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Effects of aging duration, stress ratio during aging and stress path on stress-strain behaviour of loose… Lam, Chun Kit Keith 2003

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Effects of Aging Duration, Stress Ratio during Aging and Stress Path on Stress-Strain Behaviour of Loose Fraser River Sand by Chun K i t Keith Lam B.A.Sc . , The University of British Columbia, 2000 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 R E Q U I R E M E N T S F O R T H E D E G R E E OF M A S T E R OF 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 OF G R A D U A T E S T U D I E S Department of C i v i l Engineering We accept this/thesis as cor^brming^o the required standard T H E U N I V E R S I T Y OF B R I T I S H C O L U M B I A Apr i l 2003 © Chun K i t Keith Lam, 2003 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 GvH Bqinvviy The University of British Columbia Vancouver, Canada Date Ap*~) lo, DE-6 (2/88) A B S T R A C T Recent studies on aging of sands mainly emphasize the effects of aging duration on creep deformation and soil stiffness. Factors such as stress ratio, stress path and confining stress have not been investigated extensively. This research was conducted to investigate the effects of aging duration, stress ratio during aging and stress path on the stress-strain behaviour o f loose Fraser River sand. The main objective of the work was to extend a previous study (Shozen, 2001) to longer aging times and to a greater range of stress paths and stress ratios. Loose reconstituted samples with relative densities (D r ) of approximately 20% were consolidated at stress ratios of 1.0, 2.1 and 2.5 and aged from 100 to 10,000 minutes prior to shear testing along four different stress paths. Test results showed that age stiffening effects were observable at the beginning of shearing regardless of the stress conditions applied to the samples. The effects were more pronounced at higher stress ratios and for older samples. The overall stress-strain behaviour was unaffected by aging. The magnitude of the increase in secant stiffness was greater as the strain increment decreased. Test data also indicated that for strains smaller than 0.2%, aged samples with D r of 20% had the same or greater stiffness than unaged samples with D r o f 50%. Results from this study suggest that for loose Fraser River sand, the stiffness at very small strains ( G 0 or G m a x ) may be more sensitive to age than previously thought. The observations imply that for laboratory testing or physical model testing, repeatability of test results w i l l be improved by a consistent approach to aging of samples. For interpretation of in situ tests, the age of the deposit should be carefully considered to enable the estimation of representative engineering properties of the soil. i i T A B L E O F C O N T E N T S A B S T R A C T i i T A B L E O F C O N T E N T S i i i LIST O F T A B L E S v i i LIST O F F I G U R E S v i i i A C K N O W L E D G E M E N T S xiv C H A P T E R 1 Introduction 1 C H A P T E R 2 Literature Review 2 2.1 Stress-Strain Behaviour of Sand 2 2.2 Current Thinking on Soil Stiffness 7 2.3 Aging Effects in Sands 11 2.3.1 In-Situ Evidence of Aging 11 2.3.2 Laboratory Evidence o f Aging 22 2.4 Proposed Causes of Aging 34 2.5 Proposed Research 41 2.6 Organization o f Thesis 42 C H A P T E R 3 Experimental Details 43 3.1 Introduction 43 3.2 Experimental Apparatus 44 3.3 Stress Application and Experimental Instrumentation 46 i i i 3.3.1 Stress Application 46 3.3.2 Instrument Resolutions, Accuracies and Stabilities 48 3.4 Material Tested 56 3.5 Sources of Inaccuracy in Triaxial Test Data 57 3.5.1 Ram Friction 57 3.5.2 Membrane Penetration 59 3.5.3 Membrane Force 61 3.5.4 Sample End Friction 61 3.5.5 Area Correction and External versus Internal Strain Measurement 62 3.6 Test Procedures 63 3.7 Conclusions 66 C H A P T E R 4 Test Results 67 4.1 Preliminary Considerations 67 t 4.1.1 Definition of Terms 70 4.1.2 Test Repeatability 72 4.2 Consolidation and Aging - Phases 1, 3 and 4 76 4.2.1 Effects of Stress Ratio on Strain Development during Consolidation and Aging 77 4.2.2 Effects of Confining Stress on Strain Development during Consolidation and Aging 83 4.2.3 Conclusions - Consolidation Phase 88 iv 4.2.4 Conclusions - Aging Phase 88 4.3 General Stress-Strain Behaviour - Phase 5 89 4.3.1 Introduction 89 4.3.2 Effects of Aging Duration and Stress Path 90 4.3.3 Effects of Stress Ratio and Effective Confining Stress 99 4.3.4 Maximum Contraction and Failure 102 4.3.5 Conclusions - General Stress-Strain Behaviour 104 4.4 Stress-Strain Behaviour at Shear Strains Less Than 0.2% 105 4.4.1 Effects of Stress Path and Aging on Small Strain Stress-Strain Behaviour, Hydrostatically-Consolidated Samples (R = 1.0) 105 4.4.2 Effects o f Stress Path and Aging on Small Strain Stress-Strain Behaviour, Anisotropically-Consolidated Samples 111 4.4.3 Conclusions - Stress-Strain Behaviour at Shear Strains Less Than 0.2% 126 4.5 Aging Effects on Soi l Stiffness 127 4.5.1 Effects of Aging Duration 128 4.5.2 Effects of Confining Stress and Stress Ratio 128 4.5.3 Effects o f Stress Path 134 4.5.4 Relationships between G and q/qf 140 4.5.5 Effects of Relative Density 146 4.5.6 Conclusions - Soil Stiffness 148 C H A P T E R 5 Conclusions 151 V Suggestions for Further Research 152 R E F E R E N C E 155 A P P E N D I X 160 vi L I S T O F T A B L E S Table 3.1 Resolutions and Precisions of Various Measurements 54 Table 3.2 Physical Properties of Fraser River Sand 57 Table 4.1 Different Phases of Test Programme 67 Table 4.2 Details of Test Programme 71 Table 4.3 Maximum, Min imum and Average e v / s a Ratios in Phases 3 and 4 79 Table 4.4 I G and N G Values of Fraser River Sand 140 Table 4.5 q % Ratios at Different Stress Ratios and along Different Stress Paths ..144 vii L I S T O F F I G U R E S Figure 2.1 Typical Stress-Strain Behaviour of Sand under Drained Conditions (Craig, 1997) 3 Figure 2.2 Characteristic Undrained Stress-Strain Response o f Sand (Kuerbis, et al., 1989) 6 Figure 2.3 Effective Stress Path for Undrained Behaviour o f Sand (Kuerbis et al., 1989) 6 Figure 2.4 A n Idealization for the Variation of Stiffness with Strain for Soil (Atkinson and Sallfors, 1991) 10 Figure 2.5 Identification of Zones I, II and III in Triaxial Stress Space (Jardine, 1992) 10 Figure 2.6 Penetration Resistance of Thick Sand Layer at Two Times after Disturbance (Mitchell and Solymar, 1984) 13 Figure 2.7 Penetration Resistance Profiles for a Hydraulic F i l l at Two Times after Placement (Mitchell and Solymar, 1984) 14 Figure 2.8 Increase in Average Point Resistance over 1-Day Values with Distance and Time after Blasting (Dowding and Hryciw, 1986) 15 Figure 2.9 Influence of Aging on Standard Penetration Resistance of N C Sands (Skempton, 1986) 18 Figure 2.10 Increases in Shaft Capacity with Time (Chow et al., 1997) 18 Figure 2.11 Plot of Average q c i and 1 4 C Age of Organic Material in Topset Sand of Fraser River Delta (Monahan et a l , 2000) 19 Figure 2.12 Possible Effects of Age of Deposit on C P T Penetration Resistance (Wride et al., 2000) 20 Figure 2.13 Possible Effects o f Age o f Deposit on Measured Shear Wave Velocity (Wride et al., 2000) 21 Figure 2.14 Typical Modulus Change with Time for Sand (Anderson and Stokoe, 1978) 23 Figure 2.15 The Effect of the Age of Consolidation on Stress-Strain Characteristics of Ham River Sand (Daramola, 1980) 25 Figure 2.16 Relationship between Normalized Secant Modu l i with L o g (Age of Consolidation) (Daramola, 1980) 27 viii Figure 2.17 Results of Triaxial Compression Creep Test Showing (a) Stress Ratio versus A x i a l Strain (b) Volumetric Strain versus A x i a l Strain for Antelope Val ley Sand (Lade and L i u , 1998) 30 Figure 2.18 Applied Stress Paths in Various Stress Spaces (Shozen, 2001) 32 Figure 2.19 Comparison between Effects of Time and Relative Density along Conventional Path (Shozen, 2001) 33 Figure 2.20 X - R a y Diffraction Traces of the Beaufort Sea Sand and River Sand (Joshi etal. , 1995) 36 Figure 3.1 Triaxial Testing Machine (Shozen, 2001) 45 Figure 3.2 Load Application with and without Controlling the Time for Stress Application (Shozen, 2001) 47 Figure 3.3 Variation of L V D T Readings during 130 Hours of Monitoring 50 Figure 3.4 Variation of e v Differential Pressure Transducer Readings during 130 Hours of Monitoring 50 Figure 3.5 Monitoring of s v with Reservoir Connected to Burette 52 Figure 3.6 Variation o f Load Ce l l Readings during 130 Hours o f Monitoring 52 Figure 3.7 Variation of Ce l l Pressure Transducer Readings during 130 Hours of Monitoring 53 Figure 3.8 Variation of Back Pressure Transducer Readings during 130 Hours of Monitoring 53 Figure 3.9 Variation of Effective Stress Ratio 55 Figure 3.10 Particle Size Distribution of Fraser River Sand 58 Figure 4.1a,b Applied Stress Paths in a ' l-a'3and q-p Spaces 68 Figure 4.1c Applied Stress Paths in — l——- — - Space 69 Figure 4.2 Repeatability of Stress Applications 73 Figure 4.3 Repeatability o f s a and s v Developments in Phases 1, 3 and 4 73 Figure 4.4 Comparison of Shozen's Results in the Large Strain Region 74 Figure 4.5 Comparison of Shozen's Results in the Small Strain Region 75 ix Figure 4.6 a ' 1 / 0 ' 3 and s v versus e a Curves in Phase 1, 3 and 4 at Various Stress Ratios 78 Figure 4.7 s v / £ a versus Relative Density Curves in Phase 3 at Various Stress Ratios 80 Figure 4.8 s a and s v versus Aging Duration Curves in Phase 4 at Various Stress Ratios with 100-Minute Aging Duration 82 Figure 4.9 s a and s v versus Logarithmic Aging Duration Curves in Phase 4 at Various Stress Ratios with 1000- and 10,000-Minute Aging Durations 82 Figure 4.10 s a versus s v Curves in Phases 3 and 4 with Various Effective Confining Stresses at a Stress Ratio of 2.1 84 Figure 4.11 e versus p ' Curves in Phase 3 with Various Effective Confining Stresses at a Stress Ratio o f 2.1 85 Figure 4.12 s a and s v versus Aging Duration Curves in Phase 4 with Various Effective Confining Stresses and 1000-Minute Aging Duration 86 Figure 4.13 s a and s v versus Logarithmic Aging Duration Curves in Phase 4 with Various Effective Confining Stresses and 1000-Minute Aging Duration 87 Figure 4.14 General q and s v versus s a Curves in Phase 5 along the Conventional Path at a Stress Ratio of 1.0 with 100- and 1000-Minute Aging Durations (Tests N o . 5 and 9) 91 Figure 4.15 General q and s v versus e a Curves in Phase 5 with Various Aging Durations along the Conventional Path at a Stress Ratio o f 2.1 (Tests No . 16, 20 and 24) 93 Figure 4.16 General q versus y and s v versus p ' Curves in Phase 5 at a Stress Ratio of 1.0 with 100- and 1000-Minute Aging Durations (Tests No. 5 to 12) 95 Figure 4.17 General q versus y and e v versus p ' Curves in Phase 5 at a Stress Ratio of 1.6 with 100- and 1000-Minute Aging Durations (Tests N o . 13 to 15)...96 Figure 4.18 General q versus y and e v versus p ' Curves in Phase 5 at a Stress Ratio of 2.1 with 100- and 1000-Minute Aging Durations (Tests No. 16 to 23)...97 Figure 4.19 General q versus y and s v versus p ' Curves in Phase 5 at a Stress Ratio of 2.5 with 100- and 1000-Minute Aging Durations (Tests No. 28 to 35)...98 Figure 4.20 General q and s v versus s a Curves in Phase 5 at Various Stress Ratios along the Conventional Path (Tests No . 5, 16 and 28) 100 X Figure 4.21 General Aq and s v versus e a Curves in Phase 5 with Various Effective Confining Stresses along the Conventional Path (Tests No. 1,16 and 36) 101 Figure 4.22 q versus p ' Curves at Maximum Contraction and Failure 103 Figure 4.23 Small Strain q and s v versus y Curves in Phase 5 along the Conventional Path with Various Aging Durations at a Stress Ratio o f 1.0 (Tests No. 5 and 9) 106 Figure 4.24 Small Strain q and s v versus y Curves in Phase 5 along the -2 Path with Various Aging Durations at a Stress Ratio of 1.0 (Tests No. 6 and 10) ..107 Figure 4.25 Small Strain q and s v versus y Curves in Phase 5 along the -1 Path with Various Aging Durations at a Stress Ratio o f 1.0 (Tests No . 7 and 11) ..108 Figure 4.26 Small Strain q and s v versus y Curves in Phase 5 along the 0 Path with Various Aging Durations at a Stress Ratio o f 1.0 (Tests No . 8 and 12) ..109 Figure 4.27 Small Strain q and s v versus y Curves in Phase 5 along Various Stress Paths at a Stress Ratio of 1.0 with 1000-Minute Aging Duration (Tests No. 9 to 12) 110 Figure 4.28 Small Strain q and s v versus y Curves in Phase 5 along the Conventional Path with Various Aging Durations at a Stress Ratio o f 2.1 (Tests No. 16, 20 and 24) 112 Figure 4.29 Small Strain q and s v versus y Curves in Phase 5 along the -2 Path with Various Aging Durations at a Stress Ratio of 2.1 (Tests No . 17 and 21)113 Figure 4.30 Small Strain q and s v versus y Curves in Phase 5 along the -1 Path with Various Aging Durations at a Stress Ratio of 2.1 (Tests No . 18, 22 and 25) 114 Figure 4.31 Small Strain q and s v versus y Curves in Phase 5 along the 0 Path with Various Aging Durations at a Stress Ratio of 2.1 (Tests No . 19, 23 and 26) 115 Figure 4.32 Small Strain q and s v versus y Curves in Phase 5 along Various Stress Paths at a Stress Ratio of 2.1 with 1000-Minute Aging Duration (Tests No. 20 to 23) 117 Figure 4.33 Small Strain q and s v versus y Curves in Phase 5 along the Conventional Path with Various Aging Durations at a Stress Ratio o f 2.5 (Tests No . 28 and 32) 118 xi Figure 4.34 Small Strain q and s v versus y Curves in Phase 5 along the -2 Path with Various Ag ing Durations at a Stress Ratio o f 2.5 (Tests No . 29 and 33) 119 Figure 4.35 Small Strain q and s v versus y Curves in Phase 5 along the -1 Path with Various Aging Durations at a Stress Ratio o f 2.5 (Tests No . 30 and 34) 120 Figure 4.36 Small Strain q and e v versus y Curves in Phase 5 along the 0 Path with Various Aging Durations at a Stress Ratio of 2.5 (Tests No . 31 and 35) 121 Figure 4.37 Small Strain Aq and s v versus y Curves in Phase 5 at Various Stress Ratios along the Conventional Path (Tests No. 5, 16 and 28) 124 Figure 4.38 Small Strain Aq and s v versus y Curves in Phase 5 with Various Effective Confining Stresses along the Conventional Path (Tests No. 1,16 and 36) 125 Figure 4.39 G0.03 and G0.15 versus Aging Duration Curves in Phase 5 along the Conventional and -1 Paths 129 Figure 4.40 G versus y Curves in Phase 5 with Various Aging Durations along the Conventional Path 130 Figure 4.41 G0.03 and Go. 15 versus a'3 Curves in Phase 5 along the Conventional Path 132 Figure 4.42 Determination of n 132 Figure 4.43 Normalized G versus y Curves in Phase 5 with Various Effective Confining Stresses along the Conventional Path 133 Figure 4.44 Normalized G versus y curves in Phase 5 at Various Stress Ratios along the Conventional Path 135 Figure 4.45 Normalized G versus y curves in Phase 5 along Various Stress Paths at a Stress Ratio of 1.0 136 Figure 4.46 Normalized G versus y curves in Phase 5 along Various Stress Paths at a Stress Ratio of 2.1 136 Figure 4.47a,b Normalized G0.03 and G0.15 versus a Curves in Phase 5 at Various Stress Ratios with 100- and 1000-Minute Aging Durations 138 Figure 4.48 Definition of Deviator Stress at Failure, qf 143 Figure 4.49 Normalized G0.03 and G0.15 versus q % Curves in Phase 5 with 100-, 1000-and 10,000-Minute Aging Durations 145 xii Figure 4.50 G versus y Curves in Phase 5 with Different Ag ing Durations and Relative Densities (Tests No. 24 and 27) 147 xiii A C K N O W L E D G E M E N T S I want to express my deepest gratitude to my supervisor, Dr. J. A . Howie, for his supports, comments and encouragements in this experimental study. In addition, I want to thank Dr. Y . P. V a i d and Dr. D . Wijewickreme for their outstanding experience in laboratory experimentation. It has been a great experience working with them and the lessons I learned w i l l stay with me throughout my career. This study would not be possible without the help of C i v i l Engineering Workshop in the development and maintenance of the testing equipment. Moreover, automatic loading system and electronic data acquisition system were designed by Electronics Workshop. Special thanks are given to Harald Schrempp, B i l l Leung, Scott Jackson and John Wong for their indispensable and expert technical assistance. I would like to thank my friends and colleagues for their interest in the research, as well as their encouragements and comments: Ricardo, Ganan, Megan, Park, A l i and Kumar. The assistance of all graduate students is deeply appreciated. Moreover, this study would be impossible without the financial support provided by the Natural Science and Engineering Research Council o f Canada ( N S E R C ) and their help is gratefully acknowledged. Finally, I would like to express my deepest thank to my family and friends, especially Charles, L i l y , Neon, Kit ty and H K Charles, who give me tremendous supports, both academic and psychological, during my university study. Special thanks are also given to Sandy, Jacky and Tobey, who always cheer me up at times of frustration during the research. xiv C H A P T E R 1 Introduction This thesis reports the results of a study of the changes in stress-strain behaviour of a loose Fraser River sand due to periods of aging at a constant state of stress. It is an extension of a previous study by Shozen (2001). The literature on aging in coarse-grained soils is not extensive compared to the volume of research conducted on time effects in clay as the magnitude of deformation during aging is typically small and tends to be o f little concern to foundation engineers. Nevertheless, significant time-dependent changes have been observed in in-situ tests, particularly after ground improvement. Besides in-situ observations, creep behaviour and time effects on sands have been reported in many laboratory tests. These studies have tended to focus on soil stiffness. This thesis summarizes the findings of an experimental study in which samples were prepared by water pluviation and consolidated at different stress ratios. They were then kept under constant stress states for different time periods and sheared along four different stress paths. A l l stress paths after aging involved an increase in stress ratio. Tests with different confining stresses were also conducted for comparison purposes. This thesis starts with a literature review of the basic stress-strain behaviour in sand, followed by a review of time-dependent behaviour in sand. Chapter 3 presents details of the experimental apparatus and procedures used to obtain the data. The results of the present study are presented and discussed in Chapter 4 and Chapter 5 is the summary and conclusion. 1 C H A P T E R 2 Literature Review The time-dependent behaviour of fine-grained soils has been studied comprehensively in the last few decades. The time-dependent behaviour of coarse-grained soils, however, has not been studied extensively until recently. A n y excess pore pressure dissipates very rapidly in coarse materials and the settlements that occur during such dissipation are very small. Moreover, secondary compression is thought to be insignificant under stresses that are normally encountered. However, many in-situ and laboratory data reveal that aging occurs under relatively low stresses but the causes o f aging are not fully known. This chapter provides a summary of the basic stress-strain behaviour of sand and the major findings extracted from previous investigations. 2.1 Stress-Strain Behaviour of Sand Stress-strain behaviour of sand is usually categorized into two broad types in accordance with the drainage condition during shearing: drained behaviour and undrained behaviour. In a drained test, no excess pore pressure develops during shearing. The volume of the sample is allowed to change and volumetric strain is measured. Typical stress-strain response of dense and loose sand under drained conditions is shown in Figure 2.1. The general stress-strain behaviour of a sand sample has been shown to be strongly dependent on initial void ratio (or relative density) and confining stress level (Casagrande, 1936; Vesic and Clough, 1968; Lee and Seed, 1967). In a dense sample, there is a considerable amount of interlocking between soil particles. For shear failure to occur, the interlocking must be overcome in addition to the frictional resistance at the points of 2 Volume decrease Figure 2.1 Typical Stress-Strain Behaviour of Sand under Drained Conditions (Craig, 1997) 3 particle contacts. A s shown in Figure 2.1, the stress-strain curve reaches a peak value at a relatively small strain. The peak stress occurs when the particle interlocking is overcome. At larger strain levels, the deviator stress decreases as interlocking is progressively overcome. In addition, the reduction of interlocking produces an increase in the overall sample volume, or dilation, as shearing is continued. The volumetric strain reaches an ultimate value, which indicates that the soil has become loose enough that soil particles can move over each other with the overall volume staying constant, i.e. the constant volume state. The deviator stress also reaches an ultimate value at this state. Two parameters, the friction angles at maximum deviator stress, ^ ' m a x , and constant volume, (j)'cv, are commonly employed to represent soil strengths at the maximum and constant volume states. For a dense sand, (|>'max is considerably larger than <j)'cv, the difference representing the energy required to overcome the interlocking of soil particles (Craig, 1997). In a very loose sample, there is not any significant particle interlocking to be overcome. The deviator stress increases gradually until an ultimate value is reached when (j)'cv is mobilized. During shearing, a very loose sample would decrease in volume until a constant volume is reached. According to Figure 2.1, the ultimate deviator stress of the dense and loose samples in a conventional triaxial drained test is essentially identical provided that the samples are subjected to identical stress conditions. In addition, the ultimate relative density and void ratio of the dense and loose samples are equal. The tendency for dilation does not solely depend on the density of sample but is also a function of stress level the sample is subjected to (Lee and Seed, 1967). Soil becomes more contractive under higher confining stress. A dense sample under a large confining stress may behave like a loose sample with no dilation as shearing continues. On 4 the contrary, a loose sample sheared under a small confining stress may exhibit dilation as shearing proceeds. For saturated sands deforming sufficiently rapidly that pore water cannot drain, excess pore pressures are generated. If no drainage is possible, undrained stress-strain behaviour is observed. The volume of the sample stays constant and positive or negative pore pressures, Au, instead of contractive or dilative volumetric changes, are generated. Figure 2.2 shows the typical stress-strain relationship of sand during undrained shearing. Type 1 and 2 are the typical contractive responses of loose sand or sand at high effective confining stress loaded along a conventional stress path in a triaxial test. Type 3 is the typical dilative response of dense sand or sand at low effective confining stress. Type 1 response is called liquefaction (Castro, 1969; Casagrande, 1975; Seed, 1979; Va id and Chern, 1985), a strain softening process with the development of unlimited unidirectional strain at constant void ratio, confining stress and shear resistance called steady state (Castro, 1969). Type 2 response is called limited liquefaction (Castro 1969), in which limited unidirectional strain development is followed by strain hardening after the minimum undrained strength has been reached. Unlike type 1 and 2 responses, an increase in strength with strain, or strain hardening, is observed in type 3 response. The effective stress paths of the three responses are shown in Figure 2.3. The critical stress ratio (CSR) line represents the effective stress ratio values corresponding to the peak deviator stresses that initiate the strain softening process. It has also been named as the "collapse surface" by Sladen and Hollander (1985) and the "instability line" by Lade et al. (1997). Experience indicates that the critical stress ratio values in triaxial extension are significantly lower than those i n compression. 