HARVARD SOIL MECHANICS SERIES No. 88

LIQUEFACTION AND CYCLIC DEFORMATION OF SANDS

A CRITICAL REVIEW

by

Arthur Casagrande

Presented at

Fifth Panamerican Conference

on Soil Mechanics and Foundation Engineering

Buenos Aires, Argentina, November 1975

Pierce Hall

Cambridge, Massachusetts

January 1976

Reprinted (with corrections) January 1979

LIQUEFACTION AND CYCLIC DEFORMATION OF SANDS

A CRITICAL REVIEW

by

Arthur Casagrande Professor emeri tus, Harvard University, Cambridge, MA, USA

SUMMARY

This paper reviews investigations of two basically different phenomena for which in literature the same term LIQUEFACTION is used . To prevent confusion, the term ACTUAL LIQUEFACTION is used in this paper for the response of contractive ( loose) sand that leads to loss of s trength which can cause flow s lides; and the term CYCLIC LIQUEFACTION for the response of dilative (dense) s and when subjec ted to cyc lic laboratory tests. Topics covered: Hypothesis of cr it ical void ratio and its early test ing . Liquefac tion s lide in Fort Peck Dam and hypothes is of flow s truc ture . Inves tigation of ac tual liquefaction with load control triaxial tes ts; definition of dilative and contrac tive zones; F line and l iquefac t ion potential . Investigation of response to cyclic loading in various types of cyclic laboratory tes ts; conc lus ions (1)

that cyc lic liquefac tion in tes t specimens is c aused by red is tribution of water content which is generated by mechanisms that normally are absent in situ , and (2) that cyclic liquefaction normally cannot develop in dense s ands in s i tu . Because i t is unlikely that laboratory tes ts can be devised to eliminate the severe s tress gradients in tes t specimens and t o reproduce the uniform s tresses that exist in a typical element in s itu, the author believes that the great gap between labor­atory and in s itu response to cyclic loading will require comprehens ive f ield inves tigations of full scale tes ts that nature is performing in highly seismic regions. For es timating the in situ cyclic response of medium dense and dense s ands, an interim procedure is sugges ted using cyc lic triaxial tests on anisotropically consolidated specimens.

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CONTENTS

I INTRODUCTION 1

II DEFINITIONS OF "ACTUAL LIQUEFACTION" AND "CYCLIC LIQUE-FACTION" AS USED IN THIS PAPER 1

III EARLY LABORATORY INVESTIGATIONS OF ACTUAL LIQUEFACTION AND HYPOTHESIS OF CRITICAL VOID RATIO (1935-1938) 2

IV INVESTIGATION OF PARTIAL FAILURE OF FORT PECK DAM AND HYPOTHESIS OF FLOW STRUCTURE 5

V ACTUAL LIQUEFACTION PRODUCED IN TRIAXIAL TESTS WITH MONO-TONIC LOAD CONTROL 6

VI COMMENTS ON POTENTIAL FOR ACTUAL LIQUEFACTION 10

VII CYCLIC TRIAXIAL TESTS BY PROFESSORS SEED AND LEE 12

VIII INVESTIGATIONS WITH GYRATORY SHEAR APPARATUS 14

IX COMPARISON OF CYCLIC STRESSES INDUCED IN SITU AND IN LABORATORY TESTS 18

X COMPARISON OF RESPONSE TO CYCLIC LOADING OF DENSE SANDS IN SITU AND IN LABORATORY TESTS 20

XI· LABORATORY TESTS FOR DESIGN PURPOSES - INTERIM RE-COMMENDATIONS 23

XII SUMMARY OF PRINCIPAL CONCLUSIONS AND RECOMMENDATIONS 24

XIII ACKNOWLEDGMENTS 25

XIV REFERENCES 26

LIST OF FIGURES

1 EARLY HYPOTHESIS OF CRITICAL VOID RATIO EXPLAINED BY MEANS OF DIRECT SHEAR TESTS

2 CROSS SECTION THROUGH FLOW SLIDE IN FORT PECK DAM AT STATION 22+00

3 COMPARISON OF THREE ISOTROPlCALLY CONSOLIDATED R TESTS AND ONE S TEST , USING DEAD-LOAD INCREMENTS

4 STRESS CIRCLES OF ISOTROPlCALLY CONSOLIDATED R TEST (Same Test as "A" in Figs. 3 and 5)

5 COMPARISON OF THREE TYPES OF R TESTS WITH ACTUAL LIQUEFACTION

6 CRITICAL VOID RATIO (F LINE) FROM it TESTS USING DEAD-LOAD INCREMENTS OR CYCLIC LOADING

7 CRITICAL VOID RATIO (Esc LINE) FROM R TESTS USING STRAIN CONTROL LOADING

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8 VARIABLES CONTROLLING POTENTIAL FOR ACTUAL LIQUEFACTION OF BANDING SAND (Based on Data in Ref. 8)

