt to silty sand overlying silty clay/clayey silt. The interest o f this thesis is mainly the top 15-20 m o f soil, which has the potential for liquefaction. From geological history, it is concluded that these deposits are relatively young and have not experienced any significant over-consolidation. 6.2.3  Pre- and post-compaction database on C P T classification chart Figure 6-3 shows a typical C P T U profile before and after vibro-replacement in  Richmond, B C . Generally q and f increase after ground improvement and U2 remains t  s  hydrostatic in clean sand but decreases to negative values in silty sands.  201  To show all the collected data in one plot, the data are plotted on C P T classification charts. Figure 6-4 shows all the pre-compaction data. Each data point represents the average value over a particular layer. For C P T S B T classification zone definitions, see Figure 2-6 and 2-7. Most o f the data are from 2 to 15 m depth and are expected to be normally consolidated. They would thus would be expected to fall in the N C zone shown in Figure 6-4b. However, a good number o f the pre-compaction data in zone 6, sand to silty sand, fall out o f the N C zone towards the under-consolidated side. This is despite the fact that the natural soils are aged and are expected to fall on the upper side o f the N C zone towards the over-consolidated sand. This could also be attributed to errors in measurement o f sleeve friction, to the linear normalization o f stress level, which is not well suited for sands, or the logarithmic scale which magnifies scatters o f the data with small values. It could also mean that the N C zone needs some shift to encompass the majority o f the data. Figure 6-5 shows the post-compaction data plotted on classification charts. N o attempt has been made to distinguish the data points on the basis o f the type o f vibrator or the spacing o f the compaction points. There is no significant difference between pre and post-compaction plots except for the general upward movement o f the bulk o f the data points due to increased tip resistance. In order to track the effect o f vibro-replacement for each data point, Figure 6-6 illustrates the movement paths on the classification charts with arrows. Each arrow has two data points as end points and represents the change to the C P T results in one layer due to compaction. The start point o f the arrow represents the pre-compaction test and the end point, shown by a triangle, represents the post-compaction test. In Figures 6-6-a and b, almost all o f the data show an increase in tip resistance (q and Q). The changes in friction ratio, R and F, are more t  f  variable and do not seem to follow a definitive trend. Nevertheless, the data suggest that the change in Rf is smaller in cleaner sands and greater in soils with higher friction ratio, usually indicative o f a finer soil. More data in fine grained soil are needed to confirm this trend. In finer material, the data indicate that vibro-replacement tends to decrease Rf. The random variation o f friction ratio could be due to the premise that friction sleeve resistance is generally more variable than the tip resistance as stresses vary rapidly over the length o f the friction sleeve due to its proximity to the cone tip. The measured sleeve friction is sensitive to the wear o f cone tip and friction sleeve. Moreover, f is a smaller quantity and is s  202  less reliable i f measured by subtraction cones. The U B C cone measures the cone tip and sleeve friction independently (ie does not obtain friction by subtracting measured values o f a tip load cell from a tip+sleeve load cell which occurs on a subtraction cone). For post-compaction soundings, Figure 6-6-c shows that ground treatment generally causes B to move towards B =0, i.e. the excess pore pressures (negative or positive) during q  q  penetration measured behind the tip are a lower proportion o f net tip resistance. This means more increase in q relative to the change in U2. In fine sands and finer soils, ground t  improvement usually decreases U2 indicating either an increased tendency for dilation o f the soil as it passes the shoulder o f the cone or a decreased permeability due to densification (or crushing) resulting in partially drained response during penetration. The typical trends o f the change o f O C R , age and D on C P T U data suggested by r  Robertson (1990) are indicated by arrows on the classification charts i n Figure 2-6 and 2-7 (also shown on Figures 6-4 to 6-6). The arrows suggest that increases i n O C R and ageing increase q and Rf whereas an increase in density increases q but decreases Rf. It is interesting t  t  to compare these trends with the effect o f compaction on C P T U parameters. For fine-grained soils that plot originally as Zone 2 on Figures 6-6-a and Zone 3 on 6-6-b, the post-densification results on Figure 6-6-b suggest that the soils have become normally consolidated due to ground treatment. O n Figure 6-6-c, the vectors suggest an increase in O C R for these points. For coarser soils, the vectors that start i n zones 8, 9 (silty sands to sand) moved in a direction indicating an increase in both O C R and D . r  6.2.3.1  Effect o f compaction on soil classification by C P T  The soil type is not expected to change after vibro-replacement. However, from Figure 6-6 it can be observed that vibro-replacement changes the position o f the soil on the classification charts and, in some cases, the soil behaviour type ( S B T ) assigned to the soil changes. This change seems to be larger i n fine grained material. These data confirm that the classification chart does not uniquely define the soil type. This reinforces the notion that the classification represents a Soil Behaviour Type rather than identifying the soil type as defined by gradation. Ground improvement changes the soil response to cone penetration, i.e. changes the soil behaviour type.  203  The effect o f compaction on classification may also be presented by its effect on the I  c  value (Equation 2-3). Figure 6-7 presents the data shown i n Figure 6-6 in terms o f their preand post-compaction I values. The data points fall below the 45 degree line which indicates c  that post-I is generally smaller than pre-I . In other words, the post-compaction soil appears c  c  coarser grained with lower fines content. 6.2.3.2  Effect o f compaction on estimation o f apparent fines content  Figure 6-8 compares the pre- and post-compaction apparent fines content interpreted from the C P T using Equation 2-6. Note that the data points fall below the 45 degree. The figure indicates that post-compaction apparent fines contents  are smaller than those before  compaction, while the fines content in reality should not change during ground improvement. The apparent fines content is not only a function o f soil type but also a function o f soil conditions. Changes i n soil conditions change the apparent fines content. This has implications for the interpretation o f C P T for apparent fines content and cyclic resistance ratio, C R R . 6.2.4  Effect of changes in soil conditions on classification by C P T in Calibration chamber tests The field observations after vibro-replacement showed that q increased but Rf appeared c  to exhibit no general trends. It is not known whether the direction o f these vectors on the classification chart has a random nature or whether it can be related to the changes o f ground condition during compaction. The observations based on the pre- and post-compaction database suffer from a number o f uncertainties but predominantly from the effect o f site variability. Site variability includes the natural variability and that caused by variation o f compaction energy as a function o f radial distance from the compaction point. The inclusion o f stiffer stone columns in the ground also increases the heterogeneity. This makes the result o f post-compaction C P T sensitive to the location o f the test hole. It is not always certain that the post compaction holes are put down exactly at the compaction grid centroids. In order to eliminate the effects o f site variability and to allow separation o f the individual parameters D , a'h and o' , the data from calibration chamber ( C C ) testing on Ticino r  v  sand (Lunne et al. 1997) w i l l be used to confirm and explain the observed changes in soil  204  response in the field i n attempt to answer the following questions for the idealized conditions in chamber testing: •  D o changes i n boundary conditions change the position o f the soil on the classification chart?  •  Is the direction o f changes on classification charts diagnostic o f the changes i n soil conditions?  The advantage o f C C data is that it is obtained under controlled conditions. The C C database is used here i n the context o f ground improvement, i n which the soil condition changes without any change i n soil type. To remove unnecessary complications, C C data with the following conditions were selected: •  Sand type= Ticino sand  •  Diameter o f the cone = 35.7 m m (10-cm cone tip)  •  Diameter o f chamber = 1.20 m  •  Boundary condition = B C 1 (constant lateral and vertical stress at the boundary o f the  2  chamber 150 published data points are used in this section. These data cover the following range of soil properties. from  D (%): r  18  to  96  cjv(kPa):  from  40  to  715  cjh(kPa):  from  16  to  330  OCR(-):  from  1  to  8  The effect o f the boundary condition on q has been studied (e.g. Kulhawy and Mayne c  1990, Salgado et al., 1998) but the effect on the sleeve friction has not been studied to the knowledge o f the author. Cone tip resistance is corrected for chamber size effect by the following expression suggested by K u l h a w y and Mayne (1990). N o correction for chamber size effect has been applied to sleeve friction.  1 c-con-reefed  tfic-measwed '\  70  -i-0.005.Z),.  x  D,chamber D.cone  -1  Equation 6-1  205  Figure 6-9 shows the C C data on classification charts categorized for N C and O C soil. A s may be observed, the data points plot in the sand to silty sand S B T zones on both classification charts. 6.2.4.1  Normally consolidated zone  Figure 6-9 shows that the N C data fall either in the N C zone or on the under-consolidated side similar to field observation. A similar trend was also observed in N C Fraser River sand field data (Figure 6-4a). Linear normalization for stress level was noted to be a potential reason for this scatter o f the data out o f N C zone. This could be checked by C C data in which the actual stress condition is known. Figure 6-10 has the same N C data shown in Figure 6-9 but normalized to the ( o ' )  0 5  v  instead o f normalization to  (o'v) . 1  It may be observed that even a more appropriate  normalization does not reduce the scatter o f data. It seems that the N C zone should be rotated and expanded to encompass the data. The N C zone in the C P T classification chart suggested by Jefferies and Davies (1993) also suggests a more curved N C zone (Figure 6-11). Their N C zone is over-plotted on the Robertson (1990) classification chart for comparison (Figure 6-12). Note that the vertical axis on the Jefferies and Davies (1993) chart has also a pore pressure term (1-B ), which is almost zero for sand. q  The bulk o f O C sands data plots mainly in the N C zone. In spite o f relatively high O C R values (up to almost 8), very few data points plot in the O C zone. The following factors could contribute to the scatter o f the C C data. Different batches o f Ticino sands and equipment used in C C tests cause some inconsistency. The sand in C C tests is generally considered to be fresh (not aged). However, ageing in the range o f hours could have some effect on the results. N o correction has been used for sleeve friction. In addition, the logarithmic scale tends to magnify the scatter o f the data at small range o f values o f friction ratio. 6.2.4.2  Effect o f changes in ground conditions on the direction o f movement on the classification chart  Arrows in Figures 2-8 and 2-9 show the tentative trends o f the effect o f D ' O C R and r  ageing on the position o f soil on classification chart suggested by Robertson (1986 and 1990). For example in Figure 2-8, an increase i n D increases q but decreases Rf and an increase in r  t  206  O C R , increases q and Rf. It is not known how these trends were obtained. There is no doubt t  that increases i n all these parameters increases q . What is not clear is the effect o f changes o f t  sand properties on Rf or F. The objective o f this section is to find out i f the observed changes in Rf are diagnostic o f the changes i n soil conditions. To answer this question, C C data w i l l be used to examine the suggested trends in Figures 2-8 and 2-9. Figure 6-13 shows the change o f position on the classification chart due to a change o f only D , while all the other soil conditions are kept constant. Each pair o f data represents r  identical soil stress conditions but different densities. The higher density is marked by a triangular symbol. It may be observed that the increase in density can change the soil behaviour type, by one or even two zones towards coarser material in the non-normalized chart and by one zone i n the normalized chart.. The normalized chart has larger zones and hence a lower sensitivity to changes i n soil condition. Figure 6-14 shows the effect o f an increase in D on Rf. The data suggests a very weak r  correlation with a slight trend o f increase in Rf with increased D . However, the data are too r  scattered and the results may be considered inconclusive. Figure 6-15 shows the correlation between horizontal stress and Rf. The trend is still weak and data are very scattered. Figure 6-16 suggests that O C R alone has little effect on Rf. This conclusion is contrary to the trend in the classification chart which suggests an increase i n Rf. The  apparent  contradiction can be explained as follows. In the field, the O C R is always associated with an increase in Oh and it is not possible to separate the effect lateral stress and O C R . In C C test data, it is possible to separate the effect o f O C R alone by keeping Oh constant. It may be concluded that the effect o f O C R in the field is mainly through its associated increased lateral stress. The minimal effect o f O C R is not only for Rf. Houlsby and Hitchmann (1988) also observed the same trend between O C R and q in C C test. They noted that the main factor affecting q was Oh c  c  and that O C R alone had minimal effect on q . t  The effect o f ageing cannot be investigated based on C C test results. Therefore, the trend suggested by Robertson (1990) which suggests that an increase in ageing increases friction ratio cannot be evaluated. However, the contrary may be speculated as follows. Ageing increases the tip resistance, but may not increase the sleeve friction by the same amount. The  207  friction sleeve passes through the soil which is already disturbed by passage o f the cone tip and to a large extent has lost its ageing effect. Therefore, ageing is expected to increase q more c  than sleeve friction and thus results in a decrease in Rf. More field data with a large contrast o f ageing is needed to confirm the trend. Based on the finding o f this section, it may be concluded that the scatter o f data is too great to draw any reliable conclusion from the direction o f movements o f ground improvement vectors on classification charts. The change o f Rf is not diagnostic o f changes in soil conditions. 6.2.4.3  Effect o f changes o f D and lateral stress on I value r  c  Increases in D , ah or O C R increase Q but their effect on F is somewhat random. A n r  increase in F alone increases I while an increase in Q alone decreases I . Figure 6-17 shows c  c  the effect o f ah on I for different ranges o f D obtained from C C tests on O C sand. Note that a c  r  v  is constant for all the data (a' =T 10 kPa). The data suggests that an increase in either D or ah or v  r  any combination decreases I . This confirms the trend o f changes o f I after vibro-replacement c  c  observed from field data. 6.2.4.4  Conclusions  The main conclusions from calibration chamber test results on classification by C P T are: •  Calibration chamber tests confirmed that S B T zoning on C P T classification charts is not a function o f only soil type but also soil conditions.  •  Increase in density and stress level always increases q and f but the change in Rf t  s  does not seem to have a clear trend. •  Calibration chamber tests showed very weak correlations between Rf and soil conditions such as D , a and O C R . Rf is not diagnostic o f soil conditions and changes r  h  in Rf may not be related to changes o f soil condition. •  The trends suggested on Robertson and Campanella (1986) and Robertson (1990) classification charts between Rf and soil conditions, i.e. D , a , O C R or ageing, could r  not be confirmed based on calibration chamber test results.  