5 AXIAL STRAIN E0 (%) Figure 2.2 Characteristic Undrained Stress-Strain Response of Sand (Kuerbis et al., 1989) Figure 2.3 Effective Stress Paths of Undrained Behaviour of Sand (Kuerbis et a l , 1989) 6 The phase transformation line represents the termination of the tendency towards contractive behaviour. Depending on the soil density and stress level, samples either reach a steady state or begin strain hardening along the undrained failure envelope as shearing continues. The inclination o f the phase transformation line is unique for a given type of sand but varies with soil mineralogy among different soil types. Recent work has shown that partially drained shearing can be a more severe loading condition than undrained loading (Eliadorani, 2000). 2.2 Cur ren t T h i n k i n g on Soil Stiffness In order to make use of the observed stress-strain response in engineering calculations, it is necessary to idealize the soil in some way. For stress conditions not approaching the shear strength, the simplest approach is to idealize the soil using the theory of elasticity. The stress-strain relationships of an isotropic and homogeneous elastic material can be fully described by any two of the following parameters: • Young's modulus, E • Poisson's ratio, v • Bulk modulus, K • Shear modulus, G For isotropic materials, the use of K and G allows separation o f the effects of changes in mean stress from those due to changes in shear stress. However, soils exhibit shear-volume coupling and therefore, additional parameters are required to model behaviour. To account for the non-linear behaviour of soil, it is common to define the moduli as secants to the laboratory stress-strain curve over the stress increments applicable to the problem under consideration. The non-linear stress-strain behaviour of sand can be 7 approximated by the hyperbolic approach suggested by Kondner (1963) and secant accounts for the stress dependence of the moduli. Kondner's hyperbolic approach was supported by other authors, such as Porovic and Jardine (1994), who suggested G increased with a power of effective confining stress, as well as Jovicic and Coop (1997), who showed G increased linearly with the logarithm of effective confining stress. The value of n is typically taken to be 0.5 for G m a x , but has been observed to vary with strain level (Ishihara, 1996). The use of secant moduli over the stress increments applicable to the problem under consideration treats the soil as equivalent elastic. In the equivalent elastic approach, the stiffness reduces with strain level because of the non-linearity. A typical representation of equivalent shear modulus with shear strain level is shown in Figure 2.4. In the range of very small strains, the shear modulus is essentially constant. The modulus is generally very large in this range but attenuates very rapidly when the strain level enters the small strain range. Shear modulus can drop by a factor of 10 over the first 1% of strain. A t strain levels larger than 1%, the modulus is very small, which indicates that the soil is very soft and is approaching failure. Atkinson and Sallfors (1991) defined the upper limits of the very small strain range and the small strain range to be 0.001% and 1%, respectively. Jardine (1992) conveyed a concept similar to that proposed by Atkinson and Sallfors in a different manner. He divided the area around a stress point into three distinctive zones on the q/p ' e -p7p' e space: I, II and III. q represents the shear stress (j} -I-20*' (q - <J\ -<r' 3), p ' represents the mean effective stress (p'= ——-—-) and p e represents stiffness can be represented by the equation G = kgPa , where the factor 3 8 the equivalent mean effective stress on the virgin consolidation line at a particular p ' . They are enclosed by a boundary surface, B S , and are shown in Figure 2.5. Jardine defined Zone I as a region where soil behaviour is perfectly linear elastic. However, it only occupies a very small proportion of the stress space within the boundary surface. He also defined the boundary of Zone I to be within 6 x 10~4% strain and stated that this zone is exceeded at an early stage during loading. Zone II is a region typified by non-linear but fully recoverable stress-strain behaviour. Complete load-unload cycles typically involve hysteresis and energy dissipated in such hysteresis stress-strain loops is considered to be due to small-scale local yielding at the inter-particle contacts. Jardine found for his tests that Zone II starts at a strain of 6 x 10"4% and ends at a strain level that depends on the soil type. He investigated the results from previous research and concluded that the upper limit of Zone II can vary from 0.001% to 0.06%. Zone III represents a region of highly non-linear stress-strain behaviour and the development of irrecoverable strains. Particle sliding is believed to be the dominant process in this zone, with continuous load column breakages and reformations to accommodate the changing stress conditions. If the soil is loaded further, the boundary surface w i l l be reached and large-scale changes in particle packing, either contraction or dilation, w i l l occur. In Jardine's Zone I, the shear modulus corresponds to the maximum shear modulus of the soil, G m a x or G 0 . However, its determination is challenging because the extent of the linear elastic zone is very limited and shear modulus is very sensitive to the magnitude of shear strain involved during sampling and testing. Fahey (1998) noted that G m a x could only 9 ~ 1 % Ine, very small small large < .. • Figure 2.4 A n Idealization for the Variation of Stiffness with Strain for Soil (Atkinson and Sallfors, 1991) Figure 2.5 Identification of Zones I, II and III in Triaxial Stress Space (Jardine, 1992) 10 be accurately measured by in-situ methods. Up until recently, research had been conducted either at very small strain (s s < 0.001%) using such dynamic tests as the resonant column tests or at strains within the upper portion of the small strain range (s s > 0.1%) using conventional triaxial tests. However, stiffness in the shear strain range of 0.001 % to 0.1 % had not been studied extensively. Recent advances in instrumentation have enabled study of stress-strain behaviour at strains as small as 0.0001%. 2.3 Ag ing Effects in Sands 2.3.1 In-Situ Evidence of Ag ing Increases in penetration resistance and shear modulus with time are reported in many geotechnical papers, particularly in those related to the assessment of ground improvement in sands. Mitchel l and Solymar (1984) presented cone penetration test (CPT) measurements acquired during the main dam foundation treatment for the Jebba Hydroelectric Development on the Niger River in Nigeria. In-place densification by vibrocompaction and blasting was carried out in alluvial sand to minimize foundation settlement during dam construction and reservoir filling and to prevent liquefaction of the looser zones during seismic events. A s shown in Figure 2.6, the cone penetration resistance 9 days after blasting was slightly less than that before blasting. However, 11 weeks after blasting, the penetration resistance was found to exceed that before blasting by approximately 25%. Penetration tests were also done in a 10 m thick hydraulic f i l l sandpad and the results showed a very pronounced time effect. C P T tests were performed 4 to 10 days after fi l l placement and were repeated 50 to 80 days after fi l l placement. Figure 2.7 shows that 11 the C P T tip resistance approximately doubled over this time period. Based on the C P T data presented in Mitchel l and Solymar's paper, it was clear that disturbance introduced to clean sand deposits could reduce the penetration resistance significantly. However, the penetration resistance would increase substantially over periods from days to months and such time effects were noticeable in both freshly deposited and densified saturated sand deposits. Dowding and Hryciw (1986) performed a series of laboratory tests in a tank to investigate time-dependent changes in penetration resistance after blasting. The sand used in the tests was a fine, uniform, brown, silica sand from an Evanston, IL beach. They found that the penetration resistance increased considerably with time and the most significant timewise increase in resistance occurred at a location closest to the charge, which was the zone of greatest disturbance. In order to make all o f the C P T measurements comparable, the average penetration resistance over the entire depth of soil one day after the blast was calculated and used as the base value for comparison. Figure 2.8 summarizes the modified C P T measurements and shows the timewise increase and spatial attenuation of penetration resistance readings after the blast. A t a radial distance of 10 centimetres away from the location of blast with two charges, the penetration resistance increased by 75% (from 0.12 to 0.21 kg/cm 2) in 10 days. The increase in penetration resistance was approximately 67% (from 0.09 to 0.15 kg/cm 2) at a radial distance of 20 centimetres and 60% (from 0.05 to 0.08 kg/cm 2) at a radial distance of 30 centimetres. A t a radial distance of 40 centimetres, the percentage increase in penetration resistance was 400% (from 0.01 to 0.05 kg/cm 2). This exceptionally high percentage of increase could be attributed to the low penetration resistance observed 5 days 12 FUGRO STATIC C O N E R E S I S T A N C E (MPa) FT m 0 10 20 30 40 0 10 20 30 40 0 10 20 30 40 TEST 7, CPT A BEFORE AND AFTER 9 DAYS AFTER 11 WEEKS Figure 2.6 Penetration Resistance of Thick Sand Layer at Two Times Disturbance (Mitchell and Solymar, 1984) 13 FT m FUGRO STATIC CONE RESISTANCE (MPa) ( 0 T 0 2-10 I 4 a L U Q 20 6 8 30-— 10-FT m ° l [ °1 2 10 X 4-1-a L U Q 20 6 8 30 — 10-0 40 80120 0 4080120 0 40 80120 0 40 80120 0 40 80120 0 40 80120 r f ® \ CPT 36 > I ® CPT 108 — • > ® \ ® ) 1 — . CPT 37 ® CPT 147 < CPT 107 4 P ® CPT 148 @ 4-10 DAYS AFTER DREDGING (g) 50-80 DAYS AFTER DREDGING RIGHT BANK SAND PAD DEPTH OF DREDGED SAND - 10m Figure 2.7 Penetration Resistance Profiles for a Hydraulic F i l l at Two Times after Placement (Mitchell and Solymar, 1984) 14 .20 3E u >. o 5C .10 . oo UJ u z < co CO UI ce z o Q. UI CO < UI ce u .30 .20 .10 .00 O N E C H A R G E C DAY 1 T O DAY 5 * DAY 1 TO OAY 15 15 DAYS j 5 DAYS -— ( I I i . i t » z < ) 10 20 S O 40 50 < i 15 DAYS J > ! TWO C H A R G E S G DAY 1 TO OAY 5 6 OAY 1 TO DAY 19 < < < 5 D A Y S | V i • \ > \ ( < i z < 1 4 i 0 10 20 SO 4 0 50 D I S T A N C E F R O M C H A R G E , r (CM) Figure 2.8 Increase in Average Point Resistance over 1-Day Values with Distance and Time after Blast (Dowding and Hryciw, 1986) 15 after blasting. The effect of time on penetration resistance has been observed by a number of other investigators and is widely recognized as a factor in the quality control of ground improvement contracts. The reasons for the increase are not clear. Charlie and Rwebyogo (1992) carried out an investigation of this phenomenon in which they observed a similar reduction in field tip resistance with time immediately after blasting followed by a time-dependent increase. The normalized tip resistance with time after disturbance was found to fit the following equation: V?c )/v weeks * , , , , -7—v = \ + K\ogN Wc h week where q c was the tip resistance, N was the number of weeks since disturbance and K was an empirical constant indicating the rate of tip resistance increase over time. Charlie and Rwebyogo gathered the K values obtained by other researchers and concluded that the logarithm of the K values varied linearly with temperature. Skempton (1986) analyzed a collection of field SPT data corrected to 60% of theoretical energy and normalized at 100-kPa, or 1-kg/cm2, effective overburden pressure. 2 2 In general, (Ni)6o/D r was constant for D r from 35 to 85% and a ' v from 0.5 to 2.5 kg/cm . (N) Figure 2.9 shows that the — x - ^ - ratio increased with the age of the deposit. Furthermore, Dr (N) it shows the dependence of — o n particle size. In addition to C P T tip resistance and SPT blow count, pile capacity has been observed to vary with time in sands. Chow et al. (1997) found that pile capacity increased with time in loose and dense sands for a wide variety of pile types. They concluded that the 16 increase in capacity was primarily caused by an increase in shaft capacity and the base capacity did not change considerably. Figure 2.10 shows the relationship between shaft capacity normalized by the initial shaft resistance, , and time after driving. Shaft Qso capacity can be seen clearly to increase with time in Figure 2.10 and the rate of increase was approximately 50% (± 25%) per log cycle of time once the pile had been driven for 24 hours. Monahan et al. (2000) used carbon dating to estimate the ages of organics in Fraser River sand. Figure 2.11 shows the normalized C P T resistance, q c i , versus time from a number of sites in the Fraser River Delta. Again, q c i increased with time and appeared to approximately double over 10,000 years. Wride et al. (2000) presented in-situ test data from six sites investigated during the Canadian Liquefaction Experiment ( C A N L E X ) project and from Duncan Dam. The ages of the C A N L E X sand deposits varied from 1 month to 4000 years, whereas the age of the soil deposit at the Duncan Dam was about 10,000 years. Figure 2.12 shows the C P T q ( P resistance normalized for relative density, —^y-, where qcX N = qc the logarithm of the age of the deposit. The increase in tip resistance with time is clear. plotted against Aging is also known to influence shear wave velocity. Figure 2.13 illustrates ^ 5 at the same seven sites as Wride et al. (2000), where vsi = vs / \ 0.25 The quantity — i n c r e a s e d with the age of soil deposit and the increase was approximately Dr linear with the logarithm of time. 17 80 60 40 20 • W.E.& L A B TESTS xT2y • OGISHIMI FILL <1y • K A W A G I S H I - C H O FILL >30y • NIIGATA S A N D >W0y A NIIGATA S A N D >KX)y 0 SIZEWELL S A N D * JMOOy (*)OVEFI CONSOLIDATED F - FINE SAND Dso< 0.4mm C » COARSE SAND P^>0.4mm. ' F O — C++-10 -1 1 10 100 AGE OF DEPOSITCYEARS) Figure 2.9 Influence of Aging on Standard Penetration Resistance of N C Sands (Skempton, 1986) 75% 3-5 30 2-5 1-5 i y T94 • ". !• v : / A : / A : / V T ~y* / j 'till A / ' T I T'89a« _ ^ y : -rf^Y\ 1 1 1 1 1 1 — - • : OfD i — i » i » " " " • • 1 1 1 1 M i l 1 1 1 1 1 1 1 1 1 i i i i 1 1 1 1 50% increase per log cycle 25% 10 Time after driving: days 1000 10000 Figure 2.10 Increases in Shaft Capacity with Time (Chow et al., 1997) 18 ure 2.11 Plot of Average q c ] and C Age of Organic Material in Topset Sand of Fraser River Delta (Monahan et al., 2000) 19 1000 900 + 800 + 700 + 600 + 500 + 400 + 300 + 200 + 100 + 0.01 0.1 KLiddl Massey Mildred Lake ' H M Dam LL Dam I •+- •+- 4-1 10 Age (years) D Dam 100 1000 10000 Figure 2.12 Possible Effects of Age of Deposit on CPT Penetration Resistance (Wride et al., 2000) 20 350 K i d d O • D D a m 300 + Massey 250 + LL Dam I > I Mildred Lake m HM Dam 20Q-; J-I't< 150 + 100 -4-0.1 10 100 Age (yean) 1000 10000 Figure 2.13 Possible Effects of Age of Deposit on Measured Shear Wave Velocity (Wride et al., 2000) 21 Troncoso and Garces (2000) conducted a series of in-situ downhole wave propagation tests in sandy silts tailings deposits with known history. The calculated shear moduli were normalized for effective vertical stress and were then plotted against the ages of the deposits. Troncoso and Garces concluded that normalized shear moduli, G n , increased with age according to the relationship: G„ =117.24/ 0 6 7 (8 < ^ < 41) Based on the above summaries of past researches, it can be concluded that cone penetration resistance, q c , SPT blow count, N , shear wave velocity, v s , and pile capacity increase with the age o f soil deposit. 2.3.2 Laboratory Evidence of Aging Time effects have been observed in laboratory testing. Anderson and Stokoe (1978) carried out a series o f resonant column laboratory tests to investigate the effects of time at constant confining pressures on low-amplitude shear moduli of sands and clays. They claimed that the duration of vibration did not have any influence on shear moduli as long as the shear strains did not exceed 0.001%. Results o f tests on air-dried Ottawa sand are summarized in Figure 2.14. A l l pore pressure changes and elastic deformations had taken place before the first measurement was made. The shear moduli varied linearly with the logarithm o f the duration of confinement. Anderson and Stokoe defined two parameters to describe the effects of time on low-amplitude shear moduli: the coefficient o f shear modulus increase with time, IG - a coefficient of shear modulus increase, A G , for one logarithmic cycle of time, and the increase in shear modulus with time, N G - the increase in shear modulus relative to the shear modulus measured after 1000 minutes of hydrostatic confining pressure. The two 22 24 4 1 1 1 1 1 10 1 10 2 1 0 3 10 4 DURATION OF CONFINEMENT, t (min) Figure 2.14 Typical Modulus Change with Time for Sand (Anderson and Stokoe, 1978) 23 parameters were defined as follows: A G 1G = — Equation [1] log 10 Ir Nc = — £ - 1 0 0 % Equation [2] ^ 1 0 0 0 The IQ and No values for Ba l l kaolinite were found to be 6200 k N / m 2 and 15%, respectively, while values of I G and N G for Ottawa sand were only 1725 k N / m 2 and 1%. The lower I G and N G values for sand indicated that time-dependent increase in small-strain stiffness was considerably less pronounced than for clays. Mesr i et al. (1990) calculated a N G value of 2.5% for clean granular soils. Jamiolkowsi and Manassero (1995) quoted the values of N G to be between 1% and 3.5% for silica sands. However, Fahey (1998) and Ishihara (1996), in consideration of the effects of sample disturbance, proposed that the N G value for sands should be considerably larger than 1%, the value quoted by Anderson and Stokoe. Daramola (1980) conducted a series of triaxial tests on four 38-mm by 80-mm samples made o f Ham River sand subjected to an effective confining stress o f 400 kPa. One of the samples was sheared immediately after preparation while the other three samples were consolidated hydrostatically for 10, 30 and 152 days before they were sheared. Figure 2.15 shows the results of the shearing tests. When the sample was aged for 10 days, the stress-deformation behaviour was very similar to that of a freshly deposited sample. However, as the age of consolidation increased, the stress-deformation behaviour became steeper and the strain to failure decreased. The secant modulus for each test was determined using the points of 10% and 24 (10) =Age of consolidation in days £ -1-0 Figure 2.15 The Effect of the Age of Consolidation on Stress-Strain Characteristics of Ham River Sand (Daramola, 1980) 25 50% maximum stress difference to reduce the effects of bedding errors associated with overall strain measurements on moduli determination. 