9 LIQUEFACTION IN LOOSE SAND ADJACENT TO A WATERFRONT

10 RESULTS OF A TYPICAL CYCLIC TRIAXIAL TEST ON DENSE SAND (Ref. 10)

11 REDISTRIBUTION OF RELATIVE DENSITY IN CYCLIC TRIAXIAL SPECIMEN (Ref. 8)

12 DIAGRAMS ILLUSTRATING MECHANICS OF (a) GYRATORY SHEAR AND (b) RECIPROCATING SHEAR PRODUCED BY ROTATING ARM OF GYRATORY SHEAR APPARATUS

13 SCHEMATIC SECTION OF GYRATORY APPARATUS - LEFT HALF SLIDING PLATE FOR GYRATORY TESTS, RIGHT HALF FOR RECIPROCATING TESTS

14 SCHEMATIC PLAN OF SLIDING PLATES FOR GYRATORY AND FOR RECIPROCATING TESTS

15 COMPARISON OF TYPICAL REDISTRIBUTION OF RELATIVE DENSITY IN RECIPROCATING AND GYRATORY TESTS

16 HISTOGRAMS OF RELATIVE DENSITY DISTRIBUTION IN SPECIMENS AS PREPARED AND AFTER VARIOUS NUMBERS OF CYCLES IN RECIPROCATING TESTS

17 COMPLETE RECORD OF REDISTRIBUTION IN MEDIUM LOOSE SPECIMEN AFTER 25 RECIPROCATING CYCLES

18 RECIPROCATING TEST ON DENSE BANDING SAND

19 INDUCED PORE PRESSURES AND HORIZONTAL DISPLACEMENTS VS NUMBER OF CYCLES IN GYRATORY TEST ON MEDIUM-LOOSE BANDING SAND

20 COMPLETE RECORD OF REDISTRIBUTION IN GYRATORY TEST ON MEDIUM­LOOSE BANDING SAND

21 STRESSES IN AN ELEMENT IN SITU BENEATH HORIZONTAL GROUND SURFACE SUBJECTED TO CYCLIC SHEAR STRESSES

22 STRESSES IN AN ELEMENT IN SITU WHICH IS CONSOLIDATED UNDER UNSYMMETRICAL STRESSES CAUSED BY OVERLYING LOAD AND WITH CYCLIC SHEAR FORCES SUPERPOSED

23 STRESSES IN ISOTROPICALLY CONSOLIDATED SPECIMEN SUBJECTED TO CYCLIC TRIAXIAL TEST

24 CYCLIC STRESSES ON THE SURFACES OF A SPECIMEN SUBJECTED TO RECIPROCATING SHEAR TEST AND RESULTING REDISTRIBUTION

t. INTRODUCTION

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I express my sincere gratitude to the Organizing Committee of the 5th Panamerican Conference for honoring me by their invitation to present this keynote lecture. It is indeed a great privilege to address my colleagues from the American countries stretching from Canada to Argentina, our host country, and also colleagues from other continents.

Soon it will be 50 years since the day when I started assisting Karl Terzaghi. The principal task which he assigned to me from the first day was the improvement and development of soil testing apparatus and techniques of testing. Already then, and many times since, I have observed that the introduction of soil mechanics theories into design practice was handicapped by the limitations of subsurface exploration, sampling and testing. The need of practicing engineers for �pecifica­tions, their desire to use standards and similar demands by govern­mental regulatory agencies, were often responsible for premature adoption of informal or formal standards that lingered on in engineer­ing practice for a long time after they were proven to be unsatis­factory. I have also learned during these decades that whenever I found myself in disagreement with a highly experienced and respected col­league, it was for one or more of the following reasons: (1) we looked at different aspects of the same problem; (2) we generalized too much on the basis of different sets of empirical data; and (3) we used the same terminology for different phenomena. I could describe instructive examples of such differences that had arisen also between Terzaghi and myself; examples that would demonstrate how well such differences have served to set the stage for further necessary investigations and developments. An example from recent years I will describe in this lecture, namely the differences between my views on liquefaction and those by Professor H. B. Seed and his collaborators which they devel­oped in connection with certain aspects of their pioneer work on the design of foundations and dams for earthquakes. I hope that a frank discussion of these differing views will help to clarify the issues and to promote development of reliable methods for determining the in situ response of sand strata to seismic loading.

The purpose of my talk is a critical review of two basically different phenomena which in literature are both referred to as "liquefaction". To distinguish between them, one related to the behavior of loose sands and the other to the response of dense sands under cyclic loading in triaxial tests, I found it necessary to in­troduce in this paper differentiating adjectives, as discussed under the next heading.

