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UBC Theses and Dissertations

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

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APPLICATION OF SEISMIC C O N E FOR C H A R A C T E R I Z A T I O N O F GROUND IMPROVED BY V I B R O - R E P L A C E M E N T by A L I A M I N I A S A L E M I M . A . S c , University of Science and Technology, Tehran, Iran B . S c , University of Science and Technology, Tehran, Iran A THESIS S U B M I T T E D I N P A R T I A L F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E OF D O C T O R OF P H I L O S O P H Y in . T H E F A C U L T Y OF G R A D U A T E S T U D I E S (Civ i l Engineering) T H E U N I V E R S I T Y OF B R I T I S H 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 A B S T R A C T The objective of this thesis was to gain a better understanding of the physical process of ground improvement by vibro-replacement and of how the induced changes in ground conditions affect the interpretation of seismic cone penetration testing used to assess its effectiveness. This was achieved by a combination of field testing and monitoring supported by numerical modelling of both the vibro-replacement process and of in situ testing. Field measurements were made of 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 of seismic cone testing before and after treatment at 15 sites and existing chamber test data were analyzed and additional numerical modelling of 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 of 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. If the induced heterogeneity is neglected when interpreting in situ test results, there wi l l be some over-estimation of the soil properties close to the cone hole and considerable under-estimation of the average properties of 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 of the improved native soil. Analysis of field test data showed that vibro-replacement causes an apparent shift in soil behaviour type classification. The combined effects of 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 of 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. i i T A B L E O F C O N T E N T S A B S T R A C T i i T A B L E O F C O N T E N T S i i i L IST O F T A B L E S v i i i L IST O F F I G U R E S ix G L O S S A R Y xxi A C K N O W L E D G E M E N T S xxv D E D I C A T I O N xxvi C H A P T E R 1 I N T R O D U C T I O N 1 1.1 Background 1 1.2 Focus of this research ; 2 1.3 Methodology and organization of the thesis 3 C H A P T E R 2 C U R R E N T A P P R O A C H E S T O G R O U N D I M P R O V E M E N T 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 .4 2.1 Introduction 4 2.2 Soil behaviour during monotonic and cyclic shearing 4 2.3 Characterization of granular soils 7 2.3.1 Introduction 7 2.3.2 Piezo-cone testing, C P T U 7 2.3.3 Soil classification by C P T 8 2.3.4 Engineering properties of soil 10 2.4 Mechanism of compaction of granular soil 11 2.5 Ground improvement methods for liquefaction mitigation of granular soils 12 2.5.1 Introduction 12 2.5.2 Vibro-compaction 13 2.5.3 Wet vibro-replacement 15 2.5.4 Vibrators 16 2.5.5 Quality control during vibro-replacement 17 2.5.6 Previous works on vibration measurement and the mechanism of compaction by vibro-compaction methods 18 2.6 Discussion and need for further research 21 2.7 Summary and conclusions 22 C H A P T E R 3 M E C H A N I S M O F V I B R O - R E P L A C E M E N T 45 3.1 Introduction 45 3.2 In situ ground response to vibro-replacement 45 3.2.1 Field vibration measurement 45 3.2.2 Vibration measurement equipment 46 3.2.3 Results of vibration measurement 48 3.2.4 Analysis of results 49 3.2.4.1 Frequency analysis of the time histories 49 3.2.4.2 Attenuation of vibration 49 3.2.4.3 Horizontal motion paths of the vibroflot and soil particles 55 i i i 3.2.4.4 Optimal frequency of vibration 55 3.2.4.5 Densification phase 56 3.2.4.6 Pore pressure response during penetration 58 3.3 Mechanism of penetration of the vibroflot 59 3.4 Numerical modelling of vibro-compaction 60 3.4.1 Introduction 60 3.4.2 Numerical model 61 3.4.3 Results of numerical modelling 64 3.4.4 Mechanism of compaction during vibro-replacement 65 3.4.4.1 Shear-volume coupling model 65 3.4.4.1.1 Drained condition 65 3.4.4.1.2 Undrained condition 67 3.4.4.2 Proposed mechanism of compaction during vibro-replacement 67 3.4.5 Other mechanisms of the effects of vibro-replacement 70 3.4.5.1 Increase in lateral stress 70 3.4.5.2 Geological ageing effects 72 3.5 Summary and conclusions 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 OF H E T E R O G E N E I T Y C A U S E D B Y V I B R O - R E P L A C E M E N T 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 of cavity expansion theory 122 4.4.1 Soil model and selection of parameters 123 4.4.2 Verification of the numerical analysis 125 4.4.3 Effect of soil stress dependency on limit pressure 125 4.4.4 Effect of presence of stone columns on limit pressure 126 4.4.5 Effect on limit pressure of variation of soil parameters in the grid zone between the stone columns 126 4.5 Discussion of the results of numerical analyses 128 4.5.1 Effect of G / G m a x 129 4.5.2 Assumption of Plane strain condition 129 4.6 Implications for interpretation of post-densification C P T testing 130 4.7 Effect of the heterogeneity on ground performance during earthquake shaking. 131 4.8 Summary and conclusions 132 C H A P T E R 5 E F F E C T O F H E T E R O G E N E I T Y 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 S E I S M I C C O N E T E S T I N G R E S U L T S 147 5.1 Introduction 147 5.2 Interpretation of S C P T signals for shear wave velocity 147 5.3 Observed effects of vibro-replacement on seismic cone testing 150 5.3.1 Field evidence on the effect of stiffer inclusions on seismic test results ..151 5.4 Numerical modelling for investigation of the effect of stone columns on V s 153 5.4.1 Numerical modelling of the down-hole seismic test without stone columns 153 iv 5.4.1.1 Soil model and conditions analyzed 153 5.4.1.2 Loading condition 154 5.4.1.3 Results of numerical analysis 155 5.4.1.4 Characteristics of the simulated signals compared to field data 155 5.4.1.4.1 Shape of the waveforms 156 5.4.1.4.2 Attenuation of signals with depth 156 5.4.1.4.3 Widening of the signals with depth 156 5.4.1.4.4 Compression wave arrival (near field effect) 157 5.4.1.5 Calculation of V s from field data 159 5.4.1.6 Calculation of V s from simulated signals ; 160 5.4.1.7 Summary and conclusions of the numerical analysis of S C P T without stone columns 161 5.4.2 Numerical modelling of 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 of the V s from simulated signals 163 5.4.2.4 Discussion 163 5.4.2.5 Summary of the numerical analysis of seismic cone testing in presence of 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 C H A P T E R 6 E F F E C T S 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 R E S P O N S E T O C O N E P E N E T R A T I O N T E S T I N G 200 6.1 Introduction 200 6.2 Observation of the changes in ground response to C P T U 200 6.2.1 Database of vibro-replacement projects in the Lower Mainland, B C 200 6.2.2 Geological history of Richmond 201 6.2.3 Pre- and post-compaction database on C P T classification chart 201 6.2.3.1 Effect of compaction on soil classification by C P T 203 6.2.3.2 Effect of compaction on estimation of apparent fines content ...204 6.2.4 Effect of 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 of changes in ground conditions on the direction of movement on the classification chart 206 6.2.4.3 Effect of changes of D r and lateral stress on I c value 208 6.2.4.4 Conclusions 208 6.3 Achievable penetration resistance after vibro-replacement 209 6.4 Summary and conclusions 211 C H A P T E R 7 E F F E C T OF A G E I N G O N I N T E R P R E T A T I O N O F S C P T D A T A 229 7.1 Background 229 7.1.1 Mechanism of ageing 230 7.1.2 Effect of ageing on small strain soil properties 230 7.1.3 Effect of ageing on stress-strain behaviour of sand 231 7.1.4 Effect of ageing on cone tip resistance 232 v 7.1.5 Mechanism of the effect of ageing on S C P T 232 7.1.6 Effect of ageing on liquefaction resistance 232 7.1.7 Evidence of the geological ageing. 233 7.2 Case studies 234 7.2.1 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 of ageing/destructuring 237 7.2.2.4 Implication of ageing/destructuring in estimation of soil properties 239 7.2.2.5 Effect of blasting on G m a x /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 of ageing/destructuring on interpretation of post-densification S C P T for soil properties 245 7.4.1 Interpretation of relative density and friction angle 245 7.4.2 Interpretation of soil stiffness 245 7.4.3 Effect of destructuring on liquefaction cyclic resistance ratio (CRR) of improved ground 246 7.5 Conclusions 247 C H A P T E R 8 E F F E C T O F I N C R E A S E I N H O R I Z O N T A L S T R E S S O N I N T E R P R E T A T I O N O F C P T D A T A 270 8.1 Introduction 270 8.2 Field evidence of increase in horizontal stress 270 8.3 Effect of increase in horizontal stress on interpretation of soil properties 271 8.3.1 Effect of increase in horizontal stress on interpretation of D r 271 8.3.2 Effect of increase in horizontal stress on shear modulus and footing settlement 273 8.3.3 Effect of increase in horizontal stress on interpreted friction angle from C P T results 277 8.3.4 Effect of increase in horizontal stress on interpreted cyclic resistance from C P T results 277 8.3.5 Effect of the increase horizontal stress on estimation of earthquake induced settlement 278 8.4 Summary and conclusions 279 C H A P T E R 9 S U M M A R Y A N D C O N C L U S I O N S 289 9.1 Research focus and objectives 289 vi 9.2 Methodology... : 290 9.3 Summary of major findings 290 9.4 Recommendations for future research 295 R E F E R E N C E S 297 A P P E N D I X O N E : Database of CPTs carried out before and after vibro-replacement ....313 v i i LIST O F T A B L E S Table 2-1 Factors affecting mechanical behaviour of granular soils 24 Table 2-2 Commonly used vibrators and their specifications (from www.vibroflotation.com) 24 Table 2-3 Comparison of some of ground improvement methods for liquefaction mitigation (adapted from Mitchell and Gallagher 1998) 25 Table 2-4 Main components of design of ground improvement for liquefaction mitigation 26 Table 3-1 Distance of monitored stone columns from the ground sensor... 76 Table 3-2 Calibration of 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 134 Table 4-2 Cases of numerical modelling of plane strain analysis of cavity expansion at the centroid of stone column grid 134 Table 5-1 Input soil parameters in numerical model, homogeneous soil condition 168 Table 5-2 Comparison of the V s obtained from different methods, Richmond, B . C 168 Table 5-3 Material properties used in numerical model 168 Table 5-4 Interpretation of V s (m/s) from simulated signals, depth interval of 5m- 6m 168 Table 7-1 Values of N G for various soils (After Baxter 1999- based on studies by Af i f i and Woods 1971 and Anderson and Stokoe 1978) 249 Table 7-2 Examples of ageing effects on cone penetration resistance and their main findings (after Baxter 1999) 250 v i i i LIST O F FIGURES Figure 2-1 Typical behaviour of sand under monotonic loading in drained condition (after Bolton 1979) 27 Figure 2-2 Typical behaviour of sand under monotonic loading in undrained condition (after Robertson and Wride 1998) 28 Figure 2-3 Schematic illustration of the seismic piezo-cone, S C P T U : 29 Figure 2-4 A typical C P T U profde, Kidd2 site, Richmond, B C 30 Figure 2-5 Schematic illustration of 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 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 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) 37 Figure 2-12 Cross-section of a vibroflot (adapted from website www.vibroflotation.com) 37 Figure 2-13 Soil vibroflot interaction- horizontal section- (originally from Greenwood 1991, annotated by Green 2001) 38 Figure 2-14 Schematic illustration of the effect of 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) 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) 42 Figure 2-19 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) 43 Figure 2-21 Densification zones as a function of acceleration around a compaction point proposed by Greenwood and Kirsch (1983) 44 Figure 2-22 Vibration history recorded during vibro-stone column. Depth of 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 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 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 of stone column #3 83 Figure 3-8 Recorded time histories during stone column #3, enlarged scale during densification. Note that scales are not consistent 84 Figure 3-9 Frequency spectra of acceleration time histories of the vibroflot and the ground during densification 85 Figure 3-10 Frequency spectra of acceleration time histories- enlarged scale 85 Figure 3-11 Energy loss due to damping in a visco-elastic material 86 Figure 3-12 Partial transmission and conversion at the interface (after Santamarina et al. 2001) 86 x Figure 3-13 Attenuation of radial and tangential acceleration with distance from vibroflot 87 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 Figure 3-15 Attenuation of the resultant horizontal acceleration 88 Figure 3-16 Attenuation of the resultant horizontal acceleration 88 Figure 3-17 Attenuation of radial displacement in the ground around vibrators (after Morgan and Thomson 1983) 89 Figure 3-18 Interpretation of Green (2001) for attenuation of radial acceleration around Keller S-type vibrator based on Baez (1995) data 90 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 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 94 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 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 Figure 3-25 Response of the vibroflot and ground during switch-on at 10m depth-stone column #3, enlarged from Figure 3-7 97 Figure 3-26 Ratio of the responses of ground and vibroflot as a function of frequency during switch-on 98 Figure 3-27 Comparison of the vibroflot motion and power consumption during densification phase 99 x i Figure 3-28 Pore pressure time history during stone column #3 100 Figure 3-29 Pore pressure response during penetration of vibroflot 101 Figure 3-30 Schematic of the Original Vibratory Piezocone designed by Sasaki and Koga (1982) (taken from McGi l l iv ray et al. 2000) 102 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 Figure 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 of the vibrator in the ground (after Fel l in 2000) 104 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 Figure 3-36 Motion of 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) 107 Figure 3-39 Comparison of resultant horizontal accelerations from field measurement and equivalent elastic analyses 108 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 109 Figure 3-41 Min imum required measurement points in the ground for calculation of the 3 components of shear strains 110 Figure 3-42 Distribution of shear strains in horizontal plane from equivalent linear analyses I l l 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) model 112 Figure 3-45 Cone tip resistance before and after vibro-replacement 113 x i i 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 Figure 3-47 Radial displacement of grid point at different distances from the vibroflot versus vibration time 115 Figure 3-48 Increase of average horizontal stress with the number of cycles at different radial distances, r from the vibroflot. 116 Figure 3-49 Radial stress vs. radial displacement at radial distance of r=l .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=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 r from the vibroflot (reproduced from D'Appolonia 1953) 135 Figure 4-3 Variation of q c with distance from the compaction points for two different vibrators Vibroflot V23 and V32 ( after Degen and Hussin 2001) 136 Figure 4-4 Idealization of analysis for cone penetration (after Y u and Mitchel l 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 of plane strain numerical model 138 Figure 4-7 Geometry of 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 140 Figure 4-9 Comparison of F L A C analyses with Carter et al. (1986) closed form solution 140 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 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 x i i i Figure 4-14 Effect of fixity of stone columns on cylindrical cavity limit pressure (G/G m a x =0.1) .. 143 Figure 4-15 Variation of cylindrical cavity limit pressure as a function of D r for homogeneous soil condition ( G / G m a x = 0 . 5 ) 143 Figure 4-16 Variation of cylindrical cavity limit pressure as a function of D r for homogeneous soil condition for G/G m a x =0.1 and 0.5. Note the assumption of G/G m ax does not affect the interpreted D r 144 Figure 4-17 Consideration of heterogeneity of soil within compaction grid on Q C after vibro-replacement 145 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 t results in a greater interpreted C R R 120 Figure 5-1 Comparison of S C P T seismic signals before (left) and after (right) vibro-replacement, Richmond, B C 169 Figure 5-2 V s profile from cross-over and cross-correlation methods, (left) before vibro-Replacement, (right) after vibro-Replacement 170 Figure 5-3 Variation of 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 171 Figure 5-5 S C P T profile before and after vibro-replacement, Laing Bridge, Richmond, B C 172 Figure 5-6 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 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 Figure 5-9 Schematic geometry of the F L A C model 176 Figure 5-10 Modell ing of soil behaviour in compliance with strain dependent deformation characteristics (after Ishihara 1996) 176 Figure 5-11 Input loading at the ground surface over the length of the seismic source beam 177 xiv Figure 5-12 Wave propagation in homogeneous soil, velocity vectors at 0.05 sec after the impact 177 Figure 5-13 Time histories of horizontal velocity in numerical model at 5 m, homogeneous soil 178 Figure 5-14 Time histories of horizontal acceleration in numerical model at 5 m, homogeneous soil 178 Figure 5-15 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, Kidd2, Richmond, B . C 181 Figure 5-18 Effect of material damping on the number of cycles, homogeneous soil 182 Figure 5-19 Comparison of 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 of different interval methods for calculation of the V s , Richmond, B . C 187 Figure 5-25 Profile of shear wave velocity, Kidd2, Richmond, B . C 188 Figure 5-26 The V s profile from the simulated signal, homogeneous soil, Damping=5% 189 Figure 5-27 The V s profile from the simulated signal- increasing stiffness with depth, Damping=2% 190 Figure 5-28 Variation of phase velocity, simulated signals, homogeneous soil, Damping=5%, 5m & 6m depth interval 191 Figure 5-29 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 of body waves in presence of two stone columns 194 Figure 5-32 Simulated signals in the presence of two stone column, G r =5, D = l m 195 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 r and D, simulated signals 198 Figure 5-38 Comparison of change in V s and q t after vibro-replacement 199 Figure 6-1 History of the growth of the Fraser River Delta (Source: CGS, 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) 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 & 2-7 215 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 Figure 6-6 Path of movement of the position on the classification charts due to vibro-replacement 216 Figure 6-7- Comparison of pre-I c and post-I c values 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) 218 Figure 6-10 Results of calibration chamber data for N C Ticino sand on normalized classification chart using true normalization for stress level 219 Figure 6-11 CPT-based soil classification chart proposed by Jefferies and Davies (1993) 220 xv i 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 Figure 6-13 Effect of changes in only D r on C P T classification chart, data taken from calibration chamber testing on Ticino sand 222 Figure 6-14 Effect of D r on Rf, Ticino sand, data taken from calibration chamber testing on Ticino sand 223 Figure 6-15 Effect of the horizontal stress on Rf, data taken form calibration chamber testing on Ticino sand 223 Figure 6-16 Effect of O C R on Rf, data taken from calibration chamber testing on Ticino sand 224 Figure 6-17 Effect of the increase in D r and/or a ' n on I c- from C C testing data on N C Ticino sand 224 Figure 6-18 Normalized tip resistance before and after vibro-replacement, triangular grid, Lower Mainland, B C 225 Figure 6-19 Comparison of the normalized tip resistance before and after vibro-replacement, Lower Mainland, B C with Baez (1995) correlation 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) 228 Figure 7-1 Increase in shear modulus with time (after Af i f i and Woods 1971) 251 Figure 7-2 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 . Figure 7-3 Effect of ageing on stress-strain curve, Fraser River sand (after Howie et al. 2001) 252 Figure 7-4 Comparison of modulus reduction curve of dense sand from disturbed and undisturbed samples (after Ishihara 1996- data originally from Katayama et al. 1986) 252 xvi i 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 253 Figure 7-6 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 of aged sand deposits relative to the cyclic strength of Holocene sand, age < 10,000 years (after Arango and Migues 1996) 255 Figure 7-9 Comparison of undrained simple shear response of undisturbed sand and water-pluviated sand (after Va id and Sivathayalan 2000) 255 Figure 7-10 Plot of average q c i and 14C age of organic material in topset sand (after Monahan et al. 2000) 256 Figure 7-11 Change in normalized shear wave velocity with age for uncemented sands (after Robertson et al. 1995) 256 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 Figure 7-13 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 of S C P T holes 259 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 Figure 7-18 Variation of the average values of q t and V s with time after blasting, Massey Tunnel Site '. 263 Figure 7-19 Variation of average G m a x / q t before and after blasting, Massey Tunnel Site 264 Figure 7-20 C P T U sounding, Kidd2 site, Richmond, B . C 265 xv i i i 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 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 267 Figure 7-23 Variation of Vs 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 of the effect of densification on soil modulus, #1= natural aged deposit; #2=After destructuring; #3=Young densified deposit; #4=Aged densified deposit 229 Figure 8-1 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) 281 Figure 8-2 Non-uniqueness of interpretation of cone tip resistance- different combinations of D R and ah results in the same q t 281 Figure 8-3 Application of combination of q t and V s for post-compaction site investigation, Vibro-Replacement project, Richmond, B C 282 Figure 8-4 Settlement versus foundation sizes for different K Q - D R combinations (Adapted from Jamiolkowski and Pasqualini 1992) 283 Figure 8-5 Effect of variation of K o on G m a x for constant q t. Variation of K o and D R are such that the resulting q t remains constant 283 Figure 8-6 Effect of increase in coefficient of lateral stress on the shape of the modulus reduction curve 284 Figure 8-7 Effect of increase in K o on the shear modulus (assume a' v=100 kPa) 285 Figure 8-8 Effect of increase in Ko on G normalized to G at Ko=0.45 for shear strain ofy=0.002 286 Figure 8-9 Effect of increase in K o on the interpretation of G m a x from measured V s (through the effect of estimation of soil density) 286 Figure 8-10 Effect of increase in K o on the interpretation of G from measured V s 287 Figure 8-11 Effect of increase in K o on the interpretation of peak friction angle from post-densification tip resistance 287 xix 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 xx G L O S S A R Y a: Net area ratio of the cone A : Single amplitude of acceleration A i and A 2 : Vibration amplitudes at distances ri and r 2 A C C x , t : Acceleration of the vibroflot in x direction A C C y , t : Acceleration of the vibroflot in y direction a m a x : Maximum acceleration at ground surface A s : Area of soil in stone column tributary area A s c : Cross section area of stone column A t r : Tributary area of one stone column A v s : Correlation parameter in empirical shear wave velocity equation B : Bulk modulus B v s : Correlation parameter in empirical shear wave velocity equation Ci and C 2 : Regression parameters in shear volume coupling model C S R : Cycl ic stress ratio D: Damping ratio Dchambei-: Diameter of calibration chamber Dcone: Diameter of cone D r : Relative density E : void ratio f: Frequency of vibration F: Normalized friction ratio F C : Fines content fs : Sleeve friction g: Gravitational acceleration G m a x : Small strains shear modulus G m a X (t): G m a x at time t Gm ax(tp): Gmax at end of primary consolidation G r : Ratio of shear modulus of stone column to soil. I c: Soil Behaviour Type Parameter xx i IR: A coefficient in Bolton empirical correlation K m : A coefficient in empirical correlation for soil modulus K 0 o c and K<, N C : Coefficients of lateral stresses for over and normally consolidated soil Koi coefficient of horizontal stress L 2 and Li : Slant distances between sensor in cone and source beam at two intervals 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 v s: A correlation parameter in shear wave velocity empirical equation OCR: Over-consolidation ratio Pa: A reference pressure P a 2: Atmospheric pressure PI: Plasticity index post-qci: Normalized cone tip resistance before compaction pre-qci: Normalized cone tip resistance after compaction Q: Normalized cone tip resistance qc: Measured cone tip resistance q c i : Cone tip resistance normalized to vertical effective stress q c iN : Cone tip resistance normalized to vertical effective stress (unitless) qc-measured: Cone tip resistance measured during penetration in calibration chamber Qa: Inverse of twice damping ratio qt: Cone tip resistance corrected for water pressure behind the friction sleeve r: Radial distance between the vibration source and point of interest ri and r 2 : Distances from the source of vibration ra: Stress reduction factor Rf: Friction ratio Si(t) and S2(t+x) : Two consecutive SCPT signals recorded in the time domain at upper and lower interval depths xx i i T r : A coefficient representing the reduction of amplitude due to partial transmission and mode conversion. T: Length of the time record in seconds t: Time t2-ti: Travel times of shear waves from the source to the sensor in the cone at at two successive depths intervals tp: Time to the end of primary compression V : Wave velocity V p : Compression wave velocity V s : Shear wave velocity. V s i : Shear wave velocity normalized to vertical effective stress Wp: Hysteresis area under stress-strain curve Ws: The triangular area under stress-strain curve (Ymax-Tmax/2) a : A n empirical coefficient for energy damped in vibration a i : Attenuation coefficient associated with fj A s v : Incremental volumetric strain in the current cycle A s e v : Cycl ic elastic volumetric strain A s p v : Cycl ic plastic volumetric strain A s v : Cycl ic accumulated volumetric strain A a ' v : Vertical effective stress change per half a cycle At: Interval time equal to t 2-ti in S C P T s v: Accumulated volumetric strain from the previous cycles <j)cv: Friction angle at critical state or constant-volume <j)p: Peak friction angle (j)(f): Phase difference y : Engineering shear strain in the current cycle yt = shear strain threshold Y*: Net engineering shear strain in the current cycle X: wave length v: Poisson's ratio xx i i i p : Bulk density r j ' m : Mean normal stress o"'m_B: Mean normal stress at failure in Bolton (1986) equation a ' v : Vertical effective stress a ' v o : In situ vertical effective stress r j v o : In situ total vertical stress rj r: Radial stress GQ: Tangential stress v|/ m a x: Maximum dilation angle T : Time shift in cross-correlation method T s : Shear stress of the soil xxiv A C K N O W L E D G E M E N T S First of 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 of my industrial collaborators, Dr. Alex 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 Dr Alex 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 of the University of British Columbia, Department of 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 of the Natural Science and Engineering Research Council of Canada, the G R E A T Award Scholarship of the Science Council of B . C . xxv To my dear parents, fihmadandTah To my Coving wife, fMitra To my dear son, Mehrdad And to many others that I dearly Love XXVI C H A P T E R 1 INTRODUCTION 1.1 B A C K G R O U N D Almost all construction works are done on, in 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 of bearing capacity, etc. In such cases, one may choose to improve the in situ soils to withstand the design loads with acceptable performance. Design of ground improvement for liquefaction mitigation requires answers to the following questions: • Is ground improvement necessary? • To what level should the ground be improved (specification) and how should the improved ground be assessed (QC/QA)? • Which techniques are suitable to improve the ground? Ground improvement has a long history. Van Impe (1989) noted that it is probably the oldest o f all common execution methods in c iv i l 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 in 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, in 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 of ground treatment methods had remained mainly empirical and would benefit from the application of better engineering science. He suggested that this would ideally result in the following: 1. A n improved understanding of soil behaviour and diagnosis of deficiencies, 2. A n improved understanding of 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 in situ testing before and after treatment, and 4. A more realistic appreciation of what can be achieved by ground treatment through the study of well documented case histories of long-term performance. This thesis is an attempt to achieve progress on each of the above points. 1.2 FOCUS O F THIS R E S E A R C H In the Lower Mainland of British Columbia, ground improvement is commonly required to increase the resistance of 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 (CPT) was the primary method of both site characterization and of assessment of the degree of improvement achieved. Consequently, this thesis focuses on achieving an improved understanding of 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 of the research were as follows: 1. To understand the physical process of vibro-replacement and its effects on ground conditions; 2. To understand the effects of 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 AND O R G A N I Z A T I O N O F T H E THESIS To approach the objectives of this research, the following steps were taken: 1. Investigation of the physical process of vibro-replacement method and its effects on ground conditions by vibration measurement in the field followed by numerical modelling (Chapter 3). 2 . Investigation of the effect of the heterogeneity induced by vibro-replacement, on seismic cone penetration testing by field observation and numerical modelling of the seismic cone penetration test (Chapters 4 and 5). 3. Development o f a database of pre- and post-vibro-replacement C P T U results for 15 vibro-replacement sites to observe the trends of changes in C P T response (Chapter 6). 4. Investigation of the effect of time on the S C P T results by monitoring the time effect in field case studies (Chapter 7). 5. Investigation of the effect o f increase in horizontal stress, caused by vibro-replacement, on interpretation of S C P T using parametric studies (Chapter 8) . Chapter 9 summarizes the major findings and conclusions of this study followed by recommendations for further research. 3 C H A P T E R 2 C U R R E N T A P P R O A C H E S T O G R O U N D I M P R O V E M E N T 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 of ground improvement as a remedial measure against the effects of seismic loading on sandy soils and reviews the current state of understanding of how densification is achieved and how its success is assessed. A brief review of the stress strain behaviour of sands under monotonic and cyclic loading is provided as a background to discussions on the mechanism of densification and on the use of site characterization to assess ground conditions before and after ground improvement. 