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The effect of particle gradation on the undrained behaviour of sand 1987

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THE EFFECT OF PARTICLE GRADATION ON THE UNDRAINED BEHAVIOUR OF SAND by JENNIFER M. FISHER B.E.(Civil)(hons), Canterbury University, N.Z. 1983 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF CIVIL ENGINEERING We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA OCTOBER 1987 © JENNIFER M. FISHER, 1987 4 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 Civil Engineering The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date & October ABSTRACT The e f f e c t of p a r t i c l e gradation on the undrained monotonic and c y c l i c loading behaviour i s presented. Straight l i n e gradations of Earls Creek sand with varying c o e f f i c i e n t s of uniformity and i d e n t i c a l mineralogy and D ^ Q were tested, using the t r i a x i a l t e s t . Improved sample preparation techniques were used to ensure sample uniformity. The data indicates that, under monotonic loading, the r e l a t i v e shear-induced compressibilities due to a v a r i a t i o n in the c o e f f i c i e n t of uniformity are a function of the type of loading. C y c l i c loading tests on i s o t r o p i c a l l y consolidated samples showed that the e f f e c t of p a r t i c l e gradation depends on the r e l a t i v e density. At low r e l a t i v e d e n sities, (less than about 45%), the well graded sand had greater c y c l i c strength than the uniform sand. At high r e l a t i v e densities, (greater than about 60%), t h i s trend was reversed. i i TABLE OF CONTENTS ABSTRACT i i TABLE OF CONTENTS i i i LIST OF TABLES iv LIST OF FIGURES . v NOTATION v i i ACKNOWLEDGEMENTS ix 1. INTRODUCTION 1 2. REVIEW OF PREVIOUS INVESTIGATIONS 5 2.1. GENERAL ASPECTS OF THE UNDRAINED BEHAVIOUR OF SANDS 5 2.2. MONOTONIC LOADING BEHAVIOUR 5 2.3. CYCLIC LOADING BEHAVIOUR 10 2.4. RELATIONSHIP BETWEEN MONOTONIC AND CYCLIC LOADING 16 2.5. THE EFFECT OF PARTICLE GRADATION 17 3..EXPERIMENTATION 21 3.1. TESTING PROGRAM 21 3.2. TESTING APPARATUS 22 3.3. MATERIAL TESTED 24 3.4. SAMPLE PREPARATION AND TESTING TECHNIQUES 28 4. TEST RESULTS 38 4.1. MONOTONIC LOADING BEHAVIOUR 38 4.1.1. Monotonic Compression Results 38 4.1.2. Monotonic Extension Results 52 4.1.3. Review of Monotonic Test Results .... 58 4.2. CYCLIC LOADING BEHAVIOUR 62 5. CONCLUSION 72 REFERENCES 75 LIST OF TABLES 3.1 Material properties 27 iv LIST OF FIGURES 2.1 Charac t e r i s t i c behaviour of saturated sand under monotonic loading 6 2.2 Liquefaction due to c y c l i c loading 12 2.3 Limited li q u e f a c t i o n due to c y c l i c loading 13 2.4 Cyc l i c mobility due to c y c l i c loading 14 3.1 Schematic layout of testing apparatus 23 3.2 Grain size d i s t r i b u t i o n curves 26 3.3 Relationship between volumetric s t r a i n and mean normal stress during consolidation 29 3.4A Sample Preparation by The Slurry Method 31 3.4B Sample Preparation by the Slurry Method .. 32 4.1 Undrained monotonic compression results for Gradation 3 40 4.2 Undrained monotonic compression results for 50 kPa i n i t i a l confining stress 41 4.3 Undrained monotonic compression results for 200 kPa i n i t i a l confining stress 42 4.4 Undrained monotonic compression results for 500 kPa i n i t i a l confining stress 43 4.5 Modified Mohr diagram for undrained monotonic compression for 50 kPa i n i t i a l confining stress. ...45 4.6 Modified Mohr diagram for undrained monotonic compression for 200 kPa i n i t i a l confining stress. ..47 4.7 Modified Mohr diagram for undrained monotonic compression for 500 kPa i n i t i a l confining stress. ..48 4.8 Modified Mohr diagram for undrained monotonic compression for Gradation 1 49 4.9 Modified Mohr diagram for undrained monotonic compression for Gradation 2 50 v 4.10 Modified Mohr diagram for undrained monotonic compression for Gradation 3 ....51 4.11 Modified Mohr diagram showing the phase transformation state 53 4.12 Undrained monotonic extension results for 200 kPa i n i t i a l confining stress 54 4.13 Modified Mohr diagram for undrained monotonic extension for 200 kPa i n i t i a l confining stress 55 4.14 Modified Mohr diagram for undrained monotonic extension for Gradation 1 at 200 kPa confining stress. 59 4.15 Relationship between i n i t i a l r e l a t i v e density, r e l a t i v e density after consolidation and the strength at phase transformation 60 4.16 Modified Mohr diagram for monotonic extension and compression loading for 200 kPa i n i t i a l confining stress 61 4.17 Relationship between r e l a t i v e density and no. of cycles to liq u e f a c t i o n or 2.5 % a x i a l s t r a i n at constant c y c l i c stress ratios for Gradation 1 63 4.18 Relationship between r e l a t i v e density and no. of cycles to liq u e f a c t i o n or 2.5 % a x i a l s t r a i n at constant c y c l i c stress ratios for Gradation 2 64 4.19 Relationship between r e l a t i v e density and no. of cycles to li q u e f a c t i o n or 2.5 % a x i a l s t r a i n at constant c y c l i c stress ratios for Gradation 3 65 4.20 Liquefaction resistance curves for N=10 68 vi NOTATION B Skempton's pore pressure parameter. CSR C r i t i c a l effective stress ratio. C u Coefficient of uniformity. Dr Relative density. D- Relative density after consolidation. Relative density prior to consolidation. DgQ Mean particle diameter or effective grain size of s o i l sample; 50 % by dry weight of sample is smaller than this grain size, e Void ratio. e Void ratio after consolidation, c e„ „ Minimum and maximum void ratios as determined, min max N Number of loading cycles. p' 1/2 (0 , ' + <x3' ). PT Phase transformation. s l/2(a,' + a 3'). t l/2(a,' - a 3'). u Porewater pressure. Au Excess porewater pressure. e , e Axial and volumetric strain, a v 0' Angle of internal f r i c t i o n . 0 Constant volume friction angle, cv Deviator stress. o-£Cy Cyclic deviator stress. V I 1 0 1 a 3 ' Major and minor e f f e c t i v e p r i n c i p a l stresses. o-3c' E f f e c t i v e consolidation pressure in the t r i a x i a l t e s t . r c y Cyclic shear stress = ^ d c y / 2 . T /a, ' Cyclic stress r a t i o . v i i i ACKNOWLEDGEMENTS The author wishes to express her thanks to her supervisor, Dr Y.P. Vaid, for his guidance during this research. The author also wishes to thank Dr D. Negussey for his advice and support throughout the course of thi s research. For assistance in the development of the equipment, Mr Fred Zurkirchen i s thanked. The f i n a n c i a l support of the J.R. Templin T r a v e l l i n g Fund, The National Science and Engineering Research Council of Canada, and The University of B r i t i s h Columbia i s g r a t e f u l l y acknowledged. ix 1. INTRODUCTION During rapid shearing, the development of large deformations in saturated cohesionless s o i l s may occur. These deformations may be the result of the loss of shear resistance or progressive s t i f f n e s s degradation during c y c l i c loading, c a l l e d l i q u e f a c t i o n and c y c l i c mobility respectively. (Castro 1969 & 1975, Seed 1979). Rapid shearing may be the consequence of c y c l i c earthquake loading or monotonic increases in shear stress. The rapid nature of the loading l i m i t s pore pressure d i s s i p a t i o n , hence the behaviour i s considered undrained. Liquefaction i s a s t r a i n softening response, in which highly contractive (loose) sand loses a large percentage of i t s shear resistance and deforms continuously in a state of constant normal e f f e c t i v e and shear stresses, constant volume and constant v e l o c i t y termed steady state. (Casagrande 1976, Castro 1969 & 1975, Seed 1979, Poulos 1981). Equilibrium i s restored only after enormous displacements or settlement. (National Research Council 1985). With c y c l i c mobility, the deformation i s accumulated when c y c l i c loading momentarily reduces the e f f e c t i v e stress to 1 2 zero at the instant when the c y c l i c shear stress passes through zero. Following t h i s , deformation accumulates with each cycle of loading. Deformations are lim i t e d and the earth mass remains stable following shaking without great changes in geometry. Liquefaction i s associated with c y c l i c or s t a t i c loading whereas c y c l i c mobility i s associated with c y c l i c loading only. (Vaid & Chern 1985, Castro 1975, Casagrande 1976, Seed 1979). The concern with l i q u e f a c t i o n i s s t a b i l i t y , while with c y c l i c mobility, i t i s the accumulation of undesirable deformation. Many investigations have been c a r r i e d out to study the effect of various parameters on the undrained monotonic and c y c l i c response of saturated sands. These include parameters such as void r a t i o , e f f e c t i v e confining stress, s t a t