STATIC, CYCLIC AND POST LIQUEFACTION SIMPLE SHEAR RESPONSE OF SANDS by SrVAPATHASUNDARAM SlVATHAYALAN B. Sc. Engg. , University of Peradeniya, 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 O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F M A S T E R O F A P P L I E D S C I E N C E in T H E F A C U L T Y O F G R A D U A T E S T U D I E S Department of Civi l Engineering We accept this thesis as conforming to the required standard. T H E U N I V E R S I T Y O F BRITISH C O L U M B I A December 1994 © Sivapathasundaram Sivathayalan, 1994. In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of CZ\y{] E r A Q m g e H « g The University of British Columbia Vancouver, Canada Date DE-6 (2/88) Abstract An experimental study of static, cyclic and post cyclic undrained simple shear response of reconstituted water pluviated Fraser River sand is presented and compared to its triaxial behaviour from an earlier study. Static and cyclic behaviour was assessed over a range of void ratios that included the loosest deposition state using different confining stress levels. The effect of reconstitution technique on undrained behaviour was also investigated. It is shown that the method of specimen reconstitution has a profound influence on its undrained response. If laboratory results are to be meaningful in field application, the specimen reconstitution technique must duplicate the deposition process of the deposit to be modelled. The static undrained response in simple shear is contractive only for the loosest of the accessible void ratios, regardless of the level of confining stress. For a given initial void ratio and confining stress level, simple shear response is much less contractive than triaxial extension response. The criteria for contractive deformation during cyclic loading based on triaxial studies are shown to be also valid under cyclic simple shear. The influence of confining stress level on liquefaction resistance is shown to increase with relative density in a manner similar to that found under triaxial conditions. The cyclic resistance at the loosest state is essentially independent of the confining stress level. At denser states, however, the reduction factor Ka in simple shear is not as high. as under the triaxial ii conditions. The reduction factor C r used to adjust cyclic triaxial liquefaction resistance to an equivalent field simple shear condition is shown to be larger than currently adopted in design, and its value is dependent on both density as well as confining stress level. A The strain level over which sand deforms essentially at zero stiffness in post liquefaction loading is dependent on relative density and maximum strain experienced during cyclic loading. Post liquefaction response of cyclically liquefied sand is shown to be essentially similar to that of the sand liquefied by static load-unload cycle. The undrained simple shear and triaxial behaviour of the silty Syncrude sand is shown to be, in general, similar to that of Fraser River sand. iii TABLE OF CONTENTS Abstract i i Table of Contents iv List of Figures viii List of Symbols xii Acknowledgements xiv Chapter 1 : Introduction (1) Chapter 2 : Literature Review (5) 2.1 General 5 2.2 Static Loading Behaviour 6 2.2.1 Initiation of Strain Softening 8 2.2.2 Phase Transformation and steady states 8 2.2.3 Steady state Concepts 9 2.2.4 Angle of Maximum Obliquity/Ultimate Failure Envelope . . . . 11 2.2.5 Effect of Stress Path 11 2.2.6 Effect of Soil Fabric 13 2.3 Cyclic Loading Behaviour 14 2.3.1 Mechanisms of strain Development in Cyclic Loading 14 2.3.2 Contractive Deformation during Cyclic Loading 15 iv 2.3.3 Dilative Deformation 18 2.3.4 Link between Cyclic and Monotonic Response 18 2.3.5 Comparison between Simple Shear and Triaxial Behaviour . . 20 2.4 Post Liquefaction Behaviour 21 2.5 Research Needs 24 Chapter 3 : Experimental Aspects (26) 3.1 The Simple Shear Test 26 3.2 Testing Apparatus 28 3.2.1 The Simple Shear Apparatus 28 3.2.2 The Loading System '. . 30 3.2.3 Data Acquisition system . . 31 3.2.4 Measurement Resolution 31 3.3 Specimen Reconstitution Techniques 32 3.4 Test Procedure 32 3.4.1 Specimen Reconstitution 32 3.4.2 Consolidation 34 3.4.3 Shear Loading 35 3.5 Computation of Void Ratios 36 3.6 Materials Tested 39 3.7 Testing Program 42 3.7.1 Static Tests 42 v 3.7.2 Cyclic Tests 43 3.7.3 Post Liquefaction Monotonic Tests 43 Chapter 4 : Test Results (45) 4.1 Effects of specimen Reconstitution Techniques 46 4.1.1 Static Undrained Response . 46 4.1.2 Accessible states 49 4.2 Behaviour of Fraser River Sand 52 4.2.1 Static Loading Behaviour 52 4.2.1.1 Behaviour of Loosest Deposited Sand 52 4.2.1.2 Behaviour at a fixed Confining Stress Level 56 4.2.1.3 Behaviour at a fixed Void Ratio 59 4.2.1.4 Initiation of Contractive Deformation 59 4.2.1.5 Phase Transformation and Steady State 66 4.2.1.6 Ultimate Failure State 71 4.2.2 Cyclic Loading Behaviour 71 4.2.2.1 Strain Development in Cyclic Loading 73 4.2.2.2 Cyclic Resistance Data 78 4.2.2.3 Effect of Relative Density 83 4.2.2.4 Effect of Confining Stress 83 4.2.2.5 Comparison of Cyclic Resistance in Simple Shear and Triaxial Tests 88 vi 4.2.2.6 Residual Condition at the End of Cyclic Loading 90 4.2.3 Post Liquefaction Behaviour 92 4.2.3.1 Stress - Strain Response 92 4.2.3.2 Effect of Void Ratio 95 4.2.3.3 Comparison of Cyclically Liquefied sand with that Liquefied by Static Load - Unload cycle 97 4.2.3.4 Comparison of Triaxial and Simple Shear Post Liquefaction Behaviour 99 4.2.3.5 Comparison of Pre and Post Liquefaction Behaviour . . . 99 4.2.3.6 Post Liquefaction Behaviour for Non Zero Residual Effective Stress States 101 4.2.3.7 Characteristics of Post Liquefaction Behaviour 103 4.3 Behaviour of Syncrude Sand 107 4.3.1 Static Loading Behaviour 108 4.3.2 Cyclic Loading Behaviour 116 Chapter 5 : Conclusions (121) References (127) Appendix (136) vii LIST OF FIGURES Figure 2.1 Characteristic Response of Saturated Sands in Undrained Static Compression (Chern 1985) 7 Figure 2.2 The Steady State line in two dimensional projections 10 Figure 2.3 Cyclic Loading Behaviour of contractive Sand - True Liquefaction and Limited Liquefaction (After Vaid and Chern 1985) 17 Figure 2.4 Cyclic Loading Behaviour of Dilative Sand - Cyclic Mobility (After Vaid and Chern 1985) 19 Figure 2.5 Simple Shear and Triaxial Loading Conditions 20 Figure 2.6 Pre liquefaction and Post Liquefaction Behaviour of Sand (After Kuerbis 1989) . . 2 3 Figure 3.1 (a) Simple Shear and Pure Shear 27 (b) Stress Distribution in a Simple Shear Specimen 27 Figure 3.2 Specimen Confinement in Simple Shear Tests 28 Figure 3.3 Schematic Diagram of the Simple Shear Apparatus and the Data Acquisition System 29 Figure 3.4 Error in computed Void Ratio due to error in circumferential measurement at different ambient void ratios 37 viii Figure 3.5 Error in computed void ratio due to error in height measurement of simple shear specimens 38 Figure 3.6 Particle Gradation of the Sands used in the Study 41 Figure 4.1 Static undrained response of Syncrude sand reconstituted by different techniques 47 Figure 4.2 Static undrained response of Fraser River sand reconstituted by Air and Water pluviation 48 Figure 4.3 Compressibility and Accessible states for Syncrude and Fraser River sands, Reconstituted by different techniques 50 Figure 4.4 Compressibility and Accessible states of water pluviated Fraser River sand under one and three dimensional strain 51 Figure 4.5 Static undrained simple shear behaviour of loosest deposited Fraser River sand 53 Figure 4.6 Brittleness index in Contractive response for loosest deposited Fraser River sand 55 Figure 4.7 Comparison of Simple shear, Triaxial Compression and Extension behaviour. 57 Figure 4.8 Static undrained behaviour at a fixed confining stress 58 Figure 4.9 Static undrained behaviour at a fixed void ratio 60 Figure 4.10 Effective stress conditions at the initiation of contractive deformation. 61 Figure 4.11 Dependence of mobilized friction angle at peak on void ratio 63 Figure 4.12 Dependence of peak strength on confining stress at a fixed void ratio. 64 ix Figure 4.13 Dependence of peak undrained strength ratio on void ratio 65 Figure 4.14 Effective stress conditions at Phase Transformation 67 Figure 4.15 Variation of undrained strength at PT with void ratio and confining stress. . . 