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Fabric, initial state and stress path effects on liquefaction susceptibility of sands Sivathayalan, Sivapathasundaram 2000

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F A B R I C , INITIAL S T A T E A N D STRESS P A T H EFFECTS ON LIQUEFACTION SUSCEPTIBILITY OF SANDS  by  SlVAPATHASUNDARAM SlVATHAYALAN M . A . Sc., University of British Columbia. B. Sc. Eng. (Hons), University of Peradeniya.  1995 1991  A THESIS S U B M I T T E D IN P A R T I A L F U L F I L M E N T OF T H E REQUIREMENTS FOR T H E D E G R E E OF D O C T O R OF PHILOSOPHY  in T H E F A C U L T Y OF G R A D U A T E STUDIES D E P A R T M E N T OF CIVIL ENGINEERING  We accept this thesis as conforming to the required standard  T H E UNIVERSITY OF^BRITISH C O L U M B I A  July 2000 ©  Sivapathasundaram Sivathayalan, 2000.  In  presenting  degree freely  at  this  the  thesis  in  partial  University  of  British  available for  copying  of  department publication  this or of  this  for  his thesis  scholarly  or for  her  The University of British C o l u m b i a Vancouver, Canada  DE-6 (2/88)  I further  purposes  the  requirements that the  agree that  may  representatives.  financial  permission.  of  Columbia, I agree  reference and study.  thesis by  fulfilment  It  gain shall not  be is  Library  permission  granted  by  understood be  for  allowed  an  advanced  shall make for  the that  without  it  extensive  head  of  my  copying  or  my  written  ABSTRACT  A n experimental study aimed at improving the understanding o f the mechanics of liquefaction is presented.  T w o aspects o f the undrained behaviour; (i) the influence o f initial state,  characterized by void ratio, principal stresses and their directions, and fabric under a given undrained stress path, and (ii) the effect o f undrained stress path at a given initial state, were studied in a systematic manner. Triaxial, simple shear and hollow cylinder torsional shear devices were used in the experimentation to enforce a range o f stress paths that simulate the loading i n situ. The effect of membrane penetration was duly addressed in order to confidently measure the truly undrained behaviour o f sands. The influence of soil fabric was determined using triaxial and simple shear tests on specimens reconstituted by different techniques. In addition to specimens reconstituted in the laboratory, undisturbed, in-situ frozen sands from four different sites were tested to assess the relevance o f the behaviour o f reconstituted specimens to the sand in-situ. It is shown that in-situ sands and those water pluviated in the laboratory are inherently anisotropic, and their undrained behaviour is direction dependent. A t a given initial state, they often strain soften to an essential steady state in triaxial extension, but invariably strain harden in compression. Moist tamped sands, on the other hand, strain soften both in compression and extension. The domain o f states in void ratioeffective stress space accessible to alluvial in-situ sands is shown to be similar to those that ensue on pluviation. The behaviour o f water pluviated sands is similar to that of alluvial in-situ sands, at a given initial stress state and undrained stress path, both under static and cyclic loading ii  conditions - an indication that they both possess very similar fabric. This opens up the possibility o f using water pluviated sand specimens to characterize the behaviour o f in-situ sands, an attractive economical alternative. It is shown that the initial effective stress state plays a dominant role on the subsequent undrained behaviour at a given void ratio. H o l l o w cylinder torsional shear tests on water pluviated fabric were used to assess the influence of the initial axisyrnmetric and non-axisymmetric stress states on undrained shear. The behaviour due to an increase in deviator stress alone, and that due to simultaneous changes in deviator stress and the direction o f principal stresses is investigated. A larger inclination of maj or principal stress to vertical results in a softer behaviour at all levels o f static shear. A n increase in static shear at a given inclination of the major principal stress promotes more strain softening response. Even a small undrained perturbation may trigger flow failure in a sand that is otherwise stable i f drained, in the event the initial stress state is highly anisotropic together with larger inclination o f major principal stress to the vertical. It is demonstrated that flow failure may be triggered by a mere rotation o f principal stress directions only. The sense o f principal stress rotation with respect to the initial inclination o f the major principal stress also plays a prominent role on the undrained behaviour, and hence on strain development. It is shown that the strain induced anisotropy evolves at an accelerated rate due to rotation o f major principal stress direction, compared to an increase in effective stress ratio alone at fixed direction o f principal stresses. It is shown that both steady state and quasi steady state can be treated within the same framework. The friction angle mobilised at these states is independent o f fabric, void ratio, effective confining and static shear stress levels, direction o f principal stresses, and undrained  iii  stress path. This angle appears to be a unique material property. Contrary to the commonly held notion, the minimum undrained strength is dependent on the stress path, initial confining and static shear stress levels, fabric and the directions o f principal stresses, in addition to void ratio. This implies that the steady/quasi-steady state is unique in the effective stress space, but not so in the void ratio - stress space. However, the minimum undrained strength normalised by the major principal stress appears to be dependent only on void ratio and the direction o f major principal stress (i.e loading mode). The friction angle mobilised at the trigger o f strain softening is also dependent on the initial stress state and the loading mode.  iv  Table of contents  Abstract  ii  List of Figures  xi  List of Tables  xxii  List of Symbols  xxiii  Acknowledgements  xxvi  Introduction  1  Liquefaction of Sands  6  2.1  Introduction  6  2.2  Undrained behaviour of saturated sands  8  2.2.1  Static undrained behaviour in triaxial compression  8  2.2.2  Cyclic triaxial behaviour  11  2.2.2.1 Mechanisms of strain development  12  2.2.2.2 Strain softening in cyclic loading  18  2.3  Anisotropy in sand deposits  19  2.3.1  Stress path dependent behaviour  21  2.3.2  The strain softening response  25  2.3.3  The phase transformation and quasi-steady state  26  v  2.3.4  Angle o f maximum obliquity & Ultimate/Failure state  27  2.3.5  Cyclic simple shear and triaxial behaviour  27  2.3.6  Fabric dependence o f behaviour  30  2.4  Critical/Steady state concepts  33  2.5  The stress state in-situ  38  2.6  Research Needs  41  Experimentation and Test Apparatus  45  3.1  Introduction  45  3.2  Laboratory Shear Testing o f soils  46  3.2.1  The Triaxial Test  47  3.2.1.1 The U B C Triaxial Apparatus  48  The Simple Shear Test  50  3.2.2.1 The U B C Simple shear apparatus  52  The H o l l o w Cylinder Torsion ( H C T ) Test  54  3.2.3.1 The U B C H o l l o w cylinder torsional device  55  3.2.3.2 Stresses and strains in an H C T specimen  61  3.2.2  3.2.3  3.3  3.4  Data acquisition and control systems  67  3.3.1  69  Measurement resolutions  Test Procedures  70  3.4.1  Specimen reconstitution  71  3.4.2  Specimen setup and consolidation  72  vi  3.4.3 3.5  3.6  Monotonic or cyclic undrained Shear  74  Experimental artifacts and measurement errors  75  3.5.1  Influence o f loading system (in strain softening sands)  76  3.5.2  Membrane penetration effects  79  3.5.3  Calculation o f void ratio  80  Test Program  80  Membrane Penetration Effects on Undrained Behaviour  83  4.1  Introduction  83  4.2  Magnitude o f membrane penetration  85  4.2.1  Assessment o f membrane penetration  86  4.2.2  Factors influencing the magnitude o f membrane penetration  90  4.2.3  Corrections in drained and undrained Tests  91  4.3  4.4  A N e w Method for determining the magnitude o f membrane penetration . . 92 4.3.1  Characteristics o f the new method  98  4.3.2  Experimental Investigations (using the new method)  99  4.3.3  Test Results  101  Membrane penetration and Undrained behaviour  106  4.4.1  Truly undrained behaviour o f sands  106  4.4.2  Experimental Investigations  108  4.4.3  Post test correction to pore pressure i n conventional undrained shear  110  vii  4.5  4.4.4  Test Results  112  4.4.5  Evaluation o f Post-Test Correction Methods  115  Summary  118  Fabric Dependent Behaviour of Sands  121  5.1  Introduction  121  5.2  Undisturbed sand specimens  122  5.2.1  Canadian Liquefaction Experiment ( C A N L E X )  123  5.2.2  In-situ ground freezing  125  5.2.3  Thawing and restoration o f in-situ stress state  128  5.2.3.1 Setting up o f frozen specimens  129  5.2.3.2 Disturbance during thawing and reconsolidation  131  5.2.3.3 Comparison o f different thawing techniques  136  5.3  5.4  5.5  Undrained behaviour o f undisturbed sand  142  5.3.1  Monotonic Triaxial compression and extension tests  143  5.3.2  Monotonic and cyclic simple shear response  151  5.3.3  Post liquefaction behaviour in triaxial and simple shear  158  Influence o f specimen reconstitution technique  164  5.4.1  Compressibility and Accessible states  167  5.4.2  Static Undrained Behaviour  172  5.4.2.1 Mobilised friction angle at SS/QSS/PT  178  Comparative undrained behaviour o f Undisturbed and Reconstituted sands 178  viii  5.6  5.5.1  Static undrained behaviour  180  5.5.2  Cyclic Resistance  191  5.5.3  Post liquefaction behaviour  194  Summary  204  Generalised stress state and stress path dependent behaviour 6.1  6.2  Introduction  207  6.1.1  Initial States  208  Inherent Anisotropy  209  6.2.1 6.3  6.5  Drained deformation along constant K path (and Kg) c  213  Undrained behaviour with generalised initial stress state  215  6.3.1  Response under fixed principal stress directions  217  6.3.1.1 Triggering o f strain softening  230  6.3.1.2 Steady or quasi steady state  236  6.3.1.3 Angle o f maximum obliquity  238  M i n i m u m undrained strength o f sands  238  6.3.2 6.4  207  Response under principal stress rotation  248  6.4.1  Simultaneous increase in a and a  6.4.2  Increase in a only at constant a  6.4.3  Initial state and the direction o f stress rotation  d  a  Summary  0  d  250 260 267 273  ix  Summary and Conclusions 7.1  276  Recommendations for future research  References  x  282  List of Figures  Figure 2.1 :  Typical undrained response o f sands under static loading  9  Figure 2.2(a) :  Steady state o f deformation following strain softening under cyclic loading (After V a i d and C h e m 1985)  Figure 2.2(b) :  13  Strain softening followed by cyclic mobility under cyclic undrained shear (After V a i d and C h e m 1985)  Figure 2.2(c):  14  Cyclic mobility with transient states o f zero effective stress (After V a i d and Chern 1985)  Figure 2.2(d):  15  Cyclic mobility without transient states of zero effective stress (After V a i d et al. 2000)  Figure 2.3:  16  Comparative triaxial compression and extension undrained behaviour o f sands (After V a i d and Thomas 1995)  Figure 2.4 :  Systematic softening i n undrained behaviour with increasing a (After s  Uthayakumar and V a i d 1998) Figure 2.5 :  22  23  Stress conditions prior to and during undrained shear in triaxial and simple shear tests  29  Figure 2.6 :  Ratio o f cyclic resistance in simple shear to that in triaxial  31  Figure 2.7 :  The steady state approach o f characterising the behaviour o f sands . . . . 35  Figure 2.8 :  Stress state o f soil elements in-situ  39  Figure 3.1 :  Schematic diagram o f the U B C static/cyclic triaxial device  49  xi  Figure 3.2 :  Specimen and loading arrangement i n U B C simple shear apparatus  Figure 3.3 :  Schematic diagram o f the U B C static/cyclic simple shear device  Figure 3.4 :  Schematic diagram of the U B C hollow cylinder torsional shear device . 56  Figure 3.5 :  Arrangement o f porous stones, shear ribs and drainage passage i n H C T loading cap  ...52 53  59  Figure 3.6 :  Schematic arrangement o f pore water drainage in an H C T specimen . . . 60  Figure 3.7:  Schematic arrangement o f the torsional displacement measuring system in the U B C hollow cylinder torsional shear device  62  Figure 3.8 :  Stresses and strains i n a hollow cylindrical soil element  63  Figure 3.9:  Comparison o f different approaches to find representative stresses i n a hollow cylindrical soil element  Figure 3.10:  66  The effect of loading system on the measured response in strain softening soils (After C h e m 1985)  77  Figure 4.1 :  Membrane penetration effect i n an undrained test  84  Figure 4.2 :  Evaluation o f membrane penetration using dummy brass rods (After Roscoe etal. 1963)  88  Figure 4.3 :  Stresses and strains i n a hollow cylindrical element  Figure 4.4 :  Membrane penetration induced volume changes i n a hollow cylinder test96  Figure 4.5 :  Particle gradation o f the materials used i n assessing the magnitude o f membrane penetration  Figure 4.6 :  .93  100  Variation of membrane penetration induced volume change with effective confining stress  102  xii  Figure 4.7 :  Magnitude of membrane penetration during several unload-reload loops  Figure 4.8 :  103  Comparison of the magnitude of membrane penetration calculated using the new method and Vaid and Negussey (1984)  Figure 4.9(a):  Dependence of normalised unit membrane penetration on the logarithm of D  Figure 4.9(b) :  105  50  Variation of normalised unit membrane penetration with mean grain size, D  Figure 4.10 :  107  50  Excess pore pressure and the volume of water injected or withdrawn to maintain a truly undrained state in a typical test  Figure 4.11:  I l l  Comparison of truly undrained and conventional undrained behaviour of Fraser River sand  Figure 4.13 :  113  Comparison of truly undrained and conventional undrained behaviour of coarse Silica sand A  Figure 4.14 :  109  Comparison of measured and predicted excess pore pressures (after Ansal and Erken 1996)  Figure 4.12 :  104  114  Comparison of the excess pore pressure measured in a truly undrained test with those predicted by the post correction methods in Fraser River sand  Figure 4.15 :  116  Comparison of the excess pore pressure measured in a truly undrained test with those predicted by the post correction methods in Silica sand A. .118  Figure 5.1(a):  C A N L E X phase II site locations in lower mainland, British Columbia. 124 xiii  Figure 5.1(b):  Schematic o f the freeze pipe (after Hofmann 1997)  Figure 5.2 :  Height change  during thaw and reconsolidation o f undisturbed and  reconstituted sands Figure 5.3 :  127  134  Height change during thaw and reconsolidation o f saturated Massey sands  136  Figure 5.4 :  Variation o f radial and axial strains during anisotropic consolidation. . 140  Figure 5.5 :  Ratio o f e/e o f undisturbed sands during anisotropic consolidation along z  K = 2 line  141  c  Figure 5.6 :  Undrained triaxial compression and extension response o f undisturbed Syncrude sand  Figure 5.7 :  145  Undrained triaxial compression and extension response o f undisturbed K i d d sand  Figure 5.8 :  146  Undrained triaxial compression and extension response o f undisturbed Massey sand  Figure 5.9 :  147  Undrained triaxial compression and extension response o f Syncrude J-pit sand  149  Figure 5.10 :  Constant volume simple shear behaviour o f Phase I Syncrude sand . . . 152  Figure 5.11 :  Undrained cyclic shear leading to flow failure in Syncrude sand  Figure 5.12(a):  Undrained cyclic shear leading to flow deformation in loose Massey sand  Figure 5.12(b):  154  155  Undrained cyclic shear causing deformation on account of cyclic mobility in Massey sand  156  xiv  Figure 5.13 :  Cyclic resistance o f (a) K i d d and (b) Massey sands in simple shear . . . 157  Figure 5.14 :  Cyclic simple shear resistance o f Syncrude sand  Figure 5.15:  Post liquefaction behaviour o f undisturbed K i d d sand following liquefaction  158  induced by static unloading Figure 5.16:  159  Post liquefaction response o f loose and dense Massey sand following liquefaction induced by cyclic loading  Figure 5.17:  Post liquefaction response o f undisturbed  161 Syncrude sand i n triaxial  compression and simple shear Figure 5.18 :  Post liquefaction response o f Syncrude sand under multiple unload-reload cycles  Figure 5.19:  163  165  Direct assessment of uniformity of reconstituted specimens (a) water pluviated Ottawa sand, (b) moist tamped Fraser River sand, and (c) moist tamped sand C (after Castro 1969)  168  Figure 5.20 :  Range o f accessible states by different reconstitution techniques  170  Figure 5.21 :  In-situ states o f undisturbed sands in comparison to states attainable by laboratory reconstitution methods  Figure 5.22:  Influence of specimen reconstitution technique on the undrained simple shear response o f Syncrude sand  Figure 5.23:  173  Effect of specimen reconstitution technique on undrained triaxial compression response  Figure 5.24 :  171  175  Effect o f specimen reconstitution technique on undrained triaxial extension  176  xv  Figure 5.25 :  Effective stress state at steady, quasi steady ( i f contractive) and phase transformation ( i f dilative) states o f undisturbed and reconstituted sands  Figure 5.26(a):  179  Comparative undrained triaxial compression behaviour o f undisturbed and water pluviated Massey sand  Figure 5.26(b):  Comparative undrained triaxial extension behaviour of undisturbed and water pluviated Massey sand  Figure 5.27(a):  182  Comparative undrained triaxial compression behaviour o f undisturbed and water pluviated K i d d sand  Figure 5.27(b):  183  Comparative undrained triaxial extension behaviour o f undisturbed and water pluviated K i d d sand  Figure 5.28 :  181  184  Comparative undrained simple shear behaviour o f undisturbed and water pluviated sands  186  Figure 5.29 :  V o i d ratio variation along the undisturbed Syncrude sand specimens  Figure 5.30(a):  Effective stress states at steady, quasi steady or phase transformation states in undisturbed and equivalent water pluviated sands  Figure 5.30(b):  . 187  188  Effective stress states steady, quasi steady or phase transformation state o f Syncrude sand over a range o f effective confining stress and void ratio. 189  Figure 5.31 :  Normalised effective stress states at steady/quasi steady states  Figure 5.32 :  Comparison o f cyclic simple shear behaviour o f undisturbed and equivalent water pluviated sand  Figure 5.33(a):  190  192  Cyclic resistance o f undisturbed and equivalent water pluviated sand . 193  xvi  Figure 5.33(b):  Comparison of measured cyclic simple shear resistance of undisturbed sands with a previous study on water pluviated specimens  Figure 5.34 :  Range of post liquefaction stress strain curves o f undisturbed and water pluviated Massey sand  Figure 5.35 :  196  Influence of the magnitude of maximum shear strain during liquefaction on post liquefaction stress strain resistance  Figure 5.36 :  200  Post liquefaction stress-strain response in comparison to that of virgin loading in K i d d sand  Figure 5.39 :  198  Post liquefaction stress- strain response in comparison to that of virgin loading in Syncrude sand  Figure5.38 :  197  Influence of relative density on post liquefaction stress strain response (after V a i d and Sivathayalan 1997)  Figure 5.37:  195  201  Schematic illustration of the characteristic post liquefaction response in undrained shear  203  Figure 6.1 :  Consolidation to generalised initial effective stress states  210  Figure 6.2 :  A x i a l , radial and tangential strain increments under hydrostatic stress increment  Figure 6.3 :  212  Strain increments in uniform spherical particles under hydrostatic stress increments  Figure 6.4 :  Figure 6.5 :  213  A x i a l , radial and tangential strains under axisymmetric proportional loading  214  Targeted and actual control parameters followed in a typical test  216  xvn  Figure 6.6(a):  Variation o f surface tractions with vertical strain during undrained shear at fixed principal stress directions.  Figure 6.6(b):  219  Variation o f radial, tangential and shear strain on the horizontal plane with vertical strain during undrained shear with fixed principal stress directions  Figure 6.7(a):  Variation of principal stresses and effective stress ratio during undrained shear with fixed a  Figure 6.7(b):  220  221  s  Variation o f principal strains with vertical strain during undrained shear at fixed principal stress directions  Figure 6.8 :  222  Undrained behaviour o f Fraser River sand at different fixed principal stress directions at K = 2  224  c  Figure 6.9 :  Undrained behaviour at fixed principal stress directions at initial K = 1.5  226  c  Figure 6.10:  Undrained behaviour o f Fraser River sand over a range o f initial static shear ata  Figure 6.11:  = 0°  227  Influence of initial static shear on the undrained response o f Fraser River sand ata  Figure 6.12 :  o c  o c  = 60°  228  Variation o f (a): effective stress states at the instant o f strain softening, and (b): friction angle mobilised at peak with cc  231  CT  Figure 6.13 :  Influence o f initial static shear, and direction o f principal stresses on peak undrained strength  Figure 6.14 :  232  Variation o f brittleness index I with B  xviii  o c and K oc  c  234  Figure 6.15 :  Potential instability as assessed by the modified brittleness index . . . . 235  Figure 6.16 :  Effective stress state at steady, quasi steady or phase transformation states  Figure 6.17:  236  Dependence of minimum undrained strength on static shear and direction o f major principal stress  Figure 6.18:  239  Systematic change in the direction of major principal stress along a potential failure surface  Figure 6.19(a):  240  Dependence o f undrained strength on confining stress level, and void ratio in triaxial extension  Figure 6.19(b) :  243  Dependence of undrained strength on confining stress level, and void ratio i n simple shear  Figure 6.19(c):  244  Variation of normalised minimum undrained strength with a initial static shear levels  Figure 6.20 :  at different 245  Schematic illustration o f minimum undrained strength and steady state strength  Figure 6.21 :  c  247  Variation of control parameters a , b, rj and ct during principal stress m  d  a  rotation  251  Figure 6.22(a):  Variation o f surface traction during principal stress rotation  253  Figure 6.22(b):  Variation o f radial, tangential and horizontal shear strain with vertical strain 8 during principal stress rotation  254  Z  Figure 6.23(a):  Variation of effective principal stresses and stress ratio with e during principal z  stress rotation  255 xix  Figure 6.23(b):  Variation o f principal strains during stress rotation against fixed direction strain e  Figure 6.24:  256  z  Influence of initial static shear stress level on subsequent undrained shear with simultaneous increase in a and a d  Figure 6.25 :  257  CT  Influence of degree o f stress rotation Aa /Ao* on subsequent undrained shear CT  dn  with simultaneous increase i n cr and ct d  Figure 6.26 :  259  CT  Deformation due to undrained rotation o f principal stresses alone with no increase in a at two initial K levels d  Figure 6.27 :  261  c  Trigger o f strain softening: (a) Effective stress states, (b): variation o f • , mobilised friction angled with ct  264  CT  Figure 6.28 :  Effective stress states at steady/quasi steady states during principal stress rotation.  Figure 6.29 :  Dependence o f normalised minimum undrained strength on the direction o f major principal stress a  Figure 6.30 :  265  267  CT  The direction o f stress rotation in-situ: Increasing and decreasing a initial a  Range of excess pore pressure development for increasing and decreasing ct  CT  at different initial static shear K Figure 6.32 :  from 268  ac  Figure 6.31:  CT  c  269  Influence o f the sense o f principal stress rotation on the undrained response at initial a = 3 0 °  271  xx  Figure 6.33 :  Influence o f the sense o f principal stress rotation on the undrained response at initial a = 6 0 °  272  xxi  List of Tables  Table 5.1:  Properties o f the undisturbed sands  125  Table 5.2:  C A N L E X laboratory Testing: Phase I, II & III Undisturbed sand specimens  128  Table 5.3:  Height change during restoration o f in-situ state o f Syncrude sands  138  Table 5.4:  C A N L E X Undisturbed specimens: in-situ characteristics (after Fear 1996) . 144  Table 6.1:  Initial states o f specimens tested under fixed principal stress directions . . . . 218  Table 6.2:  Initial states and loading paths in stress rotation tests  xxii  249  List of Symbols  Surface area o f the specimen covered by the inner membrane A  Surface area o f the specimen covered by the outer membrane  b  Intermediate principal stress parameter  b  Intermediate principal stress parameter at the end o f consolidation  c  D50  Mean grain size  D  r  Relative density  D  r c  e  Relative density at the end o f consolidation V o i d ratio at the end o f consolidation  c  ^max  M a x i m u m index void ratio ( A S T M D4254-83) M i n i m u m index void ratio ( A S T M D4253-83)  F  Sleeve friction ratio i n cone penetration test  IB  Brittleness Index  K  Effective principal stress ratio at the end o f consolidation (a\/a\)  c  ^rnin  M i n i m u m undrained strength  C ^peak  Peak undrained strength  ^SS/QSS  Shear strength at steady/quasi-steady state  ^SS/QSS/PT  Shear strength at steady/quasi-steady or phase transformation state  CSR  Critical stress ratio at the instant o f peak deviator stress  PT  Phase transformation  QSS  Quasi steady state  Ri  Internal radius o f the hollow cylindrical specimen  Re  External radius o f the hollow cylindrical specimen  q i  Cone tip resistance corrected to 100 k P a overburden stress  SS  Steady state  V  Volume o f the specimen  c  xxiii  Inner Cavity volume o f the hollow cylindrical specimen Shear wave velocity corrected to 100 k P a overburden stress  a  Inclination o f major principal stress to the vertical  0  a  Inclination o f major principal stress to the vertical at the end o f consolidation  CTC  X  Ratio o f external to internal radii of the hollow cylindrical specimen  8V  R  Recorded volume change o f the specimen  SV  Recorded volume change o f the inner cavity  SV  Volume change induced by penetration o f inner membrane  m  m  8V  0 M  Volume change induced by penetration o f outer membrane  6!  Major principal strain  e  2  Intermediate principal strain  s  3  M i n o r principal strain  e  a  A x i a l strain in triaxial  8  Unit membrane penetration (membrane induced volume change per 10-fold  m  change in effective confining stress) i  Normalised Unit membrane penetration ( e per unit area o f the membrane)  m  m  e  r  Normal strain in the radial direction  E  Z  Normal strain i n the vertical direction  8  e  Normal strain in the tangential direction  y  m a x  M a x i m u m shear strain  y  z6  Shear strain on the horizontal plane in the tangential direction  ^CSR  Friction angle mobilised at the trigger o f strain softening  ^SS/QSS/PT  Friction angle mobilised at SS/QSS/PT  CT,  Major principal stress  CT  Intermediate principal stress  CT  M i n o r principal stress  o"  Deviator stress  2  3  d  xxiv  Cyclic deviator stress Deviator stress normalized by effective mean normal stress Total mean normal stress Total mean normal stress at the end o f consolidation Normal stress i n the radial direction Normal stress i n the vertical direction Normal stress i n the tangential direction Effective mean normal stress at the end o f consolidation Effective major principal stress Effective intermediate principal stress Effective minor principal stress Horizontal effective stress i n triaxial Vertical effective stress i n triaxial/simple shear Cyclic shear stress i n simple shear Horizontal shear stress i n simple shear Change i n the direction o f major principal stress direction Change in deviator stress Change i n normalised deviator stress Excess pore pressure  xxv  Acknowledgements  I wish to express my sincere gratitude to my thesis supervisor Professor Y . P. V a i d . I am deeply indebted to h i m for his constant support, encouragement and guidance throughout this research program, and my stay at U B C . I would like to thank Professors P. M . Byrne, W . D . L . Finn, R. J. Fannin, J. A . Howie, R. O. Foschi, R. C . Pakalnis and Dr. M . K . Lee for being members i n the thesis supervisory, and examination committees. I was fortunate to be associated with the U B C Geotechnical Engineering group and its professors over these years. M y acquaintance with such eminent researchers was very rewarding both professionally and personally, and w i l l surely have a strong influence in my career. I would like to thank Professor Dawit Negussey for his guidance and encouragement during the latter stages o f my study, and Professor Hans V a z i r i for reviewing the manuscript as the external examiner. The technicians in the C i v i l Engineering Mechanical and Electrical workshops have helped in a timely manner at several occasions. The indispensable and expert technical assistance o f Messrs. Harald Schrempp, John W o n g and Scott Jackson in fabricating and troubleshooting test equipment and control systems is gratefully acknowledged. I would like to thank my colleagues and friends; Thava, Prem, Uthaya, Roy, Srithar, Mukunthan, Chandra, Ganan, and Dave for the camaraderie they have provided over the years. Thank you for those interesting, entertaining, critical and helpful discussions and conversations. The assistance o f all fellow graduate students working in the laboratory is gratefully acknowledged. xxvi  Financial support provided by the University of British Columbia Fellowship, and the National Science and Engineering Research Council Research Assistantship are acknowledged with deep appreciation. Finally, I would like to thank my parents, family, and my wife Ahalya for their support and encouragement throughout various stages o f this study, and my life.  Their love, support,  encouragement and sacrifices have been instrumental in guiding me to carry out my doctoral studies.  xxvii  Chapter 1  Introduction  The term liquefaction embraces all phenomena involving excessive deformation i n saturated granular soils. In short duration field events such as an earthquake or a shock, soils get loaded virtually undrained. This causes a reduction in their strength and stiffness due to the development of excess pore pressure. In the field, damage due to liquefaction may express itself as flow slides in sloping ground. Some examples o f such flow slides are Ports o f Valdez, Alaska, Nice, Lower San Fernando dam, and Chilean tailings dams (Seed at al. 1975, Jeyapalan et al. 1983, Seed et al. 1988, Ishihara et al. 1990, Bardet and Kapuskar 1993, Bardet and Davis 1996, Boulanger et al. 1997, Holzer et al. 1999). Under level ground this damage manifests as cracking or lateral spreading o f overlying embankments, and tilting or even collapse o f superstructures.  Several  examples o f such type o f damage were seen in the earthquakes of Nigaata, Alaska, M e x i c o City, Northridge, Kobe (Whitman 1987, Barends et al. 1992, Byrne et al. 1996, Finn et al. 1996, Harder and Stewart 1996, Ishihara et al. 1996, Stark and Contreras 1998, Hamada and Wakamatsu 1998) and the recent Turkey and Taiwan events. Deformations due to liquefaction are unidirectional in sloping ground, but they are generally o f cyclic nature in level ground. A s i n other engineering materials, a fundamental understanding of the physics and mechanics of sand liquefaction has been derived from laboratory element tests. The response of sand under 1  Chapter I: Introduction  2  undrained triaxial compression loading has been the mainstay o f our current knowledge i n this field. The mechanical behaviour o f soils, however, is very complex. Apart from being nonlinear and inelastic, it depends on the initial state o f the soil comprised o f density, magnitude and directions o f effective principal stresses and any prior stress/strain history, as well as the stress path during undrained shear. For a given initial density and stress state, it further depends on the soil fabric. The objective of laboratory element testing therefore is to assess the influence o f both initial state variables and fabric together with that o f the stress path during undrained shear. Most o f the databases on element tests consist o f triaxial compression tests on reconstituted specimens. In this test, the initial stress state is axisymmetric with principal stress directions aligned i n the vertical deposition, and horizontal bedding plane directions. During shear, the directions of the principal stresses and the state o f stress (axisymmetric) stay unaltered. Clearly, the behaviour under these conditions only is not sufficient to describe the undrained response under other generalised initial states and variety o f stress paths experienced by the soil element in the field. This is because of the complexity o f the mechanical response of soils, which is further influenced by inherent anisotropy in natural and hydraulic fill sands (Arthur and Menzies 1972, V a i d and C h e m 1985, V a i d et al. 1990a, Riemer and Seed 1997). There is little likelihood o f success i n developing a general constitutive model that captures all aspects o f soil behaviour. Therefore, the field behaviour is commonly assessed using the stress path approach (Lambe 1973). This approach aims at evaluating the behaviour o f soils under the initial states and the range o f loading paths that duplicate those anticipated in the given field problem. Fundamental studies on liquefaction using other testing devices, and hence stress paths, are few. Each o f these devices is intended to simulate specific field loading conditions pertinent to  Chapter I: Introduction  3  a given problem. The simple shear test, for example, has been used to simulate the behaviour o f a sand element under earthquake shaking (Roscoe 1970, V a i d and Finn 1979, Lacasse and Vucetic 1981). This test represents loading o f a sand element in horizontal plane strain. It, however, imposes uncontrolled principal stress rotation in the vertical plane. Studies i n the hollow cylinder torsional shear device do allow control o f not only the magnitude o f the three principal stresses, but also their directions in one plane. It thus permits assessment o f the response, both under generalised initial state and different stress paths. It is also possible to isolate in a fundamental manner, the effect o f each initial state variable or stress path parameter on sand behaviour. Generalised initial stress states, and undrained paths are the norm, rather than exceptions in real field problems. Three facets o f the undrained behaviour o f sand have been explored in this thesis.  The  influence o f membrane compliance on the measured undrained behaviour i n the laboratory is assessed first. This effect, i f not considered, does not yield a measure o f the intended true undrained behaviour of sands, but rather the response under a partially drained state. This aspect o f research is, therefore, directed towards confident measurement o f undrained response. Errors endemic to the penetration o f flexible rubber membranes used to enclose the test specimens are reviewed, and a new, more confident method o f evaluating membrane penetration is developed for compensation o f their compliance effects on undrained tests. Compensation, that depends on soil particle size, i f needed, is automatically made by the control system. The second facet o f the investigation is intended to determine the influence of soil fabric, under an otherwise identical initial state and subsequent undrained stress path. Comparative tests are made on undisturbed samples of sand retrieved by in-situ ground freezing, and those reconstituted  Chapter 1: Introduction  4  in the laboratory by different techniques. Although considerable evidence exists to indicate that different reconstitution techniques yield different fabrics, and that sand fabric plays a dominant role on the undrained behaviour, little consideration is accorded to it in practice. Further, the extent to which the undisturbed sand behaviour differs from that of its reconstituted counterpart is also not known. This is of crucial importance in applying the results of tests on reconstituted specimens to the undisturbed sands in-situ. The third facet of the investigation concerns the assessment of the influence of generalised initial stress states and stress paths on undrained behaviour. Triaxial, simple shear and hollow cylinder torsional shear devices are used. The influence of initial stress state variables on undrained behaviour under stress paths simulated by these devices is explored, and compared. The influence of anisotropy of sands on its undrained response is also studied in the results of these tests. Chapter 2 is devoted to an understanding of the liquefaction phenomena as revealed in fundamental laboratory studies. Results of previous studies, mostly under triaxial compression, and the few under extension, simple shear and generalised stress states are critically reviewed in an attempt to justify the studies undertaken in this thesis. Chapter 3 documents the various testing devices used in this investigation, together with details of the experimental procedures and techniques. Chapter 4 deals with the aspect of membrane compliance. A new, specimen specific method to evaluate the magnitude of membrane penetration is presented, and the influence of membrane compliance on undrained behaviour of sands is highlighted. The effect of fabric on the undrained behaviour of sands is demonstrated in Chapter 5, using reconstituted and undisturbed (in-situ frozen) sand specimens. A comprehensive treatment of the influence of initial effective  Chapter I: Introduction  5  stress state and the subsequent undrained stress path on the behaviour of sands is presented in Chapter 6. Specimens reconstituted by water pluviation only are used in these studies so that the fabric is held constant. Chapter 7 finally presents a summary and conclusions arrived at under each of the three facets of the investigations.  Chapter 2  Liquefaction of Sands  2.1  Introduction  The current state o f understanding o f the undrained behaviour and the phenomenon o f liquefaction o f sands is presented i n this chapter. considered.  Both static and cyclic liquefaction are  A s pointed out in the introduction, most o f our understanding o f undrained  behaviour of sands has been derived from fundamental studies of element tests in the laboratory under controlled conditions. A knowledge o f the undrained response o f sands is critically important in assessing their susceptibility to liquefaction, and in estimating the liquefaction induced and post liquefaction displacements. Under static loading the susceptibility to liquefaction could trigger flow failure. Under cyclic loading, on the other hand, the susceptibility is for the development of large strains due to a progressive reduction in shear stiffness. The potential for flow failure exists under cyclic loading i f initial static shear is present. Post cyclic static behaviour is relevant to the estimation o f displacements or even a delayed flow failure that could ensue after the cessation o f the earthquake. The former occurs on account o f the presence o f static shear stresses and the latter due to the redistribution o f earthquake induced pore pressures. In such cases, the earthquake  6  Chapter 2: Liquefaction of sands  7  simply initiates a trigger mechanism, and the trigger o f the flow failure occurs following the cessation o f the seismic event. The undrained behaviour is first discussed as observed in conventional triaxial compression tests on reconstituted specimens.  Such data has been, and still is the mainstay o f our  understanding of the liquefaction phenomena. The stress conditions simulated by the triaxial test, however, represent loading along a specific stress path under axisymmetric conditions. The soil elements in the field get loaded along many different stress paths and stress systems.  A  knowledge o f the undrained behaviour along such paths and stress systems is therefore o f utmost importance to assess the behaviour o f sands in the field. Evidence in support o f the inherently anisotropic nature o f sands is presented based on data from the literature. The stress path dependent undrained behaviour of sands is a consequence o f this inherent anisotropy. This facet of the undrained behaviour has largely been ignored, and only a few studies have attempted to investigate the stress path effects. Results from these studies highlighting the stress path dependency on both static and cyclic response, have been summarised and their implications in practice pointed out. Soil fabric is an additional state variable that governs its undrained behaviour at identical initial stress states and subsequent undrained paths. A limited number o f studies provide evidence in support o f this using comparative data on sands with different initial fabrics. The need to duplicate in-situ fabric is then pointed out i f laboratory tests on reconstituted sands are to be substituted for the undisturbed sands. The research needs identified from the review o f the current state o f understanding are detailed at the end o f this chapter.  Chapter 2: Liquefaction of sands  2.2  8  Undrained behaviour of saturated sands  A progressive reduction in shear stiffness due to the development o f excess pore pressure is often the cause o f large deformations in the undrained state. Therefore only the behaviour o f saturated sands is of concern under undrained shear, and as noted earlier, large deformations can develop either as a result o f static or cyclic loading. Terzaghi and Peck (1948) originally used the term "spontaneous liquefaction" to explain the sudden deformation o f loose sands, in a manner similar to that o f a viscous liquid. The term liquefaction has been defined based either on the amount of excess pore pressure, the amount o f strain developed or based on the mechanism that is responsible for the deformation. The widely accepted N R C (1985) criterion based on a specified strain level (2.5% single amplitude axial strain or equivalent) without regard to the mechanism responsible for the deformations is adopted in this thesis as the definition o f liquefaction.  2.2.1  Static undrained behaviour in triaxial compression  The static undrained behaviour o f saturated sands has mostly been studied under triaxial compression loading (e.g. Castro 1969, Castro et al. 1982, Chern 1985, Thomas 1992, Ishihara 1993, and Riemer and Seed 1997), using test specimens reconstituted by water pluviation or moist tamping. Figure 2.1 shows typical triaxial compression undrained response of a saturated sand. The type o f response is mainly dependent on its initial state conveniently represented by  Chapter 2: Liquefaction of sands  9  • Phase Transformation  (8, - 8 ) 3  1 (<*', + d ' ) / 2 3  Figure 2.1 :  Typical undrained response o f sands under static loading.  Chapter 2: Liquefaction of sands  10  relative density and the associated confining and static shear stress levels prior to undrained shear. A t a given initial state the undrained behaviour may change from a type 1 to a type 3 with decreasing void ratio (i.e. with increasing relative density). A t loose void ratios, (or at high confining stresses) a sand may develop flow failure type o f deformation (type 1) due to strain softening, after mobilizing a peak strength at small strains (typically less than 1%).  Type 2  response signifies strain hardening following an initial strain softening. Sands exhibiting strain softening response (types 1 and 2) are often termed contractive. Those that respond in a strain hardening manner (type 3) are termed dilative. Castro (1969), Casagrande (1975) and Seed (1979) called type 1 strain softening response liquefaction, whilst C h e m (1985) termed it as true liquefaction. The characteristic feature o f this type o f response is continued unlimited unidirectional deformation at constant stresses and void ratio. This is called the steady state (SS) or flow deformation (Castro et al. 1982; V a i d and C h e m 1985). The constant shear stress at which the sand undergoes unlimited unidirectional strain is called the undrained steady state strength or residual strength. The type 2 strain softening response, which occurs over a limited strain range, transforms into strain hardening behaviour with further deformation. This type o f response has been termed limited liquefaction (Castro 1969). There exists a small range o f strain over which the sand may be considered to deform essentially at constant stresses and void ratio, much in the same manner as during steady state o f deformation. The instant o f the minimum undrained strength may be viewed as the occurrence o f a transient steady state as in type 1 response. This state has been labelled as quasi steady state (QSS) by Ishihara et al. (1975). The term phase transformation  Chapter 2: Liquefaction of sands  JT  (PT), corresponds to the instant at which the behaviour of the sand transforms from contractive into dilative (i.e the commencement o f decrease in excess pore pressure). Several studies have indicated that quasi steady state and phase transformation essentially occur at the same instant in sands that exhibit contractive behaviour (Vaid et al. 1990a, Ishihara 1993, V a i d and Thomas 1995). Type 3 strain hardening response is associated with dense sands, or even loose sands at low confining stresses. The sand develops large negative pore pressures following the initial positive values. The steady state concepts contend that in addition to type 1 that realises steady state, both type 2 and type 3 responses w i l l ultimately reach a steady state after all dilation is complete. However, this can occur only at very large strains, and only i f the back pressure is high enough to accommodate large negative pore pressures so that no pore water cavitation occurs. A t a given void ratio, the undrained behaviour o f sands has been noted to become more contractive with increasing confining stress. (Vaid and C h e m 1985, V a i d and Thomas 1995). A sand that is dilative or exhibiting type 2 response at a lower confining stress may transform into a type 1 response at higher confining stresses.  