11. DEFINITIONS OF "ACTUAL LIQUEFACTION" AND "CYCLIC LIQUEFACTION" AS USED IN THIS PAPER

Until 1966, the term liquefaction was used in literature for the reaponse of saturated loose sand to strains or sbocksthat resulted in flow slides. With the development of the cyclic triaxial tests in connection with research on the response of sand under earthquake

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loading, the same term began to be used for a specific response of sand in cyclic triaxial tests (Ref. lOa). In an effort to prevent con­fusion by the use of the same term for entirely different phenomena, an informal committee of several colleagues and myself tried in 1969 to find another term for the cyclic response phenomena in laboratory tests. Finally we agreed on the term "cyclic mobility". However, by then the term liquefaction was already so well entrenched in literature for use with the cyclic triaxial tests that it proved impractical to adhere to this agreement; and the confusion continued. While I would much prefer not to use the term "liquefaction" for a phenomenon that truly is not liquefaction, I decided reluctantly to use it for both phenomena in this paper, but to differentiate between them with appropriate adjectives as follows:

1. ACTUAL LIQUEFACTION - what was simply called "liquefaction" before the development of cyclic laboratory tests. It is the response of loose, saturated sand when subjected to strains or shocks that results in substantial loss of strength and in extreme cases leads to flow slides.

2. CYCLIC LIQUEFACTION - the response of a test specimen of . dilative sand to cyclic loading in a triaxial test when the peak pore pressure rises momentarily in each cycle to the confining pressure.

A strong minority on that 1969 committee supported the term "strain softening". Superficially, the progressive softening, which develops in cyclic tests on dense sand, may resemble strain softening. True strain softening, however, is produced by stress cycles with essentially uniform distribution of stresses within the material. But the softening of a saturated sand specimen during cyclic loading is caused by redistribution of the water content, with substantial loosening and softening of certain zones in the specimen while other zones are being compacted.

III. EARLY LABORATORY INVESTIGATIONS OF ACTUAL LIQUEFACTION AND HYPOTHESIS OF CRITICAL VOID RATIO (1935-l938)

In part by observing the volume changes of dense and loose sand in direct shear tests and in part by intuition, I developed in 1935 the hypothesis that when loose sand is sheared it decreases in volume, it contracts, and eventually approaches a steady state volume (or void ratio; or density); and that the same sand in dense state increases in volume, it dilates, until it also reaches the same steady state condition as the loose sand. This state I called the "critical denatty", or "critical void ratio". In my first lecture on this sub­ject, in November 1935, (Ref. 1) , I was still under the impression that the critical density is independent of the normal stress. But a few .onths later, when performing tests using a greater range of normal stresses, I concluded that the critical density is a function of the normal stress. Because direct shear tests did not permit sufficiently accurate observation of the volume changes, I designed in 1936 for the Corps of Engineers a triaxial apparatus for investigation of the critical void ratio of fine sands for the Franklin Fall. Dam; (Refs. 2, 3, 4).

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Explanation of the concept of critical void ratio is facilitated by referring to the relationships as derived from direct shear tests, Fig. 1, but plotting the normal stress on a log scale, as will be used in subsequent figures. In Fig. l (b) the vertical scale is the void ratio, or relative density, and the horizontal scale the displacements. Curve L' shows the contractive response of loose sand; curve D' the dilative response of dense sand; and the horizontal line M' represents the critical void ratio or critical density which both samples would reach if shearing could be continued far enough, or if the shear test were started at that void ratio. In Fig. lea) are plotted on the vertical scale the applied shear stress and horizontally again the shear displacements. Curve L shows a steady increase of displacement of loose sand with increasing shear stress until eventually an ultimate shear strength is reached. But for the dense sand curve D develops first a peak strength and then, with further shearing and further volume increase, the resistance drops and the same ultimate shear strength is reached as for the loose sand. Curve M represents a test started at the critical void ratio so that in this test specimen theoretically no volume change should develop, as indicated by line M' in Fig. l (b) .

In Fig. l (c) are plotted the void ratio (or density) on the vertical scale, and horizontally on a log scale the applied normal stress an. For reference, curves Lc, Mc and Dc represent consolida­tion curves as obtained in one-dimensional consolidation tests. The direct shear tests plotted in Figs. lea) and (b) are assumed to be performed under a confining pressure of one kg/sq cm. Therefore, points x, y and z on the consolidation curves in Fig. l (c) are the' starting points of the direct shear tests. By projecting these points horizontally onto the vertical scale of diagram (b) , we find the starting points x', y' and z' of the void ratio vs displacement curves. Thus, points z and z' represent the critical void ratio for this sand when consolidated under a normal stress of one kg/sq em.