208  n  6.3  ACHIEVABLE  PENETRATION  RESISTANCE  AFTER  VIBRO-REPLACEMENT When specifying target penetration resistance values for ground improvement, many contractual disputes could be avoided i f it were possible to have a reliable assessment o f the penetration resistance that is achievable in the prevailing soil conditions. A n estimation o f the achievable penetration resistance helps the geotechnical engineer to avoid unreasonable specifications and choose an appropriate ground improvement method for the required performance. It also helps the contractors to pick the appropriate spacing o f compaction points. Our local database is examined for possible trends. To  minimize  the  inconsistencies due  to  different  vibrators  and construction  methodologies, post-compaction data from only one contractor, Geopac West L t d , are used here. The post-compaction data are for triangular patterns o f compaction points with spacings o f 2.75 m and 3.0 m. These were the most common spacings used in the projects reviewed. V-23 vibroflots were used for all the cases. Figure 6-18 shows the post-q i versus pre-q i where q i is the tip resistance normalized c  c  c  to vertical effective stress as defined below:  =  I  •  V-S  Equation 6-2  where, q is the cone tip resistance, a ' c  v  is the vertical effective stress and P is the a  atmospheric pressure in the same units as a ' . The majority o f the data are i n sandy layers with v  a few data points in sandy silt or silt. The reason for this gap i n the database is that most silty sand or sandy silt layers encountered at the location o f tested holes were thin interbedded layers and thus were excluded from this database. It may be observed from Figure 6-18, that the majority o f the data points are above the 1:1 line which means that an improvement in tip resistance was achieved. For the sake o f comparison, these trend lines are compared with the correlations developed by Baez (1995) based on 10 vibro-stone column sites in United States. H e developed a correlation between the pre and post normalized tip resistances based on the pre-compaction friction ratio and replacement ratio. Replacement ratio is the ratio o f the area o f stone column cross section to  209  the tributary area o f the each stone column. Those projects were a m i x o f bottom feed and top feed methods and the grid patterns were triangular or rectangular. The vibrator in his study was a Keller " S " vibrator operating at 30Hz, with a 20 ton centrifugal force and 165 hp (125 k W ) electrical motor. Correlations suggested by Baez for pre-Rf<l and equivalent spacing o f 2.75 and 3 m are plotted for comparison (broken lines). In order to find an equivalent spacing for Baez's correlation, 0.9m diameter and a triangular pattern for his stone columns are assumed. It should be noted that the equivalent spacing is sensitive to the assumed diameter o f stone columns and grid pattern. For example a replacement ratio o f 6.4% in a triangular pattern is equivalent to a spacing o f 2.75 ( i f stone column diameter is 0.75m) or to a spacing o f 3.7m ( i f the diameter o f stone column is 1.0m). Therefore, quantitative comparison may not be possible. However, it may be observed that trends are generally similar. A curved trend line suggests that the relative improvement in tip resistance is greater for lower initial tip resistance and that there would not be much improvement i f the initial tip resistance is very high. Another presentation o f densification results would be to correlate the post-compaction tip resistance to soil type i.e. grain size distribution or fines content. This would be similar to Figure 6-20 by Saito (1977) which shows the pre- and post-compaction penetration resistance vs the fines content. Since the gradation or fines content are not available for the database in this study, the tip resistance is plotted versus the pre-I values. Pre-I should include the c  c  information o f the soil type/fines content. Figure 6-21 shows the results o f pre- and post-compaction normalized tip resistance versus pre-I . It may be observed that the fitted lines c  follow the general trends well and the regression numbers are reasonably high. It should be noted that the relationship observed applies only to sites and construction conditions that are compatible with the database, i.e. sites in Richmond, B C densified using V 2 3 vibrators using Geopac operators with columns installed at spacings o f either 2.75 m or 3 m. Again, it may be observed that the number o f data points in the I range from 2 to 2.5 c  (silty sand to sandy silt) is scarce. The results suggest that the compaction effect is not significant for I values greater than about 2.3. Using Robertson and Fear's (1995) correlation, c  I =2.3 is equivalent to about 20% fines content, which is also in accord with Mitchell's (1981) c  suggestion for the upper limit o f compactability. Data suggests an average o f 50% increase in the normalized tip resistance is possiblefor a grid spacing o f 3. The improvement significantly  210  increases where the spacing is reduced to 2.75ih. More data are needed to confirm the correlations for 2.75m spacing. A l s o , more local data i n silty sand/sandy silt is required to fill the gap i n the database  6.4  S U M M A R Y AND CONCLUSIONS In this chapter, a database o f C P T results before and after vibro-replacement in the  Lower Mainland, B C and the trends o f changes o f tip resistance, q , sleeve friction, f , friction t  s  ratio, Rf, and dynamic pore pressure, U2 were presented. The main conclusions from this chapter are as follows: •  Vibro-replacement changes the soil conditions, which in turn changes the soil response to the C P T U .  •  Vibro-replacement generally increases q but the changes in Rf do not suggest a t  definitive trend. •  The changes i n q and Rf after ground improvement change the position o f the soil on t  the classification chart and indicate an apparent change in S B T (soil behaviour type). •  S B T interpreted by C P T U results is not only a function o f soil type but also a function o f soil conditions. This was observed from both our field data and calibration chamber data by others.  •  The soil after compaction on C P T classification charts appears to be coarser and cleaner (less fines content).  •  Ground improvement decreases the "apparent fines content" interpreted from the C P T . This has implications in the assessment o f the liquefaction potential based on post-compaction C P T results.  •  Calibration chamber data shows weak correlation between the changes in soil conditions (i.e. changes in D , stress level or ageing) and changes in Rf. r  A correlation o f achievable normalized cone tip resistance after vibro-replacement is developed for Fraser River sands for two stone column spacing o f 3m and 2.75m. This can be used as guidance during specification o f ground improvement by vibro-replacement for ground conditions, equipment and contractors that are compatible with the cases in the  211  database. Post-compaction tip resistance was found to have a strong correlation with pre-compaction tip resistance and pre-compaction I value. c  212  10,000 years ago  5,000 years ago  Envelope of majority of projects used in this thesis  Figure 6-1  History of the growth of the Fraser River Delta  (Source: CGS, http://sts.gsc.nrcan.gcca/geoscape/vancouver/fraser3.asp)  Clayey SILT- (-3 to 6m)  Interbedded silty SAND/sandy SILT (~2m)  Clean S A N D to silty Sand (~15-20m)  Silty C L A Y / Clayey SILT  Figure 6-2  Typical soil profile in Richmond, B C (not to scale)  213  the  Figure 6-3 Typical S C P T profiles before and after Vibro-Replacement (after Howie et al. 2000)  214  Figure 6-4 C P T test results before vibro-replacement (natural ground) from the local database plotted on classification charts (all sites). For C P T classification zones see Figures 2-6 & 2-7.  Figure 6-5  C P T test results after vibro-replacement from the local database plotted on  classification charts (all sites). For C P T classification zones see Figures 2-6 & 2-7  215  0  1  2  3  4  5  6  7  8  Friction Ratio, R (%) f  0  1  10  Normalized Friction Ratio, F (%)  Figure 6-6  Path of movement of the position on the classification charts due to vibro-replacement 216  3.5  3.0  .2  2  5  o  CO CL  E  8 2.0 o 0. 1.5  1.0 1.0  1.5  2.0  2.5  3.0  3.5  Pre-compaction Ic  Figure 6-7- Comparison of pre-I and post-I values c  c  20  F C ( % ) = 1.75-/c C° 15 O LL  c o CL  At  E o o I  to r£  J»  5  <t 2t  4,  • * 0  5  10  15  20  Pre-compaction FC (%)  Figure 6-8  Comparison of pre- and post apparent fines content interpreted from C P T  217  Over Consolidated  Normally Consolidated  1000  1000  100  (bars)  1000  1000 * ^^^^ *  A  100  100  0.1  10  Fr(%)  Figure 6-9  Calibration chamber data for Ticino sand plotted on C P T classification  charts- (Left) N C Ticino sand, (Right) O C Ticino sand , (Top) Classification chart (Robertson et al. 1986), (Bottom) Normalized classification chart, (Robertson 1990)  218  F (%) r  Figure 6-10 Results of calibration chamber data for N C Ticino sand on normalized classification chart using true normalization for stress level  219  11 0.1  1  1—I  I I 1111  I  I  I I I I [ 11  1.0  10  F(%)  Zone  Soil Behaviour Type  6  Clean sand to silty sand  5  Sand mixtures- silty sand to sandy silt  4  Silt mixtures- clayey silt to silty clay  3  Clays- clay to silty clay  2  Organic soils- peat  Figure 6-11 CPT-based soil classification chart proposed by Jefferies and Davies (1993)  220  1000  c- * —vV«  \  V.  %  100  / \ /  9  Jefferies and Davies (1993) N C  o  zone (approximate) 10  '  <^ ^^f  J  <  1  1  1  1  1—i—i—rn  *—i  0.1  1  1  1  1—i—i—v  10  F (%) Figure 6-12 Comparison of normally consolidated zones by Robertson (1990) and by Jefferies and Davies (1993)- Data points from calibration chamber data for N C Ticino sand.  221  0.0  1.0  2.0  3.0  4.0  5.0  Friction Ratio (%), R  0.1  6.0  7.0  8.0  f  1.0 Normalized Friction Ratio, F  10.0 r  Figure 6-13 Effect of changes in only D on C P T classification chart, data taken from r  calibration chamber testing on Ticino sand.  222  60  80  120  100  Relative Density (%)  Figure 6-14  Effect of D on R , Ticino sand, data taken from calibration chamber r  f  testing on Ticino sand.  •  •  •  0.8  T „ •  0.6  • •  0.4  •  *  •  •  ^^_>rrrrrzL.  • • •  0.2  \  •  • •  **  •  •* T • 1 «  « •  • •  ^ —  «» ____ #.?  -  -— •  •  •  •  • •  . •  50  100  1 50  200  250  Horizontal Stress (kPa)  gure 6-15  Effect of the horizontal stress on Rf, data taken form calibration chamber testing on Ticino sand. 223  0.9  8  12  10  14  16  18  OCR  Figure 6-16  Effect of O C R on Rf, data taken from calibration chamber testing on Ticino sand.  r»  — c - 7 0 /  "r  -"  . '••  °\- °  ises D increj  Q  r  o  I  c  n -7fi /O  1.60  U  r  A  OO/o  A  4  A  D =90-92°/T r  1.20  0  100  CT'  h  200  (kPa)  Figure 6-17 Effect of the increase in D and/or a \ on I - from C C testing data on N C r  c  Ticino sand  224  300 A • A •A • A  250  -A  « 200 ro  A  A  **SMf A  100  A  A  A A,-'  i  150 £  A  A A M  A " A A.-  • post- 2.75m spacing A post- 3.0 m spacing  50  50  100  150 Pre-q  c1  200  250  300  (bars)  Figure 6-18 Normalized tip resistance before and after vibro-replacement, triangular grid, Lower Mainland, B C .  Note: C P T results after vibro-replacement are heavily dependent on the construction methodology, equipment and soil conditions. Above correlations should be used with caution.  225  Spacing=2.75m  0 •> 0  1  50  1  100  1  !  i  150  200  250  Pre-q  c1  (bars)  1  300  Figure 6-19 Comparison of the normalized tip resistance before and after vibro-replacement, Lower Mainland, B C with Baez (1995) correlation  Note: C P T results after vibro-replacement are heavily dependent on the construction methodology, equipment and soil conditions. Above correlations should be used with caution.  226  Figure 6-20 Effect of fines content on the achievable penetration resistance after compaction by vibro-rod method (from Saito 1977)  227  Figure 6-21 Achievable normalized tip resistance as a function of pre-compaction I . c  (triangular grid, Lower Mainland, B C , only Geopac sites)  Note: C P T results after vibro-replacement are heavily dependent on the construction methodology, equipment and soil conditions. Above correlations should be used with caution.  228  C H A P T E R 7 E F F E C T O F A G E I N G O N INTERPRETATION O F SCPT D A T A  A n overall review o f ageing followed by 3 case studies carried out during this research w i l l be presented in this chapter. The effects o f ageing on the interpretation o f soil properties from the post-densification S C P T results are discussed.  7.1  BACKGROUND Ageing is the change in soil properties with time after deposition or disturbance under  constant effective stress. In the past 50 years, it was found that soil properties/response can change over engineering time i n the range o f weeks to years. More recent laboratory studies (Howie et al. 2002) have shown that the time effect in the range o f minutes could also be significant. The early studies o f ageing were more focused on cohesive soils (Leonards and Ramiah, 1959). Within the past 20 years, it has been realized that the ageing effect in sand is also important. Most o f the evidence on ageing o f granular soils has come from quality control testing, mainly by penetration testing, o f densified ground or placed fills. The first published data in sand was after ground densification by vibroflotation and blast densification i n Jebba Dam by Mitchell and Solymar (1984). Since then many cases have been reported on the ageing in sand based on in situ testing (e.g. Skempton, 1986; Schmertmann 1986, Jamiolkowski et al., 1988; Baez et al. 2003) and also laboratory testing (e.g. A f i f i and Woods, 1971; Anderson and Stokoe, 1978; Daramola, 1980; Mesri et al. 1990; Baxter, 1999; Howie et al., 2001 & 2002). Ageing can be divided into two groups, geological and engineering ageing. The former is the ageing effect over the age o f the deposit since deposition and could be in the range o f hundreds to thousands o f years or more. The latter is the changes over a shorter period after disturbance o f the ground in the range o f days to years. For a more detailed review o f ageing in sands, refer to Baxter (1999).  229  7.1.1  Mechanism of ageing The mechanism o f ageing is not well understood. In general, there are two main  suggested mechanisms, chemical and mechanical. Some researchers (e.g. Mitchell and Solymar, 1 9 8 4 ) attributed the ageing to cementation at the contact points between grains due to the formation o f silica acid gel films on particle surfaces and the precipitation o f silica or other materials from solution or suspension. Some researchers (Mesri et al., 1 9 9 0 ; Schmertmann, 1 9 9 1 ; Kuhn, 1 9 8 7 ) attributed ageing to particle rearrangement macro-interlocking  of  particles  and  micro-interlocking o f  resulting in a greater  surface  roughness,  and  consequently, greater frictional resistance. It seems likely that both mechanisms w i l l contribute to the effects o f ageing. 7.1.2  Effect of ageing on small strain soil properties Based on resonant column tests on sand, silt and clay, A f i f i and Woods  showed  (1971)  that the small strain shear modulus increased linearly with the logarithm o f time (Figure 7 - 1 ) . This can be expressed by the following expression  Equation 7-1  t °max  \fp)  where t is the time to the end o f primary compression, t is any time greater than t , G p  G  m a x  p  at time t, G  m a x  ( t ) is G p  m a x  max  ( t ) is  at time t . The reference time, t , is usually taken as 1 0 0 0 p  p  minutes. N Q is a coefficient that can be found from monitoring the increase in stiffness with time. N G values were found to be between 1 and 1 2 % with a typical value o f 2 % as shown in Table  7-1.  Based on bender element tests, Baxter  (1999)  found  NG  values less than  4%  and  showed that N G was influenced by sand type, pore fluid and density, but did not find any obvious effect from temperature. Fahey  (1998)  between the G  m a x  noted that the reported  NG  values could not explain the  100%  o f undisturbed and disturbed samples presented by Ishihara  difference  (1996).  This  refers to the results o f torsional cyclic testing conducted by Katayama et al. ( 1 9 8 6 ) on samples recovered by in situ freezing techniques from a dense sandy deposit (Figure 7 - 2 ) . The tests were repeated for the same sand reconstituted to the same void ratio. Fahey for an N G value o f 2 % , the undisturbed soil must have been 1 0  230  4 7  (1998)  showed that  years old and concluded that  either the N G value was too small or something else was going on within the sample such as cementation. 7.1.3  Effect of ageing on stress-strain behaviour of sand Daramola (1980) studied the effects o f ageing on the stiffness o f dense H a m River sand  in conventional triaxial testing. The stiffness was observed to be a function o f relative density, D , for fresh samples. For aged samples, time was observed to have a great influence on r  stiffness and D was not the main factor controlling stress-strain response. Secant stiffness at r  strains less than 0.5% increased by 100% over three log cycles o f time. Shozen (2001) and L a m (2003) studied the effect o f ageing periods o f up to 10,000 minutes on the stress-strain response o f very loose Fraser River sand. A period o f ageing resulted in a much stiffer response during the initial portion o f the stress-strain curve but the effect o f ageing tended to disappear after increments o f axial strain o f about 0.05%.  The  curves coincided beyond the initial stages o f loading. Figure 7-3 shows the results for ageing times o f up to 1000 minutes after consolidation at a stress ratio o f a'i/a 3=2.0 (Howie et al. r  2001). The following are observed in the figure: •  Ageing increases the stiffness at medium or small range o f strain (smaller than approximately 0.1 %)  •  Ageing does not affect the large strain stiffness and strength.  •  Shear strain reduces or removes effects o f ageing.  Resolution o f the strain measurement apparatus was not considered reliable for shear strains below about 0.02% and so the effect o f ageing on G  m a x  was not studied. The data suggest that  ageing increases initial stiffness but has little effect on larger strain properties, including shear strength. Figure 7-4 presented by Ishihara (1996) compares the shape o f the shear modulus reduction curves for undisturbed samples, obtained by in situ freezing and block sampling, and reconstituted samples for dense sand. The undisturbed samples represent aged sand. From these tests, a correction factor is proposed to obtain the variation o f stiffness versus shear strain for i n situ sand from that obtained from laboratory tests (Figure 7-5). Ishihara (1996) suggests that the stress-strain curve obtained from laboratory testing could be corrected by the C factor r  231  in Figure 7-5 to obtain the in situ stress-strain curve. It may be observed that C troughs at r  medium strain range. 