2.2 SOIL B E H A V I O U R DURING M O N O T O N I C AND C Y C L I C S H E A R I N G The mechanical behaviour of granular soils is a function of 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 of combinations of mean normal effective stress and void ratio at ultimate limit or critical state is called the Ultimate State Line (USL) or Critical State Line (CSL) . However, the shear strain required to reach this state is typically too large to be attainable during laboratory tests. In the following, we wi 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. At 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. With further increase of 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 in a tendency for generation of pore water pressure when shearing occurs under conditions of restricted drainage, with typical behaviour for a fully undrained case shown in Figure 2-2. For contractive sand (loose of critical - curve SS in Figure 2-2) positive excess pore pressure is generated, which decreases the effective stress and the shear resistance of 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 of stress ratio or shear stress at which strain softening is initiated has been given a variety of names. Two 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 Va id and Chern (1985). This behaviour could result in a flow failure under static loading i f the in situ driving stress exceeds the shear strength at U L S (qST in Figure 2-2). For sand that is dense of critical (curve S H in Figure 2-2), the initial tendency for contraction under drained loading causes positive excess pore pressure under conditions of restricted drainage but this is quickly followed by a tendency for dilation, causing a reduction of 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 of 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 (LSS 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 of 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 of excess pore pressure depend on the balance between the tendency towards volume change and the rate at which drainage is possible. Va id and Eliadorani (2000) showed that a small injection of 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 of the soil particles), direction of loading relative to the direction of deposition and length of time and stress history since deposition. Under repeated cycles of shearing as occurs during seismic loading, there is a tendency towards accumulation of 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 of sand is a function of the factors listed in Table 2-1 as well as o f the number of cycles and the magnitude of the cyclic strain. The reduction in effective stress causes a drop in stiffness and results in accumulation of shear strain as cyclic loading continues. With sufficient cyclic loading, the soil may liquefy. Liquefaction is, by definition, the transformation of 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 of relative density but that confining stress, the lateral earth pressure coefficient K Q , ageing/fabric and number of 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 of voids and thus decreases the potential to contract during shearing under drained conditions and reduces the generation of positive pore pressure under undrained conditions. This can be accomplished by ground densification. 6 2.3 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 2.3.1 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 of 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 of granular soils. Most in situ tests, including all penetration tests, are index tests and not a direct measurement of soil properties. Only the soil response to a specific imposed perturbation is measured during the tests, e.g. the response to penetration of a cone into the ground. The soil response, such as the penetration resistance, q c , is a function of the same parameters that affect the soil behaviour under monotonic or cyclic loading. This is the basis of 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 (SCPTU) 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 of a standard piezo-cone. The cone is pushed into the ground at a standard rate of 2 cm/sec. Cone tip resistance, q c , sleeve friction, fs, and pore pressure, u, are recorded. q c is the total force acting on the cone divided by the projected area, and fs is the total force acting on the friction sleeve divided by its surface area. The pore pressure is typically measured behind the shoulder of 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). Tip resistance should be corrected for unequal end area effects caused by the pore pressure acting on the back of the cone tip using the following equation: Qt =ac +u2(l-a) Equation 2-1 where q t is the corrected tip resistance and "a" is the net area ratio of the cone. In sands, where u 2 is small relative to q c , the above correction is small and thus q c and q t are almost identical. The data are usually recorded at typical intervals o f 2.5 or 5 cm. This provides a detailed and practically continuous profile of the soil response to penetration. A t the standard rate of penetration, the soil response tends to be drained in sands, undrained in clays and clayey silts, and partially drained in soils of 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 of the C P T U can be enhanced by the inclusion of 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 (SCPTU) . 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 s and, less frequently, the compression wave velocity and damping o f the soil. During pauses in 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 in wave arrival time over that increment of depth. Based on the theory of 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 where p is bulk density and V s is shear wave velocity. 2.3.3 Soil classification by CPT The C P T has a wide range of 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. G, max Equation 2-2 8 • For direct correlation to ground or foundation performance such as liquefaction resistance, pile capacity, and compactability. • For correlation to engineering properties of the soil, which are then used in design calculations to predict the performance of the ground or foundation. The C P T U profile can be interpreted to allow determination of soil stratigraphy, as shown in Figure 2-4. The near continuous profile allows identification of thin layers in the range of centimetres. For example, thin interbedding of silty sand within the sand stratum from 7 to 12m, can be clearly observed by a decrease in q t , an increase in Rf and sudden change of u 2 . Robertson et al. (1986) used the basic C P T parameters, q t , fs and u 2 in two separate classification charts (Figure 2-6). The soil behaviour type, SBT, corresponding to each zone in the classification chart is also included in the figure. These have been found generally applicable for classification of alluvial deposits to depths of up to about 30 m. Beyond that depth, it becomes necessary to account for the effect of stress level. Attempts were made to normalize the classification charts for in situ stress (e.g. Olsen 1984 & 1994, Olsen & Mitchel l 1995; Robertson 1990). Robertson (1990) used a linear normalization for q t that works best for clayey soils but is less suited for sandy soils (Figure 2-7). Jefferies and Davies (1993) introduced the concept of a material index in development of 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 c which is the radius of concentric circles in Q t versus F r space and is given by the following equation: Equation 2-3 where Equation 2-4 I P« A O *ioo Equation 2-5 9 where all the parameters are as defined previously. A contour for Ic=2.25 is shown on Figure 2-7 as an example. The top left hand corners of the charts (small I c) typically represent coarser, cohesionless soils and the soil becomes finer i f it plots towards the bottom right of the chart as I c increases. Robertson and Fear (1995) used the following equation to correlate fines content (ratio of the weight particles finer than 0.074mm to the total weight of the soil) to I c. F C ( % ) = 1.75- Ic Equation 2-6 This was an attempt to account for the effect of 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 of the same factors that affect the mechanical soil behaviour as noted in Table 2-1. The main factors for C P T response in granular soils are: • State, including relative density and effective stress conditions (a ' n and a' 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 (OCR) , 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 of the cyclic stress ratio (CSR) experienced at the site and q c iN , the normalized tip resistance given by the expression: 10 Qc\N \ P a 2 J Equation 2-7 where q c is the cone tip resistance, P a 2 is a reference pressure of 1 atmosphere in the same units as q c , P a is a reference pressure of 1 atmosphere in the same units as a'v0, and a ' 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 of V s . Thus, the seismic cone has the advantage of providing data for two independent methods of 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 of the soil particles into a more compact state. Compaction reduces the void ratio and requires concurrent expulsion of pore fluid. This in turn requires a high permeability of 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 of granular soils by static loading is not efficient. Volume change of 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 in the lab (e.g. Youd 1972; Silver and Seed 1971; Martin et al. 1975; Dobry et al. 1982). Figure 2-9a shows that the volumetric strains, s v depends on the magnitude o f shear strains, y and the number of 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 of granular soils by vertically vibrating probes and also to estimate the earthquake-induced settlement of granular soils. 11 There have also been some attempts to relate the compaction of granular soils to the magnitude of acceleration during vibration instead of to shear strains. D 'Appolonia et al. (1967) used a shaking table to subject unconfined damp sand to controlled vertical accelerations over a range of frequencies (20-35 Hz). They found that the maximum density was independent of the displacement amplitude and frequency. The main factor influencing the degree of compaction attained was found to be the peak acceleration (the product of displacement amplitude and the square of frequency). The increase in dry unit weight was small below an acceleration of l g and the peak density was achieved at an acceleration of about 2g. Higher accelerations loosened the soil. More recently, Bement and Selby (1997) conducted a laboratory test program to study the compaction of 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, Youd (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 of 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 of cycles) is the fundamental mechanism for compaction of granular soils. While acceleration can be used as an index of compaction effectiveness, it cannot be uniquely related to effectiveness of compaction because the relation between shear strains and acceleration is a function of the frequency o f vibration. 2.5 G R O U N D I M P R O V E M E N T M E T H O D S F O R L I Q U E F A C T I O N 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 of pore pressure 12 generation. Figure 2-10 shows the wide range of 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 of 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 of soil types, economy of the technique (Martin and Lew 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 in 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 of 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 of 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 fi l l 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 of the hole through a separate tube mounted on the outside of the vibrator with the help of 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 of the probe (vibro-rod methods). The source of energy is attached to the top of the rod (Mitchell 1981; Saito 1977; Massarsch and Broms 2001; Van Impe et al. 1993; Van Impe and Madhav 1995). Dynamic compaction uses repeated high energy impacts on the ground surface. Weights are typically in the range of 10 to 30 tonnes and are dropped from heights of typically 15 to 30 m (Lukas 1995). Dynamic compaction improves the soil by consolidation, vibration and increase in horizontal stress. Compaction grouting involves injection of a low slump and low-mobility soil-cement grout under pressure into the soil mass at spacing of 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 of charges placed in 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 of 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 of water and/or air jetted from its nose and side jets (Figure 2-11). Excess pore pressure caused by a combination of 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 of 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 of 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 of the vibrator, created by centrifugal forces due to rotation of an eccentric mass, are transferred to the soil. Furthermore, the tendency of 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 by the large number of cycles of shearing as well as by increases in confinement due to increase of lateral stress. Coupling between soil and vibrator is enhanced by the introduction of stones to the annular zone around the vibrator. The overall ground improvement is achieved by a combination of 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 of spacing depends on the target performance, soil gradation, vibrator characteristics and methodology. A 15 stronger vibrator in 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 of an eccentric mass about the vertical axis of 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 of the vibroflot and the extension tubes. In the ground, the pivot point moves down towards the tip of the vibroflot (Greenwood 1991). The amplitude of 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 of water and introduction of 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 of 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 of 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 of 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 of 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 of the compaction points or to the replacement ratio. Figure 2-16 and 2-17 are examples of such charts and can be used only as guidelines. However, there is a need for a means of 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 of the level of 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 of 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 of a field trial carried out before the production phase. Figure 2-18 shows an example o f such a strip chart record. More recently, Fel l in (2000) proposed that measurement of 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 of vibroflot and could be used for online quality control of 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 of soil using vibratory probes suggested by Massarsch and Heppel (1991). This figure suggests that soil is compactable, marginally compactable, or uncompactable for ranges of 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 Mitchel l (1981), a fines content of about 20% is the limit for compactability of silty sand. Using FC- I C correlation (Equation 2-6), a fines content of 20% is approximately equivalent to I c -2.25 (Figure 2-7). There are other factors involved in choosing the ground improvement technique. These factors are described in terms of 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 of 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 of the vibrator and soil is very complex. Despite the popularity of the vibro-replacement method, very little attempt has been made to explain the compaction process analytically or by numerical modelling. Very few cases could be found in the literature in which the vibrations of the vibroflot and/or ground were measured and then used to explain the soil-vibroflot interaction and the mechanism of compaction. It is l ikely that there have been some cases of vibration measurement conducted by manufacturers/contractors for improvement of the vibrator design, but these have not been published probably because they are considered proprietary. The only known case o f simultaneous vibration measurement of 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 of 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 of horizontal displacement measured near the tip of the vibroflot correlated well with penetration resistance after compaction and showed that the shape of the variation of the vibroflot amplitude and the variation of post-compaction penetration resistance with depth were similar (Figure 2-20). They only presented data on the amplitude of the vibroflot and the attenuation of 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 of 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 of accelerations for different zones came from Rodger's (1979) work. He had measured the accelerations at the ground surface. In Figure 2-21, a critical acceleration of 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 of 1.5g represents the optimum compaction. Increasing acceleration beyond 1.5g reduces the compaction efficiency due to dilation of the soil structure. At 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 of vibration intensity, and thus o f densification effort, it appears unlikely that they can fundamentally explain the mechanism of densification of 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 of 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 of about 8g to 15g at 0.5m and l g to 3g at 4m radial distance from the vibroflot. No vibration time history was presented. Baez and Martin (1992) used geophones and a pore pressure transducer in 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 of the vibroflot and the tangential vibration in the ground were not measured. The effect of the cone rods on the ground vibration measurement is not known. Figure 2-22 shows an example of their vibration time histories which were collected at 4.2m depth and a horizontal distance of 1.5m from the centre of a stone column during construction. They identified the mechanism of 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 of liquefaction occurrences are annotated on Figure 2-22. Note that the high pore pressures occurred only during penetration of the vibrator. It is apparent that penetration of the vibrator increases the pore pressure in 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 of the soil, it does not explain the densification mechanism by vibration during backfilling which is the main stage of densification. In the case of 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 Fell in (2000) who was only concerned with the motion of 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. Fel l in (2002) measured the acceleration of the vibrator and the phase difference of the eccentric mass relative to the vibrator and tried to use them for quality control o f compaction. No measurement of the ground response was carried out. Some other vibration measurement cases at the ground surface have also been published. Most of them were concerned with the noise level and the possible destructive effect of the induced vibration on the adjacent foundations (e.g. Woods and Jedele 1985). It appears that the main reason for the scarcity of published vibration data is the level of difficulty of high quality measurement of vibration and the complexity of analysis of data in a mathematical or numerical framework. In Chapter 3, the mechanism of vibro-replacement w i l l be discussed in detail based on the result of field vibration measurement and numerical modelling. 20 2.6 DISCUSSION AND 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 of ground improvement for liquefaction mitigation requires consideration of 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 of these above items. For example in item 1, the relative density or state of the sand, which is a basic parameter o f sand, is at best a good estimate in the current state of 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, Krogh and Lindgren 1997, Pan and Selby 2001), compaction grouting (Mace 1999, Shuttle and Jefferies 2000) and blast-densification (Wu 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 of site characterization since it changes the ground conditions and consequently changes the soil parameters and response of the ground to the in 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 in the same way, e.g. it increases the density of 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 of 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 of 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 of ground improvement have not had sufficient attention from researchers as noted by Charles (2002) and Raison (2004). The lack of 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 of the main points in this chapter is as follows: • Behaviour of granular soils under monotonic loading is a function of many factors including gradation, relative density, stress state, age, fabric and stress • path. The above factors plus magnitude and number of 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 of granular soils and also for Q C / Q A 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 of the same parameters that affect the soil behaviour. • Shear-volume coupling is the main factor in compaction of granular soils. Compaction of granular soils is mainly a function of magnitude and number o f shear strain cycles. • The physical process and. mechanism of compaction of 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 of the physical process and its effects on ground conditions. • Ground improvement changes the soil conditions and thus the soil response to cone penetration. Interpretation of 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 of our knowledge regarding ground improvement methods and mitigation of liquefaction, there is a need for further research on all components listed in Table 2-4. The focus o f this thesis wi l l be 22 on improving our understanding of the physical process of vibro-replacement characterization of post-treatment ground by this method. 23 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] 3.13 4.20 3.30 3.00 4.35 3.10 3.57 3.57 Diameter [mm] 300 420 290 400 290 320 350 350 Weight [kg] 1000 2090 1600 2450 1900 1815 2200 2200 Motor [kW] 105 210 50 120+ 50 100 130 130 Speed [miiW] 3250 1800 3000 1800 2000 3600 1800 1800 Ampl. [mm] 6 22 7.2 18 13.8 5.3 23 32. Dyii.Force [kN] 150 330 150 280 160 201 300 450 " 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 Advantages Disadvantages Achievable Penetration Resistance Vibro-Replacement (Vibro-Stone column) • Reinforcement • Vertical drainage • Overall homogeneity • Low noise level • Small chance of damage to the adjacent structure • Lots of previous experience • High technology • Elaborate equipment • Needs high head room • Management of the return water, relatively expensive • Difficulty in penetrating into coarse material • Densification only for fines content less than 15-20%. qcl = 10-15 MPa (N,)m=25 Dynamic Compaction • Low technology • Relatively less expensive • Works for a wide range of soil • Works for large particle size • High noise and vibrations • Potential for damage to adjacent foundation • Needs high head room • Relatively small improvement depth qci=10-l5 MPa, (Ni)M=25 B last-Densification • No depth limit • Relatively less expensive • Low technology • High noise and vibration • Relatively lower degree of uniformity qcl=10-12MPa, (N,kn=20-25 Compaction Grouting • Reinforcement, works for a wide range of soil. • Good control on the volume of the column • Low head room • Low noise and vibration • Relatively more expensive • Monotonic loading qc,=10-15MPa (N,)M=25 25 Table 2-4 Main 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 To understand how a particular ground improvement technique techniques and their effect on ground works and how it changes the ground conditions and engineering conditions 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 To predict the response of the improved ground under design loads. foundation after ground improvement 26 27 Void ratio Mean effective .stress, p f Figure 2-2 Typical behaviour of sand under monotonic loading in undrained condition (after Robertson and Wride 1998) 28 To data acquisition system o • i l / Accelerometer/Geophone 1 Sleeve friction, f s Pore pressure, u 2 Tip resistance, q t Figure 2-3 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 100r -0.2 0 0.2 0.4 0.6 0.8 1.0 1.2 Pore pressure parameter B q 1.4 2 3 4 5 6 Friction ratio (%) Zone: Soil Behaviour Type: 1. Sensitive fine grained 2. Organic material 3. Clay 4. Silty clay to clay 5. Clayey silt to silty clay 6. Sandy silt to clayey silt 7. Silty sand to sandy silt 8. Sand to silty sand 9. Sand 10. Gravelly sand to sand 11. Very stiff fine grained* 12. Sand to clayey sand* Overconsolidated or cemented. Figure 2-6 CPT classification chart (after Robertson et al. 1986) 32 1000 100 10 6 ncreasing i . OCR, age • cementation' N •% * \% \ AH - ^ a -- - N % 4 \ ^ \ \ Increasing ^ ^ sensitivity \ 3 \ \ 1 1000 0.1 10 F r (%) Q =£r^ 1 r x 1 0 0 % Zone Soil behaviour type 1. Sensitive, fine grained; 2. Organic soils-peats; 3. Clays-clay to silty clay; Zone Soil behaviour type 4. Silt mixtures clayey silt to silty clay 5. Sand mixtures; silty sand to sand silty 6. Sands; clean sands to silty sands Zone Soil behaviour type 7. Gravelly sand to sand; 8. Very stiff sand to clayey sand 9. Very stiff fine grained Figure 2-7 Normalized C P T classification charts (after Robertson 1990) 33 o OC o ^  ~ <u nj o or </) .S3 0) (0 co or g g o o >» >. Q O 0.6 0.5 + 0 M= 7 . 5 0 2 5 < Dgjjmin) < 2.0 F C (%) < 5 CPT Clean Sand Base Curve No Liquefaction NCEER (1996) Workshop Field Performance Uq. NtoUq. Stwk& 0*0/1(1995) • 0 Sujeufciet al (1S98b) * A -p 0 50 100 150 200 250 300 Corrected CPT Tip Resistance, q c iN Figure 2-8 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) 35 100 90 80 sz CD *5 5 a jcRAva. | sawo Hi c ii ** c (!) O a. 60 50 40 30 20 10 PARTICULATE S«OUT3 " 1 ' • , S H . T M O S T U O U E F 1 A J 3 L E S O U S JMfiTOflrtSttM V I S S A T O R T P R O B E S ' : CHEMICAL GROUTS i. BtpurenM COMPACTOR OEiP DYNAMIC COMPACTION? I i > COMWICTlOW GROUT O R A N S COMPACTION PILES JET GROUTING ADMIXTURES D E E P SOIL MIXING SOlLRSaffORCEMENT SUftCHARGgSUTTRESS FBXS ELECTROKJNETtC INJECTION P R E C O W R E B S I O M 10 0.1 o.ot Particle Size (mm) 0.001 00001 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 Impacting Forces W a l l of Bore Hole Locus of Gyration of Origin of Machine Axis Origin of Machine Vibration Vibrator Double Amplitude about Machine Axis Horizontal and Torsional forces T Err Rotating Eccentric Soil element and e m induced strains and stresses 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 60 100 140 Tr ibu ta ry A r e a per C o m p a c t i o n Po in t iff) •Silty Sand i 1 Uniform. Fine to i j Well-Graded (5%- 15% Silt) I ' Medium Sand (clean i I » 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) 4 0 100 90 c u U 10 5 80 70 60 50 ill 10 o o k n c c ) o -H d h-) O O H u D > VIbroflo Terraprc Upper L :atlon ibe -imit Vlbro Limit Corn} Uppe flotation taction I r Limit -Lower 3 l les -Terr Lim aprobe t - Lower 0 2 4 6 8 10 Dimensionless Spacing - D/d 12 Figure 2-17 Achievable relative Density vs. Probe Spacing for Soil Densification (From N A V F A C 1997) 41 Figure 2-18 An 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 ° Q F B L O W S / 3 0 0 m m V I B R A T I O N D i S P L A C E M £ N T . ( P k ) A 20 60 100 KO ISO I 5 „ 13 II 9 7 5 3 V^N 20 rkFREQUENCY X S MACHINE-;: Q. 1 1—I > . - I.., .)... 1, v . . I • • I NOSECONE • ACCEL EROMETER V« RESULTS 3-5h PENETROMETER RESULTS RADIUS Figure 2-20 Comparative profiles of the amplitude of the vibroflot and post-compaction —i 1— 3 0 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 C H A P T E R 3 M E C H A N I S M O F V I B R O - R E P L A C E M E N T 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 of 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 of the soil-vibroflot interaction used to analyze the data obtained and explain the observed response. • Examination o f the mechanism of ground improvement by vibro-replacement. 3.2 IN SITU GROUND RESPONSE T O V I B R O - R E P L A C E M E N T 3.2.1 Field vibration measurement Installation of 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 of about 5 m of 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 of sand and silty sand to the target depth of 9m. Stone columns were to be placed in a triangular pattern at 3m centres to a depth of 9m. Another round of stone columns was to be placed at the centroid of each of the 3-m triangles to a depth of 6m. A s shown in Figure 3-1, the sandy layers were generally medium dense to dense with some loose pockets. 45 Correlation of 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 of 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 of construction. Table 3-2 shows the horizontal distance of each stone column from the vibration sensor in the ground. The following data were gathered versus time during monitoring o f construction of the five stone columns: • 3-axis accelerations at 0.7 m above the nose on the vibroflot. • Current drawn by the electric motor of the vibroflot. • Depth of the vibroflot. • 3-axis vibration of the ground at 8.7m depth. • Pore water pressure of 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 -1800 rpm (~30 Hz), has a 130 k W electric motor and produces 300 K N of centrifugal force. Details o f the construction and operation of vibrators and of the vibro-replacement process were presented in Section 2.5. 3.2.2 Vibration measurement equipment Two sensor packages, designed and built at the University of British Columbia ( U B C ) , were used to monitor the vibration of 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 of +/- lOg, a frequency response range o f 0-600 H z and a mounted resonant frequency of 1200Hz. They were mounted rigidly in a steel cone shaped housing, about 300mm long and 45 mm in diameter. The pore pressure transducer had a capacity of 350 kPa and was manufactured by Sensym ICT. The motion of the vibroflot was monitored using an accelerometer package as shown in Figure 3-4-a. The package consisted of three orthogonal accelerometers and an amplifier 46 board. After installation of all the parts, the housing was filled with epoxy to protect the electronic parts from damage due to high impacts and leakage of 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 of 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 of ±50g, a frequency response range of 0 to 1050 H z and a mounted resonant frequency of 1800 Hz . The steel package housing was 200mm long, 35 mm 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 of 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 of the site during vibration measurement. The steel pipe was replaced by a strong hydraulic hose passing over the vibration damper to prevent breakage of 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 of +lg , 0 and - l g . Table 3-2 shows an example of calibration of accelerometers in the ground vibration sensor. A t the selected location for ground vibration measurement, a cone hole was pushed to a depth of about 8.2m. Inclination during the cone pushing was monitored and was less than 1 degree. Figure 3-6 shows the measured q t profile at the location of ground instrumentation 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 of 45 mm 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 of 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 of the package after completion of monitoring. 47 The time histories of vibration were recorded at a sampling rate of 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 of about 30 Hz . 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 of the measured parameters in the ground and on the vibroflot along with the depth of the vibroflot nose and its power consumption during construction of stone column #3. The horizontal ground accelerations were measured in the direction of the active axes of 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 in the ground, the amplitude of 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. At this point, although the vibroflot is vibrating, only a small portion of the energy gets transmitted to the ground due to the lack of shear strength. It took about 90 seconds for the vibroflot to reach the target depth of 10 m. At this point, the vibroflot and water jets were turned off to allow the pore water pressure response of the ground to be monitored. Note that this is not the conventional procedure and was done only for testing purposes. After a wait time of 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 of crushed rocks was 48 deposited into the hole by a wheel loader. From comparison of 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 of 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 of the time histories during densification showing the full signals. It may be observed that the motion of 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 l ikely 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 of the time histories Figure 3-9 shows that the predominant frequency of the input and output vibration are both about 29 Hz . A forced vibration system at steady state should theoretically vibrate at the frequency of excitation. The predominant frequency remained constant throughout the process and was independent of 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 of the predominant frequency. It is not known whether these frequencies are due to errors inherent in 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 of 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 of the predominant frequency such as 29, 58, 87 and 116 H z can be generated. 