i c shear stress, p a r t i c l e angularity, stress path, and prestrain history. (Castro et a l 1982, Chern 1981, Chung 1985, Ishihara et a l 1975, Seed 1979, Tumi 1983, Vaid & Chern 1985). However no investigation has been done which isola t e s and c l e a r l y defines the effect of c o e f f i c i e n t of uniformity on the undrained monotonic and c y c l i c loading behaviour of saturated sand. The c l a r i f i c a t i o n of i t s e f f e c t w i l l improve the understanding of the undrained behaviour of saturated sands. Also, knowledge of-those s o i l c h a r a c t e r i s t i c s which preclude li q u e f a c t i o n i s important in i d e n t i f y i n g i n - s i t u conditions where liquefaction may not be a concern. Substantial benefits w i l l be derived from a better understanding of the l i m i t s on gradation outside which dynamic loss of s o i l strength and liquefaction i n s t a b i l i t y need not be considered. (National Research Council 1985). In t h i s study, the effect of the c o e f f i c i e n t of uniformity on the undrained behaviour of sand i s investigated using undrained monotonic and c y c l i c t r i a x i a l t ests, on i s o t r o p i c a l l y consolidated samples. Three medium sands with s t r a i g h t - l i n e gradations, i d e n t i c a l mineralogy and i d e n t i c a l DgQ are tested. Although idealized s t r a i g h t - l i n e gradations are not found in nature, their use, herein, i s j u s t i f i e d for the same reason as the use of remolded clay in fundamental studies of clay behaviour. S t r a i g h t - l i n e gradations, combined with i d e n t i c a l mineralogy and constant D ^ Q ensure i s o l a t i o n of the effect of gradation for a given medium sand. Constant D ^ Q ensures that membrane penetration i s not a cause of v a r i a t i o n between the results of the d i f f e r e n t gradations. (Frydman et a l 1973). Since well graded sand tends to segregate during conventional water pluviation, improved sample preparation techniques were developed to ensure sample uniformity. Testing of uniform specimens i s a 4 prerequisite for fundamental studies of material behaviour. 2. REVIEW OF PREVIOUS INVESTIGATIONS 2.1. GENERAL ASPECTS OF THE UNDRAINED BEHAVIOUR OF SANDS The undrained response of saturated sand i s t r a d i t i o n l y investigated separately under monotonic and c y c l i c loading conditions. The desire to study each of these loading conditions i s stimulated from quite d i f f e r e n t concerns. Flow s l i d e s , caused by undrained f a i l u r e , have generated the interest in monotonic loading. The concern with c y c l i c loading of sand is mainly with the accumulation of undesirable deformation during earthquake loading. 2.2. MONOTONIC LOADING BEHAVIOUR The three types of responses of an i s o t r o p i c a l l y consolidated saturated sand, subject to undrained t r i a x i a l compression under moderate confining pressures, are shown in Figure 2.1. The st r e s s - s t r a i n curves 1 through 3 represent increasing r e l a t i v e density. Similar behaviour manifests under i n i t i a l anisotropic consolidation. Types 1 and 2 represent the s t r a i n softening or contractive response which i s a behaviour associated with a loss of shear resistance after a peak. The strai n softening response 5 6 1/2{tfi '*03) Figure 2.1: Characteristic behaviour of saturated sand under monotonic loading. (Adapted from Vaid & Chern 1985). 7 is i n i t i a t e d after attainment of a peak deviator stress. Type 1 response is liquefaction as defined by Castro (1969), Casagrande (1976), and Seed (1979). After an i n i t i a l peak strength, continuous deformation occurs at constant confining and shear stress and constant volume, in a state termed steady state. In this steady state, the sand mass flows as a f r i c t i o n a l l i q u i d and hence the association of the term 'flow f a i l u r e ' . (National Research Council 1985). Limited liquefaction i s represented by the type 2 response, in which temporary str a i n softening, similar to that of liq u e f a c t i o n , i s i n i t i a t e d . This transitory loss of shear resistance i s regained with further straining. The e f f e c t i v e stress r a t i o (o^'/o^') at which the stra i n softening response i s i n i t i a t e d i s defined as the C r i t i c a l Stress Ratio (CSR) (Vaid & Chern 1983). The CSR has been shown by a wide body of experimental data to be a constant for a given sand irrespective of the void r a t i o and stress state prior to the commencement of undrained deformation. (Chern 1985). The arrest of the st r a i n softening behaviour in lim i t e d liquefaction i s at the minimum deviator stress. This minimum deviator stress is higher than the deviator stress at steady state in the liquefaction case. At the minimum deviator stress in lim i t e d l i q u e f a c t i o n , d i l a t i o n occurs, the pore pressure begins to decrease, and the e f f e c t i v e stress path takes a sudden turnaround. The state at t h i s point of change has been designated as the Phase Transformation by Ishihara et a l (1975). The e f f e c t i v e stress r a t i o at phase transformation is a material constant for a s p e c i f i c sand. (Ishihara et a l 1975, Vaid & Chern 1985). After the phase transformation, the ef f e c t i v e stress path approaches the undrained f a i l u r e envelope with further s t r a i n i n g . At high deviatoric stresses, the sample may eventually reach steady state. (Castro 1982). With l i q u e f a c t i o n , the ef f e c t i v e stress path terminates at steady state. Failure occurs as a result of large deformations prior to and at steady state, without the stress path reaching the undrained f a i l u r e envelope. The f r i c t i o n angle at phase transformation equals the f r i c t i o n angle at steady state. (Vaid & Chern 1985). Type 3 response depicts the st r a i n hardening or d i l a t i v e response. No loss of shear resistance is experienced. The phase transformation state exists for d i l a t i v e sand also, and corresponds to the point at which d i l a t i o n commences and the pore pressure starts to drop. The phase transformation state for d i l a t i v e and contractive behaviour i s at the same 9 e f f e c t i v e stress r a t i o . (Vaid & Chern 1985). At the phase transformation, in e f f e c t i v e stress space, a turnaround occurs in the stress path although i t may not be di s c e r n i b l e for highly d i l a t i v e states. Under monotonic loading, the steady state l i n e has been proposed by Castro et a l (1977 & 1982) as a boundary in two dimensional (void r a t i o , e c, versus e f f e c t i v e confining pressure, ', at steady state) space between i n i t i a l states prior to undrained loading that are l i q u e f i a b l e and those that are not. States substantially to the right of the steady state l i n e lead to l i q u e f a c t i o n , while those below are nonliquefiable. Sladen, D'Hollander and Krahn (1958) propose the existence of a collapse surface in p'-q-e space. They combine the concepts of steady state with the c r i t i c a l state concept put forward by Roscoe et a l (1958). For a fixed e c, the peak points on the stress paths in p'-q space form a straight l i n e that passes through the steady state point, not through the o r i g i n as proposed by Vaid & Chern (1985). A possible reason for t h i s difference i s that Sladen's model was based on a small number of test r e s u l t s . Sladen also prepared his samples using moist tamping. This technique produces samples with nonhomogenieties. (Castro 1969, Castro et a l 1982). 