68 Figure 4.16 Comparison of PT strength under Simple shear and Triaxial extension70 Figure 4.17 Effective stress conditions at maximum obliquity 72 Figure 4.18 Contractive Deformation in Cyclic Loading 74 Figure 4.19 Cyclic Mobility of Contractive sand 75 Figure 4.20 Cyclic Mobility of dilative sand 77 Figure 4.21 Cyclic Resistance Data at D r c = 31 % 79 Figure 4.22 Cyclic Resistance Data at D r c = 40 % 80 Figure 4.23 Cyclic Resistance Data at D r c = 59 % 81 Figure 4.24 Cyclic Resistance Data at D r c = 72 % 82 Figure 4.25 Liquefaction Resistance - Effect of Relative Density and Confining Stress level 84 Figure 4.26 Liquefaction Resistance - Effect of Confining Stress level 85 Figure 4.27 Ka in Simple Shear and Triaxial tests 87 Figure 4.28 Cyclic Resistance in Simple Shear and Triaxial Tests 89 Figure 4.29 Residual condition at the end of cyclic loading - 100% residual pore pressure 91 Figure 4.30 Non zero residual effective stress 93 Figure 4.31 Post Liquefaction Monotonic Response 94 x Figure 4.32 Effect of Relative Density on Post Liquefaction Response 96 Figure 4.33 Post Liquefaction Response of sand liquefied by cyclic loading and static load-unload cycle 98 Figure 4.34 Pre and Post Liquefaction Response 100 Figure 4.35 Post Liquefaction Response of sand that has not realised a state of zero residual effective stress during liquefaction. . .' 102 Figure 4.36 Characteristics of Post Liquefaction Monotonic Response 105 Figure 4.37 Variation of A 7 with maximum strain during liquefaction 106 Figure 4.38 Static undrained response of loosest deposited Syncrude sand. . . 109 Figure 4.39 Brittleness Index in contractive response for loosest deposited Syncrude sand 110 Figure 4.40 Static undrained response at a fixed confining stress I l l Figure 4.41 Static undrained triaxial response of loosest deposited Syncrude sand 112 Figure 4.42 Effective stress conditions at Phase Transformation in simple shear and triaxial tests 114 Figure 4.43 Dependence of shear strength at phase transformation on void ratio. 115 Figure 4.44 Effective stress conditions at maximum obliquity 117 Figure 4.45 Contractive deformation under cyclic loading 118 Figure 4.46 Liquefaction Resistance data at 200 kPa confining stress level. . . 119 xi LIST OF SYMBOLS C S R Critical Stress Ratio C r Correction factor for triaxial cyclic resistance D r i Initial relative density D r c Relative density at the end of consolidation D 5 0 Mean grain size I B Brittleness index K a Correction factor due to the effect of confining stress N L Number of loading cycles to liquefaction N Number of loading cycles P T Phase Transformation state » SS Steady State S S L Steady State Line Spr Shear strength at phase transformation Su.peak Peak shear strength e; Initial void ratio ec Consolidated void ratio a Inclination of major principal stress direction to the vertical 7 Shear strain 7 ^ Maximum shear strain xii Ac Error in circumferential measurement of triaxial specimen Ae Error in computed void ratio Ah Error in height measurement of simple shear specimen Au Excess pore pressure 5 Inclination of major principal stress with bedding plane e a Axial strain a\ Vertical effective stress a v c Vertical effective consolidation stress a\, a 3 Major and Minor principal stresses a lc, a 3 c Major and Minor principal consolidation stresses S static cyclic uJT 3. There must be sufficient number of load cycles to lead the effective stress path to the CSR line. Chapter 2 Literature Review 17 (a) i CM N / / 1/2 (a, '+(f3') L^X.Cyclfc Mobility true -S liqulfactlon {limited liqulfactlon U-CSR crossed N Figure 2.3 Cyclic Loading Behaviour of contractive Sand - True Liquefaction and Limited Liquefaction (After Vaid and Chern 1985) Chapter 2 Literature Review 18 2.3.3 Dilative Deformation In cyclic mobility type of response (Figure 2.4), the continuing increase in pore pressure causes a progressive stiffness degradation of the sand with number of cycles. Vaid and Chern (1983) observed that the strain development is small until the stress state reaches the PT state. Significant amount of strain develops only after the PT line is crossed. Subsequent unloading from the peak shear stress state brings the sand close to a state of zero effective stress. Additional load cycles that take the sand through transient states of zero effective stress are responsible for strain accumulation. This strain accumulation occurs when the stress state in the sand moves along the line of maximum obliquity on both compression and extension sides. 2.3.4 Link between Cyclic and Monotonic Response Attempts have been made by Castro (1969), Castro et al. (1982), Chung (1985) and Chern (1985) to show possible links between monotonic and cyclic behaviour of sands. Castro (1969) and Castro et al. (1982) have shown that under triaxial compression the steady state line is unique in static and cyclic loading conditions. Vaid and Chern (1985) showed that steady and phase transformation states can be treated within the same framework for this uniqueness. Thomas (1992) and Vaid et al. (1989) showed that steady state/phase transformation state line is dependent upon stress path in the void ratio - stress plane, but unique in the effective stress plane. It is however not affected by the manner of loading, static or cyclic for a given stress path. Chapter 2 Literature Review 19 Figure 2.4 Cyclic Loading Behaviour of Dilative Sand - Cycl ic Mobility (After Vaid and Chern 1985) C h a p t e r 2 L i t e r a t u r e R e v i e w 2 0 2.3.5 Comparison between Simple Shear and Triaxial Behaviour B o t h c y c l i c s i m p l e s h e a r a n d c y c l i c t r i a x i a l t e s t s h a v e b e e n u s e d t o a s s e s s c y c l i c r e s i s t a n c e o f s a n d s . T h e t w o t e s t s d i f f e r i n t h e s t r e s s - s t r a i n c o n d i t i o n s b o t h a t t h e e n d o f c o n s o l i d a t i o n a s w e l l a s d u r i n g s h e a r ( F i g u r e 2 . 5 ) . I n i t i a l s t r e s s s t a t e i n s i m p l e s h e a r i s Ko. T r i a x i a l s p e c i m e n s c o u l d b e i s o t r o p i c a l l y (K = c r ' v c / a ' h c = 1 ) o r a n i s o t r o p i c a l l y c o n s o l i d a t e d ( a r b i t r a r y K). S i m p l e s h e a r l o a d i n g c a u s e s c o n t i n u o u s r o t a t i o n o f p r i n c i p a l a x e s s y m m e t r i c a l l y a b o u t t h e v e r t i c a l a x i s , w h e r e a s t r i a x i a l l o a d i n g m a y i n v o l v e a j u m p r o t a t i o n o f 9 0 ° w h e n s t r e s s r e v e r s a l o c c u r s . T h e s h e a r s t r e s s r e v e r s a l i n s i m p l e s h e a r o c c u r s o n t h e h o r i z o n t a l p l a n e w h e r e a s t h e m a x i m u m s h e a r s t r e s s r e v e r s a l i n t h e t r i a x i a l t e s t o c c u r s o n p l a n e s o r i e n t e d a t 4 5 ° t o v e r t i c a l . Load Application For —T For Principal Stress Rotation *x= e y = ° S i m p l e S h e a r < * . . i ± cr, 1 Load Application Principal Stress Jump Rotation of 90° Triaxial F i g u r e 2 . 5 S i m p l e S h e a r a n d T r i a x i a l L o a d i n g C o n d i t i o n s . Chapter 2 Literature Review 21 The cyclic resistance in simple shear is regarded as the ratio (T c y /a ' v c) between the applied cyclic shear stress amplitude and the initial normal effective stress a v c . In triaxial loading the corresponding resistance is taken as erd /(2a'3c) which equals the maximum shear stress normalized by the initial effective minor consolidation stress. Peacock and Seed (1968) show that for loose sands the cyclic stress required to cause liquefaction in simple shear was only 35% of the cyclic stress under triaxial conditions. Seed and Peacock (1971) introduced a factor C r to be applied to the measured triaxial cyclic resistance to arrive at the cyclic stress ratio that would cause liquefaction under simple shear conditions in field. Additional studies by Finn et al. (1971) lead to a suggestion for the adoption of C r values as low as 0.6 to 0.7. This correction factor does not recognize possible effects of stress level or relative density on its value. 