If we repeat the tests .at higher normal stresses, the starting void ratios, including the critical void ratio, would all be lower. By making several series of such tests under different normal pressures, we find the critical void ratio line E, the heavy line in diagram (c) which is substantially steeper than the void ratio-pressure curve Mc in that range of void ratios.

To obtain the critical void ratio line, ideally the tests should have been performed on s�turated specimens without allowing change of volume, and with pore pressure measurements; but such testing equipment had not yet been developed 40 years ago. Therefore, the question "what happens when saturated sand is subjected to shearing at constant volume" was answered indirectly, as follows: Suppose the sand is consolidated to the void ratio and normal pressure represented by point p, Fig. l(c). If the specimen would be sheared with volume change allowed, the void ratio would decrease vertically downward, at constant effactive stress, until the critical void ratio line E is reached at point r. However, if no volume change were permitted, the sand would still try to reduce its volume; but because this is not possible, it responds by transferring stress from the grain structure to tha pore vater; 1. e. , we move horizontally at constant volume until we reach the

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critical void rat io l ine at po int q. The init ial effective stress of about 4 kg/sq em at po int p would thus be reduced to almost one­tenth of the init ially appl ied stress; and the pore water would carry almost the entire appl ied stress. Such large reduction in effective stress and correspond ing shear strength causes actual liquefact ion; i.e., the sand changes from a sol id mater ial into a mass which flows like a viscous flu id when subjected to small shear stresses. But beneath a level ground surface, not loaded by structures, a l iquef ied mass cannot flow. The only symptoms of the liquef ied state would be sand boils at the surface produced by upward drainage of excess water. However, a structure underlain by l iquef ied sand would be in serious trouble. From Fig. l(c) we can also conclude that saturated sand below the critical vo id ratio line would be safe aga inst actual liquefact ion; that if such sand is exposed to shear forces, it would develop negat ive pore pressures, i.e., the effect ive intergranular stresses would be increased and the sand would brace itself, so to speak, against failure by increas ing its strength above that which existed before the shear stresses were applied. But cav itation would limit this increase in strength to one atmosphere negat ive pore pressure.

Tbe hypothes is of cr itical vo id rat io and the early test results led to the following conclus ions:

(1) All combinat ions of void ratio and effect ive normal stress which are located below, or to the left, of the cr it ical l ine "E", F ig. l(c), represent states � wh ich the sand would develop d ilat ive response and are safe aga inst [actual) l iquefact ion.

(2) All po ints to the right or above the cr it ical line "E" would represent combinat ions that would result in contract ive response. In order to produce a flow sl ide, and not merely a slump of l im ited dimensions, the start ing point would have to be substant ially to the right of the cr itical vo id rat io l ine so that in the l iquef ied state the effect ive stresses would drop to a small fract ion of those that existed at the start of shear.

(3) Tbe greater the effect ive conf ining pressure, e.g., the greater the depth of a sand stratum, the lower is the crit ical vo id ratio; or, in other words, the denser must be the sand to be safe against [actual] l iquefact ion. But when heav ily loaded, even a medium dense sand may be suscept ible to [actual] liquefact ion.

Essentially these were my views when I presented the second lecture on liquefaction in June 1938; (Ref. 3). Three months later, in September 1938, a major l iquefaction failure developed in the Ft. Peck d .. in Montana which was then nearing its complet ion.

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IV. INVESTIGATIONS OF PARTIAL FAILURE OF FORT PECK DAM - HYPOTHESIS OF FLOW STRUCTURE

In Fig. 2 is plotted a typical cross section through the slide, with true scale in the lower section and with the vertical scale five times enlarged in the upper section. It can be seen that the mass that moved was almost level after the slide. The major movement occurred in about 3 minutes. Some portions of the upstream toe moved to a maximum distance of about 400 meters with the speed of a rapidly moving river. About 8 million cubic meters of sands in the dam and in the foundation participated in this slide.

The Corps of Engineers carried out a major investigation (Ref. 5, 6, 7) which included the taking of large diameter undisturbed samples of the sands by freezing columns of sand in situ and then coring them with Calyx drills. From the results of many triaxial tests, using my hypothesis and testing procedure, it was concluded that these sands could not have liquefied. Probably influenced by these test results, a majority of the consulting board, which was appointed to investigate the slide, concluded that the failure was not caused by liquefaction; (Ref. 5). A minority, including myself, concluded from the speed of the movement and the topography of the slide masses after the movement, that sand at considerable depth must have liquefied. I also was forced to the conclusion that sand located below the critical void ratio line "E", as defined in Fig. 1, can also liquefy; in other words that the type of test, which I used for determining the critical void ratio (Ref. 2) , did not define correctly the boundary between sands that are safe and unsafe against actual liquefaction.