0.5(crJ -0.l((jj Secant Modulus = —r -,—r The calculated secant moduli of aged samples were then divided by the value for the freshly deposited sample and plotted against the logarithm of the age of consolidation in Figure 2.16. The relationship between the two parameters was linear and the rate of increase in modulus for every logarithmic cycle of time was approximately 50%. Skempton (1986) analyzed Daramola's data and found that the secant moduli in tests made after 30 and 150 days of consolidation increased by 60% and 100%, respectively. However, the internal friction angles of the samples were virtually identical. They only changed from 39.0° to 39.5°. Skempton proposed the inter-particle bonds developed during aging were broken when the samples approached failure and therefore, the friction angles of the two samples did not differ significantly. Murashev (1997) carried out two series of tests on undisturbed and remoulded samples of uncemented marine sand in a triaxial testing machine. The undisturbed samples were collected by a thin-walled split sampler and frozen to preserve their natural particle arrangements. They were then thawed, reconsolidated and tested in a testing cell under drained conditions with a confining pressure of 100 kPa. The remoulded samples were prepared from the same sand by remoulding. They were then compacted to their in-situ densities and tested in a manner similar to that for the undisturbed samples. Based on the collected data, average secant moduli at a vertical stress of 200 kPa and initial moduli were computed. Murashev found that both kinds of moduli for the undisturbed samples were significantly larger than those for the remoulded samples, which could be attributed to the 26 Figure 2.16 Relationship between Normalized Secant M o d u l i with L o g (Age of Consolidation) (Daramola, 1980) 27 erasure of age-strengthening effects in the remoulded samples. In addition, the natural soil particle arrangement was destroyed in the remoulded sample, which might also lead to different grain structures and mechanical properties of the undisturbed and remoulded samples. Mejia et al. (1989) performed a series of one-dimensional oedometer tests and stress-controlled triaxial tests to study the time-dependent behaviours of sands. The results of the tests suggested that the time-dependent behaviour of sand was very similar to creep behaviour of clays and metals. Creep deformations developed in the one-dimensional oedometer tests were found to increase with stress level and grain angularity. Furthermore, the logarithm of strain rate was found to vary inversely with the logarithm of time. Creep deformations developed in conventional triaxial tests were found to increase with confining stress level, stress ratio and grain angularity but decrease with relative density. Moreover, the volumetric creep shifted from contractive to dilative when the stress ratio was increased. Lade et al. (1997) conducted three series of high pressure triaxial tests to investigate the effects of time on the stress-strain behaviours o f sands. Loose samples of Sacramento River sand were aged for five different periods of time: 0, 2,20,200 and 1690 minutes, and sheared under undrained conditions with the pore pressures being monitored. The authors observed that older samples were stiffer at the beginning of shearing. Moreover, they mobilized higher undrained shear strengths and developed smaller excess pore pressures. Similar results were observed by Gananathan (2002), who studied the partially drained responses of Fraser River sand. In all o f his aging tests, Gananathan observed that the rate of strain development was the fastest at the beginning of aging and 28 decreased with time. He also discovered that aging had no effect on the mobilized friction angles of maximum obliquity, phase transformation and critical stress ratio. Aging was found to result in more dilative stress-strain behaviour during subsequent shearing and was able to transform a strain-softening response into a strain-hardening response. In addition, older samples mobilized higher undrained shear strengths and had stiffer stress-strain behaviour. Gananathan concluded that the magnitude of undrained shear strength increase varied inversely with time. He observed a 9% increase in the normalized shear strengths over the first 100 minutes of aging, whereas the shear strengths only increased by 3% in the next 900 minutes. Lade and L i u (1998) studied the time-dependent behaviours of sand taken from the Antelope Val ley in Los Angeles, California, in a conventional triaxial apparatus. The experimental program included studies of stress-strain and strength behaviour under different confining stresses, strain rates, stress ratios and strain paths. Figure 2.17 shows the stress ratio and volumetric strain versus axial strain curves o f triaxial compression creep tests with various phases of creep at constant stress levels. When the stress ratio was held stationary, axial and volumetric creep deformations were observed. Furthermore, the magnitude o f creep increased with stress ratio. The stress ratio was increased after each creep cycle and was found to rise very rapidly at the beginning of loading, which signified an increased stiffness of the sand after aging. Shozen (2001) conducted a series of laboratory triaxial tests under drained conditions to investigate the effects of aging on the stress-strain-deformation relationships of Fraser River sand. In Shozen's test program, samples were consolidated along three constant stress ratio paths and aged for 1,10,100 and 1000 minutes. After the samples had 29 5 10 15 20 Axial Strain, ei(%) -5 Axial Strain, ei(%) 5 10 15 20 5^ <4 i 5 £ 10 25 30 TC-2-1 Creep at Various Stress Ratios (b) i Figure 2.17 Results of Triaxial Compression Creep Test Showing (a) Stress Ratio versus A x i a l Strain (b) Volumetric Strain versus A x i a l Strain for Antelope Val ley Sand (Lade and L i u , 1998) 30 aged, they were sheared along one of the four stress paths shown in Figure 2.18: conventional triaxial compression path (Con), constant p ' path (-2), A G ' I = -Acr'3 path (-1) and constant a ' i path (0). Shozen found that both axial and volumetric strain developments during aging varied linearly with the logarithm of aging duration and the magnitude of creep increased with increasing stress ratio, a trend also observed by Lade and L i u (1998). Moreover, he found that older samples were stiffer than younger samples during shearing. He concluded that the effects of aging only existed at the very beginning of shearing. The stress-strain behaviour at larger strains was not affected by aging. Shozen observed that increased age caused a reduction in contractive volumetric strain during the initial stage of shearing. In addition, he observed initial expansion, or dilation, at the beginning of shearing along paths with decreasing effective confining stress and such expansion was enhanced by aging. He concluded that the degree o f stiffening due to aging increased with increasing stress ratio. He also observed that the timewise increase in soil stiffness was the greatest along the conventional triaxial compression path and decreased as stress path rotated from conventional path towards constant a ' i , or 0, path. Figure 2.19 presents the secant moduli measured at shear strains of 0.03% and 0.15% normalized by the shear modulus obtained at a stress ratio of 2.8 and with an aging duration of 100 minutes with different aging durations and relative densities. When the shear strain level was lower than 0.1%, the secant modulus o f the loose sample was, surprisingly, higher than that of the dense sample, which suggested that the effects o f time on the mechanical behaviours of sands were more significant that those of relative density in small strain levels. When the shear strain level was higher than 0.1 %, however, the 31 ;ure 2.18 Applied Stress Paths in Various Stress Spaces (Shozen, 2001) 32 2.5 2.0 CO D TS O I 1.5 c (0 o d> to I 1.0 ra E i -o z 0.5 0.0 0.01 o o a o o o G s Normalized by G s ( R = 2 8 1 0 m i n 1 0 0 k P a L o o s e ) 0.1 y (%) ° Loose (24.8%) 1000-Minute Aging o Dense (54.2%) 10-Minute Aging Figure 2.19 Comparison between Effects of Time and Relative Density along Conventional Path (Shozen, 2001) 33 dense sample was stiffer than the loose sample as expected. This reinforced the idea that effects of time were only noticeable in small strain levels. 2.4 Proposed Causes of Aging Although time-dependent behaviour has been observed in both in-situ and laboratory tests on coarse-grained geomaterials, the exact cause is not fully understood. Previous researchers have proposed different explanations for the aging phenomenon and some of them are described in detail in this section. Dowding and Hryciw (1986) suggested the gradual dissipation of explosion generated gases was responsible for the timewise increases in penetration resistance in their laboratory study of blast densification on saturated sands. However, Mitchel l and Solymar (1984) observed timewise increases in penetration resistance at the Jebba Hydroelectric Development Project on the Niger River in Nigeria after blasting and vibrocompaction had been performed. Because gases were not generated in vibrocompaction, the gradual dissipation of gases being the cause of time effects was questionable. Mitchel l and Solymar attributed the increases in penetration resistance to the formation of silica acid gel films on particle surfaces and the precipitation of silica or other materials from solution or suspension as a cement at particle contacts. Charlie and Rwebyogo (1992) carried out a series of C P T tests in poorly graded gravelly sand and discovered a linear relationship between the logarithm of the rate of penetration resistance increase, K , and temperature. Their findings supported Mitchel l and Solymar's idea that the involvement of chemical reactions as a cause of cementation bonds between particles because rates of chemical reactions increased with temperatures. Joshi et al. (1995) prepared six separate samples under different environmental 34 conditions to study the phenomenon of aging and its effects on penetration resistance of sands. Three of the samples were used for testing river sand in three different environments: dry, immersed in distilled water and sea water. Two of the remaining three samples were Beaufort Sea sand submerged in distilled water or sea water and the sixth sample was used to investigate the effects of freezing and thawing on the penetration resistance of river sand submerged in distilled water. X-ray diffraction traces of both sands are shown in Figure 2.20. It can be seen from the traces that Beaufort Sea sand consisted mainly of quartz and a trace of albite. The river sand, on the other hand, contained calcite and norsethite in addition to quartz. X-ray analysis was done on the dry river sand sample before and after aging under 100-kPa vertical stress and no mineralogy change was found. Moreover, when the dry sample was dismantled, the sand fell out of the mould like loose sand, which indicated no silica gel formation at particle contacts. The river sand samples submerged in distilled water and sea water showed a certain amount of cohesion when they were pushed out of the mould and the cohesion in the aged sea water sample was observed to be greater than that in the aged distilled water sample. Scanning electron micrographs of the river sand and Beaufort Sea sand revealed the existence of extraneous substances on the surface of the particles, which suggested the formation of cementation bonds at particle contacts and in interstices. Sea water samples had more precipitates on the particle contacts than distilled water samples. Precipitates in the river sand were analyzed by an x-ray analyzer. The precipitates in the distilled water sample were found to consist mainly of calcium whereas those in the sea water sample were found to be composed of sodium, silica and chlorine. Joshi et al. concluded that the 35 20 16 12 c <D 1 si 0 0 Q,N C N u Q C,N Q C Q . C N jlljjt Q Q,N C,N River Sand Q,C Q UuJ N - Norsethite Q - Quartz Q A - Albite C - Calcite A Q Q Q A Q Q Beaufort Sea Sand 9 Q -i r _1 (_ 10 20 30 40 50 60 70 80 2 Theta Figure 2.20 X - R a y Diffraction Traces of the Beaufort Sea Sand and River Sand (Joshi et al., 1995) 36 precipitates formed in the submerged samples mainly consisted of water-soluble components in the sands, probably calcium and other acid-soluble elements. However, the cementation could not be attributed to the precipitation of silica with confidence. While many researchers believed that chemical precipitation at particle contacts was responsible for the time-dependent behaviours of sands, others suggested that the aging phenomenon was caused by particle rearrangement and increase in frictional resistance or interlocking between particles. Mesri et al. (1990) carried out a study of the effects of aging on post-densification penetration resistance of clean sands and they questioned the hypothesis that implied the formation of cementation bonds at particle contacts of clean silica sands with time. The authors believed the continuous rearrangement of sand particles after deposition or any other process of disturbance with a net void volume decrease was a more plausible explanation for the time effects in sands. Particle rearrangement enhanced micro-interlocking of surface roughness and geometrical grain interference. A s a consequence, sliding resistance of sands was increased and resistance to deformation was improved. The authors attributed the drained aging phenomenon of clean sands to an increase of frictional resistance through macro-interlocking of particles and micro-interlocking of surface roughness. Mesri et al.'s view was supported by Schmertmann, who suggested timewise increases in soil strength and modulus in fine-grained soils (Schmertmann, 1991) and sands (Schmertmann, 1981) were caused by mobilization of additional soil friction rather than soil cohesion. Kuhn and Mitchell (1993) conducted a series of laboratory tests on medium, uniform Toyoura sand and normally consolidated San Francisco Bay mud. According to Kuhn and Mitchell 's experimental results, deviatoric or axial strain rates in 37 samples exposed to creep stresses insufficient to cause creep failure decreased rapidly with time. The authors proposed a numerical model based on rate process theory to explain the decreasing strain rate during creep. They suggested the inter-particle sliding velocity was a function of the ratio of the tangential-to-normal components of contact forces. A s creep proceeded, the soil particles rearranged to a more efficient orientation, which led to a reduction in the tangential components and an increase in the normal components of the contact forces. The ratio of the tangential-to-normal components was altered and the sliding velocity was reduced, which resulted in a reduction in the overall creep rate of soil. Besides laboratory experiments, Kuhn and Mitchell carried out a series of numerical simulations using a rectangular, two-dimensional assembly of 1002 circular disks. The calculated strain rates agreed satisfactorily with those observed in real soils, which verified Kuhn and Mitchell 's model and reinforced the concept of the frictional nature of soil aging proposed by such researchers as Mesri , Feng and Benak, as well as Schmertmann. Baxter (1999) carried out a testing programme to investigate the effects of different variables on the presence and magnitude of time effects. In his study, Baxter tested three different sands in rigid wall cells and five-gallon plastic buckets. Factors studied in his research included effective stress, density, temperature and pore fluid. In each test conducted in rigid wall cells, three independent properties were measured to examine the trends and causes of time effects: small-strain shear modulus using bender elements, electrical conductivity and mini-cone penetration resistance. Aging in the samples in five-gallon buckets was assessed by mini-cone penetration tests at different times and at different locations. 38 Baxter found that small-strain shear modulus determined in the samples in rigid wall cells increased with time of aging and the magnitude o f modulus increase was greatly affected by the sand type, pore fluid and density. In addition, Baxter found that the percentage increase in shear modulus was higher in dense samples than in loose samples. Temperature, on the other hand, was not found to have a significant influence on the time-dependent increase in modulus. Baxter's electrical conductivity tests were designed for tracking changes in the chemistry o f samples with time, which helped to determine whether or not time effects were caused by such chemical reactions as precipitations o f silica and carbonates. In two of his tests, Baxter observed a continual decrease in electrical conductivity with time, which suggested the occurrence of precipitation of silica or carbonate minerals during aging. However, he concluded that time effects in natural sand deposits were unlikely to be caused by precipitation because natural groundwater was very different from the fluid that he used to prepare the two samples (carbon dioxide-saturated water) and precipitation was unlikely to occur. Moreover, no significant evidence of precipitation was observed in the scanning electron micrographs of the two samples. Before the samples in rigid wall cells were drained and dismantled, mini-cone penetration tests were performed. Baxter discovered that the penetration resistances for the fresh and aged samples were essentially identical, which contradicted the results obtained by such researchers as Mitchel l and Solymar (1984). The penetration resistances of the bucket samples, furthermore, did not show any significant increase after aging. In order to simulate free-field conditions, in which the penetration resistance was not affected by the boundary conditions, the ratio of cell diameter to cone diameter should be at least 20 for 39 loose sand and 50 for dense sand. The cone Baxter used in his mini-penetration tests had a diameter of 0.635 centimetres and the diameter of the cell was 17 centimetres, which yielded a cell diameter to cone diameter ratio of 26. Moreover, the penetration tests were performed only 3 centimetres from the cell wall . The diameter ratio was close to the limit for loose sand (20) and the proximity to the cell wal l during penetration tests (3 centimetres) prevented free-field conditions from being achieved and might explain why an increase in penetration resistance with time was not observed in the mini-penetration tests. Moreover, Baxter proposed the mini-penetration tests carried out in his study might be incapable of capturing the factors causing the time effects observed in the field. The following conclusions on current understanding of the aging phenomenon in sands can be drawn: • Time-dependent behaviour of sand is very similar to creep behaviour of clays and metals. • The rate o f strain development varies inversely with the logarithm of time during aging. • Aging always leads to stiffer stress-strain behaviour but such effects are only observable at the beginning of shearing. Overall stress-strain behaviour is not affected by aging. • Low-amplitude shear modulus varies linearly with the logarithm of the duration of aging but the rate of increase is controversial. • In drained tests, aging prior to shearing reduces the volumetric strain developed during the initial stage of shearing. 40 • In undrained tests, aging leads to larger critical stress ratio and phase transformation shear strengths. However, it has no effect on the mobilized friction angles of maximum obliquity, phase transformation and critical stress ratio. • The exact cause of aging is not clear. Some researchers believed that it was caused by chemical reactions that occurred between particle surfaces while others thought that particle rearrangement and increase in frictional resistance or interlocking were responsible for aging. 2.5 Proposed Research The major objective of this research was to extend the study by Shozen on the effects of aging duration, stress ratio and stress path on the stress-strain response of loose Fraser River sand. In Shozen's study, all of the samples were aged from 1 to 1000 minutes. A n 10,000-minute test was attempted but the results were not reliable. Therefore, the aging effects on soil properties at aging durations longer than 1000 minutes were unknown. In addition, most of the samples were consolidated anisotropically and sheared along the conventional and 0 stress paths. On the contrary, only a limited number o f tests were conducted under isotropic conditions and along the -1 and -2 stress paths. Aging effects under such circumstances were not studied extensively. In this study, gaps in Shozen's study were filled to obtain a clearer and broader picture of aging effects on loose Fraser River sand. Shozen conducted tests with aging durations of 1 and 10 minutes but such short time periods required significant corrections for residual strains in the shearing phase, which were the strains that would have occurred without any change in stress states. In order to eliminate possible errors caused by residual strain corrections, all of the samples used in this research had been aged for at least 100 41 minutes. Shozen used a maximum aging duration o f 1000 minutes in his tests whereas an aging duration up to 10,000 minutes was used in this research. Three of such tests were successfully completed throughout the entire research programme. Besides the extended aging time, two more stress ratios, 1.6 and 2.5, were used during consolidation and more tests were conducted along the -1 and -2 stress paths during shearing. A series of hydrostatic tests were also carried out to extend the understandings of sand behaviour presented in Shozen's work. Only loose samples with average relative densities of approximately 20% were tested in this research as time effects are the most pronounced in loose samples and the effects of relative density on soil stiffness variations were not fully investigated. 2.6 Organizat ion of Thesis Experimental details, such as apparatus used, resolution and stability of the data acquisition system and various corrections involved in triaxial tests are discussed in Chapter 3, which is followed by a discussion of the test results presented in Chapter 4. The study is concluded in Chapter 5. 42 C H A P T E R 3 Experimental Details The research described in this thesis focused on the effects of time on the stress-strain properties of Fraser River sand, primarily at strains less than 0.2%. The particular details of this study required: • Independent control of cell pressure and axial load to allow consolidation along constant stress ratio paths (proportional loading); • Abi l i ty to collect stable axial and volumetric strain measurements and to control stresses during aging periods of up to one week; • Abi l i ty to acquire precise and accurate axial and volumetric strain measurements during the initial stages of shearing at strains of less than 0.1 % Because of the need for repeatable and accurate measurement of small deformations, it was necessary to pay close attention to details of sample preparation, set up and test procedures. The experimental details are described in this chapter. Observed limitations of the equipment and procedures are also discussed. 3.1 Introduction The study comprised drained triaxial tests on loose samples of Fraser River sand carried out in the geotechnical laboratory in the University of British Columbia. Fundamental research on the stress-strain behaviour on sands has been carried out in this laboratory since 1980, during which time sample preparation techniques and test procedures have been developed that ensure the preparation and testing of homogeneous samples with repeatable void ratios. 43 3.2 Experimental Apparatus The shear tests in this research were all conducted in a triaxial testing machine as shown in Figure 3.1. The machine included an electronic motor, a double-acting air piston, four pressure regulators, a load cell, a linear variable differential transformer ( L V D T ) and three pressure transducers. Samples used in the tests had an approximate diameter of 6.4 cm and an approximate height of 13 cm. They were confined in a latex rubber membrane and were drained at the base only. The drainage line was connected to a small bore burette and was subjected to a back pressure. A x i a l load was applied to the sample via a loading ram placed on top of it. The load was applied by changing the pressure inside the air piston. Cel l pressure and back pressure were applied to the sample by changing the fluid pressure of the de-aired water. These pressures were controlled by two pressure regulators connected to the air pressure lines. The axial load was measured by a load cell with a maximum capacity of 200 kgf. The cell pressure and back pressure applied to the sample were measured by two Belle-Howell pressure transducers with a pressure limit of 1700 kPa. A x i a l displacements were recorded by a 3-inch "Trans-tek" L V D T with a maximum output current of 1.6 m A . Volume changes were measured by a differential pressure transducer with a pressure limit of 69 kPa. The differential pressure transducer converted changes in height of the water column in the burette into volumetric strain readings. A l l o f the data were collected, sent to and stored in a computer connected to the testing machine. In addition to the above components, two S M C electro-pneumatic transducers with maximum 1 M P a input and 0.9 M P a output pressures were connected to the computer and could be controlled independently in a pre-programmed manner. One of 44 LEGEND Loading cap-Specimen-Porous stone-Pressvire regulator Pressure Transducer Water reservior Differential Pressure Transducer LVDT Valve Data acquisition and control system 3 a. 3 o Q Personal Computer Figure 3.1 Triaxial Testing Machine (Shozen, 2001) 45 them was connected to the double-acting air piston and the other one was connected to the cell pressure line. When the transducers detected signals sent from the computer, the air flow rates in the air piston and the cell pressure line were altered and the output pressures were regulated. Because the axial load and the cell pressure could be controlled independently, close control of stress path was obtained by independent control of a'i and a'3. 