2.4 Post Liquefaction Behaviour Liquefaction induced displacements can be quite large and may render the earth structure or the earth supporting structures unserviceable. Flow failures can occur following the cessation of the earthquake, the failure of the San Fernando dam being the most notable (Seed et al. 1975). Except for the work by Vaid and Thomas (1994), little systematic research has been carried out on the post liquefaction undrained behaviour of sands, which is necessary in estimating earthquake induced displacements and movements after an earthquake. Chapter 2 Literature Review 22 Post liquefaction behaviour of sand depend primarily on the residual effective normal stress remaining at the end of cyclic loading. In cyclic loading with stress reversal, the excess pore pressure ratio will generally reach 100% following liquefaction. Thus the sand may essentially be at a transient state of zero effective stress at the end of cyclic loading. In sands with initial static shear stress, the pore pressure development is generally small and the residual condition after the cessation of earthquake may represent considerable level of remaining confining stress. (Finn et al . , 1978; Vaid and Thomas, 1994) The stress-strain response of a tailings sand, during the cyclic and post liquefaction loading (liquefaction being defined as 2.5% axial strain) is shown in Figure 2.6 (Kuerbis, 1989). Strains prior to liquefaction are small, but upon unloading after contractive deformation during the last cycle, the sand comes to a transient state of zero effective stress. On post liquefaction loading it initially deforms essentially with zero stiffness. The stiffness increases progressively with increasing strain level. This unusual strain stiffening response is a result of dilation throughout the loading phase, commencing from the transient state of zero effective stress. Each excursion through the state of zero effective stress makes the sand behave in a strain stiffening manner regardless of the loading mode. The lack of sufficient data on the post liquefaction behaviour of sands had made the assessment of liquefaction induced displacements difficult. Byrne et al. (1992) assume that the steady state strength of a contractive sand is not affected during Chapter 2 Literature Review 23 Figure 2.6 Pre liquefaction and Post Liquefaction Behaviour of Sand (After Kuerbis 1989) Chapter 2 Literature Review 24 monotonic loading following the liquefaction induced by cyclic loading. Experimental evidence on post liquefaction behaviour presented by Vaid and Thomas (1994) shows an evidence to the contrary. Vaid and Thomas have made a comprehensive study of the post liquefaction response of a sand in the triaxial test and pointed out the various factors that influence this behaviour. These factors are the void ratio, maximum strain during cyclic loading and the mode of deformation - compression versus extension. Similar investigation under simple shear mode will be of profound importance from a practical standpoint. 2.5 Research Needs The above review indicates that undrained response of sands is stress path dependent. But to the knowledge of the author static undrained response under simple shear conditions has not been studied despite the fact this deformation mode is the most relevant during cyclic earthquake loading. Only very little work has been done on the comparative response of sand under cyclic simple shear and triaxial conditions. In particular the influence of density and confining stress on reduction factor C r is not known. Similarly little systematic research has been carried out on the post liquefaction response of saturated sands, except for the study by Vaid and Thomas (1994) in the triaxial test. No data exists on the post liquefaction stress - strain behaviour in simple shear, which is essential for estimating liquefaction induced displacements. Furthermore, specimens in the laboratory are reconstituted by methods without any regard to the Chapter 2 Literature Review 25 natural deposition process of the deposit being modelled. There are clearly needs to clarify the effect of specimen reconstitution on undrained behaviour for a meaningful application of laboratory studies in the field. This thesis is an attempt to address some of the above concerns. The effect of specimen reconstitution method and the comparative undrained behaviour of saturated sands in triaxial and simple shear conditions is the main focus of this study. Such a comparison is attempted under static, cyclic and post cyclic loadings. In view of the potential seismic risk in Greater Vancouver area the sand underlying the heavily populated Fraser delta was used for a comprehensive assessment of its static, cyclic and post liquefaction simple shear response. Chapter 3 E x p e r i m e n t a l A s p e c t s 3.1 The Simple Shear Test The simple shear test was an evolution of the direct shear test. The soil specimen is laterally confined between two pairs of parallel boundaries and thus the horizontal normal strain components ex and ey are always zero. Prior to shearing the specimen undergoes one dimensional consolidation. Constant volume simple shear is achieved by forcing the vertical normal strain ez to be zero. The change in vertical stress a v in such a constant volume test equals the excess pore pressure Au which would develop in an equivalent undrained test. The principal axes of stress and strain rotate during the application of shear stresses in a constant volume simple shear test. Because of the absence of complimentary shear stresses on the vertical boundary the stresses and strains in the specimen are not uniform. Thus the test is far from an element test. Linear stress analysis by Roscoe (1953), non linear analysis by Duncan (1969) and the experimental observations of Cole (1967), Finn et al. (1978) and DeGroot et al. (1994) indicate that the stress nonuniformities are severe only at the edges. Figure 3.1 illustrates the stress conditions in simple shear and ideal pure shear (Airey et al., 1985). Also shown in the figure is the elastic distribution of shear stress and normal stress in a simple shear specimen. Fundamental experimental research at Cambridge has revealed that the stress conditions in the middle third of the specimen are uniform. 26 Chapter 3 Experimental Aspects 27 The conclusions are based on detailed measurements of boundary shear and normal stress distribution using contact transducers. These uniform normal and shear stresses on the middle third are found to be approximately equal to the average boundary stresses applied to the specimen. A low height to diameter ratio reduces stress nonuniformities considerably (Airey et al., 1985). The stress non uniformities have little effect on the ultimate shear resistance of soil and it is sufficiently accurate to use the average stress conditions for test interpretations (Duncan and Dunlop, 1969). Shear Stress Distribution Normal Stress Distribution Figure 3.1 (a) Simple Shear and Pure shear; (b) Stress Distribution in a Simple Shear Specimen Normal and shear stresses are the only measured stress quantities in the simple shear test. These are not sufficient to specify the complete state of stress. Research work at Cambridge has shown that the horizontal plane becomes the plane of maximum shear stress at shear strains in excess of about 1 % (Roscoe, 1970). Since the concern in most undrained behaviour studies will be at and after the peak condition, it would be sufficiently accurate Chapter 3 Experimental Aspects 28 to consider the horizontal plane as the plane of maximum shear stress at these peak and post peak states. 3.2 Testing Apparatus Tests were carried out in the simple shear apparatus with fully computerised data acquisition system. This test system is capable of applying cyclic and monotonic shear loads to the soil specimen. Constant volume simple shear tests (Finn and Vaid, 1977) were carried out with this apparatus. The instrumented triaxial apparatus described by Thomas (1992) was used for a limited study on triaxial behaviour of Syncrude,sand. 3.2.1 The Simple Shear Apparatus The simple shear apparatus was of the NGI type (Bjerrum and Landva, 1966). In this apparatus, a circular soil sample is laterally confined by a reinforced rubber membrane as shown in Figure 3.2. A schematic diagram of the testing apparatus is shown in Figure 3.3. The specimens used were approximately 20 mm high and 70.4 mm in diameter. Loading Cap u Soil Sample M e m b r a n e W i r e R e i n f o r c e m e n t L o a d i n g C a p Figure 3.2 Specimen Confinement in Simple Shear Tests Chapter 3 Experimental Aspects 29 a 3 J 2 jayidwcocuow PJBQ UOIijSmbOV BJBQ 8 So O A) x 5 11 X > (D O = T3 <»> n O o TJ —I as 10 a 8 O m X > o •J3 I Q 3 i I 1 t 8P s 0.01) in all specimen sizes 2.5" diameter and less. The error in frequently used 1.4" diameter specimens is as high as 0.02. Errors of these magnitude can cause an order of magnitude difference in estimates of residual strength, if the SS line is flat as is often the case with rounded sands. Chapter 3 Experimental Aspects 37 Figure 3.4 Error in computed Void Ratio due to error in circumferential measurement at different ambient void ratios. Chapter 3 Experimental Aspects 38 Figure 3.5 illustrates the relationship between error in void ratio, Ae as a function of the error Ah in the measurement of height for dwarf simple shear specimen used in this study. An error of 0.1 mm in measurement of height can give rise to an serious error in computed void ratios in excess of 0.01 in these dwarf simple shear specimens. Similar error Ah would cause little error in triaxial specimens, because of their long height to diameter ratio of 2. 