In the years following the Ft. Peck dam slide I developed gradually the hypothesis that when sand is liquefied and is actually flowing, it must have a structure different from that when the sand is static; that during flow each grain is constantly rotating in relation to all surrounding grains so as to offer a minimum of frictional resistance. I termed this the "flow structure". I postulated that such a structure (1) spreads by a chain reaction, (2) exists only during flow, and (3) that in the moment flow stops, the grains re­arrange themselves and revert into a static structure which, after the excess water has drained, will be slightly denser than the static structure before liquefaction occurred. Thus, a mass of sand that has liquefied, would end up with increased safety against actual lique­faction. In a typical alluvial sand with little or no silt, the static structure before and after liquefaction and also the flow structure are all of the Single-grained type. A sand fill constructed by dumping sand in moist state can have a honeycomb structure because the capillary forces between the moist grains resist the sand from settling into a single-grained structure. When such "bulked" sand becomes saturated, it is particularly prone to liquefy; but afterwards tbe mass ends up with a single-grained static structure. When the structure of a sensitive clay collapses in a chain reaction, lique­faction and a flow slide will reeult. The original structure of the clay, however, is irreversibly destroyed. Experience has shown that after reconsolidation such a mass is no longer sensitive to lique­faction.

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The following observation will assist in visualizing the character of the flow structure of sand. When observing hydraulic fill placement of gravel, I once observed a boulder that discharged from the hydraulic pipe line and appeared to be larger than the diameter of that pipe. Obviously there was one position in which it could travel through the pipe provided that the mass was flowing fast enough to maintain the boulder in a position without touching the wall of the pipe and ad-j acent pebbles.

I tried several times to achieve in the laboratory a flow structure, but failed. I began to suspect that the flow structure can develop and exist only within a large mass. Then, about 11 years ago, a graduate student from Chile, Gonzalo Castro, asked me to suggest a doctoral research topic. I decided to make one more attempt and I described to him this problem, with the warning that previous attempts had failed. I mentioned that one reason may be that during flow in nature the driving forces are maintained essentially constant, i.e., that nature is applying dead load driving forces, not strain control as I had tried. Load control ensures that when a flow structure is beginning to develop, the driving force does not relax as in strain control. By keeping the driving stress constant, the mass accelerates faster and faster and more and more of the sand grains will rearrange themselves into a flow structure. Castro was willing to undertake this difficult task. Now I will explain his principal findings which are contained in his dissertation; (Ref. 8), and as supplemented later by additional tests.

V. ACIUAL LIQUEFACIION PRODUCED IN TRIAXIAL TESTS WITH MONOTONIC LOAD CONTROL

Castro performed a major portion of his investigation on "Banding Sand", a uniform, clean quartz sand with sub rounded to subangular grains, a coefficient of uniformity of 1. 8, and with about 10% by weight smaller than 0.1 mm .

In Fig. 3 are plotted the stress-strain curves of three typical R (consolidated-undrained) triaxial tests in which the axial load was increased with dead-load increments. In addition, is shown for comparison the stress-strain curve of an S test (drained test). In all four tests the specimen was first isotropically consolidated under a hydrostatic pressure of 4 kg/sq em. Then the axial load was in­creased with small dead-load increments applied at about one-minute intervals on a hanger.

In test "A", the specimen had s relative density sfter consoli­dation of Drc - 30%. After 15 minutes of incremental axial loading, the stress-strain curve (upper diagram in Fig. 3) reached a peak, at a dey1ator stress of about 2 kg/sq em and a strain of one percent. Then, under the next small load increment the specimen suddenly liquefied and in a small fraction of a second strained to about 25% when the test was stopped automatically. At about 5% strain the effective deviator stress had dropped to ad£ - 0.3 kg/sq cm and then it re-.. ined constant at this value during further flow. In the lower

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diagram, curve "A" shows how the pore pressure rose and reached during the state of flow the constant value of 3. 85 kg/sq em with the corresponding effective minor principal stress 03f· 0. 15 kg/sq cm. From the relationship sin � - 0df/(203f + 0df) - ,

0. 5, the angle of internal friction of this loose sand specimen can be computed to be 30 degrees. This agrees with the results of the S test carried out at the same relative density and which is shown by the dashed stress­strain curve in the upper diagram and by the corresponding stress circles in Fig. 4 for both tests. However. it may be a coincidence that the stresses during the state of flow reflected the same friction angle of 30 degrees as in the S test. I am inclined to believe that at equal relative density the effective friction angle in the flow structure is smaller than in the static structure. This is also supported by the observation that in Fig. 4 the effective stress circle at the peak, when liquefaction started. remains below the 30 degree strength line.

