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Effect of static shear on resistance to liquefaction Chern, Jin-Ching 1981

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EFFECT OF STATIC SHEAR CN RESISTANCE TO LIQUEFACTION by JIN-CHING CHERN B.S., N a t i o n a l Taiwan U n i v e r s i t y , 1968 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE RFJQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n the Department o f C i v i l Engineering We accept t h i s t h e s i s as conforming t o the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA © A p r i l , 1981 Jin-Ching Chern In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the University of B r i t i s h Columbia, I agree that the Lib r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study. I further agree that permission for extensive copying of t h i s thesis for s c h o l a r l y purposes may be granted by the head of my department or by h i s or her representatives. I t i s understood that copying or p u b l i c a t i o n of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of C/'i/// Z-^^ ''• The University of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 D a t e ^>>g. 2 7 , / ? < P / ABSTRACT The i n f l u e n c e o f i n i t i a l s t a t i c shear s t r e s s on undra ined c y c l i c l o a d i n g behav io r o f s a tu r a t ed Ottawa sand has been s t u d i e d u s i n g the t r i a x i a l t e s t . Improved sample p r e p a r a t i o n techniques and t e s t i n g e q u i p -ment were employed t o o b t a i n samples o f un i fo rm d e n s i t y and min imize the e f f e c t o f sample d i s t u r b a n c e . D e t a i l e d s tudy o f the e f f e c t i v e s t r e s s pa ths enabled unders tanding o f the fundamental p rocess l e a d i n g t o l i q u e -f a c t i o n o r s t r a i n development. I t was found t h a t the r e s i s t a n c e t o l i q u e f a c t i o n o r c y c l i c s t r a i M n g f o r sand w i t h i n i t i a l s t a t i c shear s t r e s s can e i t h e r be h i g h e r o r lower than t h a t f o r sand w i t h no i n i t i a l s t a t i c shear s t r e s s , depending on the r e l a t i v e d e n s i t y and the l e v e l o f i n i t i a l s t a t i c shear s t r e s s . i i i TABLE OF CONTENTS Chapter Page 1. INTRODUCTION 1 2. REVIEW OF PREVIOUS INVESTIGATIONS - 5 3. TESTING PROGRAM 10 3-1 Testing Apparatus 10 3-2 Sample Preparation Techniques and Testing Procedures 10 3-3 Material Tested 14 3- 4 Testing Program 14 4. TEST RESULTS 15 4- 1 Cyclic Loading Behavior 15 4-2 Mechanism of Liquefaction or Strain Development . . 19 4-3 Monotonic Loading Behavior 34 4-4 Resistance to Liquefaction or Cyclic Straining • . 37 4-5 Resistance to Liquefaction or Cyclic Straining vs Relative Density 53 5. CCNCLUSICNS 60 REFERENCES 63 i v LIST OF FIGURES Figure Page 1 Static and Cyclic Stress Conditions i n S o i l Elements . . . 4 2 Schematic Layout of Testing Apparatus 11 3 Cyclic Loading Behavior of Loose Sand with and without I n i t i a l Static Shear Stress 16 4 Cyclic loading Behavior of Medium Dense Sand with and without I n i t i a l Static Shear Stress 18 5 Cyclic Loading Behavior of Dense Sand with and without I n i t i a l Static Shear Stress 20 6(a) Effective Stress Path of Cyclic Loading Test on Isotro-p i c a l l y Consolidated Loose Sand (Kc = 1.0) 23 6(b) Effective Stress Path of Cyclic Loading Test on Aniso-":• tropically Consolidated Loose Sand (Kc = 1.19) 24 6(c) Effective Stress Path of Cyclic Loading Test on Aniso-tropical l y Consolidated Loose Sand (K c = 1.48) 25 7(a) Effective Stress Path of Cyclic Loading Test on Isotro-p i c a l l y Consolidated Medium Dense Sand (IT =1.0) 26 7(b) Effective Stress Path of Cyclic Loading Test an Anise— tropically Consolidated Medium Dense Sand (Kc = 1.19) . . 27 7(c) Effective Stress Path of Cyclic Loading Test on Aniso-tropically Consolidated Medium Dense Sand (Kc =1.48) . . 28 8(a) Effective Stress Path of Cyclic Loading Test on Isotro-p i c a l l y Consolidated Dense Sand (Kc = 1.0) 29 8(b) Effective Stress Path of Cyclic Loading Test on Aniso-tropically Consolidated Dense Sand (K = 1.19) 30 8(c) Effective Stress Path of Cyclic Loading Test on Aniso-tropically Consolidated Dense Sand (K =1.48) 31 9 Schematic Diagram of Effective Stress Path Illustrating the Development of Terminal Residual Porewater Pressure . 33 10 Relation between Terminal Residual Porewater Pressure and I n i t i a l Static Shear Stress Level 33 11 Stress Controlled Monotonic Loading Test Results: (a) Devi-ator Stress vs Axial Strain; (b) Excess Porewater Pressure vs Axial Strain; (c) Effective Stress Ratio vs Axial Strain; (d) Effective Stress Paths 35 V 38 39 40 Resistance to Liquefaction or Cyclic Straining of Isotro-pically Consolidated Sand (K =1.0) Resistance to Liquefaction or Cyclic Straining of Aniso-tropically Consolidated Sand (Kc = 1.19) Resistance to Liquefaction or Cyclic Straining of Aniso-tropically Consolidated Sand (Kc =1.48) Effect of Initial Static Shear Stress on the Cyclic Stress Ratio Required to Cause Specified Amount of Cyclic Strain (Loose Sand) 43 Effect of Initial Static Shear Stress on the Cyclic Stress Ratio Required to Cause Various Level of Cyclic Strain in Specified Number of Cycles (Loose Sand) 44 Effect of Initial Static Shear Stress on the Cyclic Stress Ratio Required to Cause Specified Amount of Cyclic Strain (Medium Dense Sand) 46 Effect of Initial Static Shear Stress on the Cyclic Stress Ratio Required to Cause Various Level of Cyclic Strain in Specified Number of Cycles (Medium Dense Sand) 47 Effect of Initial Static Shear Stress on the Cyclic Stress Ratio Required to Cause Specified Amount of Cyclic Strain (Dense Sand) 48 Effect of Initial Static Shear Stress on the Cyclic Stress Ratio Required to Cause Various Level of Cyclic Strain in Specified Number of Cycles (Dense Sand) 49 Effect of Initial Static Shear Stress on the Cyclic Stress Ratio (Normalized by (T^,1) Required to Cause 5% Cyclic Strain for (a) LOOSE Sand; (b) Medium Dense Sand; (c) Dense Sand 51 Comparison of Cyclic Triaxial and Simple Shear Test Results on Sand without Initial Static Shear Stress (Dr = 50%) . . 52 Relationship between Relative Density and Cyclic Stress Ratio for Sand with Various Level of Initial Static Shear Stress (2% Cyclic Strain) 56 Relationship between Relative Density and Cyclic Stress Ratio for Sand with Various Level of Initial Static Shear Stress (5% Cyclic Strain) 57 Relationship between Relative Density and Cyclic Stress Ratio for Sand with Various Level of Initial Static Shear Stress (10% Cyclic Strain) 58 v i NOTATIONS B porewater pressure parameter D r re lat ive density e void rat io K c effective consolidation stress r a t i o , O ^ ' / o ^ ' N cycles of leading A U excess porewater pressure Au r excess residual porewater pressure ( A U r ) term. terminal value of residual porewater pressure o< slope of fa i lure envelope *a ax ia l s train *1> <T 3\ major and minor pr inc ipa l stresses tflc'' ' ^ 3 c ' major and minor consolidation stresses <5d deviator stress ^dcy c y c l i c deviator stress ^ds s tat ic deviator stress ^nc* normal stress on plane incl ined at 4 5 ° toCT-^' plane O'vc' ' ^hc' v e r t i c a l and horizontal confining stresses c y c l i c shear stress, = ^ c y / 2 i n i t i a l s tat ic shear stress, Ts = tf~ds/2 angle of internal f r i c t i o n v i i ACKNOWLEmEMENTS The writer i s deeply indebted to Dr. Y. P. Vaid for introducing the S o i l Mechanics to the writer and his continuous guidance and encouragement during the course of this research. The writer also wishes to express his appreciation to Dr. P. M. Byrne and DR. R. G. Campanella for reviewing the manuscript and making valuable suggestions. The technical assistance provided by the staff of the C i v i l Engin-eering Department workshop i s gratefully acknowledged. The writer i s indebted to The University of B r i t i s h Columbia for a University Graduate Fellowship which made this study possible. CHAPTER 1 INTRODUCTION The liquefaction potential of level saturated sand deposit subjected to seismic load i s evaluated commonly by undrained c y c l i c t r i a x i a l tests on isotropically consolidated samples or cyclic simple shear tests on one-dimensionally consolidated samples. These tests are designed to simulate stress conditions i n s o i l elements beneath the level ground. On these elements, there i s no i n i t i a l static shear stress on horizontal planes prior to earthquake shaking. In the f i e l d , such conditions are approximately true for elements (a) which are sufficiently far away from structure or slope (cases C and