3.2.4.2 Attenuation of vibration The amplitude of vibration attenuates in the ground due to geometric spreading and material damping. If the propagating wave encounters an interface, partial transmission/reflection of energy and mode conversion also occurs (Santamarina et al 2001). Geometric spreading occurs because of the increase o f the size of the wave front with distance 49 from the source and thus the decrease of energy per unit area. The amplitude of vibration is a function of the square root of energy and also decreases with geometric spreading. If the soil is approximated by a visco-elastic model, the material damping causes energy loss in each cycle as shown by the area of the hysteresis loop in Figure 3-11. When a wave hits the interface of two different media at an angle, some of 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: where A i and A2 are amplitudes at distances r ( and r 2 from the source of 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 where f is the frequency, V is the wave velocity and Qd is expressed by the following equation: where D is the damping ratio and is defined as the ratio of the hysteresis area (dotted area in Figure 3-11) to the area o f the shaded triangle, all divided by 4TC (Kramer 1996): g - « ( < 2 - ' - , ) 1 T Equation 3-1 Q-V Equation 3-3 W, D D = Equation 3-4 AnWs 50 and T r is a coefficient representing the reduction of amplitude due to partial transmission and 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 of tangential and radial accelerations change with distance. It indicates that the variation of 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 of the sum of square of radial and tangential accelerations) versus distance is likely to give a better indication of attenuation of the energy of the vibration. Figure 3-14 shows the attenuation of the resultant horizontal acceleration with distance. Also 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"1 and with spherical spreading and a=0-0.1 m" 1. The effects of partial transmission and mode conversion are ignored. Woods and Jedele (1985) proposed the coefficient a=(0.03 to 0.1 m"1) for most sands, sandy clays, etc. and for a vibration frequency of 50Hz. This a can be corrected for the frequency of 30 H z as follows : where a i is the known attenuation coefficient associated with fi and f is the frequency of the vibration at which a is to be obtained. The obtained a is close to that found from spherical attenuation in Figure 3-16. Equation 3-5 :.a « 0.02 -0 .06 n i -i Equation 3-6 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 of radial acceleration. Figure 3-18 illustrates Green's (2001) interpretation of 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 Hz . He concluded that attenuation was due to cylindrical spreading (note that n=0.5 is the best fitted line) and an attenuation coefficient of 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"1 • Assuming cylindrical spreading a=0.3 to 0.6 m"1 Assuming a wave velocity of 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 in Figure 3-19 that a damping ratio of 30-50% is associated with shear strains of more than 10% and thus is l ikely to be unreasonable. On the other hand, a damping ratio of 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 of material damping on attenuation is not likely to be significant in the vibroflotation. The energy attenuated by material damping is a function of the material damping and the number of cycles. The number of cycles, N c y c is the number of 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 of interest, and X is the wavelength and can be obtained from Equation 3-9 where V is the speed of wave and f is the frequency of the wave. Using a shear wave velocity of 180m/s and a frequency of 30Hz results in N c y c = 0 . 2 8 at the centroid (r=1.7m) and N c y c =0.78 for the furthest measuring point, r=7.6m. This means that only 28% of the energy that attenuates in a full cycle w i l l be damped out of 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 of construction of stone columns #3, 4 and 5 which are equidistant from the measuring point. This could be explained by the effect of 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 of velocity measurements. Moreover, the effect of 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 of vertical acceleration in the ground. It is assumed that the vertical acceleration of 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 of 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 of 14g to 1.7 g were measured on the vibroflot and in 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 of vibration with horizontal accelerations larger than 1.7g. On the other hand, during a 7.5 magnitude earthquake with 475 year return period in the Lower Mainland, B C , 15 cycles of horizontal acceleration in the range of 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 of such vibration monitoring was to ensure that the construction vibration would not exceed a certain level (usually in terms of particle velocity) at the location of the foundations or structures (e.g. Woods and Jedele, 1985). Lacy and Gould (1985) considered a peak particle velocity of 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 of frequency of vibrations caused by blasting. For example, for a frequency of 30Hz, a maximum allowable P P V of 50 mm/sec is recommended. The horizontal peak particle velocity of the ground during vibro-replacement may be obtained by integration of measured accelerations. For horizontal acceleration of 14g tol .7g and frequency of 29 Hz , 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 of the effectiveness of the vibro-replacement method. Despite the strong vibrations that vibro-replacement generates at depth in the ground, the technique is a popular method in urban areas as the destructive radius of vibro-compaction at the usual depth of 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 of the vibroflot and soil particles The displacement paths of 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 of the motion paths in terms of accelerations. Assuming a harmonic signal, which is the case for vibroflot motion, the shape of 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 of showing the relative significance of motion in 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 of motion of the vibroflot decreases in the ground but almost maintains its circular shape (Figure 3-2 lb) . During installation of the subsequent stone columns (#4 and #5), the shape of the motion of the vibroflot turns into an ellipse (Figure 3-2 lc ) . 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 of the distance of the vibroflot from the monitoring point. A t a radius of 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 of 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 in 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 of the field motion paths. 3.2.4.4 Optimal frequency of 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 of the ground. Massarsch and Heppel (1991) suggested that this optimal frequency could be found by spectral analysis of the system response during switch-off or switch-on of the vibrator. During these periods, all the frequencies below the operating frequency of 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 of the square of frequency. The technique used by Massarsch and Heppel (1991) wi l l be applied to the present data set for vibro-replacement. Figure 3-25 shows the time history of vibration o f the vibroflot and the horizontal accelerations of 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 of 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 Hz . 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 of vibroflots is usually either 30 or 50 Hz . This historically originates from the early electrical vibroflots operating at a factor of the frequency of the alternating current, 50 H z in Europe and 60 H z in the U S . Some newly designed vibrators operate at 25 Hz . 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 of the ground due to densification is indicated by increased amperage and decreased amplitude of vibroflot motion. Amperage is conventionally used for field quality control during construction. It has also been suggested that the amplitude of the 56 vibroflot vibration is a better indication of 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 of the soil against the vibrator was small. This resulted in 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 in 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 of 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 of the vibroflot. During this 10 sec, the amperage consumption decreased, which is opposite to the usual trend. Bui ld up of 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 of the entire vibroflot and not only on the motion of the tip. The pivot point of 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 of the vibroflot shoulder. Therefore, the resistance around the tip increased but because the level of the crushed stone available in 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 of vibroflot, are required to monitor the motion of the entire vibroflot and not only the tip. At 478 sec, the densification of 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 of densification. This indicates that the vibrator amplitude and amperage could show 57 opposite trends due to the complexity of the phenomenon. Based on local experience, a diminished amperage increase occurs when fines contents are in the range of 15-20% or more. The above suggests that basing the quality control of densification on interpretation of 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) of 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 SPT blow counts and the vibroflot amplitude, Fel l in (2000) suggested that measurement of the acceleration at the tip and shoulder of the vibroflot and the phase angle of the eccentric mass relative to the motion of the vibroflot could be used to determine an average stiffness and damping of the ground. This requires further research. During densification, no residual pore pressure was observed at the location of the ground sensor. This could be due to different reasons as follows: • The rate o f dissipation was faster than generation of pore pressure. • The soil was relatively dense and generated little residual pore pressure. • The shear strains at the location of the ground sensor were not large enough to cause considerable shear induced pore pressure. On the other hand, there was a general decrease of pore pressure from t=440sec to 700sec as shown in Figure 3-7. This pore pressure had been generated by penetration of the vibroflot and water jets. The general decrease in pore water pressure is due to dissipation and increasing distance of 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 of 8.7m and at a radial distance of 1.7m from the compaction point is shown in Figure 3-28. It may be observed that during the first penetration the pore pressure increases about 50 kPa which is almost a pore pressure ratio r u =Au/a ' v o = 0.6 . The total excess pore pressure is the sum of the cyclic pore pressure caused by cyclic impacts, pore pressure due to water jets and pore pressure generated from the cavity expansion by penetration of 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 in the total stress. Figure 3-29a shows the distribution of the pore pressure during the first penetration of the vibroflot observed from stone columns #1 to 5 which are located at different radial distances from the measuring point. During construction of 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 -320 in Figure 3-28) is caused by water jets and cyclic pore pressure. Knowing 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 of the total pore pressure measured at the centroid o f the triangle is from the water jets. 3.3 M E C H A N I S M O F P E N E T R A T I O N O F T H E V I B R O F L O T The pointed nose at the tip of 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 of the follower tubes, a total weight of about 50 k N . Assuming a diameter of 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 of 20 M P a (200 bars). Two 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 of 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 of 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 of 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 of 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 of measured excess pore pressures caused by water jets alone to the radius of the vibroflot gives a pore pressure of about 350 kPa. This pressure can cause zero effective pressure around the tip of vibroflot to about 35 m depth in a saturated granular soil. The above observations suggest that the main reason for penetration of the vibroflot under relatively small tip bearing pressure is the pore water pressure generated by water jets. The vibration also helps but to a lesser extent. 3.4 N U M E R I C A L M O D E L L I N G O F V I B R O - C O M P A C T I O N Due to the complex nature of 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 of an eccentric mass. The soil-vibroflot interaction is schematically shown in the horizontal plane in Figure 3-32a. The soil is substituted by a number o f springs and dashpots. The magnitude of the cyclic force, F is constant but its direction changes with time as a function of the speed of rotation of 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 of the vibroflot can be formulated independently in only one direction (Figure 3-32b). The motion in the perpendicular direction is similar but with a TC/2 time lag. 60 Fell in (2000) used this concept and developed a mathematical model for the motion of the vibroflot in the vertical plane as shown in Figure 3-33. He further simplified the problem by substituting the soil by one spring and one dashpot and formulated the motion of the vibroflot by solving the differential equation of motion. For more detail refer to Fell in (2000). This is the only published mathematical model of soil-vibroflot interaction. Although this approach gives a framework to study the motion of the vibroflot, it does not give any insight into the soil response such as the attenuation of vibration, particle motion, shear strains, etc. Ful l modelling of 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 of modelling liquefaction and densification. Addit ion of stone backfill and changes in soil properties during the process make the modelling even more complicated. A t this stage, the main objectives of the numerical modelling are to explain the field response observed during the vibration measurement and to get a better understanding of 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 of 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 of the holding time at each depth interval when, after numerous cycles, the generation of pore pressure, volume change and the change of 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 of Continua) version 3.4 with the dynamics option was used for numerical modelling (Itasca 1998). In F L A C the equations of 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 of 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 of the elements is limited to 1/10 of the wavelength of shear waves, which is about 6m for the assumed conditions, to ensure proper modelling of wave propagation (Kuhlemeyer and Lysmer, 1973). The maximum aspect ratio of the soil elements is limited to about 2. The soil and the vibroflot in the model are connected by a row of interface elements as shown in 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 of 40° is assigned to this interface. The interface friction o f 40° is obtained by scaling up tan((pson) by the ratio o f (vibroflot radius + width of 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 of 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 of 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 ACCxl=A-sm(2-x-f-t) Equation 3-10 ACCvl = A • cos(2 -TT-f-t) Equation 3-11 where: A : Single amplitude of acceleration^ 3.4 g (obtained from the field measurement) A C C x t : Acceleration of the vibroflot in x direction A C C y , t : Acceleration of the vibroflot in y direction f : Frequency of vibration (29 Hz) 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 m a x is calculated from the shear wave velocity, V s obtained from seismic cone testing using the following equation: G , n a x = P F s 2 Equation 3-12 where p is the density and V s is about 180m/sec. A high Poisson's ratio is selected to account for the high bulk modulus of a saturated soil equivalent to a V p =1500 m/s and a V s=180 m/s. Effective in situ stresses were calculated for a depth of ~8.5 m and submerged unit weight of 10kN/m 3 . The average material damping was found to be about 5% from the back analysis of 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 of 30-60%. However, it wi l l be shown that an average damping ratio in the range of 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 m a x and the analysis was 63 repeated with the new stiffness values. This procedure was iterated a number of times until the G / G m a x converged. Figure 3-37 shows that the analyses converged after 4 iterations. 3.4.3 Results of numerical modelling Figure 3-38 illustrates the deformed shape of 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 of 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 of 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 of the motion paths and the relative significance of 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. Also 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 in both the field and numerical model. The normal and frictional impact of 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 of these body waves generates a unique particle motion pattern as a function of radial distance from the vibroflot. The results show that despite the simplifying assumptions, the numerical model is able to capture the characteristics of the field data. Also 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 of vibration at 4 points, as 64 shown in Figure 3-41. To obtain shear strains in each plane, the displacements of three points in that plane should be measured versus time. Based on numerical analyses, Figure 3-42 shows the distribution of shear strains in the horizontal plane with radial distance from vibroflot. These values wi l l be used to explain the mechanism of compaction during vibro-replacement in the next section. In order to evaluate the effect of soil-vibroflot friction, the shear strains obtained from an interface friction angle of 40° and 0° were compared. It was found that a friction angle of 40 0 increases the shear strains at 0.5m and 1.7m by factors of about 1.15 and 1.05 respectively. 3.4.4 Mechanism of compaction during vibro-replacement Densification of granular soils is mainly due to shear-volume coupling and is mainly dependent on the magnitude of the induced shear strains and the number of 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 of vibro-replacement. Firstly, the shear-volume coupling model that is used here wi l l be introduced. 3.4.4.1 Shear-volume coupling model Our understanding of shear induced volume change is based on cyclic/monotonic behavior of soil in the laboratory. Shear-volume coupling models have been formulated by many researchers. The model developed by Byrne (1991) wi 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 of 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 of sands: -7- = C,.exp —C2. Equation 3-13 r J 65 where A s v is the incremental volumetric strain in the current cycle in percent, £ v is the accumulated volumetric strain from the previous cycles in percent, y* is the net engineering shear strain in the current cycle and is obtained as follows: Y =Y ~7t Equation 3-14 where y is the engineering shear strain in the current cycle and y t is the shear strain threshold. Byrne (1991) suggested that a y t o f 0.005% fitted the laboratory data. C i and C 2 are regression parameters. d controls the volume change and is defined as: n i^£v)cycle\ 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 = W Z H Equation 3-16 Equation 3-16 may be preferable because there are considerable data on volumetric strains after 15 cycles as a function of D r . The parameter C2 controls the shape of the curve. 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 of C i as: C 2 = 0 . 4 / C , Equation3-17 C | can be obtained from the relative density as follows: C, = 7600 • (DR )"2 5 Equation 3-18 It may be observed that for this model, the shear-volume coupling o f sand depends on the relative density of 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 of y and number of 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 of pore pressure under undrained condition as formulated below. (A*r). 1 =0.5-7 -C,.exp -cycle ' 1 1 2 ' •c, Equation 3-19 where all the parameters are defined above. In undrained conditions, the total volumetric strain is: Asv = Asl +As\, = 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 =• ACT,, M Equation 3-21 where A a ' v is the vertical effective stress change per half a cycle and M is the constrained modulus of the soil given by: M = Km-Pa- Equation 3-22 Values of K m =1600 and m=0.5 are in good agreement with the Martin et al. (1975) data. From Equation 3-21 we have: Au = -A<jy = M • As, Equation 3-23 After each half cycle, the incremental Au is calculated and a ' v and stiffness are updated. 3.4.4.2 Proposed mechanism of 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 of shear strains in the field requires simultaneous measurement of vibration at 4 points as shown in Figure 3-41. This method needs 67 further research and was not used as part of this study. The other approach is to calibrate the numerical model to the field measurement and then estimate the shear strains from the results of numerical analysis. This approach is taken here. It was shown that numerical modelling captured the mechanism of soil-vibroflot interaction and obtained a reasonable match to the field measurements of acceleration. However, it should be emphasized that more work is needed before the numerical analysis can be used in a quantitative manner. Figure 3-42 shows the distribution of shear strains in the horizontal plane with radial distance obtained from the numerical analyses. Average shear strains of about 0.125%, 0.09% and 0.075% are obtained from this figure for radial distances of 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 AD r = 8 % at r=0.5m and AD r =5% at r=1.7m, which is the centroid of compaction grid. Based on the correlation between q c and Dr for Ticino sand (Baldi et al. 1986), a 5% increase in relative density at the depth o f about 9m is equivalent to an increase of less than 10 bars in tip resistance (note that geological ageing effects are ignored). Figure 3-45 compares pre- and post-q t which were both carried out within a 3 m radius of the location of the ground vibration sensor. It may be observed that the pre- and post-q t have similar profile and that the post-q t has improved very little relative to pre-q t. The reason for the limited improvement is likely to the high initial density of the sand. The sand at the location of 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 of 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 t value from about 100 bars to 120 bars and consequently the initial relative density could have been in the range of 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 of 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 of this thesis. The second and third items are discussed below. Figure 3-46 shows the application of the Byrne (1991) model assuming an undrained condition. The results suggest that the soil around the probe would liquefy in less than 25 cycles which is less than 1 second worth of vibration. However, the field measurement of pore pressure during vibration did not show any significant pore pressure at a radial distance of 1.7m. The actual condition in the field is not completely drained but partially drained. Considering the field drainage condition and the attenuation of 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 of dissipation is less than the rate of pore pressure generation. Addit ion of gravel size backfill is l ikely to reduce the extent of liquefaction during densification by providing better drainage to the sand. Addit ion 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 of 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. Also , the direction of the net movement of 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 lg 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 of increase of lateral stress and no attempt is made to match the field data. Figure 3-47 shows the radial displacement time history of some points at different radial distances from the vibroflot. It may be observed that the radial displacement is cyclic but accumulates with increasing number of cycles. The rate of the increase of the radial displacement is greater at smaller radial distances. Figure 3-48 shows that the increase in the average horizontal stress, (a r+ae)/2 is greater closer to the vibroflot. This is similar to a cavity expansion problem. Here, instead of a static internal pressure on the cavity wall , there is an impact whose contact area and direction rotate with time. The rapid rotation of 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 of cycles. This results in a gap forming between the vibroflot and the soil in the model as shown in 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 of locked in stresses in each cycle (not modelled here). The backfill also maintains the locked in lateral stress after withdrawal of the vibroflot. Figure 3-51 shows the predicted stress path of a soil element at a radial distance of r=1.7m (location of centroid of compaction grid) obtained from the numerical model. During the loading portion of 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 of an element around an expanding cavity in granular soil. A t point C, the vibroflot starts to retract from the wall of the hole, which causes unloading (CD A ) . The unloading along C D causes a reduction in radial stress and an increase in tangential stress similar to the elastic unloading portion of 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 of plane stress) as one of the principal stresses. At point A , another cycle of loading occurs similar to previous cycles but at a higher stress level. Eventually at the end of 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 of 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 of the membrane, In the case o f vibro-replacement, most of 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 of the changes in horizontal stresses. It is encouraging that the numerical model also confirmed the increase in the horizontal stress. However, a quantitative evaluation of 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 of this ageing period, a monotonic shear strain in the range of 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 of cyclic loading (Thomann 1990) and thus even a smaller shear strain may be capable of causing a loss of 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 in the ground, and vibration on the vibroflot were measured. The field data showed the details of ground response to the vibro-replacement process. Numerical modelling was used to simulate the soil-vibroflot interaction and wave propagation in the ground. The model was successful in simulating the field response. The model was also successful for simulation of the increase in 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 Hz). • The optimal frequency (resonance) of the site in this case study, interpreted from the transient state of vibration during switch-on, was found to be about 26 Hz . • 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 in the range of 14 g (adjacent to the vibrator) to a minimum of 1.7g (at the centroid of 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 of loading cycles during vibro-replacement is in the range of a few thousands, which is significantly higher than 15 major cycles expected from a 7.5 magnitude earthquake. • Peak particle velocities in the ground within the densification grid in this study were inferred to be in the range of 750mm/sec (adjacent to the vibrator) to 90mm/sec (at the centroid of compaction grid), which is significantly higher than the range of 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 of 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 of vibrator amplitude and power consumption could indicate contradictory trends and variable sensitivity to the details of the densification process. This suggests that additional performance indicators may be required to improve quality control of the densification process in the field. • The mechanism of the penetration of 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 of the main conclusions from numerical analyses of soil-vibroflot interaction is as follows: • The numerical model proved very useful in providing insight into the soil-vibroflot interaction. It captured the mechanism of wave propagation and confirmed the field observation of soil particle motion paths. It showed that the orientation of particle motion varies with distance from the vibroflot similar to observation in the field. • The numerical model also showed that the motion of 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 in the plane strain model (2-dimensional attenuation) as compared to the actual spherical attenuation (3-dimensional attenuation) in 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%. With improvement in numerical modelling, it is hoped that this procedure could be used quantitatively to predict the magnitude of densification. 74 • The magnitude of 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 of the vibro-replacement, it is concluded that the final product of vibro-replacement is a young soil (i.e. after destruction of the effects of geological ageing) with increased density and horizontal stresses. The soil density and horizontal stress decrease with radial distance from the compaction point. The variation of densification effect within the densification grid and also inclusion of 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 of the ground to in situ testing. The likely effects of 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 - l g + l g Calib. factor (volt) (volt) (g/volt) Acc. 1. Horizontal -1.005 + 1.004 0.996 Acc. 2 Horizontal -1.002 + 1.001 0.999 Acc. 3 Vertical -0,997 + 1.003 1.000 Table 3-3 Soil parameters used in the numerical model Soil parameter Value Shear wave velocity, V s (m/s) 180 Compression wave velocity, V p (m/s) 1500 Density, p (kg/m3) 2000 Small strain shear modulus, G m a x (MPa) 66 Poisson's Ratio, v 0.48 Initial horizontal effective stress, a'h (kPa) 85 Initial vertical effective stress, o'v (kPa) 38 Soil-Vibroflot interface friction angle, (p (degrees) 40 Soil-Vibroflot interface tensile strength 0 Material damping ratio (%) 18-35 Frequency of vibration, f (Hz) 29 76 Figure 3-1 Pre-compaction C P T profile 77 Stone column #1 Vibration and PP sensor package Depth=8.7m O #2 o '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 8 0 . ...... ., ' ' : , -Figure 3 - 5 A view of the site during vibration measurement 81 q t(bars) Figure 3-6 CPT 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) Pore Pressure (kPa) Vibroflot Radial Acceleration (g) Vibroflot Tangential Acceleration (g) Vibroflot Vertical Acceleration (g) Depth of Vibroflot Tip (m) Vibroflot Power Consumption (amp) 100 200 300 400 500 600 700 800 2 •a U ¥ 0.5 1 S -0.5 I "I p 100 200 300 400 500 600 700 800 100 200 300 400 500 600 700 800 1 & 1 100 200 300 400 500 600 700 800 100 200 300 400 500 600 700 800 0 3 2 * 4 » 6 1 4 10 12 200 180 160 140 120 100 J / i k *i—» r-» r 100 200 300 400 500 600 700 800 V | f | B [ L i •P^ l*1"^ ^^ ^^ ^^ ^^ ^ - — k 100 200 300 400 500 600 700 800 time (sec) Figure 3-7 Recorded time histories during construction of stone column #3 83 0.5 0.3 0.1 i< -0.1 o -0.3 -0.5 >v A, A . . *. A r \ / v .. \ I V .... \ V \ n'T^ / f.. V t V \ / 520 520.025 520.05 520.075 520.1 520.125 520.15 520.175 520.2 2 1.5 ""bo 1 ^ 0.5 S 0 « -0.5 S -1.5 -2 Si f y \ / H ! / \ / \ / \ 1 \ !^  / \ / / \ .. / \ / „ .X „ i / \ ... / \ / ! \ / \ \ 1 1 1 I '520 520.025 520.05 520.075 520.1 520.125 520.15 520.175 520.2 0.5 ® 0.3 -I 0 1 I -0.! -0.5. i ZZ\ A. t ,C\ : A A, / s \ A / I - W -J \ \. ' \ \ ! \ / 1 \ / \ \ I \ / \ / V j v / v 520 520.025 520.05 520.075 520.1 520.125 520.15 520.175 520.2 100 96 92 S 84 SO, \ .. / * \ \ ^ \ _z V\ j X - / \ / V \Z . w \ \ Y \ 520 520.025 520.05 520.075 520.1 520.125 520.15 520.175 520.2 _ 25 3$ 20 ^ 15 S 10 | -To J -15 T -20 "25, .-•-""v / v_ ' \ / / \ ^ ? V \ i \ / / i \ / / \ / i i 520 520.025 520.05 520.075 520.1 520.125 520.15 520.175 520.2 3 25 ,s 20 £ 15 10 •S 5 F -5° Q -10 f; -15 ^ -20 5i i ! l 1 i / \ '* i *• / v. / \ t \ / 1 \ • / • s. i • ; f ; V \ \ / I \ - L -520 520.02 520.04 520.06 520.08 520.1 520.12 520.14 520.16 520.18 520.2 --B 1 ^ - i 1 -3 * -5, A % \ / / " \ y \ \ / v 7 \ """ \ i \ / V >—' . 520 520.02 520.04 520.06 520.08 520.1 520.12 520.14 520.16 520.18 520.2 time (sec) Figure 3-8 Recorded time histories during stone column #3, enlarged scale during densification. Note that scales are not consistent. 