The relative magnitude of the various strength circles in Fig. 4 is a good illustration for the enormous difference in strength which the same specimen of saturated, very loose sand can display after it has been consolidated under a hydrostatic pressure of 4 kg/sq cm. In an S test, i. e. , when pore pressures are not permitted to develop, the major principal stress can be increased to 12 kg/sq'cm, i. e. , the strength (deviator stress at failure) will be 8 kg/sq cm. If no drainage is permitted during axial load increase, the specimen develops a peak strength of only 2 kg/sq cm, with induced pore pressures of 2. 5 kg/sq cm. But this peak strength represents the threshold of the change to a flow structure which is particularly prone to develop when the applied load will not relax with continued strain; in other words when a dead load is resting on the specimen. Fig. 4, and also curve "A" in the upper diagram in Fig. 3, show that the change to the flow structure reduces the peak strength of 2 kg/sq cm to a strength during flow of 0. 3 kg/sq cm. In the liquefied state, the sand in this test had an apparent friction angle of only about two degrees. Therefore, during a flow slide a mass of,such sand would spread out until its surface would slope only a few degrees.

In Fig. 3, test specimen "B" has a relative density of 44% at the start of axial loading. The upper diagram shows that it developed a peak strength somewhat greater than the loose specimen "A"; then it liquefied and strained to 18% in 0. 4 second; and then all movement stopped. To effect additional straining, the deviator stress had to be increased again with dead10ad increments. In this test, during flow the strength had decreased only little as compared to the peak strength; nevertheless, this specimen actually liquefied. The induced pore pressures in this test are shown in the lower diagram which together with the effective deviator stress (strength) during flow in the upper diagram, reflects first acceleration and then deceleration, with the specimen "freezing" at 18% strain. From the short steady state segment of flow movement one can compute the ratio 0df/ (Odf + 203f) - 0. 53 -sin � from which � - 32 degrees. This specimen was substantially denser than specimen "A" and a greater effective friction angle during flow is reasonable. In this test the effective minor principal stress

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decreased to about one-fourth of the stress under which the specimen was consolidated isotropically. This large decrease is not immediately evident from the fact that during the state of flow the peak strength

. is almost maintained. Should one describe the response of specimen "B" 88 "limited" actual liquefaction?

The third test, "C". in Fig. 3 was carried out at 41% relative density after consolidation, i.e., slightly denser than in test "B". The stress-strain curve appeared to develop into a peak at a slightly greater deviator stress than test ItB", with a suggestion of impending actual liquefaction. However, then the stress-strain curve reversed its curvature and the strength increased rapidly as a result of a s trong dilative response, as can be seen by the induced pore pressures in the lower diagram. The pore pressure dropped to zero at a strain of 14%. If this test had been continued, negative pore pressures would have developed. If the S test in the upper diagram had been performed at the same relative density, the intersection of curves "c" and "D" should have occurred at about 14% strain, when the pore pressure dropped to zero. But the S test was made on a looser specimen. For a denser specimen curve "D" would be higher and the intersection would agree better with the 14% strain corresponding to zero pore pressure.

In Fig. 5 (- Fig. 1 in Ref. 9) are compared three tests on loose specimens with relative densities of about 30% after consolidation under a hydrostatic pressure of 4 kg/sq cm. Test "A" is the same test as "A" in Figs. 3 and 4. The loading procedures in the other two tests were different, as described below.

Specimen "ANI! was first anisotropically consolidated with a minor principal stress of 4 kg/sq em (the same as for the other two tests) and a major prinCipal stress of 8 kg/sq em, thus with a principal stress ratio of 2.0. Only two small dead-load increments were applied on this specimen and then it liquefied at about 0.5� strain. This teet demonstrates that loose sand. which is susceptible to actual liquefaction, will more easily liquefy adjacent to a steep slope than beneath a horizontal surface.

Specimen "eyt' was initially consolidated isotropically to 4 kg/sq ca and then subjected to cyclic loading with a deviator stress of about ± 1 kg/sq em. The first four cycles developed almost elastic deformations, with the hysteresis loops practically coinciding, as shown by the single loop in Fig. 5, and with strains of a small fraction of one percent. However, during the 5th cycle the strains increased, a rounded peak developed at about one percent strain, and then the sample actually liquefied.

It deserves spectal emphasis that during the state of flow the .-anitude of the residual strength adf and of the residual effective aiDer principal stress ali were not only constant during flow, but they vere almost identica in all three tests. After a flow structure v .. fully developed, the sand had lost all memory of its past stre.s­strain history. Therefore, it is reasonable to asSUlll8 that the flow structure vas identical in theae three teata.