E i n Fig. 1), and (b) which are along the axis of symmetry of the structure (case A). S o i l elements beneath the sloping surface or adjacent to the structure (cases B and D) are subjected to i n i t i a l static shear stresses on the horizon-t a l plane. During earthquake shaking, these elements are subjected to additional c y c l i c shear stress due to shear wave propagating v e r t i c a l l y upward from the bedrock. The presence of these i n i t i a l static shear stresses can have a major effect on the response of the s o i l to a super-imposed cy c l i c loading. Several investigations have been made to investigate the i n f l u -ence of i n i t i a l s t a t i c shear stress on the resistance to liquefaction or c y c l i c straining. However, most of the research has been restricted to relating the resistance to liquefaction to the number of cycles of loading. Few attempts have been made to look at the behavior within cycles of loading, which i s essential for a fundamental understanding of the process leading to liquefaction. Furthermore, a wide scatter i s 2 generally present i n laboratory test results reported by various inves-tigators. This scatter might be attributed to the nature of the testing methods, different sample preparation techniques resulting i n nonuniform sample density, disturbance of the sample and the effect of system comp-liance. Consequently, contradictory conclusions may have emerged with respect to the influence of i n i t i a l s t a t i c shear stress on the r e s i s t -ence to liquefaction. The purpose of these investigations i s to better understand the process of liquefaction. This w i l l be attempted by looking at the undrained response of the saturated samples not only at the end of loading cycles as conventionally done, but also within each of cycle of loading. A further aim of this study i s to produce basic data on the effects of i n i t i a l static shear stress on resistance to liquefaction and c l a r i f y the apparently contradictory conclusions from previous studies. In this study, c y c l i c t r i a x i a l test i s used to investigate the liquefaction phenomenon. Improved sample preparation techniques to ensure uniform density throughout the specimen, improved testing equipment for better control on test variables and larger size samples to minimize the effects of membrane penetration were used. A review of previous investigations, emphasizing the conclusions regarding the effects of i n i t i a l s t a t i c shear stress on the resistance to liquefaction i s contained i n chapter 2. Chapter 3 describes the imp-rovements i n sample preparation techniques and testing equipment, testing procedures, material tested, and testing program. The c y c l i c loading test results, along with the discussion of the process leading to liquefaction and the effects of i n i t i a l s t a t i c shear stress on the resistence to liquefaction are presented i n chapter 4. Finally, conclu-3 sions drawn from these investigations are summarized i n chapter 5. p • A B • C • D Before Earthquake Earthquake During Earthquake 'vc Case A , C, E Case B, D 1 S t a t i c and C y c l i c S t r e s s C o n d i t i o n s i n S o i l E lements . 5 CHAPTER 2 REVIEW OF PREVIOUS INVESTIGATIONS Few studies have been made on the effects of i n i t i a l static shear stress on the resistance to liquefaction. The resistance to liquefaction or c y c l i c straining of s o i l deposits with i n i t i a l s t a t i c shear stresses on the horizontal planes have been studied i n the laboratory by c y c l i c t r i a x i a l test on anisotropically consolidated samples(11, 14, 15), cyc l i c ring torsion test (18), shaking table test (19), and constant volume c y c l i c simple shear test (17). In c y c l i c t r i a x i a l test, the sample i s f i r s t consolidated aniso-tropically with an effective stress ratio, K c = ^ -.'/d^' greater than one,simulating a state of i n i t i a l static shear stress existing before earthquake loading, and then tested under pulsating loading condition. The plane inclined at {45+^/2)° to the horizontal was considered to be pontential plane of failure and was assumed to be representative of horizontal plane i n the f i e l d with i n i t i a l static shear stress (11). The results of these studies show that the response of the anisotropically consolidated sample under cy c l i c loading condition depends on the effec-tive stress ratio after consolidation and the amplitude of the c y c l i c stress applied. When the c y c l i c deviator stress i s less than the deviator stress at the end of consolidation, no shear stress reversal occurs during any part of a loading cycle. The sample tends to deform progres-sively i n each successive load cycle, but the porewater pressure gener-a l l y does not increase sufficiently to cause a state of i n i t i a l lique-faction and a rapid build up of strains. On the other hand, i f the cyc l i c deviator stress i s greater than the deviator stress at the end of 6 consolidation, a state of p a r t i a l or t o t a l shear stress reversal occurs during each cycle of loading. In this case, the porewater pressure may build up progressively to the value of i n i t i a l confining stress, result-ing i n the attainment of the condition of i n i t i a l liquefaction accomp-anied by a rapid build up of strains. In contrast to the c y c l i c loading behavior of isotropically consolidated samples, significant strains start occurring from the very beginning of c y c l i c loading i n anisotro-pi c a l l y consolidated samples. The major conclusions frcm these previous studies using the t r i a x i a l test have been that the larger the i n i t i a l s tatic shear stress on a plane with a given normal effective stress, the larger i s the maximum and c y c l i c deviator stress required to induce a certain amount of strain i n a fixed number of cycles (11,15). It i s considered that simple shear test simulates f i e l d stress condition more closely. The c y c l i c loading behavior of a cohesionless s o i l which i s subjected to i n i t i a l static shear stress on the horizon-t a l plane has been studied i n ring torsional shear apparatus under nearly plane strain condition (18). Due to the shape of the sample, nonuniform stresses and strains are induced during consolidation and the condition of plane strain i s only approximately simulated, further-more, the i n i t i a l liquefaction was defined a r b i t r a r i l y as the instant when a discontinuity was observed i n the porewater pressure curve and shear strain curve, which further complicates the interpretation of test results from the point of view of engineering practice. The conclusions reached i n this study regarding the influence of i n i t i a l static shear stress on resistance to liquefaction were essentially opposite to those based on studies i n the t r i a x i a l test by Seed and Lee. (11, 14). Resistance to liquefaction, measured by the c y c l i c stress amplitude, was found to 7 decrease or remain unchanged with increase i n i n i t i a l s t a t i c shear stress level. The influence of i n i t i a l static shear stress on the resistance to liquefaction was also investigated i n shaking table tests (19). In this study, a small scale soil-structure model was used and porewater pressures were monitored at various locations i n sand during shaking. The authors drew conclusions similar to those of Yoshirni and Oh-oka. However, the effect of boundary condition and the possible drainage i n small scale samples, can seriously affect the interpretation of results. The effect of i n i t i a l static shear stress on the resistance to liquefaction under plane strain condition using the c y c l i c simple shear test was investigated by Vaid and Finn (17). Constant volume c y c l i c simple shear tests were performed on one-dimensionally consolidated sample of dry sand with i n i t i a l static shear stress on the horizontal plane. This test v i r t u a l l y eliminated the system compliance which causes significant over-estimation of the resistance to liquefaction, and very consistant results were obtained by using the improved sample preparation technique. The study showed that the prevalent belief that the presence of i n i t i a l static shear stress always increases the resistance to liquefaction as suggested by Seed et. a l . (11, 14) was found to require qualification. The resistance to liquefaction can either increase or decrease due to the presence of i n i t i a l static shear stress depending on the relative density, magnitude of static shear stress and definition of resistance to liquef-action. However i n this study also, no effort was made to look at the response of the sample within each cycle of loading for a fundamental understanding of the process leading to liquefaction. 