84 O I o 3 0.5 T3 -29 Hz i i stone Col #3- FFT of densification phase 10 20 25 Vibroflot 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 g 0.04 H-a 0.02 it a 0 20 40 60 80 100 120 140 160 180 200 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 2.0 3 c o CO ji5 CD o o co "co c o N 1.5 1.0 + • $ + A radial accel., this study • tangential, accel., this study + radial ace, Baez & Martin (1992) 0 1 9 2 3 4 5 6 7 8 Radial distance from vibroflot, r (m) Figure 3-13 Attenuation of radial and tangential acceleration with distance from vibroflot 100 D) c o *•—» CO 1_ JD 0 O O CO ~s c o N o -C c ra "5 </> 0 10 0.1 radius of vibroflot Spherical attenuation Cylindrical - ^attenuation #4 >*... — — #2 #1 0.1 1 10 Radial distance 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 -5 c o CO 1_ 0) CD O O co ~s s c TO "5 co CD 10 0.1 A radius of vibroflot Cylindrical attenuation a=0 a=0.1 \ a=0.3 a=0.6 0.1 1 10 Radial distance from vibroflot, r (m) Figure 3-15 Attenuation of the resultant horizontal acceleration. The theoretical attenuation includes cylindrical spreading and material damping. 100 Radial distance from vibroflot, r (m) Figure 3-16 Attenuation of the resultant horizontal acceleration. The theoretical attenuation includes spherical spreading and material damping. 88 1 0 r ' i l L t — ^ l l o — i - a l i - H r r 2 3 i 5 6 73 1 ,2 3 4" 5 RAOIUS r (m) Figure 3-17 Attenuation of radial displacement in the ground around vibrators (after Morgan and Thomson 1983) 89 4.0 3.5 3.0 3 " a 2,0 < i.s 0.5 •Appro*. Face of Vibraoii * Max, Accel. a Steady-Stale Accel. \ _ « , „ = 2 . 7 - - | .cxp[-0.2-(r-3)] . Tl K 1 \ a ,,,,,„ = 1.7- -i -exp[--0.2-(r 3)]" .0 1 1 i : • ! 1 ! 1 1 0 1 2 3 4 5 6 7 8 9 - 1 0 Horizontal Distance from Center Line of Stone. Col unut {ft) »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 0.64 E Q 0.4 0.24 0.0 L-0.00001 3 0 25 2 0 1 5 10 44-0.0001 0.001 0.01 Shear Strain I'M 0.1 A 0.00001 0.0001 0.001 0.01 Shear Strain (%) 0.1 10 10 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 Radial distance from vibroflot, r (m) 10 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 c _o rt _u u o o CU i >, 'o 2 1.5 1 0.5 0 "0.5 -1 "1.5 -2 St. col. #3 r=1.7m "2 "1.5 "I "0.5 0 0.5 1 soil x-acceleration (g) 1.5 0.6 e o 0.2 "0.2 -0.6 "I St.col. #2 r =4.7 m -1 -0.6 "0.2 0.2 0.6 soil x-acceleration (g) e o ta _u 13 o o C3 i >> '5 0.6 0.2 "0.2 -0.6 \ St.col. #1 r=7.6 m -1 "0.6 -0.2 0.2 0.6 1 soil x-acceleration (g) 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 94 1 S3 o 2 1.5 1 0.5 0 -0.5 -1 -1.5 -2 ''I j 1 St. col. #4 r=1.8 m -2 -1.5 -1 -0.5 0 0.5 1 soil x-acceleration (g) 1.5 2 -1 -0.5 0 0.5 1 soil x-acceleiation (g) St. col. #5 r=1.8 m 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 20 10 -a 3 "a, B < ,3 > -10 h -20 h -30 h -40 h Transient state Steady state _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 Steady state , f = 29 Hz 322 322.2 322.4 322(5 322.8 323 323.2 323.4 323.6 323.8 324 -Peak j. , j. respo use r j | J J i l l fit m 322 322.2 322.4 322.6 322.8 323 323.2 323.4 323.6 323.8 324 322 322.2 322.4 322.6 322.8 323 323.2 323.4 323.6 323.8 324 time (sec) 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 3 -J a £ a. E -1 •9 S u I ' J s ft > o ft u -a 140 128 116 104 92 80 0 2 4 6 8 10 12 Densification at 10 m 400 420 440 460 480 500 520 540 560 580 600 k m v - Ii \ A I ! J 400 420 440 460 480 500 520 540 560 580 600 / \ A j 1 \ • . ^ r f "400 420 440 460 480 500 520 time (sec) 540 560 580 600 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 100 200 300 400 500 600 700 300 900 1000 time (sec) Figure 3-28 Pore pressure time history during stone column #3 100 1000 o Q. E 3 X CD 100 CD 3 (/) a) £ 10 Q. CD 0.1 0.1 -Radius of vibroflot 1" A total X water Jets • cyclic (a) Total=Pressure induced by Cyclic+Watt Water jets= Pressure induced by water j 10 Radial distance from vibroflot, r(m) CD 0_ j*: a> CO CO a. cu o Q. E E 'x CD 1000 100 0.1 10 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 of stone columns #1 to 5. Total is the sum of pressures caused by water jets, cyclic loading and penetration of vibroflot (cavity expansion) (b) Calculated pore pressure induced by cavity expansion during installation of stone columns #2 and 3 (Cavity expansion PP= Total-water jets-cyclic) 101 C otrifugal Motion V ibl itot C omponent 41mm (lj6in) Certrifcgal Force = 32kgf (70.5 bf) Fr*q i«ncy=200Hs Lengh = 790 mm (31.1 in) Diameur= 41 mm (1.6 xi) Wei^fl. = 6.31«gf(13Pljf) Figure 3-30 Schematic of the Original Vibratory Piezocone designed by Sasaki and Koga (1982) (taken from McGillivray et al. 2000) <5 I • i i I • ' i I , i I i I . I 0 40 SO 130 100 0 40 80 120 160 Cone Tip Resistance (kg/cm2) S i t e l 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 of the vibrator in the ground (after Fel l in 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 vibioflot radial acceleration (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 "co i_ _co cu o o CO c o N c CO X CO 10 0.1 - - Equiv. Linear. Damp=18% Equiv. Linear. Damp=35% O field measurement O" •o 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) Soil acceleration (g) Soil acceleration (g) r = 0.5 m r = 1.0 m r = 1.7 m r = 4.6 m 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 0.14 0.12 c 'ns "35 » 0.1 </) cu "§ 0.08 I 006 c 0.04 CO AEquiv. Linear. Damp=18% • Equiv. Linear. Damp=35% 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 c CO o £ 2 1.8 1.6 1.4 1.2 • 1 0.8 0.6 0.4 0.2 0 = C,.exp - -- c 2 . - y=0.3 - - y=0.2 - -y=0.1 10 20 30 Number of cycles 40 50 Figure 3-43 Shear-volume coupling model for sands proposed by Byrne (1991) 70 -, 69 -68 -Q 67 -66 -to c 65 -CD Q 64 -a> > 63 -62 -V 61 -or 60 -0.1 Y=0.125% 7=0.09% 7=0.075% s -/* s T ^ ' M M •jf r=0.5m r=1 m r=1.7m 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 t(bars) 0 50 100 150 200 Figure 3-45 Cone tip resistance before and after vibro-replacement 113 r = 1.0 m y a v e = 0.09% r = 1.7 m Yave= 0.07% 10 15 20 Number of cycles, N c y c D r o=60% 25 30. 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 0> (1.0 + 0 5 ) -0.400 -0.600 -0.800 -1.000 Pi 3 -1-200 -1.400 -1.600 -1.800 0 i r~ 2 4 i — 6 i 1 1 1— 8 10 12 14 Radial displacement (m) ( I D " 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 RESISTANCE O F H E T E R O G E N E I T Y C A U S E D BY V I B R O - R E P L A C E M E N T 4.1 INTRODUCTION Vibration measurement and numerical modelling presented in Chapter 3 showed that the amplitude of 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 of vibro-replacement. Each point within this grid is affected by compaction carried out at the location of 3 stone columns. This makes the distribution of 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 of the improved ground in practice is usually based on penetration testing at the centroid o f the compaction grids. The centroids of the grids have the largest distance from the compaction points and thus are expected to be the weakest points. Interpretation of q c for engineering properties of soil is mainly based on correlations 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 of this chapter is to explore the effect of this induced heterogeneity on the interpretation of the C P T results. First, field evidence wi 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 of heterogeneity on the interpretation of cone tip resistance. 4.2 FIELD E V I D E N C E Probably the only published case of measurement of variation of soil density around a vibrator is the one reported by D'Appolonia (1953). He measured the density of 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 of density versus horizontal distance from a 23-kW vibroflot is shown in Figure 4-2. The data suggest an exponential variation of density with distance. He found similar variation of 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 in q t with distance from the compaction point. More recently, Degen and Hussein (2001) reported the variation of q t with distance within a triangular grid for two different vibroflots as shown in Figure 4-3. It may be observed that q t at 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 c h a mber /D c o n e) o f 25-120 could cause a chamber to field penetration resistance ratio in the range of 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 in denser and more dilative sand. Assuming a diameter of 35.7mm for the cone tip and an influence diameter ratio of 100, the zone of influence could be as big as 3.6 m, which is greater than the distance from grid centroid to stone columns. Therefore, q t at the centroid is expected to be affected by the surrounding denser soil and stiffer stone columns. In order to investigate such effects, a numerical modelling approach was taken here. Two dimensional numerical analysis of a plane strain condition is used to check the effect of 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 c and the limit pressure calculated from cylindrical cavity expansion theory are related. This assumption wi l l be evaluated in the next section. • The effect of 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 RESISTANCE AND C A V I T Y EXPANSION T H E O R Y Bishop et al. (1945) first noted the analogy between cavity expansion and cone penetration. Since then many investigators have tried to simplify the mechanism of 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 of 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 ' u , and cone tip resistance in calibration chamber, q c . Figure 4-5 shows that P ' 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 c and P ' u , which is close to the 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 in a heterogeneous soil condition in the presence of stone columns. The plane strain condition (horizontal plane) is assumed here. This is equivalent to the cylindrical cavity expansion. A circular block of ground with a radius of 9.6 m, represented by about 4200 quadrant elements is used to model the cavity expansion (Figure 4-6). A previous model of 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 of 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 kPa and rj'v=85 kPa. A constant stress boundary is used for both outer and inner boundaries. The cavity is then expanded in a strain controlled mode by applying a constant velocity of 10"7 m/step to the cavity wall . The cavity is expanded to strains o f Ar/ r 0 o f about 180%, where Ar is the displacement of the cavity wall and r 0 is the initial radius of the cavity. The final size of the hole after the expansion w i l l be about 0.036 m, close to the size of a standard 10 cm 2 cone tip. Also, this amount of 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 r is selected as the main variable and all the other soil model parameters are obtained from the correlations to D r . In all the cases, v is assumed 0.2. Friction angle and dilation angle are obtained from relationships recommended by Bolton (1986) as functions of D r and mean normal stress as follows: 4>P = c^v + ° - 8 • Vmax Equation 4-1 0.8-(//m a x =3.1 R (triaxial condition) Equation 4-2 0.8 • y/max = 5.1 R (plane strain condition) Equation 4-3 where IR is defined as follows: IR =Dr -(10-Lncrm B)-\ Equation4-4 where ^ is the peak friction angle, \ | / m a x is the maximum dilation angle, <j)cv is the friction angle at critical state or constant-volume, and a ' m _B is the mean normal stress at failure (kPa). 123 The small strain shear modulus can be obtained from the following equation proposed by Seed and Idriss (1970): x 0.5 G = 2 1 . 7 A " <7 max 2, max Equation 4-5 K 2. max = 0.6Dr +15 Equation 4-6 where P A is the atmospheric pressure and a' l t l is the mean normal stress and D r is the relative 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 0.67-0.7Gmax. The range increased with 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 Gm ax/10 would be appropriate. 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 m a x in the elastic-plastic model. Data reported by Ghionna et al. (1990) including the D r and stress 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 CC, 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 m a x vs a function of D r and stress level. This figure suggests that the applicable G / G m a x ratio is not constant and changes with soil conditions. The variation of G / G m a x 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 of 0.1 and 0.5 and the sensitivity of the results to this assumption wi l l be assessed. It w i l l be shown that the conclusions from these analyses wi l l not be sensitive to the selected value of G / G m a x . 4.4.2 Verification of the numerical analysis Before modelling the cavity expansion in a heterogeneous condition, a series of 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 of these analyses. One possible explanation for the softer response could be the different failure criteria used in the closed-form solution and F L A C . In the closed-form solution, the vertical stress is ignored and failure occurs in the horizontal plane. In other words, a i and 03 are always horizontal. On the other hand, in the numerical model the vertical stress is also considered in 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 of 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 of cavity expansion would decrease the amplitude of 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 of 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 of the model. A more frequent update would result in a smoother curve. In the elastic zone, the 125 effective mean normal stress, (o r+ae)/2 remains constant and so do the soil properties. In the plastic zone, the mean normal stress increases with the expansion of 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 of 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 of the inclusion of 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 of 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 in Figure 4-13. This provides some restriction to the movement of 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 of 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 of the stone columns on the limit pressure and hence on q t is negligible. 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 'Appolonia (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 of 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 of 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 r in Figure 4-2 is used here. Variation of 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 r (Table 4-1) and their soil properties are calculated accordingly. Table 4-2 shows the P L values obtained from numerical analyses for homogeneous (D r=58%) and variable soil condition with stone columns. It may be observed that the addition of the soil variability and stone columns to the model increases the limit pressure, Pi_. The magnitude of the increase depends on the choice of G/Gmax- P L increases by 11 % and 21 % for cases with G / G m a x of 1/10 and 1/2 respectively. The effect of stress dependency on the increase of limit pressure is negligible. The influence of the far field (beyond the stone columns, distance more than 1.7m in this model) on limit pressure was studied by varying the D r from 58% to 90%. This had very little 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 of P L versus D r for homogeneous soil condition obtained from the Carter et al. (1986) closed-form solution for the case G/G m a x =0.5 . The observed slope change in the trend is because the dilation angle was limited to a maximum of 15 degrees. After a certain density, where the dilation angle reaches 15 degrees, additional increase in density only increases the soil stiffness and not the soil strength (cp). The homogeneous soil condition at D r=58% is associated with P L =1300 kPa. From the numerical modelling, it was observed that the variation of D r according to Table 4-1 (from 58% at the centroid to 100% close to the stone columns) increased the P L to 1580 kPa (Table 4-2). If the homogenous curve of Figure 4-15 is used to interpret this P L a D r=66% is obtained. This interpretation ignores the heterogeneity of the ground. This is similar to interpretation of the post-compaction q t , which uses the correlations developed for a homogeneous soil condition. The interpretation of P L for relative density in this case (D r=66%) is greater than the D r at the centroid ( D r =58%) and is considerably smaller than the average D r =85%. The average D r for the case analyzed here is obtained from the following equation: Dr = 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 of the soil mass between the stone columns. • The interpreted D r is closer to the D r at the centroid and indicates the greater influence of the near field soil on q t . The above conclusions are based on a plane strain model and a G / G m a x o f 0.5. The sensitivity o f the above conclusion on these assumptions is evaluated below: 128 4.5.1 Effect of G / G m a x In order to assess the sensitivity of the conclusions from the numerical analysis to the selected value of G / G m a x , analyses with two different values of G / G m a x o f 0 .5 and 0.1 are compared. Figure 4 - 1 6 shows the variation of the P L versus D R for a homogeneous soil condition for two values of 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 of D R is 6 6 % for both assumptions of G / G m a x o f 0.1 and 0 . 5 . In other words, the interpreted D R from the limit pressure obtained in a heterogeneous condition is not sensitive to the assumed ratio of G / G m a x . 4.5.2 Assumption of Plane strain condition Cone penetration is neither spherical nor cylindrical cavity expansion. However, it seems to be closer to spherical cavity expansion. On the other hand, the plane strain assumption used in 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 of both tangential and radial stresses in the elastic region around the cavity depends on (ro/r)m+l, where r 0 is the radius of the cavity, r is the radial distance from the centre of the cavity to the point of 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 0 f r [ " m ( c t " 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 in a greater influence from the far field. It may be concluded that the plane strain analysis gives an upper bound result for the influence of the far field. In other words, the q t at the centroid is expected to be less affected by denser far field soil and tends to be more affected by the soil properties at the centroid. 1 2 9 4.6 IMPLICATIONS F O R I N T E R P R E T A T I O N O F POST-DENSIFICATION CPT T E S T I N G It has been shown that the cylindrical cavity limit pressure, P L is more affected by the properties of the soil close to the centroid and not the overall properties of the composite mass. The influence zone of the cone tip should be even smaller than that for a cylindrical cavity. Therefore, q t should be even less affected by the far field than is suggested by this numerical modelling. It may be concluded that q t slightly overestimates the density of the soil in the weakest zone at the centroid but significantly underestimates the overall stiffness and strength of the composite mass including the variable soil and the stone columns. For example, in the particular case shown in Figure 4-3, treatment by V23 failed to meet the specification of q t =15 M P a , whereas the V32 could achieve the criterion. However, the average q t in both cases is greater than the specification. In Figure 4-17, the zones with q 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 V32 vibroflot with higher dynamic force (see Table 2-2) resulted in less variable q t than the V23 vibrator. A stronger vibrator has a greater reach and the overlapping effects from the other compaction points should result in 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 V23 is greater than that for the V32 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 of 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 of the overall stiffness rather than the stiffness of the weakest point.. For liquefaction mitigation purposes, the presence of the denser soil and stiffer stone columns around the weaker centroid should increase the overall stiffness of 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 of 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 E F F E C T O F T H E H E T E R O G E N E I T Y O N GROUND P E R F O R M A N C E DURING E A R T H Q U A K E S H A K I N G 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 of the area by the shear modulus). They proposed the following expression for the reduced shear stress in the soil: where x s is the shear stress of the soil, x is the total shear stress, A t r is the tributary area o f one stone column , A s is the plan area o f the soil, A s c is the plan area o f stone column and G r is the ratio of shear modulus of the stone column to that o f the soil. For a triangular grid pattern, A t r=0.87S where S is the spacing o f the stone columns. The reduction factor for shear stress or For example for a triangular pattern, 3m spacing and 0.75 m diameter stone columns, A r=0.064 and G r=5, a ratio xJx =80% is obtained. This suggests that stone columns reduce the C S 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 Equation 4-8 C S R is: S i r ~\ + (Gr-l).Ar Equation 4-9 131 for the stress reduction in the soil similar to Baez and Martin (1992). In their expression, they considered the concentration of 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 of reinforcement by stone columns was the core of the discussion and the effect of the heterogeneity within the grid zone has been entirely neglected. The effect of 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 t o f the hatched triangle is 20 M P a and the average at the centroid is 12 M P a . Using their respective areas, the total average of 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 of heterogeneity results in a cyclic resistance that differs by more than 200% than that calculated using the measured q t at the centroid. Due to the empirical nature of the ground improvement design for liquefaction mitigation, it may be premature to suggest any changes in the state of 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 of the sources of conservatism is the ignorance of the heterogeneity. More research into this subject could result in a more relaxed specification for quality control of 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 of stiffer stone columns creates a heterogeneous ground condition. Conventionally, CPTs conducted for Q C / Q A of densification contracts are carried out at the centroids of the compaction grids, which are the weakest zones. Conventionally, interpretation 132 of C P T is based on an assumption of uniform soil conditions throughout the zone treated and ignores the horizontal heterogeneity of 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 of 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 of stone columns with the assumed spacing of 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 of the soil properties at the centroid and considerable under-estimation of the average soil properties of the composite soil-stone column mass. • The overall stiffness and strength of 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 D r Radius around centroid (%) (m) 1 58 0.01-0.1 2 63 0.1-0.35 3 72 0.35-0.7 4 87 0.7-0.9 5 100 0.9-2.4 6 58 or 90 2.4-9.6 Table 4-2 Cases of numerical modelling of plane strain analysis of cavity expansion at the centroid of stone column grid Input soil stone Gl G m a x stress P L Filename column dependency (kPa) Increase in PL (%) CPT50 CPT54 uniform variable N Y 1/10 1/10 No No 640 710 11 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 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 c with distance from the compaction points for two different vibrators Vibroflot V23 and V32 ( after Degen and Hussin 2001) 136 (a). Ladanyi & Johniloa (1974) 0>).Vtsic(1977) (c). SatRado (1993) (d). Yasufulm & Hyde (1995)" Figure 4-4 Idealization of analysis for cone penetration (after Yu and Mitchell 1998) 137 s ( 1 " • A "* A • o c l ^ > S P E C I M E N A N C J -• A \ § A i A A -C C T E S T S IN T I C I N O SAND ' 46 < O R < 9 2 % ; 60 < < ? M < 311 i kPa I i ! ! f -0.30 - 0 .25 - 0 . 20 - 0 . 1 5 - 0 . 1 0 -0.05 0 S T A T E P A R A M E T E R * Figure 4-5 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+dilatin-Homog-constant stress bound-CFT20 FLAC (Version 3.40) 16-Sep-3 23:55 step 26 -4.815E-02 <x< 3.818E-02 -4.135E-02 <y< 4.499E-02 G i i c i p l o t Civil Eng. Department UBC / / X / r„= Q.Qljpjr... -0.400 -O300 -O 200 -0.100 0 000 0,100 0 2O0 0.300 (x 0.10 m) ure 4-7 Geometry of numerical model, enlarged from Figure 4-6 139 0.16 0.14 0.12 0.10 X C O CD 0.08 0.06 0.04 0.02 0.00 — 4 6 8 relative density, D r / ( a m ) ° 5 10 12 Figure 4-8 Back calculated G / G m a x from the pressuremeter tests in calibration chamber 1600 1400 G-G i n a x /2 G=Gmax/10 (h40.5°, v=9.3°, v=0.2, GllliU=79MPa 0.2 1.8 0.4 0.6 0.8 1 1.2 1.4 1.6 Displacement for unit initial cavity radius (Ar/rQ) 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 3 in in <o u. a. •> re o 1400 1200 H 1000 800 600 400 200 0 G=Gmax/2 With 3 stone columns , j , . • " Without stone columns G=Gmax/10 With and without stone columns are identical 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 Displacement for unit initial cavity radius (Ar/ro) 1.8 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 Relat ive density, D r (%) Figure 4-15 Variation of cylindrical cavity limit pressure as a function of D r for homogeneous soil condition (G/G m ax = 0.5) 143 CL CU (/) m a> Q. E 2500 2000 1500 £ 1000 co o CO o O 500 G=Gmax/2 I • G/G m » = 0 . 5 ^ - - - - - - ^ - - G=Gmax/10 G/Gmaj=0.1 20 30 40 50 60 70 80 90 100 Relat ive density, D r (%) Figure 4-16 Variation of cylindrical cavity limit pressure as a function of D r for homogeneous soil condition for G/Gmax = 0.1 and 0.5. Note the assumption of G / G m a x does not affect the interpreted D r . 144 3.70»i Compaction J ^ ^ " ! Points Passed zone (V23) q,~ 20 > 15 MPa Failed zone (V23) qt=12 < 15 MPa 15 MPa (specification) 0 t 3.2 Distance from compaction point i along A*A (m) Figure 4-17 Consideration of heterogeneity of soil within compaction grid on Q C after vibro-replacement 145 0 6 C R R » 0.5 w 2 o TO to o c CO (ft •*£ «) S2 0) (fi is OJ (73 CC O O O O 0 . 5 + 0.4 + 0.3 + 0.2 + 0.1 + M=7.5 0.25 * Dsotmm) < 2.0 FC(%)<5 p P T Clean Sand Base Curve I No Liquefaction NCEER (1998) Workshop Raid Perfcrmlfice Uq. No Uq. Stark &Qt9t»f!1S955 • O Suzuki et aljJ9S5&) A A =1= 50 100| 150 ,200 250 3 0 0 Corrected C P t Tip Resistance, q ciN I q» at centroid I A v e r a g e q, over compaction gr id Figure 4-18 An example of interpretation of C R R with and without consideration of heterogeneity of ground conditions within the compaction grid. Using and average q t results in a greater interpreted C R R 146 C H A P T E R 5 E F F E C T O F H E T E R O G E N E I T Y 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 T E S T I N G R E S U L T S 5.1 INTRODUCTION Direct measurement of the ground stiffness is possible by measurement of the seismic shear wave, compression wave or surface wave velocity. Performance of seismic tests during the C P T has little impact on the cost and/or the time of testing. This makes the seismic cone test, SCPT, a feasible test for commercial applications in the quality control of ground improvement. Conventional interpretation methods to obtain shear wave velocity of soil from S C P T results are based on an assumption of homogeneous soil or of horizontal layering. This assumption simplifies the mathematical solution o f wave propagation and is a good approximation for natural deposits. However, in 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 of the shear wave velocity from seismic cone signals. In this chapter, numerical modelling wi l l be used to investigate the effect of the presence of stone columns on the interpreted shear wave velocity and the implications for using shear wave velocity for Q C / Q A of ground improvement w i l l be discussed. 5.2 I N T E R P R E T A T I O N 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 lm) , the penetration was stopped and the rod string was unloaded. Seismic waves were generated at the surface using a 12 kg swing hammer to strike either end of 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 of 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 in the seismic module. The signal was displayed on the computer screen. The same procedure was repeated by hitting the other end of the pad, which generated shear waves with inverse polarity and produced a mirror image response at the sensor as shown in Figure 2-5. Two or more blows on each end of 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 of British Columbia ( U B C ) cone contains two orthogonal horizontally mounted piezo-resistive accelerometers with a range of ± 2g, a flat frequency response from 0 to 500 Hz , a natural frequency of about 600Hz and damping at 70% of 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 s over a given depth interval can be calculated by an interval technique using the following equation: K = ~ — ~ Equation 5-1 where L 2 and Li are the slant distances between the sensor in the cone and the source beam taking account of the offset between the vertical axis of the cone string and the source beam (Figure 2-5). The time interval, At=t2-ti, is the difference between the arrival times of shear waves at two successive depths intervals. Since it is hard to accurately pick out the initial arrival of shear waves from the seismic signals, different approaches have been developed for definition of 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 of 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 of 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 of signals at two successive depths by shifting one signal by small time steps relative to the other signal. A t each shift, the sum of the product of the signal amplitudes is calculated as shown in the following equation: CC„ (r) = l im - f S, (t).S, (t + z).dt Equation 5-2 T->co 71 JT 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 of the signal may be used for this method. Gillespie (1990) noted that the first half cycle of 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 of the measured shear wave arrival for cross-correlation. They isolated the first shear wave cycle from the rest of the signal by a process called windowing, a common technique in signal processing (Bath 1974). Interval techniques assume no distortion and/or dispersion of signals between two adjacent depths. In this condition, both interval techniques should give similar values for V s . In a dispersive medium, the wave velocity is a function of 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 of a single frequency travels. In a dispersive medium, the above interval techniques may not give similar values of V s . A more comprehensive method of determining V s is the phase o f cross-spectrum method, which gives the phase velocity as a function of frequency. For each frequency, f, the time interval is calculated as: 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: </>(/) Equation 5-3 2Kf 149 Equation 5-4 where A L = L 2 - L i as defined in Figure 2-5. The phase velocity associated with the predominant frequency of the signal may be selected as the shear wave velocity of the soil as suggested by Stewart (1992) or an average velocity associated with a range of 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 T E S T I N G Figure 5-1 shows typical seismic signals before and after vibro-replacement in a sandy deposit in Richmond, B C . Plots such as Figure 5-1 give a general picture of the variation o f the wave arrivals and allow identification of any anomalies in the data. The increase in total travel time of 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 of 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 of 10 metres indicates a general increase in the stiffness of the deposit below that depth. On 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 of the main shear wave. The V s obtained from the first part of the post-compaction signal is about 450 m/s, which is too high for the native sand even after compaction. It is l ikely 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 of 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 in the signals with depth. The signals contain some inflections, which are marked with vertical arrows. These inflections move relative to the rest of the signal with increasing depth and seem to disappear at depths below the tip of the stone columns. Figure 5-2 compares the V s profile obtained from cross-over and cross-correlation methods for pre- and post-compaction. For pre-compaction signals, the V s profile obtained is 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 of the post-compaction V s profile with depth is not smooth and may vary significantly between adjacent intervals. The post- V s profile obtained from the cross-over method is usually spiky. This is partly due to distortion of the signals in 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 of the wave trace. Figure 5-3 is an example of a comparison of the variation o f phase velocities with frequency before and after vibro-replacement obtained from the phase of 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 of 70 Hz . On 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 of 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 t and V s . Spectral analysis of surface waves, S A S W was also carried out sometime after the post-densification S C P T as an alternative method for evaluation of bulk stiffness of 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 of Rayleigh waves when travelling through a layered medium. The velocity of Rayleigh waves depends on the ground stiffness, thickness of the layers and wavelength. For more details refer to Nazarian and Stokoe (1984) or Stokoe (1994). Figure 5-6 compares the V s profiles obtained from S C P T and S A S W methods after vibro-stone column. Note that the average post-compaction V s from S C P T is about 210 m/s. On the other hand, the V s from S A S W is about 177 m/s, which is close to the pre-compaction V s . One explanation for this discrepancy is that the V s from S C P T might have been affected by the stiffer stone column whereas the V s from S A S W is more biased towards the bulk stiffness of the ground. Schneider et al. (2000) carried out S C P T and cross-hole seismic tests to measure the V s of a native silty clayey soil and stone columns respectively after construction of stone columns. Due to the tight spacing of stone columns, they had to use the cross-hole configuration shown in Figure 5-7 whose result would be some average of V s o f the stone column and the soil. The S C P T was also performed at the centroid o f the triangular grid. It had been expected that a higher V s would be obtained from the cross-hole test due to the direct effect of the stiffer stone 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 in a higher shear wave velocity. Pinches and Thompson (1990) carried out down-hole and cross-hole seismic tests to measure the V s o f mudstone containing interbedded thin limestone bands. They found that where the limestone bands were closely spaced, the cross-hole V s was as much as 45% greater than the down-hole V s (Figure 5-8). They noted that V s from cross-hole testing in these zones was higher because shear waves refracted and preferred to travel through the stiffer limestone bands. The cases presented here suggest that the inclusion of stiffer material parallel to the travel path of shear waves may result in overestimation of the V s o f the native soil. This is important i f V s is to be used for Q C / Q A o f densification or i f V s is used to obtain the stiffness of the densified soil. The effect of the inclusion of stone columns wi l l be investigated using numerical modelling 152 5.4 N U M E R I C A L M O D E L L I N G F O R INVESTIGATION O F T H E E F F E C T O F S T O N E C O L U M N S O N V s F L A C (Itasca 1998) version 3.4, with the dynamics option, was used for simulation of the down-hole seismic test. Firstly, numerical modelling is carried out for the case of 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 of stone columns wi l l be modelled. 