2.2.2  Cyclic triaxial behaviour  Most o f the initial understanding o f cyclic liquefaction has come from cyclic triaxial tests. Undrained cyclic loading causes a progressive pore pressure increase that may eventually lead to the development o f large cyclic shear strains. Different mechanisms that cause large deformations  Chapter 2: Liquefaction of sands  12  depending on the initial state of the sands have been identified by V a i d and Chern (1985). Typical mechanisms o f strain development are illustrated in Figure 2.2. The cyclic loading resistance in a triaxial test is defined as the uniform cyclic deviator stress amplitude required to cause a specified level o f strain in a specified number o f cycles, regardless o f the mechanism o f strain development.  2.2.2.1  Mechanisms of strain development  Large strains can develop during cyclic loading, either due to strain softening response or cyclic mobility (Castro 1969; V a i d and C h e m 1985). Deformation on account of liquefaction or limited liquefaction is characteristic o f statically strain softening sands only. O n the other hand, large strains in a dilative sand develop only on account o f cyclic mobility. The mechanism that is responsible for the deformation depends on the initial state (void ratio and the effective stresses among others) of the sand and the characteristics of the dynamic event. The initial development of strains is associated with stiffness degradation due to decreasing normal effective stress with cycles o f loading. Strains are small until the excess pore pressure ratio, defined as the ratio between the excess pore pressure developed and the initial effective confining stress, exceeds at least about 60% (Seed, 1979). True liquefaction can develop during cyclic loading in the same manner as during static loading for sands that exhibit type 1 response in static loading (Castro 1969, V a i d and C h e m 1985). This type o f deformation is illustrated in Figure 2.2(a).  Figure 2.2(a): Steady state o f deformation following strain softening under cyclic loading (After V a i d and Chem, 1985).  Chapter 2: Liquefaction of sands  14  Figure 2.2(b): Strain softening followed by cyclic mobility under cyclic undrained shear (After V a i d and Chem, 1985).  Chapter 2: Liquefaction of sands  15  Figure 2.2(c): Cyclic mobility with transient states of zero effective stress (After Vaid and Chern, 1985) "  Chapter 2: Liquefaction of sands  16  N  Figure 2.2(d):  Cyclic mobility without transient states of zero effective stress (After Vaid etal, 2000b)  Chapter 2: Liquefaction of sands  _17  A state of zero effective stress (i.e, 100% excess pore pressure) is never realised (not withstanding any subsequent unloading pulses following flow deformation), but unlimited unidirectional deformation occurs at a finite level of stresses. It is important to recognize that if the definition of liquefaction is based on 100% excess pore pressure criteria (as adopted by some researchers), then sands exhibiting this flow failure type of response would deemed to have not liquefied, even though this type of response is the most damaging. Large strains induced by limited flow deformation, as illustrated in Figure 2.2(b), are characteristic of sands exhibiting type 2 response in static loading. Following the occurrence of limited deformation due to strain softening within a certain cycle, continued cyclic loading causes further strain due to cyclic mobility. The cause of liquefaction in this type of response can therefore be both due to limited flow deformation and cyclic mobility. However, the cyclic deformation mechanism in sands, that is dilative in static loading, is always cyclic mobility (Figure 2.2c). The occurrence of transient states of zero effective stress is a must for the development of large deformations due to cyclic mobility. Whether it occurs or not, depends on the relative magnitudes of the of the static and cyclic shear stress amplitudes. Cyclic stress amplitudes that cause shear stress reversal are necessary for realizing transient states of zero effective stress. These occur at the instance when the net shear stress during the cyclic shearing becomes zero. If the initial static shear stress is larger then the cyclic shear stress amplitude, then deformation progresses due to cyclic mobility, but without transient states of zero effective stress as schematically illustrated in Figure 2.2(d). Strain development is gradual in this type of loading as there are no excursions through transient states of zero effective stress.  Chapter 2: Liquefaction of sands  2.2.2.2  18  Strain softening in cyclic loading  The deformation due to strain softening in cyclic loading is triggered in the same manner as in static loading, upon mobilizing the critical stress ratio noted under static loading. The sand strain softens until it reaches the steady/quasi steady state. If the response is of steady state type, unlimited unidirectional flow deformation occurs while the stress state stays stationary. O n the other hand, the stresses would start to increase as the stress state moves above the P T line, i f the response is o f the limited liquefaction type. Subsequent unloading from the peak imposed shear stress amplitude causes a large increase in pore pressure and generally brings the sand close to a state of transient zero effective stress. Further load-unload cycles take the sand through these transient states o f zero effective stress, which is responsible for additional accumulation o f strain. Castro and Poulos (1977) and V a i d and Chern (1985) have put forward the following criteria for the occurrence o f contractive deformation during cyclic loading. 1.  Sand must be contractive in static loading.  2.  The maximum shear stress must be greater than the steady state or quasi steady state undrained strength. Tstatic + Xcyclic ,. £ Su,mm  3.  There must be sufficient number of load cycles to lead the effective stress path to the C S R line.  Chapter 2: Liquefaction of sands  2.3  19  Anisotropy in sand deposits  In-situ sand masses are formed by the deposition o f discrete sand particles, often through water under gravity. The internal structure that ensues on such deposition has been found to be anisotropic on account o f both the formation process and the shape o f individual soil grains. A microscopic study o f the internal structure o f the sand assembly would be the direct means o f assessing the existence o f any anisotropy. This, however, is not often attempted, as it w i l l be quite tedious to quantify the results except on a statistical basis. The existence o f anisotropy is easily revealed by direction dependent mechanical behaviour o f sands. The anisotropy that is attributed to the formation process o f the sand deposit is termed "inherent anisotropy". The nature o f this anisotropy changes as the sand deforms under shear, and this has been termed "induced anisotropy" by Casagrande and Carrillo (1944).  These  definitions provide a convenient means o f classifying anisotropy, and have been further extended by several researchers (Arthur and Menzies 1972, Wong and Arthur 1985, Symes et al. 1988, Rothenburg and Barthurst 1989). Oda (1972) found that the preferred alignment of the longitudinal axis o f non spherical sand particles is often horizontal, and that the majority o f the contact normals are in the vertical direction o f deposition. These observations explain the fundamental reason for the anisotropic nature of sand deposits. The existence o f anisotropy in non-spherical particles is in fact due both to the preferred orientation o f the longitudinal axis and the directions o f the contact normals. Anisotropy in spherical particles is attributed to directions o f contact normals only (Oda 1981,  Chapter 2: Liquefaction of sands  20  Haruyama 1981, Shibuya and Hight 1987). The earliest revelations o f anisotropy in sands is based on consolidation o f specimens under a hydrostatic state o f stress. Both cubical (Kjellman 1936) and cylindrical triaxial (El-Sohby and Andrawes 1972) sand specimens have been used for this purpose. Deposition o f sand particles under gravity results in a cross anisotropic structure, with a horizontal plane o f isotropy. Existence o f this cross anisotropy has been demonstrated by Lade and Wasif (1988) and Yamadaand Ishihara (1979) using the true triaxial device. In-situ seismic wave velocity measurements in the horizontal and vertical planes by Stokoe et al. (1991) further reveal that the in-situ sand deposits are cross anisotropic. Larger radial strains than axial under hydrostatic compression is the most compelling evidence of anisotropy (El-Sohby and Andrawes 1972, Ladd et al. 1977, Yamada and Ishihara 1979, Sayao 1989). Induced anisotropy results from the changes in the spatial arrangement o f sand particles due to the applied stresses and the resulting deformations. Oda et al. (1985) found that the spatial arrangement o f sand grains and the void space within the structure o f the sand deposit undergo progressive changes when subjected to shearing stresses. They found that the concentration o f contact normals tends to increase i n the direction o f the major principal stress, and that sand particles align with their longitudinal axis along the minor principal stress. The fabric changes associated with stress/strain induced anisotropy is reported to be significantly influenced by the initial anisotropic fabric (Oda et al. 1978, El-Sohby et al. 1972).  Arthur et al (1980)  demonstrated that the anisotropy induced by drained pre-shear significantly influences the stiffness of the sand.  Chapter 2: Liquefaction of sands  The undrained behaviour o f sands under different loading modes also demonstrates the existence of inherent anisotropy (Symes et al. 1984, Kuerbis et al. 1988, V a i d et al. 1990a). The simplest manifestation o f its existence is the radically different response in undrained triaxial compression and extension for identical initial states. Induced anisotropy signifies that the fabric o f the sand continually evolves as the deformation progresses. It has been hypothesised that the superposition o f inherent and induced anisotropy is what eventually leads to the presumed steady state o f deformation, discussed later in this chapter.  2.3.1  Stress path dependent behaviour  Undrained behaviour o f sands is direction dependent on account o f the inherent anisotropy. However, as noted earlier, most o f our understanding o f the phenomenon o f liquefaction has stemmed from triaxial compression test results. This test represents the behaviour of sand along one specified stress path only. A sand, at a given initial state may be contractive in triaxial extension, yet much less contractive or even dilative in compression (Bishop 1971, M i u r a and Toki 1982, Chung 1985, V a i d et al. 1989). Several studies have shown that dilative strain hardening response may ensue even in the loosest state (Vaid et al. 1990a, V a i d and Thomas 1995) for sands deposited in water. The dramatic differences noted in Figure 2.3 are a clear reflection o f the stress path dependent undrained behaviour o f sands. Sands manifest different behaviour i n triaxial compression and extension on account o f the differences in major principal stress direction and the magnitude of intermediate principal stress  21_  22  Chapter 2: Liquefaction of sands  3 0 0 I-  03  Water pluviated Fraser River sand (Loosest Deposited)  150  ' = 100 3c  CN  kPa  a.  -300 -4  0  Axial strain, s a Figure 2.3 :  (%) v  '  Comparative triaxial compression and extension undrained behaviour of sands (After Vaid and Thomas, 1995)  parameter. The major principal stress acts vertically, perpendicular to the bedding planes, in triaxial compression (ct = 0°) but horizontally in triaxial extension (ct =90°), and the CT  a  intermediate principal stress is equal to the minor in compression, but major in extension. Hollow cylinder torsional shear tests, where the inclination of the major principal stress to vertical ct can a  Chapter 2: Liquefaction of sands  23  be independently controlled, reveal a systematic change in the undrained behaviour, from dilative to contractive, as a changes from 0 ° to 9 0 ° (Symes et al. 1984, Uthayakumar and V a i d 1998, c  Yoshimine et al. 1998). A systematic softening o f the loosest deposited Fraser River sand having identical intermediate stress parameter (b = 0) but different principal stress directions is shown in Figure 2.4. Similar stress path dependent volumetric strain behaviour is noted under drained shear (Symes et al. 1984, V a i d et al. 1990b). Stronger dilative response when a = 0 ° and 0  weaker response when a =90 ° are consistent with the findings o f Oda (1972) with regard to the c  contact normal densities.  Figure 2.4 :  Systematic softening in undrained behaviour with increasing a (After Uthayakumar and V a i d , 1998). a  Chapter 2: Liquefaction of sands  24  Arthur et al. (1980) pointed out that principal stress rotations occur in several in-situ loading paths. But, not much attention has been paid to the effects o f principal stress rotation on the deformation characteristics of the sand. Rotation of principal stresses in the vertical plane w i l l result in deformations on account o f the cross anisotropic nature o f sand deposits. Arthur et al (1979) reported that cyclic rotation of principal stresses resulted in continued strain accumulation. Shibuya and Hight (1989) have shown that a progressive increase in excess pore pressure would occur under constant magnitudes of principal stresses due to their mere rotation in an undrained state. The influence o f stress rotation has, however, been assessed at relatively high initial stress ratio, and contrasting observations have been reported in the literature (Symes et al. 1985, M i u r a et al. 1986b). Sayao (1989) and Wijewickreme (1990) have performed an extensive study on the influence o f principal stress rotation under drained conditions. In addition to the direction of the principal stresses, the intermediate stress parameter has been shown to influence the behaviour of sands (Symes et al. 1984, Wijewickreme 1990, Uthayakumar and V a i d 1998, Sayao and V a i d 1996). The behaviour is found to be stronger when b=0 (equal minor and intermediate principal stresses) than with b = 1 (equal major and intermediate principal stresses). Anisotropic nature o f sand deposits has been recognized for a long time. However, sands are often treated as isotropic in deformation or stability analyses to gain simplicity. Even though the recent attempts to model the sand as a cross anisotropic material is a significant improvement, most o f these methods still do not consider the influence o f principal stress rotation.  Chapter 2: Liquefaction of sands  2.3.2  25  The strain softening response  The peak shear stress state represents the onset o f strain softening response. The effective stress ratio at the instant o f peak shear stress has been termed as critical stress ratio ( C S R ) by V a i d and Chern (1983). The critical stress ratio is unique for a given water deposited sand in triaxial compression (Chern 1985, Chung 1985, and Kuerbis 1989). However, it depends on the deposition void ratio under triaxial extension (Vaid and Thomas 1995) and simple shear (Vaid and Sivathayalan 1996a).  Strain softening in simple shear and triaxial extension modes is  triggered at smaller values o f critical stress ratio compared to triaxial compression. Sladen et al. (1985) report that the critical stress ratio o f moist tamped sand varies with void ratio and confining stress level in triaxial compression. Further, the dependency o f critical stress ratio on the sample preparation technique has been reported by Kuerbis (1989) for a given triaxial loading mode. The strain softening deformation in cyclic loading has been shown to trigger at the same critical stress ratio noted under static loading (Vaid and Thomas 1995, V a i d et al. 2000b). Strain softening leading to true liquefaction type of response results in unlimited deformation at "steady state" represented by constant void ratio and stresses. However, strain softening is only temporary in the limited liquefaction type of response, and the sand strain hardens following the quasi steady state due to the development o f negative excess pore pressure on account o f dilation.  26  Chapter 2: Liquefaction of sands  2.3.3  The phase transformation and quasi-steady state  The state at which the response o f the sand transforms from contractive to dilative is termed phase transformation by Ishihara et al. (1975). This state coincides with the instant of maximum excess pore pressure. The effective stress ratio at phase transformation, and thus the mobilised friction angle (j) has been shown to be independent of the void ratio, confining stress level, and PT  mode o f loading (Vaid and Chern 1985, V a i d and Thomas 1995, V a i d and Sivathayalan 1996a) for water deposited sands. The m i n i m u m undrained strength in limited liquefaction type o f response occurs at or just prior to the phase transformation state (Vaid and Thomas 1995, Sukumaran et al. 1996). Chern (1985) has shown that the friction angle mobilised at steady state (in true liquefaction type o f response) is equal to the friction angle at phase transformation. The stress state i n such a response remains stationary on the PT/SS  line as the deformation progresses.  Based on  extensive test data on water deposited sands, V a i d and Chern (1985) have shown that both true liquefaction and limited liquefaction states can be treated within the same framework on the basis of the uniqueness o f the friction angle and the fact that they both correspond to the minimum undrained strength of the strain softening sand. In addition to being unique for a given sand, (j)  PX  has been found equal to the constant volume friction angle (|) under drained shear (Chern 1985, cv  Negussey et al. 1988). Negussey et al. (1988) have shown that <t)  PX/ss  is only dependent on soil  mineralogy, and is independent o f any other state variables whatsoever.  Chapter 2: Liquefaction of sands  2.3.4  27  Angle of maximum obliquity & Ultimate/Failure state  O n straining beyond the P T state, the effective stress path rapidly approaches the line o f maximum obliquity (i.e. the ultimate failure envelope; Figure 2.1). This line has also been shown to be unique for a given water deposited sand (Vaid and C h e m 1985, V a i d and Thomas 1995, V a i d and Sivathayalan 1996a). The corresponding mobilized friction angle <|> is about 3 to 4 ° 0  f  larger than §  P m s  for most sands. M i u r a and T o k i (1982), however, show that this angle increases  slightly with increasing density and is soil fabric dependent. Even though this angle remains essentially constant beyond the P T state, the shear strength o f the sand increases continually with increasing strain, on account of the negative pore pressures due to dilation. The recent treatment o f the undrained response o f sand in which the stress state at the end of the test is regarded as the steady state (Konrad and Pouliet 1997, Ishihara et al. 1998) is incorrect. It is necessary to recognize that end o f test state is arbitrary (Sivathayalan et al. 2000) and cannot be used in lieu o f the ultimate steady state that a sand is expected to attain after all dilation is complete.  2.3.5  Cyclic simple shear and triaxial behaviour  Because o f the inherent anisotropy in sands, its undrained behaviour is influenced both by the stress path and the loading system. The cyclic resistance o f sands is often assessed using cyclic triaxial, and to a lesser extent by the cyclic simple shear tests even though the latter closely simulates the loading conditions imposed by a vertically propagating shear wave due to an  Chapter 2: Liquefaction of sands  28  earthquake. Undrained cyclic triaxial tests have often been substituted for simple shear tests primarily because of their relative simplicity and widespread availability. The cyclic resistance measured in the triaxial test is then adjusted to the simple shear equivalent by utilizing empirical reduction factors (Seed and Peacock 1971, V a i d and Sivathayalan 1996a). The effective stress state both prior to and during shear loading differs between cyclic simple shear and cyclic triaxial tests (Figure 2.5). Initial stress state in simple shear is always K and 0  cyclic shear stresses are applied on the horizontal plane. Triaxial specimens can be either isotropically or anisotropical ly consolidated prior to undrained shear. The cyclic stress is imposed in the vertical direction, and the principal stresses remain fixed in the vertical and horizontal directions in a triaxial test. A n alternating triaxial compression and extension loading takes place every half cycle in specimens consolidated to an isotropic stress state, or to an anisotropic stress state with cyclic shear stress amplitude exceeding static shear. This results in 90° jump rotations in the direction o f major and minor principal stresses, and a jump between 0 and 1 in the intermediate principal stress parameter. Such jump rotations w i l l not occur, and intermediate principal stress w i l l stay equal to the minor, i f the initial static shear stress is greater than the cyclic. Simple shear loading in contrast causes continuous rotation o f principal stress directions symmetrically about the vertical axis. The maximum shear stress i n simple shear occurs on the horizontal plane (Roscoe 1970) whereas the maximum shear stress in the triaxial test occurs on planes oriented at 4 5 ° to vertical.  Chapter 2: Liquefaction of sands  29  cr  For +ive r. (a) Consolidation state CT,  \jpor -ive ^ =E =8 =0 y  (b) Cyclic shearing  Z  (c) Principal Stress Rotation  Cyclic Simple Shear  cr  J,cy  CT,  •3  b + O  (a) Consolidation  (b) cyclic shear  O  o,  (c) Principal stress jump rotation of 90°  Cyclic Triaxial  Figure 2.5 :  Stress conditions prior to and during undrained shear in triaxial and simple shear tests.  Chapter 2: Liquefaction of sands  30  The measure o f cyclic resistance in simple shear is the ratio (x /a ) between the applied cyclic cy  vc  shear stress amplitude and the initial normal effective stress CT . In triaxial the corresponding vc  resistance is taken as a  dcy  / ( 2 a ' ) , i.e. the maximum cyclic shear stress normalized by the initial 3c  effective minor consolidation stress. Peacock and Seed (1968) reported that for loose sands the (x /CT ) required to cause liquefaction in simple shear was merely 35% of ci /(2cy' )required i n cy  vc  d cy  3c  a triaxial test. Seed and Peacock (1971) introduced a factor C to be applied to the measured r  triaxial cyclic resistance for arriving at the cyclic stress ratio that would cause liquefaction under simple shear conditions i n field. Additional studies by Finn et al. (1971) led to a suggestion for the adoption o f C values o f 0.6 to 0.7. Figure 2.6 indicates that the conversion from cyclic r  triaxial resistance to cyclic simple shear resistance is not unique for a given sand, but depends on the confining stress level and the relative density of the sands (Vaid and Sivathayalan 1996a). The C at loose density states changes little with effective confining stress, and is as high as 0.80. r  However, for denser states it tends to increase with increasing confining stress, and is smaller than that corresponding to loose sands.  2.3.6  Fabric dependence of behaviour  The term "fabric" is used to refer to the structure o f the sand deposit that is represented by the spatial arrangement o f the solid particles and the associated void space (Brewer 1964). The mechanical behaviour of sands is highly dependent on the fabric that ensues upon the deposition process.  Oda (1972) was one o f the first researchers to observe that specimens formed by  31  Chapter 2: Liquefaction of sands  0.90 i  0.80  O"  h  0.70 h  0.60  -  •  0.50  1  1  1  Effective confining stress  Figure 2.6 :  1  1  200  0  1  400  o~' or o~' vc  3c  (kPa)  Ratio o f cyclic resistance i n simple shear to that in triaxial (After V a i d and Sivathayalan. 1996a).  different techniques yield different mechanical behaviour. He noted that specimens prepared at identical initial void ratios by a raining technique exhibited higher strength and stiffness than those formed by a rodding technique.  Different fabrics ensue depending upon the specimen  reconstitution technique adopted to prepare the sand specimen. This has been illustrated by Oda (1972) using microscopical analysis o f the structure o f the sand specimens reconstituted using different methods. The dependency o f the static undrained behaviour on the fabric o f the sand has been demonstrated by Ladd (1974) and M i u r a and T o k i (1982). Ladd (1977) and M u l i l i s et  32  Chapter 2: Liquefaction of sands  al (1977) have shown that the cyclic resistance o f sands is also highly dependent on the method o f specimen reconstitution. The anisotropic nature o f natural in-situ sands has been studied by Oda and Koishikawa (1977) and Oda et al. (1978). They studied the particle arrangements within the soils structure using optical microscope. Their results indicate that sand grains in the natural sand deposits have preferred particle alignment and contact normal density much in the same manner as described by Oda (1972) for reconstituted sands.  Oda et al. (1978) have demonstrated that the  "characteristics of the initial fabric of the granular sand are determined not only by the shape of constituting grain particles,  but also by the manner in which they are deposited".  The  anisotropic properties of in-situ sand deposits have rarely been demonstrated using its mechanical behaviour, because o f the difficulties involved in obtaining undisturbed sand specimens from insitu sand deposits. One of the main objectives o f laboratory tests is to characterize the in-situ response o f sands. Since different reconstitution techniques may yield drastically different mechanical behaviour in the laboratory, adoption o f a proper reconstitution method is critical. If laboratory studies are to be meaningful i n modelling the behaviour o f in-situ sands, then the objective o f the specimen reconstitution technique should be to duplicate the in-situ fabric o f the sand deposits. This can only be achieved by duplicating the process and environment in which the sand deposits are formed in-situ. Pluviation of sand particles in water simulates the alluvial deposition process and sands placed in hydraulic fills. Moist tamping techniques may simulate sands which have been compacted in such a manner while being placed in a given man made earth structure. However,  Chapter 2: Liquefaction of sands  33  it is necessary to recognize that soils are usually compacted at an optimum moisture content while being placed in an earth structure unlike in moist tamping. Moist tamping techniques often compact the sands at a lower water content i n order to produce loose void ratios on account o f the capillary forces. This often results in a collapsible "honeycomb" like structure (Casagrande 1975) in the moist tamped specimen. This casts serious doubts in the applicability of the results on moist tamped specimens even in compacted fills.  2.4  Critical/Steady state concepts  Poulos (1981) defined steady state as "the state of deformation for a mass of particles in which the mass is continuously deforming at constant volume, constant normal effective stress, constant shear stress and constant velocity". A special soil structure exists at the steady state that allows the soil to deform continuously at its minimum shear resistance with no volumetric or stress changes. Casagrande (1975) and Castro (1969) called such a structure as the "flow structure" for cohesionless soils. Normally, the steady state can be reached only after large strains (Poulos, 1981). Fabric changes during steady state are a special case o f induced anisotropy. During flow deformation, new particle contacts are formed and existing contacts are lost i n such a manner so as to maintain a statistically constant fabric. The critical state of sands is defined by Roscoe et al. (1958) as the state at which "the soil continues to deform at constant stress and constant void ratio" and is often determined from drained tests. Steady state is determined from undrained tests. Poulous et al. (1988), Been et al (1991) showthat critical and steady states are  Chapter 2: Liquefaction of sands  34  coincident, whereas test results by Castro (1969), Alarcon-Guzman et al (1988) show significant differences in the two states. Based on triaxial compression tests on moist tamped specimens, the normal effective stress and shear stress during steady state deformation have been shown to be uniquely related to the void ratio regardless o f the initial stress state (Castro 1969, Castro et al. 1982). The locus o f all possible steady states is the steady state line in three dimensional space comprising void ratio, normal effective stress and shear stress (Castro et al. 1982). It is often represented by its trace in two dimensional plots as shown in Figure 2.7. The behaviour of sand at a given initial state is considered to be governed by its position relative to the steady state line (Castro et al. 1982, Been etal. 1991). Triaxial compression tests on water deposited sands by V a i d and Chern (1985) show that the steady state line also encompasses the strain softening response of the limited liquefaction type. They contend that steady state and quasi steady state lines are identical i n triaxial compression loading. Uniqueness o f steady and quasi steady states in the effective stress space has been demonstrated by V a i d and co-workers and other researchers for several sands under a variety o f loading conditions (Vaid and Chern 1985, V a i d et al. 1990a, V a i d and Thomas 1995, V a i d and Sivathayalan 1996a, V a i d and Uthayakumar 1998, Mooney et al. 1998).  Ishihara (1993),  however, has shown that the quasi steady state line always lies below the steady state line but they come closer to each other as the confining stress decreases. The concept that a unique steady state dependent only upon the void ratio exists is quite attractive because it provides a fundamental framework for modelling sand behaviour. The  Chapter 2: Liquefaction of sands  35  Consolidation line (ICL)  Steady state line (SSL) P' = 1  P'  P\  s  *  ln(pO  q  p  Figure 2.7 :  The steady state approach o f characterising the behaviour o f sands  Chapter 2: Liquefaction of sands  36  notion of a unique steady state line is so appealing that it has been considered an axiom i n critical state numerical models (Graham and Hovan 1986, Jefferies 1993, Manzari and Dafalias 1997). Several researchers have promoted the idea o f the existence o f a unique steady state (Castro 1969, Castro etal. 1982, Ishihara etal. 1975, Been and Jefferies 1985, Been etal. 1991, Ishihara 1993, Ishihara et al. 1998). However, there is an extensive body of evidence in the literature that contradicts the notion of a unique steady state (Hanzawa 1980, M i u r a and T o k i 1982, V a i d et al. 1990a, DeGregorio 1990, Negussey and Islam 1994, V a i d and Thomas 1995, Riemer and Seed 1997, Mooney et al. 1998, V a i d et al. 1999). V a i d et al (1990a) have shown that stress path plays an important role in the mobilised steady state strength. They illustrated that sand at a given void ratio may strain soften and reach steady state in triaxial extension, but yet may strain harden in compression and w i l l mobilize steady state at much higher stresses. Test results in triaxial compression and extension (Vaid et al. 1990a, V a i d and Thomas 1995), simple shear (Vaid and Sivathayalan 1996a), hollow cylinder torsional shear (Uthayakumar and V a i d 1998), and plane strain compression (Mooney et al. 1998) clearly illustrate that steady state is not unique. These studies show that the steady state strength depends on the confining stress level and the loading mode at identical void ratio. The influence of the initial anisotropic consolidation stress state on the steady state strength is not well documented in the literature even though in-situ stress states are almost always anisotropic. Steady state i n strain softening specimens is normally realised within about 10% shear strain. However, dilative specimens w i l l not reach steady state until "all dilation is complete" (Poulous 1981). Several studies show that dilative specimens do not realise steady state even at strains as  Chapter 2: Liquefaction of sands  37  high as 25 to 30% (Vaid et al. 1990a, Ishihara 1993, Konrad and Pouliet 1997). N o laboratory apparatus is capable of straining the sand to the very high strain levels that are required to realise steady state in dilative sands, without causing excessive non uniformities. Further, attempting to treat the end o f test state as a characteristic state of the sand (Konrad and Pouliet 1997, Ishihara et al. 1998, Tsukamoto et al. 1998) is fallacious. E n d o f test state is arbitrary and has no physical meaning whatsoever. In recent studies, Tsukamoto et al. (1998), Ishihara et al. (1998) and Konrad and Pouliet (1998) suggested that fabric effects disappear at about 20% axial strain. Sivathayalan and V a i d (1999) pointed out that a careful examination o f the data presented by Konrad and Pouliet would in fact indicate that fabric effects are dominant even after 20% strain. The very large scatter (by a factor of about four in steady state strength) in the data of Tsukamoto et al. (1998) and Ishihara et al. (1998) arise on account o f the influence o f the loading mode (Sivathayalan et al. 2000). The minimum undrained strength and not the steady state strength is of concern in Engineering design. These two cases coincide for strain softening specimens o f type 1. However, type 2 strain softening specimens w i l l have a much smaller minimum strength (at quasi steady state) than their steady state strength. The observed non-uniqueness o f the steady state line has serious implications in the steady state concepts of design wherein a unique steady state line is assumed based on results o f triaxial compression tests only. Such an approach ignores the dependence o f the minimum undrained strength on the confining stress, loading mode, initial static shear and fabric. In a given field problem, variation of the minimum undrained strength, depending upon  Chapter 2: Liquefaction of sands  38  the effective stress state and loading mode must be taken into account for a rational assessment of the potential for a flow slide on a sloping ground.  2.5  The stress state in-situ  The preceding discussion clearly indicates that the response o f sands is direction dependent, and is influenced by the initial stress state. In-situ sands in nature are subject to a variety o f loading modes, superimposed on a generalised three dimensional initial stress state. Figure 2.8 illustrates the stress states to which a sand element in the field may be subjected prior to and during construction and performance. There w i l l be no shear stresses on the horizontal plane, and hence the maj or principal stress w i l l act vertically downwards in a sand element under flat ground (Figure 2.8a). The construction o f an earth structure close by, (e.g., buildings, dams etc.), may induce shear stresses on the horizontal plane, ultimately resulting in a new stress state as shown in Figure 2.8(b). The effect o f shear stresses on the horizontal plane is to rotate the direction o f principal stresses. The inclination o f the major principal stresses to vertical depends on the relative values of the shear stress on the horizontal plane and the vertical stress. A n y undrained stress increment, due either to static or dynamic loading, w i l l now be superimposed on this stress state (Figure 2.8c). This often w i l l result i n rotation of principal stress directions in addition to an increase in deviator stress. This is illustrated in the Figure only in one plane for simplicity, but such generalised loading may occur in all three planes.  Chapter 2: Liquefaction of sands  (a): Initial stress state 7777  (c): stress state during undrained shear  Figure 2.8 :  Stress state o f soil elements in-situ.  39  40  Chapter 2: Liquefaction of sands  Further, the direction of principal stresses and the initial stress state w i l l possibly vary along a potential failure surface in-situ. The direction o f major principal stress w i l l often vary from about 0 ° at the top o f the failure surface to about 9 0 ° at the bottom. This type o f generalised stress state w i l l often be the rule rather than the exception in-situ. Numerical analysis o f the effective stress states and deformations o f the J-pit embankment in the C A N L E X project indicated that stress rotation as much as 60° w i l l be encountered i n the dam during construction and performance (Puebla, 1998). It also indicated that depending on the initial effective stress state, the stress rotation due to subsequent loading may either increase a or decrease it. a  It is evident that most o f the in-situ stress states are three dimensional and subject to stress rotation. Nonetheless, most o f our understanding o f the behaviour o f sands has been derived from tests on isotropically consolidated triaxial specimens under fixed principal stress directions. This was on account o f the earlier presumption, based on the steady state concepts, that the response o f sands is dependent only on the effective confining stress. However, as noted earlier several researchers have since then published results to the contrary. Triaxial compression, extension and simple shear represent specific loading modes and thus cannot be regarded as representative o f all the possible spectrum of responses. The undrained behaviour o f sands has invariably been assessed under hydrostatic, and to a lesser extent under axisymmetric consolidation stresses. Even though the influence of initial static shear ( K consolidation) has been 0  recognized by several researchers (Vaid and Chern 1983, Seed and Harder 1990, V a i d et al 2000b), no attempts have been made so far to assess the influence o f non axisymmetrical initial static stress state.  Chapter 2: Liquefaction of sands  41  The initial effective stress state o f the sand, characterized by the three principal stresses and the direction o f the major principal stress a  CTC  is represented by the effective mean normal stress  a' , the intermediate stress parameter b , and the ratio of major to minor principal stress K and mc  a  c  c  in this thesis for convenience. The hollow cylinder torsional shear device allows independent  a c  control o f each o f these four parameters.  2.6  Research Needs  The stress path dependency o f the undrained behaviour o f sands is widely recognized, primarily from comparative undrained triaxial compression and extension behaviour o f water deposited sands (Vaid et al. 1990a, Riemer and Seed 1997). This occurs on account o f the inherent anisotropy present i n sand deposits.  Our understanding is based on specimens  reconstituted i n the laboratory, and no direct evidence o f direction dependent mechanical behaviour o f natural in-situ sands is available in the literature. In addition to the stress path during undrained shear, the initial effective stress state prior to undrained shear plays an important role in the subsequent undrained response o f the sand. The effect o f initial effective stress state has been studied using anisotropically consolidated sands, but only in triaxial compression. To the knowledge of the author, the influence o f initial non axisymmetric effective stress states has not been studied, despite the fact that the effective stress conditions in embankments, and slopes prior to undrained shear is non axisymmetric, and these are the structures that are most prone to flow failure.  42  Chapter 2: Liquefaction of sands  Undrained principal stress rotation at constant magnitudes of principal stresses induces excess pore pressure, and eventually large deformations. The liquefaction susceptibility due to stress rotation is dependent on the initial stress state and the sense o f loading under non axisymmetric initial stress states; upstream loading decreases a and downstream loading increases a . Little CT  CT  systematic research has been carried out to assess the influence of stress rotation on the undrained behaviour o f sands, and no data exist on the effects o f the sense o f loading. It has been recognized that not all laboratory reconstitution techniques produce the same fabric. A s a result, the undrained behaviour o f sands vary widely depending on the method o f specimen reconstitution in the laboratory (Mulilis et al 1977, Ladd 1977, M i u r a and Toki 1982), and this often has been cited to discourage the direct application o f laboratory test data to sands in-situ.  However, no attempts have been made to assess the comparative behaviour o f  undisturbed in-situ sands, with reconstituted specimens, in order to evaluate the applicability o f reconstitution methods, except for the microscopical studies o f Oda (1972). Post liquefaction stress-strain behaviour is the primary input in assessing liquefaction induced displacements. Current analytical methods, often rely on empirical data to determine the post liquefaction stiffness and strength of a sand. The little systematic research carried out on the post liquefaction behaviour o f sands, indicates that the stiffness increases with strain, and that the virgin minimum undrained strength is not a limiting strength on post liquefaction loading. However, no data on the post liquefaction behaviour o f in-situ sand deposits is available The research reported herein is an attempt to address some of the above concerns. The static undrained behaviour o f specimens reconstituted by different techniques were compared i n order  Chapter 2: Liquefaction of sands  43  to demonstrate the influence o f fabric. These tests were carried out in triaxial and simple shear, and it is shown the domain o f accessible states is dependent on the method o f reconstitution. A loose void ratio at a given confining stress that is accessible in the laboratory by a certain method of reconstitution may not even be accessible to the natural sand in-situ. Therefore, the relevance of the behaviour o f such specimens to the field sands is highly questionable. Extreme care was taken in the laboratory testing to minimize any apparatus specimen interactions, in order to ensure high quality and reliability of the data. The effects o f membrane penetration, on the drained and undrained response was comprehensively assessed and eliminated i f necessary. The test techniques yield excellent repeatability and therefore very high confidence in the measured data. Undisturbed in-situ frozen sands are tested in triaxial compression, extension and simple shear in order to explore the stress path dependent undrained behaviour of natural in-situ sands. These sands are tested under static, cyclic and post liquefaction loading, and their response is compared with reconstituted counterparts.  A comparison o f the behaviour o f water pluviated and  undisturbed sands under is made in static, cyclic and post liquefaction loading. This is attempted to evaluate the applicability o f laboratory tests on reconstituted specimens, to the sand in-situ. The influence o f initial effective stress state prior to undrained shear, on the subsequent behaviour o f sands is demonstrated using specimens consolidated to non axisymmetric effective stress states, with varying a and K . Water pluviation was chosen as the method o f specimen c  c  reconstitution in these tests, because it duplicates the deposition process in an alluvial environment. In-situ stress states are often non axisymmetric, and therefore an understanding o f  Chapter 2: Liquefaction of sands  44  the undrained behaviour under these conditions is essential for successfully characterizing the behaviour of in-situ sands. The effect of principal stress rotation leading to liquefaction and its dependency on the initial stress state are assessed. These tests explore the uniqueness, or lack thereof, of the steady state line. This thesis comprehensively addresses these critical issues, and hopefully, the findings will inspire more rational methods of analysis and design, and better our understanding of the liquefaction phenomena.  