10 Pluviation, the technique used by Vaid & Chern, forms more homogeneous samples, therefore their results are more reliable. The position of this collapse line is shown by Sladen et al to shift with changes in void ratio, while it s slope remains constant. Drawn in p'-q-e space, these lines combine to form a surface, termed a 'collapse surface'. The behaviour of a sand is stated in terms of i t s stress state relative to the collapse surface. For this collapse surface concept to be used, contactive behaviour is necessary for the definition of a peak in the stress path, and of the steady state line. 2.3. CYCLIC LOADING BEHAVIOUR Sand liquefaction was reported as long ago as 1783 (Hobbs 1907), but i t wasn't until i t caused severe damage in the form of building settlement and t i l t i n g and slope failures during earthquakes in Niigata, Japan and Alaska in 1964 that the phenomenon was begun to be investigated. I n i t i a l research dealt purely with strain development during cyclic loading. This was attributed to the development of states of zero effective stress during some stages of loading. (Seed & Lee 1966). Later i t was recognised that there were two distinctly different mechanisms of strain 11 development : li q u e f a c t i o n , and c y c l i c mobility. (Castro 1969). True l i q u e f a c t i o n , due to c y c l i c loading, i s i l l u s t r a t e d in Figure 2.2. At some stage during c y c l i c loading, liquefaction i s triggered and the sample undergoes unlimited deformation. (Castro 1969). This occurs in a manner similar to that observed under monotonic loading. (See Figure 2.1). Limited l i q u e f a c t i o n , shown in Figure 2.3, occurs with c y c l i c loading as well as with monotonic loading also, (cf Figure 2.1). (Vaid & Chern 1985, Chern 1985). With limited li q u e f a c t i o n , the sand develops a s t r a i n softening response in a manner similar to liquefaction but over a limited s t r a i n range. The CSR, the phase transformation state associated with l i m i t e d l i q u e f a c t i o n and the steady state associated with l i q u e f a c t i o n are the same for monotonic and c y c l i c loading for a given sand. (Vaid & Chern 1985). Cyc l i c mobility due to c y c l i c loading i s shown in Figure 2.4. Cyclic mobility i s caused by the progressive b u i l d up of pore pressure with cycles of loading. If the c y c l i c shear stresses are higher than the s t a t i c shear stresses, i e . a state of stress reversal occurs, and there are s u f f i c i e n t loading cycles, the c y c l i c loading can momentarily reduce 12 Figure 2.2: Liquefaction due to c y c l i c loading. (After Vaid & Chern 1985). 13 3: Limited liquefaction due to c y c l i c loading. (After vaid & Chern 1985).  15 the e f f e c t i v e stresses to zero when the c y c l i c shear stress passes through zero. Deformation then accumulates with each cycle of loading, and attains a f i n i t e magnitude with the completion of loading. If during c y c l i c loading a sp e c i f i e d l e v e l of deformation occurs, i t could be due to limited l i q u e f a c t i o n , c y c l i c mobility or a combination of the two. It should be noted that deformation due to limited l i q u e f a c t i o n always occurs before the r e a l i z a t i o n of momentary states of zero e f f e c t i v e stress. (Vaid & Chern 1985). If liq u e f a c t i o n or limited l i q u e f a c t i o n occurs, the concern i s with s t a b i l i t y because the associated deformations w i l l be very large and unacceptable. If c y c l i c mobility occurs, the concern is with the accumulation of undesirable deformation. The resistance to c y c l i c loading i s defined as the c y c l i c stress r a t i o required to cause contractive deformation or to develop a sp e c i f i e d amount of a x i a l s t r a i n due to c y c l i c mobility in a fixed number of cycles. (Castro et a l 1982, Vaid & Chern 1985). Development of liq u e f a c t i o n i s always associated with the accumulation of a large s t r a i n . 16 2 . 4 . RELATIONSHIP BETWEEN MONOTONIC AND CYCLIC LOADING There i s a c l o s e l i n k between the type of monotonic response and the mechanism by which s t r a i n development o c c u r s under c y c l i c l o a d i n g . ( C a s t r o 1969, C a s t r o et a l 1982, V a i d & Chern 1985). For a sand t o d e v e l o p c o n t r a c t i v e b e h a v i o u r under c y c l i c l o a d i n g ( l i q u e f a c t i o n or l i m i t e d l i q u e f a c t i o n ) , t h e r e a r e 3 r e q u i r e m e n t s : 1. The i n i t i a l s t a t e of the sand must l i e i n the r e g i o n where c o n t r a c t i v e d e f o r m a t i o n would o c c u r under monotonic l o a d i n g , i e . w e l l above the s t e a d y s t a t e l i n e . 2. The maximum shear s t r e s s must exceed the shear s t r e n g t h a t phase t r a n s f o r m a t i o n f o r l i m i t e d l i q u e f a c t i o n or a t stead y s t a t e f o r l i q u e f a c t i o n . 3. There must be a s u f f i c i e n t number of l o a d i n g c y c l e s t o move the e f f e c t i v e s t r e s s s t a t e of the sand t o the CSR s t a t e . ( V a i d & Chern 1985). I t has been shown by V a i d & Chern (1985) t h a t the c o n t r a c t i v e response l e a d i n g t o l i q u e f a c t i o n or l i m i t e d l i q u e f a c t i o n i s i n i t i a t e d a t a c o n s t a n t v a l u e of the c r i t i c a l s t r e s s r a t i o , CSR, which i s independent of the type of l o a d i n g (monotonic or c y c l i c ) . I t i s a l s o independent of the i n i t i a l s t a t e of the sand ( v o i d r a t i o , e f f e c t i v e c o n f i n i n g s t r e s s , and shear s t r e s s ) and of the a m p l i t u d e of 17 c y c l i c stress. The mobilised f r i c t i o n angle at phase transformation, 0 p Pp' f for contractive or d i l a t i v e behaviour i s equivalent to the constant volume f r i c t i o n angle, 0 C V * at steady state. The mobilized f r i c t i o n angles at phase transformation and steady state are independent of confining pressure, i n i t i a l packing density, p a r t i c l e size and p a r t i c l e shape. They are dependent only on the mineral constituency of the material and are consequently unique for a granular material. (Negussey et a l 1986, Wijewickreme 1986). 2.5. THE EFFECT OF PARTICLE GRADATION Most research on the undrained response of sands to c y c l i c and monotonic loading has been done on uniform and clean sands. Uniform clean sands are rarely encounted in natural s o i l deposits and i t i s now known that liquefaction can occur in a variety of situations with s o i l s of d i f f e r e n t properties. (National Research Council 1985). Therefore, i t is necessary to determine the effect of other factors, such as p a r t i c l e gradation, on the response of sand. Lee & F i t t o n (1969) did a study on the effect of grain size, grain size d i s t r i b u t i o n , and grain shape on the strength of 18 s o i l s under simulated earthquake loading conditions. They performed c y c l i c t r i a x i a l tests on an a l l u v i a l sand and gravel deposit from E l Monte, C a l i f o r n i a . They concluded that there was no s i g n i f i c a n t difference in strength between the well-graded and the uniformly graded sand. They ensured that the mineral types were the same for a l l size ranges, although they did not is o l a t e the effect of c o e f f i c i e n t of uniformity. The comparison of samples for the ef f e c t of grain size d i s t r i b u t i o n was done with samples of varying mean diameter, ( D ^ Q ) . A report submitted to the National Science Foundation, Washington DC, by Geotechnical Engineers Inc. (1982) looked at the effect of p a r t i c l e gradation on the steady state l i n e . They concluded that r e l a t i v e l y small differences in grain size d i s t r i b u t i o n s i g n i f i c a n t l y affected the position, but not the shape and slope, of the steady state l i n e . They used fiv e gradations of Banding sand which had varying D ^ Q , so the eff e c t of c o e f f i c i e n t of uniformity was not isol a t e d . Chang, Yeh and Kaufman (1982) studied the e f f e c t of gradation and s i l t content on liquefaction p o t e n t i a l of sand. They did undrained c y c l i c t r i a x i a l tests on a Denver sand. They concluded that for coarse sand, D ^ Q greater than 0.37 mm, the resistance to liqu e f a c t i o n decreases with an 1 9 increase in the c o e f f i c i e n t of uniformity. For fine sands, DgQ smaller than 0 . 2 3 mm, the resistance increases with the c o e f f i c i e n t of uniformity. The e f f e c t of the c o e f f i c i e n t of uniformity vanishes at C u greater than about 8 . The sample preparation technique used was moist tamping, with saturation under back pressure. Moist tamping, however, gives r i s e to samples with densities that are considerably more non-uniform than other methods such as a i r and water pl u v i a t i o n . (Castro 1 9 6 9 , Castro et a l 1 9 8 2 ) . Wong et a l ( 1 9 7 4 ) performed c y c l i c t r i a x i a l tests to investigate the behaviour of "gravelly s o i l s " . They tested s o i l s of constant D ^ Q at a r e l a t i v e density of 6 0 % and found that the well graded gravelly material required a smaller c y c l i c deviator stress than the uniform material to develop 2 . 5 % a x i a l s t r a i n in 1 0 cycles. They proposed that t h i s result could be due to membrane compliance and the fact that the well graded material has some tendency to densify as the fi n e r p a r t i c l e s move into the spaces between the larger p a r t i c l e s . They compared samples at a constant D ^ Q , however the mineralogy varied through the grain si z e s . Thus, some of the observed difference may be due to t h i s aspect. Their tests were also r e s t r i c t e d to one r e l a t i v e density. The National Research Council Report 'Liquefaction of S o i l s i 20 during Earthquakes', Nov. 1985, i d e n t i f i e d the e f f e c t of grain size d i s t r i b u t i o n on dynamic loss of s o i l strength and liq u e f a c t i o n as one of the areas which required research. It was this report which i n i t i a t e d t h i s study. The l i t e r a t u r e review, herein, suggests that no fundamental study has been performed in which the effect of the c o e f f i c i e n t of uniformity has been isol a t e d from other factors which influence the undrained behaviour of sand. In t h i s study, sands of varying C , but i d e n t i c a l mineralogy, s t r a i g h t - l i n e gradations and i d e n t i c a l D ^ Q were tested such that the ef f e c t of gradation on the undrained behaviour could be i d e n t i f i e d . 