5.4.1 Numerical modelling of the down-hole seismic test without stone columns Figure 5-9 illustrates the configuration of the model. A block of ground 20 m x 20 m is represented by a mesh of 150 x 150 rectangular elements with dimensions of 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 SCPT, Stewart and Campanella (1991) measured soil shear strains in the range of 1.4 x 10"5 at 5 m to 1.0 x 10"6 at 25m. A s shown in Figure 5-10 from Ishihara (1996), the soil response at such small strain levels may be modelled using the theory of linear elasticity. In this study, a linear visco-elastic model is used to allow consideration of 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 of 182 m/s. A high bulk modulus is selected to give a compression wave velocity close to that of 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 (Mok et al. 1988). In his study of S C P T signals, Stewart (1992) found lower damping ratios in the range of 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 in a cleaner simulated signal with fewer cycles. In more complicated 153 conditions, such as where vertical inclusions are present in the ground, different kinds of waves may be generated. Fewer numbers of cycles simplifies identification of different types of waves in the simulated signal. Wave velocities are obtained from the assumed elastic properties using the following equations: Equation 5-5 B+1.33G Equation 5-6 max 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 s o f the sandy deposits increases almost linearly with depth from 5 m to 20m. To model this condition, V s is assumed to vary as follows: Vs = \Q.d +100 Equation 5-7 where d is the depth in metres and V s is in m/s. 5.4.1.2 Loading condition The impact of the hammer on the truck pad was simulated by a horizontal initial velocity of 1 m/s applied for 8x10~5 seconds to the ground surface over the length o f the source beam. This is the time required for a compression wave to travel twice the length o f the head of 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 of the velocity is of no significance in this model as the main interest is in the waveform of the seismic signals rather than their amplitudes. 154 5.4.1.3 Results of numerical analysis A horizontal impact at ground surface transmits body waves and surface waves into the ground. Figure 5-12 is a snapshot of the velocity vectors at 0.05 sec after the impact for the case of homogeneous soil. The shear wave and Rayleigh wave fronts are annotated. Note that the compression wave has already travelled beyond the boundary of 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 of the concentration of 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 of horizontal velocity and horizontal acceleration at a depth of 5 m at the centreline of the model are shown in Figures 5-13 and 5-14, respectively. These are the responses of 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 of the analysis and signals from the right impact are the mirror image of the left signals using the symmetric condition of the problem. The positive sign indicates the direction of velocity or acceleration vectors to the right of the model. The first arrival of the seismic energy can be attributed to compression waves and the second group of cycles to the shear wave, as shown in Figure 5-14. In the remainder of the chapter, the time histories of the horizontal acceleration obtained from the numerical analysis at the centreline of 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 of homogeneous soil and 5% damping. 5.4.1.4 Characteristics of 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 wi l l be compared to those of 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 of initial deflection of the compression wave component is opposite to that of 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 of 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 of the signal. However, the number of oscillations or cycles in the simulated signal is smaller than in the field data. The number of oscillations in the simulated signals depends on the damping ratio as illustrated in Figure 5-18 which compares simulated waveforms for damping values of 1% and 5%. A reduction in the assumed damping ratio results in more cycles in the simulated signals. 5.4.1.4.2 Attenuation of signals with depth The signals reduce in amplitude with depth. Attenuation of 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 of 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 of 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 of the shift in their field data was much smaller than that in Figure 5-19a. Figure 5-19c shows the F F T of full signals from three depths from the Kidd2 site shown in Figure 5-16. Figure 5-19d is the F F T of the first shear wave cycle of the same depths for comparison. In each case, the peak of the frequency spectrum remains constant with depth. Figure 5-19e shows the frequency spectra o f simulated signals obtained from the numerical model, in which V s increased linearly with depth and the damping ratio was 5%. It may be observed that the peak o f the spectrum and its rate of decrease with depth have become more similar to the field data in Figure 5-19b. Figure 5-19f shows the results of the same analysis repeated for a damping ratio of 2%. The combination of an increase in V s with depth and a smaller damping ratio resulted in a balanced condition in which the peak of 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 in stiffness with depth counterbalances the effect o f damping on the peak of the spectrum. The peak frequency o f the S C P T signals is about 80 Hz , which is smaller than peak frequency of the simulated signals of 97 Hz . This is a result of the field site being slightly less stiff (lower V s ) than the simulated soil 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 of 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 of the first component is consistent with the input compression velocity, V p , o f 1500 m/s and the interval velocity of the second component is consistent with the input V s o f 182 m/s. Despite a purely horizontal excitation at the ground 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 of such a 157 compression wave component. Sanchez-Salinero et al. (1986) carried out theoretical studies of the propagation of waves generated by 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 of 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 of the shear wave component and causes the first particle motion to be opposite to the direction of the excitation. This phenomenon is an important issue for interpretation of dynamic measurements on small samples in laboratory tests since it makes it difficult to identify the arrival of 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 s . They suggested that point 1 could be regarded as the arrival of shear wave. Brignoli et al. (1996) noted that the polarization of the near field component was opposite to the excitation pulse. Therefore point 1 is usually considered to be the arrival of the shear wave because at this point the deflection of the signal is in the same direction as the input excitation. The near field effect can also be observed in 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 of 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 of 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 of the signal is in the same direction of the excitation. The same trend exists in the signal at the subsequent depth. Figure 5-22b shows that the polarity of the compression wave component reverses when the hammer hits the opposite side of 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. Also note that the compression component is of higher frequency than the shear wave component in both S C P T and simulated signals. The near field effect is not problematic in interpretation of S C P T signals mainly because the distance between the source and the receivers is sufficiently large for attenuation of the compression component to occur and to provide enough time for the compression and shear components to separate. A s the frequency of the compression wave component is considerably higher than that of 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 in conjunction with SCPT. He noticed that whenever the arrival of 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 of the p-wave. He used this observation to interpret the arrival of the shear waves. His observation is consistent with the modelling and field test results in this study. 5.4.1.5 Calculation of V s from field data The cross-over method, cross-correlation method and phase o f cross-spectrum techniques are used on some of the signals in Figure 5-17. The interpreted shear wave velocities are shown in Figures 5-24. Values of V s obtained from the cross-over method for the time markers indicated in Figure 5-24a are shown for two depth intervals in Figure 5-24b. The V s values tend to decrease for time markers later in the trace. Figure 5-24c shows an example of the use of cross-correlation to obtain the time interval and the corresponding V s , and Figure 5-24d shows the variation of phase velocity with frequency obtained from the phase of cross-spectrum method. The variation of V s with frequency suggests a slight dispersion. In the frequency range of interest, either side of the predominant frequency of about 80Hz, the phase velocity tends to increase slightly for the depth interval of 3.6 and 4.6m and tends to decrease for the depth interval of 7.6 to 8.6 m. Table 5-2 compares the results of the values of V s obtained from the three different methods. V s varies by up to about 3%. This would result in about a 6% variation in the calculated value of 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 of V s from the cross-over technique, the first cross-over and the maximum peak were used. The first shear wave cycle of the signal was separated from the rest of the signal by rectangular windowing 159 and was used for the cross-correlation method. The V s values from the first cross-over are within 2% of the cross-correlation V s . For most depths, the results from the maximum peak are also close to the cross-correlation V s . However, for this data set, the first cross-over appears to give better agreement with the cross-correlation V s . This may be due to the peak being more sensitive to local irregularities than the first cross-over. The closeness of 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 s profile 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. Whi le Sheriff and Geldart (1995) noted that dispersion of seismic body waves has not been definitively observed over a wide range of 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 of V s from simulated signals The V s values interpreted from the simulated signals in the numerical model can be compared with the input value o f shear wave velocity in the model. Figure 5-26 presents a comparison of the V s profile calculated using the cross-over method for time markers 2, 3, C and D in Figure 5-15. The computed V s varies with the location o f the time markers on the signal. The earlier time markers give greater V s . The maximum peak and the first cross-over, time markers 3 and c, give V s values within 0.8% and 2% of the input value, respectively. This suggests that these may be the optimum time markers for estimating V s by the cross-over method in field data. The V s profile obtained by cross-correlation is also shown in Figure 5-26 and is within 1% of the input value of V s . Figure 5-27 shows the calculated values of V s by cross-over and cross-correlation approaches for the simulated case o f stiffness increasing with depth and damping of 2%. The cross-over and cross-correlation V s profiles are much closer to the input value of V s . The cross-correlation value of V s is within 0.2% of the input value. 160 The slopes of the dashed lines connecting the time markers in Figure 5-15 represent the cross-over values of V s for the respective time markers. The slopes o f the lines change depending on the choice of time marker. This is an indication of the effect of signal widening on the calculated velocity. A s mentioned earlier, material damping causes signal widening and variation of cross-over velocity in the time domain. The effect o f material damping appears as dispersion in the frequency domain and causes a variation o f phase velocity with frequency. Figure 5-28 shows the variation of 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 of about 97 Hz , the phase velocity is about 183 m/s. This is almost identical to the cross-correlation V s and is less than 1% different from the input V s o f 182m/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 of the numerical analysis of 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 in seismic cone testing and to simulate the signals received at down-hole accelerometers. Analyses were performed based on assumptions of a homogeneous ground condition and for the case in which the stiffness of the ground increased with depth. The results of the simulations were compared to field data. This process has provided insight into the factors affecting wave propagation and the determination o f V s from field seismic testing. The shape of 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 of simulation of the seismic test. In the next section, the stone columns wi 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 of stone columns on the propagation of 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 of the stone columns, D , o f 0.3 and l m . 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 of the stone columns to the soil, G r =G s tone.coi/ G Soii 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 of 5% is used. A damping ratio in the higher range, reduces the number of oscillations in simulated signals and helps in identification of different types of waves in 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 in the presence of two stone columns. The arrows show the direction of the velocity vectors. Compared to Figure 5-12 for homogeneous conditions, the inclusion of stone columns complicates the wave propagation regime and makes it difficult to identify different types of waves. However, several patterns can be observed which are designated as waves " 2 " to "4" in 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 of 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 of about 425 m/sec. This is close to the input V s o f the stone columns of 406m/s. Wave " 3 " is thought to be an interface 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 of the horizontal acceleration at the centreline of the model are shown in Figure 5-32. The simulated signals are the responses of imaginary horizontal accelerometers embedded at the centreline of 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 in 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 of 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 of wave distortion and time marker shifting diminished as the diameter of the stone columns and/or G r were reduced. 5.4.2.3 Calculation of the V s from simulated signals Table 5-4 presents V s values obtained by various techniques from the simulated signals for the depth interval of 5 to 6 m in homogenous ground and with stone columns. In each case, the input elastic V s o f the soil is 182 m/s. A s shown earlier, for the case of a uniform soil model, the V s results obtained from different methods were consistent. The results were within ± 2% from the input elastic V s . On the contrary for the case with stone columns, the results from different methods are very different and also much larger from the input soil V s in the model. 5.4.2.4 Discussion In the case of 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 s values obtained from all three interpretation techniques are similar. The phase velocity is almost constant in the frequency range o f interest. Figure 5-33 shows the post-vibro-replacement seismic signals (repeated from Figure 5-1). Comparison of Figures 5-32 and 5-33 shows that the characteristics of the field data are duplicated in the simulated signals. The inclusion o f stone columns changes the characteristics of the signals. The signals are irregular and more difficult to interpret than in the untreated case. There is an apparent arrival of some low energy waves ahead of 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 of the main shear wave, as shown in Figure 5-32. The V s obtained from this part of the simulated signal is close to the input V s o f the stone columns (406 m/s). Similarly, the interval velocity o f the same part of the measured field signal is about 450 m/s, which is considered to be close to V s o f the stone column (Figure 5-34). Selection of 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 in very high values o f V s . Time markers E and F result in much lower V s values but are still 20% higher than the input V s for the soil. The time markers between B and E cannot be used, as they are located in the portion of the signals with large distortion. For example, note that the maximum peak shifts half a cycle from 5m to 7m. Cross-correlation of the two complete signals overestimates the soil V s by about 13%. Figure 5-35 shows that the phase velocity in homogenous model is almost constant in a wide range of frequencies around the dominant frequency. Inclusion of stone columns causes the phase velocity to be frequency dependent. The variation of the phase velocity with frequency can be divided into two plateaux, m-n and u-v, with velocities of 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 s for the stone 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 of shear stiffness from the centroid of the grid towards the stone column in the field 164 case, as opposed to an abrupt change assumed in the numerical model. Figure 5-37 shows how G r and D affect the phase velocity spectrum. Small values of G r and D result in a phase velocity relatively unaffected by frequency, which is more similar to the untreated case but V s is still overestimated. 5.4.2.5 Summary of the numerical analysis of seismic cone testing in presence of stone columns This section shows the results of numerical modelling to explain the mechanism of the effects of the vertical stiffer stone columns on the wave propagation regime and the interpretation of V s from the S C P T signals. The inclusion o f stone columns creates vertical 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 of time markers within the signals with depth, due to superposition of wave arrivals. These effects are observed in field data and in the simulated signals. Conventional interpretation of the seismic signals results in V s greater than the V s o f the soil between the stone columns. For any 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 of the effect of 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 of stone columns and to determine the shear wave velocity of the in situ soil between stone columns. 5.5 IMPLICATION O N Q C / Q A O F DENSIFIED SOIL B Y S H E A R W A V E V E L O C I T Y Shear wave velocity has been used for Q C / Q A of densified soil (e.g. Addo et al. 1993, Andrus et al. 1998, Moxhay 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 of stiffer stone columns. Based on the results of numerical modelling, the increase in post-V s due to inclusion of stone columns could be in the range of 15 to 20%. If the increase in the V s due to inclusion of stone columns 165 is ignored, then the post-compaction V s w i l l overestimate the degree of improvement of the native soil. Figure 5-38 compares the increase in q t and V s for a site in Richmond, B C . It may be observed that the tip resistance has improved by about 50 to 100% whereas V s has improved by about 5 to 20%. For example in Figure 5-38 at 10m depth, consider an increase from 100 bars to 160 bars for q t and an increase from 190m/s to 220 m/s for the V s (15% increase). The following is assumed for the changes in soil conditions based on changes in the cone tip resistance. 1 ^ = 0 . 5 to Ko. p o s t =0.75 and D r - p r e =65% to D r . p o s t =75% The above changes in ground conditions should increase the V s by only 8%. This is based on the following correlation proposed by Chillarige et al. (1997). This correlation was obtained from bender element testing on reconstituted samples of Fraser River sand. (K0f'U5 Equation 5-8 where A v s =295, B v s=143 and n v s=0.26, e =void ratio, Ko=coefficient of horizontal stress and Pa=atmospheric pressure. The apparent increase of V s beyond about 8% could be attributed to the effect of stone columns. In this case the effect of stone columns may have caused about 7% of over-estimation of the shear wave velocity of the in situ sand. Ignoring the effect o f stone columns would overestimate the degree of improvement in the native soil. 5.6 S U M M A R Y AND CONCLUSIONS Shear wave velocity and cone tip resistance are different functions of the same parameters of granular soils. Therefore, an independent measurement o f shear wave velocity, V s along with tip resistance helps in better characterization of granular soils. The seismic cone penetrometer is a valuable tool that can measure both parameters in one hole. Conventional interpretation methods of seismic tests to determine the interval V s are mainly based on uniform or horizontally layered ground. On the other hand, the improved ground after vibro-replacement includes stone columns, which result in vertical layering. The conventional 166 VS={A- B.e). methods are not strictly applicable to interpretation of seismic signal in vertical layering and may result in erroneous V s . Plane strain numerical modelling was used to explore the effect of stone columns on the wave propagation seismic waves and consequently on the results of seismic tests. The numerical model was capable of 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 of the properties of in situ soils as well as the properties of stone columns. It also showed that in ground with stone columns, the V s determined from the conventional techniques would be greater than that o f the native soil. In other words, the conventional methods over-estimate the V s o f the native soil when stone columns are present. For the normal construction of stone columns in sand ( ~ l m diameter columns and 3m spacing), plane strain analyses showed the over-estimation in the V s o f native soil could be up to 15 to 20%. On the other hand, the increase in the V s after vibro-replacement in the sites studied during the course of 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 of the degree of improvement of 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 Soil Small strain shear modulus, G m a x (MPa) 66 Bulk modulus, B (MPa.) 4410 Poisson's ratio -0.49 Bulk density, p (kg/m 3) 2000 Damping ratio (%) 5 Elastic Shear wave velocity, V s (m/s) 182 Elastic compression wave velocity, V p (m/s) 1500 Table 5-2 Comparison of the V s obtained from different methods, Richmond, B.C. Depth interval Shear wave velocity, Vs (m/s) (m) 1st cross-over Max. peak Cross-correlation Cross-spectrum 3.6-4.6 157 153 153 157 7.6-8.6 169 166 171 170 Table 5-3 Material properties used in numerical model Material properties Soil Stone column Maximum shear modulus, G , n a x (MPa) 66 2.5x66 or 5.0x66 Bulk modulus, B (MPa.) 4410 4410 Density, p (Mg/m3) 2 2 Damping ratio (%) 5 5 Elastic shear wave velocity (m/s), V s 182 287 or 406 Elastic compression wave velocity (m/s), V p 1500 1500 Table 5-4 Interpretation of V s (m/s) from simulated signals, depth interval of 5m- 6m 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 s is 182 m/s for the soil and 406 m/s for the stone columns. 168 time (sec) time (sec) 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 maximum peak ^8-3.7 4.7 5.7 6.7 7.7 8.7 9.7 10.7 11.7 12.7 13.7 14.7 15.7 16.7 1 st cross-over ](-* maximum peak f^-i Tip of stone column Figure 5-1 Comparison of SCPT seismic signals before (left) and after (right) vibro-replacement, Richmond, B C shear wave velocity, V s (m/s) 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 shear wave velocity, Vs (m/s) 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 —max peak —«— x-over - o •x-correlation max. peak —m— x-over - o •x-correlation Figure 5-2 V s profile from cross-over and cross-correlation methods, (left) before vibro-Replacement, (right) after vibro-Replacement 170 240 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 requency (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 SCPT profile before and after vibro-replacement, Laing Bridge, Richmond, B C 172 Shear Wave Velocity Profile for LB Line A Or Q. Q 10 12 14 ; i . ++; - - - - - t - 4 - - -• ! + • o . O - '•• o 4 " SCPT SASW(d=4m) SASW(d=6m) SASW(d=4m) SASW(d=14m) SASW(d=8m) 50 100 150 200 Velocity (m/s) 250 Shear Wave Velocity Profile for LB Line 2 0, C L Q 10 12 - j -o 14 C SCPT + SASW(d=12) -f- SASW(d=10) -,- SASW(d=4) 50 100 • 150 200 Velocity (m/s) 250 Figure 5-6 Comparison of SCPT and SASW 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 10 20 30 a a 40 50 60 70 ** t' -1 i 1 > « —v mmm Limestone band i Mudstone h^j Sillstone/limestone US Fissile mudstone Siltstone and gypsum Down-hole measurements Cross-hole measurements Cross-hole Vs affected by limestone bands 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 Schematic geometry of the F L A C model Shear s t r a i n 10" 6 10" s 10~4 10 " 3 10~2 10"' i 1 1 I Sma l l Med ium s t r a in s t r a i n L a r g e Fa i lure s t r a i n s t r a i n E l a s t i c Elasto-plastic F a i l u r e Effect of load repetition Effect of load ing rate . •• ! M o d e l L i n e a r \ V i s c o - \ Load history e l a s t i c \ e las t i c \ t rac ing type mode l \ mode l \ mode l Me thod of r e s p o n s e a n a l y s i s L i n e a r \ Equivalent \ Step-by-step ttt. ^ . \ l i nea r \ in tegra t ion m e t h o d ^ me thod \ method Figure 5-10 Modelling of soil behaviour in compliance with strain dependent deformation characteristics (after Ishihara 1996) 1 7 6 y cu in g 4-* o o cu > -0.20 0.000 Excitation velocity Free vibration 0.001 0.002 time (sec) 0.003 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 -0.03 ? -0.02 $ -0.01 E r 0 8 o.oi v > 0.02 0.03 0.01 time (sec) 0.02 0.03 0.04 0.05 A kight impact / \ "7 \ / \ \ / Left impact •«• 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 4 11 •3 2 / T " \ ^ f\j\ time markers L\OT« U T V / • — t \ jy i \ \ / 1 1 / V \ \ J\ j *\ %*\ J\\ / \ 1 v \ * ' » \ » i i \ i i * * * 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 SCPT 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 50 100 150 200 frequency (Hz) a) Simulated signals, homogeneous, damp=5% 50 10O ISO 200 Frequency (Hz) b) Full SCPT signals, 2.7 to 9.7m in a sandy deposit (after Campanella and Stewart 1992) 50 100 150 frequency (Hz) c) Full SCPT signals Richmond, B.C. (this study) 200 50 100 150 200 frequency (Hz) d) First shear wave cycle of SCPT signals Richmond, B.C.(this study) 0.070 0.060 0.050 •S 0.040 3 ' E | 0.030 0.020 -I 0.010 0.000 - •- 5 m s - 7m —A™ 9 m , V depth increases if—r-» 200 50 100 150 frequency (Hz) e) Simulated signals, increasing stiffness with depth, dainp=5% 0.000 50 100 150 frequency (Hz) 200 f) Simulated signals, increasing stiffness with 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) time (sec) 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.00 0.01 0.02 0.03 0.04 0.05 0.06 1.7 i ' ' ' ' ' ' ' ' ' ' ' 1 1.7-2.7 Q. T3 3.7 4.7 Moves to right " B " A / \ "A" Moves to left -J—J\ / S N / w Compression x ' / \ \ i wave N \ I ' a) Left to right impact 2.7 3.7 4.7 Moves to right Moves to left - ' V X / V — — - 'viAA. b) Right to left impact Figure 5-22 Near field effect in SCPT signals, enlarged from Figure 5-17 185 0.00 5 - J % v — E Q. <D •a time (sec) 0.02 0.04 i i Moves to left Moves to right Left to right impact Figure 5-23 Near field effect in simulated signals, enlarged from Figure 5-20 186 0.02 time (sec) 0.04 0.06 0.08 180 160 120 X 3 6m - 4 6m I a 7.6m - 8.6m Linear (3.6m - 4.6m) - - - Linear (7.6m -8.6m) | number of time marker b) Variation of cross-over Vs At= 0.0058 sec Vs=171 m/s 1 240 220 1 = 180 u o o > 160 0> (A a 140 120 100 -0.01 0 0.01 0.( time shift (sec) c) Cross-correlation, depth interval 7.6m-8.6m 0 7.6-8.6m X3.6-4.6m 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 s Richmond, B.C. 1 8 7 100 2-r-200 11 Figure 5-25 Profile of shear wave velocity, Kidd2, Richmond, B.C. 1 8 8 shear wave velocity, Vs (m/s) 160 170 180. 190 200 5 6 _ 7 9 10 Cross-over cross-correlation time markers ) 3 t > / T T 1 C 2 • / i 1 + k '*? I • \ 1 + i */ • \ i Input Vs-182 m/s * Figure 5-26 The V s profile from the simulated signal, homogeneous soil, Damping=5% 1 8 9 shear wave velocity, Vs (m/s) i i J 1 Figure 5-27 The V s profile from the simulated signal- increasing stiffness with depth, Damping=2% 190 210 205 _ 200 ~ 195 2 190 a) > 85 185 re 180 from cross-correlation J 175 Input V S 170 50 100 150 Frequency (Hz) 200 250 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, Gr=5, L=12m time = 0.02 sec Figure 5-31 Propagation of body waves in presence of two stone columns 194 0 Time (sec) 0 0 0 . 0 1 0 . 0 2 0 . 0 3 0 . 0 4 0 . 0 5 0 . 0 6 0 . 0 7 1— I I I Wave"1" v^ isoo A A i i II' ' v i ' A v v II i i 1 J \ V 1 Wave "2" \ I U A V 2~400m/s \ \ J[\ A / \ v—*^ \ \ \ \ \ \ f\\ / V • •v i > V I V \ » M \ \ \ \ / v V \ * t \ \ -1 \ / \ / V Y XJV \ i > \ \ \ < > \ » « » \ 1 i \ r » » 1 1 V 1 > x-N» v » \ A-.... J > " \ l v l> \ \ l- k> \ \ Wave "3" f^> Wave M4" Vs3~297 m/s U Vs4~221 m/s U ^ 7 E Q. Q 1 0 11 Figure 5-32 Simulated signals in the presence of two stone column, G r =5, D=lr 195 time (sec) 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 16.7 Figure 5-33 SCPT signals after Vibro-Replacement - Richmond, B.C 196 frequency (Hz) Figure 5-35 Phase velocity of simulated signals, 5m & 6m 197 —•— Gr=5, D=1m f requency (Hz) Figure 5-36 Frequency spectrum of simulated signals at 5m 240 J Increase in G r or Input Vs / -®— Gr=5.0. D=1m - A — Gr=2.5, D=1m - * — Gr=5.0, D=0.3m H — Gr=2.5, D=0.3m - Uniform (no stone column) 40 60 80 100 frequency (Hz) 120 140 160 Figure 5-37 Sensitivity of phase velocity to G r and D , simulated signals 198 0 Shear wave velocity (m/s) 100 200 300 + Tip of stone columns! 