Chapter 3  Experimentation and Test Apparatus  3.1  Introduction  Triaxial, simple shear and hollow cylinder torsional shear devices have been used in this study to assess the undrained behaviour o f sands. Because o f the non linear and anisotropic nature o f soils, the usage o f different test apparatus becomes essential in order to assess their response under different stress systems and loading paths anticipated in field problems. The triaxial apparatus is limited only to axisymmetric stress states in compression and extension loading. The simple shear apparatus applies plane strain loading in one horizontal direction, and enforces zero extension in the other perpendicular horizontal direction. It also imposes uncontrolled principal stress rotation during loading. The hollow cylinder torsional ( H C T ) device is more versatile because it can apply a variety o f loading paths, including controlled principal stress rotation in one plane. The H C T device, however, has seen only a limited use in soil testing, primarily because o f the complexities o f the apparatus and test procedures. The behaviour o f soils is traditionally assessed using cylindrical specimens in the triaxial devices. The simple shear device, though more complex than triaxial, is most suitable to assess the cyclic resistance o f sands, because it closely simulates the loading caused by the vertically 45  Chapter 3: Experimentation and Test apparatus  46  propagating shear waves i n an earthquake. The configuration and capabilities o f each testing device used in this study are briefly described in the following sections. A detailed description can be seen elsewhere (Sayao 1989, Sivathayalan 1994, Thomas 1992).  3.2  Laboratory shear testing of soils  The objective o f laboratory shear tests is to characterize the behaviour of the soil element insitu.  A n y parameter that affects the response o f the soil in-situ should be appropriately  represented in the laboratory test. The entire soil specimen in the laboratory represents a single point in the soil mass in-situ and thus all laboratory tests must be element tests. Laboratory test results can be properly interpreted only i f the test remains an element test, and this demands a homogeneous specimen subjected to uniform stress state. The attempts to characterize different in-situ conditions have led to the use o f several soil testing devices, that can often be conveniently categorized as axisymmetric, plane strain or multi axial. A typical triaxial device uses a cylindrical specimen, and only the vertical and horizontal normal stresses can be controlled in this device. The axisymmetric geometry forces two o f the three principal stresses to be equal at all times. Bishop and Henkel (1962) excellently detail all aspects o f the triaxial test. Plane strain devices have gained considerable prominence because field conditions are often o f the plane strain type. The simple shear device (Kjellman 1951, Roscoe 1953, Bjerrum and Landva 1966) is one o f the most commonly used plane strain apparatus. Normal and shear stresses are applied in the horizontal plane o f the laterally confined  Chapter 3: Experimentation and Test apparatus  47  simple shear specimen. The stress conditions lead to principal stresses inclined at 45 ° to the vertical, and the direction o f the principal stresses cannot be independently controlled in a simple shear device. The directional shear cell (Arthur et al. 1981) is a plane strain device that allows controlled rotation o f principal stress directions. Annular and hollow cylindrical specimens have been used in shear testing o f soils since the early days (Cooling and Smith 1936, Hvorslev 1939). The currently used hollow cylinder torsional shear device is an evolution of these early devices, and it allows independent control o f the magnitudes of the principal stresses and their directions. This enables the device to follow any complex stress path and makes this one o f the most versatile soil testing devices. Saada and Townsend (1981) provide a detailed discussion of the advantages and limitations of various soil testing devices. Triaxial, simple shear and hollow cylinder torsional shear devices were used in the investigations undertaken herein.  3.2.1  The triaxial test  Most o f our understanding o f soil behaviour has come from controlled laboratory tests in the conventional triaxial test. Cylindrical specimens, with a height to diameter ratio o f at least two are subjected to axisymmetric loading in this test. Only compression tests where the major principal stress acts vertically and extension loading with major principal stress acting horizontally can be simulated i n a triaxial test. The major and minor principal stress magnitudes can be controlled, and the intermediate principal stress equals either the minor principal stress in a  Chapter 3: Experimentation and Test apparatus  48  compression test, or the major principal stress i n an extension test. The principal stresses in this test remain fixed in the vertical and horizontal directions at all times. A true triaxial device enables independent control o f the magnitude o f each o f the three principal stresses ( K o and Scott 1967, Arthur and Menzies 1968, Pearce 1971, Green 1971). However, their direction cannot be arbitrarily controlled. Principal stress directions are aligned with the specimen axis and only 90° jump rotations can be simulated. This is because only normal stresses can be applied on the prismatic boundaries o f the specimen. End restraint due to frictional platens in the conventional triaxial test causes progressive stress and strain non-uniformities within the specimen with increasing deformation.  This then  compromises the presumed equality of radial and tangential stresses and strains at larger strains (Casbarian and Jamal 1963, Frydman et al 1971), and introduces uncertainty in the interpretation o f the results as an element test. Lubricated end platens and free ends (Rowe and Barden 1964) have been used as means o f reducing the end restraint effects. Their usage, however, introduces bedding errors i n deformation measurements.  3.2.1.1  The UBC triaxial apparatus  A schematic diagram o f the U B C triaxial apparatus is shown in Figure 3.1.  Cylindrical  specimens o f 60mm nominal diameter and 120mm nominal height were used. A n external load cell is used to measure the axial deviatoric load, together with an essentially frictionless, continually air leaking seal on the loading ram. The cell pressure and the pore pressure are  49  Chapter 3: Experimentation and Test apparatus  XL  Motor Controller  LEGEND  NT  electro-pneumatic transducer  (R)  Pressure regulator  Q  Pressure Transducer  Water reservior Double acting piston  Differential Pressure Transducer LVDT  Data acquisition f and o control system < Q .  Personal Computer  Figure 3.1 : Schematic diagram of the U B C static/cyclic triaxial device  50  Chapter 3: Experimentation and Test apparatus  measured with pressure transducers, the volume changes o f the specimen by a differential pressure transducer, and the axial displacement by a displacement transducer. The deviatoric stress to the specimen can be applied either stress controlled by the double acting pneumatic piston or with displacement control by the variable speed motor drive connected in series with the piston. Thus, this apparatus can perform loading compression tests or unloading extension tests. The electro-pneumatic transducer connected to one chamber o f the double acting piston is controlled by the computer. This enables automated anisotropic consolidation prior to static or cyclic shear loading.  3.2.2  The simple shear test  The specimen geometry o f the simple shear specimen is either cubical or cylindrical. The horizontal normal strain components e and s are zero in this test on account o f the enforced x  y  parallel lateral boundaries. Consolidation prior to shear is one dimensional, and corresponds to the K condition. Constant volume conditions are enforced to simulate undrained shear by 0  arresting the vertical displacement and thus forcing the vertical strain e to be zero. The reduction z  in vertical stressCT in such a constant volume test then equals the excess pore pressure developed v  in an equivalent undrained test (Dyvik et al. 1987). The average boundary normal and shear stresses are the only measured stress components in a simple shear test. These are not sufficient to completely prescribe the state o f stress within the specimen. Studies in hollow cylinder torsional shear (Uthayakumar 1996) and highly instrumented Cambridge cuboidal simple shear  Chapter 3: Experimentation and Test apparatus  51  device (Roscoe, 1970) have shown that the horizontal plane i n simple shear is the plane o f maximum shear stress. Thus, the principal stresses are inclined at 45° to the vertical axis o f symmetry.  The measured normal and shear stresses together with the knowledge that the  principal stresses are inclined at 45° to the axis of symmetry, enables a complete definition of the plane strain state o f stress. It is recognized that the absence o f complementary shear stresses on the vertical boundaries, results in non uniform normal and shear stress distribution on the horizontal plane i n the simple shear specimen. However, these non uniformities are severe only at the edges (Duncan and Dunlop 1969, Cole 1967, Finn et al. 1978, DeGroot et al. 1994). In fact, detailed measurements o f the normal and shear stresses using several contact transducers on the specimen boundaries at Cambridge has shown that the stress conditions in the middle third o f the specimen are fairly uniform and their magnitude approximately equals the average boundary stresses (Cole 1967, Airey et al. 1985). Airey et al. (1985) found that a low specimen height to diameter ratio reduces stress non uniformities considerably. Further Duncan and Dunlop (1969) reported that''the stress  non uniformities have little effect on the ultimate shear resistance of soils, and it is sufficiently accurate to use the average stress conditions for test interpretations". Notwithstanding the concerns of stress uniformities, the simple shear test is very attractive i n practical applications on account o f its ability to closely model the upward propagation of shear waves during an earthquake.  Chapter 3: Experimentation and Test apparatus  3.2.2.1  52  The UBC simple shear apparatus  The simple shear apparatus used in this study was o f the N G I type (Bjerrum and Landva, 1966). A'cylindrical soil specimen is laterally confined by a steel reinforced rubber membrane in this apparatus (Figure 3.2).  Since the reinforcement enforces an essentially constant cross  sectional area, arresting the vertical displacement simulates constant volume conditions.  A  schematic diagram o f the simple shear apparatus is shown in Figure 3.3. A single acting air piston applies the vertical load to the sample. The horizontal shear stress can be applied either by the double acting pneumatic piston for stress controlled or by the variable speed motor drive for strain controlled loading. The loading mechanism is essentially identical to that in the triaxial apparatus and permits switching to displacement controlled from stress controlled loading during  Figure 3.2 :  Specimen and loading arrangement in U B C simple shear apparatus  Chapter 3: Experimentation and Test apparatus  53  rn rn  Chapter 3: Experimentation and Test apparatus  54  a test. The normal and shear stresses are measured by the vertical and horizontal load cell. Vertical strain, which equals the volumetric strain is monitored by a vertical displacement transducer. The shear strain is measured by horizontally positioned displacement transducers. Two L V D T s were used in the horizontal direction in order to increase the available displacement range and yet to have high measurement resolution at low strain levels. Cyclic loading was applied by changing the pressure in one of the two chambers o f the double acting piston, using an electro-pneumatic transducer.  The electro pneumatic transducer is  controlled by a computer. A n air volume booster is connected to the chambers o f the double acting piston in order to maintain a constant amplitude o f cyclic shear stress when large deformations occur due to liquefaction. Both undisturbed in-situ frozen and reconstituted sand specimens were tested i n order to assess their monotonic, cyclic and post liquefaction response. Pre and post liquefaction monotonic tests were performed under the displacement control whereas cyclic loading performed under stress control.  3.2.3  The Hollow Cylinder Torsion (HCT) test  Thin walled hollow cylindrical soils specimens subject to confining pressure on both inside and outside the cylindrical boundaries, together with torsional shear stress on the horizontal plane allow controlled shear loading including principal stress rotation under multi-axial stress states. The H C T device can impose deviatoric stresses on the specimen by changing the vertical stress, the torsional shear stress on the horizontal plane or by a combination o f these two. The control  Chapter 3: Experimentation and Test apparatus  55  o f internal and external confining pressures, vertical stress and torsional shear stress allows independent control o f the principal stresses and their rotation. Earlier H C T devices used equal internal and external pressure for specimen confinement. However, the ability to apply different values o f internal and external pressures is required to independently control the direction o f principal stresses. The H C T test is frequently subject to criticism on account of the non uniform stresses across the wall of the specimen when different internal and external pressures are used. The uniformity o f the stresses depends on the specimen geometry, and the H C T devices are designed to minimize the stress non-uniformities. Thin walled specimens, with large radius and a height to external diameter ratio o f about two result in minimal stress non uniformities (Hight et al. 1983, Saada 1988, Sayao 1989, V a i d et al. 1990b).  3.2.3.1  The UBC hollow cylinder torsion device  A schematic diagram of the U B C H C T device is shown in Figure 3.4.  The specimen  dimensions were adopted so as to minimize the stress non uniformities (Sayao 1989). Several modifications have been made to the original device designed in 1986 in order to facilitate strain controlled testing (Wijewickreme 1990) and combined stress and strain controlled loading (Uthayakumar 1996). Detailed description o f this device is given in Sayao (1989) and V a i d et al (1990b), and only the modifications made during the course o f this research are detailed following a description o f the apparatus.  Chapter 3: Experimentation and Test apparatus  56  I*  3  Pe  Co  >  C  Do U E  &<S 2.  J  1  H  J 1  T  o  >  <L> 13  /  on  -...I  C  —  c 3  , <L>  >3  ,o S-H  O *J |H  '2  §  <D T3 _C  T» o o  u <u o  CJ  rn  Chapter 3: Experimentation and Test apparatus  .  57  The nominal internal and external diameters of the specimen are 10 cm and 15 cm respectively, and the height to diameter ratio o f the specimen is two. The domain o f stresses that can be explored without causing excessive stress non-uniformities were delineated by considering appropriate stress strain characteristics o f sands (Wijewickreme and V a i d 1991). The stresses are applied by stepper motor driven precision regulators and/or stepper motor driven water saturated pistons called digital volume-pressure controllers (or D V P C s ) . Independent control o f four o f these stresses yield independent control o f the principal stresses (a  l 9  cr , a ) and their direction (cc ) in one plane. For testing purposes, these four independent 2  3  CT  parameters are alternatively expressed in terms of the derived stress parameters a ' , a , K and b. m  The usage o f D V P C s i n soil testing has been pioneered by Menzies (1988).  c  It enables  predetermined volumes o f water to be injected into or withdrawn out o f the loading piston, and thus provides a convenient means o f applying displacement controlled loading. Such a system does not suffer from the large compliance that is endemic i n traditional motor driven gear systems. The specimen is fixed at the top loading cap, and the vertical load is applied by a double acting piston mounted at the bottom of the loading frame. The water saturated bottom chamber o f the piston is connected to the vertical loading arrangement as shown i n the inset in Figure 3.4. This enables the application o f stress controlled loading during consolidation, by the stepper motor driven regulators and subsequent strain controlled loading by the D V P C s . Torsional shear is applied by means o f four single acting pistons. T w o o f these pistons are water saturated and connected to a loading arrangement similar to that o f the vertical piston and  Chapter 3: Experimentation and Test apparatus  58  the other two are used for balancing. The torque is generated by the differential pressures in the piston pairs and transmitted to the specimen by cables and pulleys. The entire torsional loading system is mounted on the axial loading shaft and moves up or down with the sample deformation. This eliminates any vertical or horizontal forces on the loading shaft compared to the case o f a fixed system. The torsional shear is transmitted to the specimen by twelve 1mm thick and 2mm high radial ribs that are equally spaced on the loading platen. Six equally spaced porous stones that cover only about 8% o f the specimen area provide drainage to the specimen. The radial restraint is minimized by using polished anodized aluminum end platens together with porous stones that cover only a small fraction o f the area o f the specimen. The positioning o f the porous stones and the radial ribs is shown in Figure 3.5. The bottom drainage line is connected to a burette and the top drainage to a burette and a D V P C , as illustrated in Figure 3.6.  This enables application o f back pressure with a regulator, or  alternatively the control o f the volumetric strain o f the specimen by the D V P C .  These are  necessary in strain path controlled tests, as well as for compensation o f membrane penetration induced volume changes in undrained tests. Internal and external cell pressures and the back pressure to the membrane lined, soil specimen are applied through air water interfaces. A i r diffusion into soil specimen or cell is minimized by using long narrow bore diffusion coils (Chern 1985, Sayao 1989). The internal and external cell pressures are controlled by stepper motor controlled precision regulators, and the back pressure is applied manually using a precision regulator. The pressure transducers are mounted close to the cell and specimen in order to minimize compliance effects. The vertical load on the specimen  Chapter 3: Experimentation and Test apparatus  59  Porous stones Drainage passage  Figure 3.5 :  Arrangement o f porous stones, shear ribs and drainage passage i n H C T loading cap  60  Chapter 3: Experimentation and Test apparatus  Top Drainage  LEGEND ®  Valve  —;  O  OS  D  1  8.  Bottom Drainage DVPC Figure 3.6 : Schematic arrangement o f pore water drainage in an H C T specimen  is measured by the external load cell placed at the bottom of the loading shaft and is appropriately corrected for shaft friction. The torque is measured using a torque cell placed above the torque pulley. Careful design o f the torque cell has resulted in negligible amount o f cross talk between the vertical load and torque. Four deformation components are measured in the U B C H C T device. A linear variable displacement transformer ( L V D T ) measures the axial strain, and a rotating arm connected to the loading shaft converts the rotation o f the base platen into linear tangential displacement, and enables another L V D T to measure the angular displacement and hence the shear strain. The latter L V D T is mounted at a sufficiently large distance away from the loading shaft in order to avoid  61  Chapter 3: Experimentation and Test apparatus  necessitating corrections in the measured tangential displacement due to the vertical movement o f the rotating arm (Figure 3.7).  The volume change o f the specimen is recorded using a  differential pressure transducer (DPT) and a pipette, and o f the inner chamber by another D P T . A l l volume measurements are corrected for membrane penetration effects, i f applicable, before computing the strain components.  Stresses and strains in an HCT specimen  3.2.3.2  The average stress state in an H C T specimen is computed from the measured vertical load ( F J , Torque in the horizontal plane (T ), internal cell pressure (P ) and the external cell pressure (P ). h  f  e  Figure 3.8 shows the boundary forces acting on an H C T specimen together with the stresses i n the wall element. The stress state in the element is expressed in terms o f vertical (CJ ), radial (a ) z  and tangential (cx ) normal stresses and shear stress T . e  z 6  r  The test interpretation is made by  considering the entire specimen as an element deforming as a right cylinder. Since the magnitudes of G , CT and x r  9  z6  vary across the thickness o f the wall, average representative values are  calculated. The stress state in a thick cylinder subject to internal and external pressures, axial and torsional shear loads cannot be completely solved by equilibrium considerations alone. It, in addition, requires a knowledge of the constitutive behaviour of the cylinder material. The vertical stress CT , Z  however, is independent of the material constitutive behaviour, and can be directly obtained from  62  Chapter 3: Experimentation and Test apparatus  the measured vertical load and the cross sectional area of the specimen, with appropriate corrections.  Soil specimen  <  Figure 3.7 :  loading shaft  Counter Weight  Schematic arrangement of the torsional displacement measuring system in the UBC hollow cylinder torsional shear device.  Principal stresses  „  do\ , dr  de /  Stresses acting on an element Figure 3.8 :  Displacement in Horizontal plane  Stresses and strains i n a hollow cylindrical soil element  Chapter 3: Experimentation and Test apparatus  64  Different approaches o f solving the mechanics o f the thick cylinder geometry have resulted in different equations for a , a and T r  e  . These stresses were calculated by Symes et al. (1985) and  z 6  V a i d et al. (1990b) by considering the material to be linearly elastic. The radial and tangential stresses at any radius r are then given by  °  r ( a t r = R )  ~  R -R 2  (R -  2  2  e  2  2  P^-Pj.r ° 9 (at r = R)  ,  R -R 2  2 R i  2  R  2  (3-1)  2  (P.-PJ.R^.R? j _  2  ,  )  +  7  ?  (R ~Rj)  2  2  ' ™ 2 r  where R , R are the internal and external radii respectively o f the specimen. V a i d et al. (  e  (1990b) consider the equilibrium o f forces to arrive at the average a andCT , whereas Symes et r  9  al. (1985) use the average o f the individual stresses as shown in equation 3.2.  fo.dr Symes et al. (1988): a  =  r  J  fdr  (3.2) jjo. Vaid et al. (19906):  rdQ. dr  o  r  rdQ .dr  M i u r a et al. (1986a) calculated the average stresses assuming a linear variation across the walls. Figure 3.9 shows that differences among the average values o f stresses calculated by different methods are relatively minor. The following set of expressions proposed by V a i d et al. (1990b), based on their merit of satisfying the force equilibrium are used in this thesis to calculate the stresses.  Chapter 3: Experimentation and Test apparatus  F O"  Z  +  rt.(P .R E  65  P,.R )  E +  I  =  TC(R -R ) 2  a.  (P .R  2  E  e  2  - i- i ) p  R  2.(P -P )R R, ln(R /R ))  2  2  E  J  (R -Ri ) 2  (R  2  e  ( P ^ - P ^ R (R  2 E  2  )  2  e  -R, ) 2  I  2  2  i  (3.3)  e  (R -Ri ) 2  2  H  2 E  E  2.(P -P )R R ln(R /R))  +  -R )  4.T .(R  2  E  2  2  e  3 E  -R  3 I  )  ••zB STCCR'-R^.CR'-R ) 2  The average strain components are calculated assuming linear variation of displacement across the wall o f the specimen. This assumption is consistent with the presumed linear elastic response in calculating the stresses, and yields the following expressions. Ah h  1  AR -AR^ e  (3.4) A Re + R, A R ,\ R  /  Yz6  Where  (  +  2A6(R  3 e  -R, ) 3  N  3h(R -R, ) j 2  2  e  A h and A0 are the axial displacement and the angular rotation, h is the height,  and  ARj and A R are the change i n the internal and external radii respectively. e  66  Chapter 3: Experimentation and Test apparatus  220  1  8  I  0  ,  1  180  1  200  1  i  220  180  1  int  Figure 3.9 :  1  1  200  220  ext  Comparison of different approaches to find representative stresses in a hollow cylindrical soil element.  The change in the inner chamber radius AR; is calculated from the measured volume change of the inner chamber and the axial deformation Ah. The change in the external radius AR is then e  calculated using A , Ah and the volume change of the specimen. R j  The absence of shear stresses in the r#and rz planes makes the radial stress a a principal r  stress. Often cr is the intermediate principal stress. The major and minor principal stresses can r  then be computedfromCT , a and x . The principal strains are also computed in the similar z  manner.  9  z6  Chapter 3: Experimentation and Test apparatus  3.3  67  Data acquisition and control systems  A l l three shear testing devices used in this study use sophisticated, high speed data acquisition and control systems. Data in simple shear tests is gathered using a PCL718x, 12-bit high speed data acquisition card. This data acquisition card has eight analog to digital (A/D) input channels and two digital to analog ( D / A ) output channels. Five o f the A / D channels are used in simple shear for transducer input; one each for vertical and horizontal load cells, one for vertical displacement transducer ( L V D T ) and two for horizontal displacement transducers. T w o L V D T s are used to measure the horizontal displacement in order to have a larger range, and still retain higher measurement resolution at small strain levels. One of the D / A channels is used to control the electro pneumatic transducer and the other the motor drive. The data acquisition system is capable o f gathering about 6000 data sets per second. The gathered data is averaged over sixty readings by the data acquisition program in order to reduce the electrical noise that is inherently present in the 60Hz a.c electrical supply. Both the triaxial and hollow cylinder torsional shear devices use "National Instrument ATMI016x" 16-bit high speed data acquisition card for signal input. This data acquisition card in the triaxial apparatus is set up to use eight double-ended A / D input channels and two D / A output channels. Five o f the A / D channels are used for transducer input in the triaxial test; two for pressure transducers and one each for the axial load, axial displacement and the specimen volume change. One D / A channel of this card is used i n the triaxial test to control the electro pneumatic transducer to facilitate anisotropic consolidation, and cyclic loading. The full scale range of each  Chapter 3: Experimentation and Test apparatus  68  of the channels in this card is dynamically controlled in real time using software in order to improve the measurement resolution. This system scans about 3000 data sets per second, and sixty readings are averaged to filter out the noise in the input signals. The horizontal effective stress in the triaxial test is calculated from the pressure transducer readings, and the deviatoric stress from the load cell reading. A x i a l and volumetric strains are calculated from the L V D T and D P T respectively. The radial strains are calculated from the volumetric strain (zero during undrained shear) and the axial strain, since axisymmetric conditions prevail in a triaxial test. In addition to the "National Instrument "AT-MIO-16X" data acquisition card for A / D input, a 16 bit three channel D / A "Vexta Indexer" card for controlling the D V P C s and a 15 bitequivalent, four channel D / A card for controlling the stepper motor regulators are used in a hollow cylinder test. A l l three o f these cards are used in conjunction i n real time to control the surface tractions and/or the strains in order to follow the prescribed stress/strain path. Nine o f the sixteen single ended A / D channels in the A T - M I O l O x card are used to read input from the three pressure transducers, two differential pressure transducers, two L V D T s , a load cell and a torque cell. A l l transducer signals are filtered using a signal conditioner before being fed into the A / D card. The signal conditioners are designed and built in house in the electronics workshop i n the department. About fifty sets o f data can be gathered by the software after averaging sixty scans in order to enhance the resolution o f the measurements.  69  Chapter 3: Experimentation and Test apparatus  3.3.1  Measurement resolutions  The high resolution, high speed data acquisition system enabled confident measurement of stresses and strains in all tests. The radial and axial stresses in the triaxial test are measured with a resolution of about 0.25 kPa and both the axial and volumetric strains are measured with an accuracy of about 10". The measured stresses are appropriately corrected for membrane 5  stiffness, loading ram friction, loading cap weight and the uplift force on the ram, and the volumetric strain is corrected for membrane penetration effects. No corrections are necessary for the measured vertical load in the simple shear test, on account of the positioning of the vertical load cell. The measured shear load was corrected for loading shaftfrictionand the stiffness of the reinforced membrane in simple shear test. The normal and shear stresses in simple shear have a resolution of better than 0.25 kPa and the vertical strain has a resolution of about 0.01%. The resolution of shear strain measurements is better than 0.01% for shear strains up to 10%, and is about 0.05% for shear strains in excess of 10%. The electro pneumatic transducer that was used to apply cyclic shear stress in simple shear or K  c  consolidation in triaxial has a resolution of about 0.10 kPa. The high precision pressure transducers used in the hollow cylinder torsional shear apparatus enable the internal, external and pore pressures be measured with a resolution of better than 0.05 kPa. The resolution of the vertical and the torsional shear stresses are about 0.2kPa. The DPTs enable volume measurement accurate to about 2 mm , that translates to a volumetric strain 3  resolution of better than 10". The LVDTs can detect a displacement of about 5 pm. This is 5  Chapter 3: Experimentation and Test apparatus  70  equivalent to an axial and shear strain resolution o f about IO" . L V D T s that can detect up to 1 5  pm displacement were used when finer measurement resolutions were required in certain tests. The range o f the A / D data acquisition card was dynamically adjusted using software control to further enhance the resolutions at low transducer output levels (i.e, at low stress and strain levels). The stress/strain path control was achieved by using a feedback loop to apply the required stresses/strains. A window of 0.25 k P a was used in all stress path controlled tests. The controller cards use square pulses to drive both the D V P C s and the stepper motor regulators. The stepper motor regulators are controlled with an accuracy o f about 0.1 kPa. These stepper motor regulators can apply pressure gradients from about 4 kPa per second to 40 kPa per second. The stepper motor connected to the D V P C requires 400 pulses per revolution. This is equivalent to an accuracy o f about 4 m m o f volume. The area o f the vertical and torsional shear load 3  pistons are sufficiently large to yield better than 10" accuracy in axial and shear strains. 5  3.4  Test procedures  Triaxial and simple shear tests were performed on both undisturbed and reconstituted sand specimens, and hollow cylinder torsional shear tests were carried out only on specimens reconstituted by water pluviation (Vaid and Negussey 1988). Undisturbed sand specimens were obtained using in-situ ground freezing as part o f the C A N L E X laboratory testing program. Reconstituted specimens were formed using Fraser River sand, that is similar to the undisturbed K i d d and Massey sands.  Chapter 3: Experimentation and Test apparatus  71  Frozen undisturbed specimens retrieved after in-situ ground freezing were machined to the prescribed dimensions (60 m m diameter x 125 m m height for triaxial and 69.8mm diameter x 20mm height for simple shear) at the University o f Alberta, Edmonton and shipped at regular intervals to U B C i n cold boxes with dry ice. These specimens were stored in the freezer at -20 °C until needed for testing. Details o f setting up a frozen specimen on a triaxial or simple shear apparatus and thawing it to the room temperature are given in V a i d et al. (1996). A l l undisturbed specimens were consolidated to the in-situ effective stress states, except a few in Phase III, where the specimens were consolidated to the anticipated stress levels after the construction o f the test embankment (Byrne et al. 2000).  3.4.1  Specimen reconstitution  Studies aimed at providing a fundamental understanding of the mechanical behaviour of sands require sand specimens that are homogeneous and repeatable.  Ideally, these tests would be  performed on several identical (and uniform) undisturbed sand samples. However, it is quite difficult to find in-situ sand samples that are uniform and identical. Further, the conventional sampling techniques may significantly alter the mechanical properties of sands (Seed et al. 1982), and the alternative in-situ ground freezing is very expensive. This has necessitated the use o f reconstituted, rather than undisturbed sand specimens. If the properties of the reconstituted sands are to be assigned to the in-situ sands, then the laboratory specimen reconstitution technique must mimic the in-situ deposition process.  This is because the sand behaviour is known to be  Chapter 3: Experimentation and Test apparatus  72  profoundly affected by the fabric that ensues upon reconstitution (Mulilis et al. 1977, Ladd 1974, 1977). Water pluviation was chosen as the preferred specimen reconstitution technique, after a comparison o f the behaviour o f sands reconstituted by different techniques, with the behaviour of the in-situ frozen undisturbed sands. Boiled, de-aired saturated sand slurry is deposited in the membrane lined cavity filled with de-aired water during pluviation. The sand does not come i n contact with air during the deposition process, and this results in well saturated specimens. Sand was deposited to a few millimetres above the target specimen height, and then the excess was siphoned off to form a level surface in order to reduce the bedding errors. Details o f the technique of water pluviation to reconstitute saturated sand specimens for use in triaxial tests is given in Chern (1981). The technique adapted in simple shear tests is similar to that described by Sivathayalan (1994), and that in hollow cylinder tests is detailed in Sayao (1989). Samples were prepared in the loosest state, and higher initial densities, i f needed, were obtained by applying low frequency vibrations to the base of the apparatus, while the specimen was confined under a small seating load.  3.4.2  Specimen setup and consolidation  A l l triaxial specimens were confined by an isotropic effective stress o f about 20 k P a (zero cell pressure and 20 k P a vacuum) when mounted in the apparatus. Saturation o f the specimens was ensured by requiring a Skempton's value o f at least 0.99 in all tests on reconstituted specimens  73  Chapter 3: Experimentation and Test apparatus  and most o f the undisturbed specimens. A few undisturbed specimens were tested at the in-situ saturation levels (Vaid et al. 1996). After ensuring full saturation the vertical effective stress was increased to reach the required stress ratio o f K = 2. The specimens were consolidated along c  the constant K =2 path from this initial state. c  The simple shear specimen was reconstituted in place and after siphoning off the excess sand, the specimen was confined by a vertical effective stress o f about 20 kPa. Specimens were consolidated to the desired effective vertical stress, by increasing the pressure in the vertical loading piston. Consolidation in simple shear is essentially K on account o f the lateral restraint. G  The availability o f compression time history in real time was used to determine the end o f consolidation. The vertical movement clamp was tightened at the completion o f consolidation, prior to undrained shear, in order to enforce constant volume conditions. The H C T specimen was confined by about a 25 k P a vacuum at the end o f reconstitution. Internal and external chambers are then filled with de-aired water. Sufficient volume of water was allowed to flow through the inner chamber in order to minimize the volume o f air trapped in the inner chamber. A cell pressure o f about 30 k P a was applied to the undrained specimen prior to checking saturation. Skempton's B value was checked by applying isotropic stress increments and a B value of at least 0.99 was insisted in all undrained tests. A back pressure of200 kPa, and total mean normal stress o f 400 kPa were used in all hollow cylinder torsional shear tests. Following saturation, the specimen was consolidated along a predetermined stress path to the desired stress state. Consolidation stress parameters were defined in terms of mean normal stress c x , inclination o f major principal stress to vertical o c , intermediate stress parameter b and mc  c  c  74  Chapter 3: Experimentation and Test apparatus  effective principal stress ratio K = a ,/CT . The control program applies the required stresses at c  3  desired increments of mean normal stress. Upon reaching the target consolidation stress state, the specimen is allowed sufficient time (about one hour for Fraser River sand) for all drainage to be complete. The real time graphical display of the consolidation curve (e vs time) facilitated in v  deciding adequate time for consolidation.  3.4.3  Monotonic or cyclic undrained Shear  All triaxial specimens were monotonically sheared undrained. A constant speed motor drive was used to apply displacement controlled shearing at a rate of about 12% axial strain per hour both in compression and extension tests. Liquefaction was induced by static unloading, and specimens were loaded in post liquefaction using the motor drive at the same axial strain rate. Monotonic loading in simple shear was applied by the computer controlled motor drive at a loading rate of about 20% shear strain per hour. The capability to impose both positive and negative shear strains enabled shearing with unload-reload loops. The data acquisition and control program automatically applies a predetermined loading sequence to the specimen. Data was acquired at about 100 sets per second and saved as necessary, depending on the state of the test. All monotonic tests were performed in the strain controlled mode. In contrast, all cyclic simple shear tests were carried out using stress controlled loading. A sinusoidal, constant amplitude cyclic shear stress at a frequency of 0.1 Hz was applied to the specimen until the sand liquefied. Upon liquefaction by stress controlled cyclic loading, the motor drive was connected  Chapter 3: Experimentation and Test apparatus  75  to the pneumatic piston to enable strain controlled loading. This enabled initiation of post liquefaction monotonic loading at the residual conditions following liquefaction with minimal disturbance. All transducers were monitored continually, and data were saved to file at regular intervals. The shearing phase of the hollow cylinder tests is fully automated using feedback control. The desired stress/strain path is input to the control program. Displacement controlled loading was imposed using DVPCs controlled by stepper motors. The specimen can be sheared using constant rates of strain ranging from about 2% per hour to 30% per hour. A strain rate of about 6% per hour (axial or torsional) was used in the tests. Displacement controlled loading was applied in axial direction alone, torsional direction alone or simultaneously in axial and torsional direction, depending on the required stress path. Data were monitored continually and saved to a file at regular time intervals, or when significant changes occurred in any of the stresses or strains.  3.5  Experimental artifacts and measurement errors  The objective of laboratory shear tests is to measure element properties. Test results are interpreted assuming uniform states of stress and strain within the entire specimen. However, all testing apparatus contribute to some non-uniformity in stresses/strains, and it is necessary to minimize these non-uniformities. It is also vital to ensure that apparatus specimen interactions do not adversely influence the measured response.  Chapter 3: Experimentation and Test apparatus  76  End restraint effects are a common concern i n shear tests, and they are minimized by using small porous stones, and polished anodized-aluminium pedestals. The porous stones used in the triaxial test constitute about 25% of the area o f the specimen, and in the hollow cylinder torsional shear test they constitute only about 8% o f the specimen area.  Other possible sources o f  systematic errors are identified, and steps taken to eliminate/minimize them are discussed below.  3.5.1  Influence of loading system (in strain softening sands)  The stress-strain response o f soils can be measured i n the laboratory using either a load or displacement controlled loading mechanism.  The measured response could be profoundly  influenced by the loading system, depending on the degree o f apparatus-specimen interaction. The influence o f the loading system w i l l be critical for strain softening specimens. Figure 3.10 illustrates comparative undrained strain softening response of essentially identical specimens o f Ottawa sand ( d  5 0  = 0.4 mm). The response under constant rate o f strain loading with no inertia  effects and dead weight inertial loading system recorded by an oscillographic recorder may be noted to be essentially identical. However, the non-inertial pneumatic stress controlled system with data recorded by a low frequency responding strip chart recorder yields a different measured behaviour. The measured response by the non-inertial loading system may be further modified by the rate at which the air regulator can bleed back the pressure, when reduction is required in axial load following the peak stress state. Only an inertial system, like the dead weight loading used by Castro (1969) can capture the true strain softening response o f sand under stress  77  Chapter 3: Experimentation and Test apparatus  200  150 h-  O  Strain Controlled  •  Dead Weight  A  Pneumatic piston  O  Pneumatic piston + vol. booster  A x i a l strain, s  (%) 3.  Figure 3.10 :  The effect o f loading system on the measured response in strain softening soils (after C h e m 1985).  controlled loading. The stress decrease during the strain softening after the peak then occurs automatically, on account of the increasing inertia force of the accelerating dead mass, triggered by the deforming specimen. If the true material response is of the steady state type (deformation at constant stress and volume after strain softening), the mass w i l l accelerate until a terminal constant acceleration is reached. This acceleration yields an inertia force that equals the reduction in vertical force required to reduce the peak stress to the steady state conditions. Contrary to the notion that steady state deformation in an inertial loading system occurs at constant velocity,  Chapter 3: Experimentation and Test apparatus  78  advocated by the proponents of the steady state concepts, it in fact occurs at constant acceleration (Chern 1985, V a i d and Sivathayalan 1998). A direct measure o f the true load experienced by the specimen i n the inertial loading system can only be made by an internal load transducer, located at the bottom pedestal. This indeed was done by Castro (1969). However, i f the true sand response is of the Q S S type, the load recorded before and until the minimum deviator stress dictated by the Q S S value w i l l again be reliable, but not after Q S S , due to the impact action on account o f the increasing resistance o f the material with further strain. N o such inertial problems arise when deformation is imposed under constant rate o f strain or velocity. But, even the constant rate o f strain devices may fail to continually measure the true resistance o f highly collapsible sands (with meta stable structure), especially at low effective stresses. This may happen i f the loading cap fails to follow the deformation of the sand as it collapses, and loses contact with the specimen. The recently reported zero shear strength in laboratory triaxial tests on sands (Ishihara 1993, Lade and Yamamuro 1997, Yamamuro et al. 1998) is apparently an incorrect interpretation o f the real soil behaviour because of this apparatus-specimen interaction (Sivathayalan et al. 2000). In fact the zero strength values were indeed reported only for sands with potentially collapsible meta stable structure (moist tamped, air pluviation with fines) under strain controlled loading. N o such behaviour has been recorded under the dead weight inertial loading systems for sand specimens reconstituted by the same techniques, but to much looser void ratios, even at negative relative densities (Castro 1969). A s noted earlier, all monotonic shearing tests in this study were performed using displacement controlled loading mechanisms. Displacement controlled loading ensures that the deviatoric  Chapter 3: Experimentation and Test apparatus  79  stress strain response of the water pluviated sand is properly measured both before and after the peak deviator stress.  