3. EXPERIMENTATION 3.1. TESTING PROGRAM In order to determine the eff e c t of p a r t i c l e gradation, both monotonic and c y c l i c loading tests were performed on the 3 medium sands of varying c o e f f i c i e n t s of uniformity. A l l tests were undrained and were performed on i s o t r o p i c a l l y consolidated samples. Strain controlled monotonic loading tests were conducted to determine the var i a t i o n due to gradation of the undrained response of the sand to monotonic load. The monotonic loading tests also give an indication of the mechanism of strain response during c y c l i c loading. These tests were performed on the 3 gradations at a constant r e l a t i v e density of 38.5 ± 1.5 %. This density was the minimum density obtainable for Gradation 3 under an i n i t i a l confining pressure of 500 kPa. The lowest possible density states were selected in order to provide the most favourable conditions for the occurence of contractive deformation. Tests in the compression mode were car r i e d out for i n i t i a l confining pressures of 50, 200 and 500 kPa. Tests in the extension mode were performed for an i n i t i a l confining pressure of 200 kPa only. 21 Stress c o n t r o l l e d c y c l i c loading tests were performed to determine the resistance curves to c y c l i c loading for the 3 gradations, so that the behaviour could be compared. A l l c y c l i c tests were car r i e d out for an i n i t i a l confining pressure of 200 kPa. The c y c l i c stress r a t i o , ( a a C y / 2 a 3 C ' )» was varied between 0.123 and 0.23. The r e l a t i v e density was varied between 22 and 73 % depending on the c y c l i c stress r a t i o and the gradation of the sand being tested. 3.2. TESTING APPARATUS A schematic layout of the testing apparatus for the stress controlled c y c l i c loading tests i s given in Figure 3.1. The c y c l i c a x i a l load was applied using a double-acting a i r piston. I n i t i a l l y the pressures in the two chambers of the piston are equal and the loading ram i s at rest. The pressure in the bottom chamber of the piston i s controlled by a pressure regulator. Volume boosters are connected to the top and bottom chambers of the piston to ensure that there i s no degredation of the load pulse when large deformations occur. The c y c l i c load i s applied through the top chamber of the piston. It i s applied by an electro-pneumatic transducer which i s driven by the function generator. The maximum output of the electo-pneumatic 23 LVDT Double-acting Air Piston. 'Volume ' Ratio Booster Relay l l f ^Function ( R V Generator — Load Cell A TT n TE Pressure Regulator Electro- pneumatic Transducer To Recorder i "ir" r- Cell Pressure (ft V Transducer —H I Pore Pressure Transducer Figure 3 . 1 : Schematic layout of testing apparatus. 24 transducer i s 103 kPa, so the r a t i o r e l a y was i n c l u d e d to am p l i f y the pressure p r o v i d e d to the p i s t o n . The monotonic l o a d i n g t e s t s were performed using a l a y o u t s i m i l a r to the c y c l i c l o a d i n g system, i n which the a i r p i s t o n was r e p l a c e d by a s t r a i n d r i v e . An a d j u s t a b l e speed DC motor was used to p r o v i d e the s t r a i n c o n t r o l l e d l o a d i n g r e q u i r e d f o r the t e s t s . The l o a d , deformation, and pore pressure i n the sample were recorded d u r i n g the t e s t . 3 . 3 . M A T E R I A L T E S T E D The sand used i n t h i s study i s a n a t u r a l r i v e r d e p o s i t from E a r l s Creek, B r i t i s h Columbia, obtained from the Vancouver M u n i c i p a l yards having been t r a n s p o r t e d from E a r l s Creek by barge. The sand i s used l o c a l l y f o r b a c k f i l l i n g trenches and i n the p r o d u c t i o n of a s p h a l t mix. E a r l s Creek sand i s sub-angular, with p a r t i c l e s i z e s ranging from 0.06 mm to 5 mm. The sand f r a c t i o n which passed through the #8 s i e v e was d i v i d e d i n t o 12 g r a i n s i z e ranges by s i e v e s ranging from #10 to #200. These g r a i n s i z e s were then combined to form 3 2 5 l i n e a r gradations with a constant D^Q of 0 . 4 2 mm. The gradations 1, 2 , and 3 have c o e f f i c i e n t s of uniformity of 1 . 5 , 3 , and 6 respectively. The linear grain size d i s t r i b u t i o n curves of these gradations are shown in Figure 3 . 2 , along with that of the o r i g i n a l Earls Creek sand. The mineral composition of the sand i s approximately 5 0 % quartz and 3 0 % feldspar with the remaining being hornblende, clinopyroxene, b i o t i t e mica, and sphene. The composition i s uniform over the entire range of grain sizes which allows for the i s o l a t i o n of the effect of the c o e f f i c i e n t of uniformity. Maintaining a constant D^Q was also chosen to f u l f i l l t his requirement. The membrane penetration into the voids of a specimen of granular s o i l , due to application of a p a r t i c u l a r ambient pressure, i s a function of the D^Q of the s o i l , and not i t s gradation. (Frydman et al.1973). Consequently, any differences in behaviour between the 3 gradations i s not caused by a v a r i a t i o n in the membrane penetration. The minimum and maximum void r a t i o s , c o e f f i c i e n t s of uniformity, and p a r t i c l e size range for the 3 gradations are given in Table 3.1. The minimum and maximum void r a t i o s , (e •„ and e ), were obtained in accordance with the min max ' standard test method, ASTM D 2 0 4 9 . There is a large variation  27 Gradation Cu emax emin P a r t i c l e Size Range (mm) 1 1 .5 0 .94 0.63 0.3-0.59 2 3 0.77 0.51 0.15-1.2 3 6 0.61 0.37 0.074-2.4 Table 3.1: Material properties. in e „ and e •„ between the gradations, however, there is max mm 5 ' ' not much va r i a t i o n in (e m„ -e •„). max min The s p e c i f i c gravity was obtained using the method recommended by Lambe (1951) and i s constant at 2.72 for the 3 gradations. The hydrostatic consolidation c h a r a c t e r i s t i c s of the 3 gradations, for a r e l a t i v e density of 38.5% at 500 kPa confining pressure, are shown in Figure 3.3. The consolidation c h a r a c t e r i s t i c s are given in terms of the re l a t i o n s h i p between volumetric s t r a i n and mean normal stress during consolidation. The well graded sand i s more compressible than the uniform sand, shown by the well graded sand developing higher volumetric strains than the uniform sand at constant mean normal stress. 3.4. SAMPLE PREPARATION AND TESTING TECHNIQUES Sample homogeneity, uniformity of density and saturation were the prime requirements for sample reconstitution. It was found that pluviation through a i r or water caused segregation, therefore a new method of sample preparation, c a l l e d 'the slurry method', was developed by Ralph Keurbis (1987). This method resulted in homogeneous and uniform * Gradation 1 « Gradation 2 o Gradation 3 2 0 0 I 4 0 0 P ' (kPa) Figure 3.3: Relationship between volumetric s t r a i n and mean normal stress during consolidation. 