7.1.4  Effect of ageing on cone tip resistance Table 7-2 shows some o f the references and their main findings regarding the time effect  on C P T . Charlie et al. (1992) compiled some penetration resistance data after ground improvement from a number o f cases and noted a marked difference i n the rate o f increase in q  t  (Figure 7-6). They argued that the rate was temperature dependent. There have also been some cases where q has decreased shortly after blast densification t  and then increased with time (e.g. Mitchell and Solymar 1984) or never reached the pre-densification value (e.g. Thomann, 1990). The drop o f q was despite a large ground t  settlement due to the blast, signifying an obvious increase in density. 7.1.5  Mechanism of the effect of ageing on S C P T Laboratory testing shows that ageing affects the soil stiffness at small to medium range  but has almost no effect at large strains. Thus shear wave velocity should be sensitive to ageing. Penetration testing induces large strain to the soil. However, it is a function o f both small strain and large strain soil properties. In the plastic zone around the cone tip, the large strains are expected to remove the ageing effect. Beyond this zone, a partial or full effect o f the ageing exists, which increases the confinement around the plastic zone and increases the tip resistance. Due to partial removal o f the ageing effect during cone penetration, it is expected that the shear wave velocity may be more sensitive to the ageing effect than tip resistance. This makes the seismic cone a very useful tool to study the ageing phenomenon. The S C P T can reveal the time dependent behaviour o f the soil in two ways; a gradual increase o f soil q and V t  s  with time after disturbance and a sudden drop o f q and V after disturbance o f aged soil. t  7.1.6  s  Effect of ageing on liquefaction resistance Seed (1979) conducted cyclic triaxial tests on Monterey sand o f about 50% relative  density and found an increase in liquefaction resistance o f 12 and 2 5 % for sands aged for 10 and 100 days, respectively (Figure 7-7). He also compared the resistance to liquefaction o f some undisturbed and reconstituted samples which are plotted in the same figure. He  232  concluded that the liquefaction resistance o f natural deposits might be as high as 75% greater than that o f freshly reconstituted samples in the lab. Ishihara (1985) compared the cyclic shear resistance o f undisturbed samples o f Niigata sand obtained from large diameter sampler and reconstituted samples. The results showed that the undisturbed samples had consistently greater cyclic shear resistance. Y o s h i m i et al. (1989) compared the liquefaction resistance o f undisturbed samples taken from in situ sand deposits with samples taken from the sand in a large bin (4m x 6m x 5m) freshly deposited under water. In both cases, the samples were recovered using i n situ freezing techniques. They found that the liquefaction resistance o f in situ samples were almost twice as much as freshly deposited samples. Based on this work, Ishihara (1996) concluded that the cyclic shear resistance o f in situ deposits is greatly dependent on ageing and fabric o f sand. H e recommended high-quality undisturbed samples to evaluate the actual performance o f i n situ deposits. Arango and Migues (1996) studied the liquefaction resistance o f sand deposits older than 10,000 years. They compared the liquefaction resistance o f the undisturbed samples from in situ freezing with those obtained from the Seed et al. (1984) liquefaction chart which is based on Holocene sand deposits younger than 10,000 years. Figure 7-8 shows that the measured cyclic strength o f the old deposits was up to 3 times greater than those determined by empirical method. This implies that the ageing has increased the liquefaction resistance more than the SPT blow counts. In other words, the Seed's chart underestimates the C R R value for deposits older than Holocene. This also implies that ageing alters the correlation between penetration resistance and C R R . In contradiction to the above, V a i d and Sivathayalan (2000) found that the undrained behaviour o f the undisturbed samples taken from a deposit as old as about 4000 years old obtained by in situ freezing was almost identical to that o f reconstituted samples prepared by water pluviation technique (Figure 7-9). It is not known whether this was due to sample disturbance or due to the negligible ageing effect in this case. 7.1.7  Evidence of the geological ageing  For geologically aged sands, such as those in the Fraser River delta, both V and q should be s  t  higher than for recent fills at a similar density. Monahan et al. (2000) used carbon dating o f  233  organics in Fraser River sands to estimate the age o f the deposits. The data suggest a linear increase in q i (see Equation 6-2 for definition) with age in Fraser River sand, as shown i n c  Figure 7-10. The scatter in the data is likely due to other factors such as variation o f density, grains size, etc. Robertson et al. (1995) found a linear trend between the normalized shear wave velocity, V i and the logarithm o f the age o f deposits from some o f the C A N L E X project sites (Figure s  7-11). V i defined as follows: s  v  ''p. A  = v si  Y  y  Equation 7-2  s  where a ' and P are already defined.. v  a  Wride et al. (2000) plotted the in-situ test data normalized for stress level and relative density (obtained from frozen samples) from six sites investigated during the Canadian Liquefaction Experiment ( C A N L E X ) project and from Duncan Dam. The presented data shows a clear increasing trend with age (Figure 7-12).  7.2  C A S E STUDIES During this research, 3 case studies related to ageing were performed at the following  sites: •  Arthur Laing Bridge site, before and after Vibro-replacement  •  Massey Tunnel site, before and after blast liquefaction test  •  K i d d 2 site, time effect on seismic testing  Each case study is described separately below. 7.2.1  Arthur Laing Bridge site, vibro-replacement  7.2.1.1  Introduction  This site is located in Richmond, B C . The wet vibro-replacement method with a vibroflot V 2 3 - A G was used to improve the soil around the existing foundation o f a bridge for liquefaction mitigation. The spacing o f the stone columns was 2.75 m arranged in a triangular pattern and the target depth was 12m. The S C P T was conducted by U B C at the centroid o f a 234  triangular pattern before densification, a few days and one year after the completion o f the densification. Pre- and first post-treatment S C P T holes were performed at exactly the same location. The S C P T holes after one year were conducted at a distance less than 2 m from the previous holes in the adjacent centroids o f triangular gird. 7.2.1.2  S C P T results  Figure 7-13 shows the S C P T profiles along with the interpreted soil profile. It may be observed that the densification has significantly improved the penetration resistance, sleeve friction and shear wave velocity in the sandy deposits from 5 to 12m depth. It is interesting to note that the signatures (peaks and troughs) i n the pre-compaction C P T profile are preserved after the post-compaction. If the signatures do not change, they could be attributed to the variation o f the sand type such as grain size, fines content, etc that cause different compactability. The changes in the signatures could be interpreted as initial difference in density removed by densification. Pore pressure response after compaction shows more areas with pore pressure below hydrostatic pressure. Depths o f generation o f negative excess pore pressures coincide with layers o f silt or silty sand/sandy silt. In clean sand layers, the tendency for generation o f negative pore pressure cannot be detected because o f the fast dissipation o f pore pressures. After one year (Post2 in Figure 7-13), a slight increase in q but decrease in V was t  s  observed. N o combination o f changes in D , ah and/or ageing can explain the increase i n q but r  t  decrease in V . This could be attributed to the effect o f heterogeneity (see Chapters 4 and 5) s  and/or site variability. There is little indication o f dramatic increase in stiffness due to ageing for 1 year. Comparison o f another pair o f post-compaction results in the same site (not shown here) indicated no obvious increase after one year. Site variability and uncertainty o f V  s  measurement in the presence o f stone columns can explain such different observations. The soil condition within the grid zone (between the stone columns) varies with distance from the stone columns. This variability makes q sensitive to the location o f the hole. Sensitivity o f q to t  t  the location o f cone hole makes the study o f ageing after vibro-replacement very uncertain. Although no strong indication o f ageing is observed after compaction, the destructuring (disturbance) effect o f the vibro-replacement below the target depth (tip o f the stone columns) is clear from the post-compaction V . s  235  It is speculated that stress relaxation may also occur over time after vibro-replacement. Stress relaxation reduces the locked i n residual lateral stresses caused by vibro-replacement. Therefore, the observed time effect on S C P T results could be the sum o f opposite effects o f ageing and stress relaxation. 7.2.1.3  Conclusions  •  The effect o f ageing was not observed clearly.  •  Destructuring effect o f compaction was apparent from reduction o f the V below the s  densification depth. •  Site variability makes it difficult to draw a definitive conclusion whether or not ageing occurs.  • 7.2.2  Stress relaxation may reduce or counterbalance the effect o f ageing with time. Massey Tunnel site, blast liquefaction test  7.2.2.1  Introduction  In a well characterized research site in Ladner, B C called Massey tunnel (Wride et al. 2000), a series o f blast-liquefaction tests were performed (Gohl, 2002; Rollins and Anderson, 2003). These experiments were conducted to evaluate the efficiency o f vertical drains on reduction o f the liquefaction potential. Blasts were used to simulate earthquake shaking. In one o f the experiments, which is the focus o f this case study, 12 cm diameter vertical drains were installed in the ground in a triangular grid pattern at a spacing o f about 1.2m. The drains were installed by a vibrating pipe to a depth o f about 12.7 m. A n attempt was made to minimize the vibration and the consequent densification during the installation. After installation o f drains, four explosive charges were detonated i n each o f four holes located at 90 degree intervals around a circle with a radius o f 5 m as shown in Figure 7-14. In each hole, charges were centered at depths o f approximately 5, 8, 11 and 14m. A maximum settlement o f 10 cm was observed after installation. Shortly after the blast, a large amount o f water gushed out o f the drains and resulted in some settlement. A total settlement o f about 40 cm was measured (including the settlement during the installation). In a similar experiment without vertical drains, close to this area, another test blast was conducted which generated about 50 cm settlement at the centre with the settlement profile as shown in Figure 7-15. Settlements were  236  measured at ground surface and at different depths. It may be observed that 85% o f the settlement occurred above 14m depth, the depth o f the lowest explosive charge. 7.2.2.2  S C P T results before and after the blast experiment  To investigate the time effect on q and V after the blast, a series o f S C P T tests were t  s  conducted by U B C before installation and at different times after blast; 1 day, 8 days, 6 weeks and 10 months. A t each time, a pair o f tests was performed. Figure 7 - 1 6 shows all the C P T profiles. Down-hole seismic tests were conducted at 1 or 0.5 metre intervals i n all the C P T holes. The interval shear wave velocities were obtained by cross-correlation method and are shown in Figure 7-17. 7.2.2.3  Evidence o f ageing/destructuring  The time effect w i l l be investigated i n two layers shown as layer 1, from 7 to 13m and layer 2, from 14 to 18m (Figure 7-16 and 7-17). Note that layer 1 is above the charge depth blasting and layer 2 is below the charge depth. For convenience, the average values over the layers are used to represent the results. Figure 7-18 shows the variation o f average q and V t  s  with time for layers 1 and 2. In layer 1, all the post-q values are greater than the pre-blast values, which is in accord t  with the observed settlement and consequent increase in density o f this layer. Note that except for one point (at day one), the values obtained from the pair o f C P T s at each time are close. The variation o f the average q does not suggest any apparent trend with time. The response o f V t  s  on the other hand is different. Except for one data point, all the post-V values are smaller or s  about the same as the pre-V . Ignoring one data point at day one (shown by an arrow in Figure s  7-18), V remained almost constant or increased very slightly with time. s  It should be noted that site variability and averaging the data could obscure the results. A l s o the effect o f the vertical drains on V measurement has not been considered. Flexible s  vertical drains should slightly reduce the overall stiffness o f the ground. O n the other hand the local densification around the drains during installation has the opposite effect. There is an apparent contradiction between the response o f q and V to blasting. q t  s  t  indicates that the blasting has improved layer 1, whereas V indicates that the blasting caused s  no improvement or even some destructuring effect to the ground. Conventional interpretation of S C P T based on D and ah cannot resolve this contradiction, since no scenario o f the changes r  237  in D and/or o"h can cause an increase i n q and at the same time, no increase or slight decrease r  t  in V . It w i l l be shown that consideration o f ageing/destructuring is required to explain the field s  observation. The blast not only caused densification, but also removed the geological ageing o f the deposit. The post-blast result is the net effect o f densification and destructuring. In the next section, the effect o f each factor w i l l be discussed quantitatively. The other difference observed from the post-blast data is that the results o f q at different times are more scattered, t  whereas the V is quite consistent. It is believed that the seismic test samples a greater volume s  of the ground and so it automatically averages the horizontal variation o f the soil due to different magnitude o f densification around the vertical drains. O n the other hand, it is thought that the tip resistance is more indicative o f the near field zone and thus is sensitive to lateral variation of the location of the cone hole relative to the vertical drains. Although great care was taken to push the cone holes exactly at the centroid o f the grids (triangular drain grids), it cannot be sure that it was the centroid throughout the entire sounding depth. In layer 2, (14-18m), both q and V show a definitive drop o f about 15%. From the t  s  settlement profile, it is concluded that the densification effect in layer 2 is minimal and the main effect is the destructuring effect which removed the geological ageing. This observation is interesting as it suggests that q and V may be equally sensitive to the destructuring. The t  s  drop o f the V is about AV =22m/sec which is equivalent to A V i = 2 0 m/s. This is close to the s  s  s  previous findings at Massey Tunnel by Robertson et al. (1995) (see Figure 7-11). The destructuring effect with minimal densification in layer 2 gives us the opportunity to back calculate the ageing rate, No- The target depth in Massey site during C A N L E X project (8-13m depth) was reported to be 200 years old based on Carbon dating of the organic material (Monahan et al. 1995, Wride et al. 2000). The age o f layer 2 is not exactly known but was reported to be from the same subunit as layer 1 (Monahan et al. 1995). Assuming an age o f about 200 to 1000 years for layer 2, the N  G  value is calculated about 0.055 to 0.050  respectively from Equation 7-1. This value is close to the range that has been obtained in the lab by others as given i n Table 7-1. The back calculated N G ~ 0 . 0 5 estimates a 7% increase in V , 10 months after the blast. s  This is well within the range o f site varibility and could easily be missed by seismic testing and/or interpretation o f data.  238  7.2.2.4  Implication o f ageing/destructuring in estimation o f soil properties  It was noted that blast-densification caused an increase in q and almost no change in V , t  s  which cannot be explained by the conventional site characterization procedures that only consider D  and a ' . The data from this case study w i l l be used to demonstrate that  r  h  consideration o f the geological ageing/destructuring is also necessary to explain this apparent contradiction. Here it is assumed that the area affected by the blast was large enough to make the densification and post-liquefaction consolidation in layer 1 to occur under K<, conditions. Therefore, there should be little change in a'h. This leaves only two other main factors to consider: D and destructuring. In layer 2 with negligible densification, the only remaining r  factor would be destructuring. From this, the effect of destructuring may be evaluated. A s layer 1 and 2 are about the same age, the same destructuring effect is also considered for layer 1. This leaves D as the only unknown. D may be estimated from the actual settlement and its r  r  equivalent q can be obtained from correlation to q . It w i l l be shown that the obtained q is t  t  t  consistent with the field observation. This represents an ideal example o f site characterization after densification i n which all the main factors affecting the penetration resistance are considered. It is assumed that the geological ageing o f layers 1 and 2 are similar and that the 15% drop i n q and V in layer 2 is due to destructuring o f the geological ageing. Assuming that the t  s  blast removed the geological ageing, the equivalent q o f the freshly deposited layer 2 would t  be: qto-fresh  =  50 .