3.5.2  Membrane penetration effects  The penetration o f membrane into (or out of) the interstices o f the peripheral voids causes a systematic error in volumetric measurements in drained tests and pore pressure measurements i n the undrained tests, i f the test involves changing radial effective stresses. Membrane penetration effects under changing effective confining stress were first recognized by Newland and A l l e y (1957, 1959) in drained triaxial tests; and since then have been o f considerable interest to numerous researchers. Attempts have been made by several researchers to correct for this error, both i n drained and undrained tests. Conventional drained tests are often carried out under a constant effective confining stress and thus are not affected by membrane penetration volume changes during the shearing phase. Even i f the effective confining stress is changing in a drained test (e.g drained test at constant mean normal stress), membrane penetration only affects the measured volume changes, and the correction is straight forward. The measured volume changes can be suitably corrected after the end of the test ("post test correction") with the volume changes induced by membrane penetration alone.  However, membrane penetration directly influences the effective stress path in an  undrained test. Membrane induced volume changes in fact amounts to a partially drained state and thus the measured stress strain response does not represent the undrained behaviour. This  Chapter 3: Experimentation and Test apparatus  80  necessitates corrections to be made in real time during the test, i f truly undrained conditions are to be maintained. Even though it is recognized that the influence of membrane penetration decreases as the sand gradation gets finer, there is no consensus among researchers as to the particle size below which its effects become relatively insignificant. Therefore a study was undertaken to assess the influence of membrane penetration in undrained tests on Fraser River sand, which is the coarsest sand used in the subsequent test program. A series o f tests was performed, first to accurately compute the magnitude o f specimen specific membrane penetration, and then to assess its influence in conventional undrained tests. These tests results are presented in Chapter 4.  3.5.3  Calculation of void ratio  A n accurate determination of the void ratio of the sand specimen at various stages o f the test is essential in any laboratory test. A knowledge of the specific gravity o f the solids, the amount o f dry mass o f the soil used to form the reconstituted specimen and the total volume o f the specimen are needed to calculate the void ratio. Traditionally the volume o f the specimen is calculated from the measured height and diameter. Specimen height can be determined quite accurately, but the accuracy of the diameter measurements is low. V a i d and Sivathayalan (1996b) pointed out that the measurement errors in dimensions can lead to considerable error in the calculated void ratio, and suggested alternative reliable methods for calculating the void ratio o f both reconstituted and undisturbed sand specimens. A l l void ratios reported in this thesis are  Chapter 3: Experimentation  and Test apparatus  81  calculated using volume and mass measurements, as suggested in V a i d and Sivathayalan (1996b). This method uses the volume o f the membrane lined cavity over the height o f the specimen to calculate the diameter. The cavity volume is accurately determined using the mass o f the water required to fill the cavity. The precision o f the void ratio measurement using this method is about 0.002. The initial void ratio is recorded under a confining stress of about 2 k P a in all tests. The void ratio changes are then continually monitored throughout the test, and this enables a confident measurement o f the void ratio at any stage o f the test.  3.6  Test program  The behaviour o f reconstituted sands was assessed under triaxial, simple shear and under generalised multi axial loading conditions in the hollow cylinder test. Undisturbed specimens were tested in triaxial and simple shear only. The behaviour o f specimens reconstituted to essentially identical initial states by different reconstitution techniques was compared among themselves, and to that o f the undisturbed sand. The undrained response o f undisturbed in-situ frozen sands from four different sites was studied, and compared to the behaviour of equivalent specimens reconstituted i n the laboratory. Post liquefaction behaviour of undisturbed sands was also assessed following liquefaction caused either by cyclic or static unloading. The influence of inherent anisotropy and of the initial static shear on the undrained behaviour o f reconstituted sands was evaluated using hollow cylinder torsional shear tests. A series o f tests  Chapter 3: Experimentation and Test apparatus  82  on the loosest deposited sand, consolidated to different initial stress states, was performed at fixed principal stress directions. In addition, the influence o f stress rotation on the behaviour and its dependency on the initial state were assessed. Details o f the type o f experiments performed in each category are outlined, and the results are discussed i n the following chapters.  Chapter 4  Membrane Penetration Effects on Undrained Behaviour  4.1  Introduction  Most laboratory shear tests on granular soils are carried out on specimens enclosed in flexible membranes (e.g. triaxial tests). Under loading paths involving changes in effective confining stress, the penetration o f the membrane into (or withdrawal out of) the interstices o f the granular soil specimen causes a systematic error i n the measured volume changes (in drained tests) or excess pore pressures (in undrained tests). The effect o f membrane penetration in a conventional undrained test is to induce a partially drained state as a result o f the membrane penetrating into (or withdrawing out of) the peripheral voids o f the soil specimen. A n increase in pore pressure would cause the membrane to move outwards from the interstices as illustrated i n Figure 4.1, and as a consequence the excess pore pressure generated w i l l be smaller than that in a truly undrained test. Membrane penetration in a conventional drained test introduces an error in the measured volumetric strain, and does not influence the effective stress state in the sand. In contrast, the effective stress state is directly influenced by the membrane penetration in an undrained test. This may have aprofound influence on the measured steady or quasi steady state undrained strength o f the sand, depending on the  83  Chapter 4: Membrane Penetration effects  Initial state after consolidation  Membrane withdrawal due to excess pore pressure  Figure 4.1 : Membrane penetration effect in an undrained test  84  Chapter 4: Membrane Penetration effects  85  magnitude o f membrane penetration. This undrained strength is used as the key parameter i n steady state analysis for assessing the potential o f a flow failure i n a saturated sand mass. If the membrane compliance has a considerable influence on the undrained response, then steps must be taken to minimize or eliminate these effects in order to obtain its true undrained behaviour. This is o f great importance in the confident assessment o f both static and cyclic liquefaction potential o f saturated granular materials. In a drained test with changing effective confining stress, the measured volumetric deformation consists o f both the soil skeleton volume change and the volume change due to membrane penetration. Thus, the measured volume change must be corrected for membrane volume change in order to obtain the actual volumetric strain o f the soil skeleton. This is essential i n the formulation or validation o f constitutive models o f granular materials. Clearly, the reliability o f volumetric strain measurements in drained tests (or excess pore pressure and thus the shear strength, S in undrained tests) depends on how accurately the membrane penetration magnitude u  is assessed in drained tests or how its effect on pore pressure is accounted for in undrained tests.  4.2  Magnitude of membrane penetration  The systematic error caused by membrane penetration effects on the measured drained behaviour o f sands is directly dependent on the magnitude of membrane penetration for a given specimen size. The magnitude of membrane penetration is often expressed in terms of the volume  Chapter 4: Membrane Penetration effects  86  change per unit surface area of the membrane in contact with the specimen per 10-fold change in effective confining stress, and is called unit membrane penetration e . m  The volume change induced by the penetration of membrane into the interstices depends on the change in the effective confining stress and the surface area of the membrane, in addition to the magnitude of membrane penetration. The volume change induced by membrane penetration, A V will then be m  (  AV  m  m  = e  m  x  A  m  m  log  x  m  °  o'  ,  (4.1)  current ^ initial  Where A is the surface area of the membrane and a' is the effective confining stress. A m  known s will enable corrections for the measured volumetric strain. Clearly, the effectiveness m  of any attempts to correct for membrane penetration induced errors is directly dependent on the accurate determination of its magnitude.  4.2.1  Assessment of membrane penetration  Newland and Alley (1959) were the first researchers to recognize the influence of membrane penetration, and they suggested a method of correction for membrane penetration induced volume changes by assuming material isotropy (s = s = s J under hydrostatic load increments. Later, x  y  Roscoe et al. (1963) also used the same assumption. Based on this assumption the soil skeleton volumetric strain, s equals three times the axial strain, s ; and thus the volumetric strain recorded v  z  Chapter 4: Membrane Penetration effects  87  in excess o f 3e is solely due to membrane penetration. This assumption has since then been z  shown invalid on account of inherent anisotropy in sands (Arthur and Menzies 1972, Oda, 1972, Lade and Wasif 1988). V a i d and Negussey (1984) recognized that the deformation o f sands is more isotropic i n hydrostatic unloading than in loading. They suggested a similar method assuming s = s = s , but during hydrostatic unloading. x  y  z  Since the magnitude of membrane penetration w i l l depend on the surface area of the membrane covering the specimen, and the skeleton volume change on the total volume of the specimen, most of the subsequent attempts to measure membrane penetration were aimed at using different area to volume ratio specimens. The usage of large test specimens w i l l reduce the effects of membrane penetration on account o f the decreased area to volume ratio (Wong et al. 1975, Martin et al. 1978), but it w i l l not eliminate them altogether. Roscoe et al. (1963) placed cylindrical dummy brass rods of the same height as the specimen, coaxially within the saturated sand. The diameters of dummy rods were changed from one sixth to eleven twelfths of the specimen diameter in order to vary the area to volume ratio, and infer the membrane induced volume changes as illustrated in Figure 4.2. Raju and Sadasivan (1974) noted that stress non-uniformities arise within the sand specimen due to the rigidity of the brass rod inclusions, and proposed annular flexible top platens to be used with dummy rods. W u and Chang (1982) have, however, shown that the inclusion o f a dummy rod within the specimen leads to the development o f shear stresses and thus a nonhomogeneous stress state within the specimen, even under hydrostatic loading. They noted that the sand skeleton volumetric strains would then be not identical (a necessary requirement) among specimens with different diameter rod inclusions.  Chapter 4: Membrane Penetration effects  88  In an attempt to reduce the area o f the membrane causing penetration, thus effectively changing the area to volume ratio, some researchers have used polythene strips, polyurethane coating (Raju and Venkatramana, 1980), plastic or brass plate liners (Choi and Ishibashi, 1992; Lade and Hernandez, 1977) alongside with the membranes to reduce membrane penetration. But, the usage o f such stiffeners around the specimen is bound to lead to further stress non-  Figure 4.2: Evaluation o f membrane penetration using dummy brass rods (After Roscoe et al. 1963)  Chapter 4: Membrane Penetration effects  uniformities.  89  Choi and Ishibashi concluded that the nonuniform stresses caused by the  introduction o f plastic liners were the cause o f the fallacious trend in their results. Alternatively, Kiekbusch and Schuppener (1977) used rubberized membranes and Lo et al. (1989) liquid rubbercoated membranes to enclose test specimens in an attempt to partially fill in the peripheral voids. Frydman et al. (1973) used conventional triaxial and hollow cylinder specimens to assess the membrane penetration. They achieved different area to volume ratio by using hollow cylinder specimens o f fixed external but varying internal diameters. V a i d and Negussey (1984) instead used triaxial specimens o f different diameter to get different area to volume ratios. Both o f these methods neither make any assumptions regarding the constitutive behaviour o f sand nor suffer from serious stress non-uniformities within the specimen, except for minor end effects, that are inherently present i n any soil testing device. A n accurate assessment o f the magnitude o f membrane penetration is o f critical importance in any attempt to correct for its effects. The most credible among the above discussed methods are the V a i d and Negussey (1984) and Frydman et al (1973). However, they either require multiple specimens o f different configurations (Vaid and Negussey 1984, Frydman et al. 1973) or assume isotropic response o f soils during unloading (Vaid and Negussey 1984). The multiple specimen methods have a practical disadvantage since different configurations are not readily available. The alternative assumption o f isotropic rebound may not be strictly valid for all soils. Further, these methods do not allow for specimen/membrane specific penetration correction. The most desirable method would be the one that is (i) non destructive, (ii) requires a single specimen, (iii) does not make any assumptions o f the constitutive behaviour o f soil, and (iv) allows for  90  Chapter 4: Membrane Penetration effects  specimen specific corrections. The new method proposed later in this chapter satisfies these criteria, and uses the data obtained during the consolidation (either hydrostatic or K ) phase in 0  a hollow cylinder torsional test to determine the magnitude o f membrane penetration.  4.2.2  Factors influencing the magnitude of membrane penetration  Several researchers have identified the factors that influence the magnitude o f membrane penetration (Kiekbusch and Schuppener 1977, Ramana and Raju 1982, Seed et al. 1987, Nicholson et al 1993a). The soil grain size and its gradation have been found to be the most dominant factors that control the magnitude of membrane penetration. Mean particle size D  5 0  has  been used by most researchers to represent the average grain size, and the magnitude o f membrane penetration has often been related to D . The influence o f the relative density of the 5 0  soil specimen has been investigated by several researchers (Ramana and Raju 1982, Seed et al 1989, Nicholson et al. 1993a), and all studies concur that membrane penetration magnitude decreases with denser packing o f sand particles. However, all researchers consistently indicate that the influence of density is relatively small compared to the influence o f mean particle size D . 5 0  A l s o the dependence o f membrane penetration on grain angularity or fabric has been found to be negligible (Banerjee et al. 1979, Nicholson et al 1993a). Even though there is no agreement in the literature on the influence o f membrane thickness on the membrane penetration magnitude, the majority o f the researchers are o f the opinion that the effect is only nominal for typical  Chapter 4: Membrane Penetration effects  91  membrane thicknesses (Kiekbusch and Schuppener 1977, Ramana and Raju 1982, Seed et al 1989, Nicholson et al. 1993a) used in laboratory tests.  4.2.3  Corrections in drained and undrained Tests  Membrane penetration induces a systematic error only when the effective confining stress changes during the test. Conventional drained tests are often carried out under a constant effective confining stress and thus are not affected by membrane penetration.  Even under  changing effective confining stresses during a drained test, membrane penetration only affects the measured volume changes, and the correction is straight forward. The measured volume changes can be suitably corrected after the end o f the test ("post test correction") using the volume changes induced by membrane penetration. Membrane penetration directly influences the effective stress path i n an undrained test. Membrane induced volume changes induce a partially drained state and thus intrinsically affect the measured stress strain response. This necessitates corrections to be made in real time during the undrained test. Raju and Venkatramana (1980) and Kramer and Sivaneswaran (1989) compensated for the potential volume changes induced by membrane penetration by manually injecting water into (or withdrawing out of) the specimen. The injection systems have since been improved dramatically using computer controlled feedback methods (Nicholson et al. 1993b, Wijewickreme et al. 1994). Such a real time correction procedure can ensure that essentially undrained conditions prevail during the duration o f the test.  Chapter 4: Membrane Penetration effects  92  Numerical methods have also been proposed to correct the measured pore pressure to obtain i  pore pressure under truly undrained condition (Baldi and N o v a 1984, Tokimatsu and Nakamura 1987, Ansal and Erken 1996).  These methods require assumptions regarding constitutive  relations of the sand in order to calculate the pore pressure changes from the membrane induced volume changes. These post correction methods need to be experimentally validated before they can be confidently used. N o such experimental validation o f these methods could be found in the literature.  The applicability o f these post correction methods to yield the truly undrained  behaviour o f sands is herein evaluated based directly on conventional and truly undrained tests on two sands; one coarse and one fine.  4.3  A New Method for determining the magnitude of membrane penetration  The proposed new method uses a single hollow cylindrical specimen which is loaded hydrostatically under drained conditions. The membrane penetration correction is obtained from the measured volumetric strain of the specimen and that of the inner cavity under hydrostatic load increment/decrement together with the measured axial strain. A s discussed in Chapter 3, there are four strain components s , s , e and y z  r  9  z6  in a hollow cylinder test, that are functions o f the  measured axial and torsional deformations and the volume changes o f the specimen and o f the inner cavity (Vaid et al. 1990b). The special design o f the U B C hollow cylinder torsional shear apparatus minimizes the radial end restraint effects by the use o f highly polished radially ribbed anodized aluminum end platens with porous stones that cover only 10% o f the platen area as  93  Chapter 4 : Membrane Penetration effects  illustrated in Figure 3.5. As a result, the developed radial shear stresses are insignificant under hydrostatic loading, and the normal stress at a given point in the specimen remain the same in all directions, thus closely satisfying the conditions of an element test. The force equilibrium of an element in the hollow cylinder wall (Figure 4.3) in the radial direction yields, da ° r  _  a  e  +  r  X  ~ 7 ~  dr  A =  (4.2)  0  where a and a are the normal radial and tangential stresses respectively. If u is the radial r  e  displacement of an element at radius r then consideration of the axisymmetric deformation of the cylinder yields the radial and tangential strains as  (a): Stresses acting on an element  Figure 4.3 :  (b): Displacement in horizontal plane  Stresses and strains in a hollow cylindrical element  94  Chapter 4: Membrane Penetration effects  (4.3)  As Saada (1988) pointed out, when identical pressures act inside and outside the hollow cylinder, it is quite proper to infer that there is no variation in the value of normal radial stress a  r  across the wall. Thus, under hydrostatic or K consolidation, radial and tangential stresses are 0  equal throughout the specimen and the whole specimen can be considered an element. As a consequence the tangential strain will also be identical at every radius across the thickness of the wall in a homogeneous specimen. The membrane penetration correction is obtained by enforcing the condition of this equality of tangential strains at the internal and external radii. = e,6 AR  R  I C  e  (4.4)  e  i  The inner cavity volume V  e  AR i  R  at r = R  of the cylindrical specimen of height h and radius R is given by {  V = TT R h, and 2  i c  f  (4.5) bV  lc  Dividing by V  ] C  = -K.Rf.bh  +  2-K.R bR r  j  and rearranging gives, 2.bR  j  bV  t  bh h  (4.6)  95  Chapter 4: Membrane Penetration effects  Similarly, consideration of the total volume of the specimen V and of the inner cavity together yields,  R  e  ~  V V  h  IC+  ( 4  '  7 )  The strain criterion given in equation 4.4 together with equations 4.6 and 4.7 now leads to  _w  bv  lc  IC  V,c  + bV  Vic + V + bV  6V  IC  bv  = (x - 1) 2  (4.8)  where % is ratio between the external and internal radii of the specimen. Equation 4.8 relates the actual volume change of the specimen to that of the inner cavity under hydrostatic loading. It indicates that the ratio of the true volume change of the specimen to the true volume change of the inner cavity is uniquely related to the internal and external radii. The measured volume changes, however, are subject to systematic errors caused by membrane penetration of both the inner and outer membranes. The specimen volume change is affected by both the inner and outer membranes, and the inner chamber volume change is affected only by the inner membrane, as illustrated in Figure 4.4. If 5 V and 5 V respectively are the recorded volume changes of the K  R  inner cavity and of the specimen, and 8 V outer membrane penetrations, then  [M  and 5 V  0 M  the volume changes induced by inner and  96  Chapter 4: Membrane Penetration effects  6V  IC  = 5V  IR  oV = 6V  R  + 6V  m  - bV  -  m  (4.9)  5V  0M  The membrane penetration induced volume change per unit area of the membrane e , for a m  given effective stress increment is given by  e  - e m  x  log  m  a initial + Ao, O  (4.10)  initial  (a): Membrane Penetration into the peripheral voids  (b): Inner Chamber Volume  Figure 4.4 :  (c): Specimen Volume  Membrane penetration induced volume changes in a hollow cylinder test  Chapter 4: Membrane Penetration effects  97  and the volume changes induced by the penetration o f the inner and outer membranes are given by,  bV . n  bV  IM  =e - e  OM  m '  ur  where A  I M  and A  0 M  . A,,. m  A  IM  / A  *  t\  ( 4 , 1 1 )  ^OM  are the surface areas o f the specimen covered by the inner and outer  membranes respectively. Combining equations 4.8,4.9 and 4.11 yields the following expression for each effective stress increment.  AV  - AV & '  (y -l) 2  mem  Equation 4.12 is used to calculate the membrane penetration correction from the recorded volume changes o f the inner cavity and o f the specimen together with the measured axial deformation for each axisymmetric stress increment. The unit membrane penetration correction e can then be obtained from a series o f such axisymmetric effective stress increments. m  4.3.1  Characteristics of the new method  The new method proposed for the evaluation of the magnitude o f membrane penetration has several advantages over the existing methods. It does not require any assumptions regarding the constitutive behaviour o f sands. Further, the sand is often consolidated axisymmetrically (most common consolidation stress state being a = 0; b = 0) prior to drained or undrained shearing. a  Chapter 4: Membrane Penetration effects  98  The volume change data obtained during this consolidation phase can then be utilized to obtain specimen specific unit membrane penetration. This enables the effects o f specimen density, membrane thickness and fabric, i f any, on membrane penetration to be accounted for. The specimen specific and non destructive nature of this method are not applicable i f the consolidation stress state is non-axisymmetric, but such states are not very common in research studies. H o l l o w cylinder tests are often subject to criticism on account of the nonuniform stresses that develop across the wall o f the specimen. But these occur only when different internal and external pressures are used and/or when the specimen is subjected to torsional shear. Nonuniform stresses are also caused by the end restraint effects that are inherently present i n any soil testing device. A s already pointed out in chapter 3, these were minimized by a careful design o f the apparatus (Vaid et al. 1990b). In the new method suggested, the stress state throughout the specimen is, therefore, closest to hydrostatic (equal internal and external pressures; no shear stress), making it an element test, that virtually guarantees uniform stresses and strains throughout the specimen. It is interesting to note that the condition o f constant tangential strain across the wall implies constant radial strain, and e = e across the thickness o f the wall, regardless o f any anisotropy e  r  in the granular material. Such a kinematic condition is imposed as a result o f the hydrostatic loading and the axisymmetric geometry of the specimen. In any case, for alluvial deposits formed under gravity (or specimens deposited vertically) the horizontal plane is normally the plane o f deposition, and the existence o f isotropy has been demonstrated in the horizontal plane in true triaxial tests (Yamada and Ishihara, 1979; Lade and Duncan, 1973). The vertical strain s is z  Chapter 4: Membrane Penetration effects  99  usually smaller than the radial or tangential strains measured in the horizontal plane on account of this inherent anisotropy even when the loading is hydrostatic (Ladd et al. 1977, Oda, 1972). Existence o f such a cross anisotropic structure has also been reported by Stokoe et al. (1991) based on horizontal direction independence o f measured P-wave velocities.  4.3.2  Experimental investigations (using the new method)  Membrane penetration induced volume changes were determined for Fraser River sand, that has a D  5 0  = 0.27 m m , using the hollow cylinder apparatus. These tests were also carried out on  a coarser Silica Sand, (herein called Sand A ) with D  5 0  = 0.90 m m and on uniform glass spheres  of various diameters ( D ranging from about 0.10 to 2.00 mm). This enabled quantification o f 5 0  membrane penetration as a function o f D . The gradations of the materials used are illustrated 5 0  in Figure 4.5. Specimens were formed in the U B C H C T device described in the previous chapter using 0.3 m m thick membranes on either side o f the hollow cylindrical specimen. Studies by several researchers (e.g., Kiekbusch and Schuppener, 1977, Martin et al. 1978) demonstrate that a change in the thickness o f the membranes does not significantly influence the membrane penetration induced volume change. Specimens were formed by water pluviation, in order to simulate the alluvial deposition process. A s noted earlier in chapter 3, this deposition technique leads to uniform specimens with a horizontal planes of deposition. A l l tests were carried out on the loosest deposited specimens. A s noted earlier, the effect o f density on membrane penetration has been found to be relatively  Chapter 4: Membrane Penetration effects  100  100  /  a  50  s /  bl co T  25  CO  /  t»  /1  CO  Glass -  r*W < (/  Ol  1  1  1 OJ  1  /  —1»  0.10  Figure 4.5 :  i  Jf  •  w  Q Glass -  CO  CO /  ~  •o 7 o /  ~C~  Sand A (Si]lica Sand)  75 h  p  1 1 1  •  i  i  1.00 particle size, m m  Particle gradation o f the materials used in assessing the magnitude o f membrane penetration  small i n comparison to that o f the mean grain size (Frydman et al. 1973, Ramana and Raju 1982, Nicholson et al. 1993a). Specimens were hydrostatically consolidated i n stages up to an effective stress of500 kPa. They were then unloaded hydrostatically i n several stages down to an effective stress o f 15 kPa. The height and volume changes o f the specimen and o f the inner cavity were recorded under each applied hydrostatic effective stress increment.  Chapter 4: Membrane Penetration effects  4.3.3  101  Test Results  Results o f drained tests on Fraser River sand, Sand A and glass beads are presented in this section to evaluate the magnitude o f membrane penetration. Unit membrane penetration was calculated from the measured volume changes of the sample and that o f the inner cavity using the equations derived earlier. Figure 4.6 shows the relationship between unit membrane penetration and effective confining stress for the two sands and glass beads o f different sizes. It may be noted that there is very little scatter in the data and the linear semi-logarithmic relationship between unit membrane penetration and confining stress holds very well. In order to assess whether the membrane penetration is reversible, specimens were subjected to several load-unload-reload cycles. Figure 4.7 shows the relationship o f unit membrane penetration with confining stress during several such cycles for glass bead B ( D = 0.72 mm). The data obtained during different cycles 5 0  match excellently. This indicates the very high level o f test repeatability, and that the membrane penetration effects are identical for increasing and decreasing effective stresses. Similar consistent data confirming excellent repeatability of unit membrane penetration for increasing and decreasing effective confining stresses were obtained for several other glass bead sizes. This essentially constant value o f unit membrane penetration among several unload-reload cycles is a reflection o f the fact that membrane penetration is not influenced by the fabric changes, i f any, that occur due to the hydrostatic unload-reload cycles.  102  Chapter 4: Membrane Penetration effects  20  Material FRS [D = 0.27 mm] 5Q  Sand A [D = 0.90 mm] 5Q  15  Glass A [D =0.12 mm] 50  Glass B [D = 0.72 mm] 50  Glass C [ D = 1.20 mm] 5Q  e  •  o  o" o o  * W  0  E  ,43  ...I  10  100  1000  hydrostatic effective stress /?, kPa  Figure 4.6 :  Variation o f membrane penetration induced volume change with effective confining stress.  The unit membrane penetration o f Fraser River Sand and glass beads B using the single specimen method suggested by V a i d and Negussey (1984) were also determined for comparison with the new method. The results i n Figure 4.8 show that though the average slopes of the semi linear log relationships are not that different, there is much larger scatter (and possibly a curvature) i n the data implied by the single specimen method o f V a i d and Negussey. L i n and Selig (1987) noted a similar curvature, which was more significant in the l o w confining stress  Chapter 4: Membrane Penetration effects  103  16 f _  -  -  Glass B (D = 0.72 mm) 5Q  A  Reloading I  O  Reloading II  •  Reloading III  c  Unloading I  A  Unloading II  n g  £ i  Unloading III  )  -  i  4 i  -  i  1 m  10  i  •  i  i  i  i 111  i  1000  100  hydrostatic effective stress p,  Figure 4.7 :  t  kPa  Magnitude o f membrane penetration during several unload-reload loops  range. But the test data interpreted by the proposed new method shows no curvature, even down to confining pressures as low as 15 kPa. The non linearity in data interpreted from the hydrostatic unloading i n triaxial tests apparently stems from the fact that the sand may not necessarily rebound isotropically as assumed. Thus the curvature at low stress levels in other interpretative methods should not be considered as a fundamental characteristics o f membrane penetration, but rather a manifestation o f the invalidity o f the assumption o f isotropy during unloading.  Chapter 4: Membrane Penetration effects  104  20 e  15  Calculated using  A  •  Vaid & Negussey (1984)  A  O  Proposed Method  E Glass B  s  o o o  10  CO  10  1000  Hydrostatic confining stress (kPa)  Figure 4.8 :  Comparison o f the magnitude of membrane penetration calculated using the new method and V a i d and Negussey (1984)  The dependence o f normalized unit membrane penetration S (slope o f e vs log p) on particle m  size has often been expressed i n a semi log chart by several researchers (Frydman et al. 1973; Ramana and Raju 1982, Nicholson et al. 1993a). dependence on the logarithm o f D  5 0  and also on D  5 0  A s such, Figure 4.9(a) illustrates this  in an alternative linear plot. Normalized unit  membrane penetration data from previous studies reported i n the literature are also shown i n Figure 4.9(a). It can be seen that all available data essentially falls within a narrow band for mean  105  Chapter 4: Membrane Penetration effects  30  f  E o  o o o  o  20  a c  4>  -  CL.  Data Source  •  Proposed Method  •  Using Vaid and Neguessy (1984)  A  Vaid and Neguessy (1984)  •  Frydman etal. (1973)  X  Kiekbusch and Schuppenner (1977)  *  Nicholson etal. (1993a)  S3  Raju and Venkatramana (1980)  • o  l-  £  10  *  •*  •  c 3 0)  -  o 55  c  X  • *  ..I  1  '  ,  1.00  0.10  D  5 Q  , mm  Figure 4.9(a): Dependence o f normalised unit membrane penetration on the logarithm o f D  5 0  particle sizes ranging from about 0.1 m m to 1.0 m m even though different techniques and assumptions have been used to obtain these data. This implies that the previously suggested methods, i n spite o f some theoretical concerns, may provide reasonably good estimates o f membrane penetration for fine to medium sands when compared to the proposed method, which neither makes any assumption regarding material behaviour nor is subject to questionable stress non-uniformities within the specimen during hydrostatic loading. A linear unit membrane  Chapter 4: Membrane Penetration effects  penetration vs D  5 0  106  appears to be a better approximation of the data than the semi-log plot. Plots  on linear scale as in Figure 4.9(b) should, therefore, be preferred over the semi-log relationships on account o f their simplicity.  4.4  Membrane penetration and undrained behaviour  The effective confining stress in an undrained test continuously changes on account o f excess pore water pressure development. A s a result the membrane may withdraw out o f the interstices (during increasing pore water pressure) or penetrate into them (during decreasing pore water pressure) even in a conventional test with constant total radial stress. This is equivalent to partial drainage, and would invariably influence the developed excess pore water pressure and the effective stress state in the specimen.  4.4.1  Truly undrained behaviour of sands  Compensating the potential volume changes induced by membrane penetration either by injecting water into (or withdrawing out of) the specimen w i l l ensure a truly undrained state. A n undrained test is termed truly undrained, i f the volume changes caused by the membrane penetration i n a conventional undrained test are compensated for. Raju and Venkatramana (1980) and Kramer and Sivaneswaran (1989) manually injected water into the specimen during undrained tests. Nicholson et al. (1993b) recognized the limitations o f this manual injection system and  Chapter 4: Membrane Penetration effects  107  Figure 4.9(b): Variation of normalised unit membrane penetration with mean grain size, D  50  developed a computer controlled system to automate the process. Since then, the injection systems have improved dramatically with the use of computer controlled feedback systems. The pore water injection system with a proper computer control can ensure truly undrained conditions throughout the test by continually feeding water in (or taking it out of) the specimen in order to prevent partial drainage that would otherwise occur on account of the penetration of membrane into (or its withdrawal out of) the peripheral voids.  Chapter 4: Membrane Penetration effects  4.4.2  108  Experimental investigations  Conventional and truly undrained tests were performed on Fraser River sand and Sand A to assess the influence of membrane penetration on their undrained behaviour, and its dependency on average particle size. These tests were also used to evaluate the current analytical "post correction" methods. A computer controlled feedback injection system (Wijewickreme et al. 1994) was used to compensate for membrane induced volume changes in order to yield the truly undrained response for its direct comparison with the conventional undrained behaviour. Figure 3.6 illustrates the schematic arrangement o f the pore water drainage system in truly undrained tests. Pore water pressure is measured at the bottom o f the specimen, and the membrane induced volume changes are compensated by injecting water through the top drainage line using the computer controlled D V P C . Both conventional and truly undrained tests were performed at an axial strain rate o f about 6% per hour. This ensured that the velocity head during injection was negligibly small, and the injection process does not inadvertently influence the measured pore pressure. Truly undrained triaxial compression tests were carried out by using the unit membrane penetration values obtained by the suggested new method. A l l tests were performed on saturated specimens with a Skempton B value better than 0.99. The volume o f the pore water was continuously adjusted so as to maintain truly undrained state (within a volumetric strain o f 2 x 10" ) throughout the test. The excellent continuity in pore pressure - strain relationship in Figure 6  4.10 showing the amount o f water injected (or removed) during a typical test and the measured  Chapter 4: Membrane Penetration effects  excess pore pressure is an indication o f the high reliability o f the injection process.  109  A  conventional undrained triaxial compression test was then carried out on an essentially identical specimen for comparison with the observed truly undrained behaviour. Material parameters required for the analytical prediction procedures o f truly undrained behaviour were also determined as needed.  Figure 4.10 :  Excess pore pressure and the volume o f water injected or withdrawn to maintain a truly undrained state i n a typical test  110  Chapter 4: Membrane Penetration effects  4.4.3  Post test correction to pore pressure in conventional undrained shear  The analytical school of thought has proposed corrections to the measured pore pressure in a conventional test in order to infer the pore pressure which would have been developed under truly undrained conditions.  Such methods do appear very appealing, as they may allow  resurrecting vast amounts of available undrained test data in the literature. However, direct experimental validation of such analytical methods is essential for their confident use. These correction procedures essentially involve translating the volumetric strain caused by the membrane penetration in the conventional drained test into an equivalent pore pressure in an undrained test by assuming a certain volumetric constitutive behaviour of the granular skeleton. The validity of such models, however, has never been experimentally verified. The analytical method proposed by Martin et al. (1978) to correct for system compliance in undrained simple shear tests was later adopted by Tokimatsu and Nakamura (1987) to correct pore pressures for the membrane penetration effects under undrained triaxial loading. They showed that the excess pore pressure in a truly undrained test can be related to the excess pore pressure measured in a conventional test by AU..truly undrained ^^conventional  in which  _  =  1 +  C  R  (4.13)  and e are the volumetric strains due respectively to membrane penetration and v  of the soil skeleton rebound and C = ds /ds . R  vm  v  111  Chapter 4: Membrane Penetration effects  Baldi and N o v a (1984) also suggested a similar correction procedure based on a model regarding compressibility o f the sand skeleton. The method suggested by Ansal and Erken (1996) is essentially identical to that suggested by Baldi and Nova. They both obtain the pore pressure correction by multiplying the bulk modulus of the sand skeleton by the volumetric strain induced by membrane penetration. Yet, Figure 4.11 (reproduced from Figure 14 in Ansal and Erken 1996) shows a considerable difference in the pore pressures predicted in a truly undrained test by the two methods. The measured maximum positive excess pore pressure in the conventional test  0  200  400  600  M a x i m u m Shear Stress, k P a Figure 4.11:  Comparison of measured and predicted excess pore pressures (After Ansal and Erken 1996).  112  Chapter 4: Membrane Penetration effects  was about 135 kPa. The predicted maximum excess pore pressure in a truly undrained test by Baldi and Nova's correction method would be about 270 k P a and about 330 kPa by the Ansal and Erken method.  The difference apparently arises on account o f the different constitutive  relationships adopted to relate the bulk modulus o f the sand to its stress state. Baldi and N o v a assume  C*CT'  m  as a function o f r\ only, where C * is the bulk compressibility of sand and r| is the  ratio o f deviator stress to effective mean normal stress, whereas Ansal and Erken assume C as a function o f cr' only, and not influenced by the r| level. m  4.4.4  Test results  Figure 4.12 shows the response o f a typical sample o f Fraser River sand measured in truly undrained and conventional undrained compression.  The maximum excess pore pressure  developed i n the truly undrained test was only about 10 k P a higher than that developed i n the conventional test. The corresponding phase transformation undrained strengths (1/2 a measured were 65 k P a and 72 k P a respectively.  d P T  )  The friction angle mobilized at phase  transformation was 33°, and 37° at maximum obliquity, in both the tests. A comparison o f the truly undrained and conventional undrained response o f the loosest deposited coarser Sand A is shown in Figure 4.13.  M u c h larger maximum excess pore  pressure(152 kPa) developed in the truly undrained compared to that i n the conventional undrained test (91 kPa). The specimen was marginally contractive in the conventional test, but responded i n a strain softening manner when truly undrained. The phase transformation strength  113  Chapter 4: Membrane Penetration effects  Fraser River sand  A x i a l strain E , %  Figure 4.12  Comparison o f truly undrained and conventional undrained behaviour o f Fraser River sand.  Chapter 4: Membrane Penetration effects  114  300 Sand A (D = 0.90mm) 5Q  _  •  lc  200  a' = 200 kPa 3c  CN  100 truly undrained conventional 0  200 at  100 <-i CO CO  <L> PL,  l-l  o PH  CO  <D O  •100 Conventional:  X  e =0.683 c  Truly Undrained: e = 0.677 -200 A x i a l strain 8 , % a  Figure 4 . 1 3 :  Comparison o f truly undrained and conventional undrained behaviour o f coarse Silica sand A .  Chapter 4: Membrane Penetration effects  115  in the truly undrained test was now less than half o f that recorded in the conventional test, even though the friction angle mobilized at phase transformation was essentially constant at 27° between the two tests.  The larger discrepancy between truly and conventional undrained  response in this case is clearly due to the larger membrane penetration effects in the coarser Sand A than the finer Fraser River sand.  4.4.5  Evaluation of post-test correction methods  The pore pressures measured in the conventional test were also corrected by using the suggested post test correction methods discussed earlier. The test data obtained in hydrostatically consolidated conventional drained tests (constant confining stress) were used to compute the compliance factor C for the Tokimatsu and Nakamura's method, and the experimental program R  prescribed in Baldi and N o v a was carried out to obtain the values of C*o-' at different values o f m  r\. The modulus C of Ansal and Erken method was obtained from hydrostatic compression test t  data. Figure 4.14 compares the predicted truly undrained pore pressures calculated by the three proposed methods, together with those observed i n an actual truly undrained test on Fraser River sand.  The data from the conventional undrained test is also shown. A s noted earlier the  measured maximum excess pore pressures in the truly undrained test was only about 10 k P a higher for this sand ( D = 0.27 mm; D = 2 5 % ) , whereas the post correction methods, in contrast, 5 0  r  predict values several times larger, at 40, 60 and 82 k P a respectively for the Ansal and Erken's,  116  Chapter 4: Membrane Penetration effects  -100  500  CO  PH  400 h •*->  (/} C  °E • <*: c o o _> o  o PH  300  200  200 0  2  4  6  8  Axial strain e , % a  Figure 4 . 1 4 :  Comparison o f the excess pore pressure measured in a truly undrained test with those predicted by the post correction methods in Fraser River sand.  