8 It i s f e l t that the conventional method of sample preparation by sedimentation creates nonuniform density within the specimen, particularly i n samples with higher relative densities. In the earlier procedure, den-s i f i c a t i o n of the sample to the desired relative density was carried out prior to siphoning of excess sand to achieve the f i n a l desired height and seating of the ribbed plate. A looser layer of sand tends to form at the top due partly to the siphoning action and partly to digging of the ribbed plate into the sand surface. Such a loose layer i n an otherwise dense sample would lower the overall resistance to liquefaction of the sand sample. Often the connection of the loading piston to the loading ram by the conventional tectiniques results i n premature axial loading or unloading of sample before i n i t i a t i o n of c y c l i c stressing, which may affect the sub-sequent undrained response. Furthermore, small size samples used i n the previous investigations may have resulted i n significant overestimation of liquefaction resistance on account of compliance due to membrane pene-tration. Therefore, unreliable results may have been obtained. Studies on the effect of i n i t i a l static shear stress on the resistance to liquefaction by Yoshimi et. a l . (18, 19) were done on loose samples, whereas those of Lee and Seed (11, 14), and Vaid and Finn (17) were performed on medium dense and dense samples. A comprehensive under-standing of the role of the i n i t i a l static shear stress on the resistance to liquefaction covering a wide range of relative densities would then be very desirable. Furthermore, a look at the response of samples within cycles of loading w i l l enable a fundamental understanding of the process leading to liquefaction. 9 To achieve these objectives, i t i s essential that improved sample preparation techniques and testing equipment be used i n order to have confidence i n the interpretation of test results. 10 CHAPTER 3 EXPERIMENTAL PROGRAM 3-1 Testing Apparatus A schematic layout of the testing apparatus i s shown i n TELg. 2. Axial load was applied to the sample by means of an a i r piston. The piston was f i r s t l y pressurized to the same pressure i n the top and bottom chambers. The i n i t i a l static load and c y c l i c load were then applied by an electro-pneumatic transducer driven by a function generator. In order to maintain a constant c y c l i c load amplitude when large axial strain develops near onset of liquefaction, a constant backpressure / regulator was installed on the bottom chamber of the piston. Restricted drainage from or to the c e l l can cause fluctuation in c e l l pressure due to thrusting or extracting loading ram when large strains develop. Therefore, sufficiently large drainage lin e was used for connection to the reservoir B through which the c e l l pressure was applied during c y c l i c loading stage of the test. Hence measured porewater pressures were due only to the shearing of the sample. 3-2 Sample Preparation Techniques and Testing Procedures The t r i a x i a l specimens were 2.5 i n . i n diameter by 5 i n . long. To prepare a saturated sample, sand was boiled for about 10 minutes and allowed to cool to room temperature under vacuum. Porous disks were also boiled for about 10 minutes to ensure saturation. The sample base and drainage lin e were saturated f i r s t . The rubber membrane was sealed to the base pedestal, partly unrolled and f i l l e d with deaired water. A saturated porous disk was then carefully transferred onto the pedestal. The membrane was now f u l l y unrolled and s p l i t forming jacket assembled Double-acting Air Piston Load Cell Eyed Connecting Ring Porewater Pressure Transducer To Recorder Cell Pressure Transducer F i g . 2 Schematic Layout o f T e s t i n g Apparatus . 12 around the pedestal. Finally the membrane was stretched over the top of forming jacket. A small vacuum was applied to the jacket and the sample cavity was f i l l e d with deaired water. The sand was deposited loose into the sample cavity by pouring under the deaired water. After pouring to the desired height and leveling the surface, the sample cap was placed carefully onto the sample. Extreme precausion was taken to avoid entrapping any a i r while placing the cap. The desired density was then obtained by tapping on the base of the c e l l while maintaining a gentle pressure on the sample cap. During densi-fication the drainage line at the bottom of the sample and the drainage hole i n the sample cap were kept open for the water to drain out of the sample. It has been shown that this technique of sample preparation results i n samples of uniform density throughout (9, 17). In particular, a possible loose layer i n preparing sample of high density i s avoided. while holding the sample cap i n position, the membrane was brought around the cap carefully avoiding entrapping any a i r between the cap and the membrane. The membrane and the top drainage hole were now sealed. A vacuum of approximately 5 i n . of Hg. was applied through the bottom drainage l i n e and the forming jacket removed. Sample dimensions were now measured. After assembling the t r i a x i a l c e l l , the chamber was f i l l e d with deaired water. The c e l l was placed on the loading platform, and c e l l pressure l i n e and drainage l i n e were connected to the c e l l pressure reservoir A and volume change device respectively (Fig. 2). As the c e l l pressure was being raised i n increments to the desired f i n a l value v:hile keeping the sample undrained, the porewater pressures were recorded 13 and the incremental values of porewater pressure parameter B were deter-mined to check for saturation and leakage. To ensure saturation, test was performed only i f a B value higher than 0.99 at the f i n a l stage of increment i n c e l l pressure was obtained. After saturating the sample, the loading ram was connected to the loading piston. To minimize any disturbance to the sample, an eyed conn-ecting ring was used (Fig. 2). This technique permits a much better centering, and prevents premature axial loading or unloading of the sample. A l l samples were i n i t i a l l y consolidated isotropically under an 2 effective stress of 2.0 Kg/cm . Anisotropically consolidated samples were obtained by applying static deviator stress under drained condition u n t i l the desired value of anisotropic stress ratio, K c was obtained. The drainage line was then closed and the sample was ready for undrained 2 cyc l i c loading test. A back pressure of 1.0 Kg/cm was used i n a l l tests i n order to ensure saturation. A sinusoidal wave form was used for cy c l i c loading and tests were carried out at a frequency of 0.1 Hz. Low frequency loading was used i n order to examine i n detail the phenomenon of porewater pressure and strain development within each cycle of loading. During each test, c y c l i c load, porewater pressure and axial strain were continuously monitored by electronic transducers and records obtained on st r i p chart recorders. In this test program, improved sample preparation techniques and testing methods were adopted which are believed to result i n improved sample uniformity and sample disturbance i s minimized. Essentially no necking was observed u n t i l extremely large axial extensional strains 14 developed. This enable the interpretation of results with confidence i n the strain range of interest. 3-3 Material Tested Tests were performed on Ottawa sand, ASTM designation C-109. This i s a natural s i l i c a sand consisting of rounded particle with grain sizes between 0.15 mm and 0.59 mm and L\-Q = 0.40 mm. The maximum and minimum void ratios are 0.82 and 0.50, respectively. 3-4 Testing Program In this study, the effects of i n i t i a l static shear stress level and relative density on the liquefaction resistance of normally conso-lidated sand was investigated. Therefore c y c l i c loading tests were performed on both isotropically consolidated and anisotropically conso-lidated samples. Two series of tests on anisotropically consolidated samples were carried out using K c = O^'/O^' values of 1.19 and 1.48, respectively. In each series, c y c l i c loading tests were performed over a range of relative densities. Relative density after consolidation varies from 33% to 71%. The magnitude of cy c l i c deviator stress 0^ ^= 22" relative to static deviator stress 0"^ were chosen so that both shear stress reversal and non-reversal were simulated. A l l tests were per-formed on samples consolidated under minor principal stress of 2.0 Kg/cm* Stress controlled monotonic loading undrained tests were also performed on loose and medium dense samples. This was done i n order to establish the effective stress failure envelop of the sand and the characteristics of strain development and porewater pressure generation, and their possible interrelationship with undrained behavior under cyc l i c loading. 