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In Fig. 6 are plotted (1) the starting conditions and (2) the conditions during flow of all tests performed by Castro in which actual liquefaction developed. (Ref. 8 and tests performed subsequently.) The vertical scales are void ratio and relative density; and the logarithmic horizontal scale is the effective minor, principal stress. The arrows pointing to the left indicate the starting conditions; and the plotted point to the left of each arrow is the effective minor principal stress during the state of flow. The large, heavy circles are tests on isotropica11y consolidated specimens which developed actual liquefaction with large drop in strength. The small circles are tests on isotropica11y consolidated specimens during which there was only a relatively small drop in strength during flow; the triangles are tests on anisotropica1ly consolidated specimens; and the squares represent tests with cyclic loading. The horizontal distance from the starting arrow to the effective stress in the liquefied state is the reduction in the effective stress that developed by actual liquefaction. For example, in this plot the three tests with the loosest specimens had a relative density slightly greater than 20% . One test was consolidated under 4 kg/sq em and during flow its effective minor principal stress dropped to 0.02 kg/sq em, a reduction by a factor of 200. Two other tests at the same void ratio were consolidated under 0.3 kg/sq em and during actual liquefaction they also developed about 0.02 kg/sq em effective minor principal stress, a reduction by a factor of only 15. Fig. 6 shows that no matter to what minor principal stress a specimen was consolidated initially and no matter whether it was consolidated isotropica11y or anisotropica11y, or whether it was cyclically loaded, the conditions during failure all" ended up along a fairly accurately defined line which I now call the F line; the letter F standing for critical void ratio in which lique­faction with a flow s tructure developed.

Then I asked Castro to perform tests with s train control loading and the results are plotted in Fig. 7, with the arrows on the right again indicating the starting conditions. The circular points, which represent the conditions during flow, lie close to a line which is displaced from the P line (Fig. 6) by a factor of about 2.5 in terms of the effective minor principal stress. I will refer to this line as the Esc line. The reason for the large difference in the strength during flow when using load control and strain control loading is the rate of strain. The constant driving force of a dead load produced in these tests a rate of strain about 20,000 times faster than that in the tests with strain control loading. The relatively slow straining in the latter tests causes locally groups of sand grains to lose temporarily their flow structure. I suspect that one could achieve a wide range of Esc lines with widely differing rates of strain control.

Then I asked Castro to perform triaxial S (drained) tests stmi1ar to' those I used 40 years ago, and which were used to investigate the liquefaction potential of the sands in connection with the investi­gations after the slide in Ft. Peck Dam. With a few exceptions, the results fell considerably above the E line,i.e. even further away fro. the F line, and as far as the E6 81ine in Fig. 8; and they

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acattered widely. In retrospect, it is now clear why the investi­gations of the sensitivity of the sands in and below the Ft. Peck Dam yielded strengths about 10-times greater than triaxial R (undrained) teats using dead loads. The reason is simply that a flow structu�e cannot develop in S tests.

VI. COMMENTS ON POTENTIAL FOR ACTUAL LIQUEFACTION

Referring to Fig. 8, where theEscand F lines are reproduced from Figa. 6 and 7, it seems reasonable to express the liquefaction potential, Lp, by a ratio relating the initial effective minor principal stress a 3i to the effective minor principal stress a3f on the F line. In order to make this ratio equal to zero along the F line, I use the expression Lp - (03i - 03f )/03f ' E. g. , for the initial conditions at point Mi, the conditions during actual liquefaction are found by drawing a horizontal line to its intersection Mf on the F line, corresponding to a liquefaction potential Lp - 4.0/0.15 - 1 - 26. For any starting combinations on the F line, the liquefaction potential would be zero; and below the F line it would be negative, i. e. , when the sand is strained below the F line without allowing volume change, negative pore pressures and additional strength would be mobilized. In the area below the F line, which I designate the "dilative zone", or the "D" zone, the sand for which this. particular F line was deter­mined cannot actually liquefy. Above the upper line with the short dashes, the Eu line, this sand will always develop a distinctly con­tractive response when strained; and in that zone liquefaction is likely 88 a result of any rapid straining or shocks. Between the Eu and the F line either dilative or contractive response is possible depending on the rate of strains, and also depending on how close to the F line the starting point is located. Much remains to be learned about the response of sand and the characteristics of the flow structu� within that zone. E. g., in strain control tests it is possible that flow structure will appear and disappear in small pockets or lenses; that as soon as it develops in one pocket, the stresses in that zone will drop by redistribution and the structure in that pocket may revert to a normal structure while in another pocket it may change into a flow structure. The overall resistance of a sample during strain control would then be an average resistance of a constantly changing pattern of distribution of flow structure within the aand.