100 200 300 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 s and q t after vibro-replacement 199 C H A P T E R 6 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 T H E G R O U N D RESPONSE T O C O N E P E N E T R A T I O N T E S T I N G 6.1 INTRODUCTION The changes in ground condition caused by ground improvement also change the response of ground to C P T U . This chapter presents the results of analysis of 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 C P T U after vibro-replacement. The effect of induced changes by vibro-replacement on interpretation of 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 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 RESPONSE T O C P T U 6.2.1 Database of vibro-replacement projects in the Lower Mainland, B C A database consisting of pre- and post -CPTU was gathered from 13 vibro-replacement projects in the Lower Mainland of British Columbia. A total of 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 of this research or by Conetec Investigations Ltd. for commercial projects. Liquefaction mitigation was the main purpose o f vibro-replacement at these projects. In the majority of these sites, the water table was at a depth of about 1 m below surface. A l l the cone holes were pushed at the centroids of the triangular grids. The distances between pre-CPT and post-CPT holes were usually a few metres to a maximum of 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 of thin layering which has different effects on q t and fs. These data include projects completed by three different 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 of them in Richmond, B C . A brief history of the geology of Greater Vancouver and Richmond is useful to understand the general setting of 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 of sediments. The regime of 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 km out to sea. About 5000 years ago, the large volume of sediments quickly expanded the delta. A n 11 m rise in the sea level slowed down the development of the delta. A t this time Richmond was about 10 km 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 in 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 of the delta is about 2.5m to 8.5 m/y. Figure 6-1 illustrates the growth of 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 of a few metres of silt to clayey silt overlying interbedded silt and sand, overlying clean sand with some thin layers of silt to silty sand overlying silty clay/clayey silt. The interest o f this thesis is mainly the top 15-20 m of 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 CPT classification chart Figure 6-3 shows a typical C P T U profile before and after vibro-replacement in Richmond, B C . Generally q t and fs increase after ground improvement and U2 remains 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 of 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 of 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 of the N C zone towards the over-consolidated sand. This could also be attributed to errors in measurement of sleeve friction, to the linear normalization of stress level, which is not well suited for sands, or the logarithmic scale which magnifies scatters of the data with small values. It could also mean that the N C zone needs some shift to encompass the majority of 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 of the type of vibrator or the spacing of the compaction points. There is no significant difference between pre and post-compaction plots except for the general upward movement of the bulk of the data points due to increased tip resistance. In order to track the effect of 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 of 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 t and Q). The changes in friction ratio, R f and F, are more 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 of 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 of 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 of the friction sleeve due to its proximity to the cone tip. The measured sleeve friction is sensitive to the wear of cone tip and friction sleeve. Moreover, fs is a smaller quantity and is 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 of 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 q to move towards B q =0, i.e. the excess pore pressures (negative or positive) during penetration measured behind the tip are a lower proportion of net tip resistance. This means more increase in q t relative to the change in U2. In fine sands and finer soils, ground improvement usually decreases U2 indicating either an increased tendency for dilation of the soil as it passes the shoulder of the cone or a decreased permeability due to densification (or crushing) resulting in partially drained response during penetration. The typical trends of the change of O C R , age and D r on C P T U data suggested by Robertson (1990) are indicated by arrows on the classification charts in Figure 2-6 and 2-7 (also shown on Figures 6-4 to 6-6). The arrows suggest that increases in O C R and ageing increase q t and Rf whereas an increase in density increases q t but decreases Rf. It is interesting to compare these trends with the effect of 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. On Figure 6-6-c, the vectors suggest an increase in O C R for these points. For coarser soils, the vectors that start in 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 of 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 (SBT) assigned to the soil changes. This change seems to be larger in 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 of 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 in Figure 6-6 in terms of their pre-and post-compaction I c values. The data points fall below the 45 degree line which indicates that post-I c is generally smaller than pre-I c. In other words, the post-compaction soil appears coarser grained with lower fines content. 6.2.3.2 Effect of compaction on estimation of 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 in 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 CPT in Calibration chamber tests The field observations after vibro-replacement showed that q c increased but Rf appeared to exhibit no general trends. It is not known whether the direction of 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 of uncertainties but predominantly from the effect o f site variability. Site variability includes the natural variability and that caused by variation of compaction energy as a function of radial distance from the compaction point. The inclusion of stiffer stone columns in the ground also increases the heterogeneity. This makes the result of post-compaction C P T sensitive to the location of 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 of the individual parameters D r , a'h and o' v , the data from calibration chamber (CC) testing on Ticino sand (Lunne et al. 1997) wi l l be used to confirm and explain the observed changes in soil 204 response in the field in attempt to answer the following questions for the idealized conditions in chamber testing: • Do changes in boundary conditions change the position of the soil on the classification chart? • Is the direction of changes on classification charts diagnostic of the changes in soil conditions? The advantage of C C data is that it is obtained under controlled conditions. The C C database is used here in the context o f ground improvement, in which the soil condition changes without any change in soil type. To remove unnecessary complications, C C data with the following conditions were selected: • Sand type= Ticino sand • Diameter of the cone = 35.7 mm (10-cm 2 cone tip) • Diameter of chamber = 1.20 m • Boundary condition = BC1 (constant lateral and vertical stress at the boundary of the chamber 150 published data points are used in this section. These data cover the following range of soil properties. cjv(kPa): from 40 to 715 cjh(kPa): from 16 to 330 O C R ( - ) : from 1 to 8 The effect of the boundary condition on q c has been studied (e.g. Kulhawy and Mayne 1990, Salgado et al., 1998) but the effect on the sleeve friction has not been studied to the knowledge of the author. Cone tip resistance is corrected for chamber size effect by the following expression suggested by Kulhawy and Mayne (1990). No correction for chamber size effect has been applied to sleeve friction. D r ( % ) : from 18 to 96 1 -i-0.005.Z),. D, chamber -1 c-con-reefed tfi c-measwed '\ 7 0 x D. Equation 6-1 cone 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 of the data out of 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 ' v ) 0 5 instead of normalization to (o'v) 1. It may be observed that even a more appropriate normalization does not reduce the scatter of 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 q ) , which is almost zero for sand. The bulk of O C sands data plots mainly in the N C zone. In spite of 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 of the C C data. Different batches of 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 of 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 of the data at small range o f values of friction ratio. 6.2.4.2 Effect of changes in ground conditions on the direction of movement on the classification chart Arrows in Figures 2-8 and 2-9 show the tentative trends of the effect of D r ' O C R and ageing on the position of soil on classification chart suggested by Robertson (1986 and 1990). For example in Figure 2-8, an increase in D r increases q t but decreases Rf and an increase in 206 O C R , increases q t and Rf. It is not known how these trends were obtained. There is no doubt that increases in all these parameters increases q t . What is not clear is the effect of changes of sand properties on Rf or F. The objective of this section is to find out i f the observed changes in Rf are diagnostic of the changes in 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 of position on the classification chart due to a change of only D r , while all the other soil conditions are kept constant. Each pair of data represents 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 in the normalized chart.. The normalized chart has larger zones and hence a lower sensitivity to changes in soil condition. Figure 6-14 shows the effect of an increase in D r on Rf. The data suggests a very weak correlation with a slight trend of increase in Rf with increased D r . However, the data are too 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 in 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 of O C R alone by keeping Oh constant. It may be concluded that the effect of O C R in the field is mainly through its associated increased lateral stress. The minimal effect of O C R is not only for Rf. Houlsby and Hitchmann (1988) also observed the same trend between O C R and q c in C C test. They noted that the main factor affecting q c was Oh and that O C R alone had minimal effect on q t . The effect of 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 of the cone tip and to a large extent has lost its ageing effect. Therefore, ageing is expected to increase q c more 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 of this section, it may be concluded that the scatter of data is too great to draw any reliable conclusion from the direction of movements of ground improvement vectors on classification charts. The change of Rf is not diagnostic of changes in soil conditions. 6.2.4.3 Effect of changes of D r and lateral stress on I c value Increases in D r , ah or O C R increase Q but their effect on F is somewhat random. A n increase in F alone increases I c while an increase in Q alone decreases I c . Figure 6-17 shows the effect o f ah on I c for different ranges o f D r obtained from C C tests on O C sand. Note that a v is constant for all the data (a'v=T 10 kPa). The data suggests that an increase in either D r or ah or any combination decreases I c. This confirms the trend of changes of I c after vibro-replacement 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 of only soil type but also soil conditions. • Increase in density and stress level always increases q t and fs but the change in Rf does not seem to have a clear trend. • Calibration chamber tests showed very weak correlations between Rf and soil conditions such as D r , a h and O C R . Rf is not diagnostic o f soil conditions and changes in Rf may not be related to changes of soil condition. • The trends suggested on Robertson and Campanella (1986) and Robertson (1990) classification charts between Rf and soil conditions, i.e. D r , a n , O C R or ageing, could not be confirmed based on calibration chamber test results. 208 6.3 A C H I E V A B L E P E N E T R A T I O N RESISTANCE A F T E R V I B R O - R E P L A C E M E N T 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 of 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 of 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 Ltd, are used here. The post-compaction data are for triangular patterns of compaction points with spacings of 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 ci versus pre-q ci where q c i is the tip resistance normalized to vertical effective stress as defined below: = I • V-S Equation 6-2 where, q c is the cone tip resistance, a ' v is the vertical effective stress and P a is the atmospheric pressure in the same units as a ' v . The majority of the data are in sandy layers with a few data points in sandy silt or silt. The reason for this gap in the database is that most silty sand or sandy silt layers encountered at the location of tested holes were thin interbedded layers and thus were excluded from this database. It may be observed from Figure 6-18, that the majority of 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. He 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 of the area of stone column cross section to 209 the tributary area of the each stone column. Those projects were a mix of 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 kW) electrical motor. Correlations suggested by Baez for pre-Rf<l and equivalent spacing of 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 of stone columns and grid pattern. For example a replacement ratio of 6.4% in a triangular pattern is equivalent to a spacing of 2.75 ( if stone column diameter is 0.75m) or to a spacing o f 3.7m (if the diameter of 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 of 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 c values. Pre-I c should include the information of the soil type/fines content. Figure 6-21 shows the results o f pre- and post-compaction normalized tip resistance versus pre-I c. It may be observed that the fitted lines 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 V23 vibrators using Geopac operators with columns installed at spacings of either 2.75 m or 3 m. Again, it may be observed that the number of data points in the I c range from 2 to 2.5 (silty sand to sandy silt) is scarce. The results suggest that the compaction effect is not significant for I c values greater than about 2.3. Using Robertson and Fear's (1995) correlation, I c =2.3 is equivalent to about 20% fines content, which is also in accord with Mitchell 's (1981) suggestion for the upper limit of compactability. Data suggests an average of 50% increase in the normalized tip resistance is possiblefor a grid spacing of 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. Also , more local data in silty sand/sandy silt is required to f i l l the gap in the database 6.4 S U M M A R Y AND CONCLUSIONS In this chapter, a database of C P T results before and after vibro-replacement in the Lower Mainland, B C and the trends of changes of tip resistance, q t , sleeve friction, fs, friction 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 t but the changes in Rf do not suggest a definitive trend. • The changes in q t and Rf after ground improvement change the position of the soil on 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 of soil type but also a function of 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 CPT. This has implications in the assessment of 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 r , stress level or ageing) and changes in Rf. A correlation of 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 of 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 c value. 212 10,000 years ago 5,000 years ago Envelope of majority of the 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, BC (not to scale) 213 Figure 6-3 Typical SCPT profiles before and after Vibro-Replacement (after Howie et al. 2000) 214 Figure 6-4 CPT 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 CPT 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-Ic and post-Ic values 20 C° 15 O LL c o CL E o o I to r£ 5 F C ( % ) = 1.75-/c At J» 4, <t 2t • * 0 5 10 15 Pre-compaction FC (%) 20 Figure 6-8 Comparison of pre- and post apparent fines content interpreted from CPT 217 Normally Consolidated Over Consolidated 1000 1000 100 (bars) 1000 100 * ^ ^ ^ ^ * A 1000 100 0.1 10 Fr(%) Figure 6-9 Calibration chamber data for Ticino sand plotted on CPT 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 Fr(%) 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 1 1—I I I 1111 I I I I I I [ 11 0.1 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 100 o 10 V . c - * \ / 9 — v V « % \ / Jefferies and Davies (1993) N C zone (approximate) ' <^ <^ ^f J 1 1 1 1 1—i—i—rn *—i 1 1 1 1—i—i—v 0.1 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 6.0 7.0 8.0 Friction Ratio (%), Rf 0.1 1.0 10.0 Normalized Friction Ratio, F r Figure 6-13 Effect of changes in only D r on CPT classification chart, data taken from calibration chamber testing on Ticino sand. 222 60 80 Relative Density (%) 100 120 Figure 6-14 Effect of D r on R f , Ticino sand, data taken from calibration chamber testing on Ticino sand. • • • „ \ • * • ^ -— T -• T • * • • — • • • 1 «» ____ • • ^^_>rrrrrzL. « #.? • • • • • • • « • • ** • • • • . • 0.8 0.6 0.4 0.2 50 100 1 50 200 Horizontal Stress (kPa) 250 gure 6-15 Effect of the horizontal stress on Rf, data taken form calibration chamber testing on Ticino sand. 223 0.9 8 10 OCR 12 14 16 18 Figure 6-16 Effect of O C R on Rf, data taken from calibration chamber testing on Ticino sand. I c 1.60 1.20 r » — c - 7 0 / "r -" . '•• ° \ - ° Q Dr increj ises o n -7fi A U r / O O O / o A 4 A Dr=90-92°/T 0 100 200 CT'h (kPa) Figure 6-17 Effect of the increase in D r and/or a \ on Ic- from C C testing data on NC Ticino sand 224 300 250 « 200 ro 150 £ 100 50 A • A A • A A • A M -A A A A **SMf A A A A A,-' i A " A A.-• post- 2.75m spacing A post- 3.0 m spacing 50 100 150 200 Pre-q c 1 (bars) 250 300 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 •> 1 1 1 ! i 1 0 50 100 150 200 250 300 Pre-q c 1 (bars) 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 I N T E R P R E T A T I O N O F SCPT D A T A A n overall review of ageing followed by 3 case studies carried out during this research wi l l be presented in this chapter. The effects of ageing on the interpretation of soil properties from the post-densification S C P T results are discussed. 7.1 B A C K G R O U N D 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 in the range of weeks to years. More recent laboratory studies (Howie et al. 2002) have shown that the time effect in the range of 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 of the evidence on ageing of granular soils has come from quality control testing, mainly by penetration testing, of densified ground or placed fills. The first published data in sand was after ground densification by vibroflotation and blast densification in 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. Af 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 of the deposit since deposition and could be in the range of hundreds to thousands of years or more. The latter is the changes over a shorter period after disturbance of the ground in the range of days to years. For a more detailed review of ageing in sands, refer to Baxter (1999). 229 7.1.1 Mechanism of ageing The mechanism of 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 of silica acid gel films on particle surfaces and the precipitation of 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 resulting in a greater macro-interlocking of particles and micro-interlocking of surface roughness, and consequently, greater frictional resistance. It seems likely that both mechanisms wi 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, Af i f i and Woods ( 1 9 7 1 ) showed 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 ° m a x \fp) t Equation 7-1 where t p is the time to the end of primary compression, t is any time greater than tp, G m a x ( t ) is G m a x at time t, G m a x ( t p ) is G m a x at time tp. The reference time, tp, is usually taken as 1 0 0 0 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 of 2 % as shown in Table 7 - 1 . Based on bender element tests, Baxter ( 1 9 9 9 ) found N G 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 ( 1 9 9 8 ) noted that the reported N G values could not explain the 1 0 0 % difference between the G m a x o f undisturbed and disturbed samples presented by Ishihara ( 1 9 9 6 ) . This refers to the results of 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 ( 1 9 9 8 ) showed that for an N G value of 2 % , the undisturbed soil must have been 1 0 4 7 years old and concluded that 2 3 0 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 of ageing on the stiffness of dense Ham River sand in conventional triaxial testing. The stiffness was observed to be a function of relative density, D r , for fresh samples. For aged samples, time was observed to have a great influence on stiffness and D r was not the main factor controlling stress-strain response. Secant stiffness at strains less than 0.5% increased by 100% over three log cycles of time. Shozen (2001) and Lam (2003) studied the effect of ageing periods of up to 10,000 minutes on the stress-strain response of very loose Fraser River sand. A period of ageing resulted in a much stiffer response during the initial portion of the stress-strain curve but the effect of ageing tended to disappear after increments of axial strain o f about 0.05%. The curves coincided beyond the initial stages of loading. Figure 7-3 shows the results for ageing times of up to 1000 minutes after consolidation at a stress ratio of a'i/a r3=2.0 (Howie et al. 2001). The following are observed in the figure: • Ageing increases the stiffness at medium or small range of strain (smaller than approximately 0.1 %) • Ageing does not affect the large strain stiffness and strength. • Shear strain reduces or removes effects of ageing. Resolution of the strain measurement apparatus was not considered reliable for shear strains below about 0.02% and so the effect of 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 of 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 of stiffness versus shear strain for in 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 r factor 231 in Figure 7-5 to obtain the in situ stress-strain curve. It may be observed that C r troughs at medium strain range. 7.1.4 Effect of ageing on cone tip resistance Table 7-2 shows some of 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 of cases and noted a marked difference in the rate of increase in q t (Figure 7-6). They argued that the rate was temperature dependent. There have also been some cases where q t has decreased shortly after blast densification and then increased with time (e.g. Mitchell and Solymar 1984) or never reached the pre-densification value (e.g. Thomann, 1990). The drop of q t was despite a large ground 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 of the ageing exists, which increases the confinement around the plastic zone and increases the tip resistance. Due to partial removal of 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 of the soil in two ways; a gradual increase of soil q t and V s with time after disturbance and a sudden drop of q t and V s after disturbance of aged soil. 7.1.6 Effect of ageing on liquefaction resistance Seed (1979) conducted cyclic triaxial tests on Monterey sand of about 50% relative density and found an increase in liquefaction resistance of 12 and 25% for sands aged for 10 and 100 days, respectively (Figure 7-7). He also compared the resistance to liquefaction of some undisturbed and reconstituted samples which are plotted in the same figure. He 232 concluded that the liquefaction resistance of natural deposits might be as high as 75% greater than that of freshly reconstituted samples in the lab. Ishihara (1985) compared the cyclic shear resistance of undisturbed samples of Niigata sand obtained from large diameter sampler and reconstituted samples. The results showed that the undisturbed samples had consistently greater cyclic shear resistance. Yoshimi et al. (1989) compared the liquefaction resistance of 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 in situ freezing techniques. They found that the liquefaction resistance of in situ samples were almost twice as much as freshly deposited samples. Based on this work, Ishihara (1996) concluded that the cyclic shear resistance of in situ deposits is greatly dependent on ageing and fabric of sand. He recommended high-quality undisturbed samples to evaluate the actual performance o f in situ deposits. Arango and Migues (1996) studied the liquefaction resistance o f sand deposits older than 10,000 years. They compared the liquefaction resistance of 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, Va id and Sivathayalan (2000) found that the undrained behaviour of the undisturbed samples taken from a deposit as old as about 4000 years old obtained by in situ freezing was almost identical to that of 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 s and q t should be higher than for recent fills at a similar density. Monahan et al. (2000) used carbon dating of 233 organics in Fraser River sands to estimate the age of the deposits. The data suggest a linear increase in q c i (see Equation 6-2 for definition) with age in Fraser River sand, as shown in Figure 7-10. The scatter in the data is l ikely due to other factors such as variation of density, grains size, etc. Robertson et al. (1995) found a linear trend between the normalized shear wave velocity, V s i and the logarithm of the age of deposits from some of the C A N L E X project sites (Figure 7-11). V s i defined as follows: v = v Y s i y s ''p. A Equation 7-2 where a ' v and P a are already defined.. 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 • Kidd2 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 of a bridge for liquefaction mitigation. The spacing of 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 of a 234 triangular pattern before densification, a few days and one year after the completion of 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 of 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) in 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 of 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 of generation of negative excess pore pressures coincide with layers of silt or silty sand/sandy silt. In clean sand layers, the tendency for generation of negative pore pressure cannot be detected because of the fast dissipation o f pore pressures. After one year (Post2 in Figure 7-13), a slight increase in q t but decrease in V s was observed. No combination of changes in D r , ah and/or ageing can explain the increase in q t but decrease in V s . This could be attributed to the effect of heterogeneity (see Chapters 4 and 5) and/or site variability. There is little indication of dramatic increase in stiffness due to ageing for 1 year. Comparison o f another pair of post-compaction results in the same site (not shown here) indicated no obvious increase after one year. Site variability and uncertainty of V s measurement in the presence of 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 t sensitive to the location of the hole. Sensitivity of q t to the location of cone hole makes the study of ageing after vibro-replacement very uncertain. Although no strong indication of ageing is observed after compaction, the destructuring (disturbance) effect o f the vibro-replacement below the target depth (tip of 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 in residual lateral stresses caused by vibro-replacement. Therefore, the observed time effect on S C P T results could be the sum of opposite effects of ageing and stress relaxation. 7.2.1.3 Conclusions • The effect of ageing was not observed clearly. • Destructuring effect of compaction was apparent from reduction of the V s below the densification depth. • Site variability makes it difficult to draw a definitive conclusion whether or not ageing occurs. • Stress relaxation may reduce or counterbalance the effect of ageing with time. 7.2.2 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 of 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 of the liquefaction potential. Blasts were used to simulate earthquake shaking. In one of the experiments, which is the focus of this case study, 12 cm diameter vertical drains were installed in the ground in a triangular grid pattern at a spacing of 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 of drains, four explosive charges were detonated in each of four holes located at 90 degree intervals around a circle with a radius of 5 m as shown in Figure 7-14. In each hole, charges were centered at depths of approximately 5, 8, 11 and 14m. A maximum settlement of 10 cm was observed after installation. Shortly after the blast, a large amount of water gushed out o f the drains and resulted in some settlement. A total settlement of 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% of the settlement occurred above 14m depth, the depth of 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 t and V s after the blast, a series of S C P T tests were conducted by U B C before installation and at different times after blast; 1 day, 8 days, 6 weeks and 10 months. At each time, a pair of tests was performed. Figure 7-16 shows all the C P T profiles. Down-hole seismic tests were conducted at 1 or 0.5 metre intervals in 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 of ageing/destructuring The time effect w i l l be investigated in 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 of average q t and V s with time for layers 1 and 2. In layer 1, all the post-q t values are greater than the pre-blast values, which is in accord with the observed settlement and consequent increase in density of this layer. Note that except for one point (at day one), the values obtained from the pair of CPTs at each time are close. The variation of the average q t does not suggest any apparent trend with time. The response of V s on the other hand is different. Except for one data point, all the post-V s values are smaller or about the same as the pre-V s . Ignoring one data point at day one (shown by an arrow in Figure 7-18), V s remained almost constant or increased very slightly with time. It should be noted that site variability and averaging the data could obscure the results. Also the effect of the vertical drains on V s measurement has not been considered. Flexible vertical drains should slightly reduce the overall stiffness of the ground. On the other hand the local densification around the drains during installation has the opposite effect. There is an apparent contradiction between the response of q t and V s to blasting. q t indicates that the blasting has improved layer 1, whereas V s indicates that the blasting caused no improvement or even some destructuring effect to the ground. Conventional interpretation of S C P T based on D r and ah cannot resolve this contradiction, since no scenario of the changes 237 in D r and/or o"h can cause an increase in q t and at the same time, no increase or slight decrease in V s . It w i l l be shown that consideration of ageing/destructuring is required to explain the field 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 of each factor w i l l be discussed quantitatively. The other difference observed from the post-blast data is that the results of q t at different times are more scattered, whereas the V s is quite consistent. It is believed that the seismic test samples a greater volume of the ground and so it automatically averages the horizontal variation of the soil due to different magnitude of densification around the vertical drains. On the other hand, it is thought that the tip resistance is more indicative of 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 of 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 t and V s show a definitive drop of about 15%. From the 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 t and V s may be equally sensitive to the destructuring. The drop o f the V s is about AV s=22m/sec which is equivalent to AV s i=20 m/s. This is close to the 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 of 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 of 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 in Table 7-1. The back calculated NG~0.05 estimates a 7% increase in V s , 10 months after the blast. This is well within the range of site varibility and could easily be missed by seismic testing and/or interpretation of data. 238 7.2.2.4 Implication of ageing/destructuring in estimation of soil properties It was noted that blast-densification caused an increase in q t and almost no change in V s , which cannot be explained by the conventional site characterization procedures that only consider D r and a ' h . The data from this case study wi l l be used to demonstrate that consideration of 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 r and destructuring. In layer 2 with negligible densification, the only remaining 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 r as the only unknown. D r may be estimated from the actual settlement and its equivalent q t can be obtained from correlation to q t . It w i l l be shown that the obtained q t is consistent with the field observation. This represents an ideal example of site characterization after densification in which all the main factors affecting the penetration resistance are considered. It is assumed that the geological ageing of layers 1 and 2 are similar and that the 15% drop in q t and V s in layer 2 is due to destructuring o f the geological ageing. Assuming that the blast removed the geological ageing, the equivalent q t o f the freshly deposited layer 2 would be: qto-fresh = 50 .