15 CHAPTER 4 TEST RESULTS In this chapter, f i r s t l y typical results of cy c l i c loading behavior of samples as measured by residual porewater pressure and axial strain developed as function of loading cycles are presented. For anisotropically consolidated samples, tests involving both reversal and non-reversal of deviator stress during c y c l i c loading are included. Then, the mechanism of liquefaction or cy c l i c straining i s discussed by exainining the effec-tive stress paths within cycles of loading. Finally results of resistance to liquefaction or cyclic straining as measured by c y c l i c stress ratio required to develop certain amount of axial strain i n a specified number of cycles are presented. Also the effect of i n i t i a l static shear stress on the resistance to liquefaction or cy c l i c straining for sands of various relative densities are discussed. 4-1 Cyclic Loading Behavior Typical results of cy c l i c loading behavior of loose, medium dense and dense sand with and without i n i t i a l static shear stress w i l l be discussed i n this section. Behavior of Loose Sand Typical results of residual porewater pressure and axial strain developed as function of the number of loading cycles for loose sand consolidated to different static stress ratios but equal c y c l i c stress amplitude are shown i n Figs. 3(a) and 3(b). The results of maximum effec-tive stress ratio developed with number of cycles are also shown i n Fig. 3(c). I t may be seen that for a l l samples the residual porewater pressure, Au,. increased progressively with cycles of loading. This was later 16 o e 4.0 b 2.0 0.0 (0 » ( r t _ i-i rT-rn-El / L l i__ A i 10 20 30 Number of Cycles, N 40 50 F i g . 3 C y c l i c l o a d i n g Behav io r o f Loose Sand w i t h and w i t h o u t I n i t i a l S t a t i c Shear S t r e s s . 17 ' followed by a sudden increase i n porewater pressure shortly before i t reached a terminal value. For isotropically consolidated sample, the terminal residual porewater pressure equals the confining pressure. However, i t s value i s less than the confining pressure i n the case of anisotropically consolidated sample. The values of terminal residual porewater pressure were found decreasing with increasing anisotropic consolidation stress ratio K . c From Figs. 3(a) and 3(b), i t can be seen that a sharp increase in residual porewater pressure i s accompanied by a sudden development in axial strain i n a l l cases. This phenomenon i s associated with con-trative flow deformation (1, 2) developed i n the sample which w i l l be discussed further i n later sections. By comparing the development of r e s i -dual porewater pressure and axial strain with maximum effective stress ratios developed, i t may be noted that there exists an intimate relation among them. Sudden development i n residual porewater pressure and axial strain did not occur u n t i l the maximum effective stress ratio reached a certain c r i t i c a l value. This value was found to be about 2.60 and was independent of the anisotropic consolidation stress ratio K c and cyc l i c stress ratio °d Cy/20^ c'. Behavior of Medium Dense Sand Typical cyclic loading behavior of medium dense sand i s shown i n Fig. 4. The development of residual porewater pressure with number of cycles i s essentially similar to those for the loose sand except i n the case of samples consolidated to high K c values. In this case, no accel-erated increase i n porewater pressure i s observed. The residual porewater pressure increased progressively and approached the terminal value asymp-18 F i g . 4 C y c l i c Load ing Behav io r o f Medium Dense Sand w i t h and w i t h o u t I n i t i a l S t a t i c Shear S t r e s s . 19 t o t i c a l l y . However, for a given K the terminal value of residual pore-water pressure was the same as that for the loose sand. Absence of sudden increase i n porewater pressure implies no contractive flow deformation. Similar to the behavior of loose sand , significant amount of strain started to build up (Fig. 4(b)) when accelerated increase i n porewater pressure developed. The strain increased progressively though at a slower rate when compared to loose sand. I t may again be noted that accelerated increase i n residual porewater pressure and axial strain were observed only when the maximum effective stress ratio reached a c r i t i c a l value (approximately 2.60) which was the same as for the loose sand at which flow deformation started to develop. Behavior of Dense Sand Typical results of the cyclic loading behavior of dense sand are shown in Fig. 5. It can be seen that the behavior of dense sand i s essentially similar to that .  of the medium dense sand. However, the development of residual porewater pressure and axial strain are at a slower rate then the medium dense sand. A l l test results show that maximum porewater pressure reaches the confining pressure i n samples with complete or significant amount of shear stress reversal, and i t always occurs at the instant when shear stress i s equal to zero. This finding supports the results of simple shear test obtained by Vaid and Finn (17). Lee and Seed (11), however, reported that the slightest stress reversal during c y c l i c t r i a x i a l test gave ri s e to a condition of i n i t i a l liquefaction (cT^ ' = 0). 4-2 Mechanism of Liquefaction or Strain Development 20 F i g . 5 C y c l i c Load ing Behav io r o f Dense S i n d w i t h and w i t h o u t I n i t i a l S t a t i c Shear S t r e s s . 21 A fundamental understanding of the mechanism leading to liquefac-tion or strain development i s obtained with the help of examining the effective stress paths within cycles of loading. Typical effective stress paths during cyclic loading for loose, medium dense and dense sand con-solidated both isotropically and anisotropically are shown i n Figs. 6, 7 and 8. Irrespective of relative density, anisotropic consolidation stress ratio or cy c l i c stress ratio, the effective stress paths (Figs. 6, 7, 8) moved toward the static failure envelope progressively with cycles of loading. However, for loose samples (Fig. 6), before the stress path reaches the stat i c failure envelope, a contractive flow deformation occurred i n the sample. A sudden decrease i n deviator stress with an accompanying sharp increase i n porewater pressure and sudden development i n axial strain was observed. This flow deformation stopped when the sample strained sufficiently so as to cause di l a t i o n with further straining. This phenomenon i s similar to the limited liquefaction observed by Castro (2). After the sample developed flow deformation, i t reached the failure envelope very quickly and the porewater pressure reached i t s terminal value. From the stress paths, i t can be seen that the phenomenon of flow deformation was triggered when the sample reached the state of stress corresponding to effective stress ratio of about 2.50 regardless of the K c value of the sample and the cyclic stress ratio. Results from a limited number of test show that a spontaneous liquefaction could be induced by very small cyclic stress amplitude i n loose sample, i f the sample was consolidated to a hitjn value close to about 2.80. 