3.3 Stress Application and Experimental Instrumentation Based on the work of Shozen (2001), the magnitudes o f axial and volumetric strains developed in the aging phase were expected to be in the order o f 0.1% and secant moduli were measured over shear strains o f the order of 0.03%. Therefore, the L V D T and the differential pressure transducer used in the research had to be capable o f reading strains to 0.01% or less. A strain of 0.01% represents a resolution o f about 0.013 mm on axial displacement and 0.065 m m 3 in volume change. A s aging periods of up to one week were intended, all instrument readings had to be stable for this duration. A s the stress ratio at which the sample was kept in the aging phase should not vary significantly, stable and consistent output pressures from the pressure regulators and the electro-pneumatic transducers were required. Measures taken to establish these test conditions are described below. 3.3.1 Stress Application Deviator stress and cell pressure were changed by controlling the electro-pneumatic transducers connected to the computer. Digital signals from the computer controlled the flow rates of air out of the transducers, which, in turn, imposed different axial loads and cell pressures on the sample. Figure 3.2 shows the load application with 46 150 0 10 20 30 Time (sec) Figure 3.2 Load Application with and without Controlling the Time for Stress Application (Shozen, 2001) 47 and without control of the time for stress application. If the pressure was applied in a single step, there was a possibility that the applied stress might first overshoot the target value and then drop to it. A loading-unloading cycle would thus be applied to the soil, which would likely affect the mechanical behaviour of the sample. If the pressure was applied in short pulses of magnitude considerably less than the required total increment of stress, the target value would not be exceeded and the desired stress could be reached gradually and precisely. Shozen tried different frequencies of pulse application and concluded that the desired stress could be reached accurately no matter what frequency was chosen. 3.3.2 Instrument Resolutions, Precisions and Stabilities Considerable effort was expended to ensure that the L V D T used in the research was capable of measuring strains smaller than 0.01% and the stability of e a reading within a duration of 10,000 minutes had to be examined. Figure 3.3 shows the results of L V D T monitoring in a 130-hour period. Each single data point is the average of 120 scans of the L V D T output voltage. The averaging was carried out to eliminate the effects of random noise and resolution limitations on the quality of the measured data. However, electronic noise still existed despite of the data averaging. The L V D T could only be precise to ± 0.002% and the s a readings varied by ± 0.002% about the mean value. Besides the L V D T , the stability of the differential pressure transducer used to measure volumetric strain, s v, was checked. The transducer was monitored under a constant back pressure with no volume change for 130 hours. A 200-kPa pressure, which was equal to the back pressure used in the tests, was applied to the differential 48 pressure transducer and the burette and the acquisition of e v readings was started immediately. The results are shown in Figure 3.4. The s v measurements decreased rapidly during the first 8 hours o f monitoring. Ideally, there should not be any change in the s v readings because the compressibility of water is very low and a 200-kPa pressure was insufficient to cause any significant change in the height of water column inside the burette. However, the rapid drop in volumetric strain measurements indicated a change in the height of water column in the burette. Because the burette was a closed system during monitoring, the only way the height of water column could change was through evaporation. A s the air introduced into the burette was unsaturated when the 200-kPa pressure was applied, a moisture gradient was established between the relatively dry air and the water in the burette. The air absorbed some water to increase its degree of saturation and eventually became fully saturated. The s v measurements stabilized 8 hours after the start of the monitoring when the air inside the burette became fully saturated. After 8 hours, there was a steady drift in the s v reading resulting in an apparent volume change of 0.005% over 130 hours. In order to minimize the moisture gradient between air and water, the burette was connected to a reservoir with a diameter several orders larger than that of the burette. When the back pressure was applied to the sample, the unsaturated air could absorb water from both the burette and the reservoir. However, because the reservoir had larger diameter and surface area, most of the absorption occurred from the reservoir. Evaporation in the burette was reduced and the rapid drop in s v measurements was minimized. Figure 3.5 shows the s v development within 18 hours after 200-kPa 49 -0.004 -0.006 -I 1 I L_ I | 1 Time (Hours) Figure 3.3 Variation of L V D T Readings during 13 0 Hours o f Monitoring -0.014 -L I I J I I I I I Time (Hours) Figure 3.4 Variation of e v Differential Pressure Transducer Readings during 130 Hours of Monitoring 50 pressure had been applied. Volumetric strain readings were very stable in the first 10 hours. Although Figure 3.4 and the above discussion suggest the long-term stability of volumetric strain readings was satisfactory, s v data taken in all 10,000-minute tests during the testing programme began to become unstable and varied with a range of ± 0.01% after the first 1000 minutes. The exact cause of such instability was not very clear but it was believed to be caused by the electronic noise in the measurement system. Nevertheless, this had no adverse effect on this study as its main focus was on the aging effects on stress-strain behaviour after the aging phase, not on the strains developed during aging. Figure 3.6 shows the load cell data from a 130-hour monitoring period. The mean position of the axial stress readings shifted from 0 to -0.04 kPa over 130 hours. Such a shift was insignificant compared to the axial stress applied in the tests and the stability of the load cell was, therefore, satisfactory. Figure 3.7 shows the monitoring of the cell pressure transducer. The mean position of the cell pressure readings shifted from 0 to -0.2 kPa over 130 hours. Again such a shift was relatively small compared to the cell pressure used in tests and the cell pressure transducer was judged to be stable. Figure 3.8 shows the monitoring of the back pressure transducer. The mean position of the back pressure readings stayed relatively constant at -0.1 kPa over 130 hours the back pressure transducer was stable. Table 3.1 summarizes the resolutions and precisions of the measuring devices. 51 0.0020 0.0000 1 -0.0020 ~ -0.0040 -0.0060 -0.0080 -0.0100 -i Time (Hours) Figure 3.5 Monitoring of s v with Reservoir Connected to Burette 0.15 140 Time (Hours) Figure 3.6 Variation of Load Cel l Readings during 130 Hours of Monitoring 52 140 Time (Hours) Variation of Cel l Pressure Transducer Readings during 130 Hours of Monitoring Time (Hours) Variation of Back Pressure Transducer Readings during 130 Hours of Monitoring 53 Table 3.1 Resolutions and Precisions of Various Measurements Parameter Instrument Resolution Precision Notes A x i a l strain, s a L V D T 0.0009% (0.0011 mm) ± 0.002% (± 0.0026 mm) Sample height was 130 mm Volumetric strain, s v Differential pressure transducer connected to small bore burette 0.00003% (0.0006 cm of water) ± 0.001% ( ± 0 . 0 1 8 cm of water) Sample volume was 400 cm 3 Radial strain, s r Calculated as 2 ± 0.003% Sample was assumed to deform as a cylinder Deviator stress, Load cell 0.01 kPa ± 0.025 kPa Sample area was 31.55 cm 2 Cell pressure, 03 Pressure transducer 0.025 kPa ± 0 . 1 kPa Back pressure, u Pressure transducer 0.026 kPa ± 0 . 1 kPa Figure 3.9 shows the variation of effective stress ratio, a ' i / C T ' 3 , over an aging duration o f 10,000 minutes. The cell pressure and axial stress were controlled by pressure regulators. During the 10,000-minute aging at a stress ratio of 2.1, the cell pressure fluctuated within ± 0.5 kPa and the deviator stress stayed relatively constant with a variation of ± 0.25 kPa. The fluctuations in cell pressure and deviator stress were considerably larger than the precisions stated in Table 3.1 because the pressure outputs from the electro-pneumatic transducers were not very stable during the 10,000-minute aging. The effective axial stress, a ' i , was 207 kPa at the start of aging and increased by 4.9 kPa at the end of 10,000 minutes. The effective cell pressure, cf'3, started at 99 kPa and increased by 3.2 kPa at the end of 10,000 minutes. The variations of a ' i and a '3 were caused by cyclic pressure variations of the main pressure supply line in the laboratory and led to fluctuations of effective stress ratio during aging. According to Figure 3.9, the stress ratio dropped by 0.02 throughout the entire 10,000-minute period. 54 250 200 150 100 50 t CT1 V Ln . ML mi ! 'If ' CTi/a 2.100 2.095 4- 2.090 co 2.085 J? 2.080 2.075 2.070 2000 4000 6000 Time (Minutes) 8000 10000 Figure 3.9 Variations of CT'I, c ' 3 and Effective Stress Ratio 55 As such, the effective stress ratio was maintained at a relatively constant value despite the variations in deviator stress and cell pressure. The following conclusions regarding the reliability o f the load application system and the data acquisition system can be drawn: • Pressure was applied in short pulses to ensure the desired stress could be reached precisely. • The L V D T used to measure axial strain, which had a resolution of 0.0009% and a precision of ± 0.002%, was very stable over the 130-hour monitoring period. • The differential pressure transducer had a resolution of 0.00003% and a precision of ± 0 . 0 0 1 % . • For accurate s v measurements, it was necessary to connect the burette to a reservoir with a diameter much larger than that o f the burette to compensate for evaporation of water in the burette to achieve air saturation. • The resolution of the load cell was 0.01 kPa and its precision was ± 0.025 kPa. • The resolutions of the cell pressure and back pressure transducers were 0.025 and 0.026 kPa, respectively. Both transducers had a precision of ± 0.1 kPa. • Cel l pressure and axial stress were observed to fluctuate over a 10,000-minute period. However, the stress ratio was observed to decrease by about 0.02 over a period of 10,000 minutes. 3.4 Ma te r i a l Tested Samples used in the tests were made of Fraser River sand from the Fraser River Delta in British Columbia, Canada. Table 3.2 lists the major properties of Fraser River sand used in this research. 56 Table 3.2 Physical Properties of Fraser River Sand Property Value Dio 0.150 mm D 5 0 0.270 mm D 6 0 0.280 mm Cu . 1.87 ^max 0.989 0.627 G s 2.719 Fraser River sand is a grey, uniform, semi-angular medium-grained sand composed of 70% quartz, 15% feldspar, 5% chlorite and smectite, 5% kaolinite and 5% mica (Hoffmann and Sego, 1994). Figure 3.10 presents graduation curves obtained by sieve analysis carried out in accordance with A S T M D422. The grain size distributions of the sand used by Shozen and that used in this research are very similar. Therefore, it is reasonable to assume that the maximum and minimum void ratios, emax and emm, of Fraser River sand used in this research are identical to the values determined by Shozen, which were 0.989 and 0.627, respectively. 3.5 Sources of Inaccuracy in Triaxial Test Data This section focuses on four major sources of inaccuracy of the triaxial tests and discusses the steps taken to ameliorate such errors. 3.5.1 Ram Friction The magnitude of applied axial load was measured by the load cell fixed at the end of the double-acting air piston outside the cell. The actual vertical stress experienced by the sand sample is different from that recorded by the load cell by the amount of the ram friction where the ram enters the cell. Friction was minimized by feeding air into the cavity between the loading ram and the cell continuously during a test. 57 0.01 0.1 1 10 Particle Size (mm) Average Distribution Shozen (2001) Figure 3.10 Particle Size Distribution of Fraser River Sand 58 However, a 0.2-kgf ram friction was still observed in the triaxial cell, which was equivalent to an axial stress o f 0.06 kPa. A l l load cell readings were reduced by this amount. 3.5.2 Membrane Penetration Volume changes measured in triaxial tests on coarse-grained materials where effective confining pressure changes are composed of two components: volume changes due to soil deformations and those due to membrane penetration caused by changes in the net pressure. In order to acquire the actual soil deformations, the volume changes due to membrane penetration have to be estimated and eliminated. The hydrostatic unloading method was used in Shozen's research (Vaid and Negussey, 1984). In this research, a new method proposed by Sivathayalan (2000) was used to obtain the membrane correction. The main advantage of Sivathayalan's method of determining s m over Va id and Negussey's method was that it was not based on any assumption regarding the constitutive behaviour of sands. The unit membrane penetration, s m , varied linearly with the logarithm o f effective confining pressure as shown by Sivathayalan et al. When the effective confining pressure was changed from cr'jnitiai to a'C Urrent, the volume change due to membrane penetration could be estimated by the following equation: CJ current =^mAs log \^ CJ initial J where A V , m Volume change caused by membrane penetration Unit membrane penetration Soi l surface area covered by membrane Current effective confining stress Initial effective confining stress •m G current O" initial 59 The effective confining pressure in the test to determine s m was changed in steps but that in a triaxial test was changing continuously. Shozen (2001) investigated the effects of different types of confining stress reduction on s m and concluded that the slopes of the 8m versus effective confining pressure curves were identical. Therefore, the s m values stated in this section are applicable to any triaxial test on Fraser River sand. In accordance with Sivathayalan's research, e m of Fraser River sand was 0.005, which was double the value used in Shozen's research. A larger s m value means an increase in the volume change due to membrane penetration. During consolidation at a stress ratio of 2.5 under an effective confining stress of 100 kPa, the volume changes due to membrane penetration calculated using Shozen and Sivathayalan's values are 0.37 and 0.87 cm 3 , respectively, which correspond to volumetric strains of 0.09% and 0.2%. A t the same stress ratio, during shearing along the 0 stress path, in which the confining stress at failure is the lowest and the membrane penetration effect is the most significant, the volume changes obtained using Shozen and Sivathayalan's s m values are 0.12 and 0.27 cm 3 , respectively, which represent volumetric strains of 0.03% and 0.07%. The use of Sivathayalan's s m value doubled the correction for membrane penetration and its effects were more pronounced in the consolidation phase than in the shearing phase. The membrane correction during consolidation comprised approximately 18% of the total volumetric strain measured at the end of consolidation, whereas the correction during shearing accounted for less than 1% o f the total volumetric strain developed during shearing. This is plausible because the change in effective 60 confining stress was greater during consolidation and more volumetric strain was observed during shearing. 3.5.3 Membrane Force Triaxial samples are encased by a rubber membrane, which carries a portion of the applied axial load and creates a discrepancy between the load recorded by the load cell and that experienced by the sample. Corrections for membrane force were discussed by Kuerbis and Va id (1990). The adjustments in the radial and axial effective stresses at a stress ratio of 2.5 with an effective confining stress of 100 kPa were 0.12 and 0.52 kPa, respectively, at the end of consolidation. The adjustments were insignificant compared to CT'3 (100 kPa) and a ' i (240 kPa) and therefore, membrane force was unimportant in the tests conducted in this research. 3.5.4 Sample E n d Fr ic t ion One of the major assumptions made in the execution of triaxial tests is the homogeneity of stress and strain within a triaxial specimen. The validity of such assumptions, however, depends on the magnitude of friction present at the top and the bottom of the specimen. Bishop and Henkel (1957) found that the effects of end friction were negligible when a height to diameter ratio of larger than 2 was used in the tests. The samples used in the tests in this research had an approximate diameter of 6.4 cm and an approximate height of 13 cm, with a height to diameter ratio o f 2.03. Therefore, the effects of end friction were minimized. End friction was further reduced by the use of highly polished end platens with centrally located small porous stones with a diameter of only 20 mm. Barden and Khayatt (1966), furthermore, showed that the error due to end restraint was not significant until an axial strain of 5% had been exceeded. 61 Eliadorani (2000) attempted the use of free ends in his research on partially drained response of sands and concluded that the use of free ends, though desirable in preventing non-homogeneous deformation from developing, introduced serious bedding errors in the measurement o f axial deformation that were difficult to quantify. Kuwano and Jardine (2002) studied the effects of sample end compliance on strain developments during aging. They discovered that the application of lubrication layers at sample ends considerably reduced the non-uniformity of radial straining induced by fixed end condition at axial strains greater than 2%. It did, however, introduce other bedding errors. The same conclusions were drawn by such authors as Sarsby et al. (1980), Barden et al. (1969), as well as Rowe and Barden (1964). In this study, the main interest was in soil stiffness and stress-strain behaviour after creep phases of varying lengths rather than the strain behaviour during creep. In order to avoid introducing additional sources of bedding errors, the tests were conducted with highly polished end platens to minimize the effects of end restraint. 3.5.5 Area Correction and External versus Internal Strain Measurement The dimensions of the sample are continuously changing during a test. In order to obtain the actual vertical stress acting on the sample, the area was updated continuously after each load increment. The area correction was the most significant during shearing because large strains were developed. A s the sample approached failure, its volume increased, height decreased and its area increased very quickly. Because the rate of axial stress application was fixed, the rapid increase in area resulted in a slight drop in axial stress at failure in some of the stress-strain curves in the shearing 62 phase. However, large-strain behaviour is not the focus of this research and the occurrence of such a drop does not affect the results presented in this thesis. Limitations of external measurements of stress and strain have been discussed by Atkinson and Evans (1985) and Jardine et al. (1985). However, special measures were carried out to eliminate ram friction and accurate external measurement of axial force was allowed. In addition, measures were taken to minimize bedding and seating errors. The top cap and the loading ram were permanently attached and bedding error was minimized. The use o f small diameter porous stones eliminated any false deformation due to improper seating onto the end platens. In addition, the loading ram was confined within a pair of linear ball bushings and tilting of top cap, as wel l as any possible seating error, was prevented. Sayao (1989) compared local and external strain measurements in his hollow cylinder torsional device and found that the measured local and external strain values were similar i f seating and bedding errors were largely eliminated during sample preparation. Furthermore, it was judged that any inaccuracies due to the use of external strain measurement would be similar from test to test and so would have a minor effect on the test results. 3 . 6 Test Procedures Sample preparation and test procedures followed in this research were the same as those followed by Shozen (2001). A detailed description of sample preparation technique, sample set-up and consolidation procedures is presented in Appendix A . Samples were prepared by water pluviation. After pluviation, the end cap was placed and the membrane was sealed using O-rings. A vacuum of approximately 20 kPa was applied to the specimen. The relative density of the samples ranged from 17% to 63 25% (void ratios of 0.899 to 0.927) after the application of vacuum. After sample preparation, the triaxial cell was filled with de-aired water and was taken to the triaxial testing machine for B-value determination. The cell pressure was usually increased to 220 kPa and the observed B-value was always higher than 98%. A 200-kPa pressure was established in the pore pressure line as the back pressure. The drainage valve was then opened for a minute to allow the specimen to adjust to any change in effective stress caused by the application of back pressure. A n y change in volume caused by the imbalance between the back pressure and the pore pressure inside the sample was measured and the sample dimensions before the test was started were calculated. The relative density at the end of B-value phase ranged from 17 to 24%. The sample was then consolidated at a specific constant stress ratio. For stress ratios other than 1.0, the sample was first consolidated along a conventional triaxial path until the desired stress ratio was reached. This was termed Phase 1 (Shozen, 2001). A Phase 2 was originally included in Shozen's research, in which the stress states at the end of Phase 1 were held constant and the sample was allowed to deform for a certain time period. This was subsequently omitted to avoid any inconsistency in the effects of time observed in the aging phase later in the test program. In Phase 3, the sample was consolidated at a constant stress ratio until the desired confining pressure was reached. A n automatic feedback system was used in Phase 3 to monitor and adjust the axial stress and the cell pressure simultaneously by the two electro-pneumatic transducers so that Aa ' i to Aa'3 ratio was kept constant during consolidation. However, the effective stress ratio, a ' i /a '3 , was always observed to increase slowly during consolidation and at the end of 64 Phase 3, it was always 0.1 higher than the targeted value, except at a stress ratio of 1.0 because a ' i was not increased at this stress ratio. The slight increase in stress ratio during consolidation was caused by the computer programme used to control the stresses. The objective was to increase the stresses slowly enough to maintain fully drained conditions but fast enough to minimize time for creep. A slight inaccuracy in applied stress ratio was accepted to avoid extensive iterations to adjust stress ratios during consolidation. Following completion of consolidation, the stress states at the end of Phase 3 were held constant and the sample was kept under constant stress states for a pre-determined time period varying from 100 to 10,000 minutes (Phase 4). The automatic feedback system used in Phase 3 was not used in Phase 4. The minimum aging period was 100 minutes as Shozen (2001) showed that for an aging period shorter than 100 minutes, creep was continuing fast enough to require a correction to the subsequent stress-strain curves to account for the strain that would have occurred i f no stress changes had been imposed. In the final phase of the test program (Phase 5), the sample was sheared along one of four different stress paths. These tests were stress-controlled. Stress increments of 1 kPa were applied to the sample every 15 seconds. This was the rate selected by Shozen (2001) after investigation of the effects of using different time intervals between load increments. The actual stress paths followed in Phase 5 deviated slightly from the ones originally planned for. Similar to the consolidation phase, the discrepancy was caused by the computer programme used to control stresses and was a result of an attempt to avoid extensive iterations that might slow down load application. 