30 specimens. Uniformity was v e r i f i e d by an analysis of the grain size d i s t r i b u t i o n and void r a t i o throughout the sample. A sample was formed using gel mixed with the porewater. When the sample had s o l i d i f i e d , i t was cut into 4 sections and the void r a t i o and grain size d i s t r i b u t i o n were calculated for each section. The v a r i a t i o n between the void ratios of the s l i c e s was 1.5 %, while for the grain size d i s t r i b u t i o n s , the v a r i a tion in the percent finer by weight was 2 %. (Keurbis 1987). The samples had a diameter of 637 mm and an average height of 123 mm. I n i t i a l l y , the sand and the porous disks were boiled for a period of 10 minutes to insure saturation, (see Figure 3.4a). The sand was then transferred by water pluviation into deaired water in a cylinder which was plugged at one end. (see Figure 3.4b). The cylinder has an outside diameter of 60 mm and thus can f i t inside the sample former. The length of the cylinder was such that there was s u f f i c i e n t water present to allow mixing of the sand-water s l u r r y , but not too much such that segregation did not occur on inversion. a SAND BOILED IN HATER TO DE-AIR; b SAND PLUVIATED INTO MUINS TUBE 31 RUBBER HEHBRANE SEAL GLUED TO ONTO BASE PLATEN OF TRIA1IAL TEST APPARATUS Figure 3.4A: Sample preparation by 'The Slurry Method'. (Adapted from Keurbis 1987). T K I A I I M . U S ! BASE PLATEK e H U M S TUBE PLACED UPON TRIAIIAL TEST APPARATUS BASE PLATEN IN MATER BATH; RUBBER MEMBRANE IS ROLLED UP SIDES OF fill INS TUBE RUBBER ItENBRANE STRETCHED ONTO SAMPLE FORHER TUBE f 5AHPLE FORHER TUBE ASSEMBLED AROUND M1XINB TUBE; SAMPLE MEMBRANE STRETCHED OVER SAMPLE FORMER TUBE; APPLICATION OF VACUUM TO FORMER TUBE EIPANDS MEMBRANE AND DRANS IN RESERVOIR MATER FROM ABOVE, MA1NIAININS SATURATION g till INS TUBE WITHDRAWN LEAVINS LOOSE SATURATED UNIFORMLY MIIED SAMPLE IN FORMER TUBE; TOP OF SAMPLE CAREFULLY FLATTENED Figure 3.4B: Sample preparation by 'The Slurry (Adapted from Keurbis 1987). Method'. co to 33 The s a n d - f i l l e d cylinder was then immersed in a water bath. The porous base disk, 637 mm in diameter and 4.7 mm thick, was transferred under water to the top of the cylinder and held in place by a section of membrane. It was insured that there was no a i r within the cylinder or trapped between the membrane, stone, and cylinder such that water tension would hold the stone in place when the cylinder was inverted. There was a rubber seal on the end of the cylinder so a good seal between the porous disk and the cylinder was maintained, (see Figure 3.4c). The cylinder was removed from the water bath. An aluminium disk was then placed on top of the porous disk to prevent i t s desaturation during mixing. The sample was then mixed thoroughly, (see Figure 3.4d). Preparation of the base of the c e l l was done in a water bath. The 0.012 inch thick membrane was fixed to the base pedestal with an 0 ring, and the a i r removed from between the pedestal and the membrane. The membrane was then r o l l e d down such that i t did not protrude above the top of the base pedestal. When the sand was mixed to an homogeneous state, the cylinder was inverted with care to prevent segregation, 34 porous disk down, the aluminium disk removed and the connective membrane c a r e f u l l y pulled away from the face of the porous disk. The cylinder was then placed on the base pedestal, having removed any a i r bubbles from the face of the porous disk under water, (see Figure 3.4e). A firm downwards pressure was then maintained on the cylinder, the connective membrane removed, and the test membrane r o l l e d up the outside of the cylinder. The c e l l base was then removed from the water bath and the sample former put in place. The membrane was pulled away from the cylinder, and held in place within the former with a vacuum of about 7.5 cm of Hg. This was done with the base drainage open to a reservoir and a supply of deaired water to the top of the base disk to prevent desaturation of the porous disk, (see Figure 3.4f). The plug was removed from the top of the cylinder, and the excess water on top of the sand eviscerated to prevent overflow on removal of the cylinder. The cylinder was then removed with one slow continuous movement. Continuity i s required to prevent segregation of the grainsizes. (see Figure 3.4g). The top of the sample was leveled, then the top cap placed 35 and leveled. Next the sample was densified by vibration maintaining double drainage u n t i l the i n i t i a l placement density required. A gentle pressure was maintained on the top cap during den s i f i c a t i o n to prevent the possible formation of a loose surface layer which would lead to an underestimation of the liquefaction resistance. The top drainage l i n e was then closed and the membrane sealed to the top cap with an 0 ring. The sample was applied a suction of about 12 cm of Hg (17 kPa), the sample former removed, and the c e l l put together. The c e l l was then f i l l e d with deaired water and placed and centred on the loading frame. A small c e l l pressure was applied to overcome suction, and the pore pressure l i n e s were then connected. The sample was now checked for saturation. Samples were only accepted i f a Skempton's pore pressure parameter, B, of at least 0.99 was obtained. Consolidation of the sample to the required stress with basal drainage only was then performed. This was done by increasing the c e l l pressure, step-wise, such that the consolidation c h a r a c t e r i s t i c s of the sample could be monitored. At the f i n a l consolidation stress, the equilibrium readings were taken after the secondary consolidation, i f any, had taken place. This was to ensure 36 •that pore pressure b u i l d up due to secondary consolidation did not eff e c t the results during the shearing phase. For the sands tested, the secondary consolidation phase took approximately 10 minutes. Tests were performed to determine the membrane penetration for the 3 gradations and the correction for each was applied to the volume changes in the consolidation phase. The corrections for the 3 gradations were found to be approximately equal. This is in accordance with Frydman et a l (1973) who concluded that membrane penetration i s a function of D ^ Q only and not of gradation. After consolidation the loading ram was connected to the loading piston. An eyed connecting ring was used to minimize the disturbance to the sample during connection and to prevent i t s premature loading. The sample was now ready to be loaded. The mean grain size i s 0.42 mm and thus the permeability of the sand i s high. Consequently, the rate of testing in the monotonic loading tests has no e f f e c t on the results on account of possible end r e s t r a i n t . A constant rate of s t r a i n of 0.4 % a x i a l s t r a i n per minute was used for convenience. 37 During the monotonic tests, the a x i a l load, porewater pressure, and a x i a l deformation were monitored by electronic transducers and recorded using a data a c q u i s i t i o n system, coupled to a computer. Constant shear stress amplitude c y c l i c tests were performed. A sinesoidal load pulse with a frequency of 0.1 Hz was used. The low frequency loading was used to be compatible with the low frequency response c a p a b i l i t i e s of s t r i p chart recorders. During each test, the c y c l i c a x i a l load, porewater pressure, and a x i a l deformation were continuously monitored by electronic transducers and recorded on a s t r i p chart recorder. Corrections were made to the data for rod f r i c t i o n , and membrane strength. (Bishop & Henkel 1962). 4. TEST RESULTS In t h i s chapter, the undrained monotonic loading behaviour of the i s o t r o p i c a l l y consolidated samples i s discussed f i r s t , subdivided into the compression mode, the extension mode, and a discussion of isotropy. The c y c l i c results are then discussed. The basis of comparison of the tests is i d e n t i c a l r e l a t i v e density which i s the approach taken by other researchers. 4.1. MONOTONIC LOADING BEHAVIOUR Undrained monotonic loading tests were performed on i s o t r o p i c a l l y consolidated samples at a constant r e l a t i v e density of 38.5 ± 1.5 %. Tests were performed in both the compression and extension modes. The compression modes w i l l be discussed f i r s t . 4.1.1. Monotonic Compression R e s u l t s Monotonic compression tests were performed for i n i t i a l confining pressures of 50, 200 and 500 kPa, for a r e l a t i v e density of 38.5 ± 1.5 %. Additional tests were carr i e d out at each confining pressure for every gradation in order to 38 ensure the repeatability of the t e s t s . For Gradation 3, for an i n i t i a l confining pressure of 500 kPa, Figure 4.1 presents the results of 2 tests at e s s e n t i a l l y i d e n t i c a l r e l a t i v e density, given in terms of the deviatoric stress and excess porewater pressure as a function of a x i a l s t r a i n . These results show excellent r e p e a t a b i l i t y of the tests, r e f l e c t e d in the s i m i l a r i t y in porewater pressure and deviatoric stress developed. This confirms the uniformity and consistency of the samples prepared by 'the slurry method.' The test performed at a r e l a t i v e density of 39.9% i s s l i g h t l y more d i l a t i v e than the test at 38.7% r e l a t i v e density, probably due to i t s s l i g h t l y higher density. (Seed & Lee 1966, Castro 1969, Casagrande 1976, Vaid & Chern 1985). The increased dilativeness i s shown by the s l i g h t l y higher deviatoric stresses and lower porewater pressures induced. Results of the deviatoric stress and the excess porewater pressure as a function of a x i a l s t r a i n , for i n i t i a l confining pressures of 50, 200, and 500 kPa, are given in Figures 4.2, 4.3, and 4.4 respectively. A l l samples tested in monotonic compression, regardless of the c o e f f i c i e n t of uniformity, exhibited str a i n hardening or d i l a t i v e behaviour. The response of a l l the samples was that of type 3, shown in Figure 2.1, in that the samples at no time  £ a (V.) Figure 4.2: Undrained monotonic compression results for 50 kPa i n i t i a l confining stress.  