22 For medium dense sand , the stress paths, Figs. 7(a) , 7(b) and 7(c) , show no contractive flow deformation. Instead of developing flow deformation, the stress path moved progressively toward the failure envelop. Careful study of stress paths shows that there exists a c r i t i c a l effective stress ratio line both i n compression and extension regions beyond which the sample dilates whenever i t i s loaded (increasing tf^, AB i n Fig. 7(b)) and causes no change i n porewater pressure whenever i t i s un-loaded (BC i n Fig. 7(b)). The value of this effective stress ratio was about 2.67 and was found to be approximately the same i n both compression and ext-ension regions. I t was found that when the state of stress reached this c r i t i c a l effective stress ratio line the unloading phase of the load cycle ( CD i n Fig. 7(b)) below this line induced high porewater pressure. On the other hand, loading phase of the load cycle ( DE i n Fig. 7(b)) deve-loped significant amount of axial strain. The accelerated increase i n residual porewater pressure and the nature of progressive increase i n axial strain i s due to the repetition of this mechanism with further loading cycles. Mechanism of strain development in medium dense sand i s thus different from that i n the case of loose sand where flow deformation accounts for the sudden large strain development. The effective stress paths for dense sand , Figs. 8(a), 8(b) and 8(c), are essentially similar to those for the medium dense sand . This indicates that the mechanism leading to liquefaction or straining i n the dense sand due to c y c l i c loading i s the same as that for medium dense sand. However, due to more dilatant characteristics of dense sands, the developments of porewater pressure and axial strain are at a slower rate than that for the medium dense sand. It was shown i n the previous section that the terminal value of 0.6 0.8 L0 1.2 1.4 (0i'+03)/2 (kg/cm2) F i g . 6 (a) E f f e c t i v e S t r e s s Pa th o f C y c l i c Load ing Tes t on I s o t r o p i c a l l y C o n s o l i d a t e d Loose Sand. to F i g . 6 (b) E f f e c t i v e S t r e s s Pa th o f C y c l i c l o a d i n g Tes t on A n i s o t r o p i c a l l y C o n s o l i d a t e d Loose Sand. (Oj'+ 0-3 )/2 (kg/cm2) Fig. 6 (c) Effective Stress Path of Cyclic loading Test on Anisotropically Consolidated Loose Sand. F i g . 7(a) E f f e c t i v e S t r e s s Pa th o f C y c l i c Load ing Tes t on I s o t r o p i c a l l y C o n s o l i d a t e d Medium Dense Sand. F i g . 7(b) E f f e c t i v e S t r e s s Pa th o f C y c l i c Load ing Tes t on A n i s o t r o p i c a l l y C o n s o l i d a t e d Medium Dense Sand. F i g . 7(c) E f f e c t i v e S t r e s s Pa th o f C y c l i c Lead ing Tes t on A n i s o t r o p i c a l l y C o n s o l i d a t e d Medium Dense Sand. F i g . 8(a) E f f e c t i v e S t r e s s P a t h o f C y c l i c Loading T e s t on I s o t r o p i c a l l y C o n s o l i d a t e d Dense Sand. F i g . 8 (b) E f f e c t i v e S t r e s s P a t h o f C y c l i c Lead ing Tes t an A n i s o t r o p i c a l l y C o n s o l i d a t e d Dense Sand. F i g . 8 (c) E f f e c t i v e S t r e s s Pa th o f C y c l i c Load ing T e s t on A n i s o t r o p i c a l l y C o n s o l i d a t e d Dense Sand. 32 residual porewater pressure decreases with increasing K c value but i s independent of the relative density of the sand and c y c l i c stress ampli-tude. By examining the effective stress paths ( Figs. 6, 7, 8), i t may be seen that ultimately a l l c y c l i c undrained stress paths stabilized along the stat i c failure envelop. This failure envelope was found to be essentially the same (only a small scatter +1.8* i n angle of internal friction) regardless of the relative density of the sand, i n i t i a l K value and cyclic stress amplitude applied. If such an unique failure envelop exists, i t can be shown theoretically that there exists a l i m i t -ing or terminal value of residual porewater pressure under cy c l i c loading which depends only on the K c value or the level of i n i t i a l static shear stress at the end of consolidation, and i s independent of the relative density of the sample and the amplitude of the c y c l i c stress applied. This i s illustrated by a schematic diagram of effective stress path i n Fig. 9. The theoretical terminal value of the residual porewater press-ure (AUjJ-fcg^ c a n 0 9 expressed by the relation (Auh 5c - 1 1 - Sin0 V term. = ^ ( 1 - ^ ^ ) (1-a) term. = Sc* < 1 " ^ (1"b> o i n which 7J"s - CT^/2 i s the i n i t i a l static shear stress on 45 plane from the horizontal at. the end of consolidation and 0 * i s the angle of internal f r i c t i o n . Equation (1) shows that (^ u r)^- e r m decreases linearly with increasing K c value or i n i t i a l static shear stress level. W^i-g^,, equals confining stress i n isotropically consolidated case, which corres-ponds to K = 1. For K > 1, (Au ), i s always less than the i n i t i a l confining pressure. The measured values of ( ^ u r ) t e r m for c y c l i c loading test as a function of K c value are shown by data points i n Fig. 10. 33 (OJ'+ a^)/Z W W I F i g . 9 Schematic Diagram o f E f f e c t i v e S t r e s s Pa th I l l u s t r a t i n g the Development o f Te rmina l R e s i d u a l Porewater P r e s s u r e . F i g . 10 R e l a t i o n between ' e r m i n a l R e s i d u a l Porewater P ressure and I n i t i a l S t a t i c Shear S t r e s s L e v e l (number i n p a r e n t h e s i s i n d i c a t e s the number o f da t a p o i n t s ) . 34 Theoretically predicted values using Eq. (1) are shown by a so l i d l i n e . Excellent agreement may be seen between the observed and the predicted values. From stress paths, i t can also be seen that conventional i n i t i a l liquefaction, i . e . , induced porewater pressure An = 0"^ c*, i s a momentary phenomenon during c y c l i c leading. It always occurs at the moment when shear stress i s equal to zero during cycles of loading. This phenomenon can occur i n isotropically consolidated sample or sample with significant amount of shear stress reversal. It i s clear that conventional i n i t i a l liquefaction can not be induced i n case where there i s no shear stress reversal, because the stress path never crosses the zero shear stress lin e . It may also be noted that after i n i t i a l liquefaction, sample regains i t s strength due to dilation when i t i s further sheared, thus limiting further deformation within the loading cycle. 4-3 Monotonic Loading Behavior Stress controlled monotonic loading tests were performed on loose and medium dense sands i n order to obtain the stress-strain curves, f a i l -ure envelope and the characteristics of porewater pressure development. It was intended to investigat i f the mechanism of flow deformation observed during cyclic loading test on loose sand did exist i n monotonic loading tests. The results are shown in Fig. 11. For loose samples, S-l and S-2, the deviator stress and porewater pressure increased progressively with very small strain developed as the effective stress path moved towards the failure envelope. This trend con-tinued u n t i l a state of stress was reached at which the sample became unstable. A sudden decrease i n deviator stress occurred accompanied by F i g . 11 S t r e s s C o n t r o l l e d Monotonic Load ing T e s t R e s u l t s : (a) D e v i a t o r S t r e s s v s A x i a l S t r a i n ; (b) Excess Porewater P ressu re v s A x i a l S t r a i n . 36 F i g . 11 S t r e s s C o n t r o l l e d Monotonic Load ing Tes t R e s u l t s : (c) E f f e c t i v e S t r e s s R a t i o v s A x i a l S t r a i n ; (d) E f f e c t i v e S t r e s s Pa th s . 37 sharp increase i n porewater pressure and axial strain i n a very shotr period of time. This flow deformation, which i s similar to that observed i n cy c l i c leading tests, was stopped by dilation i n the sample when large strain developed. Thereafter the sample reached the failure envelope very quickly. For medium dense sand, S-3, instead of developing into flow deformation, the sample dilated and approched the failure envelope progressively with strain development at a higher rate compared to that i n the i n i t i a l stage. The effective stress ratio at which sample started to dilate was found to be approximately equal to the c r i t i c a l effective stress ratio at which the loose samples started to develop flow deformation. Comparing the results of cy c l i c and monotonic loading tests, there seems to exist a c r i t i c a l effective stress ratio line which controlis the onset of liquefaction or straining. Once the sample reaches this state of stress, loose samples develop flow deformation and dense samples dilate. Appreciable amount of strain can be developed only when the sample i s loaded to stress states beyond this line. 4-4 Resistance to Liquefaction or Cyclic Straining Resistance to liquefaction or c y c l i c straining i s expressed by the cyclic stress ratio T^y/cT^1 (Z = ^ c y / 2 ) required to develop a specified amount of strain i n a given number of cycles. The cyclic loading behavior of isotropically consolidated sample i s shown i n Figures 12(a), 12(b) and 12(c). In these figures each contour was obtained by carrying out tests on a series of samples at different relative densities but using the same cy c l i c stress amplitude. Similarly, Figs. 13(a), 13 (b), 13(c), 14(a), 14 (b) and 14(c) show cy c l i c loading behavior of anisotropically consolidated sample to two K values ( i . e., sand with 38 30 3 rn 7 0 ^ 2 5 10 20 50 100 200 No. of Cycles to Liquefaction or Specified Amount of Cyclic Strain F i g . 