(0.85)=42 bars (of the fresh deposit at the same D r ) The relative density of layer 2 before the blast is estimated from Baldi et al. (1986) as: Pre-D r=29% Note that i f the effect o f geological ageing were not considered, the relative density would be estimated as D r=36%, which would introduce about 25% error. Note that Massey Tunnel site is only 200 years old. The error of ignoring the geological ageing would be greater i f the deposit was older. Assuming e m a x and e m j n o f about 1.1 and 0.7 respectively for Fraser River sand (Wride et al. 2000), the void ratio is estimated e=0.98 from the Pre-D r=29%. This agrees very well to the average e=0.97 obtained from frozen samples (Wride et al. 2000). 239 From the observed settlement, the vertical strain, s v e r = 0.034, so the D r after densification is estimated as post-D r=46% which is equivalent to a post-q t o f 63 bars. The average post-q t from the field measurement is 65, which agrees with the estimated value. Based on Equation 4-5, a change of D r from 29% to 46%, increases the G m a x by 30%. This is equivalent to an increase of 15% in V s . This 15% increase of V s due to increase o f density is counteracted by the 15% decrease in V s due to destructuring effect. The net change of V s then wi l l be 0%. This agrees well with the field observation in which the shear wave 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 of void ratios, etc (Lunne et al. 1997). However, for the lack of a better choice these correlations have been used. 7.2.2.5 Effect o f blasting on G m a x /qt Figure 7-19 shows the changes in G m a x /q t after blast densification. In layer 2 with minimal change by densification, the main factor is destructuring. A s the result of 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 t . This is in agreement with the observations in the lab, where the ageing effect was only observed in small to medium strain range. G m a x is only a function of small strain soil properties but q t is a function of both small strain and large strain (strength) o f 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 t . More data is needed to confirm this in the field. In layer 1, in which both densification and destructuring have occurred, G m a x /q t has a larger drop. This is because an increase in D r increases q t more than G m a x . 7.2.2.6 Conclusions The main points from this case study: • Ageing affect after densification was not apparent in this site. • The removal of geological ageing was considerable. • The rate of ageing, No, 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 of the relative density. • The apparent contradiction of increase of q t and no change in V s could be explained when geological ageing/destructuring was considered. • B y deducting the geological ageing from the q t , the relative density and void ratio 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 in 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 of using in situ tests for study of the ageing in the field is the effect of in situ test itself on ageing. This stems from the fact that ageing is sensitive to disturbance. Most of the field data on ageing have come from penetration test results, mainly C P T and SPT. Penetration tests are destructive tests and cause large strains in the soil. SPT impose some vibration to the ground, which furthers the disturbance effect. One may wonder how much of 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 of 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 of such a test is that it does not suffer from any of the above mentioned problems. Site variability is completely eliminated. Moreover, no disturbance is imposed to the ground after the start of 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 of 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; Howie et al. 1999; Wride et al. 2000). Two 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 in 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 of 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 s by 8% in only one hour (Figure 7-23). The decrease in the shear wave travel time with wait time can be explained by consideration of the disturbance and ageing effects in the soil affected by the cone penetration. A zone close to the cone wi l l experience disturbance due to the large strains during cone penetration (Figure 7-24). The extent of the disturbed zone wi l l depend on the strength and stiffness of the soil before penetration, and the magnitude of the strains wi l l attenuate with distance from the cone. A s shown earlier, the small strain stiffness of soil may be substantially reduced by disturbance and wi l l increase with logarithmic time after disturbance. A s a result, the small strain stiffness of 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 of 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 of change in arrival time of the shear waves with wait time depends on the ageing rate, No, the radius o f the disturbed zone and the initial contrast of 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 of one hour. This is in accordance with the ageing studies in the lab on Fraser River Sand by Shozen (2000) and Lam (2002) in which considerable change in 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 of 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 of the disturbed zone is approximately the same and the travel lengths and travel time in 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 s would be almost identical to V s o f undisturbed soil. 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 of penetration of 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 of minutes reduced the travel time of 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 of the soil in the disturbed zone around the cone. The advantage of 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 of this finding on the seismic cone testing is that the time between the stoppage of the penetration and execution of the seismic test should be kept consistent at different depths. This would offset any time effect occurring during stoppage time. 243 7.3 A G E I N G E F F E C T S AND G R O U N D 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 t and V s could help identify these cases by giving a relatively high G m a x /q t compared to the local expectation. It should be noted that a high Gm a x /q t could be due to 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 t could be helpful to recognise these conditions. This needs more research. Engineering ageing begins after completion of densification and is expected to increase the q t. That is why quality control tests are usually carried out after a wait period. The rate of 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 t at any time after ground 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 qt. Stress-relaxation could reduce the lateral stresses built up during densification. This could be more significant for vibro-compaction methods than blast-densification. 244 7.4 E F F E C T O F A G E I N G / D E S T R U C T U R I N G O N I N T E R P R E T A T I O N O F POST-DENSIFICATION SCPT F O R SOIL PROPERTIES 7.4.1 Interpretation of relative density and friction angle It may be argued that removal of 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 in a more reliable interpretation of soil properties. On 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 of 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 in Massey tunnel, the geological ageing may change the interpreted D r by 7% (25% error). The same argument also applies to interpreted angle of friction. 7.4.2 Interpretation of soil stiffness Ideally, i f the in 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 of in situ soil is different from that of the reconstituted samples (Figure 7-4). Applying 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 of an aged natural deposit. Densification removes the geological ageing of the ground and reduces the modulus in small to medium range of strain (curve #2). After completion of 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 of the destructuring effect. But note that even i f the post-V s is identical to the pre-V S i 245 the densified ground has a stiffer response to penetration tests, footing settlement or cyclic loading. This is because the rate of 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 of 0 . 0 0 2 and identical pre- and pos t -G M A X , should settle 4 0 % less in a young dense post-densification condition as compared to loose aged pre-densification condition. The pre-G and post-G are equivalent to G F (field stiffness of aged soil) and G L (stiffness of 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 of the art, it is generally accepted that ageing increases both the cyclic resistance ratio,CRR, and penetration resistance. However, the effect of ageing on the relationship between C R R and q t cannot be defined quantitatively due to lack of data. The C R R curve (CRR-q t ) obtained from liquefied/non-liquefied includes deposits with different ages. 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 SPT blow counts. In other words, increased SPT blow counts due to ageing do not reflect the magnitude of increase in C R R . Therefore it is likely that SPT in very old sand underestimates its C R R . Conversely, this implies that destructuring of 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 t as well . The results of two studies based on penetration resistance and undisturbed in 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 SPT 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 of dynamic cone penetration test with frictional measurement. Their 2 4 6 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 of this matter may not be practically fruitful as the liquefaction/no liquefaction database used for assessing cyclic resistance ratio of soil, includes a wide spectrum of soils with different ages. This subject needs further understanding of cyclic soil behaviour and ageing. Unti l 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 of cyclic resistance. 7.5 CONCLUSIONS The main conclusions from of 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 of natural deposits due to the effect of 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 of the following main factors: o Removal of geological ageing o Increase in D r o Increase in a'h o Time effect after completion of treatment (ageing and stress relaxation) • After completion of 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. No general trend of increased tip resistance or shear wave velocity was observed. It is thought that the site variability obscures the trends. However, the destructuring effect (removal of the 247 geological ageing) in the form of reduction of 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 of sand during seismic cone testing. It was found that at any fixed depth, the travel time of shear waves, from the source at the surface to the vibration sensor in the seismic cone, decreased with increasing wait time after stoppage of the cone penetration. This is believed to be due to the ageing of the disturbed zone around the cone. The significance of 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 of art, it is not possible to quantitatively assess the effect of ageing on q t-modulus or q t - C R R correlations. Based on 2 case studies by others, in which pre- and post-compaction correlations between C R R and penetration resistance were similar, destructuring or ageing does not seem to affect the correlation between C R R and penetration resistance. 248 Table 7-1 Values of N G for various soils (After Baxter 1999- based on studies by Afifi and Woods 1971 and Anderson and Stokoe 1978) Soil N G (%) Notes Ticino sand 1.2 Predominantly silica Hokksund sand 1.1 Predominantly silica Messina sand and gravel 2.2-3.5 Predominantly silica Messina sandy gravel 2.2-3.5 Predominantly silica Glauconite sand 3.9 50% Quartz & 50% Glauconite Quiou sand 5.3 Carbonatic Kenya sand 12 Carbonatic Ottawa Sand 1-5 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 qc 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) No increase in qc following blasting in saturated loose sands. Presence of surficial clay layer may have hindered drainage. Schmertmann et al. (1986) Increases in qc 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 qc were related to energy input. No sensitivity was observed. Jefferies etal. (1988) No increases in qc for hydraulic fill in sea water at 0°C. Increases in qc were Rogers et al. (1990) observed after blast densification in the same sand at the same temperature. No Jefferies and Rogers (1993) sensitivity was observed. Thomann(1990) Blast densification in medium dense sand. qc decreased and never reached pre-blast values. Massarch and Heppel (1991) After vibrocompaction, some increases in qc 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 qc at the site. Charlie et al. (1992) Following blast densification in dense sand, qc decreased and took 5.5 years to reach pre-blast values. Charlie et al. (1992) Suggested that increases in qc can be related to temperature. However, a Jefferies et al. (1993) discussion showed that temperature did not have a big influence on the observed increases in qc. AGRA- 1995- (Gohl et al.) Following blast densification, scattered increases in qc were observed throughout the site. No mention of sensitivity. AGRA (1995) Following blast densification, some sensitivity was observed. Significant Ground Engineering (1995) increase in qc observed after 12 days. Temperature was ~0° C. Joshi etal. (1995) Increases in penetration resistance in the laboratory for both dry and saturated conditions. Micrograph evidence of precipitation. Nget al. (1996) Following vibrocompaction, increases in qc observed with no sensitivity. 2 5 0 Ottawa Sand Air-Dry a' = 30 psi e = 0.49 I I I I M i l l I I I I I l l l l I I I I 11 11 0.0 c -\ 0.1 '2 en 0.2 .a > 0.3 1 1 10 100 1000 10000 Time (minutes) Figure 7-1 Increase in shear modulus with time (after Aflfi and Woods 1971) 140i 120r 100 a. 80 $ 60 a £ 40 IP 20f-T—rirnn|' fifU'lHH t"r tTTTfTp"T'T t UTH| I M I'll hip Co) Undisturbed samples a*0.686 Fujikawa sand Disturbed samples ft .U.LXUilii « • • ' • ""I i i i i h h ! , , J » '„) "" l 1 UULLLUlLj 10"* 10-* 10"* NT* 10"1 Amplitude of shear strain, 7, r Figure 7-2 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) 2 5 1 160 co 140 120 w o 100 Q 80 R=o ' 1 /o ' 3 =2 -- / / f J f 1 -A.L J / l J I 1 10 10( i I 1,000 I I 1 1 -0.1 0 0.1 0.2 0.3 Axial Strain (%) 0.4 0.5 Figure 7-3 Effect of ageing on stress-strain curve, Fraser River sand (after Howie et al. 2001) 1.0 CD <3 o to o p 03 35 0.5 10" 10' -s 10" 10" 10" Amplitude of shear strain, 7a -1 - T-—' ' Fuj isawa sand 1 ^ \ e ° 0 6 9 3 | D i s t u r b e d V x \ V 1 samples V n \ \ 0.732 J -Undis tu rbed f 6=0720 , s amples [ a M 6 I 1 1,.., 1 1 10" Figure 7-4 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 r : correction factor 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 of the reconstituted sample in the lab G L : Shear strain dependent shear modulus of the reconstituted sample in the lab 253 •j 1 1 1 — i — I i i I ' 1 1 1 r — i — T — I - T MITCHELL ANO — \ MITCHELL AND SOLYMAR WW \ / SOLYMAR (1984) VBROCOMRMJION V j 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). so * 2 5 zoh ? is 2 i of 0 5 0 1 1 i r • L o b p r o l o r y l e s i 0010 - M o n i i f e y K o 0 S o i O O H f d r p u l i c l a n d f i l l I ' w n U p p t ' S o * F t f M K i d o O o m A H y d r a u l i c w n d M l liom L e a v e r S o n f e i n c n d o D o m D $Qvth 7 e i g f *OJNJ 7 S o n M a t e o s e n d T i m e o N e D * p o i i h o n - y t o r t 10 100 10 1 0 " T i m e o l ' C D « u O » r l i e n - d O » » Figure 7-7 Time effect on liquefaction resistance (after Seed 1979) 2 5 4 Upper Tobacco Rd Sed etal. 1986 0 L _ j — j — i i i — I to 2 to 3 i a 4 ID5 i o s 1a 7 i o 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 %| WP (10135 Sand) "'(r,c=114&R* y ec=o.892±aoo2 (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) 255 110 100 90 cr 0 co 2 80 > < FD95-6i FD96-1 FD93-4 FD93-2 K2V2 FD92-4 FD95-6 'FD94-1 BHFD93 FD94-3 R a = a 7 6 FD94-1 70 60 50 0 2000 4000 6000 8000 10000 A g e 1 4 C years Figure 7-10 Plot of average q c i and 14C age of organic material in topset sand (after Monahan et al. 2000) 50 n 40 Ifi > _c 30-CD CD CO 20 sz o 10 0 ^ MASSEY laboratory ^ * SYNCRUDE unaged,, ^ 10" 1 104 10 s 102 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) 256 900 + 800 + ^ 500 + 400 + 300 + 200 + 0.01 J-pit4 0.1 Kidd# # Massey • Mildred lake •HMDam LLDam# _) 1 1 10 Age (years) 100 1000 10000 350 300 + 250 + > D Dam 20^  +. 100 0.1 Kjdd# #DDam 0 Massey IX Dam# ^ Mildred Lake A HM Dam -+- -+-10 100 Age (yean) 1000 10000 Figure 7-12 Possible effects of age of deposit on C P T penetration resistance and shear wave velocity (after Wride et al. 2000) 2 5 7 FRICTION RATIO Rf(%) 0.0 0.5 1.0 0 CONE TIP RESISTANCE SLEEVE FRICTION PORE PRESSURE INTERPRETED qt(bar) f, (bar) U2(mofH20) PROFILE 100 200 300 0.0 1.0 -10 0 10 20 before post 1 - after treatment post 2- after 1 year a o a V \ \\ •\\ -pre-drilled silty sand to sandy silt sand End of treatment Vs (m/sec) 100 150 200 250 0 o • before -»— postl - after treatment -•— post2-1 year after 5H Q. O) Q 10 15 H Go (bars) Go I qt 500 1000 2 4 6 8 10 12 i i i i (Go/Pa)/(qt/Pa)0-25 150 250 0.1 0.3 0.5 0.7 Figure 7-13 SCPTU profiles before and after Vibro-Replacement, Laing Bridge site, Richmond, B C . 258 U-01 W-Staka \ N-Stake U-03 U-OS u-oa CPT U-07 U-09, C P T - 0 9 • # U - 1 0 5m radius E-Stake U-02 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 .Q 0 as > < 120 110 100 90 80 70 60 50 40 30 20 Before 250 • Layer 1 & Laye r 2 1 10 Time after blast (days) 100 1000 200 { 150 A 1 ~ i _ 100 • Layer 1 A Layer 2 50 Before 1 10 Time after blast (days) 100 1000 Figure 7-18 Variation of the average values of q t and V s with time after blasting, Massey Tunnel Site. 263 12 10 4 | 6 O CD CD 5 cu > < 2 4 0 1000 Time after blast (days) (b)Layer 2 A 1 10 100 . Time after blast (days) 1000 o|i Before Figure 7-19 Variation of average G m a x /qt before and after blasting, Massey Tunnel Site. 264 265 Time (sec) 0.080 0.082 0.084 0.086 0.088 0.090 0.092 -0.06 i • ' ' 1 ' ' ' 1 1 1 1 1— 0.12 J — 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 1 — 1 1 1 0 10 20 30 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 Wait time (min) 60 70 Figure 7-23 Variation of Vs with wait time at depth interval 10.95-11.95m 267 Shear beam Disturbed Zone V S 2 Upper accelerometer Lower accelerometer Undisturbed zone VSI=125 m/s *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 INCREASE 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 CPT D A T A 8.1 INTRODUCTION In Chapter 3 it was shown that lateral impacts of vibroflot cause radial displacements. Accumulation of the radial displacement increases the horizontal stresses in the ground, which become locked in by the introduction of stones. In this chapter, parametric analyses w i l l be used to study the effect of the increase in lateral stress on interpretation of post-compaction soil properties/performance from the C P T results. 8.2 FIELD E V I D E N C E O F INCREASE 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 1 9 9 2 , Salgado et al. 1 9 9 7 , Howie et al. 2 0 0 1 , Massarsch 2 0 0 3 , Pitt et al. 2 0 0 3 ) 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 in 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 ( 1 9 7 7 ) performed pressuremeter tests in boreholes and concluded that coefficients of lateral stress were 3 to 6 times greater after compaction with a vibro-rod. Pitt et al. ( 2 0 0 3 ) used the K o 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 of aggregate piles was 2 to 3 times greater than interpreted K o in natural ground. Massarsch ( 2 0 0 3 ) directly related the increase of 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 of an increase in lateral stress during compaction. 2 7 0 The main objective of this section is to evaluate how increases in lateral stress could affect the interpretation o f the desired soil properties, mainly D r , C R R and modulus. This w i l l be done through a parametric study. 8.3 E F F E C T O F INCREASE 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 PROPERTIES 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 (CPTU) 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 t , and soil properties have been developed and much research has been carried out on the factors influencing such correlations (Lunne et al., 1997). Most of the early works used relative density, D r as an intermediate parameter in the determination of soil properties and there is now a tendency to use D r and penetration resistance interchangeably. This is not necessarily valid as many other factors affect penetration resistance. Saito (1977) found that ignoring the increase in lateral stress in interpretation of post-compaction SPT blow counts led to interpretation of 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 of sand have been based on calibration chamber testing on clean, unaged sands. The dominant influence of initial horizontal stress on q t has been emphasized by a number of researchers ( Baldi et al. 1985, Jamiolkowski et al. 1985, Houlsby and Hitchman 1988). A correlation between q t , and D r in moderately compressible, normally consolidated young sands such as those of the Fraser river delta, is the relationship for unaged Ticino sand by Baldi et al. (1986): qt = 248 • a],0'55 • exp[2.38Z). ] Equation 8-1 271 where q t is the tip resistance in kPa and a'h is the horizontal effective stress in kPa. In N C ground conditions, a'h can be estimated. This makes it possible to estimate D r from correlation to q t . After ground densification, the magnitude of the increase in lateral stress is not known. This introduces uncertainty to the estimation of D r from the correlation to q t. Based on Equation 8-1, there are many combinations of D r and ah that could result in the same q t . This is illustrated in Figure 8-2. For example a post-densification tip resistance of q t=l 5 M P a and a vertical effective stress of a' v=100 kPa, could be interpreted as ( D r = 85% and K o = 0.5) or ( D r = 55% and K o = 1.5). It is not possible to obtain 2 unknowns (a'h and D r ) from one equation. The estimated D r based on KO_NC which neglects the increased lateral stress, overestimates the D r . Therefore, it is not possible to do the quality control o f improved ground based on interpretation of D r from C P T . There have been some attempts to use a combination of two in situ tests to solve for the two unknowns, D r and a'h (Howie et al. 2000). One of such attempts is the combination of q t and V s measurement. Both are different functions of D r and ah. Therefore it should be possible to solve a system of two equations for two unknowns. Bellotti et al. (1996) suggested the following correlation for V s : where C s is a function of grain characteristics, F(e) is a function o f void ratio, a ' a is the effective stress in the direction of particle motion, a'b is the effective stress in the direction of propagation, and n a and nb are empirical coefficients. For Ticino sand, Bellotti et al. (1996) found C s to be around 85 and na=nb=0.122. For the S C P T U case where waves propagate in an approximately vertical direction, a ' a is equivalent to a'h and a'b to a ' v . If the expression is written in terms of K o , the following equation is obtained: Vs=Cs\F{e)r\cr:Y{ab) nb Equation 8-2 0.122 Equation 8-3 where V s is in m/s and a ' v is in kPa. 272 More recently, Eslaamizaad and Robertson (1996) combined Equation 8-1, 8-2 and 8-3, and solved Ko based on q c and G m a x- They obtained the following expression: If it is assumed that for any particular depth a ' v remains constant during densification, the change in Ko or lateral stress induced by ground improvement may be estimated from this expression. A n increase in K Q should result in an increase in the parameter, [(GmaX/pa)/(qc/pa) ]• In Figure 8-3, it can be seen that, in general, it has increased within the sands as a result of vibro-replacement. The estimated values of Ko before and after ground improvement indicate a significant increase in lateral stress in the range of 200%. If G m a x calculated from equation is substituted in 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 s . There is still a good indication that an increase in lateral stress has occurred. The issue of ageing in 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 r and ah should be considered for interpretation of post-compaction tip resistance. They showed how variation of lateral stress would affect the estimated settlement of a footing. To demonstrate this concept, they used the Schmertmann (1978) method to compare the settlement for three different combinations of lateral stress and relative density which resulted in the same q t (Figure 8-4). It may be observed that the combination with higher lateral stress and lower density resulted in higher stiffness and lower settlement. The combinations of D r and ah were calculated using the 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): ^ = 3 . « o< -« ) ( p , / C T ; r " - [ ( G , „ » / /> j 4 / p „ r ; ! :.165 Equation 8-4 Gmax=p-Vs2 Equation 8-5 273 K 0 0 C = K 0 N C • (OCR 0 5 ) Equation 8-6 where K o o c and K o N C are the coefficients of 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 Young's modulus, E , from q t at an axial strain level of ea=0.1%. The obtained E was used in Schmertman's method to calculate the settlement of footing. Although this approach shows the trend of the effect of lateral stress, it has some ambiguity which stems from the fact that the effect of lateral stress was not incorporated directly but was considered by converting to O C R in 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 of sand with increased lateral stress due to over-consolidation. Calibration chamber data shows that the Young's Modulus is a function of D r , O C R and confining stress (Lunne et al 1997) whereas q t is a function of D r and stress level and not O C R (Baldi et al. 1986). Therefore, in case o f a direct increase in lateral stress, E/q t correlations could be 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 a=0.1% and one value of q t. It is of interest to see i f the trend holds over a larger range of strains and values of q t. The key to a good estimation of deformation including the settlement of the footing is a good knowledge o f G m a x and the modulus reduction of soil (Poulos, 2000). A parametric analysis is performed here to evaluate the effect of K o on the interpretation of soil modulus from q t. It w i l l be shown that the post-densification interpretation o f q t neglecting the increase in K Q , underestimates the modulus and thus overestimates the settlements. Therefore, neglecting increase of the lateral stress may be considered conservative. In this parametric analysis, different combinations of D r and ah that result in the same q t are found (Figure 8-2). Note that an increase in K Q requires a decrease in D r to keep the resulting q t constant. For each combination, G m a x and modulus reduction curves are calculated and compared. The q t is varied from 10 M P a to 20 M P a . The following assumptions are used in this parametric analysis: • Vertical effective stress a' v=100 kPa, equivalent to 10m depth in a saturated deposit. 274 • D r and horizontal stress level are the main factors affecting q t and G . The effects of other parameters are neglected. • The variation of D r and K o are such that they result in a constant q t. • Baldi et al. (1986) correlation is used for q t (Equation 8-1). • Seed and Idriss (1970) is used to for G m a x (Equation 4-5). • Ishibashi and Zhang (1993) used for the modulus reduction curve. Ishibashi and Zhang (1993) suggested the following expressions to account for the effect of confining stress, a ' m and plasticity index, PI. n(r,Pl)-n Equation 8-7 where K(r, PI) =0.5 1 + tanh Ln 0.000102 + n(Pl) . 0.492 Equation 8-8 m (y, PI)-m0 =0.272 1-tanh Ln 0.000556 Y ,0.4 •exp^O.OHSF/ 1 3 ) Equation 8-9 where n(PI) = 0 3.37 x 10-6 7.0 x 10-7 2.7 x 10-5 for PI=0 f o r 0 < P I < 15 for 15 < PI < 70 for PI > 70 Figure 8-5 shows the sensitivity of calculated G m a x , to the variation o f Ko . It may be observed that as Ko increases (or D r decreases), G m a x increases. The rate of increase is higher for larger tip resistance. Figure 8-6 shows the sensitivity of the shape of the modulus reduction to the variation of K o . It may be observed that an increase in K o decreases the rate of modulus 275 reduction with shear strain. The effect of K o on shear strain dependent shear modulus is the combined effect on G m a x and modulus reduction as shown in Figure 8-7. Each curve represents one combination of ( D r , Ko) . The combinations with higher Ko (and lower D r ) result in a larger G at any shear strain level. It should be noted that the correlation of G m a x to D r and stress level is approximate. For example, based on experience in the Lower Mainland, B C , V s is about 180 to 200 m/sec for q t in the range of 100-200 bars and depth of 10-20m. Also shown in Figure 8-7 are the V s values equivalent to the calculated G m a x for comparison with the real measurements in the field. The calculated values of V s are higher than what is normally measured locally. This is of no 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 of qnet/quit where qnet is the net bearing pressure o f the footing and q u i t is the ultimate bearing pressure of the footing. For range of qnet/quit = 0.1 to 0.33, which is equivalent to a safety factor of 10 to 3 respectively, the average shear strains are in the range o f about 0.002 to 0.02. The effect of K o on G at y=0.002 is calculated as an example and shown in Figure 8-8. This figure shows the ratio of shear modulus at any Ko normalized to the shear modulus at Ko=0.45. This shows that the equivalent secant shear modulus of the soil increases with K o . For example for q t=l 5 M P a , the combination of Ko=2 and D r=50% is 60% stiffer than the N C soil condition (1^=0.45 and D r=84%). The results o f the parametric analyses suggest that the D r - K o combinations with higher Ko (or lower D r ) give higher stiffness at any shear strain level. Therefore, i f the increase in lateral stress is neglected and a Ko_NC condition is assumed, this results in estimation of 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 s is also a function of D r , vertical stress and horizontal stress. Therefore, the changes in D r and a'h are already included in the measured V s . Now the question becomes how could the increase in lateral stress affect our interpretation of G from the measured V s ? This can have two effects, one on the G m a x through the estimation of density, p, which is a function of D r and secondly through the modulus reduction. G m a x can be obtained from Equation 5-4. 276 Figure 8-9 shows the effect of K Q on the interpreted G m a x through the effect on the soil density. A s the KQ increases, D R and p decrease which also decreases G m a x . However, its effect is negligible (less than 3% for the case analyzed here). On the other hand, considering the increase in K Q would result in a slower rate of 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 R results in slightly lower G at smaller range o f strains and larger G in medium to large strains (which is the range of average strain level under footings). It is concluded that in the case of calculating G from measured V s , neglecting the 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 of granular soils, friction angle is a function of 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 r and consequently in a lower interpreted peak friction angle (see Equation 4-1). Figure 8-11 shows the general trend o f the effect of K o on the interpreted peak triaxial friction angle. A s an example, at vertical stress of 100 kPa and post-compaction q t o f 150, by increasing Kofrom 0.5 to 2, the friction angle decreases from 45 to 37 degrees (20% decrease). 