400 Figure 4.4: Undrained monotonic compression results for 500 kPa i n i t i a l confining stress. 44 experienced a loss of shear resistance. It was not possible to explore the region of contractive behaviour at other r e l a t i v e densities over the range of confining pressures used, since specimens looser than a r e l a t i v e density of about 38 % could not be prepared by the slurry deposition technique. The deviatoric stress and the excess porewater pressure as a function of a x i a l s t r a i n for the compression test for an i n i t i a l confining pressure of 50 kPa i s given in Figure 4.2. The re s u l t s show that an increase in the c o e f f i c i e n t of uniformity causes the behaviour to be less d i l a t i v e . This is ref l e c t e d by the fact that the well graded sample sustained lower deviatoric stresses and developed higher porewater pressures than the uniform sample. This relationship can also be observed for the compression tests at 200 and 500 kPa i n i t i a l confining pressure, Figures 4.3 and 4.4 respectively. The stress paths for the monotonic compression loading for 50 kPa i n i t i a l confining pressure, plotted on the Modified Mohr diagram are given in Figure 4.5. As evidenced in the deviatoric stress and excess porewater pressure vs a x i a l s t r a i n p l o t , Figure 4.2, the stress paths indicate the strai n hardening response, type 3, as shown in Figure 2.1. 100 90 H 80 70 H 62c' = 50 kPa Gradation 1 , D r c * Gradation 2 , D r c 0 Gradation 3 / D 1 0 20 40 60 80 100 120 V2(0^6f3) (kPa) Figure 4.5: Modified Mohr diagram for undrained monotonic compression at 50 kPa i n i t i a l confining stress. 46 The effect of the increasing c o e f f i c i e n t of uniformity, causing a less d i l a t i v e tendency, can also be seen in thi s Figure. This i s reflected by the well graded sand developing greater porewater pressure than the uniform sand. This i s shown by the r e l a t i v e horizontal s h i f t s of the e f f e c t i v e stress paths from the drained loading condition. The Modified Mohr diagrams for the monotonic compression tests at i n i t i a l confining pressures of 200 and 500 kPa, Figures 4.6 and 4.7 respectively, show that t h i s trend i s continued at higher confining pressures, i e . an increase in the c o e f f i c i e n t of uniformity causes the behaviour to become less d i l a t i v e . The undrained f r i c t i o n angle at maximum obli q u i t y i s found to be constant at 37.2 ± 0.7 degrees regardless of the gradation as shown in Figures 4.8, 4.9 and 4.10. The undrained f r i c t i o n angle at maximum obliquity i s a constant for a given sand. (Seed & Lee 1967, Chern 1985). The drained f r i c t i o n angle, however, i s affected by the dilatancy of the sand at f a i l u r e , which i s controlled by the l e v e l of confining pressure and r e l a t i v e density. (Lambe & Whitman 1 969) . The stress state at phase transformation for a l l monotonic compression tests performed, regardless of r e l a t i v e density, Figure 4.6: Modified Mohr diagram for undrained monotonic compression at 200 kPa i n i t i a l confining stress. 500 1 / 2 ( a l ' * a 3 / ) (kPa) Figure 4.7: Modified Mohr diagram for undrained monotonic co compression at 500 kPa i n i t i a l confining stress.  600 Gradation 2 0 200 400 600 V 2 W 1 / * ( J 3 / ) (kPa) Figure 4 . 9 : Modified Mohr diagram for undrained monotonic compression for Gradation 2. 500 0 200 400 600 800 V 2 ( C T 1 ' + Cfj) ( k P a ) ure 4.10: Modified Mohr diagram for undrained monotonic compression for Gradation 3 52 is shown in Figure 4.11. The data points may be seen to l i e on a straight l i n e passing through the o r i g i n . Hence the f r i c t i o n angle mobilized at phase transformation i s a constant at 32.9 degrees regardless of gradation. This would have been expected since the mineralogy is constant over the f u l l p a r t i c l e size range. Negussey et a l (1986) determined that, for a given mineralogy, the f r i c t i o n angle mobilized at phase transformation was independent of the p a r t i c l e s i z e , confining pressure, porewater pressure, and density. This observation can now be extended to include gradation. 4 .1.2. Monotonic Extension R e s u l t s Monotonic loading tests in the extension mode on the 3 gradations were performed for a constant i n i t i a l confining stress of 200 kPa. Comparative results at i d e n t i c a l r e l a t i v e density in terms of the deviatoric stress and excess porewater pressure vs a x i a l s t r a i n and the stress paths on the Modified Mohr diagram are given in Figures 4.12, and 4.13 respectively. The results~indicate that as the c o e f f i c i e n t of uniformity increases, the behaviour becomes more d i l a t i v e under extension loading. This i s re f l e c t e d by the fact that as the c o e f f i c i e n t of uniformity increases, the sand sustains higher deviatoric stresses as shown in Figure 4.12, and i t develops lower porewater pressures as es 150 E Q ( V . ) Figure 4.12: Undrained monotonic extension results for 200 kPa i n i t i a l confining stress. •160 -180 - -200 - -220 -240 H -260 CC = 200 kPa A Gradation 1 * Gradation 2 o Gradation 3 Drc = Drc = Drc = 36- 7 % 37- 9 V . 39-3 V . 100 200 1 /2 ( t f 1 / *<$ 3 ) (kPa) 300 Figure 4.13: Modified Mohr diagram for undrained monotonic extension for 200 kPa i n i t i a l confining stress. 400 56 shown in Figures 4.12 and 4.13. This i s the reverse to the trend i d e n t i f i e d when similar samples are subject to compression loading. Gradation 1, the more uniform sample, exhibits contractive behaviour. The response i s that of type 2, Figure 2.1, li m i t e d l i q u e f a c t i o n . The sample suffers a temporary loss of shear resistance which i s regained with further s t r a i n i n g . Gradations 2 and 3, with c o e f f i c i e n t s of uniformity of 3 and 6 respectively, on the other hand, show a s t r a i n hardening response, type 3, Figure 2.1. The plateau of deviatoric stress observed, in Figure 4.12, in Gradation 3 at 3.8 % a x i a l s t r a i n , and in Gradation 2 at 4.2 % a x i a l s t r a i n i s caused by necking of the sample. This necking also causes the sharp turn around in the stress paths in Figure 4.13. Necking in Gradation 1 occured gradually, and i s shown by the gradual change of the slope of the stress path after the phase transformation state in Figure 4.13. The f r i c t i o n angle mobilized at phase transformation, under extension loading is 32.9 degrees. Thus, th i s angle i s the same under compression and extension loading. This was also observed by Chern (1985) and Chung (1985) for other sands. I n i t i a l conditions which give r i s e to a d i l a t i v e response under monotonic loading, can develop only c y c l i c mobility under c y c l i c loading. If a contractive response i s obtained under monotonic loading, c y c l i c loading can give r i s e to l i q u e f a c t i o n , limited l i q u e f a c t i o n , or c y c l i c mobility. Contractive response was obtained only with Gradation 1 under extension loading at r e l a t i v e densities of less than about 48 %. for the selected i n i t i a l confining pressure of 200 kPa. In extension, provided contractive response ensues, the strength at phase transformation, S p T, is a function of i n i t i a l r e l a t i v e density, D^, as well as the r e l a t i v e density a f t e r consolidation, D r c • (Chung 1985). Consequently, further tests were performed on Gradation 1 under monotonic extension loading to determine the r e l a t i o n s h i p between D^, D r c, and S p T to a s s i s t in a rat i o n a l interpretation of the c y c l i c loading results in respect of the mechanism of s t r a i n development. Extension tests were performed on samples for a constant i n i t i a l confining stress of 200 kPa, with the r e l a t i v e density before consolidation, Dr^, varying between 16.3 and 47.8 %. Figure 4.14 shows the stress paths on a Modified Mohr diagram for 2 of these tests, for a constant i n i t i a l 58 confining stress of of 200 kPa. The angle of internal f r i c t i o n mobilized at phase transformation can be seen to be a constant of 32.9 degrees regardless of r e l a t i v e density. The r e l a t i v e density, however, governs the strength at phase transformation. The angle of internal f r i c t i o n mobilized at the C r i t i c a l Stress Ratio i s also a constant at 17.8 degrees, regardless of the r e l a t i v e density, as shown in Figure 4.14. The relationship between S p T, D^, and D r c i s given in Figure 4.15. The relationship between D r c and S fc was determined at Dr^ = 34.5 %. For additional D ri's» one test was ca r r i e d out and the relationships were assumed p a r a l l e l . As D r c and/or Dr^ increases, the strength at phase transformation, S p T, increases. 