(0.85)=42 bars (of the fresh deposit at the same D ) r  The relative density o f layer 2 before the blast is estimated from Baldi et al. (1986) as: Pre-D =29% r  Note that i f the effect o f geological ageing were not considered, the relative density would be estimated as D =36%, which would introduce about 25% error. Note that Massey Tunnel site is r  only 200 years old. The error o f ignoring the geological ageing would be greater i f the deposit was older. Assuming e  m a x  and e j o f about 1.1 and 0.7 respectively for Fraser River sand m  n  (Wride et al. 2000), the void ratio is estimated e=0.98 from the Pre-D =29%. This agrees very r  well to the average e=0.97 obtained from frozen samples (Wride et al. 2000).  239  From the observed settlement, the vertical strain, s  = ver  0 . 0 3 4 , so the D after densification r  is estimated as post-D =46% which is equivalent to a post-q o f 63 bars. The average post-q r  t  t  from the field measurement is 65, which agrees with the estimated value. Based on Equation 4-5, a change o f D from 29% to 46%, increases the G r  m a x  by 30%.  This is equivalent to an increase o f 15% in V . This 15% increase o f V due to increase o f s  s  density is counteracted by the 15% decrease in V due to destructuring effect. The net change s  of V then w i l l be 0%. This agrees well with the field observation in which the shear wave s  velocity did not change after the blast. Although, the result agrees very well to the values obtained from frozen samples, it would be naive to expect a high accuracy in estimation o f the soil properties o f the Fraser River sand from the empirical correlations developed for Ticino sand. Ticino Sand and Fraser River Sand have some differences in mineralogy, range o f void ratios, etc (Lunne et al. 1997). However, for the lack o f a better choice these correlations have been used. 7.2.2.5  Effect o f blasting on G x /qt m a  Figure 7-19 shows the changes in G  m a x  / q after blast densification. In layer 2 with t  minimal change by densification, the main factor is destructuring. A s the result o f destructuring, G  m a x  /q  t  has decreased slightly. This implies that G  m a x  is more sensitive to  destructuring (or ageing) than q . This is in agreement with the observations in the lab, where t  the ageing effect was only observed in small to medium strain range. G  m a x  is only a function o f  small strain soil properties but q is a function of both small strain and large strain (strength) o f t  the soil. Therefore, changes in ageing (small to medium strain range) w i l l have a bigger impact on G  m a x  than q . More data is needed to confirm this in the field. t  In layer 1, in which both densification and destructuring have occurred, G larger drop. This is because an increase in D increases q more than G r  t  m a x  m a x  / q has a t  .  7.2.2.6 Conclusions The main points from this case study: •  Ageing affect after densification was not apparent in this site.  •  The removal o f geological ageing was considerable.  •  The rate o f ageing, N o , obtained from the geological ageing is close to that obtained from the lab by other researchers. 240  •  Site variability can mask the ageing effect.  •  Ignoring the geological ageing causes over-estimation o f the relative density.  •  The apparent contradiction o f increase o f q and no change i n V could be explained t  s  when geological ageing/destructuring was considered. •  B y deducting the geological ageing from the q , the relative density and void ratio t  estimated for the Fraser River sand was found very close to those obtained from undisturbed samples. 7.2.3  Kidd2 site, time effect on seismic testing  7.2.3.1  Introduction  Site variability is a big obstacle for the study o f the ageing i n the field by in situ tests. This is especially a problem after ground improvement methods such as vibro-replacement, which produces a heterogeneous ground mass. It would be ideal to monitor the effect o f time on soil properties with no effect from site variability. The other problem o f using i n situ tests for study o f the ageing in the field is the effect o f in situ test itself on ageing. This stems from the fact that ageing is sensitive to disturbance. Most o f the field data on ageing have come from penetration test results, mainly C P T and S P T . Penetration tests are destructive tests and cause large strains i n the soil. S P T impose some vibration to the ground, which furthers the disturbance effect. One may wonder how much o f the actual ageing is sensed by penetration resistance. A testing program was conducted to investigate the time effect on the shear wave velocity during seismic cone testing. The seismic cone was pushed to a depth and shear wave velocity was measured at different wait times after stoppage. The cone pushing disturbs a zone around the cone and sets the ageing time to zero for this zone. Ageing stiffens up the disturbed zone with time which can be detected by seismic tests. This is similar to the long-term set up o f driven piles in sand, in which the pile shaft friction has been observed to increase with time (e.g. Chow et al. 1998; Axelsson, 2000). The advantage o f such a test is that it does not suffer from any o f the above mentioned problems. Site variability is completely eliminated. Moreover, no disturbance is imposed to the ground after the start o f the ageing process. Seismic tests impose very small shear strains on the soil and hence their destructuring effect  241  would be negligible. Therefore, any change to the soil response with time can be directly attributed to the changes o f soil properties with time. 7.2.3.2  Test procedure  Figure 7-20 is a cone profile from Kidd2 research site in Richmond, B C which has been extensively studied during the research programs at U B C and the C A N L E X project (e.g. Stewart, 1992; Monahan et al. 1995; H o w i e et al. 1999; Wride et al. 2000). T w o soundings were carried out. In the first sounding, pseudo interval seismic tests were performed at 0.5m intervals in Zone 1 (Figure 7-20). A t each depth, the shear beam was struck at 1, 5, 10, 20, 40 and 60 minutes after cone penetration stopped. In the second sounding, conducted 3 m from the first hole, a true interval cone was used i n zone 2 (Figure 7- 20). Seismic tests were conducted at every 5 minutes up to one hour after penetration stopped. Shear wave arrivals were recorded at upper and lower accelerometers simultaneously for each hammer blow. A l l the seismic data were sampled at a frequency o f 20 k H z (50 psec per sample). 7.2.3.3  Test results  Figure 7-21 shows the typical seismic signals obtained by the pseudo-interval method at one depth at different wait times. These signals were windowed for the first complete cycle o f the shear waves. A s the wait time increased, the signals shifted to the left, indicating a shorter travel time. This trend was observed at all test depths. The time shift o f each signal is obtained from the cross-correlation to the signal at 1 minute and is shown in Figure 7-22. The signal shift is significant and increases the interpreted V by 8% in only one hour (Figure 7-23). s  The  decrease in the shear wave travel time with wait time can be explained by  consideration o f the disturbance and ageing effects in the soil affected by the cone penetration. A zone close to the cone w i l l experience disturbance due to the large strains during cone penetration (Figure 7-24). The extent o f the disturbed zone w i l l depend on the strength and stiffness o f the soil before penetration, and the magnitude o f the strains w i l l attenuate with distance from the cone. A s shown earlier, the small strain stiffness o f soil may be substantially reduced by disturbance and w i l l increase with logarithmic time after disturbance. A s a result, the small strain stiffness o f the disturbed zone in Figure 7-24 drops first, due to disturbance, and then begins to increase, due to ageing, immediately after cone penetration ceases. Increase of the stiffness o f the disturbed zone with time results in the observed faster arrival of the shear 242  waves with wait time at any particular depth. The rate o f change in arrival time o f the shear waves with wait time depends on the ageing rate, N o , the radius o f the disturbed zone and the initial contrast o f the stiffness between the disturbed and undisturbed zone. The main conclusion to be emphasized here is that the shear wave velocity is found to be time dependent. This effect is significant even over a short period o f one hour. This is i n accordance with the ageing studies i n the lab on Fraser River Sand by Shozen (2000) and L a m (2002) in which considerable change i n stiffness was found over periods as short as minutes as discussed earlier. This finding has implications for performing seismic cone testing, as discussed in detail by Howie and A m i n i (2004). It was recommended to perform the test at consistent times after the stoppage o f the cone for both the upper and lower intervals. This would offset most o f the time effect from the test results. If both accelerometers at lower and upper interval depths are located in the same deposit, then the radius o f the disturbed zone is approximately the same and the travel lengths and travel time i n the disturbed zone are almost identical (Figure 7-24). Therefore, the interval time, At would be due to the travel time in the undisturbed zone. Calculations based on the idealized configuration shown in Figure 7-24, indicate that the interpreted V would be almost s  identical to V o f undisturbed soil. s  7.2.3.4  Summary and Conclusions  A seismic test procedure is developed to detect the ageing effect on shear wave velocity in the field during seismic cone testing. In this test after stoppage o f penetration o f the cone at a target depth, seismic testing was repeated at different wait times. It was clearly observed that a wait time in the range o f minutes reduced the travel time o f shear waves from the seismic source at the surface to the down-hole seismic receiver. The faster arrival o f shear waves is attributed to the ageing o f the soil in the disturbed zone around the cone. The advantage o f this test is that it clearly shows the time effect and it is not affected by site variability since the tests at different times are carried out without changing the location. The implication o f this finding on the seismic cone testing is that the time between the stoppage o f the penetration and execution o f the seismic test should be kept consistent at different depths. This would offset any time effect occurring during stoppage time.  243  7.3  AGEING EFFECTS AND GROUND I M P R O V E M E N T Ageing can have two main effects on ground improvement design and quality control.  Ground improvement destroys the geological ageing which causes a reduction in the results of in situ tests. In order to achieve the required performance, there should be enough densification and/or increase in confinement to compensate for the destructuring effect and to increase the response to the in situ test. In dynamic compaction and vibro-compaction methods, this is usually achieved due to the repeated application of compaction energy and increase in lateral stress. In blast-densification, the lateral pressure does not change as in the vibro-compaction and thus the loss of geological ageing appears to be more significant. This is why despite a significant settlement and obvious increase in soil density, the penetration resistance could drop below the initial value. The post-blast penetration test results depend on the relative effects of destructuring, densification and ageing. Blast-densification of aged/cemented loose sand is a good example of the relatively high influence of destructuring. Aged soil needs more energy to break the initial interlocking/cementation of the soil and also more compaction effort to compensate for the drop in tip resistance caused by destructuring. It is suspected that the combination of q and V could help identify these cases by giving a relatively high G t  s  m a x  /q  t  compared to the local expectation. It should be noted that a high G m / q could be due to ax  t  compressible or crushable condition too. This is why local experience is important. Extreme cases of aged loose to medium dense deposit could misleadingly show no need for ground improvement. As was mentioned above, G  m a x  /q could be helpful to recognise these t  conditions. This needs more research. Engineering ageing begins after completion of densification and is expected to increase the q . That is why quality control tests are usually carried out after a wait period. The rate of t  this increase is not known and could vary significantly. In some cases, the ageing was monitored and used systematically in the quality control process (e.g. Schmertmann 1986). Mesri et al. (1990) even suggested a method to estimate the q at any time after ground t  improvement based on the test results shortly after. However, ageing is not sufficiently understood to allow such an approach. It should be emphasized that time dependent changes do not always result in an increase in q . Stress-relaxation could reduce the lateral stresses built up during densification. This t  could be more significant for vibro-compaction methods than blast-densification. 244  7.4  EFFECT  OF  AGEING/DESTRUCTURING  ON  INTERPRETATION  OF  P O S T - D E N S I F I C A T I O N SCPT F O R SOIL P R O P E R T I E S  7.4.1  Interpretation of relative density and friction angle It may be argued that removal o f the geological ageing should make the soil conditions  closer to those in calibration chamber. Therefore, it is expected that the post-densification q  t  should result i n a more reliable interpretation o f soil properties. O n the other hand, correlations obtained from calibration tests on Ticino sand are being used by practising engineers in the Lower Mainland to estimate the properties o f the natural (aged) Fraser River Delta sand. It is not known which condition (aged or unaged) gives better results. In any event, geotechnical engineers should know that correlations are affected by ageing/destructuring. The case study provided in Section 7.2.2 showed that for a relatively young deposit i n Massey tunnel, the geological ageing may change the interpreted D by 7% (25% error). The same argument also r  applies to interpreted angle o f friction. 7.4.2  Interpretation of soil stiffness Ideally, i f the i n situ G  m a x  and the shape o f modulus reduction curve are known, one  should be able to obtain shear modulus at any strain level. G  m a x  can be found with a good  approximation from the measured shear wave velocity. Modulus reduction curves are developed in the lab based on reconstituted samples. A s noted by Ishihara (1996), the modulus reduction curve o f in situ soil is different from that o f the reconstituted samples (Figure 7-4). A p p l y i n g the same concepts to the ground improvement, Figure 7-25 schematically shows the effect of ground improvement on the shear modulus. Curve #1 presents the stiffness o f an aged natural deposit. Densification removes the geological ageing o f the ground and reduces the modulus in small to medium range o f strain (curve #2). After completion o f densification and increase in density and stress level, the modulus changes from curve #2 to #3. This curve represents a young densified deposit with higher confining stress. It is expected that time effects change curve #3 to curve #4, which represents an aged densified deposit. Points A and B are the G  m a x  before and after densification, respectively, measured by seismic test. The  post-densification soil may not seem much stiffer than the pre-densification soil mainly because o f the destructuring effect. But note that even i f the post-V is identical to the pre-V s  245  Si  the densified ground has a stiffer response to penetration tests, footing settlement or cyclic loading. This is because the rate o f modulus reduction is smaller for densified soil. For example, using recommendations by Ishihara ( 1 9 9 6 ) in Figure 7 - 5 , a footing with an average shear strain o f 0 . 0 0 2 and identical pre- and p o s t - G  MAX  , should settle 4 0 % less in a young dense  post-densification condition as compared to loose aged pre-densification condition. The p r e - G and post-G are equivalent to G F (field stiffness o f aged soil) and G L (stiffness o f disturbed or reconstituted soil) in Figure 7 - 5 , respectively. 7.4.3  Effect of destructuring on liquefaction cyclic resistance ratio (CRR) of improved ground A t the current state o f the art, it is generally accepted that ageing increases both the  cyclic resistance ratio,CRR, and penetration resistance. However, the effect o f ageing on the relationship between C R R and q cannot be defined quantitatively due to lack o f data. The C R R t  curve (CRR-q ) obtained from liquefied/non-liquefied includes deposits with different ages. t  Limited data from undisturbed sampling in aged sands older than 1 0 , 0 0 0 years (Arango and Migues, 1 9 9 6 ) , suggests that ageing increases the cyclic resistance more than it increases the S P T blow counts. In other words, increased S P T blow counts due to ageing do not reflect the magnitude o f increase in C R R . Therefore it is likely that S P T i n very old sand underestimates its C R R . Conversely, this implies that destructuring o f very old sand by densification may have a more detrimental effect on C R R than what is reflected by the reduced SPT. It is not known whether or not this trend could be extended to q as well. t  The results o f two studies based on penetration resistance and undisturbed i n situ frozen sampling suggest that the correlation between the penetration resistance and C R R remains unchanged before and after densification by sand compaction piles (Tokimatsu et al. 1 9 9 0 and Okamura et al. 2 0 0 3 ) .  