65 3.7 Conclusions The equipment used in this study and the details regarding its resolution, accuracy and stability have been described. In addition, possible sources of error and limitations have been discussed. Significant conclusions are as follows: • Samples could be prepared to a very loose state in a reproducible manner. • After measures were introduced to compensate for the tendency for evaporation for the burette to the incoming dry air from the regulator, the e v reading was very stable during monitoring although some drift was observed. • s v in 10,000-minute tests was not reliable but such unreliability did not have any negative effect on this study because the main focus was on the aging effects on stress-strain behaviour after the aging phase, not on the strain developments during aging. • The effective stress ratio, a ' i /a '3 , varied by 0.02 over a 10,000-minute aging duration. 66 CHAPTER 4 Test Results This chapter presents and discusses the results of the testing programme. The testing programme was designed to study the effects of aging and stress path on the stress-strain behaviour of loose Fraser River sand. First, test repeatability is discussed. Then the general behaviour observed during the shearing phase is presented. After the general behaviour, the variation of stress-strain behaviour at shear strains less than 0.2% is examined. Finally, the effects of aging duration, stress ratio, confining stress and stress path on shear modulus are discussed. 4.1 Preliminary Considerations Figure 4.1 illustrates the stress paths followed in the triaxial tests in three different stress systems and Table 4.1 summarizes the different phases of the test programme. Table 4.1 Different Phases of Test Programme Phase Description 1 Samples were consolidated from an 20-kPa effective confining stress to a stress ratio of 2.1 or 2.5 along a conventional path 2 First aging phase; Shozen (2001) preliminarily eliminated this phase and it was omitted in this study 3 Samples were consolidated at a constant stress ratio until the desired confining pressure was reached 4 Samples were aged under constant stress states from 100 to 10,000 minutes 5 Samples were sheared along one of the following stress paths: • Conventional path with Ao~'3 = 0 cr', +2<j\ • Constant — — — - or -2 path with A a ' i = -2Aa '3 o~\ +o~\ • Constant — — — - or-1 path with A a ' i = - A C T ' 3 • Constant a ' i or 0 path with A a ' i = 0 67 (a) 350 300 250 200 ra 150 100 50 Cr )n / n W . 0 a / / Phase 5' "1 ' / ° / • • Phase 4 > Phase 5 Phase 4^  Phas e 3 / .'' R / / a = 2.1 in R = 2.5 / < -Z n Phase 5' / u—• — y' y ' ' R = 1.0 Phase 4, CL V 50 100 o", (kPa) 150 (b) n 0. 250 200 150 P ^ 100 50 -2 -1 Conventional (Con) / Phase 5 - Shear Phase 3 -1 > • ; -^f Phase 4 Phase 5 | R; : 2 - 5 -2 R = 2.1 lase 4 - Aging Phase 1 -1 \ 0 . \ = 1.0 s . \ / Con /' / Phase 5 A 50 100 p' ((o'1+2o,3)/3) (kPa) Phase 4 150 200 Figure 4.la,b Applied Stress Paths in a'i-a'3 and q-p Spaces 68 69 A total of 39 tests at different stress ratios, effective confining stresses, aging durations and shearing stress paths were carried out in the entire test programme. Details of the test programme are summarized in Table 4.2. 4.1.1 Definition of Terms For triaxial tests along the conventional path, deviator stress and volumetric strain are usually plotted against axial strain. From such plots, changes in Young's modulus can be interpreted directly as the effective confining stress is constant. However, when comparing test results from different paths, it is more desirable to use a way of presenting data that allows the effects of changes in mean effective stress and those of changes in shear stress to be differentiated. Atkinson and Sallfors (1991) suggested the use of deviator stress, q, mean effective stress, p ' , volumetric strain, ev, and shear strain, es, to present data obtained from triaxial tests in which radial symmetry exists. Their definitions of deviator stress, q, mean effective stress, p ' , volumetric strain, ev, and shear strain, s s , are as follows: q = o\-cj\ 3 sv=sx+ 2s3 In this thesis, q, p ' and s v are used as defined above but the shear strain y = Si - £3 is used rather than s s . 70 Table 4.2 Details of Test Programme Test Number C J ' 3 (kPa) D r (%) (Phase Taging (Minutes) <*Vo"'3(Phase5) 1 19.3 100 Conventional 2 50 18.3 2.1 -1 3 20.9 1000 Conventional 4 20.2 -1 5 22.5 Conventional 6 23.9 100 -2 7 25.6 -1 8 18.6 1.0 0 9 18.9 Conventional 10 20.2 1000 -2 11 19.9 -1 12 21.1 0 13 21.0 Conventional 14 20.0 1.6 100 -1 15 20.3 0 16 20.5 Conventional 17 21.2 100 -2 18 19.2 -1 19 17.4 0 20 100 18.6 Conventional 21 17.7 2.1 1000 -2 22 18.2 -1 23 21.9 0 24 18.6 Conventional 25 24.4 10000 -1 26 19.7 0 27 47.4 100 Conventional 28 23.7 Conventional 29 24.9 100 -2 30 24.6 -1 31 23.3 2.5 0 32 23.5 Conventional 33 19.7 1000 -2 34 19.5 -1 35 23.0 0 36 19.2 100 Conventional 37 150 22.7 2.1 -1 38 21.6 1000 Conventional 39 21.6 -1 71 4.1.2 Test Repeatability It was important that load applications and test results in this study were repeatable. Figure 4.2 shows the stress paths followed in two tests using samples with different relative densities in a q-p' plot. Both samples, one with a relative density of 20% and the other with a relative density of 47%, were sheared along the conventional path after aging for 100 minutes. Figure 4.2 clearly indicates very good repeatability of the control system with regard to testing along identical stress paths. In addition to stress applications, the response of samples loaded along identical stress paths had to be compared to examine repeatability of sample preparation. Figure 4.3 shows the developments of axial and volumetric strains during consolidation and aging in two tests with identical confining stress, stress ratio and aging duration, as well as very similar relative densities (21% and 22%). The axial and volumetric strain curves in the two tests were almost identical, indicating that excellent repeatability in sample preparation. Figures 4.4 and 4.5 compare the results of the stress-strain behaviour and volume change observed by Shozen (2001) with those from this study for identical stress paths. As noted in Chapter 3, the two sands used in these studies were almost identical. The stress ratio used in Shozen's test was 2.0 whereas the stress ratio used in this research was 2.1. Because the stress-strain curves start at different values of q, they are plotted in terms of incremental deviator stress, Aq, i.e. the difference between current q and that at the beginning of shearing, instead of q to make comparison of results more convenient. According to both figures, the tests in this research produced stiffer stress-strain behaviour and very similar though slightly more contractive volumetric response in the 72 _ 200 CjV<73(Phase3 = 2.1 a'3=10( ) kPa Tag i ng — Conventional 00 Minutes <j'i /03(Phase5) _ 0 50 100 150 200 250 p' (kPa) Figure 4.2 Repeatability o f Stress Applications 0.8 Figure 4.3 Repeatability of s a and s v Developments in Phases 1, 3 and 4 73 200 150 50 oYa31 = 2 Phase 3) 0 a'3 = K )0 kPa T„ . =1001 ing flinutes a' 3 (Phase j = Conve itional s lozen Th s study s / f 0 1 2 3 4 5 6 7 8 ea (%) 6 A (%) 0 1 2 3 4 5 6 7 8 9 \ ... = 2 (Phase 3) £ .0 o 3 = 1 )0 kPa T a ! . =1001 ling flinutes d l ' C T 3 (Phase! j = Conve itional \ .•'Thi ! study \ \ # * ' ' St lozen Figure 4.4 Comparison of Shozen's Results in the Large Strain Region 74 50 45 40 35 30 n a. £. 25 cr < 20 15 10 5 0 (Phase 3) " 2.0 = 100 kPa "''aging 100 Minu tes a',/q 3 (Phase 5) = Conver tional X < X Th is study x x X X x x x><A < X < X-Ol 1 }z©n V 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 E a (%) 6 a (%) 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 x* * A X X X X X < x x x V Shozen This X study X x X x X X X < X > X V Phase 3) ~ 2.0 a' 3 = 100 kPa T = aging 00 Minu es a',/a 3 (Phase 5) = Conver A tional gure 4.5 Comparison of Shozen's Results in the Small Strain Region 75 early part o f shearing. The test in this research resulted i n dilation commencing at an axial strain o f about 3% whereas Shozen's test continued to contract until about 4.5%. Shozen did not continue his tests to failure. Shozen's sample had a relative density of 18.3% whereas the sample used in this research had a relative density of 25.6%. Higher relative density led to stiffer stress-strain response and earlier commencement of dilation. A t strains less than 0.2%, Shozen's samples were less contractive and less stiff. 4.2 Consolidation and Aging - Phases 1, 3 and 4 Application o f axial stress in Phase 1 was controlled by an electro-pneumatic transducer with a loading rate o f 0.13 kPa/s. The effective confining stress at the end o f the B-value phase was set to be 20 kPa and the time spent in Phase 1 depended on the desired stress ratio that was to be reached. It took approximately 3 and 4 minutes for the stress ratio to reach 2.1 and 2.5, respectively. During Phase 3, the rate o f cell pressure increase was kept constant at 0.16 kPa/s. Therefore, the rate o f axial stress increase varied with stress ratio. It was 0.17 kPa/s at a stress ratio of 2.1 and 0.24 kPa/s at a stress ratio of 2.5. Most of the tests were conducted under an effective confining stress of 100 kPa and it took 9 minutes for the effective confining stress to be raised from 20 kPa to 100 kPa. The following sections summarize the strain developments during consolidation and aging at different stress ratios and confining stresses. 76 4.2.1 Effects of Stress Ratio on Strain Development during Consolidation and Aging Figure 4.6 shows the stress ratios in phases 1, 3 and 4, as well as the axial and volumetric strain developments in these phases in tests conducted with 100-kPa effective confining stress and 100-minute aging duration. The stress ratio increased gradually during Phase 3 from 2.05 to 2.1 and from 2.38 to 2.55. The reason of such increase was detailed in section 3.6. A s may be noted from Figure 4.6, the magnitudes of axial and volumetric strain developments were higher at higher stress ratios. This was primarily due to the higher mean stress for higher stress ratios under constant effective confining stress of 100 kPa. Table 4.3 summarizes the slopes of the strain paths, the s v / s a ratios, in the consolidation and aging phases, i.e. Phases 3 and 4. The s v / s a ratios in Phase 3 decreased with increasing stress ratio. The strain paths in all three stress ratios showed a curvature at the beginning but all followed a linear pattern as consolidation proceeded as the applied stress ratio became relatively constant. The s v / s a ratio is a useful indicator of sample anisotropy during consolidation. For an isotropic sample, the s v / s a ratio should be 3.0. A n s v / s a ratio of 1.0 under any loading path indicates a condition of zero lateral strain or the KQ condition. For s v / s a larger than 1.0, both si and S3 are compressive, while si is contractive and S3 is expansive for s v / s a smaller than 1.0. The stress ratio during consolidation, Rc, at s v /e a o f 1.0 w i l l be representative of the Ko condition or KQ = 1 / Rc. Based on Table 4.3, the K<, condition of the Fraser River sand samples tested should be represented by a stress ratio slightly higher than 2.1, i.e. KQ < 0.48. This is in general agreement with the findings of 77 2.8 ea (%) 0.0 0.2 0.4 0.6 0.8 1.0 1.2 \ V < Phase 1 o Tr ansition betwe I 1 — 1 1 — en Phases \ — r T i ^ <H —O— W = 4.! 54 5 61 Phase; Rt 1.0 n - 9 9 5 ° / , \Phase 3 , = 1 . 1 l \ ^ = 0.78 X f/f =1.13 R = 2.1 Dr = 25.6( 1.83 N. Dr = 2OT% Figure 4.6 a ' i /a '3 and s v versus s a Curves in Phases 1, 3 and 4 at Various Stress Ratios 78 Sivathayalan (2000) (Ko = 0.48) and Gananathan (2002) (Ko = 0.44). Again Shozen's results were slightly different. He concluded that Ko of Fraser River sand was about 0.5. Table 4.3 Maximum, Minimum and Average ev / ea Ratios of Loose Fraser River Sand in Phases 3 and 4 0"' l /0" '3 (Phase 3) 1.0 1.6 2.1 2.5 Smallest sv / s a (p n a Se 3} 3.65 1.63 1.01 0.69 Largest S v / S a (Phase 3) 5.58 1.75 1.23 0.85 Average S v / S a (Phase 3) 4.54 1.68 1.11 0.78 Smallest sv / s a (Phase 4) 4.16 1.71 0.88 0.70 Largest sv / s a ( P h a S e 4) 7.89 1.92 1.20 0.91 Average sv / s a ( P h a s e 4) 5.61 1.82 1.13 0.83 Figure 4.7 shows the s v / s a ratio versus relative density at the beginning of Phase 3 curves for Shozen's samples and the samples used in this study. The s v / s a ratios in tests with a stress ratio of 1.0 were more inconsistent than those with stress ratios of 1.6, 2.1 and 2.5, a trend also noticed by Shozen. Strain gradients in the hydrostatically-consolidated tests were strongly influenced by the relative density of the sample after deposition. On the contrary, strain gradients in tests with Rc not equal to 1.0 depended primarily on the imposed stress ratio and were not strongly affected by the relative density after deposition. Therefore, the ev / s a ratios at stress ratios of 1.6, 2.1 and 2.5 were more consistent. From Figure 4.7, it is clear that for hydrostatic consolidation, the ev / ea ratio decreases with increasing relative density. For stress ratios around 1/KQ and above, the sv / s a appears to increase slightly with increasing relative density. During the consolidation phase, an s v / s a ratio smaller than 1.0 indicates compressive si and expansive S3. 79 0 o o o CT3 = 100 kPa o o 0 « S R = 1.0 • »° 0 a * - _ • o o i • - - ' n " • •• • • SR = 2.1 v \ ^ S R = 1.6 / / n SR = 2.0 (Shozen) SR = 2. (Shozer J ao. S R = 2.£ 0 10 20 30 40 50 60 Dr(%) o S R = 1.0 " S R = 1.0 (Shozen) Figure 4.7 sv / sa versus Relative Density Curves in Phase 3 at Various Stress Ratios 80 Figure 4.8 shows the axial and volumetric strains during aging for 100 minutes with an effective confining stress of 100 kPa but at stress ratios o f 1.0, 2.1 and 2.5. Both axial and volumetric strains increased with time and the rates of strain development decreased with time. A t stress ratios of 1.0 and 2.1, more volumetric strain was developed than axial strain (si and 83 both compressive) but the opposite was true at the stress ratio of 2.5 (si was compressive and S3 was expansive). Figure 4.9 shows the strain development with time on a logarithmic scale up to 10,000 minutes. It is evident that both axial and volumetric strains had an approximately linear relationship with the logarithm of aging duration up to an aging duration of 1000 minutes and such linear relationship was also observed by Lade (1998). The s v reading in the 10,000-minute test was unreliable after the first 1000 minutes due to electronic noise in the measurement system but the increasing trend of s v with time is clear. A s shown in Figure 4.6, strain paths were approximately linear in Phases 3 and 4. The s v / s a ratios during aging are summarized in Table 4.3. The s v / s a ratios differed slightly from those during consolidation because, as mentioned in section 3.3.2, the effective stress ratio dropped slightly in the aging phase. The s v / s a ratios of hydrostatically-consolidated samples were more variable than those o f the samples aged at the other three stress ratios as the magnitudes of axial strains of hydrostatically-consolidated samples were small and the measurements approached the resolution of the measuring device. The linear relationships between axial and volumetric strains were observed regardless of the time the sample was aged and therefore, for Rc not equal to 81 0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00 CT3 = 100 "'"aging — 1C 0 Minutes v X SR = 2.> x x x v x xxx xx x <xx x X X X C X X X X : X x x x x x x x X \ \ \ »<xxx ^ y X x xx x x * > < x > < C X * SR = 2.1 1 1 X ^ A A A A « ^ ^ A ^ V * V A A pQA^.AA AA ' A A A A A X * ^ x JA a A i 1 A . • i • • • • A—agp a—A-o D Q D a O a a n ( A i i i X A *i A ^ X x A ^ < >R = 1.0 1 1 1 & a 1 V 6a 20 40 60 Aging Duration (Minutes) 80 100 Figure 4.8 s a and s v versus Aging Duration Curves in Phase 4 at Various Stress Ratios with 100-Minute Aging Duration 10 100 1000 Aging Duration (Minutes) 10000 Figure 4.9 s a and s v versus Logarithmic Aging Duration Curves in Phase 4 at Various Stress Ratios with 1000- and 10,000-Minute Aging Durations 82 1.0, it can be concluded that the slopes of the strain paths were primarily controlled by the stress ratio. 4.2.2 Effects of Confining Stress on Strain Development during Consolidation and Aging Although most of the samples were consolidated to an effective confining stress of 100 kPa, eight samples were consolidated to 50 and 150 kPa to study the effects of effective confining stress on the aging phenomenon. It took approximately 3 and 14 minutes for the effective confining stress to reach 50 and 150 kPa, respectively. Figure 4.10 shows the strain paths of three samples consolidated to and aged at different effective confining stresses, 50, 100 and 150 kPa. A l l o f the strain paths showed a slight curvature at the beginning but they all followed a linear strain path as consolidation proceeded, i.e. s v / s a was constant. A l l o f the three strain paths overlapped each other. More deformation occurred at higher effective confining stress. Figure 4.11 shows the void ratio, e, versus mean effective stress, p ' , curves at the three confining stress levels. This curve illustrates the repeatability of the sample preparation procedures used in this study. Figure 4.12 shows the developments of axial and volumetric strains with time in samples with 50-, 100- and 150-kPa confining stresses and at a stress ratio of 2.1. Both axial and volumetric strains increased with time, with the rates o f strain development decreasing with time. Curves under different effective confining stresses had a similar shape but strains were larger at higher confining stresses. Figure 4.13 shows the strain developments with time in a logarithmic scale up to 1000 minutes and it is evident that both axial and volumetric strains had an 83 84 0.920 1000 P" (kPa) 0.920 -, , , , , , r 0.915 0.910 0.905 -0.900 -0.895 -• 0 20 40 60 80 100 120 140 160 180 200 220 P" (kPa) Figure 4.11 e versus p ' Curves in Phase 3 with Various Effective Confining Stresses at a Stress Ratio of 2.1 85 r 3 (Phase: , = 2.1 " = 1 aging )00 Mini tes 150 A. M 1 Jiff] r » Oo < _ • 100 o o jA w r r f • 50 w u kPa 0 100 200 300 400 500 600 700 800 900 1000 Time (Minutes) Figure 4.12 £ a and s v versus Aging Duration Curves in Phase 4 with Various Effective Confining Stresses and 1000-Minute Aging Duration 86 Figure 4.13 s a and s v versus Logarithmic Aging Duration Curves in Phase 4 with Various Effective Confining Stresses and 1000-Minute Aging Duration 87 approximately linear relationship with the logarithm of aging duration, regardless of the effective confining stress imposed on the sample. 4.2.3 Conclusions - Consolidation Phase The following conclusions can be drawn regarding strain development during consolidation: • Effective confining stress level affected the magnitude of soil deformation during consolidation but had no influence on the strain gradient, i.e. s v / s a ratio. • For a given target effective confining stress, more strains developed at higher stress ratios. • The s v / s a ratio decreased with increasing stress ratio. • The s v / s a ratios in hydrostatic tests were more inconsistent than those in anisotropic tests as strain developments in the hydrostatically-consolidated tests were strongly influenced by the relative density of the sample after deposition. • KQ of Fraser River sand inferred from experimental data is close to 0.48, which was in agreement with previous studies. 4.2.4 Conclusions - Aging Phase Conclusions regarding the soil behaviour during aging are as follows: • Both axial and volumetric strains increased linearly with the logarithm of aging duration and the rates of strain development decreased with time. • The magnitudes of strains developed during aging were small, with a maximum of 0.16%. • The slopes of the strain paths were primarily controlled by stress ratio. • More strains were observed during aging at higher effective confining stresses. 88 4.3 General Stress-Strain Behaviour - Phase 5 4.3.1 Introduction Upon completion of the aging phase (Phase 4), the samples were subjected to shearing along one of the following stress paths shown in Figure 4.1: • Stress slope of 0 (unloading compression path and A C T ' I = 0) • Stress slope of-1 (constant ° 3 path and A a ' i = -Aa ' 3 ) • Stress slope of -2 (constant p ' path and A a ' i = -2Aa '3) • Conventional triaxial compression path This section discusses the observations from these tests. The effects of stress ratio, aging duration, stress path and effective confining stress on stress-strain behaviour and soil stiffness are also discussed. Along each of the four stress paths, 1 kPa of axial stress was applied to the sample every 15 seconds, which was a large enough time interval to avoid excess pore pressure from building up during shearing and to allow both axial and confining stresses to be adjusted so that the applied stresses could follow the desired stress path. Stress and strain measurements were taken immediately before a new stress increment was applied so that any excess pore pressure induced or unexpected response due to stress application had enough time to stabilize after the stress had been applied. The intended stress paths were not followed exactly but the actual stress paths were close to the intended ones. The reason of the discrepancy between actual and intended stress paths was accounted for in section 3.6. A l l strains were calculated relative to the dimensions at the beginning of Phase 5. 89 Shozen (2001) suggested the stress-strain curves in Phase 5 should be corrected for residual creep, which was the magnitude of strain that would have occurred with no change in deviator stress. However, he found that the correction was only significant in tests with aging durations of 1 and 10 minutes. Modifications to strains were small in samples with aging durations longer than 100 minutes. Because all o f the test results presented in this thesis were obtained from samples aged for 100 minutes or more, the correction for residual creep was not applied. The following sections present and discuss the effects of aging duration, stress path, stress ratio during consolidation and effective confining stress on the stress-strain behaviour from the start of shearing until failure. 