4.1.3. Review of Monotonic Test Results The e f f e c t i v e stress paths on a Modified Mohr diagram for the monotonic compression and extension tests at D f c = 38.5 ± 1.5 % and for 200 kPa i n i t i a l confining pressure are shown in Figure 4.16. Under compression loading, the well graded sand i s more contractive than the uniform sand, as i t develops higher porewater pressures. This appears to be in * Drj = 47-8 7. , D r c = 52-3 V. I I I I 1 1 1 1 1 1 ! — f — 0 40 80 120 160 200 240 v 2 (cr; • cr;) (kPa) Figure 4.14: Modified Mohr diagram for undrained monotonic vo extension for Gradation 1 at 200 kPa i n i t i a l confining s t r e s s . 60 Figure 4.15: Relationship between i n i t i a l r e l a t i v e density, relative density after consolidation and the strength at phase transformation. * Gradation 2 ° Gradation 3 0 200 400 600 V2(0 , 1 /*0 3 /) (kPa) Figure 4.16: Modified Mohr diagram for monotonic extension and compression loading for 200 kPa i n i t i a l confining stress. 62 conformity with consolidation test r e s u l t s , Figure 3.3, that show that the well graded sand i s more compressible than the uniform sand under hydrostatic load. The e f f e c t i v e stress paths in Figure 4.16 show that the r e l a t i v e porewater pressure development of the 3 gradations under compression loading i s reversed under extension loading. Thus, r e l a t i v e shear-induced c o m p r e s s i b i l i t i e s under monotonic loading are not constant for a given sand but a function of the type of loading, i e . compression or extension. 4.2. CYCLIC LOADING BEHAVIOUR Cycl i c loading tests were performed on i s o t r o p i c a l l y consolidated samples at a constant i n i t i a l confining stress, a 3 c ' , of 200 kPa. The c y c l i c stress r a t i o / a 3 c ' ) , and r e l a t i v e density were the variables. The results are presented in the plots of r e l a t i v e density against the no. of cycles to liq u e f a c t i o n (or limited liquefaction) or 2.5 % a x i a l s t r a i n for constant c y c l i c stress r a t i o s in Figures 4.17, 4.18, and 4.19, Gradations 1, 2, and 3 respectively. For gradations 2 and 3, a l l samples achieved 2.5 % a x i a l s t r a i n through c y c l i c mobility, following f i r s t r e a l i z a t i o n of a state of transient zero e f f e c t i v e stress. For the same i n i t i a l density and stress states, the behaviour of — i 1 r Gradation 1 ^cy/oVc ° 0-124 * 0 1 3 5 D 0 - H 8 A 0 1 9 0 * 0-230 20 40 60 80 100 Liquefaction I 62c = 200 kPa 2 4 6 o 10 20 40 60 80 100 No. of Cycles to Liquefaction or 2-5% Axial Strain Figure 4.17: Relationship between r e l a t i v e density and no. of cycles to l i q u e f a c t i o n or 2.5 % axial strain at constant c y c l i c stress r a t i o s for Gradation 1. 80 100 No. of Cycles to Liquefaction or 2-5% Axial Strain Figure 4.18: Relationship between relative density and no. of cycles to liquefaction or 2.5 % axial strain at constant c y c l i c stress r a t i o s for Gradation 2. i r 20 AO 60 80 100 Gradation 3 £cy/03c 0 0-136 " 0H8 ° 0-163 A 0-213 tf3'c z 200 kPa l X 2 4 6 8 10 20 40 60 80 100 No. of Cycles to Liquefaction or 2-5% Axial Strain Figure 4.19: Relationship between relative density and no. of cycles to liquefaction or 2.5 & axial strain at constant cyclic stress ratios for Gradation 3. 0 1 66 Gradations 2 and 3 under monotonic loading was d i l a t i v e in extension and compression, therefore l i q u e f a c t i o n (or limited liquefaction) under c y c l i c loading in t h i s stress range could not occur. Under monotonic extension loading, Gradation 1 was contractive over a range of r e l a t i v e densities for the selected 200 kPa i n i t i a l confining pressure. Thus under c y c l i c loading, Gradation 1 can develop d i l a t i v e or contractive behaviour. Contractive behaviour under c y c l i c loading was developed i f the 3 requirements l i s t e d in Section 2.4 were met, i e . the i n i t i a l state would lead to contractive behaviour under monotonic loading, the shear stress was greater than the strength at phase transformation, and there were s u f f i c i e n t cycles. Those samples that met these requirements, i e . developed li q u e f a c t i o n or limited l i q u e f a c t i o n , are marked by an 'L' in Figure 4.17. If liquefaction occured, the r e l a t i o n s h i p in D r vs log N space, for a fixed c y c l i c stress r a t i o , i s approximately l i n e a r . This relationship is exhibited by tests at c y c l i c stress ratios of 0.124, 0.135 and 0.148, in Figure 4.17. This behaviour i s similar to observations made by Castro (1982) and Vaid & Chern (1983). As the r e l a t i v e density increases, the shear strength at 67 phase transformation, s p T » increases. Consequently, the c y c l i c shear stress required to i n i t i a t e contractive deformation also increases. Therefore as the r e l a t i v e density increased, the range of i n i t i a l stress states for d i l a t i v e behaviour increased, and the response of the sand tested changed from liquefaction to c y c l i c mobility. When lique f a c t i o n occured, i t was i n i t i a t e d in the extension phase in a l l cases. Gradation 1 portrayed contractive behaviour under monotonic extension only. Consequently, the potential for l i q u e f a c t i o n under c y c l i c loading in t h i s stress range was in the extension phase. A comparison of the resistance of the 3 gradations to c y c l i c loading i s given in Figure 4.20. The data i s presented in terms of the c y c l i c stress r a t i o required to induce liquefaction or 2.5 % a x i a l s t r a i n in 10 stress cycles for a range of r e l a t i v e d e n s i t i e s . From Figure 4.20, c e r t a i n trends can be i d e n t i f i e d . At low r e l a t i v e densities, (less than about 45 % ) , the uniform sand, Gradation 1, has the least resistance to c y c l i c loading. This i s the range of densities over which Gradation 1 was contractive under extension loading. The resistance increases as the sand becomes more well graded. The increase may be related to both improved gradation, as 0.25 0.24 0.23 0.22 0.21 0.2 ^ 0 . 1 9 "^0.18 o I ° 0.17 0.16 0.15 0.14 0.13 0.12 0.11 0.1 N = 10 A Gradation 1 x Gradation 2 o Gradation 3 0 3 C = 200 k P a E a = 2 -5 % 20 Liquefaction 40 ~T~ 60 80 D r c (°/o Figure 4 . 2 0 : Liquefaction resistance curves for N=10. 69 well as the change in the mechanism of deformation from liquefaction to c y c l i c mobility. The c y c l i c strength of every sand increases with increasing r e l a t i v e density. As the c o e f f i c i e n t of uniformity increases, less benefit appears to be derived from increasing the r e l a t i v e density, i e . less strength i s gained. This i s evident from the slopes of the l i n e s in c y c l i c stress r a t i o - r e l a t i v e density space. (Figure 4.20). This trend causes the r e l a t i v e strengths of the gradations to be reversed at high r e l a t i v e densities, (greater than about 60 % ) , with the well graded sand sustaining a lower c y c l i c stress r a t i o than the uniform sand at the same re l a t i v e density. These res u l t s are generally supported by those of Wong et a l (1974), who showed that at a r e l a t i v e density of 60 %, a well graded sand required a smaller c y c l i c deviator stress than a uniform material to develop 2.5 % a x i a l s t r a i n in 10 cycles. The basis of the comparison of the undrained behaviour of the 3 gradations of Earls Creek sand i s i d e n t i c a l r e l a t i v e density. This basis, however, may not be completely sati s f a c t o r y due to the large range in absolute density. The 70 stress-deformation and shear strength are not only affected by the r e l a t i v e density, but also by the absolute density, i e . the grain size d i s t r i b u t i o n , (de Beer 1965). For the 3 gradations of Earls Creek sand tested, the large variation in absolute density between the gradations preclude i t s use as a basis of comparison. On examination of Figure 4.20, i t can be seen that at high D r, (greater than about 60 % ) , an attempt to compare the l i q u e f a c t i o n resistance curves at an i d e n t i c a l absolute density, however, would push the curves further apart. This i s due to the fact that the uniform sand, Gradation 1, has the highest c y c l i c shear strength but the lowest absolute density. Consequently, normalization of the liquefaction resistance curves with respect to absolute density would exaggerate the trend already shown at high r e l a t i v e densities. The state parameter has been proposed as an alternative i n i t i a l parameter to r e l a t i v e density. The state parameter defines the state of the sand as a function of i t s position r e l a t i v e to the steady state l i n e in e-log p' space. (Been & J e f f e r i e s 1985). However the state parameter i s not unique in extension and compression. (Chern 1985). Also the state parameter i s only defined for sands which exhibit contractive behaviour, as for d i l a t i v e behaviour, the steady state l i n e does not e x i s t . The state parameter cannot be used here as, for the stress range considered, of the 3 gradations that were tested, only Gradation 1, the more uniform sand, tested in extension, exhibited contractive behaviour. The stress range considered here i s relevant most applications. 