Tokimatsu et al. ( 1 9 9 0 ) developed a correlation between C R R obtained from cyclic shear tests on undisturbed samples and S P T blow counts. This was done before and after densification. The correlations were found to be almost identical. Okamura et al. ( 2 0 0 3 ) obtained a correlation between C R R from cyclic tests on undisturbed samples and R R S after compaction. R R S is a type o f dynamic cone penetration test with frictional measurement. Their  246  correlation compared well with the previously developed correlation by Japan Road Association (1996) for natural ground conditions. These results seem to be in accord with Seed (1979) who noted that any changes to the ground condition changes the penetration resistance and liquefaction resistance similarly. More scrutiny o f this matter may not be practically fruitful as the liquefaction/no liquefaction database used for assessing cyclic resistance ratio o f soil, includes a wide spectrum o f soils with different ages. This subject needs further understanding o f cyclic soil behaviour and ageing. Until then we have no other practical choice than accepting Seed (1979) statement- that all the factors affecting the soil behaviour is automatically taken care by the response to the penetration resistance. Alternatively, for more important projects, high quality undisturbed sampling should be used for direct measurement o f cyclic resistance.  7.5  CONCLUSIONS The main conclusions from o f this chapter are as follows: •  Ageing is sensitive to disturbance. Shear strains could decrease or remove the previous ageing effects.  •  Correlations based on calibration chamber overestimate the density o f natural deposits due to the effect o f the geological ageing.  •  Ground improvement removes the geological ageing and produces a young deposit.  •  Post-treatment S C P T results are the net effect o f the following main factors: o  Removal o f geological ageing  o  Increase in D  o  Increase in a'h  o  Time effect after completion o f treatment (ageing and stress relaxation)  r  •  After completion o f densification, ageing is expected to increase the test results.  •  In two cases in this study, penetration resistance and shear wave velocity were monitored with time up to about 1 year after ground improvement. N o general trend o f increased tip resistance or shear wave velocity was observed. It is thought that the site variability obscures the trends. However, the destructuring effect (removal o f the  247  geological ageing) in the form o f reduction o f S C P T results after blast-densification was clear. A new test procedure was developed to assess the time effects on the shear wave velocity o f sand during seismic cone testing. It was found that at any fixed depth, the travel time o f shear waves, from the source at the surface to the vibration sensor i n the seismic cone, decreased with increasing wait time after stoppage o f the cone penetration. This is believed to be due to the ageing o f the disturbed zone around the cone. The significance o f this finding is that the time effect can be directly observed in the field without any interference from the site variability. A t the current state o f art, it is not possible to quantitatively assess the effect o f ageing on q -modulus or q - C R R correlations. Based on 2 case studies by others, i n t  t  which pre- and post-compaction correlations between  C R R and  penetration  resistance were similar, destructuring or ageing does not seem to affect correlation between C R R and penetration resistance.  248  the  Table 7-1 Values of N for various soils (After Baxter 1999- based on studies by Afifi and G  Woods 1971 and Anderson and Stokoe 1978) Soil Ticino sand Hokksund sand Messina sand and gravel Messina sandy gravel Glauconite sand Quiou sand Kenya sand Ottawa Sand  N  (%) 1.2 1.1 2.2-3.5 2.2-3.5 3.9 5.3 12 1-5  Notes  G  Predominantly silica Predominantly silica Predominantly silica Predominantly silica 50% Quartz & 50% Glauconite Carbonatic Carbonatic Silica  249  Table 7-2  Examples of ageing effects on cone penetration resistance and their main findings (after Baxter 1999)  Reference  Main Conclusions  Mitchell and Solymar (1984)  Increases in q in hydraulic fill, as well as after blast densification and vibrocompaction. Sensitivity observed following blasting.  Dowding and Hryciw (1986)  Increases in penetration resistance observed at near zero effective stress conditions in both hydraulic fill and after blast densification in the laboratory.  Hryciw(1986)  c  No increase in q following blasting in saturated loose sands. Presence of surficial clay layer may have hindered drainage. c  Schmertmann et al. (1986)  Increases in q increased with the number of drops for dynamic compaction (related to energy input). No sensitivity was observed.  Dumas and Beaton (1988)  Profile of improvement with depth following dynamic compaction suggested that increases in q were related to energy input. No sensitivity was observed.  c  c  Jefferies etal. (1988) Rogers et al. (1990) Jefferies and Rogers (1993) Thomann(1990)  No increases in q for hydraulic fill in sea water at 0°C. Increases in q were observed after blast densification in the same sand at the same temperature. No sensitivity was observed. c  c  Blast densification in medium dense sand. q decreased and never reached pre-blast values. c  Massarch and Heppel (1991)  After vibrocompaction, some increases in q were observed. However, a lot of scatter was reported.  Human (1992)  Following an earthquake, some increases in qc were observed. However, they were discounted because of large variability in q at the site.  c  c  Charlie et al. (1992)  Following blast densification in dense sand, q decreased and took 5.5 years to reach pre-blast values.  Charlie et al. (1992) Jefferies et al. (1993)  Suggested that increases in qc can be related to temperature. However, a discussion showed that temperature did not have a big influence on the observed increases in q .  c  c  AGRA- 1995- (Gohl et al.)  Following blast densification, scattered increases in q were observed throughout the site. No mention of sensitivity.  AGRA (1995) Ground Engineering (1995)  Following blast densification, some sensitivity was observed. Significant increase in q observed after 12 days. Temperature was ~0° C.  Joshi etal. (1995) Nget al. (1996)  c  c  Increases in penetration resistance in the laboratory for both dry and saturated conditions. Micrograph evidence of precipitation. Following vibrocompaction, increases in q observed with no sensitivity. c  250  0.0 -\ 0.1  c '2 en  Ottawa S a n d Air-Dry a' = 30 psi e = 0.49 I  1  1  10  100  I I I Mill  I  I I I Illll  1000  I  0.2  .a  0.3  >  I I I 11 111  10000  T i m e (minutes) Figure 7-1 140i  120r 100 a.  Increase in shear modulus with time (after Aflfi and Woods 1971) T—rirnn|'  fifU'lHH  t"r tTTTfTp"T'T t UTH|  I M I'll hip  Co) Undisturbed samples a*0.686  Fujikawa sand  80  $ 60  a  Disturbed samples  £ 40 IP  ft 20f-  .U.LXUilii  10"*  Figure 7-2  « • • ' • ""I  10-*  i i i i h h ! , , J » '„) " " 10"*  Amplitude of shear strain, 7,  l  NT*  1 UULLLUlLj 10"  1  r  Comparison of strain-dependent shear modulus of dense sand from  disturbed and undisturbed samples (taken from Ishihara 1996, data originally from Katayama et al. 1986)  251  R=o' /o' =2 1  3  160  co 140  w  120  o  -  J  100  Q  l  1  J  -A.L  J  1 10  10( I  I  80  /  /  / f f  1,000  i  -0.1  I  0  0.1  I  0.2  1  1  0.3  0.4  0.5  Axial Strain (%) Figure 7-3  Effect of ageing on stress-strain curve, Fraser River sand (after Howie et al. 2001)  -  -1  T-—'  '  Fujisawa  1  sand  1.0 CD <3  ^  o to  Vx \ V n \  0.5  \  e°0693 | V \  0.732  Disturbed  -  1 samples J  Undisturbed f 6=0720, samples [ a  M  6  o p  03 35 I  10"  Figure 7-4  10'-s  1  1,..,  10"  10"  Amplitude of shear strain, 7a  1  10"  1  10"  Comparison of modulus reduction curve of dense sand from disturbed and  undisturbed samples (after Ishihara 1996- data originally from Katayama et al. 1986)  252  Figure 7-5  Comparison of modulus reduction curve in the field and in the lab (after  Ishihara 1996). Correction factor may be used to obtain the in situ modulus reduction curve.  C : correction factor r  G O F : Small strain shear modulus in the field (from seismic test) G F : Shear strain dependent shear modulus in the field G O L : Small strain shear modulus o f the reconstituted sample in the lab G L : Shear strain dependent shear modulus o f the reconstituted sample in the lab  253  •j  1  1  1—i—I  i  i I  '  MITCHELL ANO — \ SOLYMAR WW \ VBROCOMRMJION V  1  j  /  1  1  r—i—T—I-T  MITCHELL AND SOLYMAR (1984) BLASTING  TIME AFTER (DISTURBANCE (weeks)  Figure 7-6  Normalized dp resistance in saturated sands versus time after disturbance  (originally by Charles et al. 1992; updated by Jefferies and Rogers 1993).  *  2 5  Time  1  so  i •  Lobprolory  O  Hfdrpulic  land  A  Hydraulic  w n d M l liom  D  $Qvth  7  S o n Mateo  7eigf  lesi  0010 - M o n i i f e y fill  I'wn U p p t ' Leaver  Ko 0  o N e D*poiihon  10 r  100  -ytort  SoiO  S o * FtfMKido Oom Sonfeincndo Dom  *OJNJ send  zoh  ? is 2 i  of  0 5  01  10  10" Time  Figure 7-7  o l ' C D«uO»rlien - dO»»  Time effect on liquefaction resistance (after Seed 1979)  254  Upper Tobacco Rd  Sed etal. 1986  0  L to  2  _  j to  — 3  j  — ia  i  i ID  4  5  —  i  io  1a  s  I io  7  9  Age, Years  Figure 7-8  Field cyclic strengths of aged sand deposits relative to the cyclic strength of  Holocene sand, age < 10,000 years (after Arango and Migues 1996).  200  Lfodtetsod | %  (10135 Sand)  WP  "'(r,c=114&R* y  e =o.892±aoo2 c  (MssseySand) 0997 ±0.003  10  20  30  Shearstaita, J (%) Figure 7-9  Comparison of undrained simple shear response of undisturbed sand and water-pluviated sand (after Vaid and Sivathayalan 2000)  255  110  FD95-6i FD92-4 FD93-2  100 cr 0  90  2  80  'FD94-1  FD96-1 K2V2 FD93-4  co  > <  FD95-6  BHFD93  70  FD94-3  60  R  a  =  a  7  6  FD94-1  50 0  2000  4000  6000  8000  10000  A g e C years 1 4  Figure 7-10 Plot of average q i and 14C age of organic material in topset sand (after c  Monahan et al. 2000)  50 Ifi  n  40  > _c 30CD CD CO  sz  o  20 10 laboratory unaged,, 0 10"  ^ ^ * ^  MASSEY  SYNCRUDE  10  1  2  10  4  10  s  AGE Time Since Deposition, t (years) Figure 7-11 Change in normalized shear wave velocity with age for uncemented sands (after Robertson et al. 1995)  256  350 Kjdd#  900 + 300 +  800 +  #DDam  0 Massey  Kidd#  250 + ^  # Massey  500 + 400 +  ^ Mildred Lake A HM Dam  > D Dam  • Mildred lake  IX Dam#  20^ +.  •HMDam  300 + LLDam# 200 + J-pit4  0.01  0.1  _) 1  1 10  100  1000  100 0.1  10000  Age (years)  -+-+10 100 Age (yean)  1000  Figure 7-12 Possible effects of age of deposit on C P T penetration resistance and shear wave velocity (after Wride et al. 2000)  257  10000  FRICTION RATIO  Rf(%)  0.0  0.5  CONE TIP RESISTANCE q (bar) 100 200 t  1.0 0  300 0.0  SLEEVE FRICTION f, (bar)  PORE PRESSURE U (mofH20) 1.0 -10 0 10 20 2  before post 1 - after treatment post 2- after 1 year  INTERPRETED PROFILE  pre-drilled  silty sand to sandy silt  a o a  V  sand  \  100  Vs (m/sec) 150 200  250 0  o • before -»— postl - after treatment -•— post2-1 year after  Go (bars) 500  4  6  End of treatment  (Go/P )/(q /P ) -  Go I qt 1000 2  \\ •\\ -  a  8 10  12  150  t  a  0  25  250  0.1  0.3  0.5 0.7  i ii i  5H  Q. O)  Q 10  15 H  Figure 7-13  S C P T U profiles before and after Vibro-Replacement, Laing Bridge site, Richmond, B C .  258  N-Stake  U-01  5m radius  U-OS  U-03  u-oa W-Staka U-07  CPT CPT-09  \  E-Stake  U-02  •  U-09, #  U-10  U : SCPT by U B C CPT: By Conetec Ltd.  Figure 7-14 Massey Tunnel blast experiment, location of SCPT holes  259  Settlement (mm)  0  10  20  30  40  50  60  Figure 7-15 Settlement as a function of depth below the ground surface at the test area with no drains, (after Gohl 2002)  260  Figure 7-16 Result of 10 cone penetration testing before and at 4 different times up to 10 months after the blast-liquefaction experiment at Massey Tunnel Site.  261  Figure 7-17 Result of seismic cone testing before and at 4 different times after blasting, Massey Tunnel Site.  262  120  •  110  Layer 1  & Layer 2  100 90 80 .Q 0  as > <  70 60 50 40 30 20 1  10  100  1000  Time after blast (days) Before 250  200 {  1  A ~i  _  150  100  •  Layer 1  A  Layer 2  50 1  10  100  1000  Time after blast (days) Before  Figure 7-18 Variation of the average values of q and V with time after blasting, Massey t  Tunnel Site.  263  s  1000 Time after blast (days)  12 (b)Layer 2 10 4  A  |  6  O  CD CD  5  cu >  <  24 0 o|i  1  10  100  1000  . Time after blast (days)  Before Figure 7-19 Variation of average G  max  / q t before and after blasting, Massey Tunnel Site.  264  265  Time (sec) 0.080 -0.06 i  0.12 J  •  0.082 '  '  0.084 1  '  0.086 '  '  —  0.088 1  1  0.090 1  1  0.092 1—  1  Figure 7-21 Windowed signals at 11.95m at wait times of 1, 5, 10, 20, 40 and 60 minutes after the stoppage of penetration- left hammer hit - low pass 250Hz- Kidd2 site, Richmond, B . C  266  co -400  -I  1  1  0  10  20  1  —  30  1  1  1  40  50  60  70  Wait time (min)  Figure 7-22 The shift of the signals relative to that at one minute for left and right hits at depth interval 10.95-11.95m  215  190 4 0  10  20  30  40  50  60  70  Wait time (min)  Figure 7-23 Variation of Vs with wait time at depth interval 10.95-11.95m  267  Shear beam  Undisturbed zone  Disturbed Zone V  V =125 m/s SI  S 2  Upper accelerometer  Lower accelerometer  *ure 7-24 Schematic seismic wave travel path  268  Figure 7-25 Conceptual representation of the effect of densification on soil modulus, #1 natural aged deposit; #2=After destructuring; #3=Young densified deposit; #4=Aged densified deposit  269  C H A P T E R 8 E F F E C T O F I N C R E A S E IN H O R I Z O N T A L STRESS O N INTERPRETATION OF CPT DATA  8.1  INTRODUCTION In Chapter 3 it was shown that lateral impacts o f vibroflot cause radial displacements.  Accumulation o f the radial displacement increases the horizontal stresses in the ground, which become locked in by the introduction o f stones. In this chapter, parametric analyses w i l l be used to study the effect o f the increase i n lateral stress on interpretation o f post-compaction soil properties/performance from the C P T results.  8.2  F I E L D E V I D E N C E O F I N C R E A S E IN H O R I Z O N T A L STRESS It is generally accepted (e.g. Saito 1 9 7 7 , Mitchell 1 9 8 1 , Leonard and Frost 1 9 8 8 ,  Jamiolkowski and Pasqualini Pitt et al.  2003)  1992,  Salgado et al.  1997,  Howie et al. 2 0 0 1 , Massarsch  2003,  that deep vibratory compaction methods using vertically or horizontally  vibrating probes increase the horizontal stresses. However at present, no practical method exists to measure the i n situ horizontal stress directly. This is even more difficult after ground improvement where the soil conditions are altered. The available tools such as pressuremeter, stepped blade, tapered cone, dilatometer, etc., require correlations or back analysis. Saito (1977)  performed pressuremeter tests in boreholes and concluded that coefficients o f lateral  stress were  3  to  6  times greater after compaction with a vibro-rod. Pitt et al.  (2003)  used the  Ko  stepped blade test to measure the lateral stresses adjacent to stone columns and Geopier elements (Rammed Aggregate Piles) as shown in Figure 8 - 1 . They noted the average interpreted K o after installation o f aggregate piles was 2 to 3 times greater than interpreted K o in natural ground. Massarsch  (2003)  directly related the increase o f the lateral stresses after  densification to the increase in sleeve friction. It should be noted that these measurements may not give the absolute magnitude o f the lateral stress but are good indications o f an increase in lateral stress during compaction.  270  The main objective o f this section is to evaluate how increases in lateral stress could affect the interpretation o f the desired soil properties, mainly D , C R R and modulus. This w i l l r  be done through a parametric study.  