12 Res i s t ance t o L i q u e f a c t i o n o r C y c l i c S t r a i n i n g o f I s o t r o p i c a l l y C o n s o l i d a t e d Sand (K 1) 39 0.75 | 2 5 10 20 50 100 200 No. of Cycles to Liquefaction or Specified Amount of Cyclic Strain F i g . 13 R e s i s t a n c e t o L i q u e f a c t i o n o r C y c l i c S t r a i n i n g o f A n i s o t r o p i c a l l y (Consolidated Sand (K =1.19). 40 I (b) 5% Ci relic Strain 1 ~~~ - < 1 ) A ^ n ~ —~ct Jj, -^-a. .^ 1 -t- ' i 1 j j : ! 70 rn < m 50 o m 6 o | (c) 10% Cyclic Strain 70 m 2 5 10 20 50 100 200 No. of Cycles to Liquefaction or Specified Amount of Cyclic Strain F i g . 14 R e s i s t a n c e t o L i q u e f a c t i o n o r C y c l i c S t r a i n i n g o f A n i s o t r o p i c a l l y C o n s o l i d a t e d Sand (K = 1 . 4 8 ) . c 41 i n i t i a l static shear) of 1.19 and 1.48 respectively. For these anisotro-p i c a l l y consolidated samples, cy c l i c stress was normalized with respect to static consolidation stress o~ 1 on the plane inclined at 45° to 0"n' nc -L plane. This plane i s subjected to the maximum amplitude of the shear stress during c y c l i c loading and i s considered to simulate c y c l i c earths quake stress conditions on the horizontal planes i n the ground. Test data i n Figs. 12, 13 and 14 may be seen to be very consistent and show l i t t l e scatter. Earlier data reported on the same sand which was i n i t i a l l y isotropically consolidated (8) shows considerable scatter, particularly i n the higher relative density range. Improved sample prep-aration techniques which result i n samples of uniform relative density throughout (9, 17) i s believed to responsible for consistency and high reproducibility i n the test results. I t may be seen i n Figs. 12(a), 12(b) and 12(c) that for samples with no i n i t i a l static shear stresses (i.e., isotropically consolidated) constant c y c l i c stress contours of D r vs cycles to liquefaction tend to converge at higher number of cycles. For samples with i n i t i a l s t a t i c shear stress (Figs. 13 and 14), however, these curves are more or less p a r a l l e l . Furthermore, a l l curves flatten at higher number of cycles. By cross plotting the basic data i n Figs. 12(a), 12(b) and 12(c), relationship between cy c l i c stress ratio and number of cycles to lique-faction for any relative density can be obtained for isotropically consolidated sand. Similar relationships can be derived from Figs. 13 and 14 for sand with i n i t i a l static shear stress, i . e . , for K =1.19 and 1.48. Relative densities of 45%, 55% and 65%, which represent loose, medium dense and dense state were chosen for deriving the aforesaid 42 relationship between c y c l i c stress ratio and cycles to liquefaction. These are il l u s t r a t e d i n Figs. 15, 17 and 19. In these figures, the i n i t i a l static shear stress TJ i s the shear stress on 45° plane at the s end of consolidation. For loose sand, Fig. 15(a), i t may be seen that c y c l i c stress ratio Tj^y/^c' required to develop 2% c y c l i c strain for sample with i n i t i a l static shear stress can either be higher or lower than the case with T = 0 depending on the level of T . This i s also true for c y c l i c strain level of 5% and 10% as shown i n Figs. 15(b) and 15(c). The variation of c y c l i c stress ratio required to cause 2%, 5% and 10% c y c l i c strain i n 10 cycles with the level of i n i t i a l static shear stress i s shown i n Fig. 16(a). I t may be seen that an increase i n cyclic stress ratio occurs i n order to develop any level of c y c l i c strain at low level of i n i t i a l static shear stress. However, significant reduc-tion i n cyclic stress ratio occurs when Z" /<r n c' i s higher than about 0.1. This reduction i n resistance to liquefaction or c y c l i c straining i s a t t -ributed to the fact that the i n i t i a l state of stress i s closer to the c r i t i c a l effective stress ratio line for samples with high i n i t i a l static shear stress level. Due to the contractive nature of the loose sand, i t i s easier to reach this c r i t i c a l state of stress. From the trend of the curves, i t appears that very small c y c l i c stress ratio may be required to cause large deformation i n sand i f the i n i t i a l static shear stress i s high enough. This corresponds to the phenomenon of spontaneous lique-faction. Data similar to Fig. 16(a) on the stress condition to reach specified c y c l i c strain level i n 30 cycles of loading i s given i n Fig. 16(b). I 2 5 10 20 50 100 No. of Cycles to Liquefaction or Specified Amount of Cyclic Strain F i g . 15 E f f e c t o f I n i t i a l S t a t i c Shear S t r e s s on the C y c l i c S t r e s s R a t i o Required t o Cause S p e c i f i e d Am; ant o f C y c l i c S t r a i n (Loose Sand). 44 0.2 b c 0.1 D r= 45% (a) N=I0 10% - 5% , - - 2 % 0.1 0.2 0.3 0.3 (b) N = 30 0.2 b= >\ o I-0.1 <b— 10% 2% 8 5% S 0.1 0.2 03 T s /cr n ' c F i g . 16 E f f e c t o f I n i t i a l S t a t i c Shear S t r e s s on the C y c l i c S t r e s s R a t i o Requ i red t o Cause V a r i o u s L e v e l o f C y c l i c S t r a i n i n S p e c i f i e d Number o f C y c l e s (Loose Sand) . 45 The c y c l i c loading behavior of medium dense sand under i n i t i a l static shear stress was found to be similar to that for the loose sand. The relationship between cy c l i c stress ratio and cycles of loading to develop 2%, 5% and 10% c y c l i c strain are shown i n Figs. 17(a), 17(b) and 17(c). In contrast to the behavior of loose sand, for samples with i n i t i a l static shear stress the cy c l i c stress ratio required to cause fixed amount of cy c l i c strain i n a specified number of cycles i s always greater than that for sample with no 7JS« The influence of i n i t i a l static shear stress on the cyclic stress ratio required to cause 2%, 5% and 10% cy c l i c strain i n 10 cycles and 30 cycles i s shown i n Figs. 18(a) and 18(b). For lower level of cy c l i c strain considered, the relationship i s essentially similar to that for the loose sand, except that the cyclic stress ratio starts to decrease from a maximum value at a higher i n i t i a l static shear stress level. However, for larger strain development and larger number of loading cycles (e.g. 10% cyclic strain developed i n 30 cycles of loading; Fig. 18(b)) cyclic stress ratio increases continuously with increasing static shear stress. For dense sand, the cyclic stress ratios required to develop 2%, 5% and 10% cyclic strain are shown i n Figs. 19(a), 19(b) and 19(c). m contrast to the loose or medium dense sand, the cyclic stress ratio required to develop certain amount of cyclic strain was found to be higher with increasing i n i t i a l s t a t i c shear stress level. The variation of cy c l i c stress ratio required to cause 2%, 5% and 10% cy c l i c strain i n 10 cycles with the level of i n i t i a l static shear stress i s shown i n F..g. 20(a). I t may be seen that the cyclic 46 0.2 0.1 \ „ 1 (c) 10% Cycl ic Strain • •< — I ) -—( ) G  v I 2 5 10 20 50 100 No. of Cycles to Liquefaction or Specified Amount of Cyclic Strain F i g . 17 E f f e c t o f I n i t i a l S t a t i c Shear S t r e s s on the C y c l i c S t r e s s R a t i o Requ i red t o Cause S p e c i f i e d Amount o f C y c l i c S t r a i n (Mediuiii Dense Sand) . 47 u 0.1 0.2 0.3 T s /Ohc F i g . 18 E f f e c t o f I n i t i a l S t a t i c Shear S t r e s s on the C y c l i c S t r e s s R a t i o Requ i red t o Cause V a r i o u s L e v e l o f C y c l i c S t r a i n i n S p e c i f i e d Number o f C y c l e s (Ifedium Dense Sand) . 48 >» I? 0.2 j (c) 10 % Cyclic Str< i in I i 1 2 5 10 20 50 100 No. of Cycles to Liquefaction or Specified Amount of Cyclic Strain Fig. 19 Effeet of I n i t i a l Static Shear Stress on the Cyclic Stress Ratio Required to Cause Specified Amount of Cyclic Strain (Dense Sand). 49 F i g . 20 E f f e c t o f I n i t i a l S t a t i c Shear S t r e s s on the C y c l i c S t r e s s R a t i o Requi red t o Cause V a r i o u s L e v e l o f C y c l i c S t r a i n i n S p e c i f i e d Number o f C y c l e s (Dense Sand) . 