0.04 Ambient Void Ratio 1.0 0.03 H 0.9 0.8 B_B_BBB 0.7 3 0.02 A o.oi H 0.00 0.00 0.05 0.10 Ah, mm 0.15 0.20 Figure 3.5 Error in computed void ratio due to error in height measurement of simple shear specimen. In order to reduce the error in the computation of void ratio of reconstituted specimens associated with physical measurements, the following procedure was followed in Chapter 3 Experimental Aspects 39 this study. The cross sectional area of the sample cavity was evaluated by weighing the amount of water required to fill the cavity over a height that was approximately equal to the height of the specimen. The average cross sectional area of the cavity was thus calculated from the weight of the water, the density of water at the ambient temperature and the height over which filling was done. This average area together with the precisely measured height of the specimen gave the most credible assessment of the void ratio of the test specimen. In simple shear tests, since the reinforced membrane imparts one dimensional consolidation conditions, the changes in void ratio associated with consolidation are accurately calculated from the recorded changes in height. In the triaxial tests, both the change in height and volume were recorded during the application of the confinement to the specimen (i.e. 20 kPa of vacuum) and during subsequent consolidation of the sample. Since the samples were prepared by water pluviation, both the sample and the drainage lines were fully saturated since the beginning. As such, all the recorded volume changes reflect an equal amount of volume change of the sample. Thus the void ratio could be computed with a better accuracy since this method does not rely on any circumferential measurements that are shown to be the major factor causing errors in the computed void ratio. 3.6 Materials Tested Two sands were used in the testing program. The main focus was on the undrained behaviour of Fraser River sand. This sand underlies the heavily populated and seismically active (Milne et al., 1978) Fraser River delta in Western Canada. This is the same sand used by Thomas (1992) in extensive triaxial testing. The main focus in this testing program Chapter 3 Experimental Aspects 40 was the assessment of the behaviour of Fraser River sand under simple shear conditions and its comparison with the behaviour under triaxial conditions. Fraser River sand is grey coloured medium grained with an average particle size D 5 0 of 0.30 mm. Its average mineral composition is 40% quartz, quartzite and chert, 11% of Feldspar, 45% unstable volcanic rock fragments and 4% miscellaneous detritus (Garrison et al., 1969). The original Fraser River sand has about 1% of clay fraction. For testing purposes, the fine particles below 0.1 mm (ASTM Sieve #140) were removed by wet sieving. The sand as tested still had a fine content of about 1 %. The specific gravity of this sand is 2.72 and the maximum and minimum void ratio in accordance with ASTM (D4353-91 and D4254-91) are 1.00 and 0.68 respectively (Thomas 1992). The gradation curve for this sand is given in Figure 3.6. The second sand used was the Syncrude sand, a material resulted from the processing of oil sand at the open pit mine near Fort McMurry, Alberta Canada operated by Syncrude Canada Ltd. This sand was tested in simple shear and triaxial conditions. Syncrude sand is beige coloured, fine, uniform angular to sub angular with traces of silt and clay. This predominantly quartz sand has an average particle size D 5 0 of 0.20 mm and contains about 12% fines. The mineral composition is 95% quartz, 2% Feldspar and 1% each of Amphiobole, Pyrite and Muscivite. (Sladen and Handford, 1987). The maximum and minimum void ratio in accordance with ASTM (D4353-91 and D4254-91) were determined to be 0.962 and 0.522 (wet method) respectively. Figure 3.6 gives the gradation curve of Syncrude sand. Chapter 3 Experimental Aspects Figure 3.6 Particle Gradation of the Sands used in the Study Chapter 3 Experimental Aspects 42 3.7 Testing Program 3.7.1 Static Tests • Comparative tests on moist tamped, air pluviated and water pluviated specimens of Syncrude sand were carried out in simple shear. These tests were performed at identical initial conditions to investigate the effect of the method of sample reconstitution on the behaviour of a silty sand. • Comparative tests on air pluviated and water pluviated Fraser River sand were carried out to assess the effect of the method of pluviation on the behaviour of a uniform sand. • Comprehensive static simple shear tests were carried out on water pluviated Fraser River sand at the loosest deposited state and at other deposition void ratios over a range of confining stress levels. This was intended to delineate the domain of contractive and dilative responses and to compare the behaviour of Fraser River sand under triaxial and simple shear stress conditions. • A series of not so comprehensive tests were carried out on air pluviated Syncrude sand at the loosest deposited state over a range of confining stresses and a series of tests over a range of void ratios at a fixed confining stress of 200 kPa. • A limited number of triaxial compression and extension tests were carried out on the loosest deposited water pluviated Syncrude sand in order to study the differences in response between the two modes of loading for this sand. Chapter 3 Experimental Aspects 43 3.7.2 Cyclic Tests • Comprehensive cyclic simple shear tests were carried out on water pluviated Fraser River sand at different void ratios over a range of vertical confining stress, a'vc to assess its cyclic loading resistance. This was intended to assess the cyclic loading resistance in simple shear at several density and confining stress levels, and its comparison with its resistance under triaxial conditions. • A limited number of cyclic tests were carried out on air pluviated Syncrude sand at different void ratios and a constant confining stress. 3.7.3 Post Liquefaction Monotonic Tests • Following the end of cyclic loading Fraser River sand sample was loaded monotonically both in the direction of residual strain and opposite to the direction of residual strain. Post cyclic monotonic loading yielded the behaviour of sand after liquefaction representing different levels of residual pore pressure generation including 100% pore pressure ratio. One of the objectives was to find the strain levels required for the sand to regain appreciable strength, together with its overall stress strain response. Static tests were carried out on Fraser River sand to induce liquefaction by static load - unload cycle. Different strain levels were imposed under static loading prior to unloading and the post liquefaction behaviour was studied by subsequent monotonic Chapter 3 Experimental Aspects 44 loading. The objective was to examine the differences, if any, on the post liquefaction behaviour of statically and cyclically liquefied sands. Chapter 4 Test Results Undrained behaviour of Fraser River sand and Syncrude silty sand is presented and discussed in this chapter. The effect of sample reconstitution method on undrained static response is discussed first. It is followed by a presentation and discussion of a comprehensive series of static, cyclic and post liquefaction simple shear tests on Fraser River sand. Comparison is made between simple shear and triaxial behaviour (Thomas, 1992) of this sand. Finally, the results of tests on Syncrude silty sand are presented. The behaviour of Syncrude sand was not assessed as comprehensively as that of Fraser River sand. Under simple shear conditions, only the effective vertical normal stress a\ and horizontal shear stress T are the measured stress quantities and therefore test results are presented in terms of these two stress parameters. The measured shear strain y is used to characterize deformation in simple shear. The sands were deposited in the loosest state resulting in void ratios approximately equal to the maximum obtained by the ASTM-D4254 method. Higher densities, i f necessary, were achieved by densification under a small seating load. The void ratio under a seating load of about 1 kPa is referred to as the initial deposition void ratio e; and that after consolidation to the required confining stress level 0.80 H 0.75 H 0.70 Fraser River Sand (Water Pluviated) — Triaxial — Simple Shear 10 . 