8.3  E F F E C T O F I N C R E A S E IN H O R I Z O N T A L STRESS O N I N T E R P R E T A T I O N O F SOIL P R O P E R T I E S  8.3.1  Effect of increase in horizontal stress on interpretation of D  r  Early work on correlations between penetration resistance and soil properties in cohesionless materials was based on the Standard Penetration Test (SPT) N-value. Since the 1970's, the electric piezometer cone penetration test ( C P T U ) has gained increasing acceptance for site characterization. This is because C P T provides much more detailed information, is repeatable, and needs minimal corrections. Correlations between cone tip resistance, q , and t  soil properties have been developed and much research has been carried out on the factors influencing such correlations (Lunne et al., 1997). Most o f the early works used relative density, D as an intermediate parameter i n the determination o f soil properties and there is r  now a tendency to use D and penetration resistance interchangeably. This is not necessarily r  valid as many other factors affect penetration resistance. Saito (1977) found that ignoring the increase in lateral stress in interpretation o f post-compaction S P T blow counts led to interpretation o f very high relative densities. Mitchell (1981) called the relative density inferred from post-compaction penetration tests "equivalent relative density" which is the D  r  that a young normally consolidated deposit would have to possess to give the same penetration resistance. Most correlations to engineering properties o f sand have been based on calibration chamber testing on clean, unaged sands. The dominant influence o f initial horizontal stress on q has been emphasized by a number o f researchers ( Baldi et al. 1985, Jamiolkowski et al. t  1985, Houlsby and Hitchman 1988). A correlation between q , and D t  r  in moderately  compressible, normally consolidated young sands such as those o f the Fraser river delta, is the relationship for unaged Ticino sand by Baldi et al. (1986):  q = 248 • a], '  0 55  t  • exp[2.38Z). ]  Equation 8-1  271  where q is the tip resistance in k P a and a'h is the horizontal effective stress i n kPa. t  In N C ground conditions, a'h can be estimated. This makes it possible to estimate D  r  from correlation to q . After ground densification, the magnitude o f the increase in lateral stress t  is not known. This introduces uncertainty to the estimation o f D from the correlation to q . r  t  Based on Equation 8-1, there are many combinations o f D and ah that could result in the same r  q . This is illustrated in Figure 8-2. For example a post-densification tip resistance o f q =l 5 t  t  M P a and a vertical effective stress o f a' =100 kPa, could be interpreted as ( D = 85% and K o = v  r  0.5) or ( D = 55% and K o = 1.5). It is not possible to obtain 2 unknowns (a'h and D ) from one r  r  equation. The estimated D based on KO_NC which neglects the increased lateral stress, r  overestimates the D . Therefore, it is not possible to do the quality control o f improved ground r  based on interpretation o f D from C P T . r  There have been some attempts to use a combination o f two in situ tests to solve for the two unknowns, D and a'h (Howie et al. 2000). One o f such attempts is the combination o f q r  t  and V measurement. Both are different functions o f D and ah. Therefore it should be possible s  r  to solve a system o f two equations for two unknowns. Bellotti et al. (1996) suggested the following correlation for V : s  V =Cs\F{e)r\cr:Y{a ) s  nb  Equation 8-2  b  where C is a function o f grain characteristics, F(e) is a function o f void ratio, a ' s  a  is the  effective stress in the direction o f particle motion, a'b is the effective stress i n the direction o f propagation, and n and nb are empirical coefficients. For Ticino sand, Bellotti et al. (1996) a  found C to be around 85 and n =nb=0.122. For the S C P T U case where waves propagate in an s  a  approximately vertical direction, a ' is equivalent to a'h and a'b to a ' . If the expression is a  v  written i n terms o f K o , the following equation is obtained: 0.122  Equation 8-3  where V is in m/s and a ' is in kPa. s  v  272  More recently, Eslaamizaad and Robertson (1996) combined Equation 8-1, 8-2 and 8-3, and solved Ko based on q and G x - They obtained the following expression: c  ma  ^=3.«o<-«)(p,/ ;r"-[(G,„»//>j4/p„r;  !  :.165  Equation 8-4  C T  If it is assumed that for any particular depth a ' remains constant during densification, v  the change i n Ko or lateral stress induced by ground improvement may be estimated from this expression.  An  increase  [(Gma /p )/(qc/pa) X  in  K Q should  result  in  an  increase  in  the  parameter,  ]• In Figure 8-3, it can be seen that, in general, it has increased within the  a  sands as a result o f vibro-replacement. The estimated values o f Ko before and after ground improvement indicate a significant increase i n lateral stress in the range o f 200%. If G  m a x  calculated from equation  G =p-V max  Equation 8-5  2 s  is substituted i n Equation 8-4, the resulting expression includes the term ( V ) s  4  3 3  . The estimated  Ko values w i l l thus be very sensitive to errors in V . There is still a good indication that an s  increase in lateral stress has occurred. The issue o f ageing i n Equation 8-4 has not been considered by Eslaamizaad and Robertson (1996). Therefore using this equation for comparison of pre- and post-compaction is questionable. 8.3.2  Effect of increase in horizontal stress on shear modulus and footing settlement Jamiolkowski and Pasqualini (1992) acknowledged that both D and ah should be r  considered for interpretation o f post-compaction tip resistance. They showed how variation o f lateral stress would affect the estimated settlement o f a footing. To demonstrate this concept, they used the Schmertmann (1978) method to compare the settlement for three different combinations o f lateral stress and relative density which resulted in the same q (Figure 8-4). It t  may be observed that the combination with higher lateral stress and lower density resulted in higher stiffness and lower settlement. The combinations of D and ah were calculated using the r  Baldi et al. (1986) correlation (Equation 8-1). They converted the lateral stress to O C R using the following equation suggested by Kulhawy and Mayne (1990):  273  K  0 C 0  where K o  o  c  = K  N C 0  and K o  • (OCR  N C  0 5  )  Equation 8-6  are the coefficients o f lateral stresses for O C and N C conditions  respectively. The O C R was then used in the Baldi et al. (1989) correlation to obtain the Y o u n g ' s modulus, E , from q at an axial strain level o f e =0.1%. The obtained E was used i n t  a  Schmertman's method to calculate the settlement o f footing. Although this approach shows the trend o f the effect o f lateral stress, it has some ambiguity which stems from the fact that the effect o f lateral stress was not incorporated directly but was considered by converting to O C R i n O C soil. There are conditions that the lateral stress could increase without any overconsolidation (e.g. vibro-compaction or compaction grouting). The stiffness o f sand with only increased lateral stress could be different from the stiffness o f sand with increased lateral stress due to over-consolidation. Calibration chamber data shows that the Young's Modulus is a function o f D , O C R and confining stress r  (Lunne et al 1997) whereas q is a function o f D and stress level and not O C R (Baldi et al. t  r  1986). Therefore, in case o f a direct increase in lateral stress, E / q correlations could be t  different from those obtained for the equivalent O C R . The other ambiguity is that the conclusion from Jamiolkowski and Pasqualini (1992) showed the trend only for s =0.1% and a  one value o f q . It is o f interest to see i f the trend holds over a larger range o f strains and values t  of q . t  The key to a good estimation o f deformation including the settlement o f the footing is a good knowledge o f G  m a x  and the modulus reduction o f soil (Poulos, 2000). A parametric  analysis is performed here to evaluate the effect o f K o on the interpretation o f soil modulus from q . It w i l l be shown that the post-densification interpretation o f q neglecting the increase t  t  in K Q , underestimates the modulus and thus overestimates  the settlements. Therefore,  neglecting increase o f the lateral stress may be considered conservative. In this parametric analysis, different combinations o f D and ah that result in the same q r  t  are found (Figure 8-2). Note that an increase in K Q requires a decrease in D to keep the r  resulting q constant. For each combination, G t  m a x  and modulus reduction curves are calculated  and compared. The q is varied from 10 M P a to 20 M P a . The following assumptions are used i n t  this parametric analysis: •  Vertical effective stress a' =100 kPa, equivalent to 10m depth i n a saturated deposit. v  274  •  D and horizontal stress level are the main factors affecting q and G . The effects o f r  t  other parameters are neglected. •  The variation o f D and K o are such that they result in a constant q .  •  Baldi et al. (1986) correlation is used for q (Equation 8-1).  •  Seed and Idriss (1970) is used to for G  •  Ishibashi and Zhang (1993) used for the modulus reduction curve.  r  t  t  m a x  (Equation 4-5).  Ishibashi and Zhang (1993) suggested the following expressions to account for the effect o f confining stress, a ' and plasticity index, PI. m  n(r,Pl)-n  Equation 8-7  where  0.000102 + n(Pl)  K( , PI) =0.5 1 + tanh Ln  . 0.492  Equation 8-8  r  =0.272 1-tanh Ln  m(y, PI)-m  0  0.000556  ,0.4  •exp^O.OHSF/ ) 13  Y  Equation 8-9  where  n(PI) =  0  for PI=0  3.37 x 10-6  f o r 0 < P I < 15  7.0 x 10-7  for 15 < PI < 70  2.7 x 10-5  for PI > 70  Figure 8-5 shows the sensitivity o f calculated G observed that as Ko increases (or D decreases), G r  m a x  m a x  , to the variation o f Ko. It may be  increases. The rate o f increase is higher  for larger tip resistance. Figure 8-6 shows the sensitivity of the shape of the modulus reduction to the variation o f K o . It may be observed that an increase i n K o decreases the rate o f modulus  275  reduction with shear strain. The effect o f K o on shear strain dependent shear modulus is the combined effect on G  and modulus reduction as shown i n Figure 8-7. Each curve represents  m a x  one combination o f ( D , K o ) . The combinations with higher K o (and lower D ) result in a larger r  r  G at any shear strain level. It should be noted that the correlation o f G  m a x  to D and stress level is approximate. For r  example, based on experience in the Lower Mainland, B C , V is about 180 to 200 m/sec for q s  t  in the range o f 100-200 bars and depth o f 10-20m. A l s o shown in Figure 8-7 are the V values s  equivalent to the calculated G  m a x  for comparison with the real measurements in the field. The  calculated values o f V are higher than what is normally measured locally. This is o f no s  concern here because the objective of the parametric analysis is to obtain the trends rather than absolute values. Stroud (1989) derived the average shear strain over the influence depth (2B) o f the footing as a function o f q et/q it where q t is the net bearing pressure o f the footing and q i is n  u  ne  u  t  the ultimate bearing pressure o f the footing. For range o f q t/quit 0 . 1 to 0.33, which is =  ne  equivalent to a safety factor o f 10 to 3 respectively, the average shear strains are i n the range o f about 0.002 to 0.02. The effect o f K o on G at y=0.002 is calculated as an example and shown i n Figure 8-8. This figure shows the ratio o f shear modulus at any K o normalized to the shear modulus at Ko=0.45. This shows that the equivalent secant shear modulus o f the soil increases with K o . For example for q =l 5 M P a , the combination o f Ko=2 and D =50% is 60% stiffer than t  r  the N C soil condition (1^=0.45 and D =84%). r  The results o f the parametric analyses suggest that the D - K o combinations with higher r  K o (or lower D ) give higher stiffness at any shear strain level. Therefore, i f the increase in r  lateral stress is neglected and a Ko_NC condition is assumed, this results in estimation o f settlements greater than what w i l l occur in the real situation. This is conservative. Another case is where the shear wave velocity is actually measured after densification. V is also a function of D , vertical stress and horizontal stress. Therefore, the changes in D and s  r  r  a'h are already included in the measured V . N o w the question becomes how could the increase s  in lateral stress affect our interpretation o f G from the measured V ? This can have two effects, s  one on the G  m a x  through the estimation o f density, p, which is a function o f D and secondly  through the modulus reduction. G  r  m a x  can be obtained from Equation 5-4.  276  Figure 8-9 shows the effect o f K Q on the interpreted G x through the effect on the soil m a  density. A s the KQ increases, D and p decrease which also decreases G R  m a x  . However, its effect  is negligible (less than 3% for the case analyzed here). O n the other hand, considering the increase in K Q would result in a slower rate o f modulus reduction. Figure 8-10 shows the combined effect on the. interpreted G at any shear strain. It may be observed that the combinations with higher KQ and lower D results in slightly lower G at smaller range o f strains R  and larger G in medium to large strains (which is the range o f average strain level under footings). It is concluded that in the case o f calculating G from measured V , neglecting the s  increase in KQ underestimates the soil modulus and thus is conservative. 8.3.3  Effect of increase in horizontal stress on interpreted friction angle from C P T results For any type o f granular soils, friction angle is a function o f state (relative density and  stress level) besides other factors, which are ignored here. For any particular post-densification tip resistance, an increase in K o results in a lower interpreted D and consequently in a lower r  interpreted peak friction angle (see Equation 4-1). Figure 8-11 shows the general trend o f the effect o f K o on the interpreted peak triaxial friction angle. A s an example, at vertical stress o f 100 k P a and post-compaction q o f 150, by increasing K o f r o m 0.5 to 2, the friction angle t  decreases from 45 to 37 degrees (20% decrease). 8.3.4  Effect of increase in horizontal stress on interpreted cyclic resistance from C P T results The effect o f increase in horizontal stress on evaluation o f liquefaction potential by q is t  investigated by Salgado et al. (1997) which can be consulted for more details. They used the result o f laboratory cyclic tests and a cone penetration theory developed by Salgado (1993) to evaluate the effect o f K Q on cyclic resistance ratio, C R R and q separately. A n increase i n K o t  increases C R R . Increase in K<, also increases the tip resistance. However, the effect is such that it changes the correlation between the q and C R R . They developed a theoretical correlation t  between q and C R R and compared it to the empirical correlation suggested by Robertson and t  Campanella (1985) for N C sand (Figure 8-12). They concluded the following: •  For q ,<12 M P a c  For K o < 1.5 KO.NC: The C R R - q i is almost independent o f K Q c  277  For K o > 1.5 KO,NC: Neglecting the effects o f K gives slightly conservative 0  C R R (obtained C R R would be smaller than the actual C R R ) •  Forq i>12 M P a c  The nearly vertical portion o f C R R - q i curve shifts to right. This shift is more c  than 5% for KO>1.2KO,NC- Neglecting the effects o f K o on C R R - q i correlation c  could lead to unconservative estimates o f C R R (the obtained C R R would be greater than the actual C R R ) . In the above, q i is the tip resistance normalized with respect to effective over-burden pressure. c  A great accuracy should not be expected due to the generally approximate nature o f this issue. For example the C R R - N S P T curve from liquefaction/ no-liquefaction database developed by Seed et al. is approximate and includes all sorts o f sands with different in situ conditions. The N C curve shown i n Figure 8-12 is obtained based on correlation between N and q , which c  adds to the approximation. The indication o f liquefaction i n the Seed's database is usually sand boils, whereas the K o - C R R correlation used by Salgado et al. (1997) is based on 5% double strains i n cyclic triaxial tests. In addition, analytical methods for tip resistance are still i n the development stage. It may be concluded that studies o f these type cannot be used quantitatively. Even i f this study were quantitatively reliable, it would not be useful i n practice due to difficulties in finding in situ K in granular soils. However, this study provides a framework to show that the 0  changes in soil conditions affect the penetration test and C R R differently. In other words, the correlation between penetration resistance and C R R is not unique. 8.3.5  Effect of the increase horizontal stress on estimation of earthquake induced settlement The methods developed by Tokimatsu and Seed (1987), and Ishihara and Yoshimine  (1992) are widely used in practice for estimation o f earthquake induced settlement. These methods are based on laboratory cyclic tests on sands. The shear-volume coupling is established for sands with different relative densities. Correlation between relative density and penetration resistance, S P T blow counts or C P T , is the basis o f these methods. A n increase in lateral stress changes the correlations between density and penetration resistance. To answer the question as to how the increase in lateral stress affects the settlement  278  predicted by the above mentioned methods needs more research. Simplistically, the increase in lateral stress causes overestimation o f D which in turn should cause an underestimation o f r  settlement. In other words, ignoring the increase in lateral stress results in predicting too small settlements. For example a post-compaction q o f 15 M P a at a' =100, could be achieved b y two t  v  different post-compaction conditions, (Ko =0.45, D =85%) or (Ko =2, D =50%) as shown in r  r  Figure 8-2. Assuming a factor o f safety o f one against liquefaction, the Ishihara and Yoshimine (1992) method predicts e =0.75% and e =l .5% for the case o f Ko=0.45 and K o =2 respectively. v  v  This means that i f increase i n lateral stress is ignored, the settlement would be underestimated by 50%>. Note that the effect o f lateral stress on estimation o f settlement decreases significantly with increase in the factor o f safety against liquefaction. The above example is a simplistic demonstration o f the effect o f lateral stress on prediction o f settlement. In fact, an increase i n lateral stress increases the stiffness o f the soil and changes the variation o f stiffness with shear strain. This likely decreases the induced strains during shaking and offsets to some extent the unconservative estimation o f volumetric strains. For systematic analysis o f the effect o f lateral stress on the earthquake settlement the following should be known: •  The effect o f lateral stress on shear-volume coupling  •  The effect o f lateral stress on penetration resistance  •  The effect o f lateral stress on relation between shear modulus and shear strain  •  The effect o f lateral stress on earthquake demand ( C S R )  The main unknown at this point is the first item, the effect o f lateral stress on shear-volume coupling. More research is needed on this subject.  