Baldi and Nova's and Tokimatsu and Nakamura's methods. This amounts to an over prediction by about 400% to 800%. It is important to note that the predicted excess pore pressures even exceed the initial confining stress in two o f the methods, an impossible scenario, which would imply negative effective confining stresses. This phenomenon may also be noted in the results reported by Ansal and Erken. These researchers were apparently oblivious to the fact that the upper limit o f excess pore pressure cannot exceed the initial confining stress. The computed  117  Chapter 4: Membrane Penetration effects  effective confining stress states which become negative is a clear indication that the corrections applied are extreme. The predicted pore pressures similar to those for the Fraser River sand in Figure 4.14 are illustrated in Figure 4.15 for the coarser Sand A . Again, the maximum excess pore pressure predicted in this case by both the Tokimatsu and Nakamura and Ansal and Erken's methods are extremely high compared to those recorded i n the truly undrained test, which again amount to impossible values, larger than the initial confining stress. The test results presented clearly demonstrate that the available post correction methods w i l l yield predicted pore pressure under truly undrained conditions to be too large for both the Fraser River sand ( D = 0.27 mm) and Sand A ( D = 0.90 mm). The data reported by Ansal and Erken 5 0  5 0  for the coarser Podima sand ( D o f about 1.20 mm), also predict much higher truly undrained 5 0  pore pressures than observed in actual truly undrained tests. The evaluated post correction methods predict truly undrained maximum excess pore pressures that are too large. Apparently, the constitutive soil models assumed i n the correction procedures are not realistic for the tested sands. Figures 4.14 and 4.15 also show that the rate o f pore pressure development with strain is much faster when the sand is truly undrained compared to when conventionally undrained. Such differences would lead to erroneous prediction o f effective stress paths and stress strain behaviour o f sand by the post-correction methods. In particular, the failure to recognize the transformation o f the behaviour o f Sand A from essentially strain hardening in conventional undrained shear to strain softening when truly undrained, would be err on the unconservative side in problems needing safeguard against flow failures.  118  Chapter 4: Membrane Penetration effects  -200  600 Sand A a' =200kPa lc  200 kPa  400  200  200 Measured in conventional undrained Measured in truly undrained Predicted by Ansal & Erken (1996) Predicted by Tokimatsu & Nakamura (1987) l i l i l 0.00  2.00  4.00  6.00  400 8.00  A x i a l strain 8 , % Figure 4 . 1 5 :  4.5  Comparison o f the excess pore pressure measured i n a truly undrained test with those predicted by the post correction methods i n Silica sand A .  Summary  A new method for reliable estimates of membrane penetration induced volume changes using a single specimen has been developed. This non destructive method enables determination o f specimen specific membrane penetration correction. In contrast with the existing single specimen  119  Chapter 4: Membrane Penetration effects  methods, this method does not make any assumption regarding the constitutive behaviour or isotropy o f the sand specimen, and no special measurements other than those obtained in a conventional hollow cylinder test are required. The stress and strain conditions within the H C T specimen are virtually uniform on account o f the imposed hydrostatic stress state. For a given sand, membrane penetration is found to be linearly related to the logarithm o f effective stress for stresses varying from as low as 15 k P a to 500 kPa. The normalized unit membrane penetration can be better approximated as a linear function of D D  5 0  5 0  in preference to log  It is also found that most o f the existing methods give reasonably good estimates o f  normalized unit membrane penetration for particle sizes ranging from 0.10 to 1.0 mm, despite assumptions that are not strictly valid. The maximum excess pore pressure in a truly undrained triaxial compression test was experimentally found to be larger than that under conventional undrained compression by about 7% for Fraser River sand ( D = 0.27 mm), but a high 70% for Sand A ( D = 0.90 mm). The 5 0  5 0  currently available analytical post-correction methods predict much larger excess pore pressures, and i f used in practice w i l l lead to very conservative designs. Transformation o f the strain hardening response o f sand noted in conventional undrained tests into the strain softening type, i f truly undrained state has persisted, is experimentally illustrated. This is a matter o f great concern from a practical standpoint. The comparison of the conventional and truly undrained tests reveal that the error induced by membrane penetration effects is quite small in Fraser River sand, that has a D  5 0  o f about 0.27mm.  Unlike in the coarse Silica Sand A , the results o f conventional undrained tests are very  Chapter 4: Membrane Penetration effects  120  representative o f the truly undrained response i n Fraser River sand. Therefore the membrane induced volume changes were not compensated in subsequent undrained tests on Fraser River sand reported in the following chapters. However, i f any undrained tests are to be performed on Sand A , then it would be essential to compensate for membrane induced volume changes, in order to represent the true undrained behaviour.  Chapter 5  Fabric Dependent Behaviour of Sands  5.1  Introduction  The influence of fabric on the undrained behaviour of sands is highlighted in the results presented in this chapter. Fabric dependency is demonstrated using test results from static and cyclic undrained tests in triaxial and simple shear loading modes. A direct comparison of the behaviour of sand specimens prepared to the same density and effective stress state by different reconstitution techniques with that of the in-situ sands facilitates the assessment of the influence of fabric. The behaviour of in-situ sands is assessed using "undisturbed" specimens obtained by in-situ ground freezing. Undisturbed specimens were obtained from four different sites; two of them are natural sand deposits in the Fraser River Delta in British Columbia and the other two are hydraulically placed tailings sand deposits associated with the mining industry in Alberta. Reconstituted specimens were formed from bulk samples of sands obtained from these sites, and from the sand retrieved during in-situ ground freezing. The undrained triaxial and simple shear  121  Chapter 5: Fabric dependent behaviour of sands  122  behaviour o f undisturbed specimens reveals the influence of the loading mode on the response o f alluvial or hydraulically placed in-situ sands.  5.2  Undisturbed sand specimens  Ideally, undisturbed sampling should enable replication o f all in-situ conditions in the laboratory. This includes stress state, void ratio, fabric and past stress history. However, a truly undisturbed specimen cannot be tested because of the additional stress history imparted to the soil element on retrieval, due to the stress release as part o f the sampling process and subsequent reinstatement o f in-situ stresses. Ladd and Lamb (1963) define a sample as perfect i f it has not been disturbed by the boring, sampling and trimming except by in-situ stress release. Hvorslev (1949) considered a sample to be undisturbed i f the disturbance is so small that the material is suitable for all laboratory tests and can be used to determine the strength, consolidation and permeability characteristics, and other properties o f the soil in-situ. The emphasis is thus to minimize the disturbances during sampling and subsequent restoration o f in-situ stress state. Obtaining undisturbed samples o f sands using conventional sampling methods often fails to provide satisfactory results. Conventional sampling using thin walled tubes causes disturbance during drilling, sampling, transportation, storage and setting up of the test. This irreversibly alters the stress history of the specimen sampled. Brooms (1980) and Seed et al. (1982) describe such techniques used in sampling undisturbed specimens, and discuss the causes o f disturbance in detail. In-situ ground freezing, on the other hand, has the potential for yielding high quality  Chapter 5: Fabric dependent behaviour of sands  123  undisturbed sand specimens i f proper procedures are followed. These consist o f minimizing disturbances during sampling and in-situ ground freezing.  5.2.1  C a n a d i a n Liquefaction E x p e r i m e n t ( C A N L E X )  Assessment o f the behaviour o f in-situ sand deposits using undisturbed specimens was undertaken as part of the Canadian liquefaction experiment ( C A N L E X ) - a co-operative research endeavour. Several Canadian universities and industrial participants took part in this collaborative research project that involved extensive laboratory testing, in-situ testing and numerical modelling to characterise the behaviour o f in-situ sands. The main objective of the C A N L E X project was to assess the liquefaction susceptibility of loose sand deposits. Preliminary in-situ investigations were carried out at several sites, in order to identify sites with loose sand layers. The identified loose sand layers were then comprehensively characterised using a combination of laboratory and in-situ tests. The behaviour in laboratory tests of undisturbed sands specimens obtained from four different sites in three phases is presented in this chapter. Phase I and III sites are located at an o i l sand mine operated by Syncrude Canada Ltd., north o f Fort M c M u r r a y i n Alberta. T w o natural sand deposits in the Fraser River Delta, just south of Vancouver were investigated in Phase II. Figure 5.1 (a) shows the location of the Phase II sites in the lower mainland. Phase I and Phase III sands are similar except for the deposition environment; Both are rounded sands with about 10% fines and are predominantly quartz. The Phase II Fraser Delta sands are sub rounded with a mineral composition o f 40% quartz, quartzite and chert, 11% feldspar and about 4 5 % unstable rock  Figure 5.1(a):  C A N L E X phase II site locations in lower mainland, British Columbia.  Chapter 5: Fabric dependent behaviour of sands  125  Table 5.1: Properties o f the undisturbed sands  Phase  Undisturbed sand  D , (mm)  c„  0  e  max  e  min  I  Mildred Lake sand  0.2  2.2  0.958  0.522  II  K i d d sand  0.35  2.5  1.061  0.703  Massey sand  0.3  2.1  1.102  0.610  Syncrude J pit sand  0.2  2.2  0.901  0.579  III  fragments (Garrison et al. 1969). Table 5.1 lists maximum and minimum void ratio o f the undisturbed sands according to A S T M D4253 (1991a) and D4254 (1991b), together with other key index properties.  5.2.2  In-situ ground freezing  In-situ ground freezing has been used for soil stabilization and ground freezing for a long time. Langer (1937) and Kollbrunner and Langer (1939) were the first to use ground freezing to facilitate sampling o f sands and silts. Even though the potential o f ground freezing for providing relatively undisturbed samples has been recognized for a long time, its usage did not gain widespread acceptance because o f the high costs involved. The recognition that ground freezing is the only technique that can yield relatively undisturbed specimens o f sands has led several researchers to refine the freezing techniques i n order to improve the quality o f the retrieved undisturbed specimens. The void ratio and fabric o f the sand could be altered due to any volume expansion associated with pore water freezing into ice. Unlike in clayey soils, the attractive  Chapter 5: Fabric dependent behaviour of sands  126  forces between soil particles and water molecules are extremely weak in sands. In addition, sands are highly permeable. Therefore, much less energy is required to expel pore water out of the void space than to move apart the sand grains under the confining stresses. Under appropriately slow rates of freezing, the excess volume of water is driven out ahead of the freezing front i n order to accommodate the volume increase associated with water freezing into ice, without disturbing the sand particle assembly. Yoshimi et al. (1977, 1978), Hatanaka et al (1985) provide valuable data on the practical aspects o f freezing sand samples in ground. Yoshimi et al (1978) has shown that the process o f freezing and subsequent thawing does not alter the static shear strength of the sand. Singh et al (1982) found that the freezing process does not induce significant volume changes, i f the confining pressure is maintained and drainage not impeded. Based on cyclic loading tests on hydrostatically consolidated sand specimens, they have shown that the cyclic shear strength characteristics are not significantly altered by a "freeze-thaw" cycle. The freezing system used at the C A N L E X sites used a two inch nominal diameter steel pipe installed in the ground to the desired depth. Liquid nitrogen was fed into this freeze pipe using V2 inch copper tubes. Nitrogen gas was expelled through another coaxial tube after the phase change o f nitrogen in the ground. Figure 5.1(b) shows a schematic o f the freeze pipe systems used at the C A N L E X sites. Frozen ground was cored using either a 100mm or 200mm inside diameter Cold Regions Research Engineering Laboratory ( C R R E L ) core barrel. The frozen cores were transported to the University o f Alberta ( U o A ) in dry ice and stored in a cold room. Triaxial and simple shear specimens were trimmed to the required size in a cold room at the University of Alberta before shipment to the University of British Columbia ( U B C ) in dry ice for  Chapter 5: Fabric dependent behaviour of sands  127  Freeze pipe \ Sample Borehole Ground Surface Casing for Frozen core Sampling  P V C Casing Drill pipe Casing for -Frozen core Sampling  Bentonite Seal  Target Freeze Zone  Freeze pipe (50 mm diameter)  Figure 5.1(b): Schematic o f the freeze pipe (after Hofmann 1997).  128  Chapter 5: Fabric dependent behaviour of sands  testing. Some undisturbed specimens obtained from these sites were also tested at the University of Alberta and Laval University, but the majority of the testing was carried out at U B C . Ground freezing procedures employed at each o f the C A N L E X sites together with the details o f coring and trimming o f specimens are explained in detail elsewhere (Hofmann 1997). Table 5.2 summarizes the scope o f the C A N L E X laboratory testing program.  Table 5.2: C A N L E X laboratory Testing: Phase I, II & III Undisturbed sand specimens  Phase  Phase I  Phase II  Phase III  UBC  UoA  Laval  Consulting Engineers  Triaxial  8  11  8  2  29  Simple Shear  8  -  -  -  8  Triaxial  21  -  12  -  33  Simple Shear  26  -  -  -  26  Triaxial  23  -  -  -  23  Simple Shear  13  -  -  -  13  99  11  20  2  132  Total Tests (Phases I, II & III)  5.2.3  Total  Laboratory  Test Type  Thawing and restoration of in-situ stress state  The frozen sand specimen has to be thawed and the in-situ stresses need to be reinstated prior to testing. It is crucial that the process o f thawing and/or restoring the in-situ stresses does not cause excessive disturbance to the specimen. Ideally all in-situ conditions including stress state,  Chapter 5: Fabric dependent behaviour of sands  129  void ratio, fabric and stress history that prevailed prior to freezing would get restored i n the laboratory in atruly undisturbed specimen. This, however, is virtually impossible. The mechanics o f freezing soils is quite complex, as it deals with four phase systems viz. sand particles, ice, water and gaseous components.  The complex physico-mechanical phenomena accompanying the  freezing of soils is given by Tystovich (1952). The most effective means o f freezing sand with least disturbance is to invoke radial freezing outwards at a rate slow enough to expel the excess volume o f water. The thermal conditions during thawing o f the laboratory specimens would rarely facilitate such a unidirectional phase change. The specimen thaws radially inwards and axially from the pedestals during thawing. It is important to recognize that a sheer reversal of the boundary conditions during freezing w i l l not necessarily yield the best procedure for thawing. Several procedures have been proposed for thawing frozen sand specimens ( B C Hydro 1993, Hofmann 1997, Konrad and Pouliet 1997). The method adopted herein was the method that resulted in minimal disturbance to the specimen. Because o f the difficulty o f directly tracking all the volume changes during thawing o f the specimen, the change i n its height, which can be measured with much greater confidence was considered as the most suitable index o f their void ratio change.  5.2.3.1  Setting up of frozen specimens  The loading caps, porous stones and the membranes used in testing frozen specimens were kept in the refrigerator together with adequate amounts o f de-aired water. The drainage reservoir  130  Chapter 5: Fabric dependent behaviour of sands  was filled with cold de-aired water so that the specimen would not begin to thaw when connected to the drainage reservoir. The undisturbed specimen was removed from the dry iced storage compartment in the freezer and setup in the apparatus using the cold loading caps, porous stones and membrane.  A vacuum o f about -80kPa was applied through the cold water drainage  reservoir, immediately after sealing the membranes to the loading caps to remove the air trapped between the specimen and the membrane and porous stones. The cell was assembled and filled with cold water, and a cell pressure of about 20kPa was applied with the drainage reservoir open to the atmosphere. The vacuum on the specimen was then released. The entire setup procedure was streamlined, and the entire process (from the removal of the specimen from the freezer to the application o f cell pressure) was completed within about six minutes. Since all surfaces o f the specimen contact are essentially at close to 0 ° C , no thawing occurred during the setup process. This was confirmed by continuously monitoring the height o f the specimen, which remained essentially constant during the setup process. The specimen was then allowed to thaw under a controlled room temperature o f 23 °C for at least 18 hours with both top and bottom drainage lines open. The height change o f the specimen from the beginning o f setup to the end o f thaw was recorded. Following thawing, the specimen was consolidated to the anticipated in-situ stress state. In-situ vertical stress was calculated from the unit weight o f the sand and the water table depth, and the horizontal stress was calculated assuming a K value of 0.5. The recorded volume 0  and height changes during consolidation were considered indicative o f the disturbance o f the undisturbed specimen.  131  Chapter 5: Fabric dependent behaviour of sands  5.2.3.2  Disturbance during thawing & reconsolidation  Ideally, the restoration of the in-situ state, by the thawing and the subsequent reconsolidation o f the undisturbed frozen specimen should not cause any void ratio change. This, however, is impossible to achieve because o f the unavoidable minor disturbances an in-situ frozen specimen is bound to experience during sampling and subsequent storage prior to testing. The in-situ stress state is normally anisotropic in natural fluvial and hydraulic fill deposits, with vertical effective stress generally higher than the horizontal. Ideally the stress state should remain unaltered in the soil element after freezing, except that the pore water would have been transformed into pore ice. However, tensile stresses would develop in ice when the specimen is removed from the ground, similar to the development o f negative pore water pressure when sampling a saturated clay specimen. In contrast to pore water, ice can carry some shear stresses, at least temporarily i n the early stages of sampling (Ladanyi 1981). However, ice has an extreme propensity to creep under shear and therefore cannot sustain large shear stresses for long periods o f time ( M c C l u n g 1998, Voitkovsky 1967). Thus, the stress state in the retrieved frozen specimen w i l l approach a hydrostatic state as ice creeps. Since undisturbed specimens were in storage for several weeks prior to testing, the stress state prior to thawing would have been virtually isotropic due to the inevitable unloading o f the in-situ shear stresses. A n accurate determination of the in-situ lateral stress is quite difficult. The coefficient o f earth pressure at rest K is estimated to be about 0.5 at all four sites using pressuremeter tests (Hughes 0  1996), and consequently undisturbed specimens were re-consolidated to a K o f 0.5. A n y 0  deviations from the actual in-situ value o f the lateral stress would inevitably result i n some  Chapter 5: Fabric dependent behaviour of sands  132  disturbance causing alterations o f the void ratio. Singh et al (1982) have shown that freeze - thaw cycles do cause insignificant volume changes, but their evidence was confined to initially hydrostatically consolidated specimens only. It is essential to recognize that their evidence cannot be translated to soils frozen under an initially anisotropic stress state. A s pointed out earlier, the void ratio change during thawing and reconsolidation to the in-situ stresses would be the best index o f the degree o f disturbance in the undisturbed specimen. However, the measured volume change during thawing consists o f several components and that corresponding to the volumetric strain o f the specimen cannot be easily separated out. The measured volume change includes (1) the volume intake due to ice thawing into water, (2) volume change o f the specimen and (3) the high volume compliance o f the system because the specimen is set up in air. Thus a confident measure o f the void ratio change during thaw is difficult to achieve unless some unverifiable assumptions are made to calculate the volume change o f the specimen. The height change during thaw, on the other hand, can be confidently measured using a dial gauge positioned along the loading ram connected to the loading cap of the specimen. The height changes are therefore regarded as a more reliable substitute index o f void ratio changes. The measured net height changes, during thawing and reconsolidation o f specimens, indicate relatively larger disturbance in Phase I Mildred Lake sand. The average axial strain during the restoration o f in-situ stresses was about 1.5% in this phase. The height changes in both Phase II sands amounted to an equivalent average axial strain o f about 0.14%. Unlike Phase I Syncrude sand, restoration o f in-situ stress state in Phase III Syncrude sand also resulted in small height changes. These differences are believed to arise on account of the initial degree o f saturation o f  Chapter 5: Fabric dependent behaviour of sands  133  the in-situ sands. B - value measurements at the end o f thaw under 20 k P a effective stress, but at the in-situ level o f the pore pressure revealed that Phase I Mildred Lake sand was unsaturated. The degree o f in-situ saturation o f Phase I sand was much smaller than the Phase III sand. The unsaturated Phase I specimens were saturated by applying differential vacuum. Both the pore space and the cell pressure chamber were subjected to negative (relative to atmospheric) pressure. The effective stress on the specimen was maintained within the range of 20 to 25 k P a during the application of differential vacuum. It is believed that the large height and thus void ratio changes in Phase I specimens occur in part due to freezing in the unsaturated state and in part due to the saturation process. The B-value measurements o f K i d d and Massey sands established that both Phase II sands were fully saturated. B-value o f better than 0.99 were recorded in these sands. The Phase III Syncrude sand gave B-values in the range o f 0.92 to 1 with an average o f about 0.98. Thus both Phase II and Phase III sands were tested without subjecting them to any saturation process, in contrast to Phase I sands. The total height change during thaw and reconsolidation o f the undisturbed specimen as a function of the degree o f saturation is shown in Figure 5.2. Data are shown for both undisturbed specimens, and specimens frozen and thawed under controlled conditions in the laboratory. A t a given degree o f saturation, the height change in the undisturbed specimens may be noted to be higher than those that were subjected to a freeze-thaw cycle in the laboratory. This suggests that the in-situ sampling process is imparting some disturbance to the sands. It can also be noted that Phase I sand, which is essentially identical to the Phase III sand with regard to the mineral composition and gradation, underwent much larger height change, and therefore disturbance,  134  Chapter 5: Fabric dependent behaviour of sands  0.00  •  (a) Laboratory Freeze-Thaw tests  .A  A  1.00 r  Modified after Hofmann (1997) This study  2.00 0.00 GO  (b) In situ frozen sand specimens  o  o  o  %  1.00 h o A  2.00  3.00  A  Phase I  O  Phase II  •  Phase III  A AA A  n  A A  AA  4.00 70  Figure 5.2  80 90 Degree o f saturation, (%)  100  Height change during thaw and reconsolidation o f undisturbed and reconstituted sands  135  Chapter 5: Fabric dependent behaviour of sands apparently on account o f its low in-situ degree o f saturation.  Fully saturated specimens  underwent minimal height changes. This data supports the contention that partial saturation might be a cause of the disturbance, and suggests that freezing is more suitable for sampling fully saturated sands. When partially saturated soils are frozen, gas/air pockets are likely to exist within the frozen specimen, which might cause collapse during thawing. Since partial saturation appears to influence the degree o f disturbance in sampling sands by in-situ ground freezing, the height changes o f the unsaturated Phase I sand specimens are not considered indicative o f the quality of the freezing technique in assessing the liquefaction susceptibility o f sands. Figure 5.3 illustrates the height change during thaw and subsequent reconsolidation o f fully saturated Massey sand triaxial specimens. Since the effective stress during thaw was smaller than the in-situ stresses, the specimens were expected to rebound slightly, and all specimens did rebound. This could be viewed as an indication that the undisturbed specimens are o f high quality. The subsequent application of the in-situ stresses w i l l cause compression, and in the ideal case, the magnitude o f the initial rebound would be approximately equal to the compression during reconsolidation, because hysteresis during a small unload/reload cycle is small. The very small overall height change is an indication that relatively undisturbed samples of saturated sands can be obtained using in-situ ground freezing, and by allowing them to thaw under a small effective stress prior to reinstating in-situ stresses.  Chapter 5: Fabric dependent behaviour of sands  136  1.00  Saturated Massey sand  -1.00 c  0.50  3  O  -0.50 u 60  Initial frozen  0.00  state  B  o.oo  ' 5  03  op  < 0.50 Height Change o U  During Thaw  1.00 h  0.88  Figure 5.3 :  5.2.3.3  -0.50  J  0.92  Total (initial to EoC)  0.96 initial void ratio  1.00  •1.00  1.04  Height change during thaw and reconsolidation o f saturated Massey sands.  Comparison of different thawing techniques  The effective stress state during thaw was maintained hydrostatic, at about 20 kPa in all tests reported herein. This methodology was developed during an extensive testing program of frozen sand specimens for seismic assessment of the stability o f sands in the foundation o f Duncan Dam in British Columbia ( B C Hydro, 1993). Other techniques proposed in the literature (Konrad and Pouliet 1997, Hofmann 1997) suggest thawing the specimen under in-situ stresses and pore  Chapter 5: Fabric dependent behaviour of sands  137  pressure. It is contended that thawing specimens under in-situ stress levels w i l l cause lesser disturbance than thawing under a small hydrostatic effective stress and subsequently reconsolidating to the in-situ stress state (Hofmann 1997). The merits and shortcoming of these two methods are evaluated by examining the measured height change data. Comparative specimens of Phase I Syncrude sand were thawed both under a small hydrostatic effective confining stress (Method I) and under estimated in-situ stresses (Method II). Specimens thawed by Method I were subsequently reconsolidated to the estimated in-situ stress state. A summary o f the total height changes, from the initial frozen state to that after the restoration o f the in-situ stresses is given for both methods in Table 5.3. Both undisturbed in-situ frozen Mildred Lake sand specimens, and specimens reconstituted i n the laboratory and then unidirectionally frozen were used in these studies. Only those specimens identified as good quality (Hofmann 1997) are included in the data. A s noted earlier, the actual void ratio change o f a specimen during thawing and the restoration o f in-situ effective stresses cannot be measured without resorting to some assumptions. The height change measurements, on the other hand, can be reliably measured, and used as an alternative index o f the void ratio changes. In this light, the data in Table 5.3 indicates that the specimens thawed under a small hydrostatic effective stress and then reconsolidated to in-situ stresses undergo lesser disturbance than those thawed under high in-situ stresses. Specimens reconstituted i n the laboratory were well saturated compared to the undisturbed in-situ frozen sand specimens. The in-situ frozen specimens undergo much larger height change in both methods, partly due to the degree o f saturation and partly due to the disturbances caused by sampling in-situ.  138  Chapter 5: Fabric dependent behaviour of sands Table 5.3: Height change during restoration o f in-situ state o f Syncrude sands Method II  Method I undisturbed  reconstituted  undisturbed  reconstituted  8  61  52  22  Minimum  1.81  0.06  0.70  0.50  Maximum  3.49  0.29  8.65  0.86  Average  2.06  0.20  2.85  0.68  N o o f Specimens A x i a l Deformation (mm)  1  part o f the data from Hofmann (1997),  2  data from Hofmann (1997)  Frozen specimens were allowed to thaw under room temperature i n Method I, and in Method II, warm glycol solution was circulated through the end platens in an attempt to simulate unidirectional thaw, as the inverse of the unidirectional freezing process in-situ. A n increase in the rate of axial thawing would be achieved by circulating warm liquids through the end platens. However, thawing in the radial direction cannot be completely prevented because o f the temperature differences between the cell fluid and the soil specimen. Thus, unidirectional thawing is only an idealized scenario, and in reality the specimens would thaw radially inwards as well as axially from the end platens. A s a result, a frozen sand core, that continually decreases in size, would exist in the middle of the specimen surrounded by the thawed sand. Such a rigid inclusion would induce shear stresses in the specimen, even under hydrostatic boundary stresses. Consequently a non-uniform stress distribution w i l l occur within the specimen. The severity o f this non uniformity w i l l be greatly enhanced, i f thawing occurs under large non hydrostatic stresses. In contrast, the magnitude of these non uniform stresses would be small i f the specimen  Chapter 5: Fabric dependent behaviour of sands  139  is thawed under small hydrostatic stresses as in Method I. The influence o f these small nonuniformities on the measured mechanical behaviour would diminish after the specimen is subsequently reconsolidated to the higher in-situ stresses. Since specimens are not reconsolidated to higher stresses in Method II, the non-uniform stress history w i l l persist, and could influence the measured response to an unknown extent. Numerical simulations of the thawing process using F L A C (1992) by Byrne (1998) indicates very high non uniform stress distributions i f the specimens are thawed under anisotropic in-situ stresses, rather than under a small hydrostatic stresses. Analytical simulations also show that shear strains developed during thawing by Method II to be an order o f magnitude higher than those developed in Method I (Hofmann 1997). Even though simplifying assumptions were made in the analyses regarding the complex constitutive relations of frozen soils, these results support the experimental observations reported in Table 5.3. It has been argued, based on the data in Table 5.3, that Method II causes the least disturbance while thawing frozen specimens (Hofmann 1997). The disturbance quantified by the void ratio change, computed by assuming an arbitrary and questionable radial to axial strain ratio, was used as the index instead of the measured axial strain. Radial strain was assumed to be twice the axial strain for Method I, but zero for Method II. It was believed that the presumed unidirectional thawing o f specimens i n Method II would not induce any radial strains. A s noted earlier, unidirectional thawing is only an idealized scenario, and even i n the theorized case o f unidirectional thawing, the circumferential stress boundary o f the specimen, with flexible membrane cannot also be deemed to be a strain boundary at the same time.  140  Chapter 5: Fabric dependent behaviour of sands  Figure 5.4 shows the measured axial and radial strains during reconsolidation (along the K  0  line) of all undisturbed specimens thawed by Method I. The radial strain during consolidation is consistently smaller than the axial strain during K consolidation. The ratio of radial strain to axial 0  strain, eje is plotted in Figure 5.5. This ratio is very small for most of the specimens, and the a  Undisturbed Sands ^  Mildred Lake  A  Syncrude J Pit  •  Kidd  O  Massey  v  J  O O  0.0  0.5  1.0 Axial strain, s  Figure 5.4 :  1.5 a o  2.0  2.5  (%)  Variation of radial and axial strains during anisotropic consolidation.  few higher values are a reflection of the very low radial strains (as low as 0.02%) recorded in those tests, and does not imply large volumetric strains nor a change in void ratio. Several specimens in Figure 5.5 exhibit negative eje ratios ranging from 0.0 to about -0.3. It is a  interesting to note that an e/s ratio of -0.50 would correspond to zero volumetric strain. In a  141  Chapter 5: Fabric dependent behaviour of sands  3.0  Undisturbed Sands  2.0  ^  Mildred Lake  A  Syncrude J Pit  •  Kidd  #  Massey  1.0  co  -0—•  0.0 \A  A  A  A  -1.0 0.0  2.0  1.0  Axial strain, e  Figure 5.5 :  a  3.0  (%)  Ratio of ejs of undisturbed sands during anisotropic consolidation along K - 2 line. c  z  contrast to consolidation along K path, the e/s ratio in hydrostatically consolidated sands is 0  a  very large (often greater than 2) on account of the inherent anisotropy. Consolidation along the K line in itself should result in zero radial strain. However, the in-situ 0  K is not exactly known and all undisturbed specimens were consolidated assuming a K of 0.5. 0  0  Chapter 5: Fabric dependent behaviour of sands  142  Small radial strain would therefore occur during reconsolidation, partly on account o f the difference between this laboratory K value and the actual unknown in-situ K , and partly due to 0  0  disturbances during sampling. It can be noted in Figure 5.5 that almost all Syncrude J-Pit sand specimens exhibit negative s / s values. This might be an indication that the in-situ K o f the a  0  Syncrude J-Pit sands might be higher than 0.50. Nevertheless, the measured radial strains are very small in all these tests. The data in Figure 5.4 demonstrates that assuming the radial strain to be twice that of the measured axial strain during K consolidation is not rational, and such an 0  assumption leads to progressively erroneous results with increasing axial strain (Figure 5.5). For a given axial strain, the radically different assumptions as to the 8 / s ratio result in a  volumetric strain five times higher for specimens thawed by Method I than by Method II (Hofmann 1997). Thus even when the sand specimens undergo equal axial displacement under both methods, these assumptions lead to five time larger calculated void ratio changes in Method I. The calculated void ratio change using this scenario is therefore a manifestation o f the assumptions, and is not indicative o f the actual void ratio change o f the sand. The measured height change data, which is an indirect indicator o f the void ratio change, clearly suggest that Method I causes lesser change in the specimen void ratio at the conclusion of restoring the in-situ effective stresses, compared to Method II.  5.3  Undrained behaviour of undisturbed sand  The undrained behaviour o f in-situ frozen undisturbed specimens from four different sites is presented in this section. Extensive in-situ tests were carried out at these sites to characterize the  Chapter 5: Fabric dependent behaviour of sands  143  soil deposits. Some results o f these tests are summarized in Table 5.4, together with the location of the water table, and the estimated age o f the deposits (Fear 1996). A l l sands retrieved by i n situ ground freezing are uniform, and have D  5 0  ranging from 0.20 to 0.35 mm. The fines content  (passing A S T M #200 sieve) in K i d d and Massey site sands is less than 5%. Both Syncrude sands have a fines content o f about 12%. The grain shape o f these sands is a direct reflection o f their source origin and subsequent transport and deposition at the current locations. The undrained response in triaxial compression, extension and simple shear is discussed below.  5.3.1  Monotonic Triaxial compression and extension tests  Figure 5.6 shows undrained triaxial compression and extension response o f undisturbed Mildred Lake sand specimens, consolidated to the estimated in-situ stress state. The stiffest and the softest extremes of the measured response is shown in the figure. Denser specimens exhibited more dilative response both in compression and extension loading. None o f the specimens exhibited true liquefaction type o f response, either in compression or extension loading mode. Further, no significant strain softening was noted in the compression mode. In extension mode, however, looser specimens strain softened and exhibited limited liquefaction type o f response. This indicates a very strong direction dependent behaviour o f undisturbed sands. Undrained behaviour o f undisturbed Mildred Lake sand reported by other researchers is also shown in Figure 5.6 for comparison (Vaid et al. 1996). These results also support the finding that undisturbed Mildred Lake sand does not significantly strain soften in the triaxial compression mode of loading even i n its loosest in-situ state.  144  Chapter 5: Fabric dependent behaviour of sands Table 5.4: C A N L E X Undisturbed specimens: in-situ characteristics (after Fear 1996)  Mildred Lake  Massey  Kidd  Syncrude J-Pit  Approximate age (years)  30  200  4000  0.1  Depth (m)  27 to 37  8 to 13  12 to 17  3 to 7  Water Table (m)  21  1.5  1.5  0.5  Ko  0.5  0.5  0.5  0.5  Unit weight above G W T below G W T  18.5 19.5  18.5 19.5  18.5 19.5  18.5 19.5  in-situ test indices (average & standard deviation) SPTN CPT  l i 6 0  qi c  18.2(3)  10.3(3.8)  17.2(4.8)  3.4(2)  7.5(1.7)  5.3(1.0)  6.5(1.8)  2.4(1.5)  0.73(0.15)  0.40(0.09)  0.37(0.05)  0.87(0.33)  156(20)  168(6)  177(5)  127(3)  (MPa) F(%) V s ! (ms ) 1  Similar triaxial data on the behaviour o f K i d d and Massey sands is shown in Figure 5.7 and 5.8. The K i d d sand is very dilative i n triaxial compression. Little positive excess pore pressures developed, and the very strong strain hardening response resulted in very high strength associated with the generation of very high negative excess pore pressure that eventually led to cavitation of the pore fluid. The essentially constant shear strength exhibited by the medium dense K i d d sand (e = 0.886) with strain, at about 900 k P a is a result o f deformation at constant effective c  confining stress due to pore fluid cavitation. Cavitation of pore water has i n effect rendered the undrained  test a drained one.  The  sand  would  have  exhibited an even  higher  Chapter 5: Fabric dependent behaviour of sands  Figure 5.6:  145  Undrained triaxial compression and extension response o f undisturbed Syncrude sand.  Figure 5.7:  Undrained triaxial compression and extension response of undisturbed K i d d sand.  Chapter 5: Fabric dependent behaviour of sands  Figure 5.8 :  147  Undrained triaxial compression and extension response o f undisturbed Massey sand.  148  Chapter 5: Fabric dependent behaviour of sands  strength, had the initial back pressure been higher than its in-situ value o f 100 kPa. In such scenarios involving very dilative soils, the maximum operating strength would be the drained strength. In contrast to triaxial compression, K i d d sand exhibits limited liquefaction type o f response in triaxial extension. The minimum undrained strength measured in triaxial extension is only a fraction o f that measured in triaxial compression. Massey sand also exhibits similar direction dependent behaviour i n triaxial compression and extension. A l l but one specimens are strain hardening in triaxial compression. The void ratio o f the specimen that exhibited limited strain softening deformation is 0.926. This void ratio is much denser than those o f several other specimens that are strain hardening. This inconsistency in the data suggests that this individual specimen might have suffered larger disturbance during sampling. Again, the strength o f the sand i n triaxial extension is much smaller on account o f the strain softening behaviour in this loading mode. Figure 5.9 shows the response o f Syncrude J-pit sand specimens. These specimens were tested at in-situ as well as at higher stress levels. The higher stress levels were used to simulate the stresses after the building o f the test embankment. One specimen at the in-situ stress level and one at higher stresses exhibit marginally strain softening response in triaxial compression. Increasing confining stress appears to have increased the potential for strain softening. Similar observation as to the effect o f increasing confining stress at a given K was made by V a i d and c  Thomas (1995) and V a i d et al (2000b). In contrast to being dilative in triaxial compression, the sand is very strain softening in triaxial extension. Consequently its strength in extension is quite small compared to that in compression.  Chapter 5: Fabric dependent behaviour of sands  Figure 5.9 :  149  Undrained triaxial compression and extension response o f Syncrude J-pit sand  Chapter 5: Fabric dependent behaviour of sands  150  Specimens that were exhibiting dilative behaviour after reaching phase transformation would presumably realise steady state after all dilation is complete. However, the specimens would have to be subjected to very large strains to realise this state. The end restraint effects that are inherently present in all soil testing devices often restrict the range of strains that can be imposed in a laboratory. During these triaxial tests, the specimens remained essentially uniform up to an axial strain o f 12-15% in compression and to about 10-12% in extension. Excessive bulging in compression and necking in extension was clearly noted beyond these strains. Several researchers have imposed axial strains in excess o f 30% in conventional triaxial apparatus in order to find the ultimate or steady state strength o f sands. Extreme caution is required in interpreting such data as the specimen at that large strain is far from being an element. The measured stresses and strains rather than being reflective o f one state, are in reality now the average of excessively non uniform states o f stresses and strains within the specimen. The results presented above, comparing the triaxial compression and triaxial extension behaviour o f four undisturbed sands clearly indicate that the behaviour of in-situ sands is direction dependent. Sands tested are rarely strain softening, and never exhibit significant loss in strength beyond its peak in compression even in their loosest state. Yet, they are almost always strain softening in triaxial extension. This direction dependent behaviour is a manifestation o f the inherent undrained anisotropy in sands.  Bjerrum (1972) recognized the existence o f this  anisotropy i n clays a long time ago. There is no reason to expect any difference in the response o f sands.  The existence o f such anisotropy in reconstituted sand specimens has been  demonstrated by several researchers over the years (Miura and Toki 1982, V a i d et al 1990a, V a i d  Chapter 5: Fabric dependent behaviour of sands  151  and Thomas 1995, Riemer and Seed 1997 among others). The results presented above indicate that this direction dependence in undrained behaviour is predominant in undisturbed sands as well.  5.3.2  Monotonic and cyclic simple shear response  Figure 5.10 shows the undrained simple shear behaviour o f undisturbed Mildred Lake Syncrude sand specimens over a range o f v o i d ratio. The loosest specimen exhibits strain softening response, but with little loss o f shear strength beyond the peak. The response gradually transforms from contractive into dilative as the relative density increases. The simple shear response appears to be stiffer than the triaxial extension, but is softer than the triaxial compression. V a i d and Sivathayalan (1996a) have reported similar findings i n specimens o f this sand reconstituted by water pluviation. This implies a systematic softening in the response as the direction o f major principal stress moves from 0° to the vertical in triaxial compression to 45 ° in simple shear (Roscoe 1970) and finally to 9 0 ° in triaxial extension. The friction angle at steady, quasi steady or phase transformation state, however, is essentially constant regardless o f the void ratio or confining stress level. The undrained simple shear behaviour of the other undisturbed sands is also essentially similar, in that they marginally strain soften in the loosest state, and increasingly strain harden as the void ratio decreases. However, an increase in density did not always produce a more dilative response. This inconsistency is apparently due to the possible non uniformity o f the in-situ sand deposit, associated with changes in both the composition and gradation with depth, and due to variations within an individual specimen. It is essential to recognize that the void ratio (or relative density)  Figure 5.10 :  Constant volume simple shear behaviour o f Phase I Syncrude sand.  