100 . 1000 Confining Stress crvc or o , 3 c , kPa Figure 4.4 Compressibility and Accessible states of water pluviated Fraser River sand under one and three dimensional strain. Chapter 4 Test Results 52 dimensional strain despite smaller mean normal stress for a given confining stress (V v c in simple shear and a'3c in hydrostatic triaxial). This further illustrate that accessible void ratio states not only depend on the method of specimen reconstitution but also on the strain condition during compression. If the results of the laboratory tests are to be meaningful for field application, the specimen reconstitution technique should simulate closely the formation process of the deposit being modelled. Water pluviation in the laboratory has been shown to resemble the process of water deposition of natural and hydraulic fill sands or silty sands. The fabric of water pluviated specimens has been found to be similar to that of natural deposits formed by sedimentation (Mori et al . , 1977; Oda et al . , 1978). The comprehensive study undertaken on water pluviated Fraser River sand is thus an attempt to gain an understanding of the undrained simple shear behaviour of natural fluvial or hydraulic fill sands. 4.2 Behaviour of Fraser River Sand 4.2.1 Static Loading Behaviour 4.2.1.1 Behaviour of Loosest Deposited Sand. Simple shear behaviour of the loosest deposited Fraser River sand (e; = 0.962) at several confining stress levels is shown in Figure 4.5. The sand is slightly contractive at each initial state and the response is of the limited liquefaction type. A convenient way of quantifying the degree of contractiveness is the brittleness index I B where, Figure 4.5 Static undrained simple shear behaviour of loosest deposited Fraser River sand. Chapter 4 Test Results 54 PeakStress(Speak) - Minimum Stress (S^) I b = PeakStress(Speak) Brittleness Index for the data shown in Figure 4.5 is plotted in Figure 4.6. Largest values of IB may be noted to be associated with the loosest void ratio states. Increasing confining stress causes a gradual reduction in IB. Clearly the densification associated with increasing confining stress level has a more dominating influence on reducing brittleness index than the increase in contractiveness associated with higher confining stresses. Figure 4.6 also shows the brittleness index of Fraser River sand under triaxial extension for the loosest deposited state (Thomas, 1992). The Fraser River sand may be seen to be much more contractive in triaxial extension than in simple shear. In the triaxial compression mode it shows dilative response (Thomas, 1992). In triaxial compression loading the major principal stress direction coincides with deposition direction (a = 0°) and in triaxial extension a = 90°. In simple shear principal stresses rotate during shearing until a becomes close to 45° (Roscoe, 1970). Currently ongoing research work at U.B.C on Fraser River sand in the hollow cylinder torsional device shows a systematic transformation of undrained behaviour from dilative to strongly contractive as a changes from zero to 90°. Similar data on other sands has been reported by Symes et al. (1985), Shibuya and Hight (1987) and Hight et al. (1983). The observed simple shear response (a— 45°) is not as highly contractive as triaxial Chapter 4 Test Results 55 Figure 4.6 Brittleness index in Contractive response for loosest deposited Fraser River sand. Chapter 4 Test Results 56 extension (a — 90°) is thus consistent with the data from hollow cylinder torsional studies. Figure 4.7 shows a direct comparison of undrained stress- strain behaviour of Fraser River sand under triaxial compression, extension and simple shear conditions. The initial void ratio state and the confining stresses (a'vc in simple shear and a3c in triaxial) are identical in each case. Shear strain in the triaxial test is taken as 1.5 axial strain and r and y in simple shear are regarded as the maximum shear stress and maximum shear strain respectively (Roscoe, 1970). The initial shear stiffness may be noted to be smallest under the simple shear mode. Part of the reason for the stiffness to be less than triaxial extension may be the anisotropic initial stress state (cr'vc, K$ a've) in simple shear as opposed to isotropic stress state (CSR mobilized at peak has a range between 16 to 21°. There appears to be tendency for this CSR to increase with a decrease in void ratio ec. This is illustrated further in Figure 4.11. Contractive response was associated with looser void ratios only. For a given ec, <£CSR is not dependent on the initial confining stress level. Figure 4.11 also shows the CSR values in triaxial conditions. These values in triaxial extension show a similar small decrease with ec as noted under simple shear. ^CSR values in simple shear and triaxial extension may be noted to be not too different. They vary from about 20° for ec = 0.860 to about 16° for ec = 0.910. In contrast $ C S R in triaxial compression is about 10° higher than in simple shear. Differences between triaxial compression and extension $ C S R values have also been reported by Chung (1985) and Kuerbis (1989). Figure 4.12 shows the dependence of peak shear strength on confining stress c'v c at a void ratio of 0.891. Over the range of confining stresses imposed, S U J ) e a k may be noted to vary linearly with confining stress just as in clays. In sands, however the ratio S U J ) e a k / a ' v c is dependent on void ratio as shown in Figure 4.13. This ratio may be seen to decrease linearly with increase in void ratio and does not seem to be affected by the presence of static shear. The peak shear strength ratio aA I 2a'3c under triaxial extension is also shown in Figure 4.13 and shows a behaviour similar to that under simple shear. For a given ec, however, the simple shear peak undrained strength ratio is somewhat larger than the Chapter 4 Test Results 63 50 40 H "b \ ^0.10 -o a . 3 CO 0.05 -0.00 -\ 1 r— 1 1 1 0.86 0.87 0.88 0.89 0.90 0.91 Void Ratio, e c Figure 4.13 Dependence of peak undrained strength ratio on void ratio. Chapter 4 Test Results 66 triaxial extension value. The difference between the two decreases as ec increases and practically vanishes at the loosest void ratio. 4.2.1.5 Phase Transformation and Steady State N o initial void ratio and effective confining stress states gave rise to contractive behaviour of the steady state type. Figure 4.14 shows effective stress conditions at phase transformation. The data points lie along a unique straight line passing through the origin, regardless of the void ratio, the type of response (contractive or dilative), the level of initial confining stress, with or without static shear. This, implies that the friction angle at phase transformation, in simple shear deformation is a constant at about 3 0 ° for the Fraser River sand, regardless of the initial state or the type of response. Figure 4.14 also shows similar results in triaxial tests (Thomas, 1992). Phase transformation friction angle is independent of the loading mode, compression or extension, for triaxial stress conditions. It may be noted that simple shear and triaxial phase transformation friction angles are not too different and thus ^ may be regarded as unique for a sand, regardless of the void ratio, confining stress or loading mode. Additional data on Fraser River sand (Uthayakumar, 1994) in the hollow cylinder torsional device suggest that even under multiaxial stress states $pr is essentially identical to that observed in triaxial and simple shear conditions. Figure 4.15(a) shows the relationship between shear strength at phase transformation Spy and the void ratio ec for contractive response. At a given void ratio Chapter 4 Test Results 67 Figure 4.14 Effective stress conditions at Phase Transformation. Chapter 4 Test Results 68 150 100H D Q. t 50 (a) o-¥C = 400 kPa * * * * * Ai r Pluviated * * 0.5 0.4 H -.>0.3 A 3.75% used herein. Studies in the triaxial test reveal that the occurrence of contractive deformation or cyclic mobility depends on the void ratio, confining stress level and the relative values of cyclic shear stress and the phase transformation strength. Similar conclusions also apply to cyclic loading in simple shear, from which typical data is presented in Figures. 