8.3.4 Effect of increase in horizontal stress on interpreted cyclic resistance from CPT results The effect of increase in horizontal stress on evaluation of liquefaction potential by q t is 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 of K Q on cyclic resistance ratio, C R R and q t separately. A n increase in K o 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 t and C R R . They developed a theoretical correlation between q t and C R R and compared it to the empirical correlation suggested by Robertson and Campanella (1985) for N C sand (Figure 8-12). They concluded the following: • For q c,<12 M P a For K o < 1.5 KO.NC: The C R R - q c i is almost independent of K Q 277 For K o > 1.5 KO,NC: Neglecting the effects of K 0 gives slightly conservative C R R (obtained C R R would be smaller than the actual C R R ) • Forq c i>12 M P a The nearly vertical portion of C R R - q c i curve shifts to right. This shift is more than 5% for KO>1.2KO,NC- Neglecting the effects o f K o on C R R - q c i correlation could lead to unconservative estimates of C R R (the obtained C R R would be greater than the actual C R R ) . In the above, q c i is the tip resistance normalized with respect to effective over-burden pressure. 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 of sands with different in situ conditions. The N C curve shown in Figure 8-12 is obtained based on correlation between N and q c , which adds to the approximation. The indication of liquefaction in 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 in cyclic triaxial tests. In addition, analytical methods for tip resistance are still in the development stage. It may be concluded that studies of these type cannot be used quantitatively. Even i f this study were quantitatively reliable, it would not be useful in practice due to difficulties in finding in situ K 0 in granular soils. However, this study provides a framework to show that the 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 of 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, SPT blow counts or C P T , is the basis of 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 of D r which in turn should cause an underestimation of settlement. In other words, ignoring the increase in lateral stress results in predicting too small settlements. For example a post-compaction q t o f 15 M P a at a'v=100, could be achieved by two different post-compaction conditions, (Ko =0.45, D r=85%) or (Ko =2, D r =50%) as shown in Figure 8-2. Assuming a factor of safety of one against liquefaction, the Ishihara and Yoshimine (1992) method predicts ev=0.75% and e v=l .5% for the case of Ko=0.45 and K o =2 respectively. This means that i f increase in lateral stress is ignored, the settlement would be underestimated by 50%>. Note that the effect of lateral stress on estimation of settlement decreases significantly with increase in the factor of safety against liquefaction. The above example is a simplistic demonstration of the effect of lateral stress on prediction of settlement. In fact, an increase in lateral stress increases the stiffness o f the soil and changes the variation of stiffness with shear strain. This l ikely decreases the induced strains during shaking and offsets to some extent the unconservative estimation o f volumetric strains. For systematic analysis of the effect of lateral stress on the earthquake settlement the following should be known: • The effect of lateral stress on shear-volume coupling • The effect o f lateral stress on penetration resistance • The effect of lateral stress on relation between shear modulus and shear strain • The effect of lateral stress on earthquake demand (CSR) The main unknown at this point is the first item, the effect of 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 of increase in horizontal stress on interpretation of 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 of horizontal stress on site characterization should be considerd. However, at the present state of practice and even state of 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 of horizontal stress quantitatively. More research is needed to approach a quantitative solution to this problem. 280 3 a • Stone Column O RAP Element 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. All tests oriented to measure radial stress (after Pitt et al. 2003). Figure 8-2 100 0.5 1 1.5 2 Coefficient of horizontal stress at rest, K0 i 2.5 Non-uniqueness of interpretation of cone tip resistance- different combinations of D r and ah results in the same q t 281 V s (m/sec) G 0 (bars) G 0 / q t (G0/pa )/(qt/pa)0-25 K 0 100 200 0 500 1000 2 4 6 8 10 150 250 0.1 0.3 0.5 0 i — i 1 1 1 -I ' — ^ — I -i ' ' 1 -t—' 1 u~ 282 I it 32 2 » 24 20 tz — 1 — 1 — -L . K , * 0 . 4 S ( O C « « f -DR « 6 0 % -r - K « * O J 5 5 {OCR« « ) " \ DR * 7 5 * — >— K « a l 4 2 ( O C * « 10) -O B * 55% t 1 1, I 1 1 I , fl 1 7 3 4 8 • 7 Footing breadth (m) Figure 8-4 Settlement versus foundation sizes for different K O - D R combinations 150 125 \ TO 0_ 100 50 i i 0 0.5 1 1.5 2 2.5 Coefficient of horizontal stress at rest, K 0 (-) (Adapted from Jamiolkowski and Pasqualini 1992) Figure 8-5 Effect of variation of Ko on G m a x for constant q t. Variation of K Q and D R are such that the resulting q t remains constant 283 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 ~VS=220 m/s K,, increases, Dr decreases q t = 10 MPa -Ko=0.45, Df=67% -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 Shear strain, y (-) 1.E-02 1.E-01 150 -Vs=240 m/s IC, increases, D, decreases 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 Shear strain, y (-) 1.E-02 1.E-01 ~VS=250 m/s ~K,, Increases, Dr decreases : 20 MPa Ko=0.45, Dr=96% Ko=0.80, Dn=83% 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 Shear strain, y (-) 1.E-02 1.E-01 Figure 8-7 Effect of increase in Ko on the shear modulus (assume o'v=100 kPa) 285 1.8 1.6 CM o o o II >-1.4 d 1 2 qt =20 MPa A qt=15MPa qt=10 MPa 0.5 1 1.5 2 Coefficient of horizontal stress at rest, K0 (-) 2.5 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 Coefficient of horizontal stress at rest, K 0 (-) 2.5 Figure 8-9 Effect of increase in K<> on the interpretation of G m a x from measured V s (through the effect of estimation of soil density) 286 q, = 15 Mpa V s = 240 m/sec 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 in <D cn CD •o 03 CD Q-45 CD 40 o as co 35 30 a\= 100 kPa <t»cv = 33° A q, =20 MPa qt=15 MPa q,=10 MPa 0.5 1 1.5 2 Coefficient of horizontal stress at rest, K 0 (-) 2.5 Figure 8-11 Effect of increase in K o on the interpretation of peak friction angle from post-densification tip resistance 287 0.8 0.7 0.6 0.5 0.4 Derived curves for typical intrinsic parameters Rrfwence curve fiarKojgc-045 Derived curve for Kg"0.68 Derived curve fbrKQ-0.90 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 R E S E A R C H FOCUS AND O B J E C T I V E S This thesis has provided a better understanding of ground improvement by vibro-replacement and of the major in situ testing methods used to characterize the ground before and after ground treatment. A survey of the technical literature showed that little progress had been made in the profession's fundamental understanding o f ground improvement by deep compaction since the first Geotechnique Symposium in 1976 and a survey of local practice indicated that, from 1990 to 2000, the most popular ground improvement method for granular soils in urban areas in the Lower Mainland, B C was vibro-replacement. Over the same period, cone penetration testing, CPT , was identified as the main method of characterization of the natural ground before treatment and for assessment o f the improved ground. A s a result of these findings, this research focused on vibro-replacement with the following objectives: 1 To understand the physical process of vibro-replacement and its effects on ground conditions; 2 To understand the effects o f changes in ground conditions induced by vibro-replacement on interpretation of the S C P T results. 289 9.2 M E T H O D O L O G Y The following major works were carried out during the course of this research. • Investigation of the physical process of vibro-replacement and its effects on ground conditions. This included the design of vibration sensors, field measurement of vibration of the vibroflot and ground response during the vibro-replacement process followed by numerical modelling of soil-vibroflot interaction; • Investigation of the effect of soil heterogeneity on cone tip resistance using numerical modelling. • Detailed study of the evaluation of the in situ shear wave velocity using seismic cone testing and numerical modelling; • Investigation of the effect o f stone columns on the interpretation of seismic cone testing using numerical modelling; • Development of a database of C P T U 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 of a correlation between the initial soil behaviour type and achievable cone penetration resistance for Fraser River sands. • Investigation of time effects on soil response in 3 case studies of 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 of the mechanism of vibro-replacement produced the following major findings: • The vibroflot generates mainly horizontal but also vertical vibrations in the ground. The frequency of the ground vibration and of the vibroflot is the same. For the case studied here, a resonant frequency of 26 H z was obtained for the natural ground. Attenuation of the vibrations is due to geometrical spreading and to material damping. The observed geometrical spreading is similar in form to theoretical predictions of spherical spreading from a horizontally vibrating source in a homogeneous, isotropic material. Vertical vibrations attenuate at a slower rate than horizontal Vibrations. The direction of the principal horizontal acceleration changes with the distance from the vibroflot. • B y considering a combination of 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 in agreement with the small increase in post-densification cone tip resistance observed in the case studied. The small amount of improvement achieved in the tip resistance was attributed to the initially high cone tip resistance and also to confinement of the monitored layer between two dense sandy layers. More research is required to calibrate this procedure for quantitative prediction of the magnitude of densification. • Vibro-replacement increases the horizontal stresses by accumulation of radial displacement due to horizontal impacts by the vibroflot. • Vibro-replacement induces heterogeneity to the ground. This heterogeneity is due to variation of the vibration amplitude with radial distance from the 291 vibroflot and also to the inclusion of stone columns. The centroid of the compaction grid experiences the least increase in density. The study of the effects of changes induced by vibro-replacement on the measurement and interpretation of in situ tests produced the following important findings: • Based on numerical modelling of 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 of 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 of stone columns on q t at the centroid is minimal for the assumed 3m spacing of stone columns. Ignoring the heterogeneity o f post-vibro-replacement conditions results in some over-estimation o f the soil properties at the centroid and considerable under-estimation of the average properties of the composite soil-stone column mass. The current Q C method based on the cone tip resistance at the centroids of compaction grids is l ikely conservative. More research is needed to quantify the degree of conservatism. • Numerical modelling of shear wave propagation in homogeneous soils captured the characteristics of seismic signals obtained from seismic cone testing in natural ground (before inclusion of stone columns). The results o f numerical modelling confirmed the accuracy of conventional techniques for interpretation of the shear wave velocity from seismic signals. • Numerical modelling of 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 of these waves changes the characteristics of the signals recorded at the centroid of a triangular arrangement of stone columns compared to the case o f homogeneous ground. Irregularity of seismic signals introduces the potential for errors in estimating shear wave arrival times using the conventional cross-over method of interpretation. The shear wave velocity profile with depth obtained from the cross-over method is usually jagged due to shifting of the characteristic points (crossover or peak). Either the cross-correlation method or cross-spectrum method is preferable for interpretation of 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 of the native soil between the stone columns. The magnitude of this over-estimation is a function o f the ratio o f the stiffness of the stone columns to the native soil, and of the size and spacing of stone columns. This magnitude of over-estimation is significant when the interpreted shear wave velocity is used as an indicator o f the degree of improvement obtained by vibro-replacement. More research is needed to quantify the effect of the stone columns. Vibro-replacement increases density and horizontal stresses, and removes the effects of geological ageing. The combined effect o f these changes on C P T response is normally an increase in the cone tip resistance, an increase in sleeve friction, and a change in Rf (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 of the changes in soil conditions. Based on observation of 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 of q t or soil behaviour index I c . This relationship is only applicable to Fraser River sand improved by vibro-replacement with stone columns installed in a triangular arrangement at spacings of 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 of ageing effects, no apparent increase in q t or V s with time was observed during repeated testing after ground treatment by vibro-replacement or explosive compaction. However, a reduction in both q t and V s was observed immediately after ground treatment in soil below the effective zone of densification. This was interpreted to be due to destruction of the effects of 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 of 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 of shear waves, from the source at the surface to the vibration sensor in the seismic cone, decreased with increasing time after stoppage of penetration. This is believed to be due to time dependent increases in the stiffness of the zone around the cone disturbed during penetration. The significance of this finding is that the time effect can be directly observed in the field without any effect of site variability. 294 • Correlations between properties of sand and q t are mainly based on 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 of soil. Using these correlations for interpretation of C P T test results obtained in aged natural deposits results in overestimation of some soil properties such as D r and (p. A s vibro-replacement removes or significantly reduces any effects of geological ageing on soil properties in the treated soil, the available correlations should be applicable to the interpretation of 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 of the correlations to result in over-estimation of post-compaction density and strength. • Ideally, the combination of 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 of improvement in soil properties achieved by ground treatment processes. However, at the current state of knowledge, there is no robust method for measuring in situ horizontal stress or for assessing the effects of 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 of the performance of treated ground in geotechnical engineering designs. 9.4 R E C O M M E N D A T I O N S F O R F U T U R E R E S E A R C H Some of the conclusions from this research were conceptual and qualitative due to the nature of the problem. In order to draw quantitative conclusions, more extensive research wi l l be required. The main objective would be to quantify the actual changes in the soil conditions 295 and the resulting effects on in situ test results and on post-treatment soil response. Further research could include the following main components: 1 Selection of a well characterized site with a uniform loose layer(s). 2 Instrumentation of the soil to monitor vibrations, changes in 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 of the soil using ground freezing before and after treatment. 5 Drained cyclic simple shear testing with large number of cycles to develop shear-volume coupling of the sand. 6 Cycl ic tests on the undisturbed samples to measure the degree of improvement. 7 Numerical modelling of the soil response to the compaction process and the response of the ground to the in situ test(s). 8 Comparison of the results of the numerical modelling to the results of post-compaction in situ testing, This comprehensive program would further advance our understanding o f the complex processes of vibro-replacement and site characterization of improved ground. 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Evaluation of Settlements in Sands Due to Earthquake Shaking. Journal of the Geotechnical Engineering Division, V o l . 113, No. 8, pp. 681-878. Tokimatsu, K . and Seed, H . B . 1987. Evaluation of Settlements in Sands due to Earthquake Shaking, Journal of Geotechnical Engineering, A S C E , 113, 8, pp.861-878. Tokimatsu, K . Yoshimi , Y . and Ar i izumi , K . 1990. Evaluation of liquefaction resitance of sand improved by deep vibratory cojpaction, Soils and Foundations, 30(3), pp. 153-158. Vaid , Y . P. and Chern, J. C. 1985. Cycl ic and monotonic undrained response of saturated sands, Advances in the Art of Testing Soils Under Cycl ic Conditions, A S C E , pp. 120-147. Vaid , Y . P . and Eliadorani, A . 2000. Undrained and drained (?) stress-strain response. Can. Geotech. J. 37, pp.1126-1130. Van Impe, W.F . 1989. Soil improvement techniques and their evolution. A A Balkema, Rotherdam. Van Impe, W.F . and Madhav, M . R . 1995. 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Geotechnique, 41, No . 2, pp. 173-183 Y u , H.S. (2000). Cavity Expansion Methods in 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 of the research on the effects of vibro-replacement on the results of in 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 of the sites were in the Richmond, B C area. The general location of each site is noted in Table A - l . CPTs were carried out by U B C (University of British Columbia) using the U B C cone truck or by well known local in 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 in the range of 0.5 to 1.0m (if applicable) to obtain a match between similar layers and to account for the effects of elevation changes due to volume change and changes in site grade. Occasionally pre- and post-CPT profdes were significantly different. These cases were excluded. • Matching layers were visually selected (based on similar q c signatures). Only thick layers (generally thicker than 1.0m and a few cases of about 0.5 to lm) were selected to prevent the thin layer effect on different response of cone tip and sleeve friction resistance (Lunne et al. 1997). • The pre- and post-CPT values, q t , fs, Rf and U2 values were averaged over each layer 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 t. This was to ensure consistency of equipment and of operational methodology. For all these cases, a V23 vibrator was used. The compaction grids were all triangular with spacing of either 2.75m or 3m. Results This database formed the basis of figures presented in Chapter 6. 314 Site Vibro-Replacement CPT Selected Layers Pre-Densif. Average Values Post-C ensi F. Ave rage Va ues Water No. Location Specialty Vibrator Spacing by Before After Top Bott. q t K, r. B, q t Kr 0 . F, B q Table (all in BC) Type (m) (m) (m) (bars) (%) (-) (%) (-) (bars) (%) (-) (%) H (m) 1 LuLu Island Geopac Electric 3 Conetec 207-CP1&2 215-CP02&03 1.50 3.50 7 0.7 22 0.8 0.08 11 0.9 34 • 1.0 0.02 1.2 1 LuLu Island Geopac Electric 3 Conetec 207-CP1&3 215-CP02&04 5.50 6.00 98 0.4 165 0.4 -0.01 121 0.4 193 0.4 -0.01 1.2 1 LuLu Island Geopac Electric 3 Conetec 207-CP1&4 215-CP02&05 8.50 10.00 198 0.3 211 0.3 0.00 220 0.3 225 0.3 0.00 1.2 2 LuLu Island Geopac Electnc 3 UBC RICPT2 RICPT6 4.35 4.90 19 1.0 35 1.1 -0.02 110 0.4 231 0.4 0.00 1.0 2 LuLu Island Geopac Electnc 3 UBC RICPT2 RICPT6 7.80 8.80 158 0.4 178 0.4 0.00 177 0.4 211 0.4 0.00 1.0 2 LuLu Island Geopac Electric 3 UBC RICPT3 RICPT4 4.00 5.00 13 3.5 25 3.9 -0.04 42 0.9 89 0.9 -0.02 1.0 2 LuLu Island Geopac Electric 3 UBC RICPT3 RICPT4 6.60 7.60 77 0.6 103 0.6 0.00 150 0.6 208 0.6 0.00 1.0 2 LuLu Island Geopac Electric 3 UBC RICPT3 RICPT4 7.80 8.80 153 0.5 178 0.5 0.00 227 0.5 272 0.5 0.00 1.0 2 LuLu Island Geopac Electric 3 UBC RICPT3 RICPT4 9.20 10.80 81 0.6 77 0.6 0.00 166 0.6 166 0.7 0.00 1.0 3 LuLu Island Agra Electric ? UBC PIZA1 PIZA3 1.00 3.00 4 1.7 11 1.9 0.15 7 2.7 16 2.9 0.07 1.0 3 LuLu Island Agra Electric ? UBC PIZA1 PIZA3 6.00 7.50 95 0.3 134 0.3 0.00 195 0.3 237 0.3 0.00 1.0 3 LuLu Island Agra Electric ? Conetec 147CPT1 190CPT5 2.50 3.65 2 6.1 4 9.0 0.25 4 1.9 9 2.2 0.17 1.2 3 LuLu Island Agra Electric ? Conetec 147CPT1 190CPT5 7.50 12.00 113 0.5 110 0.5 0.00 163 0.3 150 0.3 0.00 1.2 3 LuLu Island Agra Electric .7 Conetec 147CPT2 190CPT5 2.00 4.00 2 5.3 3 8.1 0.34 4 1.7 10 1.9 0.10 1.2 3 LuLu Island Agra Electric ? Conetec 147CPT3 190CPT5 7.50 12.00 156 0.5 147 0.5 0.00 163 0.3 150 0.3 0.00 1.2 3 LuLu Island Agra Electric ? Conetec 147CPT3 190CPT3 2.00 4.00 2 5.3 3 8.1 0.35 4 2.1 10 2.4 0.16 1.2 3 LuLu Island Agra Electric ? Conetec 147CPT3 190CPT3 7.50 12.00 156 0.5 147 0.5 0.00 174 0.3 160 0.3 0.00 1.2 4 Roberts Bank Agra Electric ? Conetec 170CP9510 209CP20A 4.50 7.50 69 0.2 94 0.2 0.00 160 0.6 218 0.6 0.00 1.5 4 Roberts Bank Agra Electric ? Conetec 170CP9510 209CP20A 12.75 14.75 120 0.3 79 0.3 0.00 150 0.9 102 0.9 -0.01 1.5 4 Roberts Bank Agra Electric ? Conetec 170CP9510 209CP20A 17.50 19.00 17 1.4 7 1.9 -0.08 21 1.3 9 1.6 0.02 1.5 4 Roberts Bank Agra Electric ? Conetec 170CP9510 209CP20A 19.50 20.50 35 1.5 15 1.8 -0.07 27 1.5 11 1.8 -0.08 1.5 4 Roberts Bank Agra Electric ? Conetec 170CP955 CPT7-7 11.00 13.50 92 0.3 63 0.3 0.00 96 0.4 72 0.4 0.00 3.0 4 Roberts Bank Agra Electric ? Conetec 170CP955 CPT7-7 7.00 9.00 7 1.1 5 2.6 -0.21 22 0.8 23 0.9 0.00 3.0 4 Roberts Bank Agra Electric ? Conetec 170CP956 CPT7-4 4.75 6.25 5 1.6 5 2.5 -0.08 33 0.8 40 0.8 -0.05 3.0 4 Roberts Bank Agra Electric ? Conetec 170CP956 CPT7-4 11.50 14.50 99 0.3 67 0.3 0.00 116 0.3 77 0.3 0.00 3.0 4 Roberts Bank Agra Electric ? Conetec 170CP958 193CPT18 1.70 2.85 21 0.2 50 0.2 0.00 84 0.4 265 0.4 0.00 3.0 4 Roberts Bank Agra Electric ? Conetec 170CP958 193CPT18 2.90 3.50 81 0.3 161 0.3 0.00 114 0.3 277 0.3 0.00 3.0 4 Roberts Bank Agra Electric ? Conetec 170CP958 193CPT18 5.00 10.00 29 1.0 30 1.1 -0.03 37 1.0 44 1.2 -0.05 3.0 4 Roberts Bank Agra Electric ? Conetec 170CP958 193CPT18 10.50 13.50 101 0.3 75 0.3 0.00 141 0.4 111 0.4 -0.01 3.0 5 Sea Island Bauer Hydraulic 2.75 Foundex CPT92-27 CPT5 6.00 8.50 86 0.3 99 0.3 0.00 117 0.2 139 0.2 -0.01 2.0 5 Sea Island Bauer Hydraulic 2.75 Foundex CPT92-27 CPT5 11.00 14.00 119 0.5 84 0.3 0.00 143 0.3 104 0.3 0.00 2.0 5 Sea Island Bauer Electric 2.75 Foundex CPT92-27 CPT05 2.00 3.00 5 0.2 20 0.3 0.05 41 0.4 76 0.4 -0.01 1.7 5 Sea Island Bauer Electric 2.75 Foundex CPT92-27 CPT05 5.20 6.20 64 0.2 117 0.2 0.00 122 0.2 143 0.2 -0.01 1.7 5 Sea Island Bauer Electric 2.75 Foundex CPT92-27 CPT05 12.50 13.50 119 0.2 93 0.2 0.00 197 0.2 124 0.2 0.00 1.0 5 Sea Island Bauer Electric 2.75 Foundex CPT92-27 CPT05 6.00 8.50 67 0.2 113 0.2 0.00 115 0.2 152 0.3 -0.01 1.0 5 Sea Island Bauer Electric 2.75 Foundex CPT92-27 CPT05 11.00 14.00 121 0.3 104 0.3 0.00 135 0.4 102 0.4 0.00 1.0 6 LuLu Island Geopac Electric 2.75 UBC LB9901 LB9903 5.40 6.20 57 0.4 78 0.4 0.00 175 0.3 239 0.3 0.00 1.5 6 LuLu Island Geopac Electric 2.75 UBC LB9901 LB9903 6.80 7.60 78 0.4 90 0.4 0.00 184 0.3 212 0.3 0.00 1.5 6 LuLu Island Geopac Electric 2.75 UBC LB9901 LB9903 9.20 10.00 102 0.4 91 0.4 0.00 200 0.4 180 0.4 0.00 1.5 6 LuLu Island Geopac Electric 2.75 UBC LB9902 LB9904 8.50 9.50 50 0.4 50 0.4 0.00 196 0.3 196 0.4 0.00 1.5 6 LuLu Island Geopac Electric 2.75 UBC LB9902 LB9904 10.30 11.00 119 0.3 102 0.3 0.00 246 0.4 210 0.4 0.00 1.5 6 LuLu Island Geopac Electric 2.75 UBC LB9902 LB9904 7.00 8.00 95 0.3 113 0.3 0.00 204 0.3 241 0.3 0.00 1.5 7 McKenzie Bauer Electric ? Conetec 155CP1 155CP24 7.00 9.00 65 0.7 57 0.7 -0.00422 79 0.5 78 0.5 -0.006 3.4 7 McKenzie Bauer Electric Conetec 155CP1 155CP24 4.75 6.75 76 0.4 86 0.4 -0.00141 80 0.3 102 0.3 -0.001 3.4 7 McKenzie Bauer Hydraulic Conetec 155CP1 189CP48 3.00 6.85 78 0.4 100 0.4 0.00 90 0.3 159 0.3 0.00 3.4 7 McKenzie Bauer Hydraulic Conetec 155CP1 189CP4B 6.95 8.35 77 0.7 73 0.7 -0.01 78 0.6 87 0.6 0.00 3.4 7 McKenzie Bauer Hydraulic Conetec 155CP4 189CP17 3.00 4.50 30 0.4 43 0.4 -0.01 34 0.2 71 0.3 -0.01 3.4 7 McKenzie Bauer Hydraulic Conetec 155CP4 189CP17 4.55 6.10 86 0.5 101 0.5 0.00 86 0.3 118 0.3 0.00 3.4 7 McKenzie Bauer Hydraulic Conetec 155CP4 189CP17 6.15 8.75 86 0.8 83 0.8 0.00 82 0.6 88 0.6 0.00 3.4 7 McKenzie Bauer Hydraulic Conetec 155CP5 189CP41 2.75 3.90 53 0.7 87 0.7 0.00 64 0.4 280 0.4 0.00 3.4 7 McKenzie Bauer Hydraulic Conetec 155CP5 189CP41 4.20 6.00 106 0.6 136 0.6 -0.01 107 0.4 192 0.4' 0.00 3.4 8 North Van. Geopac Electric 3 UBC hrbsd-1 hr4 5.50 7.50 127 0.3 161 0.3 0.00 143 0.4 203 0.4 0.00 1.4 8 North Van. Geopac Electric 3 UBC hrbsd-1 hr4 8.75 11.00 101 0.3 88 0.3 0.00 104 0.3 99 0.3 0.00 1.4 8 North Van. Geopac Electric 3 UBC hrbsd-1 hr4 12.75 15.50 68 0.5 43 0.5 0.00 93 0.3 63 0.3 0.00 1.4 8 North Van. Geopac Electric 3 UBC hrh2 hr-5 5.50 7.25 115 0.3 159 0.3 0.00 169 0.3 239 0.3 0.00 1.4 8 North Van. Geopac Electric 3 UBC hrh2 hr-5 8.75 10.25 90 0.2 86 0.2 0.00 107 0.3 104 0.3 0.00 1.4 8 North Van. Geopac Electric 3 UBC hrh2 hr-5 13.25 15.00 68 0.5 44 0.5 0.00 110 0.3 74 0.3 0.00 1.4 8 North Van. Geopac Electric 3 UBC hrh3 hr-6 5.50 7.00 108 0.5 178 0.5 0.00 205 1.1 287 1.1 0.00 1.4 8 North Van. Geopac Electric 3 UBC hrh3 hr-6 7.25 9.00 67 0.6 84 0.6 -0.01 91 0.6 101 0.6 0.00 1.4 8 North Van. Geopac Electric 3 UBC hrti3 hr-6 11.25 12.75 121 0.3 102 0.3 -0.01 170 0.4 131 0.4 0.00 1.4 8 North Van. Geopac Electric 3 UBC hrh3 hr-6 15.25 17.25 124 0.3 77 0.3 -0.01 170 0.4 99 0.4 0.00 1.4 9 LuLu Island Geopac Electric 3 UBC CPT1 CPT7 2.00 5.00 7 1.7 15 1.9 0.13 9 1.7 18 1.8 0.07 1.0 9 LuLu Island Geopac Electric 3 UBC CPT1 CPT7 7.00 9.00 135 0.3 152 0.3 0.00 142 0.4 162 0.4 0.00 1.0 9 LuLu Island Geopac Electric 3 UBC CPT3 CPT7 2.00 5.00 7 1.8 14 2.1 0.18 9 1.7 18 1.8 0.07 1.0 9 LuLu Island Geopac Electric 3 UBC CPT3 CPT7 7.00 9.00 126 0.3 142 0.3 0.00 142 0.4 162 0.4 0.00 1.0 9 LuLu Island Geopac Electric 3 UBC CPT4 CPT5 2.00 4.40 8 1.7 17 1.9 0.08 9 1.9 20 2.0 0.01 1.0 10 LuLu Island Geopac Electric 3 UBC BTP1 BTP4 2.00 3.40 73 0.5 228 0.5 0.00 97 0.3 265 0.3 0.00 0.0 10 LuLu Island Geopac Electric 3 UBC BTP1 BTP4 5.00 6.30 97 0.4 160 0.4 0.00 143 0.3 218 0.3 0.00 0.0 10 LuLu Island Geopac Electric 3 UBC BTP1 BTP4 7.20 9.00 59 0.5 59 0.5 0.00 147 0.3 163 0.3 0.00 0.0 10 LuLu Island Geopac Electric 3 UBC BTP1 BTP4 9.00 11.50 102 0.5 94 0.5 0.00 186 0.4 167 0.4 0.00 0.0 10 LuLu Island Geopac Electric 3 UBC BTP1 BTP4 12.50 14.00 98 0.5 71 0.5 0.00 104 0.3 73 0.3 0.00 0.0 10 LuLu Island Geopac Electric 3 Conetec 95-145CPT2 00-219CPT6 2.00 3.50 62 0.4 165 0.4 0.00 104 0.2 284 0.2 0.00 1.0 10 LuLu Island Geopac Electric 3 Conetec 95-145CPT2 00-219CPT6 3.50 5.00 75 0.3 141 0.3 0.00 128 0.2 247 0.2 0.00 1.0 10 LuLu Island Geopac Electric 3 Conetec 95-145CPT2 00-219CPT6 8.00 9.50 128 0.3 132 0.3 0.00 139 0.3 143 0.3 0.00 1.0 10 LuLu Island Geopac Electric 3 Conetec 95-145CPT2 00-219CPT6 10.50 12.00 89 0.3 71 0.3 0.00 122 0.3 100 0.3 0.00 1.0 10 LuLu Island Geopac Electric 3 Conetec 95-145CPT2 00-219CPT6 12.00 13.00 78 0.3 57 0.3 0.00 76 0.2 56 0.2 0.00 1.0 10 LuLu Island Geopac Electric 3 Conetec 95-145CPT2 00-219CPT8 2.30 6.00 76 0.3 153 0.3 0.00 122 0.2 250 0.2 0.00 1.0 10 LuLu Island Geopac Electric 3 Conetec 95-145CPT2 00-219CPT8 7.00 8.50 116 0.3 132 0.3 0.00 130 0.3 150 0.3 0.00 1.0 10 LuLu Island Geopac Electric 3 Conetec 95-145CPT2 00-219CPT8 8.50 11.00 112 0.3 105 0.3 0.00 165 0.3 155 0.3 0.00 1.0 10 LuLu Island Geopac Electric 3 Conetec 95-145CPT2 00-219CPT8 12.00 13.00 78 0.3 57 0.3 0.00 75 0.3 55 0.3 0.00 1.0 10 LuLu Island Geopac Electric 3 Conetec 95-145CPT4 00-219CPT14 2.00 4.80 79 0.3 204 0.3 0.00 131 0.2 344 0.2 0.00 1.0 10 LuLu Island Geopac Electric 3 Conetec 95-145CPT4 00-219CPT14 5.80 8.20 74 0.3 98 0.3 0.00 152 0.2 203 0.2 0.00 1.0 10 LuLu Island Geopac Electric 3 Conetec 95-145CPT4 00-219CPT14 9.00 13.50 123 0.3 107 0.3 0.00 192 0.3 164 0.3 0.00 1.0 10 LuLu Island Geopac Electric 3 Conetec 95-145CPT5 00-219CPT10 2.20 4.00 69 0.2 170 0.2 0.00 134 0.2 339 0.2 0.00 0.5 10 LuLu Island Geopac Electric 3 Conetec 95-145CPT5 00-219CPT10 4.50 6.50 82 0.2 124 0.2 0.00 129 0.2 202 0.3 0.00 0.5 10 LuLu Island Geopac Electric 3 Conetec 95-145CPT5 00-219CPT10 7.00 8.00 50 0.2 58 0.2 0.00 146 0.3 173 0.3 0.00 0.5 10 LuLu Island Geopac Electric 3 Conetec 95-145CPT5 00-219CPT10 8.00 10.50 91 0.2 89 0.2 0.00 157 0.3 154 0.3 0.00 0.5 10 LuLu Island Geopac Electric 3 Conetec 95-145CPT5 00-219CPT10 10.50 12.00 92 0.2 75 0.2 0.00 189 0.3 155 0.3 0.00 0.5 10 LuLu Island Geopac Electric 3 Conetec 95-145CPT5 00-219CPT10 13.00 14.00 78 0.2 53 0.2 0.00 86 0.3 58 0.3 0.00 0.5 12 LuLu Island Geopac Electric 2.75 Conetec 02-167CPT10 02-167CPT11 1.00 4.00 7 1.5 21 1.6 0.00 9 1.1 23 1.2 -0.03 1.0 12 LuLu Island Geopac Electric 2.75 Conetec 02-167CPT10 02-167CPT11 4.00 5.50 11 1.0 18 1.2 -0.04 9 0.9 14 1.0 -0.08 1.0 12 LuLu Island Geopac Electric 2.75 Conetec 02-167CPT10 02-167CPT11 8.00 9.20 92 0.3 95 0.3 0.00 275 0.3 289 0.3 0.00 1.0 12 LuLu Island Geopac Electric 2.75 Conetec 02-167CPT10 02-167CPT11 12.00 14.10 90 0.4 63 0.4 0.00 241 0.4 172 0.5 0.00 1.0 12 LuLu Island Geopac Electric 2.75 Conetec 02-167CPT10 02-167CPT12 2.00 5.00 8 1.2 17 1.3 -0.01 13 1.1 27 1.2 -0.04 1.0 12 LuLu Island Geopac Electric 2.75 Conetec 02-167CPT10 02-167CPT12 7.60 8.90 84 0.4 90 0.4 0.00 251 0.3 274 0.3 0.00 1.0 12 LuLu Island Geopac Electric 2.75 Conetec 02-167CPT10 02-167CPT12 9.50 10.70 117 0.3 105 0.3 0.00 244 0.3 222 0.3 0.00 1.0 12 LuLu Island Geopac Electric 2.75 Conetec 02-167CPT10 02-167CPT12 12.00 14.00 90 0.4 63 0.4 0.00 164 0.4 117 0.4 0.00 1.0 12 LuLu Island Geopac Electric 2.75 Conetec 02-167CPT10 02-167CPT13 2.00 5.00 8 1.1 17 1.3 -0.01 11 1.4 23 1.6 -0.05 1.0 12 LuLu Island Geopac Electric 2.75 Conetec 02-167CPT10 02-167CPT13 7.70 8.90 84 0.4 90 0.4 0.00 193 0.4 209 0.4 0.00 1.0 12 LuLu Island Geopac Electric 2.75 Conetec 02-167CPT10 02-167CPT13 12.65 14.00 92 0.4 64 0.4 0.00 205 0.4 146 0.4 0.00 1.0 13 Sea Island Geopac Electric 3 Conetec 9S-256CPT1 98-256CPT4 9.60 10.90 82 0.4 70 0.4 -0.02 177 0.3 152 0.3 0.00 1.5 13 Sea Island Geopac Electric 3 Conetec 98-256CPT2 98-256CPT10 3.00 3.90 11 0.9 22 1.0 0.05 10 0.8 19 0.9 0.13 1.5 13 Sea Island Geopac Electric 3 Conetec 98-256CPT2 98-256CPT10 7.10 7.60 57 0.5 64 0.5 -0.02 144 0.3 164 0.3 0.00 1.5 13 Sea Island Geopac Electric 3 Conetec 98-256CPT2 98-256CPT10 11.50 12.50 119 0.4 88 0.4 0.00 158 0.3 118 0.3 0.00 1.5 13 Sea Island Geopac Electric 3 Conetec 98-256CPT2 98-256CPT18 3.00 4.00 12 0.9 23 1.0 0.05 9 1.0 16 1.1 0.11 1.5 13 Sea Island Geopac Electric 3 Conetec 98-256CPT2 98-256CPT18 7.80 8.80 149 0.4 153 0.4 0.00 211 0.3 218 0.3 0.00 1.5 13 Sea Island Geopac Electric 3 Conetec 98-256CPT2 98-256CPT18 9.30 10.50 126 0.4 111 0.4 -0.01 225 0.3 199 0.3 0.00 1.5 13 Sea Island Geopac Electric 3 Conetec 98-256CPT2 98-256CPT1B 12.00 13.50 125 0.4 88 0.4 0.00 141 0.4 99 0.4 0.00 1.5 14 Sea Island Geopac Electric 3 Conetec 97-153CPT3 97-190CPT22 3.00 3.60 9 1.2 19 1.3 0.19 12 . 1.0 23 1.1 0.06 1.5 14 Sea Island Geopac Electric 3 Conetec 97-153CPT3 97-190CPT22 7.00 7.80 140 0.4 158 0.4 0.00 230 0.3 261 0.3 0.00 1.5 14 Sea Island Geopac Electric 3 Conetec 97-153CPT3 97-190CPT22 8.60 9.00 31 1.1 28 1.1 -0.03 145 0.5 141 0.5 0.00 1.5 14 Sea Island Geopac Electric 3 Conetec 97-153CPT3 97-190CPT22 9.70 10.90 189 0.3 161 0.3 0.00 330 0.4 283 0.4 0.00 1.5 14 Sea Island Geopac Electric 3 Conetec 97-153CPT3 97-190CPT22 11.10 12.20 97 0.4 73 0.5 -0.01 246 0.5 188 0.5 0.00 1.5 14 Sea Island Geopac Electric 3 Conetec 97-153CPT3 97-190CPT8 3.00 4.00 16 1.1 30 1.2 0.12 15 1.3 30 1.4 0.03 1.5 14 Sea Island Geopac Electric 3 Conetec 97-153CPT3 97-190CPT8 4.00 5.00 28 0.9 44 0.9 -0.03 42 0.7 69 0.7 -0.01 1.5 14 Sea Island Geopac Electric 3 Conetec 97-153CPT3 97-190CPT8 7.20 8.00 149 0.4 164 0.4 0.00 213 0.3 236 0.3 0.00 1.5 14 Sea Island Geopac Electric 3 Conetec 97-153CPT3 97-190CPT8 9.90 10.80 194 0.4 164 0.4 0.00 226 0.3 193 0.3 0.00 1.5 14 Sea Island Geopac Electric 3 Conetec 97-153CPT3 97-190CPT8 11.20 12.00 75 0.5 56 0.5 -0.01 196 0.4 151 0.4 0.00 1.5 14 Sea Island Geopac Electric 3 Conetec 97-153CPT3 97-190CPT8 12.00 13.00 210 0.3 151 0.3 0.00 214 0.3 153 0.3 0.00 1.5 14 Sea Island Geopac Electric 3 Conetec 97-153CPT3 97-190CPT4 6.00 6.50 97 0.4 125 0.4 -0.01 147 0.5 192 0.5 0.00 1.5 14 Sea Island Geopac Electric 3 Conetec 97-153CPT3 97-190CPT4 7.20 7.90 148 0.4 164 0.4 0.00 204 0.5 227 0.5 0.00 1.5 Filename: GIVector-average-all projects-24 TABLE A1: Summary of CPT database before and after vibro-replacement in BC Notes: 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,, Rf, F r and Bq please refer to Chapter 6. 316 

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