Chapter 5: Fabric dependent behaviour of sands  153  assigned to an undisturbed specimen is only an average value, and there can be variations within the specimen. Figure 5.11 shows effective stress path and the stress-strain loops o f an undisturbed Syncrude sand specimen in undrained cyclic simple shear loading. The specimen suffers liquefaction in twelve cycles due to strain development on account of strain softening. This flow deformation is characteristic o f the true liquefaction type of response identified by Castro (1969). Unlimited unidirectional flow, characteristic o f steady state o f deformation would have ensued at constant stresses, i f not for the externally imposed unloading pulse that terminated the strain development at about 10% shear strain. A t this point the shear stress amplitude dropped below the steady state strength o f the sand. The excess pore pressure at the steady state of deformation was a constant at about 85% o f the initial confining stress. A state o f zero effective stress i n sands occurs only when the shear stress is zero. Thus, a state o f zero effective stress (or 100% excess pore pressure) is not realised when liquefaction occurs as a result of flow deformation, and the sand deforms at a constant non zero shear stress. However, a state o f 100% excess pore pressure is realised when the unloading pulse in the cyclic wave form reduces the shear stress to zero. F l o w deformation resulting from cyclic shearing o f Massey sand at a void ratio e = 0.968 is c  shown in Figure 5.12(a).  The sand realises steady state in the 7  th  cycle with a steady state  strength o f about 10 kPa. The behaviour o f Massey sand, at a slightly denser void ratio o f e = 0.958 is shown i n Figure 5.12(b). The sand now exhibits dilative response and progressively c  large strains develop as the effective stress path traverses through transient states o f essentially zero stresses. This type o f deformation is termed cyclic mobility (Ishihara et al. 1975, V a i d and Chern 1985). Figures 5.13 and 5.14 show the measured cyclic resistance i n the form of number  154  Chapter 5: Fabric dependent behaviour of sands  20 a' =217kPa e = 0.741  Syncrude J Pit sand  vc  c  10 h  GO CO  d>  C/3  -10 T  Flow deformation -20 -10  C Y  / a ' — 0.082 vc  _L  -5  0  Shear strain,  y  c y  (%)  - Unloading pulse after liquefaction cd  2a o CO co CD  0J  -75 100 V e r t i c a l effective stress,  Figure 5 . 1 1 :  200 G'  v  (kPa)  Undrained cyclic shear leading to flow failure i n Syncrude sand  155  Chapter 5: Fabric dependent behaviour of sands  I 0  i  l  i  40 V e r t i c a l effective stress,  Figure 5.12(a):  i  I  80 a'  v  I  120 (kPa)  Undrained cyclic shear leading to flow deformation in loose Massey sand  156  Chapter 5: Fabric dependent behaviour of sands  20 CT' = 118kPa e .= 0.958  Undisturbed Massey Sand  vc  c  H x 1  -20  / o ' = 0-098  cy  vc  1  0  •10  Shear strain,  5 y  c y  (%)  25  -25 h  40 V e r t i c a l effective stress,  Figure 5.12(b):  120  80 a'  v  (kPa)  Undrained cyclic shear causing deformation on account o f cyclic mobility in Massey sand.  157  Chapter 5: Fabric dependent behaviour of sands  0.20  Undisturbed Kidd Sand  a' = 171 to 138 kPa vc  •  e =0.970 0.10  A  e =0.878 • e =1.037 - 1.012 c  0.00  (a)  i  i  i i  100  10 0.20  a' = 132 to 105 kPa  Undisturbed Massey Sand  vc  e =0.940 • 0.10  0.00  e =0.862 c • A A .^  • e = 1.005 c  (b)  ,  e =0.809 •  c  e =0.998 -0.953 c  , 10  No of Cycles to Y = 3.75%  Figure 5.13 : Cyclic resistance of (a) Kidd and (b) Massey sands in simple shear.  100  158  Chapter 5: Fabric dependent behaviour of sands  0.20 a'  =217 kPa  vc  e =0.716 >  0.10  e =0.729  0.00 10  100  No of Cycles Figure 5.14 : Cyclic simple shear resistance of Syncrude sand.  of cycles vs cyclic stress ratio, for the undisturbed sands. These cyclic tests were carried out at the in-situ void ratio and stress levels. As such not enough data points are available at a given void ratio to develop the cyclic resistance curve of the sand at a given void ratio. Nevertheless, the trend lines are drawn linking specimens having similar void ratios. The rather flat cyclic resistance curves observed are typical of many reconstituted sands.  5.3.3  Post liquefaction behaviour in triaxial and simple shear  The post liquefaction behaviour of undisturbed sands was assessed both in triaxial compression and simple shear following liquefaction by cyclic loading or by static unloading. Figure 5.15  159  Chapter 5: Fabric dependent behaviour of sands  800 Phase I Essentially zero stiffness  Phase II Increasing stiffness  Phase III Essentially constant stiffness  400  e = 0.893 c  a' = 138 kPa vc  G' = h  8  12  69kPa  16  A x i a l strain (%)  Figure 5.15:  Post liquefaction behaviour o f undisturbed K i d d sand following liquefaction induced by static unloading  160  Chapter 5: Fabric dependent behaviour of sands  illustrates the post liquefaction response of loose undisturbed K i d d sand in triaxial compression. The sand, which was consolidated to a '  v c  =138 kPa, realised quasi steady state conditions at an  axial strain o f about 1.5%, in triaxial extension (Figure 5.15 inset).  The unloading o f the  deviatoric stress after an axial strain o f about 10% liquefied the sand by inducing 100% excess pore pressure. The sand was now loaded i n compression at a constant rate o f strain. Figure 5.15 indicates that post liquefaction stress strain curve is comprised o f three distinct regions o f deformation; initial deformation at essentially zero strength and modulus, followed by deformation with increasing modulus, and finally deformation at essentially constant modulus. The effective stress state is confined along the angle o f maximum obliquity right from the commencement of the post liquefaction loading. Similar behaviour has been reported for sands reconstituted by water pluviation (Vaid and Thomas 1995, V a i d and Sivathayalan 1996a). Figure 5.16 shows the post liquefaction behaviour of two undisturbed Massey sand specimens in simple shear. Both specimens were consolidated to essentially identical effective confining stress, and then were cyclically loaded with identical cyclic shear stress amplitude. The denser sand liquefied in 30 cycles with a maximum shear strain of about 5.5%, and the looser sand in 7 cycles with a maximum shear strain o f about 6.5%.  The relative density can be noted to  significantly influence the post liquefaction response, o f the otherwise similar sands. The post liquefaction stress strain curves i n simple shear may be noted to be similar to those under triaxial conditions, with three distinct regions o f deformation. The residual effective stress state at the onset of post liquefaction loading directly influences the first phase o f deformation. The magnitude o f the strain developed at essentially zero modulus is directly dependent on the residual effective stress. The stiffness o f the sand increases steadily  Chapter 5: Fabric dependent behaviour of sands  Figure 5.16:  161  Post liquefaction response of loose and dense Massey sand following liquefaction induced by cyclic loading  Chapter 5: Fabric dependent behaviour of sands  162  with strain during the second phase o f deformation. This phenomenon of increasing stiffness with strain is the reverse o f the assumed behaviour o f soils, where straining is commonly associated with a loss o f stiffness. This unusual response arise from the fact that on post liquefaction loading the sand dilates all the way from the beginning, causing the effective confining stress to increase with strain. In contrast, in pre liquefaction monotonic loading almost all sands initially contract, and thus cause a decrease in effective confining stresses, which i n turn leads to stiffness degradation. The deformation during all three phases o f the post liquefaction loading occurs at a mobilised friction angle that equals the angle o f maximum obliquity noted under static loading. The characteristics o f the post liquefaction stress strain curve are apparently independent o f the nature o f the loading that induced liquefaction, i.e either static or cyclic, and the mode o f loading, triaxial or simple shear. Figure 5.16 indicates that shear modulus and the rate o f strength recovery in post liquefaction loading is dependent on the density o f the sands. However, the response in the effective stress space is unique, since the angle o f maximum obliquity is independent of stress level, density and loading mode (Vaid et al. 1990a, V a i d and Thomas 1995). A s noted i n the pre liquefaction static and cyclic loading, the post liquefaction stress strain curve (and the associated shear modulus and strength) is also heavily dependent on the loading mode. The post liquefaction resistance o f undisturbed Syncrude sand measured in triaxial compression and simple shear is compared in Figure 5.17.  Both specimens were initially  consolidated to essentially identical void ratio and confining stress level, and were liquefied by static load-unload cycle with a maximum shear strain of about 10%. The sand has a much higher modulus in triaxial compression than i n simple shear. This loading direction dependent behaviour is a reflection o f the anisotropic nature o f the undisturbed sand. It appears that neither the large  163  Chapter 5: Fabric dependent behaviour of sands  400  Undisturbed Syncrude sand  e = 0.734 c  G' =100kPa vc  300  /  /  ; i  200 e = 0.737 c  CT' = 100 kPa  100  vc  0  10  30  20 Shear strain (%)  300 Loading Mode Triaxial Compression Simple shear  200  100  _L  200  300  (G\+G' )/2 3  Figure 5.17:  400  500  (kPa)  Post liquefaction response of undisturbed Syncrude sand in triaxial compression and simple shear.  Chapter 5: Fabric dependent behaviour of sands  164  strains (up to about 10%) the sand had experienced in pre liquefaction loading nor the development o f 100% excess pore pressure has altered the anisotropic nature of the fabric o f the undisturbed sand. The post liquefaction behaviour o f undisturbed Syncrude sand under multiple unload-reload cycles is shown in Figure 5.18. Liquefaction was initially triggered by the development o f 100% excess pore pressure by a static load-unload cycle in triaxial extension. O n post liquefaction loading in compression the sand required about 8% shear strain to mobilize a shear strength o f a mere 5 kPa, before entering the second phase o f deformation where the modulus increased with strain. However, after the second unload cycle in compression which also terminated in 100% excess pore pressure, the sand mobilized the same 5 k P a strength in only about 1% strain i n its subsequent reloading in compression.  This implies that the amount o f post liquefaction  deformation required for the sand to exhibit commencement of any appreciable modulus increase with strain is dependent on the sense o f post liquefaction loading with reference to the loading that induced liquefaction. A change in the direction o f strain results in reduction in modulus compared to straining i n the same direction. The post liquefaction response during the third phase o f deformation in each cycle, however, may be noted to occur at an essentially constant modulus regardless o f the number o f load cycles.  5.4  Influence of specimen reconstitution technique  Several specimen reconstitution techniques, tamping and pluviation being the most common, are in use in current practice. The objective in all of these is to replicate a uniform sand specimen  Figure 5.18:  Post liquefaction response o f Syncrude sand under multiple unload-reload cycles  Chapter 5: Fabric dependent behaviour of sands  166  at the desired void ratio and effective stresses to simulate the sand mass in-situ. Moist tamping has been used to reconstitute very loose specimens (even looser than the A S T M maximum void ratio). This becomes possible due to capillary effects between grains. The loose, collapsible structure that ensues upon moist tamping often leads to a contractive strain softening response, that may unjustifiably condemn a sand as potentially liquefiable. A s noted in chapter 2, pluviation in water has been shown to resemble the alluvial deposition process, because the fabric that ensues upon water pluviation has been found to be similar to that o f the naturally deposited alluvial and hydraulic fill sands (Oda et al. 1978). The influence of the method of specimen reconstitution was assessed from triaxial and simple shear tests. Syncrude sand from the Mildred Lake site (site used to sample undisturbed Phase I specimens) was consolidated to identical void ratio and effective stress following reconstitution by water pluviation, air pluviation and moist tamping. Specimens o f Fraser River sand (similar to those obtained during Phase II undisturbed sampling) were also reconstituted using different techniques and were tested in triaxial compression, extension and simple shear loading (Vaid et al. 1999). In previous studies, the dominant interest on the effects of specimen reconstitution on undrained response has centred primarily around the cyclic resistance o f sands (Mulilis et al. 1977, Ladd 1974, 1977).  A direct comparison o f the behaviour o f undisturbed sand with its  reconstituted counterpart using the same solids is pivotal in field characterisation using laboratory tests on reconstituted specimens. A critical requirement of any specimen reconstitution method is the ability to produce uniform test specimens. Uniformity o f specimens is essential since all laboratory tests are intended to measure element properties. Uniformity o f reconstituted specimens is often tacitly assumed, and  Chapter 5: Fabric dependent behaviour of sands  167  only a few researchers (Castro 1969, Emery et al. 1973, M u l i l i s et al. 1977, V a i d and Negussey 1988) have sought its direct confirmation. These limited studies demonstrate that the specimens reconstituted by moist tamping ( M T ) tend to be less uniform than those prepared by water pluviation (WP). Water pluviated specimens are much closer to being uniform with height (Vaid and Negussey 1988). Figure 5.19 illustrates the void ratio profile of test specimens reconstituted by water pluviation and moist tamping. The specimen was solidified using the gelatin technique (Emery et al. 1973), and cut up in a number o f horizontal slices, after peeling the rubber membrane away. The void ratio o f each slice was then computed after drying the solids in each slice. Serious non uniformities o f void ratio may be noted in the moist tamped specimen over the specimen height. The local relative density varies by as much as ± 1 0 % from the average o f the entire specimen, when the method o f reconstitution was moist tamping. Similar serious non uniformities have been reported by Castro (1969) in moist tamped specimens. The local deviation of relative density from the average may be noted to be much smaller (within about 3%) for water pluviated sands. Unlike a moist tamped specimen, the water pluviated specimen therefore closely approaches an element test, in its requirement o f homogeneity.  5.4.1  Compressibility and Accessible states  One-dimensional compressibility o f Syncrude sand specimens during consolidation in the simple shear apparatus is shown i n Figure 5.20.  The specimens were reconstituted by air  pluviation, water pluviation and moist tamping. Moist tamping yielded the loosest void ratio after reconstitution with an initial relative density o f about -20% (i.e. looser than the A S T M e  max  ) . The  168  Chapter 5: Fabric dependent behaviour of sands  Top  Bottom 25  100  75  50  Top  Bottom 10  20  30  20  30  Relative Density, %  Figure 5.19 :  Direct assessment o f uniformity o f reconstituted specimens (a) water pluviated Ottawa sand, (b) moist tamped Fraser River sand, and (c) moist tamped sand C (after Castro 1969).  Chapter 5: Fabric dependent behaviour of sands  169  loosest initial relative density that could be attained was about 2% when the specimens were air pluviated, and about 10% when water pluviated. During subsequent set up and after application o f a vertical confinement o f about 20 kPa, relative density increased by about 15% for W P and about 2 5 % for M T specimens. The compressibility of the moist tamped sand may be noted to be very high compared to that o f the air and water pluviated sand. This is believed to be due to the potentially collapsible fabric that ensues upon moist tamping. Evidence of such collapse resulting in large decrease in void ratio may be found even while saturating such specimens, in the results reported by several researchers (Sladen et al. 1985, Chang et al. 1981, Marcuson and Gilbert 1972). Figure 5.20 vividly indicates that the range o f accessible states in the void ratio - confining stress domain is highly dependent on the method o f specimen reconstitution. Similar data for Fraser River sand also indicate that the domain o f accessible states is dependent on the method of reconstitution, in addition to the confining stress level (Sivathayalan 1994).  Meaningful  application of laboratory studies to in-situ sands require that the states attained in the laboratory be compatible with those in the field. In-situ void ratio and effective stress state of two hydraulic fill tailings sands and a water laid deltaic sand at the C A N L E X research sites are shown in Figure 5.21. In-situ void ratios were directly computed from the ice content o f the frozen sand specimens. Accessible void ratio effective stress states o f these sands, when water pluviated in the loosest state, (assuming estimated K,, = 0.5), and states attained by moist tamping (Wride and Robertson 1997) are also illustrated in the figure for comparison. For all three sands, virtually all in-situ states are accessible by reconstituting the sand by water pluviation.  Chapter 5: Fabric dependent behaviour of sands  170  -25  1.00 h ASTM e  6  0.90 25  "5  'o  c T3  0.80 h  >  r  0.70 V  Reconstituted By:  ai  A  Moist tamping  •  Air Pluviation  A 50  Water Pluviation _i  _i  i  i  i  10  ' ' i ' i  i  i  i  i  i i i  100 11  Vertical consolidation stress, a'  i  i  i i  75 1000  i i  (kPa) vc  Figure 5.20 : Range o f accessible states by different reconstitution techniques The few data points that fall above the compressibility curve of the water pluviated specimens can be regarded as a normal scatter expected in experimentation. Looser void ratios might also have been caused by any upward gradient i n the deposition environment. These undisturbed specimens were retrieved from sites identified as loose deposits after consideration o f several alternative sites (Wride & Robertson, 1997). Further, the test embankment in Phase III o f the C A N L E X project was built by deposition o f sand i n water under gravity. A s such these in-situ void ratio effective stress relationships illustrated in Figure 5.21 can be assumed to be representative o f the loosest possible in-situ states. There is no evidence in the literature to  Chapter 5: Fabric dependent behaviour of sands  Figure 5.21  In-situ states o f undisturbed sands in comparison to states attainable by laboratory reconstitution methods.  171  Chapter 5: Fabric dependent behaviour of sands  172  suggest that the in-situ void ratio o f a fluvial or hydraulic fill sand at a given vertical confining stress can be looser than that obtainable by water pluviation in the loosest state. The data in Figure 5.21 could thus be viewed as evidence in support o f the contention that water deposited in-situ sands are unlikely to exist in states looser than those achievable after loosest deposition by water pluviation. Similar evidence was found for another sand by V a i d and Pillai (1992) in a comprehensive study to assess the liquefaction susceptibility of Duncan D a m i n BC. Several researchers have reported sand liquefaction data at very loose density states -even looser than the A S T M (1991b) maximum void ratio. This has been made possible by adopting moist tamping as the method o f reconstitution. The presence o f capillary tension during moist tamping promotes the formation o f very loose specimens. However, it seems inconceivable that such negative relative density states are accessible to the in-situ sands in an alluvial environment. Thus, the relevance of the looser states (that are inadmissible in an alluvial environment) simulated by moist tamping in characterizing the liquefaction response of in-situ sands seems questionable. Attempts to assign the flow characteristics o f such artificially loose sand specimens to in-situ sands would be overly conservative (even i f the influence of the collapsible moist tamped fabric on the undrained behaviour o f sands is neglected).  5.4.2  Static Undrained Behaviour  Figure 5.22 shows direct comparative static undrained simple shear response o f three specimens o f Syncrude sand, reconstituted by different techniques to an essentially identical  173  Chapter 5: Fabric dependent behaviour of sands  80.0  Mildred Lake sand  Water pluviated e = 0.777 c  -  40.0  y—  Air pluviated  Moist Tamped 0.0  e = 0.767 i  1  i  1  i  10 Shear strain y  1  c  i  15  20  15  20  (%)  1.00  0.50 h  0.00 10 Shear strain y  Figure 5.22 :  (%)  Influence o f specimen reconstitution technique on the undrained simple shear response o f Syncrude sand  Chapter 5: Fabric dependent behaviour of sands  174  effective confining stress o f 200 kPa, and void ratio o f about 0.770. Water and air pluviated specimens were reconstituted at targeted initial deposition void ratios so that the void ratio after consolidation to the desired vertical confining stress of200 kPa was essentially identical to that o f the moist tamped specimen. The measured undrained response may be noted to be drastically different even though the initial void ratio and effective stress state were all essentially identical. The moist tamped sand is very strain softening and exhibit true liquefaction type o f response associated with a very small steady state strength. The air pluviated sand, though contractive, shows only a marginal drop in shear strength beyond peak and exhibits limited liquefaction type o f response. In contrast, the water pluviated sand does not even exhibit any strain softening. Instead, it behaves dilatively. Undrained simple shear tests on air and water pluviated specimens of Fraser River sand also exhibit similar differences in response (Vaid et al. 1999). The undrained triaxial compression behaviour o f Fraser River sand specimens reconstituted by moist tamping and water pluviation to essentially identical initial states are illustrated in Figure 5.23. Similar data i n triaxial extension is shown in Figure 5.24. Like in undrained simple shear, the moist tamped sand strain softens and suffers true liquefaction type of response both in triaxial compression and extension. The water pluviated sand on the other hand does not strain soften in compression. It does strain soften in triaxial extension in the limited liquefaction manner. But the minimum undrained strength o f the water pluviated sand is about an order o f magnitude higher than that o f the moist tamped specimen. The strain softening response o f the moist tamped sand is primarily due to the collapsible "honeycomb like" (Casagrande, 1975) structure that ensues upon reconstitution by moist . tamping. In addition, considerable variations from the average specimen void ratio occur in a  Chapter 5: Fabric dependent behaviour of sands  175  Figure 5.23 : Effect o f specimen reconstitution technique on undrained triaxial compression response  Chapter 5: Fabric dependent behaviour of sands  176  Figure 5.24 : Effect o f specimen reconstitution technique on undrained triaxial extension  Chapter 5: Fabric dependent behaviour of sands  111  moist tamped specimen (Figure 5.19), and the existence o f such looser regions may also contribute to the softer response. However, it is important to recognize that non-uniformities within the specimen have be to small in order to satisfy the requirements o f an element test. Figures 5.23 and 5.24 clearly indicate that the characteristic response o f water pluviated sands is highly influenced by the mode o f loading. A s noted in chapter 2, such direction dependent response o f water deposited sands has been reported by several other researchers as well. In contrast, moist tamped sands exhibit true liquefaction type o f response in both triaxial compression and extension implying that loading direction has little bearing on the response. Similar essential independence o f the response o f moist tamped sand on the loading mode may also be seen in the result reported by other researchers (Ishihara 1993, Castro et al 1982, Wride and Robertson 1997, Eshtehard 1996). This has often been cited as evidence in support o f the existence o f a unique steady state line in sands that is independent o f the loading mode. The results presented herein demonstrate that undrained response of water deposited sands is highly influenced by the loading mode, but that o f the moist tamped sands is not. Therefore any postulates o f the existence of a unique steady state line in sands may be limited to moist tamped sands only and cannot be generalised for sands reconstituted by other techniques nor to in-situ sands. Dilative behaviour in an undrained test is characterized by the development of negative pore pressures.  This increases the effective confining stress and thus the shear strength.  It is  significant to note that the moist tamped sands did not develop any negative pore pressure i n any loading mode. Other test data on moist tamped sands also show that moist tamped specimens do not develop negative pore pressures, unless when the specimens are reconstituted to a very  178  Chapter 5: Fabric dependent behaviour of sands  dense state (Wride and Robertson 1997). Water pluviated sands, on the other hand, develop negative pore pressures even at the loosest reconstituted state. This difference is very critical, in that the liquefaction susceptibility and stability of sand deposits is directly linked to the fact whether a sand develops positive or negative pore pressures on undrained loading.  5.4.2.1  Mobilised friction angle at SS/QSS/PT  Figure 5.25 illustrates the effective stress states at steady or quasi steady state of contractive, and at phase transformation of dilative sand specimens of Syncrude sand reconstituted by different techniques. The effective stress states of all specimens lie on an essential straight line passing through the origin regardless of the method of reconstitution or the mode of loading implying a unique mobilized friction angle. Several other researchers have also reported that the mobilised friction angle at steady state, quasi steady state or phase transformation, ( | >  ss/  p  X  is independent of  the confining stress level, relative density or the loading mode (Ishihara et al. 1975, Vaid and Chern 1985, Vaid et al 1990a, Uthayakumar and Vaid 1998). The results shown in Figure 5.25 further demonstrate that <t> /pT * independent of the fabric as well. This suggests that § s  SS  SS/PT  of  a given sand is unique and is dependent only on the mineralogy (Negussey et al. 1988).  5.5  Comparative undrained behaviour of undisturbed and reconstituted sands  Test results presented in the preceding sections demonstrate that the undrained behaviour of undisturbed sands is direction dependent. None of the undisturbed in-situ sands from the four  Chapter 5: Fabric dependent behaviour of sands  179  tests sites are highly strain softening in triaxial compression even in their loosest state. However, they do exhibit strain softening behaviour in simple shear and triaxial extension. Such a behaviour is a confirmation o f the existence o f inherent undrained anisotropy in in-situ sand deposits.  300  cj' = 50~520kPa  Type of Response  OH  200  •  SS  A  QSS  +  PT  VC  e =0.667-0.814  oo  m b i  100 PT/QSS/SS  Syncrude Sand 100  (c\+a'j)/2  Figure 5.25 :  300  200 atss/QSS/PT  (  k  P  a  )  Effective stress state at steady, quasi steady ( i f contractive) and phase transformation (if dilative) states o f undisturbed and reconstituted sands.  The triaxial compression and extension behaviour o f reconstituted sands reported in the preceding sections, however, illustrates that not all types o f reconstituted specimens exhibit direction dependent behaviour. Unlike the water pluviated sands that strain softened in extension, but strain hardened in compression at identical initial states, the moist tamped sand strain softened  Chapter 5: Fabric dependent behaviour of sands  180  in both loading modes culminating in steady state of deformation. This implies that the effect o f inherent anisotropy is more pronounced in water pluviated compared to moist tamped sands, and points to a qualitative equivalence in the behaviour o f water pluviated and natural alluvial (or hydraulic fill) sands in regard to their inherently anisotropic nature.  5.5.1  Static undrained behaviour  Test results illustrating a direct quantitative equivalence in the response of undisturbed sand and its water pluviated counterpart are presented i n this section. A s noted in Chapter 3, the reconstituted specimens were formed using the entire solids retrieved at the end of the undrained test on the undisturbed specimen. The void ratio and effective stresses o f the reconstituted specimens prior to undrained shear were targeted to be identical to those o f the undisturbed specimens. Figure 5.26(a) compares the static undrained triaxial compression response o f undisturbed Massey sand and its counterpart reconstituted by water pluviation to an essentially identical initial density and stress state. Similar response in triaxial extension is illustrated in Figure 5.26(b). Both undisturbed and water pluviated specimens are dilative in triaxial compression, but exhibit strain softening of the limited liquefaction type in extension. Similar comparison of the behaviour o f K i d d sands in triaxial compression and extension loading modes is illustrated in Figure 5.27.  The K i d d sand specimens were densified by tapping the base o f the triaxial  apparatus following reconstitution i n the loosest state by water pluviation so that the void ratio  Chapter 5: Fabric dependent behaviour of sands  Figure 5.26(a):  181  Comparative undrained triaxial compression behaviour of undisturbed and water pluviated Massey sand  182  Chapter 5: Fabric dependent behaviour of sands  100  Triaxial Extension  a' = 98 kPa vc  rj' = 49kPa hc  e = 0.910 c  c3  -100  -200 12 Axial strain, s  (%)  120 Undisturbed at  60 h  b  Water pluviated  z  -60 h  -120 100  200 ( G ' + G' )/2 V  Figure 5.26(b):  h  300  400  (kPa)  Comparative undrained triaxial extension behaviour of undisturbed and water pluviated Massey sand  183  Chapter 5: Fabric dependent behaviour of sands  1000  Triaxial Compression  CT' = H6kPa vc  a' = hc  58kPa  e = 0.846  750 -  c  2a  „„. e = 0.854 c  500 h  250  1  I  ,  1  10 A x i a l strain, 8  a  .  15  20  600  800  (%)  480 Undisturbed  cd  CN  360 h  Water pluviated  240  b 120  200  400  (cj\ + & )/2 h  Figure 5.27(a):  (kPa)  Comparative undrained triaxial compression behaviour o f undisturbed and water pluviated K i d d sand  Chapter 5: Fabric dependent behaviour of sands  184  100 G' =  134 kPa  he  67 kPa  VC  Triaxial Extension  0  -100  e = 0.924 c  -200  -12  -9 A x i a l strain, s  (%)  120  Undisturbed Water pluviated  60 h  -60 h  Failure by Necking *  l_  -120 100  200 (&  Y  Figure 5.27(b):  + & )/2 h  300  400  (kPa)  Comparative undrained triaxial extension behaviour of undisturbed and water pluviated Kidd sand.  Chapter 5: Fabric dependent behaviour of sands  185  after consolidation to the in-situ stresses were essentially similar. The characteristics o f the response can again be seen to be reasonably similar in both loading modes.  Such direction  dependent undrained response indicates that both alluvial in-situ and water pluviated sands are inherently anisotropic. Static undrained simple shear response of undisturbed and their water pluviated counterparts from the Massey and K i d d sites is shown in Figure 5.28 . The behaviour of water pluviated and undisturbed sands may be noted to be much closer in simple shear compared to that in triaxial. This could apparently arises from the fact that the sands in-situ are likely to have a somewhat non uniform void ratio with depth.  The computed in-situ void ratio o f the o f the undisturbed  specimen is in fact a representation o f the average void ratio over the entire height o f the specimen. Water pluviated specimens, on the other hand, are very uniform as illustrated earlier in Figure 5.19. This could render the response of the undisturbed triaxial specimen differ from those o f their uniform water pluviated counterparts. The simple shear specimens are relatively thin (~20mm) and therefore are more likely to uniform over this small depth. A number o f undisturbed triaxial specimens were cut into several slices at the end o f the undrained test, and the void ratio o f each o f the slices were measured and compared to the average void ratio. A variation in void ratio o f as much as ± 0.03 from the average specimen void ratio were noted over the specimen height.  The void ratio distribution i n two undisturbed  Syncrude sand specimens is shown in Figure 5.29. These results tend to substantiate the postulate behind the larger difference in behaviour noted in triaxial than in simple shear. Figure 5.30(a) illustrates the effective stress conditions o f all undisturbed in-situ frozen specimens at steady, quasi steady or phase transformation states, and their water pluviated  Chapter 5: Fabric dependent behaviour of sands  Figure 5.28:  186  Comparative undrained simple shear behaviour of undisturbed and water pluviated sands.  Chapter 5: Fabric dependent behaviour of sands  0.60  0.70  187  0.80  0.70  0.80  0.90  Void ratio  Figure 5.29 : V o i d ratio variation along the height o f undisturbed Syncrude sand specimens  counterparts o f K i d d and Massey sands. The minimum undrained strength for each pair o f specimens may be noted to be essentially similar for both states. Even though individual specimens realise steady/quasi steady state at different effective stresses at due to the differences in void ratio and confining stress levels prior to undrained shear, the friction angle <J> s/ss Q S  mobilized is essentially constant This suggests that the behaviour o f the sand i n the water pluviated state is consistent with that o f the same sand in the undisturbed state. Test results similar to those in Figure 5.30(a) for Syncrude sand specimens are shown in Figure 5.30(b). Unlike in K i d d and Massey sands, reconstituted specimens o f Syncrude sand were not tested at identical void ratio and confining stresses as the undisturbed specimens. Rather, tests  Chapter 5: Fabric dependent behaviour of sands  80  Open Symbols : undisturbed Closed Symbols : water pluviated  03 OH  H  5: OO OO  cy  60  oo  OO  00  Q' on oo  188  a' (kPa)  •  vc  v  '  e  c  119  0.873  o  100  0.997  A  100  1.000  V  102  0.972  <C>  114  0.962  40  "03  (Kidd sand)  is 03 <L>  J=  00  20  s  S  A  X  03  (Similar Symbols indicate equivalent tests) 0  40  80  120  Effective vertical stress at SS/QSS/PT, a'V, SS/QSS/PT (kPa)  Figure 5.30(a):  Effective stress states at steady, quasi steady or phase transformation states in undisturbed and equivalent water pluviated sands.  were performed over a range of void ratio and confining stress levels. The locus of the effective stress states is again a straight line passing through the origin implying that the friction angle <j)  QSS/ss  mobilised at this state is also constant for Syncrude sand.  The minimum undrained strength at steady or quasi steady state normalised by the initial vertical effective stress in shown in Figure 5.31 for undisturbed and reconstituted Syncrude sand. The normalised shear strength of undisturbed and water pluviated specimens are very similar. In  Chapter 5: Fabric dependent behaviour of sands  189  250 Syncrude sand  #  Moist tamped  vc  A  Water pluviated  c  +  Air pluviated  O  Undisturbed (in situ frozen)^  a'  = 50~520kPa  e =0.667-0.814 200  20  e:  oo oo S> oo oo  t/3  <b  =28  TSS/QSS/PT  100  150  200  250  CT' at SS/QSS/PT (kPa)  Figure 5.30(b):  Effective stress states steady, quasi steady or phase transformation state o f Syncrude sand over a range o f effective confining stress and void ratio.  contrast, the moist tamped sand yielded very low normalised strength. Despite this low shear strength of moist tamped sands, the mobilized friction angle <t> /ss essentially independent o f ls  QSS  the method o f specimen reconstitution. D y v i k and Hoeg (1998) have recently reported that the undrained behaviour o f undisturbed sands is quite different to that o f the moist tamped sands. They tested silty sand and silty specimens obtained from a fluvial deposit in Sweden, and found that moist tamped sand exhibited  190  Chapter 5: Fabric dependent behaviour of sands  1.0  Syncrude Sand 520 kPa 0.8  h  0.6  Fabric  •  e = 0.667 c  0.814  Moist tamped  A  Water pluviated  +  Air pluviated  O  Undisturbed  6: CO GO  io  CO  c/2  0.4  Vr/ss~  2 8  0.2  0.0 0.0  0.2  0.4  a' v,  0.6  0.8  1.0  SS/QSS/PT^ vc  Figure 5.31 : Normalised effective stress states at steady/quasi-steady states.  much lower strength than the undisturbed sands. They concluded that".. specimens prepared to in-situ density by moist tamping cannot be used to predict in-situ behaviour". Their results are a reflection of the different fabrics that ensue upon deposition in a fluvial environment and reconstitution by moist tamping, and it provides supporting evidence to the findings of this study. On the other hand, Ishihara et al. (1998) report a comparative study on the behaviour of undisturbed and reconstituted specimens of Masado soils, and conclude that "there is no strong evidence to decide which of the sample preparation methods can best duplicate the in-situ  Chapter 5: Fabric dependent behaviour of sands  191  process of deposition". The contrasting finding o f Ishihara et al (1998) are likely due to flaws in their methodology and experimentation as pointed out by Sivathayalan et al. (2000).  5.5.2  Cyclic Resistance  The equivalence in the cyclic resistance o f undisturbed and water pluviated sands were assessed by performing cyclic simple shear tests. A s i n monotonic tests, the reconstituted specimens were formed using the entire solids retrieved at the end of the test on the undisturbed specimen. The void ratio and effective stresses at the end o f consolidation were targeted to be essentially identical to those of the undisturbed specimen. The specimens were then subjected to the same cyclic shear stress amplitude, as the undisturbed specimens. Figure 5.32 compares the measured cyclic response o f an undisturbed and equivalent water pluviated Massey sand. The undisturbed sand developed strains in excess of 3.75% i n the last half of the eighth cycle, and the water pluviated counterpart developed large strain in the first half o f the ninth cycle.  The  characteristics of the effective stress path during cyclic loading can also noted to be similar. The primary interest in cyclic behaviour o f sands is the number o f stress cycles o f a given amplitude required to induce liquefaction, and as the cyclic resistance o f sands is expressed in the form o f cyclic stress ratio vs number of load cycles, as illustrated in Figure 5.33(a). The data in this figure summarise the cyclic resistance of both undisturbed and equivalent water pluviated sands. The relative density o f the specimens shown in Figure5.33(a) ranges from about 22 to 30%. The cyclic resistance o f the undisturbed sands may be seen to be reasonably similar to that o f the equivalent water pluviated sands. This suggests that the cyclic resistance o f in-situ sand deposits  192  Chapter 5: Fabric dependent behaviour of sands  20 Water pluviated Undisturbed  C3  -20  4  6  10  Number of cycles  Figure5.32:  Comparison ofcyclic simple shear behaviour of undisturbed and equivalent water pluviated sand  Chapter 5: Fabric dependent behaviour of sands  193  0.16 D =22-30%  a  rc  0.14 h  CD  v  X  /a'  eye  7  vc  o  111  0.090  >  110  0.100  A  132  0.107  O  112  0.108  •  118  0.105  +  0.12 co CO  (kPa) vc  Undisturbed sand (Equivalent reconstituted tests not available)  »  CO O  0.10  +  +  Open Symbols : undisturbed Closed Symbols : water pluviated i  0.08  i  i  i  i  i  i  '  I  i  i  10  1  I  I  I  L  100  N o o f cycles to liquefaction (y > 3.75 %)  Figure 5.33(a)  Cyclic resistance o f undisturbed and equivalent water pluviated sand  can be conveniently assessed by testing specimens reconstituted by water pluviation i n the laboratory. This is a highly attractive economical alternative to testing undisturbed in-situ sands. Several previous studies have shown that the cyclic resistance o f sands is highly dependent on the method o f specimen reconstitution that controls the ensuing fabric i n the laboratory (Mulilis e t a l 1977, Ladd 1977).  Chapter 5: Fabric dependent behaviour of sands  194  The results in Figure 5.33(a), therefore imply that the laboratory characterization of the cyclic resistance o f in-situ sands could be reliably made only i f specimens are reconstituted by water pluviation. Water pluviation closely mimics the deposition process, and the ensuing fabric o f fluvial and hydraulic fill sands. The cyclic resistance of undisturbed Massey sand and its water pluviated counterparts is now compared in Figure 5.33(b) to the cyclic resistance of water pluviated Fraser River sand reported in the literature from earlier studies (Sivathayalan 1994, V a i d and Sivathayalan 1996a). Even though the Massey sand used in this study was obtained from a depth o f about 10 to 12m, and Fraser River sand was simply dredged from the river, they are both comprised o f the same geologic source material. A close equivalence is therefore noted in the measured cyclic resistance o f the two sands. These results clearly suggest that water pluviated sands can be used to assess the liquefaction susceptibility o f in-situ sands even under dynamic loading conditions. They would provide an inexpensive alternative to obtaining undisturbed sand sample for testing.  5.5.3  Post liquefaction behaviour  Figure 5.34 compares the range o f post liquefaction response o f both undisturbed and water pluviated Massey sand. Unfortunately, no direct comparison o f the post liquefaction response can be attempted due to the large number of factors that influence the post liquefaction behaviour. Nevertheless, both undisturbed and water pluviated Massey sand may be noted to display the same three distinct phases of deformation; (i) the initial deformation at essentially zero stiffness, (ii) deformation with modulus increasing with strain and (iii) deformation at essentially constant  Chapter 5: Fabric dependent behaviour of sands  195  0.16 Cyclic simple shear resistance  0.14  o 'id  Line: Fraser River sand D =30% (After Sivathayalan 1994) rc  0.12  <u Ul  -*-»  +•  (Zl  Symbols: Massey sand D =22-30%  O  0.10  rc  Open Symbols : undisturbed Closed Symbols : water pluviated i  0.08  i  1  i  i  i  i  i  i  '  I  10  I  I  I  I L  100  N o o f cycles to liquefaction (y > 3.75 %)  Figure 5.33(b):  Comparison o f measured cyclic simple shear resistance o f undisturbed sands with a previous study on water pluviated specimens.  modulus. Similar characteristics o f the liquefied water pluviated sands have been reported by V a i d and Thomas (1994) and Yasuda et al. (1995) in triaxial loading, and by V a i d and Sivathayalan (1997) i n simple shear. Figure 5.35 shows the magnitude o f the shear strain required in post liquefaction simple shear loading to mobilize a small arbitrary shear strength o f 2.5kPa as a function o f the maximum shear strain developed during liquefaction. Results for both undisturbed and water pluviated sands are  Chapter 5: Fabric dependent behaviour of sands  196  03  Vi Vi  CZ5  20.0  40.0  Shear strain (%)  Figure 5 . 3 4 :  Range of post liquefaction stress strain curves of undisturbed and water pluviated Massey sand.  shown. This figure reflects the influence of the strain history prior to the initiation of the post liquefaction loading on the subsequent post liquefaction deformation. The data indicates that the strain range during which the sand deforms with essentially zero stiffness is dependent on the maximum shear strain developed during liquefaction. The large scatter in the data signifies that other parameters such as the relative density and confining stress level, may also influence this phase of deformation. The data shows that in particular the domain of strain over which the  197  Chapter 5: Fabric dependent behaviour of sands  30 Massey sand e = 0.940- 1.005 c  ?  20 h  ^  "  ^at G=0  o ca >-  CN  1 _ H  10 Specimen Type  o oo  ^  Undisturbed  #  Water pluviated  10 20 30 M a x i m u m shear strain during liquefaction  Figure 5.35 :  40 (%)  Influence of the magnitude of maximum shear strain during liquefaction on post liquefaction stress strain resistance.  stiffness remains essentially zero is highly dependent on the maximum past strain experienced during the loading that resulted in liquefaction. Post liquefaction behaviour of water pluviated sands over multiple load cycles was also found to be similar to that o f the undisturbed sand (Figure 5.18). Water pluviated sands also exhibit essentially constant shear modulus during the third phase o f deformation among different post  Chapter 5: Fabric dependent behaviour of sands  198  liquefaction load cycles (Vaid and Thomas 1995). The dependence of the shear modulus during third phase o f post liquefaction deformation of undisturbed sands on the relative density and on the loading mode may be noted i n Figures 5.16 and 5.17. Similar dependency o f shear modulus on density and loading mode o f water pluviated sands, illustrated in Figure 5.36, has been reported by V a i d and Sivathayalan (1997).  