50 stress required to develop certain amount of strain increases with incr-easing i n i t i a l static shear stress level. The increase in cyclic stress ratio tends to level off at high level of "r • Data similar to Fig. 20(a) but for 30 cycles of loading is given in Fig. 20 (b). It shows that the cyclic stress ratio required to develop certain amount of cyclic strain increases progressively and shows no tendency of decrease for the 7/g levels studied. From the results discussed above, the resistance to liquefaction or cyclic straining for sand with i n i t i a l static shear stress can either be higher or lower than the case with 7 = 0 depending on the relative density of the sand and TS level. Previous study (12) has suggested that a more homogeneous representation' of results could be obtained by using major principal consolidation stress U^J to normalize the cyclic stress. However, this study showed that this may not be true in loose to medium dense sand, since higher i n i t i a l static shear stress could decrease the cyclic stress ratio required to cause specified amount of cyclic strain in a given number of cycles. This is illustrated in Figs. 21(a) and 21(b) for cyclic strain level of 5%. It may be valid only in dense sand (Fig. 21(c)) for which the cyclic stress ratio required to cause certain amount of cyclic strain generally increases with increasing K value, i.e. T level. For comparison purposes, a plot of cyclic stress ratio required to develop 2%, 5% and 10% cyclic strain or shear strain vs number of cycles in cyclic triaxial test and cyclic constant volume simple shear (CVSS) test on sand of 50% relative density and no i n i t i a l static shear stress i s shown in Figs. 22(a), 22(b) and 22(c). The results show that two curves agree very well with cyclic triaxial results slightly higher than the cyclic CVSS test results. It was found that ( ^ v A ^ - , 'J^ss = 0.89 to 51 0 0.3 0.2 0.1 1 j le ) D r= 65% i i i ! i i : ^ E f e A ^ ^ ! I l l ! 1 | i ! 1 i i ' i — * 2 5 10 20 50 100 No. of Cycles to Liquefaction or 5% Cyclic Strain Fig. 21 Effect of I n i t i a l Static Shear Stress on the Cyclic Stress Ratio (Normalized by Cn^ 1 ) Required to Cause 5% Cyclic Strain for (a) Loose Sand; (b) Medium Dense Sand; (c) Dense Sand. 52 0.3 £ 0 . 2 2 o.i o 0.3 ^0.2 0.1 0 0.3 v o £ 0 . 2 i f " D r = 50% (a) 2% Cyclic Strata or Shear Strain - o — Cyclic Triax. Results CVSS Results (1 j) 5% C or 5 1 /die S1 >hear (rain Strain — - © — —— I (< I :) 10% C or 1 lyclic S Shear >train Strain ' — — — © 1 2 5 10 20 50 100 200 500 1000 No. of Cycles to Liquefaction or Specified Amount of Cyclic Strain Fig. 22 Ccmparison of Cyclic T r i a x i a l and Siirple Shear Test Results on Sand without I n i t i a l Static Shear Stress (D_ = 50%). 53 0.94(t: cy/(f 3 c ,) T r^ a x depending on the level of cy c l i c strain considered. Previous studies (3, 8, 16) have shown that for a given EL simple shear stress ratio i s about 55% to 72% of t r i a x i a l stress ratio. The d i f f e r -ence i n c y c l i c stress ratios i n the two tests i s considered to be a consequence of the difference i n stress conditions at the end of con-solidation. The results i n this study indicate that by using similar techniques of sample preparation and reducing the effects of sample disturbance and system compliance, a much better correlation i s found to exist between t r i a x i a l and simple shear results. I t i s , therefore, apparent that the previously observed differences i n resistance to liquefaction or c y c l i c straining was not simply a function of the state of stress at the end of consolidation. Part of the difference could be attributed to not adhering to careful testing techniques. In addition to the difference i n state of stress, more fundamental factors, e.g., change i n mean normal stress, rotation of principal axes and lack of complementary shear stress i n simple shear testing may contribute to the difference i n the stress ratio. Further research i s required to examine these factors quantitatively i n order to obtain a better corre--lation of results i n these two test types. 4-5 Resistance to Liquefaction or cy c l i c straining vs Relative Density The influence of relative density on the cy c l i c stress ratio required to cause 2% cyclic strain i n 10 cycles and 30 cycles of loading for sand with no i n i t i a l static shear stress can be obtained by cross plotting the basic data i n Fig. 12(a). Similarly, same relationship can be obtained for sand with i n i t i a l static shear stress from FigsJ-3(a) and 14(a). These relationships are shown i n Figs. 23(a) and 23(b). The plots 54 for higher strain level of 5% and 10% can also be obtained from Figs. 12(b), 13(b) and 14(b), and Figs. 12(c), 13(c) and 14(c). These results are shown i n Figs. 24(a), 24(b), 25(a) and 25(b). The results obtained by Vaid and Finn (17) using c y c l i c constant volume simple shear test on same sand with no i n i t i a l static shear stress on the horizontal plane are also shown i n Figs. 25(a) and 25(b). The plots showing the i n f l u -ence of relative density on the resistance to liquefaction or cy c l i c straining for anisotropically consolidated samples have never been reported i n literature up to now. Figs. 23, 24 and 25 show that similar relationship exist between cy c l i c stress r a t i o and relative density regardless of the cy c l i c strain level considered. For sand with no i n i t i a l static shear stress, there i s a gradual increase i n resistance to liquefaction or c y c l i c straining with increasing relative density up to D^ . - 60%. The increase i n resistance to liquefaction occurred at a much faster rate for relative density i n excess of about 60%. This observed relationship i s very similar to that reported under cyclic constant volume simple shear results by Vaid and Finn (Figs. 25(a) and 25(b)). Studies on large simple shear samples by De Alba et a l (5) , however, show that c y c l i c stress ratio increases linearly with relative density up to D^ of about 80%. The observed dramatic increase i n resistance to liquefaction at high relative density i s believed to be a consequence of the improved sample preparation techniques. This improved sample preparation technique produced a sample of uniform density throughout and minimize the effect of sample disturbance which tends to create a loose layer at the top of an other-wise dense sample. These results are also i n agreement wi h the empirical 55 f i e l d liquefaction correlations analyzed by Castro (3) and Christian and Swiger(4). I t appears that there i s no evidence of liquefaction for sites with blowcounts (normalized to a pressure of 40 psi) greater than 40, which corresponds to relative density of about 70% based on the Gibbs and Holtz (10) correlation between N value and the relative density. It may be seen i n Figs. 23, 24 and 25 that for sand with low level of i n i t i a l static shear stress, the resistance to liquefaction or c y c l i c straining i s higher then the case with no i n i t i a l s t a t i c shear stress over a wide range of relative density. The resistance could be less than that for sand with T g = 0 only i n the very loose state. For higher level of T , the relationship between the resistance to liquefaction or c y c l i c straining with increasing relative density i s different from those with no or small i n i t i a l static shear stress. In case of loose sand, the resistance could be substantially less than that for sand with T g = 0. This i s attributed to the fact that for large K values the i n i t i a l state of stress i s much closer to the c r i t i c a l c effective stress ratio lin e . Due to the contractive nature of the loose sand, rather small c y c l i c stress amplitude i s required i n order to reach this c r i t i c a l effective stress ratio l i n e , at which flow deform-ation or large strain starts to develop, i n a given number of cycles. For medium dense to dense states, however, no contractive flow deforma-tion w i l l occur when the state of stress approaches the c r i t i c a l effect-ive stress ratio lin e . Due to the dilatant nature of the sand, dilation tendency i s then responsible for a rapid increase i n the resistance to liquefaction. For very dense sand, however, t i e resistance to liquefac-56 F i g . 23 R e l a t i o n s h i p between R e l a t i v e D e n s i t y and c y c l i c S t r e s s R a t i o f o r Sand w i t h V a r i o u s L e v e l o f I n i t i a l S t a t i c Shear S t r e s s (2% C y c l i c "Strain). 57 0 20 40 60 80 100 RELATIVE DENSITY, Dr(%) Fig. 24 Relationship between Relative Density and Cyclic Stress Ratio for Sand with Various Level of I n i t i a l Static Shear Stress (5% Cyclic Strain). 