4.3.2 Effects of A g i n g Durat ion and Stress Path Figure 4.14 compares the general stress-strain behaviour and volumetric response along the conventional path for samples that were initially consolidated to a hydrostatic stress of 100 kPa and then aged for 100- and 1000-minutes (Tests No . 5 and 9). The general stress-strain behaviour was identical, indicating no effect of age. The axial strain at which maximum contraction occurred was independent o f age. The volumetric strain at maximum contraction was slightly greater for the older sample but it was also slightly looser. According to the general volumetric response shown in Figure 4.14, the volumetric strain changed abruptly after the point of maximum contraction had been reached. The sudden change in volumetric strain was always observable and always occurred right after the point of maximum contraction. The exact cause of such abrupt change in volumetric strain was uncertain but one possible cause may be the reversal of 90 Ea (%) 0 1 2 3 4 5 6 7 8 9 10 « 0.5 r 3 (Phase 3) = 1.0 <T' = 100 kF a CTVCT'3 Phase 5) Donventi >nal 1 00 Minute !S • Rat Ma ximumQ intractior " ^ 3 3.E 5 8 ^ ^ 8^ 1 000 Minu es / / Figure 4.14 General q and s v versus e a Curves in Phase 5 along the Conventional Path at a Stress Ratio o f 1.0 with 100- and 1000-Minute Aging Durations (Tests No . 5 and 9) 91 the moving direction of the water column in the burette. A t the point o f maximum contraction, the water column shifted from rising to dropping. Because the diameter of the burette was small, surface tension at the meniscus was significant and hindered the water column from dropping at the outset of sample dilation. However, the water column continued to drop as dilation proceeded and a downward tension was created and intensified at the meniscus. The surface tension was broken when the downward tension became sufficiently large and the obstacle against the downward movement of water column was overcome. The sudden change in volumetric strain on every volumetric response curve marked the disappearance of surface tension and the start of smooth downward movement of the water column. The surface tension was overcome when the water level in the burette had dropped by 5 millimetres, which was insignificant compared to the total volume change occurred during dilation. In addition, the main focus of this study was on the stress-strain behaviour before the commencement of dilation and therefore, the volume change caused by surface tension did not have any adverse influence on this study. Figure 4.15 shows the general stress-strain behaviour and volumetric strain response along the conventional path under 100-kPa confining stress on samples at a stress ratio of 2.1 aged for periods ranging from 100 to 10,000 minutes (Tests No. 16, 20 and 24). Similar to Figure 4.14, the q versus s a behaviour was identical beyond an axial strain of 3%, indicating no effect of age at large strains. The volumetric strain to maximum contraction decreased with increased age and the axial strains at which maximum contraction occurred were independent of age. 92 360 310 260 OL cr 210 160 110 o',/a'3 =; (Phase 3) .1 a'3-1 XJkPa a'. ' C T 3 (Phase 5 , = Convei tional 1 rest No. 2 )00 Minuti Test No. 0000 Mn 24 jtes Test 100 fv •to. 16 inutes /  / f 0 1 2 3 4 5 6 7 8 9 Ea (%) 0 1 Ea (%) 2 3 4 5 6 7 8 9 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 a',/0'3 (Phase 3) ' 2.1 0-3 = 1 OOkRa a'. ' a 3 (Phase 5 = Conver tional 23.8°/< 10001 /fnutes/ / / / 25.6°/ / 2 4^3%^/ 100C 3.66 0 Minutes 3.6 8 ^ ^ lOO Min Jtes Ratl\ bximumC ,.y 3.6 ontractior 9 Figure 4.15 General q and e v versus s a Curves in Phase 5 with Various Aging urations along the Conventional Path at a Stress Ratio of 2.1 (Tests No . 16, 20 and 24) 93 Figures 4.16 to 4.19 show the q versus y and s v versus p ' curves for tests with 100-kPa confining stress at stress ratios of 1.0 (Tests No. 5 to 12), 1.6 (Tests No. 13 to 15), 2.1 (Tests No . 16 to 23) and 2.5 (Tests No. 28 to 35). Samples were aged for 100 and 1000 minutes, except at a stress ratio of 1.6, at which the sample was aged for 100 minutes only. The results indicate that aging has little effect on the stress-strain behaviour at strains greater than 1% or 2% or on the maximum deviator stress. A s expected, the samples were strongest along the conventional path and became weaker as the stress path rotated from -2 to 0. Negussey (1984) conducted a series of triaxial tests to study the small-strain behaviour of Ottawa sand. He found that the strength of samples decreased as the stress path during shearing rotated in a counter-clockwise fashion and his observation can be clearly seen in Figures 4.16 to 4.19. There were some observable differences between curves on the s v versus p ' plots. The -2 path was the constant p ' path and s v developed along this path can be attributed to shearing of the sample. Along the other three stress paths, both shearing and changes in p ' contributed to the overall observed ev. Along the conventional path, the increasing p ' resulted in the largest s v. On the contrary, along the -1 and 0 stress paths, p ' was decreasing during shearing, which in some cases induced initially expansive s v. At a stress ratio of 1.0, aging did not have any obvious effect on the general volumetric response. A t higher stress ratios, on the other hand, aging generally rotated the s v versus p ' curve slightly counter-clockwise and reduced the volumetric strain developed during shearing. 94 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 oVc3(P iase 3) - 1 -0 C 3 = 100 kPa 1 100 0 Minutes ) 5 01 1 1B0 11 •0 21 )0 2! o (3.o: '•)\/ \ I P' (kPa) -1 (3.26^ - I (3.39) ^ 100 Minutes R at Maxi num Contracti on \ / Conventional ( $.58) Figure 4.16 General q versus y and s v versus p ' Curves in Phase 5 at a Stress Ratio of 1.0 with 100- and 1000-Minute Aging Durations (Tests No . 5 to 12) 95 Figure 4.17 General q versus y and s v versus p ' Curves in Phase 5 at a Stress Ratio of 1.6 with 100-Minute Aging Duration (Tests No . 13 to 15) 96 Figure 4.18 General q versus y and s v versus p ' Curves in Phase 5 at a Stress Ratio of 2.1 with 100- and 1000-Minute Aging Durations (Tests No . 16 to 23) 97 220 0.4 J Figure 4.19 General q versus y and s v versus p ' Curves in Phase 5 at a Stress Ratio of 2.5 with 100- and 1000-Minute Aging Durations (Tests No . 28 to 35) 98 4.3.3 Effects of Stress Ratio and Effective Confining Stress Figure 4.20 shows the general stress-strain behaviour and volumetric response for those samples loaded along the conventional path but consolidated to different initial stress ratios (Tests No . 5,16 and 28). A l l samples were aged for 100 minutes. For this discussion, the strains are calculated with reference to the sample dimensions at the start of consolidation. The axial stress and volumetric strain at failure were very similar for all three samples, as were the axial strain to maximum contraction and the overall volumetric strains. Initial secant stiffness over the initial 0.2% axial strain of shearing, En.2, is represented by the straight lines. E0.2 decreased as the stress ratio during consolidation increased, a finding that coincided with that drawn by Y u and Richart (1984), who conducted a series of resonant column tests and suggested that small-strain soil stiffness decreased with increasing stress ratio. Samples sheared at different stress ratios were subjected to different mean effective stresses, p ' . Therefore, the results shown in Figure 4.20 are combinations of the effects of different stress ratios and effective confining stresses. In order to clarify the effects o f the two factors, the stress-strain behaviour of samples with different effective confining stresses is compared. Most of the samples were consolidated to an effective confining stress of 100 kPa but several samples were consolidated to 50- and 150-kPa effective confining stresses for comparison purposes. Figure 4.21 shows the overall stress-strain behaviour and volumetric response of samples with an aging duration of 100 minutes, along the conventional path and with three different confining stresses: 50,100 and 150 kPa (Tests No. 1, 16 and 36). Because samples with different confining stresses were 99 350 Figure 4.20 General q and e v versus s a Curves in Phase 5 at Various Stress Ratios along the Conventional Path (Tests No. 5, 16 and 28) 100 Figure 4.21 General Aq and s v versus s a Curves in Phase 5 with Various Effective Confining Stresses along the Conventional Path (Tests N o . 1, 16 and 36) 101 sheared at different initial shear stress levels, incremental deviator stress, Aq, was used to make comparison of results easier. Higher effective confining stress led to stiffer stress-strain behaviour and higher strength, an observation also made by Negussey (1984). The s v / s a ratio at maximum contraction was about 0.2 for both 50-kPa and 100-kPa tests. The test at 150 kPa was not taken to maximum contraction. When Figures 4.20 and 4.21 are compared, it can be seen that effective confining stress affects the stress-strain behaviour in a way opposite to that of stress ratio. Higher stress ratio reduces the initial stiffness during shearing while larger effective confining stress leads to stiffer stress-strain behaviour at the commencement of shearing. 4.3.4 M a x i m u m Contract ion and Failure Figure 4.22 shows the q versus p ' plot at maximum contraction and failure of all of the tests listed in Table 4.2. A l l of the data points agree well with straight best-fit lines passing through the origin, which indicates that maximum contraction and failure occur at constant q/p' ratios independent of the consolidation stress ratio, stress path followed during shearing, duration of aging and effective confining stress level. The slopes of the best-fit lines for maximum contraction and failure are 1.36 and 1.50, respectively, which are equivalent to mobilized friction angles at maximum contraction, (j>'m c, and failure, <))'f, o f 33.6° and 36.9°, respectively. Wijewickreme (1986) conducted a series of ring shear tests and triaxial tests to investigate the relationship between <j)'mc, <j)'f and relative density of Ottawa sand. He found that in loose samples, the values of <}>'mc and were similar. In this study, (j)'mC and <j)'f of loose Fraser River sand samples differed by 3 degrees. Wijewickreme also concluded that <|)'mc decreased with increasing relative density but this observation could 102 103 not be proven as only one medium-dense sample was tested in this programme and the effects of relative density on stress-strain behaviour were not studied thoroughly. 4.3.5 Conclusions - General Stress-Strain Behaviour Based on the test data, the following conclusions on the general stress-strain behaviour of Fraser River sand can be drawn: • Aging had little effect on the stress-strain behaviour at strains larger than 2% or the strength at failure. • Aging did not have any pronounced effect on the general volumetric response in hydrostatically consolidated tests but reduced the volumetric strain developed during shearing at other stress ratios. • A s expected, at any consolidation stress ratio, the shear resistance mobilized decreased as the stress path rotated from conventional towards 0. • The sample along the conventional path contracted the most during shearing. The amount of contraction reduced as the stress path rotated from -2 to 0. • Initial stiffness at the beginning of shearing decreased with increasing stress ratio despite an increase in p ' , which would be expected to increase initial stiffness. • A t a given stress ratio, higher effective confining stress led to stiffer stress-strain behaviour, higher strength and more contractive volumetric response. • The q/p' ratios at which maximum contraction and failure occur were independent of the consolidation stress ratio, stress path followed during shearing, duration of aging and effective confining stress level. • The friction angles at maximum contraction and failure o f the sand used in the study were 33.6° and 36.9°, respectively. 104 4.4 Stress-Strain Behaviour at Shear Strains Less Than 0.2% A s noted in the above discussion, aging effects can only be observed at the beginning of shearing. This section describes the effects of stress ratio, aging duration, stress path and effective confining stress on the early portion of stress-strain curve in detail. 4.4.1 Effects of Stress Path and Aging on Small Strain Stress-Strain Behaviour, Hydrostatically-Consolidated Samples (R = 1.0) Figures 4.23 to 4.26 show the effects of aging on the stress-strain behaviour and volumetric response along various stress paths under 100-kPa confining stress and at a consolidation stress ratio of 1.0 (Tests No. 5 to 12). For the conventional and -2 paths, increased aging time appeared to result in slightly stiffer and more contractive response despite the greater density of the younger sample in each case. For the -1 path, there was a possible tendency towards expansion during the initial stages of shearing on the younger sample, although the strains involved were close to the resolution of the instrument. This tendency was not observed on the 1000-minute sample. For the 0 path, initial expansion was observed for both 100- and 1000-minute samples, with the expansion greater for the younger sample. Again the expansive strains were close to the instrument resolution. Figure 4.27 shows the stress-strain behaviour and volumetric response at axial strains less than 0.2% along the four different stress paths in terms of deviator stress, q, and shear strain, y (Tests No. 9 to 12). The sample along the conventional path contracted the most and the extent of contraction decreased as the stress path changed from -2 to 0. Initial dilation was observed along the 0 path. Shozen (2001) observed 105 aye; 3 {Phase 3) = 1.0 a \ = 100kP Phase 5) Conventi anal . . y X * X * „ 0 0 x x xx X * X x r. ° x x x* 0 >° * Test is (22.7 •i nnn R/F; 0. 9 Yo) ~x x x * nuuu ivn lutes v / . o x x x ' /] O ° Test N< (25.9° >. 5 X * V J X o . ^ 7 100 Min jtes V < ?/* to, , X 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 Y (%) Y (%) 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.00 0.05 0.20 •x x X* X *x > X X X X o 5 o X X " x x * xx V 0 ** *x 10001 /Inutes 6 O * X x X X 101 O ° o ) Minutes ^x 0 0 ° o * * \ 0 3 (Phase 3) = 1.0 CT'3 = 100 kF 'a o\ldz [Phase 5) ~~ Convent X X *x onal O 0 o X Figure 4.23 Small Strain q and s v versus y Curves in Phase 5 along the Conventional Path with Various Aging Durations at a Stress Ratio of 1.0 (Tests No. 5 and 9) 106 90 80 70 60 „ 50 ra Cu o- 40 30 20 10 0 <J\/G\ ( P ~ 1 iase 3) 0 a', = 1 OOkPa < l' C T3 (Phas e 5) X X S X * O T est No. 1 0 X x x X > *< * o o o ° U 10 (24.0%) 00 Minut 5S x x x X x 4 xx x* xx Tnct Mi-! o • IcSl INO. (27.2% 00 Minut O 5S xx] X * xx / 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 Y (%) Y (%) 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.00 0.05 0.10 0.15 0.20 0.25 -i x X * x y x X % o 0 t b * * * x X < X * x : x X v * inn 0 ° 8 * x x x > ) Minute? * o X 100 Min » o Jtes ° o ° ° o X; x X * > : X x X o — CTVCT3 (P = 1 ase 3) 0 CT'3 = 1 OOkPa < VC T 3 (Pha = -2 e5) £-Figure 4.24 Small Strain q and s v versus y Curves in Phase 5 along the -2 Path with Various Aging Durations at a Stress Ratio o f 1.0 (Tests No . 6 and 10) 107 _ 50 ra Q _ c 40 a\h'3 P lase 3) ^ 0 0 ' 3 = 1 OOkPa c '/CT3phas e5) "1 X X x x X x „ o X o 0 x x x* x * < o o ° ° o 0 Tes (2 fOOTJ No. 11 S.9%) X X X x* x x X est No. 7 Minutes X , X X 1C 29.0%) 0 Minute X X * X . o * X O *>? e, V O V 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 y (%) y (%) -0.05 -, , , , , r— O.tlO 0.02 0.04 0.06 0.08 0 0.00 0.05 £ 0.10 0.15 0.20 0.25 % 0 „ x<xx CT/CT3(p(iass3) - * X -1000 Minutes 10 0. h2 0. tOOiMintrtes-' » o 0 CT'3 = '00kFa „',/«,•, p h i s ) = " 1 4 h6 0.rt8 0.20 Figure 4.25 Small Strain q and e v versus y Curves in Phase 5 along the -1 Path with Various Aging Durations at a Stress Ratio of 1.0 (Tests No . 7 and 11) 108 90 80 70 60 _ 50 ra Q . 40 30 20 10 X X • 1 est No. ' (24.9%) IDfl Minn 2 < x x x * ' > o X o ' o 6 l\J\J IVIMU < * v X X o ° Test f *>*> No. 8 r c ^ $ & o (22. 100 M J7o) inutes x $ > o *V aVcT'3 (I hase 3) ~ ^ .0 a', = ' OOkPa r l ' ° " 3 (Pha ,0 5) = ° 0 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 Y (%) Y (%) -0.05 0.00 0.05 ~ 0.10 0.15 0.20 0.25 32 0. )4 0. 36 0. 38 0. 10 0. 12 0. 14 0. 16 0. 18 0. 100 3 Minute . x x°x<f 10( < X ° p ) Minute; > X 0 X x 0 i 0 > 0 x „ x 0 avtj'3 (P iase 3) ~ ^ .0 o'3 = 100 kPa se 5) - 0 gure 4.26 Small Strain q and e v versus y Curves in Phase 5 along the 0 Path with Various Aging Durations at a Stress Ratio o f 1.0 (Tests No . 8 and 12) 109 c\h'3 =>riase 3) .0 a", = 100 kPa l aging ^ DO Minute s • • * X X * A < x & A > * * A P A*0 o Conve ntional o -2 A -1 ) <0 a 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 Y (%) Y (%) -0.05 O.pO 0.02 0.04 0.D6 0.08 0 0.00 0.05 - 0 . 1 0 0.15 0.20 0.25 A *A * x I N 10 0. • Conventional o -2 A -1 x 0 l ' f f 3(PhasL3) 1-u P'3 = 12 0 = 100kPaT, aging 14 0. 16 0.18 0.20 1000 Minutes gure 4.27 Small Strain q and s v versus y Curves in Phase 5 along Various Stress Paths at a Stress Ratio of 1.0 with 1000-Minute Ag ing Duration (Tests No. 9 to 12) 110 similar behaviour. The observed magnitude of expansion is close to the resolution of the measurement system. However, there is a clear trend towards less contractive response as the stress path rotates counter-clockwise from the conventional path as the degree of unloading is increased. From Figure 4.1 and Figures 4.16 to 4.19, it is seen that for stress paths -2, -1 and 0, the confining stress is being reduced and for the -1 and 0 paths, p ' is being reduced. It appears that the contraction due to increasing stress ratio is insufficient to counter the expansion due to p ' unloading along the 0 path. 4.4.2 Effects of Stress Path and Aging on Small Strain Stress-Strain Behaviour, Anisotropically-Consolidated Samples Figures 4.28 to 4.31 show the effects of aging at a stress ratio of 2.1 on the stress-strain behaviour and volumetric response in the small strain region along conventional, -2, -1 and 0 stress paths, respectively, under 100-kPa confining stress and at a consolidation ratio of 2.1 (Tests No. 16 to 26). On the conventional path, all three samples commenced contraction upon commencement of shearing. The older sample demonstrated less contractive response and stiffer stress-strain behaviour at a stress ratio of 2.1, although the difference in volumetric behaviour was not very pronounced. There was little difference in response between the two samples along the -2 path. The older sample had slightly lower density. Along the -1 path, the older sample is stiffer but it is slightly denser, which may explain the greater observed stiffness. A l l o f the samples along the -1 path appeared to dilate during the initial part of shearing before commencing contraction. Along the 0 path, the older sample had stiffer stress-strain behaviour. A l l samples appeared to dilate at the beginning of shearing. I l l 200 190 180 170 „ 160 n 0. CT 150 140 130 120 110 TesTNo. 24 8 »4 10000 Minutes 24.3%) 2.1 a ' lOOkFfe a ' / c ^ ^ s . "TesnvoT20" 1000 Minutes (23.8%) Conventional Test No. 100 Minutes (B5.6%) 16 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 Y (%) Y (%) 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.00 0.02 0.04 £ 0.06 0.08 0.10 V 0 ^ x^ X o t o 0 l x 4 * A 0 o X ' o 0 o A 10000 h inutes 100 1 o i/lnutes X £ 0 0 < A X t 1 1 / / A X X A 100C Minutes 0 o ( X O 3 (Phase 3) = 2.1 a' 3 = 100 kF a <j\ld3 Phase 5) - Convent onal Figure 4.28 Small Strain q and s v versus y Curves in Phase 5 along the Conventional Path with Various Aging Durations at a Stress Ratio of 2.1 (Tests No. 16, 20 and 24) 1 1 2 200 190 180 170 ^ 160 n Q . o" 150 140 130 120 110 d lAj3(Phas .31=2.1 CF3 - 1 C 0 kPa ( lVcJ3(Ph< SB 5) - "2 Test J^o. 21 X x > x X > 1 )00 Minu X x X x es (23.1 x x o ° % > X x x o X x o 0 0 o Test No. o ° 17 j/ 0 x * ° * o ' 100 I /linutes ( >6.2%) ' X 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 Y (%) Y (%) -0.05 o.po OO O i o.oo r ^ i »„x 0.05 2- 0.10 0.15 0.20 0.25 0.02 0.04 0.06 0.08 0.10 0 dl/a3(PhaJe3) , = 2.1 12 0.14 0. 100 Minutes CT'3= lp0 kPa |aVa3(Priase5) 16 0.18 0.20 >p000 M(nutes x— Figure 4.29 Small Strain q and s v versus y Curves in Phase 5 along the -2 Path with Various Aging Durations at a Stress Ratio of 2.1 (Tests N o . 17 and 21) 113 200 190 180 170 _ 160 m CL J< o- 150 140 130 120 110 O'l'o 3 (p| = 2 aso 3) 1 o',= 1 OOkPa < 'l'°"3(Pha :e5) Test No. 22 1 000 Mini (23.2% tes ) 100C Test No 0 Minute .25 s (29.3% fl >A < A A A A *• Sc X A * A ; x >< A ** O X * o O o O » 10 0 TestN ) Minutes ). 18 (24.3% 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 Y (%) Y (%) -0.05 ° - P 9 # * * ° P 4 ° f 6 ° P 8 0 0.00 0.05 ^ 0.10 0.15 0.20 0.25 x* )AA° 0„ x a'Ja\ 100 IVinutes ase 3) HO 0.H2 0 100O0 Minutes 1 CT3-1 OOkPa crVaspha.es)--1 14 0.16 0 1000 Mir utes hs o.eo Figure 4.30 Small Strain q and s v versus y Curves in Phase 5 along the -1 Path with Various Aging Durations at a Stress Ratio of 2.1 (Tests No . 18, 22 and 25) 114 200 190 180 170 ~ 160 co CT 150 140 130 120 110 c7c ' 3 <p = 2 lase 3) .1 r / 3 - OOkPa ^/^(Ph: se5, = 0 1 "est No. 300 Mnu !3 es Test N 10000 IV ). 26 nutes (27.4% ' (25.2 %) A A A x 1 X X * X X o A X x X  0 o o o o i Test No. (22.5°/i 19 ) o 100 Mnu tes 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 y (%) y (%) -0.05 0.00 1000 Minutes O.pO 0.b2 O.U 0.06 0.D8 0 0.05 ^ 0.10 0.15 0.20 0.25 A4i"o*Ag < A» , X X a'Jd f° 3 (Phase 3) , = 2 ho o 1 a', = |00kRa 12 0 10000 Minutes X [14 0. It ' 116 x 0. 3 (Phise 5) 100 Minutes 18 0.20 Figure 4.31 Small Strain q and s v versus y Curves in Phase 5 along the 0 Path with Various Aging Durations at a Stress Ratio of 2.1 (Tests No . 19, 23 and 26) 115 Figure 4.32 shows the q and s v versus y curves along the four different stress paths at the same stress ratio in the small strain range (Tests No . 20 to 23). The conventional path gave the stiffest response and the 0 path gave the softest response. This trend was also observed at larger strains. The initially stiff behaviour along the 0 path observed under hydrostatic conditions (Figure 4.27) was not observed at a stress ratio of 2.1. The sample sheared along the conventional path contracted the most and the extent of contraction decreased as the stress path changed towards 0. Initial dilation was observed along the -2, -1 and 0 paths, with the magnitude of the initial expansion increasing as the stress path rotated towards the 0 path. Again, the magnitude of the measured volumetric strain is close to the measurement resolution and so the magnitudes are unreliable but the trend is clear. A l l three paths exhibiting initial expansion involve decreasing G ' 3 and increasing axial strain. In addition, the rate of increase in stress ratio increases as the stress path rotates towards the 0 path. For negative s v, samples must be experiencing lateral expansion with s r larger than 0.5s a. Because initial dilation was caused by the reduction in effective confining stress, more dilation was expected along paths with higher rate of confining stress reduction. Figures 4.33 to 4.36 show the stress-strain behaviour and volumetric response along the conventional, -2, -1 and 0 paths after aging for 100 and 1000 minutes at a stress ratio of 2.5 (Tests No . 