Thus, there is a strong indication that the  characteristics o f the post liquefaction response of undisturbed sands is also similar to that of their water pluviated counterparts.  0  10  20  30  40  Shear Strain Y , % Figure5.36:  Influence ofrelative density on post liquefaction stress strain response (after V a i d and Sivathayalan, 1997).  Chapter 5: Fabric dependent behaviour ofsands  199  The post liquefaction behaviour does not appear to be dependent on the deformation mechanism, v i z true liquefaction or cyclic mobility, that was the cause o f strain development. Even i f large deformations develop as a result o f true liquefaction, the unloading pulse o f the dynamic load causes an essentially zero effective stress state in the sand.  A l l subsequent  deformation from a state o f zero effective stress is associated with strain hardening where the sand dilates all the way from its initial zero effective stress state. This strain hardening response does not show any tendency to diminish, so as to reach a residual state, even when the sand is sheared in excess o f about 20% shear strain. Figure 5.37 shows the post liquefaction behaviour of undisturbed Syncrude sand specimen that exhibits true liquefaction type of response during cyclic loading. The sand reaches steady state o f deformation in the twelfth loading cycle, and deforms at a constant residual strength o f about 15 kPa. The unloading pulse in the applied cyclic load terminates the steady state deformation at about 8% strain. In post liquefaction loading the sand strain hardens and deforms at an essentially constant modulus after a strain o f about 15%, without any approach to a residual state. The steady state strength o f the sand i n virgin loading does not appear to be a limiting strength on post liquefaction loading. Similar behaviour o f undisturbed K i d d sand is shown in Figure 5.38.  These results imply that a sand may yield higher strength after liquefaction,  compared to the minimum undrained strength of the virgin sand. The stiffness, o f course is much smaller in post liquefaction. It appears that a sand that originally exhibited steady state type o f response that led to liquefaction w i l l not realise a steady state in post liquefaction loading, even at strains in excess of 20%. V a i d and Thomas (1995) and Sivathayalan (1994) have also reported that the minimum undrained strength o f the virgin contractive water pluviated sand does not  Chapter 5: Fabric dependent behaviour of sands  100  200  Undisturbed Syncrude sand  a' = 217 kPa e = 0.741 vc  c  T  c y  / o'vc  =  °-  0  8  2  75 V  Post liquefaction stress-strain curve  0 3  3  50 -  E H  25 / I  I  Residual strength in virgin loading  /  r—^^  i  i  i  I  10  15  20  25  Shear strain, Y Figure 5.37:  m a x  30  (%)  Post liquefaction stress- strain response in comparison to that o f virgin loading in Syncrude sand.  represent a cap on the post liquefaction strength. Both water pluviated and undisturbed sands exhibit similar characteristics in this regard as well (Figures 5.37 and 5.38). This dramatic change apparently occurs because such a sand in the virgin state could undergo contractive deformation, whereas its deformation in post liquefaction loading is always dilative. O n virgin loading, a contractive sand deforms at a constant friction angle  (|>QSS/SS  during steady state, but in post  liquefaction it deforms at a mobilized friction angle <|> that is a few degrees higher than <|>Q for f  all sands.  SS/ss  Chapter 5: Fabric dependent behaviour of sands  201  Undisturbed Kidd sand  o' =138kPa vc  e = c  T  c y  1.031 /o'  v c  =  0.118  75  y  Post liquefaction stress-strain curve  y  -  25 /  0 , 0  Residual strength in virgin loading  I  I  I  10  20  30  Shear strain, Y Figure 5.38:  m a x  40  (%)  Post liquefaction stress- strain response i n comparison to that of virgin loading i n K i d d sand.  The prediction o f earthquake induced displacements in sands requires the knowledge o f its post liquefaction stress-strain response. The initial attempts to model the seismically induced displacements treated the failed sand mass as a rigid plastic system (Newmark 1965). Newmark's method was later refined and extended by several researchers (Ambraseys and Sarma 1967, Sarma 1975, Makdisi and Seed 1978, Byrne et al. 1992). Improved analytical techniques using effective stress analysis suggested by Prevost (1981) and Finn et al. (1986) modelled the behaviour within loading cycles assuming hyperbolic stress strain relationship that imply modulus  Chapter 5: Fabric dependent behaviour of sands  202  degradation. But in all cases it was assumed that the steady state, and thus the residual strength, remains unaltered at its pre liquefaction value. Furthermore, the current analytical methods for determining liquefaction induced displacements assume the stress strain relationship o f the liquefied soils as shown schematically in Figure 5.39. The earlier methods assumed a linear relationship until the residual state. The recent models (Beaty and Byrne 2000), however, do accommodate stiffness increase with strain. Both approaches, however, limit the maximum post liquefaction strength at a residual value, that is often assumed to be slightly smaller than the strength o f the virgin contractive sand. The test data on the undisturbed sands do not exhibit such a residual state in post liquefaction loading even up to about 40% shear strain. A s a result, the current analytical methods would be conservative, and thus may over predict the earthquake induced displacements. Sands that exhibit true liquefaction type of response never dilate on virgin loading. Their effective stress path is bound within the contractive region below the steady state line as schematically shown in Figure 5.39(b). However, upon unloading after a controlled amount o f steady state o f deformation and on subsequent reloading in post liquefaction the deformation occurs due to dilation. The locus o f the stress path in post liquefaction loading stays confined along the angle o f maximum obliquity associated with strain hardening. The higher strength i n post liquefaction is apparently caused by the imposition o f deformation i n the dilative region as a result o f initial zero effective stress on the sand that would have otherwise deformed within the contractive region under virgin loading. In virgin loading, strain hardening sands (both dilative and limited liquefaction type) could ultimately realize steady state at very high stresses,"a/ter all dilation is complete'''' (Poulos 1981). A t this stage, the confining stress would increase to a very large value making the sand respond contractively. Such large negative pore  203  Chapter 5: Fabric dependent behaviour of sands  Post Liquefaction Response Measured oo. cu  Assumed in analysis  u  oo s-  B  cu  (a) Shear strain  A B : Locus of post liquefaction stress path SS : Pre liquefaction steady state  Contractive Region  SS/QSS/PT Line  (b)  Figure 5.39:  Schematic illustration ofthe characteristic post liquefaction response in undrained shear  Chapter 5: Fabric dependent behaviour of sands  204  pressure cannot, however, develop in the field because it will be limited to the initial pore pressure + 1 atm. Cavitation of pore water would occur at this pressure and the sand would then deform drained, and not undrained. However, it is essential to recognize that very large strains would be required to mobilise the strength in post liquefaction loading.  5.6  Summary  The undrained behaviour of undisturbed in-situ sands from four different sites, and specimens reconstituted by different techniques in the laboratory are presented in this chapter. The effect of fabric was assessedfromtriaxial compression, extension and simple shear tests. A comparison of the response of these undisturbed and reconstituted specimens clearly indicate that •  Undrained response of sands is highly dependent on the fabric, and thus on the method of specimen reconstitution. A sand at a given void ratio and stress state may Serious nonuniformities exist in moist tamped specimens compared to those pluviated in water.  •  Designs based on the very low shear strength of moist tamped sands could be very conservative as they would likely condemn a sand as being liquefiable, whereas in reality the sand may not be strain softening in the specified loading mode.  •  In-situ ground freezing yields high quality "undisturbed" samples in saturated sand. Thawing the frozen specimen at a low effective stress state and subsequently reconsolidating to the in-situ stress state causes minimal disturbance. Ground freezing is an expensive endeavour and may not be economically justifiable or even affordable in all projects.  Chapter 5: Fabric dependent behaviour of sands •  205  The behaviour o f in-situ sands is direction dependent, on account o f the inherent anisotropy.  •  The behaviour o f water pluviated sands is quantitatively and qualitatively very similar to that o f water deposited in-situ sands in triaxial compression, extension and simple shear loading modes, both under static and cyclic loading conditions, and i n post liquefaction loading.  •  the friction angle mobilised at steady state, quasi steady state, or phase transformation appears to be a unique property o f the sand. It is independent of the void ratio, confining stress level, loading mode or fabric.  •  Provided cy  3residual  = 0, the post liquefaction stress strain curve is characterised by an  increasing shear modulus with strain. Pre liquefaction steady state/quasi steady state strength o f the sand is not a limiting strength in post liquefaction loading. The essential characteristics o f the post liquefaction response o f the undisturbed sands are similar to those o f the water pluviated sands.  These results clearly demonstrate that the behaviour o f in-situ sand masses can be conveniently assessed from specimens reconstituted by water pluviation in the laboratory. This is an attractive alternative to testing undisturbed sands, as sampling undisturbed sand specimens is quite tedious and expensive. The ultimate objective of any fundamental studies on the behaviour of sands is to characterize the behaviour o f in-situ sands, that are often fluvial or hydraulically placed. A s these results clearly indicate that the behaviour o f moist tamped sands has little resemblance to the behaviour  Chapter 5: Fabric dependent behaviour of sands  206  of in-situ sands, extreme caution is required in assigning the characteristics of the moist tamped sand to the sand in-situ. These results clearly indicate that the characteristics of water pluviated sands in static, cyclic and post liquefaction loading can be directly assigned to in-situ sand deposits that are fluvial or hydraulically placed.  Thus water pluviation should be the  reconstitution method of choice in fundamental laboratory studies, if the results of these studies are to have any relevance to in-situ sand deposits.  Chapter 6  Generalised stress state and stress path dependent behaviour  6.1  Introduction  Undrained behaviour o f reconstituted Fraser River sand is presented in this chapter. Only loose density states that are reconstituted by water pluviation are considered. Since the fabric and density are held constant, the effective stress state was the sole initial state variable. The generalised initial effective stress state is completely specified by the magnitudes and the directions o f the three principal stresses. For convenience, it is represented by the derived stress parameters, effective mean normal stress cr' , inclination of major principal stress to vertical ct , mc  CTC  intermediate stress parameter b , and effective stress ratio K = a\j'G' . c  uniquely related to cr a Ic  2 c  a  3 c  c  3c  and ot or the applied surface tractions a oc  These, o f course, are  z c  a  r c  a  9 c  and x . ze  Water pluviated fabric was selected because it mimics the behaviour o f natural fluvial and hydraulic fill sands (Chapter 5). The findings o f this study w i l l therefore be o f direct relevance to the behaviour o f such sands in-situ. The loosest density state was chosen because o f its greatest susceptibility to liquefaction. The hollow cylinder torsional shear (HCT) device was used for performing the tests. It enables control o f the magnitudes o f all three principal stresses, and the directions o f two i n the vertical plane o f deposition. The undrained stress paths imposed  207  208  Chapter 6: Stress state dependent behaviour of sands  consisted o f no change in the direction of principal stresses as well as changing principal stress directions.  6.1.1  Initial States  A variety o f generalised initial stress states, characterised by a ' , a mc  CTC  b , and K were c  c  simulated. They were selected with the specific objective of isolating the influence of each state variable pn undrained response from that o f the others.  In order to keep the scope o f the  investigations within tractable limits, the effect of cr' level was, however, not explored. This was mc  kept constant at 200 k P a in all tests. The influence o f the direction o f major principal stress a '  l c  that was not coincident with the  principal axes o f anisotropy o f the sand (vertical or horizontal) was also explored (i.e. a A l l previous investigators focussed only on initial states characterised by a  o c  o c  *0).  = 0. The former  constitutes non-axisymmetric, and the latter axisymmetric initial stress states. The intermediate principal stress parameter b selected was 0.4 or 0.5. This is typical o f field problems, the c  majority o f which closely approximate plane strain. Some axisymmetric initial states with b = c  0 were also investigated. The influence o f static shear bias as the initial state variable was assessed by choosing a range o f K values from 1 to 2.5. The initial stress conditions and the c  subsequent undrained loading paths selected are those typically encountered in soil elements insitu; below sloping ground, embankments and other gravity structures.  Chapter 6: Stress state dependent behaviour of sands  209  A t the end o f reconstitution the H C T specimens were confined by a hydrostatic effective stress state o f about 30 kPa. The desired initial stress state was arrived at by first loading drained at K  c  = 1 to f j ' = 200 kPa, followed by further drained shear at constant a ' , a , and b , until the m  m  o c  c  target K level (Figure 6.1a). In a few tests, where the target oc and b were zero, drained c  CTC  c  loading to the initial state consisted o f first loading to the target K under constant a ' = 30 kPa, c  followed by further loading along the K line to the desired a ' c  6.2  m c  3  (Figure 6.1b).  Inherent Anisotropy  The behaviour of Fraser River sand under axisymmetric effective stress increments is presented in this section (Figure 6. lb). The major principal stress acts vertically and the intermediate and minor principal stresses are equal in these tests. The relative magnitudes of the measured axial, radial and tangential strains, which are the principal strains during axisymmetric loading, are used to illustrate the existence o f anisotropy in water deposited sands. The strain increments in Fraser River sand under hydrostatic stress increments from an initial hydrostatic effective stress state o f about 30 k P a to 500 k P a are illustrated in Figure 6.2. The radial and tangential strains are properly corrected for membrane penetration effects, as discussed in Chapter 4. The essentially identical values the strain components s and s under hydrostatic r  e  loading implies that the sand is isotropic in the horizontal plane. But the vertical axial strain s , 2  perpendicular to the bedding planes is much smaller than the radial and tangential strains along the bedding planes. This implies greater stiffness in the vertical than horizontal direction, and a  210  Chapter 6: Stress state dependent behaviour of sands  Paths: AB 100  -a  b  : Hydrostatic consolidation  B C : Drained shear at constant a 'mc, a C a  a  n  d  b  c  50  B J L  50  &  100  150  100  200  (a) 250  (kPa)  m  Axisymmetric consolidation: A B : Hydrostatic consolidation A C : Drained shear at constant cj'3c C D : Drained shear at constant K  CN  0  50  Oh'  (b) 50  100  150  200  (a',+ a* )/2 (kPa) 3  Figure 6.1 : Consolidation to generalised initial effective stress states  250  Chapter 6: Stress state dependent behaviour of sands  211  cross anisotropic fabric that ensues on deposition in water. Identical strains would have resulted in all three directions (i.e. s = s = e ), i f the sand was isotropic. The essential linearity o f the r  9  z  strain paths shown in Figure 6.2 further indicates that the initial degree o f anisotropy is not altered over the range of stresses probed. Similar findings have been reported in the literature by several other researchers from triaxial and torsional shear tests (Rowe 1971, El-Sohby and Andrawes 1972, Negussey 1984, Wijewickreme 1990). The existence o f inherent anisotropy has been attributed to both higher frequency o f contact normals in the vertical deposition direction, and the preferred orientation o f the longitudinal axis of the sand grains in the horizontal direction (Oda 1972). Fraser River sand grains are not spherical, but sub-angular.  Therefore, when deposited in water the sand would assume an  anisotropic fabric on account o f both the larger frequency o f contact normals, as well as the preferred horizontal orientation o f the longitudinal axis of the grains. The existence o f inherent anisotropy in the essentially rounded Ottawa sand, in contrast, would occur predominantly due to the higher frequency o f contact normals in the vertical direction. This gives rise to the higher compressibility in the horizontal direction than the vertical (Sayao 1989). This contention is supported by the data from hydrostatic compression o f mono-sized spherical glass beads from about 25kPa to 450 k P a (Figure 6.3). It may be noted that the radial strains are still larger than the axial, but the ratio s / s is essentially independent o f the size o f spheres. It is o f interest to a  note that the radial strains are about 100% larger than axial in Fraser River sand, but only about 50% larger in spherical glass beads. This suggests that the degree of inherent anisotropy may be much higher i n angular sands compared to rounded sands. The former owes its fabric both to  Chapter 6: Stress state dependent behaviour of sands  212  higher frequency o f contact normals in the vertical directions and the preferred horizontal orientation o f the longitudinal axis o f the grains, whereas, little preferred orientation would be expected in the latter.  Figure 6.2:  A x i a l , radial and tangential strain increments under hydrostatic stress increment.  Figure 6.3 :  6.2.1  Strain increments in uniform spherical particles under hydrostatic stress increments.  Drained deformation along constant K path (and KQ) C  Figure 6.4 illustrates the strains induced in Fraser River sand under drained axisymmetric effective stress increments at constant effective stress ratio K . The sand was loaded along c  Chapter 6: Stress state dependent behaviour of sands  214  0.50 Strains  o  •  0.25 h  Radial Tangential  0.00 to  -0.25  -0.50 0.0  Figure 6.4 :  A x i a l , radial and tangential strains under axisymmetric proportional loading  constant effective stress ratio path, from a '  m  = 30 k P a to 200 kPa.  This type o f loading  constitutes what is commonly known as the proportional loading path. The essentially linear strain path at each K level implies that the nature o f inherent anisotropy is fixed by K and is not c  c  significantly altered during loading at a constant effective stress ratio. The very small strain in the horizontal plane(Figure 6.4) when K = 2 implies that the coefficient o f earth pressure at rest K c  0  Chapter 6: Stress state dependent behaviour of sands  215  for loose Fraser River sand is slightly less than 0.5. Even though all test specimens were consolidated to a constant effective mean normal stress a' = 200 kPa, much larger axial strains mc  develop when K = 2.5 compared to the hydrostatically consolidated sand (K =1). This occurs c  c  because of increase in maximum vertical effective stress with increase in K for identical a' . c  6.3  mc  Undrained behaviour with generalised initial stress state  Undrained behaviour of sand consolidated to a generalised initial effective stress state was investigated under two types of loading paths. (i) principal stress directions fixed in directions identical to those prior to shear. This involves shear under constant a  a  ( = oc ), CTC  a (= a ) and b (= b ). m  mc  c  (ii) principal stress directions allowed to rotate in a controlled manner. This involves shear under constant a (= a ) and b (= b ). m  mc  c  The response under a given static shear K , but at different initial a , as well as under given c  oc  a , but different levels of K was explored under each of the two categories of tests. The desired CTC  c  undrained stress path was followed using feedback control in real time. The maximum excursions from the targeted parameters a  mc  a and b in a typical test in type (i), shown in Figure 6.5, may a  c  be noted to be relatively insignificant. This indicates that the prescribed undrained stress paths are faithfully followed by the control system.  216  Chapter 6: Stress state dependent behaviour of sands  90 a  m c  = 400kPa  - a  =30 CT  b = 0.4  8°  45.  Aa =1°  0 1.0  Solid lines : Actual parameters Dashed lines : Target parameters  0.5 L--'  —"—'  ~-  "*  Ab = 0.02 0.0 500  Aa  m  = 2.5 kPa  400  300 0.0  0.5  1.0  1.5  8, Figure 6.5 :  Targeted and actual control parameters followed in a typical test.  2.0  217  Chapter 6: Stress state dependent behaviour of sands  6.3.1  Response under fixed principal stress directions  The series o f tests carried out i n this category were aimed at investigation of the influence o f the initial static shear and the direction of major principal stress, and are listed i n Table 6.1. The initial effective stress state, and the subsequent undrained loading path i n each test have been identified. The variations in the surface tractions a '  z  <y\ a '  e  and T and the corresponding strains z9  induced i n specimens consolidated to an initial K = 2.0 and sheared at several constant values o f c  a  CT  = a  CTC  are illustrated in Figure 6.6. The computed principal stresses and induced principal  strains, and the mobilized effective stress ratio are shown in Figure 6.7 for the same series o f tests. The vertical strain e , referred to the fixed direction, is the monotonically changing z  independent variable against which all stresses and strains are plotted. 8 gradually changes from Z  the major principal strain at a  CT  = 0 ° to minor at a  a  = 9 0 ° . The magnitude o f the intermediate  principal strain is much smaller than either the major or minor, confirming that the chosen stress path with b = 0.4 imposes conditions close to plane strain during undrained shear.  Other  researchers have also demonstrated similar value o f b during undrained plane strain deformation (Uthayakumar and V a i d 1998, Yoshimine et al. 1998). The strain paths referred to fixed co-ordinate directions are essentially linear (Figure 6.6b) at small strains, and hence until a threshold mobilised stress ratio R=CT' ,/CT' at each a . This implies 3  that the degree o f initial anisotropy that is determined by the magnitude o f  a  o c and K stays ac  c  preserved for small increments in R in excess o f the initial value o f K . The paths, however, c  218  Chapter 6: Stress state dependent behaviour of sands  Table 6.1: Initial states of specimens tested under fixed principal stress directions  Test ID  Remarks  Initial State e  b  c  K  c  c  A01  200  0.897  0.4  0  1.00  A02  200  0.892  0.4  30  1.00  A03  200  0.890  0.4  60  1.00  A04  200  0.883  0.4  60  1.00  A05  200  0.880  0.4  0  1.25  A06  200  0.893  0.4  30  1.25  A07  200  0.895  0.4  60  1.25  A08  200  0.889  0.4  90  1.25  A09  200  0.889  0.4  0  1.50  A10  200  0.889  0.4  30  1.50  All  200  0.891  0.4  60  1.50  A12  200  0.894  0.4  90  1.50  A13  200  0.891  0.4  0  1.75  A14  200  0.883  0.4  90  1.75  A15  200  0.888  0.4  0  2.00  A16  200  0.884  0.4  30  2.00  A17  200  0.886  0.4  60  2.00  A18  200  0.880  0.4  90  2.00  Shearing at constant values of a , b m  ana a  CT  a-'  m  K  (•A  0'  3(rV  .b  Chapter 6: Stress state dependent behaviour of sands  219  300 h 200 100  a  = 90°  a  0 300 a'  m c  = 200  kPa  K = 2.0  200  100 a„ =  = 90°  %  30°  0 300 200 100  a  = 90"  a  0 100  y a N  50  a  = 30°  h  H  a  o  = 90»  a 1  -6  -3  =0°  i  0  3  6  Figure 6.6(a): Variation o f surface tractions with vertical strain during undrained shear at fixed principal stress directions.  Figure 6.6(b): Variation of radial, tangential and shear strain on the horizontal plane with vertical strain during undrained shear with fixed principal stress directions.  ]  I  I  I  I  I  -6  -3  0  3  6  Figure 6.7(a): Variation o f principal stresses and effective stress ratio during undrained shear with fixed a . 0  Chapter 6: Stress state dependent behaviour of sands  Figure 6.7(b):  222  Variation of principal strains with vertical strain during undrained shear at fixed principal stress directions.  Chapter 6: Stress state dependent behaviour of sands  223  become progressively non linear with increasing stress ratio at all oc levels, which demonstrates CT  a gradual evolution o f strain induced anisotropy. A t each a , the change i n anisotropy can be CT  attributed to the increase in effective stress ratio alone, since a stays constant in these tests. The c  degree o f induced anisotropy characterised by the curvature of the strain path is small, but does increase with increasing effective stress ratio, and strain. The relationships o f maximum shear stress (a, - a )/2 with the maximum shear strain y 3  m a x  =  (s, - 8 ) and the effective stress path for the data in Figure 6.6 are shown in Figure 6.8. The sand, 3  which is hardly strain softening when a = 0°, becomes increasingly contractive as a 0  CT  increases,  and finally responds in an essential steady state manner at cc = 90°. Such a systematic softening a  o f sand occurs on account of the inherent anisotropy on deposition and its evolution, i f any, until loading to the initial K = 2 (Arthur and Menzies, 1972). A s noted in the results presented i n the c  previous section, the higher compressibility along the bedding planes contributes to progressively softer undrained response as the direction of major principal stress moves from the vertical and approaches the direction o f the bedding plane. This is consistent with the findings o f larger volumetric strains at higher a in drained shear (Symes et al. 1985, Sayao 1989, Wijewickreme CT  1990). A systematic softening in undrained response of Fraser River sand with initial hydrostatic state ( K = 1) has been reported by Uthayakumar and V a i d (1998) as oc increases from 0 to 90 0  c  0  CT  The maximum shear stress at steady or quasi steady state, (the minimum undrained strength, SSS/QSS)  which is about 80 k P a for loading at oc = 0 ° , reduces to about 38 k P a as a CT  a  increases  to 9 0 ° . Thus, at a given void ratio, effective confining stress and static shear stress level, the minimum undrained strength of the sand is highly dependent on the direction of principal stresses  Chapter 6: Stress state dependent behaviour of sands  Figure 6.8 :  224  Undrained behaviour o f Fraser River sand at different fixed principal stress directions at K = 2. c  Chapter 6: Stress state dependent behaviour of sands  225  relative to the bedding plane. Data similar to that i n Figure 6.8, but at a lower initial static shear level corresponding to K c = 1.5, (Figure 6.9) again shows increased propensity toward strain softening at higher a . a  Comparative behaviour of sand at identical initial a = 0°, but different K levels illustrate the CT  c  effect o f static shear level only on the undrained response (Figure 6.10). N o strain softening to any significant degree is now noted when the sand is sheared at oc = 0°, regardless of the initial 0  level o f static shear. Larger K does promote marginally more strain softening, but the differences c  are relatively minor at this a = 0°. The sand starts strain hardening at shear strain in excess o f CT  about 2%, and there is no tendency to approach a steady state up to a shear strain o f about 10%. Similar influence o f static shear, but in axisymmetric triaxial compression ( a = 0 ° a n d b = 0) in c  contrast to the essentially plane strain conditions in these tests, has been reported by V a i d et al. (2000b). The influence of the level of initial static bias K , but now at an a = 60 °is assessed in Figure c  a  6.11. The sand becomes very contractive when sheared at this higher oc = 60°, and the resulting CT  strain softening leads to an essential steady state type o f response at each K level. This is i n c  significant contrast to the dilative behaviour that was noted at a  a  = 0° (Figure 6.10). The  minimum undrained strength of sand at identical initial void ratio and effective mean normal stress may be seen to be dependent on the initial static shear stress level. Its magnitude at K = l .25 is c  about half that o f that at K =2.0 at a = 60° even though the differences were minor at a - 0°. c  c  a  Thus the influence o f initial static shear stress level on the minimum undrained strength is more prominent when the direction o f a is larger at 60° (Figure 6.11) than at 0° (Figure 6.10). CT  226  Chapter 6: Stress state dependent behaviour of sands  Figure 6.9 : Undrained behaviour at fixed principal stress directions at initial K = 1.5. c  Chapter 6: Stress state dependent behaviour of sands  Figure 6.10 :  227  Undrained behaviour o f Fraser River sand over a range o f initial static shear at a  n  = 0°  Chapter 6: Stress state dependent behaviour of sands  Figure 6.11:  228  Influence of initial static shear on the undrained response of Fraser River sand at a„ = 60° P  Chapter 6: Stress state dependent behaviour of sands  229  The influence o f static shear on the liquefaction potential is often assessed from triaxial compression tests, and is considered relatively minor for loose sands, based on these test results at a = 0 °. However, test results in Figure 6.11 imply that static shear level may have a profound CT  influence depending on the initial direction of  oc , CT  and that triaxial compression loading w i l l fail  to fully describe the dependence o f minimum undrained strength for initial generalised stress conditions. Further, a sand that is stable at a = 0 ° at given initial static shear level may even c  possess the potential o f a flow slide at values o f a  a  > 0 (Figure 6.8). The most commonly  adopted triaxial compression results in practice w i l l , therefore, err on the unsafe side. This direction dependence of the minimum undrained strength is consistent with the nature of inherent anisotropy in sands. The minimum undrained strength at a = 90 ° and K = 2 is much smaller than the initial static a  c  shear stress o f 67 k P a (Figure 6.8). A relatively minor undrained perturbation i n deviator stress of about 5 k P a triggers strain softening and causes the sand to flow with a minimum undrained strength o f about 35 kPa. The potential for such instability is o f great concern in engineering design. Conventional undrained triaxial compression tests w i l l not reveal the potential for such a catastrophic failure. This emphasizes the need to duplicate the generalised initial effective stress states that exist in the field for estimating meaningful minimum undrained strength values of insitu sands  Chapter 6: Stress state dependent behaviour of sands  6.3.1.1  230  Triggering of strain softening  The peak of the stress-strain curve signifies the initiation of strain softening, and the mobilised effective stress ratio at that instant is termed the critical stress ratio, C S R (Vaid and C h e m 1985). The effective stress states at the onset o f strain softening in Figure 6.12(a) for a range o f a and a  K values show that the friction angle O c  a  CT  C S R  mobilised at this state is essentially constant at each  level, regardless o f K . The minor scatter in the data at a c  CT  = 90°, is apparently due to the  influence o f initial static shear level, but is relatively insignificant. It can be noted that (j)  CSR  is  strongly influenced by the direction of principal stresses. It varies from a l o w of about 19° for a  a  = 90° to about 30° for a = 0° (Figure 6.12b). Triaxial compression, extension and simple shear CT  studies on Fraser River sand also show similar dependency o f (j)  CSR  on the loading mode (Vaid and  Thomas 1995, V a i d and Sivathayalan 1996a). A systematic decrease in peak shear strength S  up e a k  may be noted with increase in oc at each 0  K level (Figure 6.13). The greatest decrease in the peak undrained shear strength appears to be c  associated with l o w levels o f static shear stress, and when a systematic decrease in S ^ u  a  is between 0 ° and 3 0 ° . Similar  with increasing a has been reported for hydrostatically consolidated a  sands by Uthayakumar (1996) and Shibuya and Hight (1987). Figure 6.13 also shows that at a given a , S a  up e a k  increases somewhat at higher K , the larger increases being associated with shear  at higher a values. CT  c  Chapter 6: Stress state dependent behaviour of sands  Figure 6.12 :  231  Variation o f (a): effective stress states at the instant of strain softening, and (b): friction angle mobilised at peak with a  CT  Chapter 6: Stress state dependent behaviour of sands  Figure 6.13:  232  Influence o f initial static shear, and direction of principal stresses on peak undrained strength.  Triaxial compression test results presented by C h e m (1985), V a i d and Thomas (1995), and V a i d et. al. (2000b) also confirm that S  u  ^ of strain softening sands at essentially identical initial  void ratio and confining stress is dependent on the initial static shear level.  Chapter 6: Stress state dependent behaviour of sands  233  The degree of strain softening is often characterized by the brittleness index I (Bishop 1971), B  which is considered to be a good indicator o f the flow potential o f a contractive sand. Bishop defined brittleness index as j  _  ( Speak  ^min )  7;  B  1  ( ) 6-1  peak  in which  and S  m i n  are the peak and minimum undrained strengths. The brittleness index  at a given K increases dramatically as a increases from 0 ° towards 9 0 ° (Figure 6.14 ). The c  CT  behaviour o f sand in triaxial compression, extension and simple shear loading also supports the contention that flow potential o f sands increases with a (Vaid and Thomas 1995, V a i d and CT  Sivathayalan 1996a). I , however, does not appear to be significantly influenced by the initial B  static shear stress level, at a given oc . I increases marginally with increasing static shear level 0  B  at cc = 0 ° , but decreases somewhat at a = 9 0 ° suggesting that I may not be a good index to a  c  B  assess the influence o f initial static shear on impending strain softening. The initial stress state with high K and higher oc may strain soften to a much lower steady state strength than the initial c  a  static shear stress (Figure 6.11). Such a response where the undrained steady state strength is lower than the current in-situ stresses w i l l have catastrophic consequences once the flow is triggered. The original definition of brittleness index by Bishop was intended to characterize the behaviour of hydrostatically consolidated soils. A s noted earlier, this definition is unable to fully describe the flow potential for anisotropically consolidated sands. A modified brittleness index 1^ defined by  Chapter 6: Stress state dependent behaviour of sands  Ir  ( ^peak  234  ^min )  peak  static  (6.2)  )  is used in this thesis to conveniently characterize the flow potential o f sands consolidated to initially anisotropic stress state. This definition uses the shear stress increment ( S ^ - S  static  )  required to initiate strain softening deformation, and for hydrostatically consolidated soils the expression o f  reduces to I . A value o f Ig = 0 would represent no strain softening and a value B  of 1 would imply minimum undrained strength equal to the initial static shear stress. Values o f Ig  1.00  0.75  H-P  0.50 h  0.25 h  0.00 h  1.00  2.00  1.50  Figure 6.14 : Variation o f brittleness index I with a B  a c  and K . c  Chapter 6: Stress state dependent behaviour of sands  235  larger than 1 correspond to minimum undrained strength lower than the static shear stress, and would imply a catastrophic collapse if equilibrium is disturbed by a small undrained perturbation. The modified Ig indicates that the flow potential of a sand depends both on the initial static shear level and the direction of major principal stresses during shear (Figure 6.15). Higher initial static shear levels represent a potential for catastrophic consequences at larger values of a , but its influence at a = 0° is only marginal. It is important to emphasize that this CT  0  modified definition of brittleness index is applicable only when principal stress directions remain fixed throughout the shearing phase.  10.0  5.0 ICQ  0.0  1.00  1.50  2.00  Figure 6.15 : Potential instability as assessed by the modified brittleness index  Chapter 6: Stress state dependent behaviour of sands  6.3.1.2  236  Steady or quasi steady state  Figure 6.16 shows the effective stress conditions at steady state or quasi steady state corresponding to the minimum undrained strength over the full range o f ot and K values. Quasi CT  c  steady state essentially coincides with the instant of maximum excess pore pressure which occurs when the undrained response transforms from contractive (positive excess pore pressure generation) to dilative (negative excess pore pressure generation) during shear. Thus, this state  250  200  23  b  150  100 h  50  50  100  (a,+  a )/2 3  150  200  250  (kPa)  Figure 6.16 : Effective stress state at steady, quasi steady or phase transformation states.  Chapter 6: Stress state dependent behaviour of sands  237  is synonymous with the phase transformation state for sands that exhibit strain softening behaviour. The data points i n the figure lie along a straight line passing through the origin regardless o f the initial a  a  or K , and correspond to a friction angle O c  s s / Q S S  o f about 34°.  Therefore, the friction angle mobilised at the instant o f minimum undrained strength is independent o f both the direction o f principal stresses during shear and the level o f initial static shear. Even though there exists a general agreement in the literature regarding the uniqueness o f (j)  ss/QSS  for a sand there has been some reluctance in accepting that both steady and quasi steady  states can be treated within the same framework (Been 1998). V a i d and Chern (1985) were the first to experimentally demonstrate that in triaxial compression both steady and quasi steady states can indeed be treated within the same framework i n the effective stress space.  Test data  presented in Figure 6.16 includes data for initial states that culminated in steady state following flow failure, as well as those that exhibited quasi steady state type of response. These results thus do support the contention that both steady state and quasi steady state (i.e., phase transformation) can be treated within the same framework i n the effective stress space, even under generalised stress conditions. It has also been demonstrated in a number o f earlier studies that the friction angle mobilised at steady or quasi-steady state is independent o f the void ratio, confining stress levels, and mode o f loading, triaxial or simple shear (e.g. Bishop 1971, Ishihara etal. 1975, V a i d and Chern 1985, Kuerbis et al. 1988, V a i d et al. 1990a, V a i d and Sivathayalan 1996a, Riemer and Seed 1997). Negussey et al (1988) have further shown that ^  S S / Q S S  equals the constant volume friction angle,  Chapter 6: Stress state dependent behaviour of sands  238  <|> measured i n a drained test. The results i n Figure 6.16 thus extend the earlier findings in that cv  ^SS/QSS is  a  l  s  o  independent of the level o f static shear, direction o f a during shear and the loading CT  mode, and suggests that steady and quasi-steady states are unique in the effective stress space. However, as noted elsewhere in this chapter, uniqueness o f steady/quasi steady state in the effective stress space neither guarantees nor requires uniqueness in the void ratio-effective stress space.  6.3.1.3  Angle of maximum obliquity  Sand that strain softens in a quasi steady state manner or dilative reaches the line of maximum obliquity with continued straining beyond the phase transformation state, and thereafter deforms along this line of maximum obliquity. The mobilised friction angle at maximum obliquity, rj), is f  about 3 to 4 ° larger than that at phase transformation. Its value for Fraser River sand is about 37°.  This angle, like  (J) /QSS SS  n  a  s  been demonstrated to be unique for a given sand regardless o f  its initial effective stress state, stress path in triaxial or simple shear or loading history (Vaid and Chem  6.3.2  1985,  Chung  1985,  V a i d and Thomas  1994,  Uthayakumar  1996).  Minimum undrained strength of sands  The shear stress at steady state (for sands exhibiting true liquefaction type o f response) or at quasi steady state (for sands exhibiting limited liquefaction type of response) corresponds to the  Chapter 6: Stress state dependent behaviour of sands  minimum undrained strength S  239  o f a strain softening sand. This is also called the residual  S S / Q S S  strength. Figure 6.17 illustrates the dependence o f the minimum undrained strength on oc and a  K . A systematic decrease i n the strength may be seen with increasing cc at a given initial K . c  a  c  The strength in loading paths with ct = 90 ° is only about a third o f that under loading paths with a  a = 0 at K = 1, and about half at K = 2. 0  CT  Figure 6.17:  c  c  Dependence o f minimum undrained strength on static shear and direction o f maj or principal stress.  Chapter 6: Stress state dependent behaviour of sands  240  Principal stress directions would normally vary along potential failure surfaces that are commonly encountered in field problems. The essentially plane strain in-situ conditions are often simulated using axisymmetric triaxial compression and extension. A s illustrated in Figure 6.18, a  c  in soil elements along the potential failure surface in a slope is close to 0 ° at the crest, but  gradually increases to about 9 0 at the toe. Based on the test results in Figure 6.17, this implies 0  a gradual reduction in the undrained strength along the failure surface, for a given initial void ratio. However, a constant undrained strength measured in triaxial compression tests is normally assigned i n practice to all elements along the failure surface regardless o f the direction o f a  0  Stress states simulated in:  a  Figure 6.18 :  3  SS  Systematic change i n the direction o f major principal stress along a potential failure surface.  