58 0 20 40 60 80 100 RELATIVE DENSITY, Dr(%) 0.3 v 20 40 60 80 100 RELATIVE DENSITY, Dr(%) Fig. 25 Relationship between Relative Density and Cyclic Stress Ratio for Sand with Various Level of I n i t i a l Static Shear Stress (10% Cyclic Strain). 59 tion at high i n i t i a l static shear stress level could be less than that for no or low level of T . Sand at this relative density requires very high c y c l i c stress i n order to liquefy or cause certain amount of c y c l i c strain i n both cases. For sample with high level of however, the state of stress i s much closer to the c r i t i c a l effective stress ratio line, hence small amount of strain i s always accumulated i n each cycle of loading from early stage of the c y c l i c loading test (Fig. 5). Hence the relative value of the resistance to liquefaction or c y c l i c straining depends on the relative density of the sand and the level of i n i t i a l s t a t i c shear stress. The prevalent belief that the presence of i n i t i a l s t a t i c shear stress always increases the resistance to liquefaction can not be upheld i n the l i g h t of results of the present investigations. 60 CHAPTER 5 CONCLUSIONS Cyclic leading behavior of Ottawa sand has been studied under t r i a x i a l conditions with and without i n i t i a l static shear stress to simulate the stress conditions on the horizontal planes of s o i l elements beneath the sloping surface or adjacent to the structure. Based on the results obtained i n this study, the following conclusions may be made: (1) In these investigations, improved sample preparation techniques and testing equipment were used i n order to obtain samples of uniform density and minimize the effect of sample disturbance. Also larger size samples were employed i n order to ntinimize the effect of membrane pene-tration. No significant deformation inhomogeneity was observed within the range of strain studied, and a much better correlation with simple shear results was obtained. Non-uniform sample density, sample disturbance and membrane penetration are believed to be the major reasons for wide scatter i n results reported i n literature. Thus unreliable conclusions may have been drawn from those results. (2) By looking at the behavior within cycles of loading enabled us to understand the process leading to liquefaction or cyclic strain development. It was found that before the stress state reaches the failure envelope, there exists a c r i t i c a l effective stress ratio line at which loose sample develops flow deformation and dense sample starts to dilate. In loose sample, the subsequent unloading below the c r i t i c a l effective stress ratio line gave rise to high porewater pressure and brought the sample to the state of i n i t i a l liquefaction i n case there i s shear stress reversal. In dense sand, similar behavior was also 61 observed except the porewater pressure developed at a lower rate and the sample took large number of loading cycles to reach the state of i n i t i a l liquefaction. Therefore, i t always shows progressive developments of pore-water pressure and cyclic strain with number of cycles. (3) From effective stress paths, i t may be seen that only limiting value of the residual porewater pressure can be developed due to c y c l i c loading, and this value can be predicted by Eq. (1). The residual pore-water pressure decreases linearly with increasing K c value and i s indep-endent of the relative density of the sand and the amplitude of the c y c l i c stress applied. (4) From the effective stress paths, i t can also be seen that i n i t i a l liquefaction can occur i n samples with complete or significant amount of shear stress reversal. This i s however, a momentary phenomenon and sample regains i t s strength due to dilation whenever i t i s sheared further. The sample can sustain a very high deviator stress without causing excessive deformation especially i n dense sample. (5) Generally, a sample with i n i t i a l static shear stress develops lower porewater pressure, hence sometimes i t was inferred that the exist-ance of i n i t i a l static shear stress always increases the resistance to liquefaction. However, this study shows that the resistance to liquefac-tion or c y c l i c straining for sample with i n i t i a l static shear stress can either be higher or lower than those with no i n i t i a l static shear stress depending on the relative density of the sand and the level of the i n i t i a l s tatic shear stress. Hence this conclusion i s true only i n certain range of relative density and i n i t i a l static shear stress level. The conclusions drawn from this study i s based on test results 62 of Ottawa sand with confining stress of 2.0 kg/cm2. Extrapolation of results concerning the resistance to liquefaction or c y c l i c straining beyond this range or to different material should be done with caution. 63 REFERENCES 1. Casagrande, A., "Liquefaction and Cyclic Deformation of Sands -A C r i t i c a l Review," Havard S o i l Mechanics Series No. 88, Havard University, Cambridge, Mass., 1976. 2. Castro, G., "Liquefaction of Sands," Havard S o i l Mechanics Series No. 81, Havard University, Cambridge, Mass., 1969. 3. Castro, G., "Liquefaction and Cyclic Mobility of Saturated Sands," Journal of the Geotechnical Engineering Division, ASCE, Vol. 101, GT6, 1975, pp. 551-569. 4. Christian, J . T., Swiger, W. F., "Statistics of Liquefaction and SPT Results," Journal of the Geotechnical Engineering Division, ASCE, Vol. 101, GT11, 1975, pp.1135-1150. 5. DeALba, P., Seed, H. B., and Chan, C. K., "Sand Liquefaction i n Large-Scale Simple Shear Tests," Journal of the Geotechnical Engineering Division, ASCE, Vol. 102, GT9, 1976, pp. 909-927. 6. Finn, W. D. L., and Byrne, P. M., "Liquefaction Potential of Mine Tailings Dams," Commission Internationale Des Grands Barrages, Mexico, 1976, Q44, R9, pp. 153-177. 7. Finn, W. D. L., LEE, K. W., Maartman, C. H., and LO, R., "Cyclic Pore Pressure Under Anisotropic Conditions," Presented at the June 19-21, 1978, ASCE Specialty Conference on Earthquake Engin-eering and S o i l Dynamics, held at Pasadena, C a l i f . , pp. 457-470. 8. Finn, W. D. L., Pickering, D. J., and Bransby, P. L., "Sand Liquefaction i n T r i a x i a l and Simple Shear Tests," Journal of the So i l Mechanics and Foundations Division, ASCE, Vol. 97, SM4, 1971 pp. 639-659. 9. Finn, W. D. L., and Vaid, Y. P., "Constant Volume Cyclic Simple Shear Testing," Proc., 2nd International Conference on Microzon-ation for Safer Construction, Vol. II, 1978. 10. Gibbs, H. J., and Holtz, W. G., "Research on Determining the Density of Sands by Spoon Penetration Testing," Proc., 4th International Conference on S o i l Mechanics and Foundation Engineering, London, England, 1957. 11. Lee, K. L., and Seed, H. B., "Dynamic Strength of Anisotropically Consolidated Sand," Journal of the S o i l Mechanics and Foundations Division, ASCE, Vol. 93, SM5, 1967, pp. 169-190. 12. Prater, E. G., "On the'Interpretation of Cyclic T r i a x i a l Test Data with Application to the Seismic Behaviour of F i l l Dams," International Symposium on Soils under Cyclic and Transient Leading, Swansea, January 7-11, 1980, pp. 495-508. 64 13i. Seed, H. B.f and Lee, K. L., "Licjuefaction of Saturated Sands during Cyclic Loading," Journal of the S o i l Mechanics and Foundations Division, ASCE, Vol. 92, SM6, 1966, pp. 105-134. 14* Seed, H. B., and Lee, K. L., "Pore-water Pressure i n Earth Slopes Under Seismic Loading Conditions," Proc., 4th World Conference on Earthquake Engineering, Santiago, Chile, 1969, Vol. 3, A-5, pp.1-11. 15. Seed, H. B., Lee, K. L., Idriss, I. M., and Makdisi, F., "Analysis of the Slides i n the San Fernando Dams during the Farthquake of February 9, 1971," Report No. EERC 73-2, Earthquake Engineering Research Centre, University of California, Berkeley, C a l i f . , 1973. 16. Seed, H. B., and Peacock, W. H., "Test Procedures for Measuring Soi l Liquefaction Characteristics," Journal of the S o i l Mechanics and Foundations Division, ASCE, Vol. 97, SM8, 1971, pp. 1099-1119. 17. Vaid, Y. P., and Finn, W. D. L., "Static Shear and Liquefaction Potential," Journal of the Geotechnical Engineering Division, ASCE, Vol. 105, GT10, 1979, pp.1233-1246. 18. Yoshimi, Y., and Oh-oka, H., "Influence of Degree of Shear Stress Reversal on the Liquefaction Potential of Saturated Sand," Soils and Foundations, Vol. 15, No. 3, 1975, pp. 27-40. 19. Yoshimi, Y., and Tckimatsu, K., "Two-Dimensional Pore Pressure Changes i n Sand Deposits During Earthquakes," 2nd International Conference on Microzonation for Safer Construction, Vol. II, 1978, pp.853-863. 

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