4.18 to 4.20. The critical stress ratio CSR and the phase transformation strength in triaxial extension is much smaller than in compression for a given initial contractive state (Thomas 1992). As a result, contractive deformation during cyclic loading is always Chapter 4 Test Results 77 Figure 4.20 Cyclic Mobility of dilative sand. Chapter 4 Test Results 78 triggered in the extension phase. In simple shear there is a symmetry of response to horizontal shear stress about the vertical axis. As a result strain development is symmetrical in simple shear [See Figures 4.18, 4.19 and 4.20] and contractive deformation can develop in either direction. 4.2.2.2 Cyclic Resistance Data Cyclic tests were performed at different void ratios and confining stress levels of 50, 100, 200 and 400 kPa. At each confining stress several cyclic resistance curves e c vs cycles to liquefaction N L were developed at several cyclic stress ratios. The basic liquefaction resistance data are shown in Figures A l to A4 in Appendix I. Cyclic resistance curve Tcy/o-\c vs N L at any void ratio is then obtained by interpolation from these Figures. Figures 4.21 through 4.24 illustrate these cyclic resistance curves at four selected relative densities (or void ratios). At each relative density, the cyclic resistance curves are plotted for all selected levels of confining stress. It may be noted in Figure 4.21 that at the loosest state (D r c = 31 %) the test data at different confining stress levels falls on a single line, implying that the confining stress does not influence the cyclic resistance of loose sands. At higher density states, however, the confining stress level does influence cyclic resistance (Figures 4.22 through 4.24), the cyclic resistance at a given void ratio then decreases with increasing confining stress. Chapter 4 Test Results 7 9 0.18 0.16 0.14 0.12 H o.io H 0.08 e c = (D r c = 0.900 31 %) • • • • • 50 kPa A A A A A 100 kPa • • • • • 200 kPa • • • • • 400 kPa T I I I I I I -1 10 No of Cycles T 1 1 1—I I I 100 Figure 4.21 Cyclic Resistance Data at D r c = 31 %. Chapter 4 Test Results 80 0.18 0.16 H 0.14 H o > b 0.12 I? 0.10 0.08 ec = 0.872 (Dre = 40 %) • • • • • 50 kPa A A A A A 100 kPa • • • • • 200 kPa • • • • • 400 kPa T 1 1 1—I I I | 10 No of Cycles ~i—i i i 100 Figure 4.22 Cyclic Resistance Data at D r c = 40 %. Chapter 4 Test Results 81 0.18 0.16 0.14 H 0.12 H 0.10 H 0.08 ec = 0.810 (Dre = 59 %) C T V C • • • • • 50 kPa A A A A A 100 kPa 200 kPa 400 kPa ~i 1 1 1—i—i i i | r 10 No of Cycles - \—i—i—i i i 100 Figure 4.23 Cyclic Resistance Data at D r c = 59 %. Chapter 4 Test Results 82 0.18 0.08 -\—i—i—i—| T 1 1 1 1 — i — i — 1 — | — 10 * 100 No of cycles Figure 4.24 Cyclic Resistance Data at D r c = 72 %. Chapter 4 Test Results 83 4.2.2.3 Effect of Relative Density The relationship between cyclic stress ratio to cause liquefaction in 10 stress cycles versus relative density is shown in Figure 4.25. A separate relationship exists for each confining stress level. Like other sands, the cyclic resistance increases with increasing relative density at all levels of confining stress. From the loosest state, the rate of increase in resistance with relative density is however more pronounced at lower confining stress of 50 kPa and decreases with increasing confining stress level. The convergence of the resistance curves towards looser void ratio indicates that the cyclic resistance of loose sands is independent of the confining stress level, as is also illustrated by data in Figure 4.25. The same trend is present in the variation of cyclic resistance with relative density and confining stress in cyclic triaxial tests. 4.2.2.4 Effect of Confining Stress Figure 4.26 shows cyclic stress ratio required to cause liquefaction in 10 stress vs effective confining stress at different void ratios (or D r c). These relationship were obtained from the data presented in Figures 4.21 through 4.24. As already pointed out, confining stress does not have much influence on the cyclic resistance at the loosest state (D r c= 31%). At denser states however the cyclic stress ratio required to cause liquefaction in 10 cycles (or generally the cyclic resistance) decreases with increasing confining stress level. This decrease in cyclic resistance with increasing confining stress level increases with increasing density. It is evident from Figure 4.26 that the rate of Chapter 4 Test Results 84 Relative Densi ty , D r o 25 35 45 55 65 75 N L = 10 cycles .10 - | 1 1 1 0.92 0.88 0.84 0.80 0.76 void rat io , e c Figure 4.25 Liquefaction Resistance - Effect of Relative Density and Confining Stress level Chapter 4 Test Results 85 Figure 4.26 Liquefaction Resistance - Effect of Confining stress level at different relative densities Chapter 4 Test Results 86 this decrease is higher at the lower consolidation stress levels. This is consistent with the known dilatancy characteristics of sands, where increasing confining stresses has a minor effect on the dilatancy of loose sand. Increasing confining stresses in dilative, dense sands on the other hand causes a progressive reduction in dilatancy or enhanced contractancy. Since cyclic stress ratio is generally used to characterize the liquefaction susceptibility of sands, a correction factor for the level of confining stress has been introduced. The cyclic stress ratio causing liquefaction at a given confining stress level is related to the cyclic stress ratio causing liquefaction at 100 kPa (or one atmosphere) by the correction factor K„. (Seed and Harder, 1990). T —— Causing Liquefaction at a ' v c K J a t < / v = —— Causing Liquefaction at a / v c = 100 kPa K a values deduced from the data presented in Figure 4.26 are shown in Figure 4.27 for three relative density states. The K a value corresponding to liquefaction in 10 load cycles is seen to be dependent on both the confining stress level and the relative density. At the loosest state (D r c = 31%), K„ is essentially unity. At higher relative densities K„ increases with confining stress level. The largest decrease in liquefaction resistance is about 15% when the confining stress changes from 100 kPa to 400 kPa for the dense (D r c = 59%) relative density. Chapter 4 Test Results 87 1.10 1.05 H 1.00 H 0.95 H b 0.90 H 0.85 H 0.80 H 0.75 H 0.70 o o o o o 0.900 A A A A A 0.872 0.810 31* 40s? 59* Triaxial Simple Shear 1 1 1 r~ 0 100 200 300 400 Confining stress cr v c or C T 3 c , kPa 500 Figure 4.27 K„ in Simple Shear and Triaxial tests. Chapter 4 Test Results 88 A wide range of K„ values have been reported in the literature for a given confining stress. (Seed and Harder, 1990). Failure to account for the different relative density states may have contributed to this wide scatter in K„. In the part of the database where relative densities have been specified a clear decrease in K„ with relative density is noted, as observed in Figure 4.27 for Fraser River sand. It is important to note that for loose sands which have the largest potential to liquefaction, K„ is essentially unity regardless of the stress level. Adoption of lower values in design based on some average value from the body of data presented by Seed and Harder (1990) could result in very conservative design. For comparison with simple shear results, K f f in cyclic triaxial tests are also shown in Figure 4.27 (Thomas 1992). For the medium dense state, D r c = 40% K„ values in triaxial and simple shear are essentially identical. But at the denser relative density (D^ = 59%) the triaxial K„ values are smaller than the simple shear values. Adoption of K„ values measured in cyclic triaxial tests would thus lead to further conservatism in design for dense relative density states, since the field conditions are approximated more closely by the simple shear and not the triaxial test. 4.2.2.5 Comparison of Cyclic Resistance in Simple Shear and Triaxial Tests Figure 4.28 presents the ratio C r of cyclic stress ratio required to cause liquefaction in simple shear (T c y/a' v c) to that required in triaxial ad/(2 * a'3c) tests as a function of confining stress level (cr'vc in simple shear and a'3 c in triaxial). The data is Chapter 4 Test Results 89 0.80 Figure 4.28 Comparison of Simple Shear and Triaxial Cyclic Resistance Chapter 4 Test Results 90 shown at two relative density states of 40% and 59%. The cyclic stress ratio required to induce liquefaction in 10 cycles may be noted to be smaller in simple shear than in the triaxial test (C r < 1). The difference is primarily dependent on the void ratio of the sample. At relative density of 40%, C r is about 0.78 irrespective of the confining stress level. At the denser relative density of 59% however, C r increases from about 0.66 to 0.73 when the confining stress increases from 50 to 400 kPa. In practice the cyclic resistance measured in triaxial tests is converted to equivalent simple shear value, without regard to the normal stress level and relative density state. Commonly a value of 0.6 is adopted for the ratio C r (Seed and Peacock, 1971). If C r data for Fraser River sand shown in Figure 4.28 is typical of other sands, the currently used low value of C r would render the design too conservative. The conservatism will be largest for loose sands which happen to have the greatest potential for liquefaction. 