8.4  S U M M A R Y AND CONCLUSIONS This chapter used parametric studies to investigate the effect o f increase in horizontal  stress on interpretation o f post-compaction soil parameters such as relative density, friction angle, soil modulus and cyclic stress resistance. Where possible, the results were presented  279  quantitatively. Otherwise, the results presented in a qualitative manner, i.e. whether the interpreted results would be conservative or unconservative. It was shown that interrelationships between horizontal stress and soil parameters are complex. Ideally, the effect o f horizontal stress on site characterization should be considerd. However, at the present state o f practice and even state o f the art, there is no robust technique to measure the in situ stresses including horizontal stress. Therefore, at present state it is not practical to consider the effects o f horizontal stress quantitatively. More research is needed to approach a quantitative solution to this problem.  280  • O  Stone Column RAP Element  3  a  Estimated Ko for normally consolidated soil (Ko = 1 - sins')  Figure 8-1  Ko measurement by Stepped Blade, conducted at 70 cm from Stone  Column and 85 cm from Geopier Element. A l l tests oriented to measure radial stress (after Pitt et al. 2003). 100  0.5  1  1.5  2  2.5  Coefficient of horizontal stress at rest, K i 0  Figure 8-2  Non-uniqueness of interpretation of cone tip resistance- different combinations of D and ah results in the same q r  281  t  V  100 0 i  s  (m/sec)  200  G  0  —i1  0  (bars)  500 1  G /q 0  1000 2 1 -I  (G /p )/(q /p ) -  t  0  a  4 6 8 10 150 ' — ^ — I -i '  282  t  a  0  250  '  K  25  0.1  1 -t—'  0  0.3 1  0.5 ~ u  32  —1—1—  2»  I  it  -  24  K,*0.4S ( O C « « f DR « 6 0 %  L .  -  20  -  r - K « * O J 5 5 {OCR« \ DR * 7 5 *  «)  "  K « a l 4 2 ( O C * « 10) OB * 55%  -  tz  — >—  fl  t  1  7  1 4  3  1, 8  1 7  I  •  1  I  ,  Footing breadth (m)  Figure 8-4  Settlement versus foundation sizes for different K O - D R combinations  150  125 \  TO 0_  100  i  50 i 0  0.5  1  1.5  2  Coefficient of horizontal s t r e s s at rest, K  2.5 0  (-)  (Adapted from Jamiolkowski and Pasqualini 1992) Figure 8-5  Effect of variation of Ko on G for constant q . Variation of K Q and D are such that the resulting q remains constant m a x  t  t  283  R  Shear strain, y (-)  Figure 8-6  Effect of increase in coefficient of lateral stress on the shape of the modulus reduction curve  284  Equivalent V  s  ~V=220 m/s  q = 10 MPa t  S  -Ko=0.45, Df=67%  K,, increases, D decreases r  -Ko=0.80, Dr=54% Ko=1 20, Df=45% • Ko=1.50. Dr=40% Ko=2.00, Dr=33%  1.E-06  1.E-05  1 E-04  1.E-03  1.E-02  1.E-01  Shear strain, y (-) 150  -V=240 m/s  IC, increases, D, decreases  s  q, = 15MPa ——Ko=0.45, Dr=84% Ko=0.80, Dr=71% Ko=1.20, Dr=62% Ko=1.50, Dr=57% Ko=2.00, Or=50  1.E-06  1.E-05  1.E-04  1.E-03  1.E-02  1.E-01  Shear strain, y (-)  ~K,, Increases, D decreases  : 20 MPa  r  Ko=0.45, Dr=96%  ~V=250 m/s  Ko=0.80, Dn=83%  S  Ko=1.20, Dr=74% Ko=1.50, Dr=69% Ko=2.00, Dr=62%  1.E-06  1.E-05  1.E-04  1.E-03  1.E-02  1.E-01  Shear strain, y (-)  Figure 8-7  Effect of increase in Ko on the shear modulus (assume o' =100 kPa) v  285  1.8 q =20 MPa t  A  q =15MPa t  CM  o o o  1.6 q=10 MPa t  II  >1.4  d  1  2  0.5  1  1.5  2  2.5  Coefficient of horizontal stress at rest, K (-) 0  Figure 8-8  Effect of increase in K„ on G normalized to G at Ko=0.45 for shear strain of Y=0.002.  0.95  E  0.85  0.5  1  1.5  2.5  2  Coefficient of horizontal stress at rest, K (-) 0  Figure 8-9  Effect of increase in K<> on the interpretation of G  m a x  (through the effect of estimation of soil density)  286  from measured V  s  q, = 15 Mpa V = 240 m/sec s  1.E-06  1.E-05  1.E-04  1.E-03  1.E-02  1.E-01  Shear strain, y (-) Figure 8-10  Effect of increase in K„ on the interpretation of G from measured V  s  50  a\= 100 k P a  in  <t» = 33°  <D  cn  v c  CD  45  CD  40  •o  o  A  q, =20 MPa q=15 MPa t  as  co 35  q,=10 MPa  03 CD Q-  30 0.5  1  1.5  2  Coefficient of horizontal stress at rest, K  2.5 0  (-)  Figure 8-11 Effect of increase in K o on the interpretation of peak friction angle from post-densification tip resistance  287  0.8 Derived curves for typical intrinsic parameters  0.7 0.6  Rrfwence curve fiarKojgc-045 Derived curve for Kg"0.68 Derived curve fbrKQ-0.90  0.5 0.4  10 20 Normalized Cone Resistance*  (MPa)  Figure 8-12 Comparison of derived C R R correlation with the empirical correlation suggested by Robertson and Campanella (1985), (after Salgado et al. 1997)  288  C H A P T E R 9 S U M M A R Y AND CONCLUSIONS  9.1  RESEARCH FOCUS AND OBJECTIVES This  thesis  has  provided a better understanding  o f ground  improvement  by  vibro-replacement and o f the major in situ testing methods used to characterize the ground before and after ground treatment. A survey o f the technical literature showed that little progress had been made i n the profession's fundamental understanding o f ground improvement by deep compaction since the first Geotechnique Symposium in 1976 and a survey o f local practice indicated that, from 1990 to 2000, the most popular ground improvement method for granular soils i n urban areas in the Lower Mainland, B C was vibro-replacement. Over the same period, cone penetration testing, C P T , was identified as the main method o f characterization o f the natural ground before treatment and for assessment o f the improved ground. A s a result o f these findings, this research focused on vibro-replacement with the following objectives: 1  To understand the physical process o f vibro-replacement and its effects on ground conditions;  2  T o understand  the  effects  o f changes  in ground  vibro-replacement on interpretation o f the S C P T results.  289  conditions induced  by  9.2  METHODOLOGY  The following major works were carried out during the course o f this research.  •  Investigation o f the physical process o f vibro-replacement and its effects on ground conditions. This included the design o f vibration sensors,  field  measurement o f vibration o f the vibroflot and ground response during the vibro-replacement  process  followed  by  numerical  modelling  of  soil-vibroflot interaction;  •  Investigation o f the effect o f soil heterogeneity on cone tip resistance using numerical modelling.  •  Detailed study o f the evaluation o f the in situ shear wave velocity using seismic cone testing and numerical modelling;  •  Investigation o f the effect o f stone columns on the interpretation o f seismic cone testing using numerical modelling;  •  Development  of  a  database  of  CPTU  results  before  and  after  vibro-replacement from 15 projects in Lower Mainland B C to observe the changes  in ground response  to cone penetration. This included the  development o f a correlation between the initial soil behaviour type and achievable cone penetration resistance for Fraser River sands.  •  Investigation o f time effects on soil response in 3 case studies o f seismic cone penetration testing (SCPT).  9.3  S U M M A R Y O F M A J O R FINDINGS  290  The study o f the mechanism o f vibro-replacement produced the following major findings:  •  The vibroflot generates mainly horizontal but also vertical vibrations i n the ground. The frequency o f the ground vibration and o f the vibroflot is the same. For the case studied here, a resonant frequency o f 26 H z was obtained for the natural ground. Attenuation o f the vibrations is due to geometrical spreading and to material damping. The observed geometrical spreading is similar i n form to theoretical predictions o f spherical spreading from a horizontally vibrating source in a homogeneous, isotropic material. Vertical vibrations attenuate at a slower rate than horizontal Vibrations. The direction o f the principal horizontal acceleration changes with the distance from the vibroflot.  •  B y considering a combination o f cyclic shear strains obtained from a numerical model that included shear-volume coupling, a procedure was proposed to explain the mechanism o f densification by vibro-replacement. For the case studied in this research, this procedure estimated less than 5% increase in relative density. This was i n agreement with the small increase in post-densification cone tip resistance observed in the case studied. The small amount o f improvement achieved in the tip resistance was attributed to the initially high cone tip resistance and also to confinement o f the monitored layer between two dense sandy layers. More research is required to calibrate this procedure for quantitative prediction o f the magnitude o f densification.  •  Vibro-replacement increases the horizontal stresses by accumulation o f radial displacement due to horizontal impacts by the vibroflot.  •  Vibro-replacement induces heterogeneity to the ground. This heterogeneity is due to variation o f the vibration amplitude with radial distance from the 291  vibroflot and also to the inclusion o f stone columns. The centroid o f the compaction grid experiences the least increase i n density.  The study o f the effects o f changes induced by vibro-replacement on the measurement  and interpretation o f i n situ tests produced the following important  findings:  •  Based on numerical modelling o f cylindrical cavity expansion in a heterogeneous ground mass including stone columns, it was concluded that the cone tip resistance at the centroid is mainly a function o f the soil properties within a zone that extends a small radius from the centroid. The denser soils at greater distance from the centroid have much less influence. The effect o f stone columns on q at the centroid is minimal for the assumed t  3m  spacing  of  stone  columns.  Ignoring  the  heterogeneity  of  post-vibro-replacement conditions results in some over-estimation o f the soil properties at the centroid and considerable under-estimation o f the average properties o f the composite soil-stone column mass. The current Q C method based on the cone tip resistance at the centroids o f compaction grids is likely conservative. More research is needed to quantify the degree o f conservatism.  •  Numerical modelling o f shear wave propagation in homogeneous soils captured the characteristics o f seismic signals obtained from seismic cone testing i n natural ground (before inclusion o f stone columns). The results o f numerical modelling confirmed the accuracy o f conventional techniques for interpretation o f the shear wave velocity from seismic signals.  •  Numerical modelling o f shear wave propagation in a heterogeneous material with inclusions to represent stone columns showed that the inclusion o f stone columns in the ground changes the wave propagation regime and generates different types o f waves during seismic cone testing. 292  Interaction o f these waves changes the characteristics o f the signals recorded at the centroid o f a triangular arrangement o f stone columns compared to the case o f homogeneous ground.  Irregularity o f seismic signals introduces the potential for errors i n estimating shear wave arrival times using the conventional cross-over method o f interpretation. The shear wave velocity profile with depth obtained from the cross-over method is usually jagged due to shifting o f the characteristic points (crossover or peak). Either the cross-correlation method or cross-spectrum method is preferable for interpretation o f shear wave velocity from seismic signals.  Based on numerical modelling, the shear wave velocity interpreted from seismic cone signals after vibro-replacement could be 15 to 20% higher than the actual shear wave velocity o f the native soil between the stone columns. The magnitude o f this over-estimation is a function o f the ratio o f the stiffness o f the stone columns to the native soil, and o f the size and spacing o f stone columns. This magnitude o f over-estimation is significant when the interpreted shear wave velocity is used as an indicator o f the degree o f improvement obtained by vibro-replacement. More research is needed to quantify the effect o f the stone columns.  Vibro-replacement increases density and horizontal stresses, and removes the effects o f geological ageing. The combined effect o f these changes on C P T response is normally an increase i n the cone tip resistance, an increase in sleeve friction, and a change in R f (with no apparent general trend). Where the sand contains some fines content, the excess dynamic pore pressure measured at the U2 location tends to become more negative. This results in the improved ground appearing coarser and cleaner (less fines content) on C P T classification charts. A similar observation was made from the published C P T data in calibration chamber tests. Rf was not found to be 293  diagnostic o f the changes i n soil conditions.  Based on observation o f cone penetration resistances measured before and after vibro-replacement, a relationship was developed between achievable normalized C P T tip resistance and the initial pre-compaction value o f q or t  soil behaviour index I . This relationship is only applicable to Fraser River c  sand improved by vibro-replacement with stone columns installed in a triangular arrangement at spacings o f 2.75 m and 3.0 m. This should be used only as a guideline since the performance  o f vibro-replacement is  dependent on the equipment, methodology and operators.  In two case studies o f ageing effects, no apparent increase in q or V with t  s  time was observed during repeated testing after ground treatment by vibro-replacement or explosive compaction. However, a reduction i n both q and V was observed immediately after ground treatment in soil below t  s  the effective zone o f densification.  This was interpreted to be due to  destruction o f the effects o f geological ageing by the shear strains induced by the ground treatment.  It was also observed that variability in both  naturally occurring ground conditions and those induced by soil treatment make it difficult to study the phenomenon o f ageing after ground treatment.  Changes in sand shear wave velocity with time after disturbance were also studied by monitoring shear wave arrivals at various times after cone penetration had been stopped.  It was found that at any fixed depth, the  travel time o f shear waves, from the source at the surface to the vibration sensor in the seismic cone, decreased with increasing time after stoppage o f penetration. This is believed to be due to time dependent increases in the stiffness o f the zone around the cone disturbed during penetration. The significance o f this finding is that the time effect can be directly observed in the field without any effect o f site variability.  294  •  Correlations between properties o f sand and q are mainly based on t  calibration chamber tests. A s most chamber tests have been carried out on normally consolidated freshly deposited sand, such correlations are thus most relevant to that type o f soil. Using these correlations for interpretation of  C P T test results  overestimation  of  vibro-replacement  obtained  some  soil  removes  or  in aged  natural  properties  such  significantly  deposits as  D  reduces  results  and  r  any  in  (p. A s  effects  of  geological ageing on soil properties i n the treated soil, the available correlations should be applicable to the interpretation o f post-compaction in situ test results. However, as vibro-replacement also tends to increase the in situ lateral stresses, there is still potential for use o f the correlations to result in over-estimation o f post-compaction density and strength.  •  Ideally, the combination o f changes in relative density, horizontal stress and ageing should be considered in the interpretation o f C P T results used to assess the degree o f improvement in soil properties achieved by ground treatment processes. However, at the current state o f knowledge, there is no robust method for measuring in situ horizontal stress or for assessing the effects  o f soil ageing. Therefore, their effects  cannot be practically  quantified. Nevertheless, geotechnical engineers should be aware o f the limitations  of  current  interpretation  procedures  and  the  possible  repercussions for the design and specification o f ground improvement and for prediction o f the performance o f treated ground in geotechnical engineering designs.  9.4  RECOMMENDATIONS FOR FUTURE RESEARCH Some o f the conclusions from this research were conceptual and qualitative due to the  nature o f the problem. In order to draw quantitative conclusions, more extensive research w i l l be required. The main objective would be to quantify the actual changes i n the soil conditions  295  and the resulting effects on i n situ test results and on post-treatment soil response. Further research could include the following main components: 1 2  Selection o f a well characterized site with a uniform loose layer(s). Instrumentation o f the soil to monitor vibrations, changes i n the horizontal and vertical stresses, and changes in the shear wave velocity (with permanent geophones in the ground) during ground improvement.  3  Calibration chamber testing to develop correlations for the local sands.  4  Undisturbed sampling o f the soil using ground freezing before and after treatment.  5  Drained cyclic simple shear testing with large number o f cycles to develop shear-volume coupling o f the sand.  6  C y c l i c tests on the undisturbed samples to measure the degree o f improvement.  7  Numerical modelling o f the soil response to the compaction process and the response o f the ground to the in situ test(s).  8  Comparison o f the results o f the numerical modelling to the results o f post-compaction i n situ testing,  This comprehensive program would further advance our understanding o f the complex processes o f vibro-replacement and site characterization o f improved ground.  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Geotechnique, 41, N o . 2, pp. 173-183 Y u , H . S . (2000). Cavity Expansion Methods i n Geomechanics. 