28 to 35). A s was the case for a stress ratio of 2.1, the older samples along all stress paths exhibited stiffer stress-strain behaviour. In addition, all older samples, except the one on the conventional path, showed less contractive volumetric response even though the 100-minute specimen was slightly denser. Along the -2 path, there was little difference i n the volumetric response between the two 116 200 190 180 170 — 160 ro 0. O-150 140 130 120 110 n\fo'3 phi = 2 se3) o'3=1C OkPa T L =10 4ging )0 Minute s • Co nventionj ll O -2 A - 1 x 0 a , ° 0 i £ < n ° X • " J • * x X A« * < X X X x x x i l t ? — 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 Y (%) Y (%) -0.05 o.po 0.0; o.oo 0.05 2- 0.10 0.15 0.20 0.25 4 0.06 0.08 0 x X 4 3 (Phas e 3) 2.1 10 0. 12 0. 14 0. o Conventional o -2 A -1 x 0 a'3 = 10bkPa T, 16 0. = 1000 Minutes 18 0.20 Figure 4.32 Small Strain q and s v versus y Curves in Phase 5 along Various Stress Paths at a Stress Ratio of 2.1 with 1000-Minute Ag ing Duration (Tests No. 20 to 23) 117 240 230 220 210 ~ 200 <2 c 190 180 170 160 150 tr7< 3 (Phase 3) 2.5 100 kFfa CT'^O-'; 1000 Phase 5) ' est No. i/linutes : !2" (29. 0%) x Test No. 28 100 Minutds (29.7% Convent lonal 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 Y (%) Y (%) 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 X-f oo *x ° V 0 o s 0 < o X X X 0 o \ c X X o y 0 X < o 0 100 Mini tes 1000 Mi lutes 0 X X o o X X o X X 3 (Phase 3) = 2.5 = 100 kF (Phase 5) — Convent onal Figure 4.33 Small Strain q and s v versus y Curves in Phase 5 along the Conventional Path with Various Aging Durations at a Stress Ratio of 2.5 (Tests No . 28 and 32) 118 240 230 220 210 ~ 200 ra CL °" 190 180 170 160 150 T l ' C T 3 (Ph ise3) 2. 5 0' 3 = 1 00 kPa T / C T 3 (Ph ise 5) TestN 1000 M 3. 33 nutes X x X * X (20.4 X o % > * O X o o X o * * >o ° 0 T 1C ;st No. 2 0 Minute 9 s (2535%) 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 Y (%) y (%) -0.05 O.PO 0.02 0.04 0.06 0.08 0. 0.00 * 1 x * 0.05 2- 0.10 0.15 0.20 0.25 3 (Phase 3) 100 Mhutes 10 0. 12 0. 5 c ' 3 = 100kPa k / 0 ' 14 0. 1000 Minute^  _x 16 0. 3 (Phbse 5) = 4 18 0.20 gure 4.34 Small Strain q and s v versus y Curves in Phase 5 along the -2 Path with Various Aging Durations at a Stress Ratio of 2.5 (Tests No . 29 and 33) 119 240 230 220 210 — 200 ra Q . c 190 180 170 160 150 ^ Test No. 34 1000 Minutes (25.8%) a'Ja'z ( pi l a s e 3 ) - 2 5 CJ'3 - 100 kPa (^/a^(p h aL 5 ) - -1 Tesl No. 30 [100 Minuses (30.61%) 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 Y (%) Y (%) -0.05 0.00 O.DO 0.02 0.D4 0.D6 0.D8 0. 0.05 ^ 0.10 0.15 0.20 0.25 -1 -ItJOIvtrrates-100Q Mnutes hO 0.12 0 c ' i / o ' 3 ( p i i a s e 3 ) ~ 2 5 a' 3 - 100 kPa ' j ' 1 /a ' 3 ( P h a 3 e 5 ) - -1 14 0. 16 0.18 6.20 Figure 4.35 Small Strain q and s v versus y Curves in Phase 5 along the -1 Path with Various Aging Durations at a Stress Ratio of 2.5 (Tests No . 30 and 34) 120 „ 200 ro D -c 190 oVa'3 p = 2 lase 3) .5 CT'3- 00 kPa 7/°3(Ph« se5) ^ Tnr t M A l e s i 1000 (29 (NO. OO Minutes 3%) X x x X X x o o X D Test No X 0 ° 31 X o > * o 100 Minutes (29.4%) 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 Y (%) Y (%) -0.05 0.00 O.pO 0.02 0.04 0.06 0.08 0.10 0 0.05 'o* 0 x| 1000 Mnutes 400-MtntrteiV 12 0.14 0. 16 0.18 0.20 ^ 0.10 > 0.15 0.20 0.25 ° y a ' 3 ( p n a s e 3 ) = 2 - 5 CT3 = I OOkPa k / O j (p hL 5 ) = 0 ;ure 4.36 Small Strain q and s v versus y Curves in Phase 5 along the 0 Path with Various Aging Durations at a Stress Ratio of 2.5 (Tests No . 31 and 35) 121 samples. The older sample showed a possible tendency towards dilation upon the commencement of shearing, although the strains involved were close to the resolution of the instrument. Initial dilation was clearly observed along the -1 and 0 paths and the extent of dilation increased with increasing age. Moreover, for older samples, net dilation continued to a higher stress ratio. Shozen (2001) observed identical trends in his tests with stress ratios of 2.0 and 2.8. The observed volumetric response in Figures 4.28 to 4.36 was the combined effect of changes in shear stress and mean effective stress. For all paths to the right of the -2 path, both shear stress and mean stress were increasing. For the approximately constant p ' (-2) path, the volume change is almost completely due to shear-induced volume change. For paths to the left of the -2 path, the mean effective stress was being reduced while shear stress was increasing. If the expansion due to mean effective stress reduction is greater than contraction during shearing, then net expansion may be expected. On the 0 path, the rate of mean effective stress reduction was sufficient to result in net expansive strain being greater than the contraction due to shear in the very early stages of shearing. At consolidation stress ratios of 2.1 and 2.5, samples were observed to become stiffer and less contractive during shearing as they aged. Consequently, expansion due to reduction in p ' would be expected to be less on older samples. In addition, contraction during shearing would be expected to decrease with age. Figures 4.35 and 4.36 suggest an increasing tendency for net dilation during the early stages of shearing along stress paths with p ' decreasing and q increasing in loose samples consolidated to stress ratios greater than 1/Ko, a conclusion also drawn by Negussey (1984). 122 Furthermore, when stress-strain curves at different stress ratios are compared, it can be seen that the extent of initial dilation increases with increasing stress ratio. Figure 4.37 combines the stress-strain behaviour and volumetric response at strains less than 0.2% along the conventional stress path at consolidation stress ratios of 1.0, 2.1 and 2.5 (Tests No . 5, 16 and 28). Because samples at different stress ratios were sheared at different initial shear stress levels, incremental deviator stress, Aq, i.e. the difference between current deviator stress and that at the beginning of shearing, was used in the stress-strain curves instead of deviator stress, q, to allow direct comparison of stiffness. Samples at lower consolidation stress ratio demonstrated more contractive volumetric response and stiffer stress-strain behaviour. A s noted in section 4.3.3, samples sheared at different stress ratios were simultaneously influenced by different effective confining stresses. In order to differentiate the effects of stress ratio from those of effective confining stress, a comparison of the stress-strain behaviour of samples with different effective confining stresses is necessary. Figure 4.38 shows the small-strain stress-strain behaviour and volumetric response of samples consolidated to a stress ratio of 2.1 but at effective confining stresses of 50, 100 and 150 kPa (Tests No . 1,16 and 36). The sample became stiffer at higher effective confining stress. The s v / y ratios for the 100- and 150-kPa tests were identical and slightly larger than that for the 50-kPa test. A consistent trend between s v and y with increasing effective confining stress could not be concluded from Figure 4.38 and is an area of future study. It can be seen from Figures 4.37 and 4.38 that initial stiffness is reduced by higher stress ratio and increased by larger effective confining stress. 123 90 80 70 60 50 5 40 30 20 10 100 kPa "'aging 00 Mnut BS cr'/a'; (Phase 5) ~ Convent onal „ o o 0 SF Test No {=1.0(2 . 5 5.9%) ^ ,° * 1 "est No.' 6 r / ' SR = 2.1 (25 < x ^ x .6%) X * X x . / v * x * , A X x A * x x A A 4 A SR A Test No. = 2.5(2! A 28 (7%) X A 4 " A A A i 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 y (%) y (%) 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.00 0.05 0.20 0.25 ( p x > \ % ' * A * A X A A V A A A SF A = 2.5 \ * X X X SR = 2.1 x A x x 6 O SR = °°, 1.0 °o 0 c 0 O ° o • • • • c o 100 kRa T . = 1 aging 00 Minut . (Phase 5) " ; Conven tional o 0 Figure 4.37 Small Strain Aq and e v versus y Curves in Phase 5 at Various Stress Ratios along the Conventional Path (Tests No . 5, 16 and 28) 124 90 80 70 60 1? 50 40 30 20 10 0 0"Vcf3(Phase3] = 2.1 1raging = 100 Miriutes ai/fj'3(Phas95) = Cdnventidnal T<bt No. 36 45olpa-(2&;J%} Test No. 1 $0 kPa {:±9%± TestNor 100 kPa (25 6%) 6" 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 Y (%) 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.00 0.05 • • • C A -" AO a * % • c * AO • -A * • • 50 kPa « 100 kPa A 150 kP a oVa; (Phase 3) = 2.1 1 aging ~ 00 Min utes a /o"'3(Phas e5) = C )nventi )nal Figure 4.38 Small Strain Aq and s v versus y Curves in Phase 5 with Various Effective Confining Stresses along the Conventional Path (Tests No . 1,16 and 36) 125 4.4.3 Conclusions - Stress-Strain Behaviour at Shear Strains Less Than 0.2% Several generalizations regarding the stress-strain behaviour and volumetric response at shear strains less than 0.2% are drawn: • The behaviour observed by Shozen (2001) was confirmed in this study. • Aging led to stiffer stress-strain behaviour in the small strain region at all stress ratios and along all stress paths. • A t a stress ratio of 1.0, the 0 path was the stiffest at the beginning of shearing whereas it was the softest path at the other three stress ratios. • A t a stress ratio of 1.0, aging did not have any obvious effect on the volumetric response in the small strain region. However, older samples generally exhibited less contractive volumetric response under anisotropic conditions. These trends were also observed by Shozen (2001), who used stress ratios of 1.0, 2.0 and 2.8 in his research. He discovered that aging led to more contractive volumetric response at the beginning of shearing under hydrostatic conditions and less contractive volumetric response at stress ratios of 2.0 and 2.8. • A greater tendency for net dilation upon the commencement of shearing was observed along stress paths with p ' decreasing and q increasing in loose samples consolidated to stress ratios greater than 1/Ko. The amount of expansion appeared to increase with higher stress ratio. • Initial stiffness at the beginning of shearing decreased with increasing stress ratio. • Samples at lower stress ratios demonstrated more contractive volumetric response and stiffer stress-strain behaviour. 126 • Higher effective confining stress led to stiffer stress-strain behaviour and higher strength. 4.5 Aging Effects on Soil Stiffness This section discusses the effects on soil stiffness of various factors, including stress path, stress ratio, aging duration and effective stress. Secant shear moduli were calculated according to the following relationship: 7 2(ff,-ff3) 3sa-sv A s mentioned in section 3.3.2, the precision of the L V D T was 0.004% of the sample height and the precision of the differential pressure transducer was 0.002% of the sample volume. Shear strains were calculated from axial and volumetric strains. When the precisions of the L V D T and the differential pressure transducer were combined, the precision of the calculated shear strain was approximately 0.01%. However, the actual precision of shear strain was not as good as 0.01% when electronic noise was taken into consideration. In order to ensure the precision of the calculated shear moduli, shear strains larger than 0.01%) should be selected for shear moduli calculations. In this research, shear moduli evaluated at shear strains of 0.03% and 0.15% were compared. Stiffness at 0.15% shear strain was estimated to study the stiffness attenuation with strain. The following sections discuss the effects on secant shear moduli determined at shear strains of 0.03%o (G0.03) and 0.15% (G0.15) o f different aging durations, stress ratios, confining stresses, stress paths and relative densities. 127 4.5.1 Effects of Aging Duration Figure 4.39 shows the variations of G0.03 and G0.15 with time along the conventional and -1 paths in Phase 5 up to an aging duration of 10,000 minutes with an effective confining stress of 100 kPa and at a stress ratio o f 2.1. Both G0.03 and G0.15 increased as aging duration was lengthened. The data in Figure 4.39 could be well approximated by a straight line, which indicated that both Gn.03 and Go. 15 varied linearly with the logarithm of aging duration, a trend also observed by Shozen. The rate of increase with logarithm of time is greater for G0.03 than for Go. 15. Figure 4.40 shows the G versus y curves at a stress ratio of 2.1, along the conventional path, under an effective confining stress of 100 kPa and with three different aging durations. The increase in G with time was greater at smaller shear strains, indicating that time effects were more pronounced in the small strain range. Shear moduli at small shear strains were considerably larger than those at large shear strains. The degree of modulus attenuation with strain increased with aging duration. The G0.03 value in the sample with 10,000-minute aging duration diminished by a factor of 9 over the first 1.0% of shear strain. The G0.03 value in the sample with 100-minute aging duration, on the contrary, only diminished by a factor of 5 over the first 1.0% of shear strain. 4.5.2 Effects of Confining Stress and Stress Ratio The shear tests in this study were performed at a variety of stress ratios and mean effective stresses. In order to examine the effects of stress ratio on the attenuation of stiffness with strain, it is necessary to account for the effects of mean effective stress on stiffness. Figure 4.41 shows the variations o f G0.03 and G0.15 with effective confining 128 gure4.39 G0.03 and G0.15 versus Aging Duration Curves in Phase 5 along Conventional and -1 Paths 129 ra Q. 0.01 0.1 10 Figure 4.40 G versus y Curves in Phase 5 with Various Aging Durations along the Conventional Path 130 stress along the conventional path with an aging duration o f 100 minutes. Effective confining stresses used in the research were 50, 100 and 150 kPa. Both G0.03 and Go. 15 increased with effective confining stress but the increase was non-linear. A s discussed in section 2.2, the secant stiffness of sand can be represented by the equation G = kgPa rp,Y , with the factor accounts for the stress dependence of the moduli. The parameter n is typically 0.5 but may vary with soil type and strain level. The n value of the Fraser River sand used in this study was investigated through examination of the slopes of the bilogarithmic G0.03 versus p ' curves with different aging durations. The bilogarithmic G0.03 versus p ' curves obtained in tests with a stress ratio of 2.1 and with aging durations of 100 and 1000 minutes under 50-, 100- and 150-kPa effective confining stresses are shown in Figure 4.42 and the n value was concluded to be 0.7. Shozen (2001) found the n value to be 0.6 for a stress ratio of 2.0. Figure 4.43 shows the G normalized by f • V versus y curves under different effective confining stresses with 100-minute aging duration along the conventional path. At a stress ratio of 2.1, the mean normal stresses, p ' , at effective confining stresses of 50, 100 and 150 kPa were 68, 137 and 205 kPa, respectively. Through normalization of G , differences in effective confining stresses were automatically corrected for. A l l o f the three normalized G versus y curves converged into a single curve and the observation that G varied with a power of effective confining stress was confirmed. There were insufficient data to allow the determination of n along the other stress paths. For the purposes of this discussion, an n value of 0.7 is assumed to be valid along 131 45 40 35 30 « 25 CL S O 20 15 10 5 0 0"Va3(Pt ase3)~2-1 T; ging = 100 Mi lutes a'i/o-'3 Phase5) ~ Con ventional < D r = 2 6.2% n ' i r p n / D r - i • D r = ; !1.9% > G 0 15 > ' - - ' * " 25 50 75 100 125 o'3(kPa) 150 175 Figure 4.41 G0.03 and G0.15 versus a'3 Curves in Phase 5 along the Conventional Path 1.8 1.7 1.6 s 1.4 1.3 1.2 Log G 0 ( 1000 Mini 3=0.6911 L ites jg p' + 0.10E 1000 5 Minute sy* X Minutes L °9 G 0 . 0 3 = 100 Minutes 0.7131 Log 3'-0.0543 1.8 1.9 2.0 2.1 2.2 2.3 2.4 Logp' Figure 4.42 Determination of n 132 Figure 4.43 Normalized G versus y Curves in Phase 5 with Various Effective Confining Stresses along the Conventional Path 133 all stress paths. A s the n factor effectively takes the stress dependency o f shear moduli into account, a fair evaluation of the effects of stress ratio on soil stiffness can now be made by comparing shear moduli normalized by the n factor. Figure 4.44 shows the attenuation of normalized shear modulus with strain along the conventional path at stress ratios of 1.0, 2.1 and 2.5. The mean normal stresses at stress ratios of 1.0, 2.1 and 2.5 were 100, 137 and 150 kPa, respectively. In accordance with Figure 4.44, soil stiffness decreased with increasing stress ratio. Y u and Richart (1984), who conducted a series of resonant column tests on dry sands, suggested that increasing stress ratio decreased small-amplitude shear modulus. The data collected in this study led to observations similar to those concluded by Y u and Richart. Moreover, it was observed that shear modulus at larger strain level, i.e. G0.15, was less sensitive to changes in stress ratios than that at smaller strain level, i.e. Go.o3-Because the normalized shear modulus at lower stress ratio was much larger than that at higher stress ratio, modulus attenuation with strain was faster at lower stress ratio. 4.5.3 Effects of Stress Path Figure 4.45 shows the attenuation of normalized shear modulus with strain at a stress ratio of 1.0 along different stress paths. A s shown in Figure 4.27, the -2 path was the softest and the 0 path was the stiffest for shear strain up to about 0.06%. For shear strains greater than 0.06%, the conventional path is the stiffest. The 0 path becomes the softest path at shear strains greater than 0.15%. The G values obtained along the - 2 and -1 paths were similar in magnitude because the rate of effective confining stress reduction along the two stress paths did not differ very much and similar stress-strain response was observed in the small strain range. Figure 4.46 shows the attenuation of 134 60000 Y (%) Figure 4.44 Normalized G versus y Curves in Phase 5 at Various Stress Ratios along the Conventional Path 135 80000 70000 60000 1.0 CJ'. = 100 kpa hOOO Mhutes • SR = Conventional o SR = -2 a SR = -1 x SR=0 Y (%) Figure 4.45 Normalized G versus y Curves in Phase 5 along Various Stress Paths at a Stress Ratio of 1.0 30000 25000 20000 1=2.1 = 100 kpa 1000 Mihuted • SR = Conventional o SR = -2 A SR = -1 X SR = 0 Y (%) Figure 4.46 Normalized G versus y Curves in Phase 5 along Various Stress Paths at a Stress Ratio of 2.1 136 normalized shear modulus with strain at a stress ratio of 2.1 along different stress paths. The conventional curve was at the top whereas the 0 curve was at the bottom, confirming that the conventional path gave the stiffest response and the 0 path gave the softest response, an observation made in Figure 4.32. Identical trends were observed in the normalized shear modulus versus strain curves at a stress ratio of 2.5. A s noted in section 4.2.1 that, apart from hydrostatic consolidation, the s v / e a ratio was primarily controlled by the stress ratio imposed on the sample. This could be interpreted as the establishment of a preferential soil particle arrangement under a specific stress ratio during consolidation and aging under hydrostatic conditions (Kuhn and Mitchell , 1993). When the sample was sheared on different stress paths after aging, the preferential soil arrangement was destroyed. In order to measure the effects of preferential structure built up during consolidation and aging on stress-strain behaviour during shearing, a new variable, a , was defined, which accounted for the rotation of stress path from the conventional to the 0 path, a , shown in Figure 4 . la , is defined as the angle of rotation between the stress path in Phase 5 and the consolidation stress path. It provides a clear and explicit way to quantify the amount of deviation o f a particular stress path during shearing from that during consolidation. Increasing a indicated that the stress path was rotated in a counter-clockwise direction and changed from the conventional path to the 0 path. Figure 4.47 shows the normalized G0.03 and Go. 15 with a and aging duration at stress ratios of 1.0, 1.6, 2.1 and 2.5. The mean normal stresses at stress ratios of 1.0, 1.6, 2.1 and 2.5 were 100, 120,137 and 150 kPa, respectively. Normalized G0.03 was always larger than Go. 15. Moreover, normalized G0.03 and Go. 15 with 1000-minute aging 137 (a) G0o3 80000 (°) G 0 , 5 30000 25000 20000 a. -A 1.0(100) •A---1.0(1000) -• 1.6(100) -• 2.1 (100) -0---2.1 (1000) —2.5(100) •••-•2.5(1000) a'=10bkRa Conventional -»0 20 40 60 80 100 120 140 160 180 200 a ( ° ) ;ure 4.47a,b Normalized G0.03 and Go. 15 versus a Curves in Phase 5 at Various Stress Ratios with 100- and 1000-Minute Aging Durations 138 duration were larger than those with 100-minute aging, which confirmed that aging led to stiffer stress-strain behaviour along all stress paths. Both normalized G0.03 and Gn.15 decreased with increasing a at consolidation ratios larger than 1.0, with G0.03 always larger than Go. 15 at a particular stress ratio. Nevertheless, for samples consolidated under hydrostatically stress conditions, the 0 path was the stiffest at small strains but became the softest as strain increased, which suggests that the shape of boundary surface defined by Jardine (1992) around a hydrostatic stress point may be different from that under anisotropic stress conditions. In general, the decreasing trend of normalized G with increasing a was more consistent in Go. 15 than by G0.03 because the axial and volumetric strain measurements at 0.03% shear strain were more sensitive to electronic noise than those at 0.15% shear strain. Yasufuku et al. (1991) investigated the anisotropic characteristics of yield curves of sand using a series of drained triaxial tests with a variety of stress paths and consolidation stress levels. They observed that anisotropically-consolidated samples became less stiff when the stress path followed during shearing rotated from the conventional compression path in a counter-clockwise fashion, i.e. a direction of increasing a. The same conclusion was drawn by Negussey (1984), who conducted a series of triaxial tests to study the small-strain behaviour of Ottawa sand and found that samples became less stiff as the stress path during shearing rotated in a counter-clockwise fashion. Yasufuku et al. and Negussey's findings were reinforced in this study. A s introduced in section 2.3.2, Anderson and Stokoe (1978) defined two parameters, IG and N G , to account for the time-dependent variation of soil stiffness given by: 139 NG = - ^ - 1 0 0 % Equation [2] 1^000 Table 4.4 lists the values of IG and N Q obtained at shear strains of 0.03% and 0.15%> in this investigation and Shozen's (2001) study. Several trends regarding the effects of aging duration, stress ratio and stress path on soil stiffness can be observed in Table 4.4. I G and No at 0.03% shear strain are always significantly larger than those at 0.15%) shear strain, which confirms that the effects of age on soil stiffness is much greater at small strains than those at moderate to large strains as stated in section 4.5.1. Table 4.4 I G and N G Values of Fraser River Sand Stress Ratio Stress Path Y = 0.03% Y = C 1.15% I G (MPa) N G (%) I G (MPa) NG(%) 1.0 Conventional 14.10 23.4 2.90 11.1 -2 11.41 27.2 4.04 19.2 -1 5.06 13.3 0.32 1.7 0 11.43 16.2 1.08 5.4 2.1 Conventional 5.79 16.3 1.40 11.1 -2 3.02 11.3 1.57 