4.2.2.6 Residual Condition at the End of Cyclic Loading Cyclic loading was terminated at the end of the load cycle that had caused liquefaction (7 = 3.75%). Since a strain criterion was used to define liquefaction, the stress conditions at the conclusion of cyclic loading varied widely. A state of zero effective stress was realised in cases of looser sand that exhibited limited liquefaction type of contractive response during cyclic loading. A typical example is shown in Figure 4.29. Liquefaction occurred in the first half of the second load cycle. Unloading of the shear stress from its peak amplitude takes the sand to a state of zero effective stress. In Chapter 4 Test Results 91 10 5H o Q_ -* 0--5 --10-e c = 0.895; D r c = 3 355 tr'vc = 50 kPa Tcy/o-'vc = 0.150 (a) { , J -10 - 5 Shear Strain y, % 10 15 a Q- 10 W a> 0-to o a> CO -5H -15-(b) 10 20 30 40 * Normal Stress, trv, kPa 50 60 Figure 4.29 Residual condition at the end of cyclic loading - 100% residual pore pressure. Chapter 4 Test Results 92 the case of denser sand, a residual state of zero effective stress was not always realised when cyclic loading was terminated upon reaching a shear strain of 3.75% [Figure 4.30]. These specimens would have developed cyclic mobility associated with excursions through states of zero effective stress had sufficient cyclic pulses been applied. 4.2.3 Post Liquefaction Behaviour. Sand liquefied as a result of cyclic loading was monotonically sheared, starting from the residual strain conditions in order to study the post liquefaction response, and its dependency on void ratio and strain history. Post cyclic loading was done both in the direction of the residual strain as well as in the opposite direction. The latter simulated strain reversal whereas the former did not. The purpose was to study possible effects of strain reversal on post liquefaction response. The post liquefaction behaviour of sand that ended in a state of zero effective stress following cyclic loading is discussed first. This is followed by a discussion of post liquefaction behaviour of sand that retained a substantial part of initial effective stress at the end of cyclic loading, but was deemed to have liquefied based on the strain criterion. 4.2.3.1 Stress - Strain Response Figure 4.31 shows typical stress path and stress - strain response of Fraser River sand in post liquefaction monotonic loading. The sand had ended in a state of zero effective stress following cyclic loading. The response during the last cycle of cyclic Chapter 4 Test Results 93 Figure 4.30 Non zero residual effective stress at the end of cyclic loading. Chapter 4 Test Results 94 D Q_ in © o a> to 30 20 H 10H - 1 0 o-'vc = 100 kPa e e = 0.910 D r o = 28 55 Cyclic Loading (Last Cycle) Post Cyclic Monotonic Loading ** [ - (a) - 1 5 - 10 - 5 Shear Strain 10 7, ss 15 20 25 25 O Q_ in in a> i_ to D to - 2 5 (b) Cyclic Loading (Last Cycle) Post Cyclic Monotonic Loading 25 50 75 100 Normal Stress c r v , kPa Figure 4.31 Post Liquefaction Monotonic Response. Chapter 4 Test Results 95 loading and post liquefaction behaviour are shown in the Figure. Following triggering of contractive deformation the sand developed large strain, up to about -10%. The unloading pulse resulted in a state of zero effective stress, with very little strain recovery. Thus the post liquefaction monotonic loading commenced at the residual strain of about -8%. In post liquefaction monotonic loading, the sand initially deforms essentially at zero stiffness. The stiffness increases with straining, but the rate of increase is very small until a strain of about +7% is exceeded. This phenomenon of increasing stiffness with strain is opposite to the commonly assumed behaviour of soils where straining is associated with loss of stiffness. Strain hardening behaviour is exhibited, because the sand dilates all the way causing increase in effective stresses, right from the initiation of post cyclic loading. The deformation progresses along the line of maximum obliquity as the sand strain stiffens [Figure 4.31(b)]. At large strains the stiffness becomes essentially constant but is much smaller compared to the initial stiffness of the virgin sand. 4.2.3.2 Effect of Void Ratio Figure 4.32 compares post liquefaction monotonic behaviour of the sand at different consolidated void ratios. For this comparison, the zero strain is taken as the configuration at the conclusion of cyclic loading with its associated residual strain. The initial confining stress was 100 kPa prior to cyclic loading and the end of cyclic loading gave rise to a state of zero residual effective stress. The sand initially deforms at virtually Chapter 4 Test Results 96 0 10 20 30 40 Shear Strain y, % Figure 4.32 Effect of Relative Density on Post Liquefaction Response. Chapter 4 Test Results 97 zero stiffness irrespective of the density. The rate of stiffness increase is smaller for loose sand and therefore it deforms at zero stiffness over a larger range of strain. The sand at a relative density of 27% required 17% shear strain to mobilize a shear stress of only 2.5 kPa stress, whilst the specimens at 40% and 59% relative densities required smaller 13% and 5% shear strains respectively. In post liquefaction monotonic loading, the interest is on the strain level required for the sand to regain adequate strength. The aforementioned test results indicate that sands with looser void ratio will go through much larger deformation, before regaining substantial strength after liquefaction. 4.2.3.3 Comparison of Cyclically Liquefied Sand with that Liquefied by Static load - unload cycle The post liquefaction behaviour sand liquified by static load -'unload cycle is compared to that of the cyclically liquefied sand in Figure 4.33. The behaviour at relative densities of 40% and 59% is shown. The specimens were consolidated to an effective stress of 100 kPa. Liquefaction by static load - unload cycle was induced by unloading the specimen after straining it to a maximum shear strain (10%) approximately equal to the maximum shear strain experienced under liquefaction by cyclic loading. Following liquefaction a state of zero effective stress was realised at both density states, regardless of the manner in which liquefaction was induced. In order to facilitate comparison the response of the cyclically liquefied specimen was taken as the reference and that of the statically liquefied sand was shifted along the strain axis so as to match Chapter 4 Test Results 98 S h e a r Strain y, % Shear Strain y, % Figure 4.33 Post Liquefaction Response of sand liquefied by cyclic loading and static load-unload cycle. Chapter 4 Test Results 99 2.5 kPa shear stress on each curve. The post liquefaction response may be noted to be essentially similar at both relative densities, regardless of the manner by which the state of zero effective stress was realised. Thus, post liquefaction response can be conveniently assessed by carrying out tests on sand liquefied by static load - unload cycle rather than using cyclic loading to induce liquefaction. 