404 pp, Kluwer Academic Publishers  312  APPENDIX O N E  Database of CPTs carried out before and after vibro-replacement  Introduction A s part o f the research on the effects o f vibro-replacement on the results o f i n situ testing,  a  database  was  assembled  of  C P T profiles  obtained  before  and  after  vibro-replacement.  Site locations The data gathered here are all from sites in which vibro-replacement was carried out for commercial projects in B C by different ground improvement specialty contractors. The majority o f the sites were in the Richmond, B C area. The general location o f each site is noted in Table A - l . C P T s were carried out by U B C (University o f British Columbia) using the U B C cone truck or by well known local i n situ testing specialty contractors.  Methodology • C P T U data were collected before and after vibro-replacement. • Pre- and post-CPT holes carried out in the same general vicinity were selected and superimposed. C P T profiles were shifted i n the range o f 0.5 to 1.0m ( i f applicable) to obtain a match between similar layers and to account for the effects o f elevation changes due to volume change and changes i n site grade. Occasionally pre- and post-CPT profdes were significantly different. These cases were excluded. • Matching layers were visually selected (based on similar q signatures). Only thick c  layers (generally thicker than 1.0m and a few cases o f about 0.5 to l m ) were selected to prevent the thin layer effect on different response o f cone tip and sleeve friction resistance (Lunne et al. 1997). • The pre- and post-CPT values, q , f , Rf and U2 values were averaged over each layer t  s  and plotted in the classification charts. Table A l presents the average values for the selected layers.  313  • Only the data from vibro-replacement projects carried out by Geopac West Ltd.were used to develop the correlation for achievable post-q . This was to ensure consistency t  o f equipment and o f operational methodology. For all these cases, a V 2 3 vibrator was used. The compaction grids were all triangular with spacing o f either 2.75m or 3m.  Results This database formed the basis o f figures presented i n Chapter 6.  314  No.  Site Location  Vibro-Replacement Vibrator Spacing  Specialty  (all in BC)  Type  (m)  by  CPT Before  After  Selected Layers Bott. Top  (%)  1.50  3.50  7  0.7  198 19  0.3  13  3.5  153 81  0.5  Geopac  Electric  3  Conetec  207-CP1&2  1  LuLu Island  Geopac Geopac  Electric  3  Conetec  207-CP1&3  215-CP02&03 215-CP02&04  207-CP1&4  215-CP02&05  8.50  10.00  RICPT6  RICPT2  Electric  UBC  RICPT3 RICPT3  RICPT6 RICPT4  7.80  Geopac  3  UBC  RICPT2  RICPT4  6.60 7.80  RICPT4  UBC  RICPT3 PIZA1  Conetec  147CPT1  190CPT5  2 2  LuLu Island LuLu Island  2 2  LuLu Island  2 3  LuLu Island LuLu Island  2  3  3 3 3 3 3 3  4 4 4 4 4 4  4 4 4 4 4 4  5 5 5 5 5 5 5  LuLu Island LuLu Island  LuLu Island  LuLu Island  LuLu Island LuLu Island LuLu Island  LuLu Island LuLu Island  Roberts Bank Roberts Bank Roberts Bank  Roberts Bank Roberts Bank Roberts Bank Roberts Bank  Roberts Bank Roberts Bank Roberts Bank Roberts Bank  Agra Agra  Agra  Agra Agra Agra Agra  Agra  Agra Agra Agra  Agra Agra Agra Agra  Agra Agra Agra  Agra  UBC  3 3  UBC  Electric  Electric  3 ?  Electric  ?  Electnc  Electric Electric  3  UBC  Electric  ?  Electric Electric Electric  ? .7 ?  Electric  ?  Electric  ?  Electric  ?  Electric  ? ?  Electric  ?  Electric  ? ?  Electric Electric Electric  ? ? ?  Electric  ?  Electric  170CP955  CPT7-7  11.00  Conetec Conetec Conetec  170CP956  CPT7-4  LuLu Island LuLu Island LuLu Island  Geopac  Electric  Geopac  Electric  Conetec  193CPT18 CPT5 CPT5 CPT05  10.50 6.00 11.00 2.00  2.75  CPT05  12.50  Conetec  155CP5  189CP41  2.75  3.90  UBC UBC  hrbsd-1 hrbsd-1  hr4 hr4  5.50 8.75  7.50 11.00  UBC  hrh2  hr-5  5.50  UBC  hrh2  hr-5  Electric  3 3  UBC  hrh3  hr-6  hrh3  6.15  8.75  86  0.8  83  4.20  6.00  106 127  3  8  North Van.  Geopac  Electric  North Van.  Geopac  North Van.  Geopac  Electric Electric  Conetec Conetec  3 3  UBC  189CP41  hr4  LuLu Island  Geopac  Electric Electric  3  UBC UBC  3  UBC  UBC  CPT1 CPT1  CPT3  0.3 0.3  77  7 135  0.3  152  124  7  Geopac  Electric  LuLu Island  Geopac  Electric  Geopac Geopac  Electric Electric  Geopac  Electric  3  Conetec  95-145CPT2  3  Conetec  3  10  LuLu Island  Geopac  Electric  3  Electric Electric  3 3  280  0.4  0.00  3.4  0.00 0.00 0.00  143 104 93  0.4 0.3 0.3  203 99 63  0.4 0.3 0.3  0.00 0.00 0.00  0.5  1.4 1.4 1.4  162  0.4  1.8  14  1.7  0.00 0.00  1.8  0.07  1.0  0.08  9  1.9  20  2.0  0.01  218  0.3  0.00  0.3  76  265  0.3  0.00  1.0 1.0 1.0  0.00  0.0  143  163  0.3  0.00  0.0  0.5  0.00 0.00  0.3  94  0.5  147  165  0.4  0.00  104  0.2  0.00  1.0  0.3  0.3  132 71  0.3  0.00  0.3  0.00 0.00  0.3  153  0.3  0.00  122  0.2  250  0.2  0.00  1.0  0.00  165  0.3  155  0.3  0.00  1.0  12.00  13.00  78  Conetec  95-145CPT2  00-219CPT8  7.00  8.50  116  57  0.3  0.00  0.3  132  0.3  0.00  0.3  57  0.3  0.00  0.3  105  0.3  186 104  0.3  1.4 1.4 1.0  0.00  1.9  0.3  1.4  0.07  0.4  97  1.4  1.8  162  6.00  18  0.4 0.4  0.00  0.4  2.30  1.7  18  0.6  1.4  0.00  00-219CPT6  78  131 99  101  0.00  3.4  0.00  95-145CPT2  13.00  3.4 3.4  0.4  Conetec  112  0.4 0.4  0.6  1.1  142  89  17  287  0.00  0.18  12.00  1.7  9  1.1  0.3  0.00  2.1  10.50  8  0.3  9  104  0.4'  0.4  91  0.3  192  142  0.3  107  0.4  0.00  9.50  12.00  0.00 0.00  3.4  0.4  0.13  8.00  95-145CPT2  0.00  64  0.00  0.3 0.6  1.9 0.3  95-145CPT2  Conetec  1.5  82  141  11.00  1.5 1.5  107  0.6  15  1.7  0.4  8.50  1.5  -0.01  87  -0.01  75 128  00-219CPT8 00-219CPT8  0.00  1.5  0.00  86  0.6  170 170  62  95-145CPT2  0.00 0.00  1.0 1.5  3.4 3.4  -0.01  3.50  Conetec  0.00  1.0  -0.006 -0.001  0.3  2.00  00-219CPT8  Electric  0.00 0.00  1.0  0.5 0.3  102  00-219CPT6  95-145CPT2  Geopac  0.3  0.6  0.5  Conetec  LuLu Island  0.4 0.4  205  102  3  10  78 102  241  0.00  0.4  0.00  11.50  95-145CPT2  0.5 0.3  0.3  0.3  0.5  9.00  Conetec  196 210  178 84  160  3  LuLu Island  180  212  0.3 0.4  0.00  0.4  00-219CPT6 00-219CPT6  10 10  0.4  0.3  0.4 0.3  0.2  97  95-145CPT2  196 246  102 239  86  6.30  Conetec  184  0.4 0.3  -0.01  0.2  5.00  3  135 175  0.00  0.3  2.0 2.0 1.7 1.7  0.8  0.3 0.3  00-219CPT6  LuLu Island  0.2  152  3.0  3.4  5.00  12.50  BTP4  124  0.2  139 104 76 143  118 88  3.50  BTP4  BTP1  0.2  115  0.2 0.3 0.4 0.2  0.3 0.6  71  BTP1  UBC  197  117 143 41 122  -0.01  -0.01  0.5  UBC  3  0.4  44  0.3  98  3  Electric  111  1.0  3.0 3.0  71  14.00  9.00  Electric  -0.01 0.00 -0.01 -0.01  0.4  0.00 0.00  0.2  0.5  7.20  Geopac  0.2 0.3 0.4 0.2  141  37  0.4 0.3  34  59  BTP4  LuLu Island  3.0  265 277  -0.01  0.5  BTP1  LuLu Island  -0.05  0.4 0.3  0.4  59  UBC  BTP4  1.2  84 114  3.4  0.00  3  BTP1  3.0 3.0  0.00  0.5  Electric  UBC  -0.05 0.00  0.3  228  73  3  0.8 0.3  159  0.5  3.40  Electric  40 77  0.3  0.3  2.00  Geopac Geopac  0.8 0.3  90  142  BTP4  Geopac  33 116  0.00  0.00  BTP1  LuLu Island  Geopac  121  12.75  UBC  10  0.4 0.9  -0.01  67  3  Geopac  72 23  0.6  9.00  Electric  LuLu Island  1.5  0.4 0.8  1.4  126  10  3.0 3.0  96 22  0.00  7.25  4.40  0.00 0.00  1.5  0.3  108  2.00  -0.08  1.5  74  11.25  CPT5  1.5  1.8  11  0.02  0.3  9.00  CPT4  -0.01  1.6  110  7.00  UBC  0.9  9  0.00  hr-6  3  102  1.3  0.5  7.00  Electric  1.2  0.00  44  5.50  Geopac  0.00  0.6  1.4  CPT7  Electric  0.3  218  0.00  CPT3  Geopac  1.2 1.2 1.2  0.3  UBC  LuLu Island  1.2  239  3  9  0.10 0.00 0.16  1.2  0.3  0.5 0.5  5.00  1.9 0.3 2.4  0.00  1.0  169  68  2.00  0.3  0.17  1.0 1.0  0.00  15.00  CPT7  2.2  0.00  1.0  0.3  43  13.25  5.00 9.00  0.3  0.00 0.07  159  0.5  0.3  2.00 7.00  0.7 2.9  101 68  hr-6  CPT7  0.00  161 88  90  17.25  0.5  1.0  160  0.6  1.5  -0.02  0.3  136  115  15.25  10 150 10  0.9  1.2  0.6 0.3 0.3  0.6 0.3  7.25  hr-6 CPT7  27  1.7 0.3 2.1  9  0.00  0.7  10.25  hrti3  3  12.75  15.50  21  1.9  0.3  B  53  8.75  UBC  Electric  Electric  hrbsd-1  189CP17  hrh3  Geopac  3  155CP5  189CP17  UBC  North Van.  3  155CP4  189CP48  hrh2  Geopac  Electric  155CP1  UBC  North Van.  3  155CP1  LB9904  hr-5  Geopac  Electric  3  Conetec  North Van.  LuLu Island  0.7  0.5  Electric  10  87  86  Geopac  Geopac  0.00  6.10  43  North Van.  LuLu Island  0.5  4.55  0.4  8  10  101  189CP17  30  3  LuLu Island  78  4.50  Electric Electric  10  -0.01  155CP4  Hydraulic  LuLu Island  0.7  3.00  Geopac  10  73  155CP1 155CP4  North Van. North Van.  10  -0.00141  0.4  8 8  10  0.4  -0.00422  100  Hydraulic  10  86  79 80  0.7  0.7  Bauer  LuLu Island  204  57  0.4  Bauer  10  0.00  0.3  77  Hydraulic  LuLu Island  0.3  102  0.4  78  Conetec  LB9902  0.00  0.3  50  6.85  McKenzie  9  113  0.4  0.00 0.00  8.35  Bauer  Geopac  0.3  11.00  90  0.4  6.95  Hydraulic  LuLu Island  200  0.4  3.00  7  9  0.00  78  0.00 0.00  102  189CP4B  Bauer  Geopac  0.4 0.4  7.60  10.00 9.50  0.4  76  McKenzie  LuLu Island  91 50  14.00 6.20  65  Conetec  9 9  0.00  0.00 0.00  9.00  Hydraulic  8  0.00  0.2 0.3 0.4  67 121 57  0.3  7.00  Bauer  8 8  0.2  113 104 78  0.2 0.2 0.3  64  -0.21  155CP24 155CP24  McKenzie  8  0.2  93  119  6.20  0.3 0.5 0.2 0.2  30  2.6  155CP1  Conetec  8  117  13.50 8.50  1.0  5  -0.07  Conetec Conetec  UBC  0.9  0.00 0.00 0.05 0.00  0.3  29  6.75  2.75 ?  Hydraulic  North Van.  8.50 10.30  150  1.8  LB9904  Bauer  8  6.80  0.00  0.00  101 86 119 5  4.75  Electric Hydraulic  Geopac Geopac  9.20  5.40  0.3  160  -0.03  13.50 8.50 14.00 3.00  10.00  0.7 0.4  Bauer  McKenzie  6.00 11.00  174  1.1  0.3  15  LB9902  McKenzie  7  CPT05  0.00  4 163 4  0.3 0.3 0.3 0.3  81  8.00  McKenzie  McKenzie  5.20  CPT92-27  150  75 99 84 20  1.1  7.00  Electric  0.00  94  UBC  7  7  5.00  7  119 95  Electric  0.2  3  0.3  -0.08 0.00  193CPT18  170CP958  UBC  8.1  0.34 0.00 0.35  272  163  2.5 0.3 0.2  170CP958  Conetec Foundex Foundex Foundex Foundex  2.75 2.75  0.00  5 67 50 161  CPT7-4 193CPT18  LB9903 LB9904  0.5 8.1 0.5  4  1.6 0.3 0.2  170CP956 170CP958  LB9903  0.25  0.5  89  237  5 99 21  9.00  LB9901 LB9902  9.0  0.9  0.3  6.25 14.50 2.85 3.50  7.00 4.75  1.0  11  0.3  CPT7-7  0.00  166 16  63  170CP955  UBC  195  1.0 1.0  0.6 2.7  166 7  0.3  Conetec  2.75  0.00  0.00 0.00  0.00 0.15  92  20.50  LB9901  Electric  0.3  1.2  0.6 1.9  13.50  19.50  UBC  Geopac Geopac  134  225  -0.01  0.6  1.4  209CP20A  LB9901  227  0.3  0.4  208  17  19.00  170CP9510  UBC  0.00  1.2  193  0.6  42  79 7  Conetec  193CPT18  220  0.4  150  0.00  Conetec  0.2  121  0.00  35  17.50  2.75  0.5  0.02  0.6  1.5  209CP20A  2.75  Geopac  Electric  178 77  (m)  • 1.0  103  -0.08  69  0.9  178  1.9  170CP9510  Electric  LuLu Island  Bauer Geopac  3.9  H  0.4 0.4  0.3  Conetec  CPT05 CPT05 LB9903  25  0.00 -0.04  Table  (%)  231 211  0.3  7.50 14.75  5.3  11  (-) 34  0.4 0.4  120  4.50 12.75  2  (%)  110 177  0.5  209CP20A  6.1  (bars)  Water  q  -0.02  147  4.00  2  F,  1.1 0.4  0.5  170CP9510  Foundex Foundex  0.00  156  Conetec  2.75 2.75  0.3  12.00  7.50  4  0.6  0.  -0.01  0.5 5.3 0.5  7.50  CPT92-27 CPT92-27 CPT92-27  Sea Island Sea Island  0.6  Kr  t  0.4  165  113 2 156  2.00  Foundex  211 35  0.8  4 110 3 147  190CPT3  2.75  (-) 0.08  95  190CPT3  Electric Electric Electric  (%)  3.65 12.00 4.00 12.00  6.00  147CPT3  Bauer Bauer  Bauer  (-) 22  1.7 0.3  147CPT3  CPT92-27 CPT92-27 CPT92-27  q  3.00  170CP958  2.75 2.75 2.75  B,  1.00  Conetec  ?  77  9.20  11.50 1.70 2.90  ?  7.60  8.80 10.80  Conetec  209CP20A  158  5.00  Conetec  170CP9510  8.80  1.0 0.4  4.00  190CPT5 190CPT5 190CPT5  7  7  PIZA1  PIZA3 PIZA3  0.4  4.90  147CPT1 147CPT2 147CPT3  Bauer Bauer  7  RICPT4  98  6.00  4.35  Conetec Conetec Conetec  McKenzie McKenzie  7  RICPT3  5.50  2.50 7.50 2.00 7.50  Conetec  Electric Electric  UBC UBC  Sea Island  Sea Island  LuLu Island  7  Geopac Geopac  3  Electnc  Electric Hydraulic Hydraulic Electric Electric  6 6 6  Geopac  Conetec  Agra Bauer Bauer Bauer  LuLu Island  6  Geopac  3  Electric  Roberts Bank Sea Island Sea Island Sea Island  6 6  Geopac  Post-C ensi F. Average Va ues  r.  K,  t  (bars)  LuLu Island  LuLu Island  q  (m)  (m)  1 1  Pre-Densif. Average Values  0.4 0.3  167 73  0.4 0.3  0.00 0.00  0.0 0.0 0.0  0.2  284  128  0.2  247  0.2  0.00  1.0  76  0.2  56  0.2  0.00  1.0  139 122  130 75  0.3 0.3  0.3 0.3  143 100  150 55  0.3 0.3  0.3 0.3  0.00 0.00  0.00 0.00  1.0 1.0  1.0 1.0  10  LuLu Island  Geopac  Electric  3  10 10  LuLu Island  Geopac  Electric  3  10  10  LuLu Island LuLu Island LuLu Island  10 10 10 10  LuLu LuLu LuLu LuLu  12 12  LuLu Island LuLu Island  12  LuLu Island  12  Island Island Island Island  LuLu Island  Geopac  Electric  Geopac Geopac  Electric  Geopac Geopac Geopac Geopac Geopac  Geopac Geopac  Electric  2.75  12  LuLu Island  Geopac  Electric  12 12  LuLu Island  13 13  13 13 13 13  13 13 14 14 14  14 14  14 14 14  14 14  14 14 14  LuLu Island Sea Island Sea Island Sea Sea Sea Sea  Island Island Island Island  Sea Island Sea Island Sea Island  Sea Island Sea Island Sea Island Sea Island Sea Island Sea Island Sea Island  Conetec  2.75  2.75  Conetec  Geopac  Electric  2.75  Conetec  Geopac  Electric  2.75  Conetec  Geopac Geopac Geopac Geopac Geopac  Geopac  Geopac Geopac Geopac Geopac Geopac Geopac  Geopac Geopac Geopac Geopac Geopac Geopac  Geopac  2.75  Conetec  2.75 2.75  Conetec  2.75 3  Conetec  Electric Electric Electric Electric Electric  3 3 3 3  Electric Electric Electric  Electric  Electric Electric  Conetec  Conetec Conetec Conetec Conetec Conetec Conetec  3  Electric Electric  Geopac Geopac  Conetec Conetec Conetec Conetec  3 3  Electric  Sea Island Sea Island  Geopac  Conetec  3 3 3 3  Electric Electric Electric  Electric  Conetec  3  Electric Electric Electric  Geopac Geopac Geopac  Conetec Conetec  2.75  Electric  Sea Island Sea Island Sea Island  3 3 3  Electric Electric  12 12  95-145CPT5  Conetec Conetec Conetec Conetec Conetec Conetec  Geopac  LuLu Island LuLu Island  Conetec  Conetec  2.75  Electric  LuLu Island  LuLu Island  95-145CPT4  3  3 3  Conetec  3 3  Conetec  3  Electric Electric  Conetec Conetec  3 3  Electric  Conetec Conetec  3 3 3  95-145CPT4  Conetec Conetec  Electric Electric Electric Electric Electric  12  12  Conetec  3  Conetec Conetec  95-145CPT4 95-145CPT5  95-145CPT5 95-145CPT5  02-167CPT10 02-167CPT12 02-167CPT10 02-167CPT12 02-167CPT10 02-167CPT13 02-167CPT10 02-167CPT13 02-167CPT10 02-167CPT13 9S-256CPT1 98-256CPT4 98-256CPT2  98-256CPT2 98-256CPT2 98-256CPT2 98-256CPT2  98-256CPT2 98-256CPT2  97-153CPT3 97-153CPT3 97-153CPT3 97-153CPT3  97-153CPT3  97-153CPT3 97-153CPT3  98-256CPT10 98-256CPT10 98-256CPT10 98-256CPT18 98-256CPT18  98-256CPT18 98-256CPT1B 97-190CPT22 97-190CPT22 97-190CPT22 97-190CPT22 97-190CPT22 97-190CPT8 97-190CPT8  97-153CPT3 97-153CPT3 97-153CPT3  97-190CPT8 97-190CPT8  97-153CPT3 97-153CPT3  97-190CPT4 97-190CPT4  97-153CPT3  97-190CPT8 97-190CPT8  Geopac = Geopac West Lid Agra = Agra Foundations Limited Bauer = Bauer Spezialtiefbau GmbH Conetec = ConeTec Investigations Foundex= Foundex Explorations Ltd W.T.= Water table interpreted from CPT ? = Information not available For definition of q,, Q,, R , F and B please refer to Chapter 6. f  r  q  316  -0.04  0.3  0.00  275  63  0.4  0.00  1.2  17  1.3  -0.01  13  90  0.4  8.90  84  0.4  0.4 1.1  8  10.70  117  0.2  0.2 0.2 0.2 1.5 1.0  0.3  12.00 2.00  14.00 5.00  90  92  9.60  14.00 10.90  0.4 0.4  11  0.9  TABLE A1: Summary of CPT database before and after vibro-replacement in BC Notes:  1.2  0.3  7.60  5.00  6.00 7.20  1.6  0.00 0.00 0.00  18 95  0.4  12.00  0.00 0.00  0.2 0.2 0.2  90  9.20  9.90 11.20  0.3 0.3  89 75 53  14.10  8.00  4.00 7.20  202 173  0.00  12.00  91 92 78 7 11 92  3.00  0.2 0.3  124  5.50  11.10  129 146  0.2 0.2  1.00  7.00 8.60 9.70  0.00 0.00  82  4.00  9.30 12.00 3.00  0.2  6.50  12.00 14.00 4.00  7.80  0.00  134  50  11.50 3.00  0.3  0.00  8.00 10.50  7.10  164  0.2 0.2  7.00 8.00 10.50 13.00  3.00  0.3  0.3  0.00  69  7.70 12.65  192  107  0.3  4.00  9.50  1.0  0.00  0.3  8.20  2.20  2.00  1.0  0.00  13.50  4.50  02-167CPT10 02-167CPT12 02-167CPT10 02-167CPT12  0.00  0.2  0.00  00-219CPT10  02-167CPT10 02-167CPT11 02-167CPT10 02-167CPT11  0.2  203  0.3  9.00  00-219CPT10 95-145CPT5 00-219CPT10 95-145CPT5 00-219CPT10 02-167CPT10 02-167CPT11 02-167CPT10 02-167CPT11  344  0.2  204  0.3  4.80  5.80  00-219CPT10  0.2  152  0.3  74 123  2.00  00-219CPT14 00-219CPT14  00-219CPT10  131  79  00-219CPT14  8.90  3.90  7.60 12.50 4.00 8.80  10.50 13.50 3.60 7.80 9.00  10.90 12.20 4.00 5.00  8.00 10.80 12.00 13.00 6.50 7.90  8 84  82  0.4  57 119 12 149  0.5 0.4 0.9 0.4  126  125 9 140  31 189 97  0.4 0.4  1.2 0.4  1.1 0.3 0.4 1.1  16 28  0.9  194 75 210  0.5 0.3  149  97 148  0.4 0.4  0.4 0.4  98  170 58  21  105 63  0.3 0.4  164 164 56 151  125 164  244  11 193  1.4 0.4  23 209  0.5 0.5 1.0 1.0  1.0 1.0  1.2  -0.04  1.0  0.3  0.00  1.0  0.00  0.00  1.6 0.4  -0.05 0.00  1.0  1.0  1.0 1.0  205  0.4  146  0.4  0.00  1.0  0.05  10  0.8  19  0.9  0.13  1.5  177 144  158 9 211 225  0.00  230 145 330  0.9  -0.03  15 42  0.5 0.3  -0.01 0.00  141 12 .  1.3 0.4 1.1  0.00 0.19 0.00 -0.03  0.5 1.2  -0.01 0.12  246  0.00 0.00  213  -0.01  147  0.4 0.4  222  0.00  0.5 0.5  0.00 0.00  -0.01  0.4 0.4  0.3  0.5  0.00  0.4  0.4  30 44  27  0.00  0.5  0.3  117  88 19  0.3  1.1  172  0.4  -0.02 0.00 0.05 0.00  73  289  0.4  0.5  0.00 0.00 -0.03 -0.08  164  0.5  158 28 161  0.3  1.0  0.00  0.3 0.3 1.2 1.0  0.00 -0.01  0.00  64 88 23 153 111  155 58 23 14  0.3  -0.02  0.4 1.0 0.4 0.4  0.3 0.3 1.1 0.9  0.3  274  0.4  1.0  154  0.3  70 22  241  0.3  0.2  251  1.3 0.4 0.4  189 86 9 9  339  0.00  17 90 64  157  0.2  226  196 214  0.3 0.3  152 164  0.3 1.0 0.3  118 16 218  0.4 1.0  99 23  0.3  199  0.3 0.5 0.4  261 141 283  1.3 0.7  30 69  0.5  188  0.3  236  0.4 0.3 0.5  151 153 192  0.3  193  0.3 0.3  0.3 1.1 0.3  0.3 0.4 1.1  0.3 0.5 0.4 0.5  0.00  0.00  0.00 0.11 0.00 0.00 0.00 0.06  0.00 0.00 0.00 0.00  1.4 0.7  0.03 -0.01  0.3  0.00  0.3 0.4 0.3 0.5  0.00 0.00 0.00 0.00  0.00 204 0.5 227 0.5 0.00 Filename: GIVector-average-all projects-24  1.5  1.5 1.5 1.5 1.5  1.5  1.5 1.5  1.5 1.5 1.5 1.5 1.5 1.5  1.5 1.5 1.5 1.5 1.5 1.5  

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