5. CONCLUSION In order to determine the effect of the coefficient of uniformity on the undrained behaviour of sand, undrained monotonic and cyclic t r i a x i a l tests were performed on 3 sands of varying straight line gradations, with identical mineralogy and identical Dgg. Monotonic tests in compression and extension were performed at constant relative density, D r c ' a n c^ " i t * 1 i n i t i a l confining stresses varying up to 500 kPa. Undrained cyclic tests were performed from a constant isotropic effective confining stress of 200 kPa, with varying relative density and cyclic stress ratios. A l l the samples that were tested, were isotropically consolidated. Based on the test results, several conclusions can be drawn. Under monotonic compression loading, the sand becomes less dilative as the coefficient of uniformity increases, ie. as the sample becomes more well graded. The compressibility of the sand increasing with gradation is also exhibited under hydrostatic loading during consolidation. Under monotonic extension , the opposite trend is observed, with the sand becoming more dilative as the gradation increases. Thus, the relative shear-induced compressibilities are a function of the undrained stress path. 72 73 Under c y c l i c loading, at low r e l a t i v e densities, (less than about 45 % ) , increased c y c l i c strength is obtained by increasing the c o e f f i c i e n t of uniformity. C y c l i c loading induced l i q u e f a c t i o n or lim i t e d l i q u e f a c t i o n in the uniform sample, while the deformation in the more well graded samples accumulated by c y c l i c mobility. Increasing the r e l a t i v e density causes a greater c y c l i c strength increase in the more uniform samples. Thus at high r e l a t i v e d e n sities, (greater than about 60 % ) , the well graded samples show greater propensity towards deformation accumulation. At these high r e l a t i v e densities the deformation was caused by c y c l i c mobility. At low r e l a t i v e d e n sities, the uniformly graded sand was found to have a much lower c y c l i c resistance than the well graded sand. When compared at low c y c l i c strength l e v e l s , equivalent r e l a t i v e density states for the uniform sand can be 15 to 20 % greater than for the well graded sand. For uniform sand, l i q u e f a c t i o n was experienced over a range of r e l a t i v e d e n sities, from the loosest state at 33 % to 43 % r e l a t i v e density. The more well graded sands, even at their loosest r e l a t i v e density states, (approximately 23 % ) , experienced c y c l i c mobility. This implies that, at low 74 r e l a t i v e densities, gradation might control the occurrence of l i q u e f a c t i o n . The effectiveness of f i e l d d e n s i f i c a t i o n i s dependent on the gradation of the sand at low r e l a t i v e d ensities. The c y c l i c shear strength of a uniform sand i s greatly improved by an increase in r e l a t i v e density. For a well graded sand, similar increases in r e l a t i v e density w i l l cause much smaller c y c l i c shear strength increases. At high r e l a t i v e densities, there i s not much improvement in c y c l i c shear strength with gradation. Consequently, the effect of gradation on the undrained response may not be s i g n i f i c a n t at high r e l a t i v e d e n s i t i e s . REFERENCES 1. Been, K. and J e f f e r i e s , M.G., (1985). "A S t a t e Parameter f o r Sands," G6otechnique, V o l . 35, No. 2, 1985, pp. 99-122. 2. B i s h o p , A.W. and H e n k e l , D.J., (1962). "The T r i a x i a l T e s t , " Edward A r n o l d L t d . , London, 1962. 3. Casagrande, A., (1976). " L i q u e f a c t i o n and C y c l i c D e f o r m a t i o n of Sands, A C r i t i c a l Review," H a r v a r d S o i l Mechanics S e r i e s No. 88, H a r v a r d U n i v e r s i t y , Cambridge, Mass., 1976. 4. C a s t r o , G., (1969). " L i q u e f a c t i o n of Sands," H a r v a r d S o i l Mechanics S e r i e s No. 81, H a r v a r d U n i v e r s i t y , Cambridge, Mass., 1969. 5. C a s t r o , G., (1975). " L i q u e f a c t i o n and C y c l i c M o b i l i t y of S a t u r a t e d Sands," J o u r n a l of the G e o t e c h n i c a l E n g i n e e r i n g D i v i s i o n , ASCE, V o l . 1, GT6, 1975, pp. 551-569. 6. C a s t r o , G. and P o u l o s , S . J . , (1977). " F a c t o r s A f f e c t i n g L i q u e f a c t i o n and C y c l i c M o b i l i t y , " J o u r n a l of t h e G e o t e c h n i c a l E n g i n e e r i n g D i v i s i o n , ASCE, V o l . 103, No. GT6, P r o c . Paper 12994, June, 1977, pp. 501-516. 7. C a s t r o , G., P o u l o s , S.J., F r a n c e , J.W. and Enos, J . L . , (1982). " L i q u e f a c t i o n Induced by C y c l i c L o a d i n g , " Report S u b m i t t e d t o N a t i o n a l S c i e n c e F o u n d a t i o n , March, 1982. 8. Chang, N.-Y., Yeh, S.-T., Kaufman, L.P., ( 1 9 8 2 ) . " L i q u e f a c t i o n P o t e n t i a l of C l e a n and S i l t y Sands," P r o c . 3rd M i c r o z o n a t i o n C o n f e r e n c e , S e a t t l e , 1982, pp. 1017-1032. 9. Chern, J . C , (1981). " E f f e c t of S t a t i c Shear on R e s i s t a n c e t o L i q u e f a c t i o n , " M.A.Sc. T h e s i s , The 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 , Vancouver, Canada. 10. Chern, J . C , (1985). "Undrained Response of S a t u r a t e d Sands w i t h Emphasis on L i q u e f a c t i o n and C y c l i c M o b i l i t y , " Ph.D. T h e s i s , The 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 , Vancouver, Canada. 11. Chung, E.K.F., (1985). " E f f e c t s of S t r e s s Path and P r e s t r a i n H i s t o r y on the U n d r a i n e d Monotonic and C y c l i c L o a d i n g Behaviour of S a t u r a t e d Sand," M.A.Sc. T h e s i s , The 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 , Vancouver, Canada. 75 76 12. de Beer, E., (1965). 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Poulos, S.J., (1981). "The Steady State of Deformation," Journal of the Geotechnical Engineering D i v i s i o n , ASCE, Vol. 107, GT5, 1981, pp. 553-562. 24. Roscoe, K.H., Schofield, A.N. and Wroth, CP., (1958). "On the Yielding of S o i l s , " Geotechnique, Vol. 8, No. 1, 1958 pp. 22-52. 25. Seed, H.B., (1979). " S o i l Liquefaction and C y c l i c Mobility Evaluation for Level Ground During Earthquakes," ASCE, J. of the Geot. Engng. Div., Vol. 105, No. GT2, pp. 201-225. 26. Seed, H.B. and Lee, K.L., (1966). "Liquefaction of Saturated Sands During Cy c l i c Loading," ASCE, J . of the S o i l Mech. and Found. Div., Vol. 92, No. SM6, 1966, pp. 105-134. 27. Seed, H.B. and Lee, K.L., (1967). "Undrained Strength Charact e r i s t i c s of Cohesionless S o i l s , " ASCE, J . of the S o i l Mech. and Found. Div., Nov. 1967, p. 333. 28. Sladen, J.A., D'Hollander, R.D. and Krahn, J., (1985). "The Liquefaction of Sands, a Collapse Surface Approach," Canadian Geotechnical Journal, Vol. 22, 1985, pp. 564-578. 29. Tumi, H.O.Z., (1983). "Effect of Confining Pressure and P a r t i c l e Angularity on Resistance to Liquefaction," M.A.Sc. Thesis, The University of B r i t i s h Columbia, Vancouver, Canada. 30. Vaid, Y.P. and Chern, J . C , (1983). "Mechanism of Deformation During Undrained Loading of Saturated Sands," International J . of S o i l Dynamics and Earthquake Engng., Vol. 2, No. 3, 1983, pp. 171-177. 31. Vaid, Y.P. and Chern, J . C , (1985). "Cyclic and Monotonic Undrained Response of Saturated Sands," Session No. 52, Advances in the Art of Testing S o i l s Under C y c l i c Conditions, Annual Convention and Exposition, Detroit, Michigan, 1985. 32. Wijewickreme, D., (1986). "Constant Volume F r i c t i o n Angle of Granular Materials," M.A.Sc. Thesis, The University of B r i t i s h Columbia, Vancouver, Canada. Wong, R.T., Seed, H.B. and Chan, C.K., (1974). "Liquefaction of Gravelly S o i l s Under Cy c l i c Loading Conditions," Earthquake Engineering Research Centre, Report No. 74-11, 1974, University of C a l i f o r n i a , Berkeley, 18 pp.

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