4.2 .3 .4 C o m p a r i s o n o f T r i a x i a l a n d S i m p l e S h e a r P o s t L i q u e f a c t i o n B e h a v i o u r A detailed examination of the simple shear test data reveals that the post liquefaction monotonic behaviour is dependent upon the maximum strain during cyclic loading in addition to its dependency on void ratio and confining stress level. Similar conclusions were arrived at by Thomas (1992) in the study carried out using the triaxial test. A direct comparison of triaxial and simple shear post liquefaction behaviour is possible only if cyclic loading test data was available in both test types on identical state (ec, f is unique at about 3 3 ° for Syncrude sand. Uniqueness of the angle of maximum obliquity has been demonstrated for several other sands (Vaid and Chern, 1985; Chung, 1985; Vaid and Thomas, 1994) 4.3.2 Cyclic Loading Behaviour A limited number of cyclic simple shear tests were carried out on air pluviated Syncrude sand at a confining stress of 200 kPa. Figure 4.45 shows cyclic loading response of a specimen that shows contractive deformation in cyclic loading. The cyclic shear stress amplitude r c y of 20 kPa was larger than the phase transformation shear strength of 14 kPa (See Figure 4.43). Thus contractive deformation under cyclic loading was expected (Chern, 1985). Figure 4.46 shows the relationship between number of cycles to liquefaction and void ratio at a cyclic stress ratio of 0.10 for specimens consolidated at 200 kPa. As expected, the liquefaction resistance increases with decreasing void ratio. The testing program on Syncrude sand was not so comprehensive so as to study the effects of other parameters on liquefaction resistance. The data in Figure 4.46 shows that the liquefaction Chapter 4 Test Results 117 400 Normal Stress crv, kPa Figure 4.44 Effective stress conditions at maximum obliquity. Chapter 4 Test Results 118 Figure 4.45 Contractive deformation under cyclic loading Chapter 4 Test Results 119 Figure 4.46 Liquefaction Resistance data at 200 kPa confining stress level. Chapter 4 Test Results 120 resistance of Syncrude sand at 34% relative density and 200 kPa confining stress would be 0.100. This may be compared to the value of about 0.110 at D r c = 31 % and 200 kPa confining stress for Fraser River sand. (Figure 4.21) Chapter 5 C o n c l u s i o n s The undrained static, cyclic and post liquefaction response of saturated angular to sub angular Fraser River sand was studied under simple shear conditions and compared to its triaxial behaviour investigated by Thomas (1992). Sand in simple shear was tested over a range of confining stresses and void ratios. The purpose of the study was to delineate the effects of consolidation stress, void ratio and the stress path on undrained behaviour. The following conclusions are drawn from the test results presented in this thesis. 1. Specimen Reconstitution Technique a. Different reconstitution techniques give rise to different initial densities and compressibility characteristics. Therefore the domain of accessible states is not the same among different reconstitution methods. Compressibility also depends on the imposed consolidation conditions (ID or 3D). A i r pluviation and moist tamping give rise to density states that are unattainable by water pluviation. b. The static undrained response is highly influenced by the method of specimen reconstitution for identical initial density and stress state. Loosest deposited air pluviated and moist tamped Syncrude sand is highly contractive, but water pluviated sand is dilative even in the loosest deposited state. 121 Chapter 5 Conclusions 122 2. Monotonic Behaviour a. Loosest deposited Fraser River sand is much less contractive in simple shear when compared to triaxial extension. In contrast the behaviour in triaxial compression is dilative. b. The contractive tendency decreases with decreasing void ratio at a given confining stress. At a given void ratio contractiveness depends slightly on the ambient stress level in simple shear. c. The friction angle $ C S R mobilized at the initiation of contractive deformation in simple shear increases somewhat with increasing density of sand. $ C S R at the loosest deposited state is about 16° and increases at the rate of about 1° per percent reduction in void ratio. The values of f » C S R obtained in simple shear and in triaxial extension are essentially identical. The peak shear strength ratio is uniquely related to the void ratio and decreases linearly with increasing void ratio, in a manner similar to that in triaxial extension. For a given void ratio the peak strength ratio, however, is somewhat less under triaxial loading. d. The effective stress states at the phase transformation state lie on a unique straight line, regardless of the confining stress, void ratio or type of response, contractive or dilative. The shear strength at P T state depends not only on void ratio but also on confining stress level. For a given void ratio Chapter 5 Conclusions 123 and confining stress this strength in simple shear is larger than that under triaxial extension. e. The friction angle at maximum obliquity is essentially unique for a given sand regardless of the stress level, void ratio or the type of test, simple shear or triaxial. 3. Cyclic Loading Behaviour a. Criteria set out by Chern (1985) for contractive deformation to occur in cyclic loading based on triaxial studies are also applicable under simple shear conditions. b. A t a given void ratio, the resistance to liquefaction decreases with increasing stress level as is true for other sands. This effect of stress level increases with relative density. Its influence is negligible at the loosest state implying K„ = 1, for all levels of confining stress. c. The residual stress conditions at the end of cyclic loading vary widely when the usual strain criterion is used to define liquefaction. Realization of the state of zero residual effective stress depends on the void ratio of the sample and on the cyclic stress ratio imposed. Looser samples commonly end in the zero effective stress state, especially if contractive deformation is triggered during cyclic loading. Chapter 5 Conclusions 124 d. The liquefaction resistance assessed from triaxial tests is different from simple shear values. The triaxial test over estimates the resistance to liquefaction. The ratio of liquefaction resistance in simple shear to triaxial C r is found to be dependent upon the void ratio and confining stress level. A t the looser relative density of 40%, C r is essentially constant at 0.77 but at denser a relative density of 59 %, C r is smaller but increases with confining stress level. These values imply that the correction factor C r used in practice to correlate triaxial and simple shear cyclic resistance may be too conservative. The demonstrated dependency of C r on confining stress level and void ratio is not generally taken into consideration in current practice. Liquefaction Response Post liquefaction response primarily depends on the residual stress conditions after liquefaction. If a state of zero residual effective stress has been realised following liquefaction then the sand deforms essentially with zero stiffness over a very large range of strains. The stiffness finally gradually increases with further strains, and at large strains essentially becomes a constant. The rate of stiffness increase increases with relative density. If the sand had not realised a state of zero residual effective stress, then it initially exhibits a stiffness degrading behaviour until the P T state. 4. Post b. Chapter 5 Conclusions 125 Subsequent deformation past the P T state is strain stiffening, as in the case of sand that had realized a state of zero residual effective stress. c. The post liquefaction stress - strain curves can be characterized by three distinct phases. The initial phase is dictated by the residual stress conditions. If the sand had reached a state of zero residual effective stress then it will deform at zero stiffness during this phase of deformation. If substantial effective stress had been retained after liquefaction, then the sand exhibits stiffness degrading behaviour in this phase. During the second phase of deformation (past the P T state), the stiffness increases steadily until it reaches a constant value and the sand deforms essentially with constant stiffness during the third phase of deformation. d. The post liquefaction response of sand that realized a state of zero residual effective stress was found to be independent of the manner in which liquefaction was induced, whether cyclically or by a static load-unload cycle. This behaviour was noted at all density states. e. 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M. , Drescher, A. and Budhu, M., (1979), "On the Determination of Stress State in the Simple Shear Apparatus", Geotechnical Testing Journal, GTJODJ, Vol 42, No 4, pp 211 - 221 Appendix I 135 Appendix I 136 1 10 100 No of Cycles Figure A l Liquefaction Resistance at 50 kPa confining stress Appendix I 137 0.96 12.5 Figure A2 Liquefaction Resistance at 100 kPa confining stress Appendix I 138 0.92 •25.0 = 200 kPa 0.87 a or o > 0.82 0.77 • • • • • 0.100 A A A A A 0.120 • • • • • 0.140 0.160 r-37.5 h-50.0 h62.5 h-75.0 0.72 i i i i i | 5 6 7 8 9 H—I I I 5 6 7 8 1 -87.5 10 No of Cycles 100 Figure A3 Liquefaction Resistance at 200 kPa confining stress Appendix I 139 0.92 25 0.76 0.72 \- TCy / 0\ •50 h75 0.68 • • • • • 0.090 A A A A A 0.1 1 0 0.130 - i 1 — i — | 1 r 2 3 4 S 6 7 8 9 2 3 10 No of Cycles n—i—r 4 5 6 7 8 1 100 100 Figure A 4 Liquefaction Resistance at 400 kPa confining stress