Chapter 6: Stress state dependent behaviour of sands  241  Since the minimum undrained strength is a critical parameter in the deformation and stability analyses o f earth structures, the use o f triaxial compression strength (cc = 0 ° ) as the operating CT  strength would err on the unsafe side. It is encouraging to note that the dependency o f undrained strength on a is being accepted by the profession and has been incorporated in recent models for a  predicting earthquake induced displacements and i n stability analysis (Beaty and Byrne 2000, Puebla 1999). A s noted by V a i d et al. (1990b) the failure to recognize the dependency o f undrained strength on oc might have been the cause o f the difficulties Castro et al (1985) and a  Sladen et al. (1985) experienced in predicting liquefaction induced failure or displacements in San Fernando dam and Nerlerk berm slides respectively. Castro et al. (1985) had to apply a reduction factor o f 20 to the oc = 0 ° strength in order to match the back calculated average operating CT  strength along the failure surface. Even though an increase in K promotes more severe strain softening response as quantified c  by Ig, (Figure 6.15) it does not seem to increase the minimum undrained strength substantially at a given a . The dependency o f S 0  small dependence o f S  S S / Q S S  S S / Q S S  on K is much smaller than its dependency on oc . A c  CT  on K can also be noted in the triaxial compression test data reported c  by V a i d et al (2000b). Furthermore, the rate o f increase in S  s s / Q s s  with increasing K appears to c  be not dependent on the value of a (Figure 6.17). Even though the minimum undrained strength c  increases with K , it may be smaller than the static shear stress particularly at higher levels o f K . c  Thus, regardless o f the higher S  c  S S / Q S S  mobilised, the sand at a higher initial static shear might  undergo the most damaging strain softening response leading to flow failure at a given oc . a  242  Chapter 6: Stress state dependent behaviour of sands  It is important to emphasize that results shown in Figure 6.17 represent initial states with essentially identical void ratios and mean normal effective stresses. Yet they yield significantly different steady state (or quasi steady state) strengths depending on oc and K . The specimens CT  c  that realised a steady state following strain softening are identified in the Figure by solid symbols. The data clearly shows that the minimum undrained strength (whether steady state strength or quasi steady state strength) is not uniquely related to the void ratio alone, but rather is dependent, in addition on a , K and confining stress level, a' . CT  c  3c  Triaxial extension (Vaid and Thomas, 1995) and simple shear (Vaid and Sivathayalan, 1998) test data on contractive sands reproduced in Figures 6.19(a) and 6.19(b) also confirm the dependency of steady/quasi steady state strength on confining stress level and the loading mode, in addition to void ratio. However, the minimum undrained strength when normalised by the initial confining stress appears essentially independent of the confining stress level. The loading mode plays an important role in the magnitude of the realised steady state strength, and the results shown in Figure 6.17 showing a systematic decrease in S  ss/Qss  with oc is consistent with these CT  simple shear and triaxial test results. The data shown Figure 6.17, is replotted in Figure 6.19(c) with minimum shear strength normalised with respect to the major principal stress. This is attempted in order to assess whether the normalised minimum undrained strength under generalised loading conditions is independent of initial stress state as observed in triaxial and simple shear tests. Unlike the minimum undrained strength, which is considerably influenced by the initial static shear (K level), the normalised c  shear strength does not appear to be dependent on K regardless of the value of a . Apparently, c  a  Chapter 6: Stress state dependent behaviour of sands  Figure 6.19(a):  243  Dependence of undrained strength on confining stress level, and void ratio in triaxial extension  Chapter 6: Stress state dependent behaviour of sands  Figure 6.19(b):  244  Dependence of undrained strength on confining stress level, and void ratio in simple shear  Chapter 6: Stress state dependent behaviour of sands  245  0.5 K„  o  0.4 h  a  0.3  h  b GO  O'  t/5 c/f  1.00  •  1.25  o  1.50  A  1.75  V  2.00 >  0.2  0.1  h  0.0 30  60  90  (Degrees)  Figure 6.19(c):  Variation o f normalised minimum undrained strength with a at different initial static shear levels a  normalising the minimum undrained strength with major principal stress results in response essentially independent o f static shear at a given a . This is i n contrast to common practice CTC  where shear strength is often normalised with respect to the effective confining (or mean normal) stress This provides a rationale for using a '  v  in simple shear and o"'i ( = a ' under hydrostatic 3  consolidation) triaxial as the normalising parameters. The combined treatment o f quasi-steady state and steady states has often been criticized by the proponents o f the steady state concepts based on the argument that shearing at quasi-steady state takes place at constant stresses and void ratio only temporarily. Steady state concepts  Chapter 6: Stress state dependent behaviour of sands  246  contend that all sands w i l l reach this state ("a state at which the soil continues to deform under constant stresses at a constant void ratio") that is uniquely related to their void ratio only. Pluviated sands rarely strain soften under loading modes involving major principal stress direction essentially perpendicular to the bedding planes. In such dilative sands (Figure 6.8; a  CT  = 0 ° ) steady state can only be realised after all dilation is complete, and it occurs at very large strains as illustrated schematically i n Figure 6.20.  Dilative specimens, i f undrained, must  accommodate very large negative excess pore pressure in order to reach the steady state. If the in-situ pore pressure (or the laboratory back pressure) is not large enough, cavitation o f pore water would render the undrained test a virtually drained one. The undrained strength in such a case may be even higher than the drained strength, and is o f little interest in designing for such loading. In fact, the steady state o f a dilative sand is often inaccessible in the laboratory on account o f the very large strains required to mobilise it. According to the steady state concepts a sand at a given initial state, which may be strain softening i n triaxial extension, but strain hardening in triaxial compression should realise steady state at the same effective stress conditions. In Figure 6.8, for example, at a = 9 0 ° , there is no CT  dilation (i.e. no negative pore pressure developed) and the soil w i l l reach steady state at effective stresses lower than its value prior to undrained shear. In contrast, when a = 0 ° , the sand w i l l a  develop high negative excess pore pressures, and hence w i l l reach steady state at very high effective stresses. Thus, i f the soil at a given initial state responds in flow failure type strain softening in one loading mode (Figure 6.8, ct = 6 0 ° or 90°) but exhibits limited liquefaction or oc  dilative response in another mode (Figure 6.8, a  a c  = 0 ° or 3 0 ° ) then it is highly improbable that  Chapter 6: Stress state dependent behaviour of sands  Figure 6.20  247  Schematic illustration o f minimum undrained strength and steady state strength.  Chapter 6: Stress state dependent behaviour of sands  248  it w i l l reach steady state at identical effective stresses, as presumed in the steady state theory. Thus, the steady state concepts that may be valid i n a specific loading mode may not hold true among different modes. Further, it is essential to recognize that a steady state that is mobilised at very large strains, after all dilation is complete, is of little practical interest from the perspective of performance o f an earth structure.  Only the steady state strength (or quasi steady state  strength) following strain softening that corresponds to the minimum undrained strength w i l l be of primary concern in engineering design.  6.4  Response under principal stress rotation  The series of tests carried out for investigating the influence o f initial static shear K and ct c  ac  on undrained behaviour that also involves principal stress rotation are listed in Table 6.2. The initial state and subsequent undrained loading path in each test has been identified. Three distinctly different types o f undrained stress paths were considered. (a) a and a allowed to increase simultaneously from their initial values of a d  a  d c  and oc . For CTC  convenience the ratio AaJAc , which is called herein as the degree o f stress rotation, dn  was held constant. (b) a held constant at its initial value cr , while a is increased over its initial value oc . This d  dc  n  cc  represents deformation by a mere rotation o f principal stress directions, while their magnitudes stay constant.  Chapter 6: Stress state dependent behaviour of sands  249  Table 6.2: Initial states and loading paths in stress rotation tests  Test ID  Undrained Shear  Initial State e  c  b  K  c  c  AtVAo-j,,  Remarks A t constant values o f a , b and increasing  B01  200  0.907  0.0  0  1.0  1.75  B02  200  0.904  0.0  0  1.5  1.75  B03  200  0.901  0.0  0  2.0  1.75  B04  200  0.892  0.0  0  2.5  1.75  B05  200  0.898  0.0  0  2.0  0.70  B06  200  0.898  0.0  0  2.0  3.50  B07  200  0.898  0.5  30  2.0  1.75  B08  200  0.894  0.5  60  2.0  1.75  B09  200  0.893  0.0  0  2.0  OO  BIO  200  0.887  0.5  0  2.0  oo  m  c  A t constant values o f o m , b , a and increasing a c  d  CT  Bll  200  0.89  0.4  0  1.5  oo  B12  200  0.882  0.4  30  2.0  oo  B13  200  0.892  0.4  45  2.0  oo  B14  200  0.896  0.5  45  2.0  oo  B15  200  0.889  0.4  45  2.0  - oo  B16  200  0.886  0.4  45  2.0  - oo  A t constant values o f CT , b , ad and decreasing a m  c  a  B17  200  0.879  0.4  30  1.5  - oo  B18  200  0.896  0.5  90  2.0  - oo  B19  200  0.897  0.5  30  2.0  -1.75  B20  200  0.891  0.5  60  2.0  -1.75  A t constant values o f CT , b and decreasing m  c  Chapter 6: Stress state dependent behaviour of sands  250  (c) Comparative response at identical initial stress states, and increasing a , both with d  increasing as well as decreasing cc from its initial value a . This was intended to find the c  o c  influence o f the sense o f rotation o f a', under increasing a . d  A finite value of AaJAa  in  represents simultaneous change in deviator stress and direction o f  principal stresses which often is the case in-situ. Smaller values o f A a / A a corresponds to lower CT  dn  levels of stress rotation, and A a / A a = 0 implies shearing under fixed principal stress directions. CT  The value o f A a / A o " 0  dn  dn  in pure rotation tests with no change in deviator stress is infinity. It is  recognized that the changes in deviator stress and principal stress direction in-situ w i l l result i n continually changing values o f AaJArs . dn  However, tests were carried out at fixed values o f  A c c ^ A a ^ in order to isolate the influence o f the degree o f stress rotation. External control of the stresses cannot be exercised in these tests i f the sand cannot carry the applied stresses and strain softens. a was held approximately constant at its value at the trigger c  o f strain softening, whereas o~ automatically assumed values consistent with the strain softening d  characteristics o f the sand under this ambient a . a  Prescribed stress paths were followed i f the  sand recovered from strain softening upon realising the quasi steady state.  6.4.1  Simultaneous increase in o~ and ct d  A n axisymmetric initial state o f stress ( a  o c  0  = 0°) with equal intermediate and minor principal  stresses (b = 0) is considered, and undrained shear is imposed under displacement controlled c  loading, both in axial and torsional directions. Figure 6.21 shows typical excursions from the  251  Chapter 6: Stress state dependent behaviour of sands  Figure 6.21 :  Variation o f control parameters a , b, a and a during principal stress rotation m  d  CT  Chapter 6: Stress state dependent behaviour of sands  target parameters a  m  252  (= cr ), b (= b ), a and a with s under the control rate A a / A c i = 0.7. mc  c  d  0  z  CT  dn  A s pointed out earlier, the prescribed stress path cannot be strictly followed during the strain softening phase o f deformation (from A to B ) . This resulted in minor fluctuations i n the targeted a  m  and b values. Since oc was held essentially constant at its value at the trigger o f strain CT  softening until its recovery, the ratio AaJAa  increased slightly during this phase o f shearing.  dn  The variations i n the surface tractions a a CT and x and the corresponding strains induced z  r  9  z9  versus s are shown in Figure 6.22. A l l specimens had essentially identical initial states, but were z  subjected to different degrees o f stress rotation Aa /Acr . The computed principal stresses, and CT  dn  principal strains for this series o f tests are shown in Figure 6.23. The strain paths, though essentially linear at low strain levels, become progressively non linear as the deformation progresses (Figure 6.22b). The evolution o f strain induced anisotropy during such shearing is due both to the increase i n effective stress ratio, and the change in principal stress directions. M u c h larger non linearity noted in these strain paths compared to those in Figure 6.7(b) suggests that the strains accompanied by stress rotation induce anisotropy at a more accelerated rate than an increase in effective stress ratio alone. Moreover, the non linearity o f strain paths increases systematically as the sand undergoes larger principal stress rotation (increasing AajAo ) dn  - a  further illustration of the prominence of principal stress rotation over increase in stress ratio on the evolution o f strain induced anisotropy. The maximum shear stress - shear strain response and the effective stress paths for a series o f tests on specimens at different initial static shear levels, but subjected to identical degree of stress rotation  AOC^ACTJ,, =  1.75 are illustrated in Figure 6.24. Also shown in the figure are the direction  Chapter 6: Stress state dependent behaviour of sands  Figure 6.22(a):  Variation o f surface traction during principal stress rotation  253  Chapter 6: Stress state dependent behaviour of sands  Figure 6.22(b)  254  Variation o f radial, tangential and horizontal shear strain with vertical strain e during principal stress rotation. z  255  Chapter 6: Stress state dependent behaviour of sands  Figure 6.23(a):  Variation o f effective principal stresses and stress ratio with s during principal stress rotation. z  Chapter 6: Stress state dependent behaviour of sands  Figure 6.23(b):  256  Variation of principal strains during stress rotation against fixed direction strain e . z  Chapter 6: Stress state dependent behaviour of sands  257  Figure 6.24 : Influence o f initial static shear stress level on subsequent undrained shear with simultaneous increase i n o" and a . d  0  Chapter 6: Stress state dependent behaviour of sands  258  of major principal stress a at the trigger of strain softening and at minimum undrained strength. a  It is clear that the higher the level o f static shear level, K , the smaller is the increase in A a until c  d  peak and the trigger o f strain softening. For the selected degree o f stress rotation, an increase in static shear promotes higher strain softening response, as quantified by the modified brittleness index. The associated increase i n principal stress rotation A a at the trigger o f strain softening, 0  however, is least at the highest level o f static shear. Aa  CT  is a high 45° for the hydrostatic initial  stress state, but is only about 5° for K = 2.5. c  Figure 6.25 now illustrates the influence of the degree of principal stress rotation AaJAG on in  the maximum shear stress-strain relationship and stress path in undrained shear at identical initial state. The sand was subjected to different degrees o f stress rotation, quantified by A a ^ A c ^ , , = 0.70,1.75,3.50. A s noted earlier, these prescribed paths can not be strictly enforced during the strain softening phase of the deformation, in case strain softening is triggered. A n increase in the degree of stress rotation mobilises the smallest minimum undrained strength apparently because of the largest rotation incurred i n the principal stress directions. Both undrained rotation o f principal stress directions and increase in a induce excess pore d  pressure. This decreases the effective confining stress and hence increases the effective stress ratio. The inability of the sand then to carry the applied a at a threshold effective stress ratio and d  a  a  triggers strain softening deformation. This is apparent from the results presented in the  previous section, where the trigger o f strain softening was shown to be dependent on a  c  at a  certain o~ . The flow deformation may be triggered due to an increase in effective stress ratio or d  increase in ot or a combination of the two. The sand strain softens until the minimum strength a  259  Chapter 6: Stress state dependent behaviour of sands  300  a' = 200 kPa mc = 2.00 K c  b = 0.4  A  <V  —--^^Ill-I  200 -  300  dn= 0  70  1-75 3.50  —"  1  100  Acj  ,  Y i  max  1  v  Shearing at const c? , b & Aa/Arj.  ,  (%) '  Aa /Ao- =0.70 a  ed  dn  200 3.50, A  a  a  /  A  C  T  d n =  0  0  100  100  200  a' (kPa)  Aa /Aa a  3.5  20  d n  1.75  0.70  1  1  1  ^  Trigger of strain softening  A  Quasi-steady state  U  60 D  Q  10 5  h  0.0  0.5  1.0 A ( T  Figure 6.25 :  d„  / A a  1.5  2.0  a  Influence of degree of stress rotation AajAa on subsequent undrained shear with simultaneous increase in fj and a . dn  d  CT  Chapter 6: Stress state dependent behaviour of sands  260  at this threshold oc is reached. If the minimum strength at this new a is smaller than the initial CT  a  static shear, trigger o f strain softening w i l l lead to catastrophic flow failure. The characteristics of the stress strain curves during principal stress rotation with respect to the initial strain softening and subsequent strain hardening are similar to the limited liquefaction type o f response observed in typical triaxial tests. Therefore, for response o f the quasi steady state type, further straining beyond phase transformation is associated with strain hardening. Aa /Aa s  6.4.2  d n  The prescribed constant  path can once again be enforced during this phase o f deformation.  Increase in a only at constant cr 0  d  Undrained behaviour o f sand at three different initial a , but otherwise identical initial state o c  ( a ' = 200 kPa, b = 0.5, K = 2.0) under principal stress rotation prescribed by m  c  c  = °° is  ACLJAG^  shown in Figure 6.26. The changes in a and the mobilisation of stress ratio R , in addition to the a  stress-strain relationships and the effective stress paths are also illustrated in the figure. The stress strain response may be noted to be highly dependent on the initial magnitude o f a . A s explained CTC  earlier, constant deviator stress a cannot be maintained i f strain softening is triggered on account d  of the increases in stress ratio and a . 0  The sand at initial a  CTC  = 0 ° strain softens only marginally, and therefore the deviator stress  stays essentially constant as a increases from 0 ° to about 3 5 ° . However, at initial ct a  CTC  of 45°  (or 9 0 ° ) strain softening leads to true liquefaction type o f response, and results in essentially steady state conditions at a shear strain o f about 6%. This strain softening gets triggered  Chapter 6: Stress state dependent behaviour of sands  Figure 6.26:  261  Deformation due to undrained rotation o f principal stresses alone with no increase in a at two initial K levels. d  c  Chapter 6: Stress state dependent behaviour of sands  spontaneously when initial a  CTC  262  = 90°, and the minimum undrained strength mobilised is much  lower than the static shear stress. The sand strain softens because o f its inability to carry the initial static shear stress o f 67 k P a at the ambient confining stress, effective stress ratio, and a at the initiation o f strain softening. Strain softening at initial a when a  CT  o c  CT  = 45°, however, is triggered  increases to about 65° under constant a , at a small shear strain o f about 0.2%. The d  increase in cc due to principal stress rotation alone progressively aligns the direction o f major CT  principal stress toward the weaker horizontal plane. This decreases the corresponding minimum undrained strength (Figure 6.17), and triggers strain softening, once a threshold effective stress ratio is reached due to increasing pore pressure. The realised strength may even be less than the initial static shear stress o f 67 kPa. In contrast, at initial cc = 90°, CTC  principal stress rotation decreases a right from the start, and CT  progressively aligns the major principal stress towards the stronger vertical plane. This, in fact, would result i n an increase i n the minimum undrained strength as a deviates away from the a  weakest horizontal direction. The increase in effective stress ratio, nevertheless, triggers strain softening, and results i n flow deformation, despite the decrease in a . CT  The magnitude o f excess pore pressure generated as a result o f stress rotation may be noted to be the largest when a  a c  = 90°,  and smallest when oc  CTC  = 0°.  A t initial a  = 0° rotation of the  o c  major principal stress direction from the vertical by about 35° induces about 100 k P a excess pore pressure. But approximately the same amount of rotation at initial a (150 kPa) excess pore pressure. When o c kPa  o c  = 90°,  c c  = 45°  induces much larger  a mere 14° rotation of a induces a high 160 CT  excess pore pressure even though a', is i n fact moving away from the weakest horizontal  direction.  Chapter 6: Stress state dependent behaviour of sands  263  The inclination of major principal stress cc during steady state deformation for both initial a a  CTC  = 4 5 ° and 9 0 ° was essentially identical at about 7 9 ° . This was coincidental, but nevertheless reveals another important characteristic o f the mobilised minimum undrained strength. Even though the sand reached steady state at a = 79 ° i n both cases, the minimum undrained strengths CT  mobilised are somewhat different. This occurs, despite a unique mobilised friction angle at steady state, due to higher excess pore pressure developed for initial a  0 C  = 9 0 ° . Even though the  difference is relatively minor (about 10% difference in the minimum undrained strength), this suggests stress path/stress history dependency o f the minimum undrained strength. The influence o f the level of initial static shear on the undrained response under increasing a from the initial a  a c  c  = 45° is also included in Figure 6.26. A t lower static shear o f K = 1.5, very c  little strain (< 0.1%) develops even after a  CT  is increased to 90°. The excess pore pressure  developed was about 40 kPa. This increases the effective stress ratio to about 1.67, but not high enough to trigger any strain softening and therefore, the deviator stress can be held constant. In contrast, a higher initial K o f 2.0, under otherwise identical initial state has resulted in c  catastrophic flow deformation. Therefore, the influence o f rotation o f principal stresses for a given a  c c  is likely to be much less severe at lower K levels. c  The effective stress states at the trigger o f strain softening in stress rotation tests are illustrated in Figure 6.27(a) for a range o f initial K and a c  CTC  values. A l s o superimposed in the figure is the  range o f effective stress states noted in the constant a tests. The stress ratio mobilised at the a  trigger o f strain softening is found to gradually decrease with increasing a . The associated CT  mobilised friction angle is shown i n Figure 6.27(b) as a function o f the a at the instant o f the c  264  Chapter 6: Stress state dependent behaviour of sands  0  50  100  150  (rj,+ o ) / 2 3  200  250  (kPa)  10 0  30  60 a  Figure 6.27 :  a  90  (Degrees)  Trigger o f strain softening: (a) Effective stress states, (b): variation o f mobilised friction angled with  oc . CT  Chapter 6: Stress state dependent behaviour of sands  0  50  100 (cj|+ G )/2 3  Figure 6.28:  265  150  200  (kPa)  Effective stress states at steady/quasi steady states during principal stress rotation.  peak deviator stress, together with the relationship noted in the constant a tests. O CT  C S R  mobilized  at fixed direction of principal stresses forms an essential upper bound to the data. Stress rotation appears to induce strain softening at a slightly lower stress ratio compared to deformation at fixed direction o f principal stresses at all levels o f a . The effective stress conditions corresponding CT  to steady/quasi steady states i n tests with principal stress rotation are shown i n Figure 6.28, together with the measured unique SS/QSS line in constant a tests. The mobilised friction angle CT  at steady state or quasi steady state can now be noted to be essentially identical to the friction angles measured in constant a tests. This indicates that the friction angle (j)p a  T/ss  corresponding  to minimum undrained strength is a material property, and unlike the friction angle mobilized at peak deviator strength, it is not influenced by the rotation o f principal stresses.  Chapter 6: Stress state dependent behaviour of sands  266  Figure 6.29 shows the variation o f normalised minimum undrained strength, S Q /a', with ss/  SS  the direction a of the major principal stress at the steady/quasi-steady state. A l s o superimposed a  in the figure is the relationship noted during undrained shear at fixed ct . The small scatter in the 0  data at a given ct suggests that stress history/stress path may have a minor influence on the 0  minimum undrained strength, as noted earlier in Figure 6.26. The influence o f stress rotation on the normalised shear strength, for practical purposes, can be considered insignificant. This implies that the direction o f the major principal stress a at steady/quasi-steady state, and not that at the a  initial state (oc ) is o f concern in assessing the undrained strength. oc  Figure 6.29:  Dependence o f normalised minimum undrained strength on the direction o f major principal stress oc . 0  Chapter 6: Stress state dependent behaviour of sands  6.4.3  267  Initial state and the direction of stress rotation  The direction of principal stress rotation during shear should have no influence on the resulting deformations i f the principal stresses are initially aligned along a  CTC  = 0 ° or 9 0 ° . This is because  these directions constitute principal axes of anisotropy. However, when the initial oc is not along oc  either of these axes, the imposed principal stress rotation would align the major principal stress either towards the weaker horizontal direction or along the stronger vertical direction. Many field problems involve shearing that includes principal stress rotation, and hence a  a  could either  increase or decrease depending on the initial state. Analysis of the C A N L E X test embankment using F L A C (1992) shows that the direction o f major principal stress a\ within the dam may rotate by as much as 60 ° from its initial direction. A t the end of construction, a', directions were inclined at about 25 ° on either side of the vertical axes, When the reservoir was filled, a  CT  on the  upstream slope of the embankment decreased and that on the downstream increased as a result of pressure build up (Puebla 1998). In addition, the superposition o f earthquake induced shear stresses on these initial non-axisymmetric stress state may either increase or decrease the inclination o f rs\ depending on the direction o f the shear stress increment (Figure 6.30). The following data is intended to examine the influence of the direction o f similar stress rotation on undrained behaviour, and its dependency on the initial stress state. The development o f excess pore pressure due to rotating principal stresses under different initial and undrained loading conditions is shown in Figure 6.31 against the magnitude of rotation Aa . c  Sand at different initial states was subjected to the same degree o f stress rotation. The  268  Chapter 6: Stress state dependent behaviour of sands  Initial State Element  U  Element  D  -ct„  During loading Stress rotation  Stress rotation  Figure 6.30 : The direction of stress rotation in-situ: Increasing and decreasing ct from initial c  a „  269  Chapter 6: Stress state dependent behaviour of sands  a 15  o  (Degrees)  30  45  60  90  75  200  1.00  1.5  150  0.75  2.0  cd  5a  100  0.50  3  50 V-  0.25  decreasing a  increasing q -15  -45  0 Aa  Figure 6.31 :  g  30  15  0.00 45  (Degrees)  Range of excess pore pressure development for increasing and decreasing oc at different initial static shear K„. a  initial states considered were a' = 200 kPa, b = 0.5, a mc  c  principal stress rotation was imposed using Aa /AoCT  dn  CTC  = 45 °, and K = 2.0 and 1.5. Undrained c  = °° at initial oc = 45°. At K = 2.0, an oc  c  increase in a causes much higher excess pore pressure than a decrease in oc Increasing oc from CT  CT  a  45 ° to about 65 ° induces about 150 kPa of excess pore pressure, in contrast to only about 50 kPa when oc is decreased from 45° to zero. For a given initial cc , an increase in a aligns a', closer a  oc  0  to weaker horizontal direction, whereas a decrease towards zero aligns it closer to the stronger  Chapter 6: Stress state dependent behaviour of sands  270  :  vertical direction. Hence larger excess pore pressures develop when a increases towards 90° a  compared to when it decreases to zero. Excess pore pressure development is smaller for lower initial static shear K =1.5. Increasing c  a from 45 ° to about 9 0 ° induces about 40 k P a of excess pore pressure, in contrast to only about CT  20 k P a when a is decreased from 45° to zero. The magnitudes o f the strains induced due to this 0  stress rotation are much smaller (< 0.1%) compared to those at the initial K =2. A s noted earlier, c  this implies that the influence of stress rotation is less severe at low initial static shear, regardless o f whether a is increased or decreased. CT  Figure 6.32 now compares the undrained response of sand at identical initial state ( e ~ 0.898, c  c i ' = 200 kPa, b = 0.5, K 2.0 and a m  c  Aa /Ac n  d n  c  CTC  = 30°), subjected to identical degree o f stress rotation  = 1.75, for increasing a with that o f decreasing a . The response under increasing a CT  0  0  may be noted to be strain softening compared to strain hardening for decreasing a . Under CT  increasing a the sand strain softens at oc ~ 3 5 ° , a rotation o f merely 5°. In contrast, when oc CT  CT  CT  decreases from 30°,CT',progressively gets aligned with stronger vertical direction until it becomes zero. The sand in this case reached its phase transformation state at about 2% shear strain, (at a  CT  = 10°), and on subsequent shearing it developed negative excess pore pressure due to strain  hardening. Comparative undrained tests, similar to those shown i n Figure 6.32, but at an initial a = 60° oc  are shown in Figure 6.33. In contrast to the results shown in Figure 6.32, principal stress rotation induces strain softening in both cases, regardless o f whether oc is increased or decreased from CT  its initial value of 60°. The inability of the sand to carry the ambient deviator stress when sheared  Chapter 6: Stress state dependent behaviour of sands  Figure 6.32 :  271  Influence o f the sense o f principal stress rotation on the undrained response at initial cc„ = 3 0 ° .  Chapter 6: Stress state dependent behaviour of sands  Figure 6.33 :  272  Influence o f the sense o f principal stress rotation on the undrained response at initial a „ = 6 0 ° .  Chapter 6: Stress state dependent behaviour of sands  273  undrained at a threshold effective stress ratio (perturbation i n the form o f excess pore pressure) is the cause for strain softening to trigger when a is decreased. However, when a is increased, c  c  both the threshold effective stress ratio and the lower minimum undrained strength at the new higher a „ contributes to the trigger o f strain softening. The minimum undrained strength mobilised in these tests decreases with increasing a , and its c  value at a given a  c  level is consistent with the data shown for initial K  c  = 2 in Figure 6.17.  Furthermore, the friction angle mobilised at steady/quasi steady state is also essentially identical to that observed in the tests with fixed principal stress directions.  6.5  Summary  Results o f hollow cylinder torsional shear tests on water pluviated Fraser River sand are presented in this chapter. The undrained behaviour is assessed both under fixed and changing principal stress directions including simultaneous change in a and a . The initial effective stress d  c  state o f the sand, characterized by K and a , plays a major role in the subsequent undrained c  CT  behaviour o f the sand at a given confining stress level. Test results clearly demonstrate: •  The behaviour of water deposited sands transforms from being dilative to contractive as the direction o f major principal stress during shear changes from the direction o f deposition (a = 0°) to the direction o f bedding planes (cc = 90°) regardless o f the level CT  of initial static shear.  CT  Chapter 6: Stress state dependent behaviour of sands  •  274  Undrained conditions may trigger a sudden flow in sand, that is otherwise stable under drained conditions on account o f the initial static shear. The peak shear strength and the friction angle mobilised at peak are dependent on the direction o f the principal stresses. The potential for flow deformation dramatically increases with ct . a  •  Contrary to the commonly held steady state concepts, the minimum undrained strength of a sand at a given void ratio is not uniquely related to its void ratio. It is dependent on the direction of the major principal stress and to a lesser extent on the initial static shear. However, the friction angle corresponding to minimum strength is essentially constant, and appears to be a unique material property.  •  Rotation o f principal stress directions alone at constant magnitude can trigger strain softening deformation due to the generation o f excess pore pressure. The susceptibility to liquefaction is most severe at high initial K and a c  a c  levels  The undrained behaviour under simultaneous increase in deviator stress and the major principal stress direction depends on the relative magnitudes o f the degree o f stress rotation and the change in deviator stress. The friction angle mobilised at peak, cj)  CSR  due  to stress rotation at a given a is about 2 to 3 ° smaller than the corresponding friction 0  angle mobilised under fixed principal stress directions. The friction angle mobilised at steady/quasi steady state, however, is not influenced by the principal stress rotation. •  The minimum undrained strength realised under rotation of principal stresses depends on the direction o f major principal stress at the instant o f steady state or quasi steady state.  Chapter 6: Stress state dependent behaviour of sands  275  It is also influenced by the stress path/stress history that brought the sand to its current state, but to a lesser extent.  These tests clearly demonstrate that the measured undrained properties of sands are highly dependent on their initial state characterised by effective confining and static shear stresses, void ratio and fabric. Therefore it is of critical importance to simulate conditions in the laboratory tests that duplicate those anticipated in the field problem. This will lead to a more credible assessment of the undrained response of sands.  Chapter 7  Summary and Conclusions  The influence o f fabric, initial effective stress state and stress path during undrained shear on the behaviour of sands has been studied using triaxial, simple shear and hollow cylinder torsional shear tests. Triaxial and simple shear represent specific loading paths with independent control of two stress parameters. Torsional shear tests, however, enable independent control o f each o f the three principal stresses and the directions o f two i n one plane. Proper cognizance o f the influence of membrane penetration on undrained response is taken in order to assess liquefaction susceptibility under truly undrained conditions. The new method proposed for determining the magnitude of membrane penetration has several advantages over the existing methods. It enables specimen and membrane specific corrections to be made. This method does not make any assumptions regarding the constitutive behaviour of the sand, and is non destructive.  The following conclusions may be drawn from this  component o f the investigation. •  Membrane penetration induced volume changes in a given sand was found proportional to the logarithm o f the effective confining stress.  •  The normalised unit membrane penetration may be approximated as a linear function o f D  5 0  for average grain sizes ranging from about 0.1mm to 2.0 mm. 276  277  Chapter 7: Summary and Conclusions •  The partially drained state induced i f membrane penetration is not accounted for may transform a strain softening sand into a strain hardening one. The strain hardening response o f the coarsest sand tested ( D  5 0  = 0.90 mm) i n conventional undrained tests  transformed into strain softening type i f the test was truly undrained (i.e. constant volume). •  The available post correction methods exaggerate the influence o f membrane penetration on undrained response. The error in the induced excess pore pressure in a conventional undrained tests is typically only about 10% for medium/fine ( D < 0.30 mm) sands. 5 0  The influence o f the fabric on undrained response was assessed using comparative tests on undisturbed in-situ frozen sand and specimens o f the same sand reconstituted by different techniques. Undisturbed sand specimens were sampled from four different sites; two alluvial deposits in British Columbia, and two tailings sands from Alberta. Reconstituted specimens were prepared using bulk sands from each o f these four sites, and also from sand dredged from the Fraser River. The fabric studies indicate that: •  The technique o f in-situ ground freezing yields very high quality undisturbed sand specimens in saturated sands. The negligible amount o f axial and volumetric strains during thawing and reinstatement o f the in-situ stresses was taken as evidence in its support. Frozen specimens suffer only minimal disturbance i f thawed at low effective stresses and subsequently consolidated to the in-situ stresses. In-situ ground freezing, however, is an expensive endeavour, and might not be economically justifiable except in critical/large projects.  Chapter 7: Summary and Conclusions •  278  A l l undisturbed sands tested were found to be inherently anisotropic. Even loose sands rarely strain softened in triaxial compression, but did so invariably and realised a quasi steady state, prior to the commencement of dilation, or an eventual steady state in triaxial extension.  •  Loose undisturbed sands marginally strain softened in simple shear. The m i n i m u m undrained strength in simple shear was in between the values noted in triaxial compression and extension.  •  Water pluviated sands also exhibit direction dependent response similar to those o f undisturbed sands on account o f their inherent anisotropy. Moist tamped specimens, however, strain softened and realized essentially steady state both in triaxial compression and extension.  •  Even the loosest water pluviated Syncrude sand was found dilative at an initial void ratio of 0.768 and a '  vc  = 200 kPa in simple shear. But, after air pluviation at the same void  ratio and effective stress, it marginally strain softened to an essential steady state. The same sand moist tamped to an identical initial state strain softened and realised steady state at much lower strength. This implies that the fabric effects are not destroyed at large strains as claimed by the proponents o f the steady state concepts even when the sands strain soften. The fact that a sand at the same void ratio can realize steady state at two distinct values o f stresses clearly indicates that the initial fabric does play an important role on undrained behaviour and the steady state strength o f sands.  In general, the  undrained behaviour at identical void ratio and effective stress states under a given  Chapter 7: Summary and Conclusions  279  loading mode is profoundly affected by the method o f specimen reconstitution which controls the ensuing fabric. •  Specimens reconstituted by water pluviation to essentially identical void ratio and effective stress state o f corresponding undisturbed specimens exhibit characteristics very similar to those o f undisturbed sands. This was noted under both static and cyclic loading conditions.  This equivalence was both qualitative and quantitative under triaxial  compression, extension and simple shear states. •  The post liquefaction stress strain curves o f undisturbed sands were found to posses three distinct phases o f deformation. The post liquefaction deformation progressed along the line o f maximum obliquity. This is consistent with the post liquefaction behaviour o f water pluviated sands that have been reported in the literature. The minimum undrained strength under virgin loading does not appear to limit the strength o f the undisturbed sand in post liquefaction loading.  •  Static, cyclic and post liquefaction characteristics o f water pluviated sands can be confidently assigned to alluvial or hydraulic fill in-situ sand deposits. Water pluviation thus provides an attractive economical alternative to the very expensive undisturbed samples using ground freezing techniques.  The influence of initial non axisymmetric stress state on liquefaction susceptibility was assessed using water pluviated fabric i n the hollow cylinder torsional shear device. Because o f the demonstrated equivalence o f the behaviour o f water pluviated and undisturbed sands, findings from this study can be confidently applied to alluvial and hydraulic fill in-situ sands.  The  280  Chapter 7: Summary and Conclusions  undrained behaviour was assessed both under fixed and continually changing principal stress directions. The initial effective stress state of the sand, characterized by K and a plays a critical c  c  role in the subsequent undrained behaviour o f sand at a given confining stress level.  The  following conclusions may be drawn from the data presented. •  Water deposited sands, at a given initial state systematically transform from being dilative to contractive as the direction o f major principal stress changes from the direction o f deposition (a  CT  = 0°) to the direction o f the bedding planes ( a = 90°), when sheared a  undrained. This is a clear manifestation o f the inherent anisotropy. •  Liquefaction potential increased with increase in static shear K and inclination o f major c  principal stress to the vertical a . Even though an increase in static shear results i n CT  marginally higher peak shear strength, the minimum undrained strength mobilised might even be lower than the initial static shear, especially under high K and a . A s a result, c  c  undrained loading may trigger a sudden flow in a sand deposit that is otherwise stable i f fully drained. In addition to the peak shear strength, the friction angle mobilised at the trigger o f strain softening is also dependent on the direction o f the principal stresses. •  The minimum undrained strength o f a sand is highly dependent on the void ratio, effective confining stress level, loading direction, and the fabric, and to a lesser extent on the initial static shear. This conflicts with the prevalent belief o f a unique relationship between steady state strength and void ratio. The concept of a unique steady state was formulated based on triaxial compression tests on moist tamped sands, and it appears those concepts are not applicable to the inherently anisotropic alluvial and hydraulic fill sands. The  281  Chapter 7: Summary and Conclusions  friction angle corresponding to the minimum strength, however, is essentially constant and appears to be a material property. A mere rotation o f principal stress directions with no increase in a may trigger strain d  softening and lead to flow failure. Both the initial static shear level and the direction o f a', plays an important role on the undrained response due to principal stress rotation only. The undrained behaviour under simultaneous change in deviator stress cr and principal d  stress directions a depends on the initial direction of principal stresses, shear stress level c  and the sense o f principal stress rotation. •  Both an increase in effective stress ratio, and change in principal stress directions induce anisotropy. Principal stress rotation was noted to accelerate the evolution o f strain induced anisotropy.  •  The minimum undrained strength mobilised under rotation of principal stresses is primarily dependent on the direction o f major principal stress at steady or quasi steady state. <)>  CSR  at the trigger o f strain softening with principal stress rotation is about 2 to 3 ° smaller than the corresponding angle under fixed principal stress directions. However, the friction angle mobilised at steady/quasi steady state is not influenced by principal stress rotation, and appears a unique property o f the sand.  Test data reported herein clearly demonstrate that the undrained response of in-situ and water deposited sands under a given stress path is highly dependent on initial effective stress state, void ratio and the fabric, and that under a given initial state on the undrained stress path. Therefore  Chapter 7: Summary and Conclusions  282  it is essential to simulate actual field loading conditions both prior to and during shear in laboratory tests in order to confidently characterize their in-situ response. The fabric of in-situ alluvial and hydraulic fill sands appear to be similar to that of water pluviated sands, in that they both are inherently anisotropic and possess similar characteristics under static, cyclic and post liquefaction loading modes. This opens the possibility of using reconstituted instead of very expensive in-situ frozen undisturbed samples for characterising in-situ behaviour.  7.1  Recommendations for future research  This thesis highlights the importance of using specimen reconstitution techniques that simulate the in-situ fabric together with duplicating the in-situ stress states and loading conditions in laboratory assessment of liquefaction susceptibility of in-situ sands. Principal stress directions and the presence of static shear at the end of consolidation is shown to profoundly influence the monotonic undrained response. The influence of undrained principal stress rotation is shown to be complex and dependent on the initial state. Further research in the following related topics will complement the findings reported in this thesis. •  Extend the fabric studies to assess the relevance of moist tamped specimens to compacted fills in-situ. Issues regarding accessible density states and the associated mechanical behaviour need to be resolved.  •  Assessment of the influence of initial stress state on specimen density and confining stress level. This is of particular interest since denser sands are less anisotropic than loose ones.  Chapter 7: Summary and Conclusions •  283  Influence o f initial non-axisymmetric stress states on the cyclic resistance o f sands at different stress levels. 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