14.8 -1 8.50 26.0 1.81 17.4 0 15.07 55.8 1.64 19.9 2.5 Conventional 6.14 19.8 1.92 17.6 -2 7.27 25.4 1.54 17.0 -1 6.19 22.7 1.40 16.8 0 4.51 20.5 0.62 9.27 2.8 Conventional 6.97 25.2 2.58 28.3 0 4.37 27.4 0.96 21.3 140 In general, IQ decreases and N Q increases with increasing stress ratio although the trend is not very clear. Moreover, IG at stress ratios other than 1.0 is similar in magnitude and is significantly smaller than those in hydrostatically-consolidated samples. These observations imply that the increase in G0.03 and Go. 15 with time at stress ratios of 2.1 and 2.5 is very similar. The increase in G0.03 and Go. 15 at a stress ratio of 1.0, in addition, is always larger than those at the other two stress ratios. However, because G at a stress ratio of 1.0 is considerably larger than those at the other two stress ratios, the percentage increase in G represented by N G is the smallest under hydrostatic conditions. As may be noted in Go. 15 along the conventional and 0 paths, N G appears to increase with higher stress ratio, which implies that the effects of aging on stiffness are more pronounced at higher stress ratio. Y u and Richart (1984), as well as Shozen (2001), concluded that the effects of stress path on soil stiffness were relatively unimportant. However, according to Table 4.4, it appears that stress path has effects on soil stiffness, although not as clear as those of stress ratio. A t a constant stress ratio, No usually varies by 10% to 15% along different stress paths but the way N Q varies with stress path is not consistent at different stress ratios. A t stress ratios of 1.0 and 2.5, No seems to decrease when the stress path rotates from the conventional towards the 0 path. The reverse is observed at a stress ratio of 2.1. IG varies from 3 to 15 M P a at 0.03% shear strain and from 0.3 to 4.0 M P a at 0.15%) shear strain. When the increase is considered with respect to the stiffness at 1000 minutes, N G is about 20% at 0.03% shear strain and 13% at 0.15% shear strain on average. The range of N G is considerably larger than the value quoted by Anderson and 141 Stokoe, i.e. substantially higher than 1%, which suggests that G m a x maybe significantly more sensitive to age than previously thought. The study of variation of G m a x with time is not the scope of this research and further investigation is required. The increase in soil stiffness with time implies that the effects of aging have to be taken into account when laboratory results on reconstituted samples are used to estimate the behaviour of sands in nature. Because the effects of geologic aging are erased in reconstituted samples, laboratory soil stiffness tends to be conservative and likely underestimates the in-situ stiffness of soil. Conversely, stress-strain properties derived from in-situ test data should be used with caution because they likely overestimate the actual properties of soil as aging effects are always incorporated in the data. 4.5.4 Relationships between G and q / q r The sudden increase in G0.03 on the 0 path in the hydrostatically-consolidated samples does not agree well with the decreasing trend of G with a. An alternative way to consider the variation of shear moduli is to compare the shear stress at the beginning of shearing, q, and that at failure, qf, i.e. the q/qf ratio, qf was defined at a stress ratio of 4.0 in the q-p' space, which was estimated to be the failure point of samples, and is shown in Figure 4.48. The n value of the Fraser River sand used in this study was 0.7. As a increases, the shear stress at the beginning of shearing is closer to the failure shear stress and q/qf is higher. The normalized shear moduli presented in Figure 4.47 are plotted against the new parameter, q/qf. Table 4.5 shows the q/qf ratios at different stress ratios and along different stress paths. 142 250 200 50 Fa ilure Line ( 1 1 / 0 3 = 4.0) / 1 \ -2 / Con o\ \ Phase 5 / P hase 3 Phase 4 / / Pha se 1 0 50 100 150 200 p' (kPa) Figure 4.48 Definition of Deviator Stress at Failure, q f 143 Table 4.5 q /q f Ratios at Different Stress Ratios and along Different Stress Paths 0"'l /0" '3 (Phase 3) 0"'l/CT'3 (Phase 5) q/qr 1.0 Conventional 0.00 -2 0.00 -1 0.00 0 0.00 1.6 Conventional 0.17 -1 0.33 0 0.44 2.1 Conventional 0.33 -2 0.50 -1 0.56 0 0.67 2.5 Conventional 0.47 -2 0.64 -1 0.69 0 0.78 Figure 4.49 shows the variations of normalized G0.03 and G0.15 with q/qf with 100-, 1000- and 10,000-minute aging durations. The 10,000-minute curve lay at the top while the 100-minute curve lay at the bottom, which showed that shear moduli increased with aging duration. The gap between the 100- and 1000-minute curves of G0.03 was wider than that of G0.15, which confirmed that time effects were more pronounced at small shear strains. The gaps between the 100- and 1000-minute curves of both G0.03 and Go. 15 were relatively constant in width, which suggested the increases in shear moduli along different stress paths and at stress ratios of 2.1 and 2.5 were relatively uniform. A major disadvantage of plotting G against q % was the inability to distinguish the G values along various stress paths at a stress ratio of 1.0. Because the shear stress at the beginning of phase 5 at a stress ratio of 1.0 was zero, the q/qf ratio was zero regardless of the stress path followed in the shearing phase. Therefore, all o f the G values obtained along different stress paths lay along the zero q/qf axis and the effects of stress paths on 144 80000 70000 60000 ra 50000 CL CL 40000 <f 30000 20000 10000 0 Toe s w ith Dif reare»nt ^1000 Mi lutes ... V \ 1 \ )000 Mini 1 J es 100 Min J t e s ^ v ^ ' *!;' "J 1 • •""""""•"Tl 30000 25000 • 20000 (0 a. o." 15000 "a 10000 5000 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 q/qf 1000 Min jtes Tes ts w 'rth Dif ferent a'3 100 Mini t e s ^ V ^ > 1 v . > D . % 100( )0 Minute s ^•^-^ L * - k * 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Figure 4.49 Normalized G0.03 and G0.15 versus q/qf Curves in Phase 5 with 100-, 1000-and 10,000-Minute Aging Durations 145 shear moduli could not be shown clearly. However, the effects of aging duration were still observable in Figure 4.49, as the G values with 1000-minute aging duration were significantly larger than the G values with 100-minute aging duration. Moreover, the range of normalized G values in hydrostatically-consolidated samples was much larger than those at other stress ratios. Effects of different effective confining stresses on shear moduli are also shown in Figure 4.49. It is evident that G0.03 and Go. 15 with different effective confining stresses converged to a single point after normalization. The G0.03 values at a stress ratio of 2.0 and along the -1 stress path were slightly scattered around the best-fit line, which could be attributed to their susceptibility to electronic noise and errors. A l l o f the other data points that involved different confining stresses collapsed to a point very close to the best-fit line, which verified that shear moduli were not significantly influenced by differences in effective confining stresses after they had been normalized. 4.5.5 Effects of Relative Density Most of the samples were prepared to a loose state as aging effects were the most pronounced in loose samples. However, a medium-dense sample was prepared and tested in the research programme to obtain a general idea on the effects of relative density on soil stiffness. Figure 4.50 shows the G versus y curves at a stress ratio of 2.1 and along the conventional path with two different relative densities and aging durations (Tests No. 24 and 27). The young sample was prepared to a relative density of 47% and aged for 100 minutes, while the old sample was prepared to a relative density of 19% and aged for 10,000 minutes. When the G versus y curves were compared, it was found that the G values of both samples were very similar at a shear strain of 0.03%. Shozen 146 1.0 0.9 0.8 0.7 0.6 13 (S 0.5 O 0.4 0.3 0.2 0.1 0.0 ° ( (Phs ise i) = 2 1 a'3=1C 0 kf 'a i( a E 5) = CO wen tioi la <f> df • °8 0, • c a & > C fi? t M a J (' 7 ><> t ; v 10 0I\ / lin ut e 3.9%) / / / f / T es :N 0 2 4 10 300 Mir lUt 2 4 :$%) 0.01 0.1 10 Figure 4.50 G versus y Curves in Phase 5 with Different Aging Durations and Relative Densities (Tests No. 24 and 27) 147 observed similar results in his tests on samples with different relative densities and concluded that the effects o f aging duration would outweigh the effects o f relative density in the range of small shear strains. His conclusion was verified in this study. This observation indicates that aging may have a greater effect on soil stiffness at strains smaller than 0.2% than relative density. Moreover, it suggests that the G versus y curve may be affected in a different manner by aging than by relative density. How aging and relative density affect soil stiffness is an area that needs further study. 4.5.6 Conclusions - Soi l Stiffness In accordance with the results presented in previous sections, the following trends were concluded: • G0.03 and Go. 15 increased with aging duration and G0.03 was always larger than Go. 15-• Effects of aging duration on shear modulus disappeared at shear strains larger than 1.0% for samples aged up to 10,000 minutes. • A s aging caused a greater increase in shear moduli at small shear strains than large shear strains, the degree of modulus attenuation with strain increased with aging duration. • Shear modulus at 0.03% shear strain increased exponentially with effective confining stress, with the exponent n to be 0.7. • For a given effective confining stress, G0.03 and Go. 15 decreased with stress ratio at which the sample was consolidated. • G0.03 was more sensitive to the effects of time and stress ratio than G0.15. 148 At consolidation stress ratios of 1 .6 , 2 . 1 and 2 . 5 , Gn.03 and Go. 15 decreased with increasing a, i.e. the more rapidly the stress ratio approached failure, a was defined as the angle between the stress path in phase 5 and the consolidation stress path. The decreasing trend of G with increasing a was more consistent for Go. 15 than for G0.03. The effect of a was very different at a stress ratio of 1 .0 for measurements of Go.o3- hi this case, G0.03 first decreased with a but increased dramatically when the 0 stress path was reached. The same effect was not evident for Go. 15, which decreased with a and did not show any significant increase along the same stress path. IG and N Q of G0.03 are always larger than those of G0.15. I G at stress ratios other than 1.0 is similar in magnitude and is significantly smaller than those in hydrostatically-consolidated samples, indicating that the increase in G0.03 and G0.15 at a stress ratio of 1.0 is always larger than those at the other two stress ratios. Nevertheless, N G is the smallest under hydrostatic conditions because G at a stress ratio of 1.0 is the largest in all four consolidation stress ratios used in the study. At a particular stress ratio, N G varies by 1 0 % to 1 5 % along different stress paths, which shows that soil stiffness is affected by stress path although a clear trend cannot be determined. N G varies from 9% to 34% in all of the tests carried out in this study. These values are significantly larger than those previously published. 149 A t strains of around 0.03%, the shear modulus of a loose, aged sample was about the same as the shear modulus of a young, medium-dense sample. This suggests that loose, aged samples may be stiffer than young, dense samples. This could have considerable importance in site characterization and requires further study. 150 C H A P T E R 5 Conclusions The effects of aging duration, stress ratio during aging and stress path on the stress-strain behaviour of loose Fraser River sand were investigated in this research. The research was conducted on reconstituted samples, which were aged at stress ratios of 1.0, 2.1 and 2.5 prior to shear testing along several stress paths. The focus of the study was not the stress-strain behaviour during aging. Instead, the study focused on the effects of the duration of aging and the stress ratio during aging on the stress-strain response observed after aging. The stress-strain response after aging was studied along four different linear stress paths. Each path involved an increase in shear stress but mean effective stress increased in one case (conventional triaxial compression path), stayed constant in another case (-2 path) or decreased in the other two cases (-1 and 0 paths). Test results indicated that aging had little effect on the stress-strain behaviour at strains larger than 2%; it did not affect the q/p' ratios and friction angles at maximum contraction and failure. Aging effects were the most pronounced at strains smaller than 1%. Older samples exhibited stiffer stress-strain behaviour at the beginning of shearing regardless of the stress ratio used during consolidation or the stress path followed during shearing. The effects o f the duration of aging on the volumetric response depended on the consolidation stress ratio and on the stress path imposed. For samples consolidated under hydrostatic stress states, aging did not have any obvious effect on the volumetric response under any imposed stress path, whereas it led to less contractive volumetric response for samples consolidated under anisotropic stress states. 151 For loose samples, it is expected that soil would contract at the commencement of shearing. However, results from this study revealed that loose samples consolidated and aged under stress ratios greater than 1.0 started to dilate at the beginning of shearing. The degree of initial expansion appeared to increase with increasing consolidation stress ratio and the tendency for net dilation during the early stages o f shearing was greater along stress paths with decreasing p ' and increasing q (-1 and 0 paths) in loose samples consolidated to stress ratios greater than 2.1. Moreover, net dilation continued to a higher stress ratio in older samples. It appeared that the consolidation stress ratio representing the Ko condition formed the boundary between stress ratios where net dilation occurred and those where there was net contraction. For consolidation stress ratios greater than 1.0, the initial stiffness of the stress-strain curve reduced as the stress path rotated in a counter-clockwise direction, i.e. the initial stiffness was the least along the 0 path with constant a ' i and reducing a '3 . However, for samples consolidated under hydrostatic stress conditions, the 0 path was the stiffest over the first 0.06% shear strain. At higher strains, the 0 path again became the softest of the four stress paths. The reason for this anomalous behaviour is not clear and needs further investigation. Experimental data from this research revealed that soil stiffness at moderate strain levels, i.e. 0.03% and 0.15%, increased approximately linearly with the logarithm of aging duration for samples aged up to 10,000 minutes. However, the rate of increase in shear modulus with respect to the stiffness at 1000 minutes was significantly larger than previously published values and was observed to increase as the strain increment decreased. This suggests that G m a x might be significantly more sensitive to age than 152 previously thought. The degree o f modulus attenuation with strain increased with increasing aging duration and decreasing consolidation stress ratio. The effects o f relative density on stress-strain behaviour and soil stiffness were not investigated extensively. Nevertheless, comparison o f tests conducted on a loose, aged sample and a medium-dense, young sample found that both samples displayed very similar stiffness at a strain level of 0.03%, suggesting that aging might have a greater effect on soil stiffness at small strains or the attenuation o f shear modulus with strain might be affected in a different manner by aging than by relative density. A l l o f the above findings suggest a strong effect o f age on the early stages of the stress-strain curves of loose Fraser River sand, especially at strains smaller than 1%. This implies that soil stiffness obtained from laboratory tests on reconstituted samples w i l l underestimate the in-situ stiffness of soil. The degree of underestimation w i l l vary with the age and stress-strain history of the soil deposit. On the contrary, in-situ data have to be analyzed with great caution because aging effects are always incorporated in the results and the in-situ properties of the soil deposit may be overestimated i f interpretation is based on correlations obtained using unaged soil specimens. Suggestions for Further Research Based on the observed effects of aging on stress-strain behaviour and small-strain shear moduli o f loose Fraser River sand, the following aspects are considered worthy o f further research: to clarify the effects o f aging on stress-strain behaviour and soil stiffness. • The effects of aging, stress ratio and shearing stress path should be studied in the very small strain range, i.e. 10"4% to 0.01%. This w i l l require improvements to 153 experimental apparatus and test control. Methods such as resonant column tests and bender elements combined with high resolution strain measurement system in static testing w i l l have to be used to study the aging effects in the very small strain range. In addition, improvements to control of the laboratory environment w i l l be required to allow study of aging effects for times greater than about 1000 minutes. Based on the observation that a loose, aged sample and a medium-dense, young sample displayed very similar stiffness at a strain level of 0.03%, the study of aging effects should be extended to other relative densities. The understanding of the effects of aging on the stress strain response of sands at small strains should be extended by carrying out tests on additional stress paths. The effect o f aging duration on the size and shape of the region of small-strain behaviour around a point in stress space should also be studied. 154 R E F E R E N C E Anderson, D . G . and Stokoe, K . H . 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(1968), "Behaviour of Granular Materials under High Stresses", Journal of the Soi l Mechanics and Foundations Divis ion, A S C E , 94 (SM3), p. 601 - 6 8 8 . Wijewickreme, D . (1986), "Constant Volume Friction Angle of Granular Materials", M . A . S c Thesis, Department of C i v i l Engineering, The University o f British Columbia, Vancouver, Canada. Wride, C . E . et al. (2000), "Interpretation of In Situ Test Results from the C A N L E X Sites", Canadian Geotechnical Journal 37, p. 505 - 529. Yasufuku, N . , Murata, H . and Hyodo, M . (1991), " Y i e l d Characteristics o f Anisotropically Consolidated Sand under L o w and High Stresses", Soils and Foundations, V o l . 31, No . l , p . 9 5 - 109. 159 APPENDIX 160 A P P E N D I X A Sample Preparation and B-Value Determination Samples were prepared by water pluviation. Water pluviation is a common technique used to replicate the deposition process in natural environments and mechanically placed hydraulic fills. When carried out with great care, it can lead to completely saturated samples that closely resemble natural sand deposits. A known mass of Fraser River sand was first boiled in a flask for approximately 30 minutes and allowed to cool under vacuum. It was then pluviated into a sample mould filled with de-aired water. The flask was inverted and the sand was allowed to fall into the mould. During pluviation, the flask was kept moving in a circular fashion to keep the sample surface level. After the sample surface had exceeded a certain height, a siphon attached to a flexible tube was used to remove the excess sand and to level the sample surface. A top cap was then placed on top o f the sample and the sample height was calculated by comparing the dial gauge reading after top cap placement with that with a dummy sample of known height. Once the sample height was known, the void ratio could be determined from the sample volume and the mass of the sand used. After the top cap had been placed, one or two O-rings were slid onto the cap to seal the sample. A vacuum of approximately 20 kPa was then applied to the specimen. The change in sample volume during vacuum application was measured by the change in water level in a reservoir with an inner diameter of 2.34 cm and was used to calculate the final void ratio and relative density, D r , o f the sample prior to the triaxial test. The final step in sample preparation was to assemble the top part of the triaxial cell and f i l l the cell 161 with de-aired water with the 20-kPa vacuum on the sample to prevent possible liquefaction due to excess pore pressure generated by sample disturbance. The triaxial cell was originally designed to have drainage on both ends of the sample. However, the connection between the top cap and the drainage line created considerable sample disturbance and therefore, the top drainage line was not used in the research. Besides loose samples, the water pluviation technique was used to prepare samples with higher relative densities. Most of the procedures were the same as those in loose samples preparation except that low frequency vibration was applied to the base of the triaxial cell during water pluviation. After the top cap had been placed, low frequency vibration was applied to densify the specimen to the desired relative density. Because the dimensions of the mould were known, the relative density during vibration could be estimated from sample height measurements. Vibration was carried on until the height that represented the desired relative density was reached. The sample was then subjected to the 20-kPa vacuum and the cell was filled with de-aired water. The triaxial cell was brought to the triaxial testing machine after it had been filled with de-aired water. Electronic pulses were first applied to the electro-pneumatic transducer connected to the air piston to bring the load cell into contact with the triaxial ram and the L V D T was placed firmly on a rigid plate tightened to the loading ram. Zero readings for the L V D T , pressure transducers and load cell were then taken and the cell and pore pressure lines were connected to the cell and pore pressure transducers, respectively. The existence of air bubbles inside the line was investigated before it was connected to the transducer. Afterwards, the cell and pore pressure valves on the triaxial cell were opened and a negative pore pressure of approximately 20 kPa was recorded by 162 the pore pressure transducer. Ce l l pressure was then increased until the pore pressure reading was zero. In order to determine B-values, the cell pressure was increased in a stepwise fashion and the pore pressure induced in each increment was measured. In each increment of cell pressure increase, the B-value was defined as the ratio of pore pressure increase to cell pressure increase. After a satisfactory B-value had been measured, the drainage valve was opened for a minute to allow the specimen to adjust to any change in effective stress caused by the application of back pressure. Moreover, any change in volume caused by the imbalance between the back pressure and the pore pressure inside the sample was measured and the sample dimensions before the test was started were calculated. 163 

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