When the strength during actual liquefaction drops only slightly below the peak strength, as e. g. , in test "B" in Fig. 3. the lique­faction potential ranges between about 2 and 3, i. e. , the starting points would be located in Fig. 8 approximately alo�g the Esc line. In apite of the drop in pore pressure by a factor of 3 to 4, the strength drops only little.

The P line is of prime interest for engineering applications. On the basis of my present knowledge and judgment, I consider the entire area above the F line to be a hazard with respect to actual liquefaction in foundations of dame and important structures in highly seismic

11

zones . Below the F line actual lique faction is not possib le , although small s trains may develop .

From the F line in Fig . 8 we can quickly es timate the s trength of this particular s and in liquefied s tate . Assuming a fric tion angle of 30 degrees and a relative density of 30%, during flow the effect ive minor principal s tress would be about 0 . 1 kg/sq em and the deviator s trength about 0.2 kg/sq em. However, at a relative density of 50%,

the minor effective principal s t ress during flow would be about 3 k g/sq em and this would require a deviator strength of about 6 kg/sq em , corresponding to an effective major principal stress of about 9 kg/sq cm. Therefore , in liquefied state there is an enormous difference in the s trength of the same sand at relative densities of 30% and 50%. For all practical purposes , this s and wi th a relative density of 50% could not develop actual liquefaction.

Now let me ask this question: Is it conceivable that a mass of sand located well below the F line , say at point Ao in Fig . 8, where it is s afe agains t actual liquefaction, could expand or dilate by natural causes to point A 1 well above the F line where it would then b e suscep tible to actual lique faction? Let me describe a natural phenomenon which in the European Alps is known by the name HUREN. Occasionally large masses of rather dense granular talus will l iquefy and flow down a valley causing great des truc tion . It is well documented in literature that jus t prior to such an avalanche the mountain b rook, which emerges from the toe of the talus deposi t , stops flowing . The native popul at ion in mountain valleys have known and heeded such w arning signals for centuries . I consider it possib le that a combina­tion of heavy rainfall or snow mel t, perhaps combined with a thick zone of s till fro zen and relatively impervious t alus adjacent to the slope , will raise the groundwater level in the talus mass and create large shear s t resses which cause s trong dilation, i.e . , a substantial increase in volume which soaks up large volumes of wate r . Such changes could conc eivably change the position of large masses adjacent to the talus slope from below the F line to well above the F line . Perhaps the feasibility of such a mechanism could be inves tigated at relatively small expense by means of laboratory tes ts .

Liquefaction slides sometimes create the impression of a succession of shear s lides . Assume a river b ank in loose sand , Fig . 9, and that an element "A" some dis tance from the slope is subjec t to a s afe principal s t ress ratio; but that an element "B" near the slope is subjec t to a much greater principal stress ratio which renders it more vulnerable to liquefaction . This, combined wi th progressive s teepening of the slope by erosion, can c ause a limited zone to liquefy as illus trated in Fig . 9 (a) . As the hatched wedge of sand flows out, the principal s t ress ratio will increase quickly in an adjacent zone in which, in addition , also the seepage forces will be greater as we move further b ack into the river b ank; Fig . 9 (b) . In this manner lique- . faction can progress b ackward and a large volume of sand may flow into the river, leaving behind a s lope surface with a very flat angle that reflects the low strength of the liquefied s and . However , t o a shallow depth below the ground sur face and next to the face of the s lope. i.e . ,

12

the zones not shaded in Fig. 9(c) , the sand is so light ly loaded that it may lie below the critical F line where it cannot lique fy . On the ground sur face an observer may see only a progression of shear cracks , conveying the impression that the entire movement consists of a succession of ordinary shear s lides , whereas in fac t the major por tion of the m ass is moving like a viscous mass without shear sur faces . Such flow s lides usually s tar t along a short s tretch of the bank . As lique­faction progresses landward , the area widens such that in plan the final area appears like a flask wi th a narrow zone through which the lique fied sand has flowed out .

VII . CY CLIC TRIAXIAL TESTS BY PROFESSORS SEED AND LEE

When finally , after so many years , I believed that with Cas tro's help I h ad solved the prob lem of lique faction of sand in a satis­fac tory manner, Professors Seed and Lee published their well-known paper entitled LIQUEFACTION OF SATURATED SANDS DURING CYCLIC LOADING; ,

(Ref . lOa). Professor Seed and his disciples had then already carried out important pioneer work on the response of ear th mas ses and struc tures to ear thquakes . To app ly their theories, they needed soil parameters that express the response of sand to earthquake loading. I t was logical to experiment wi th cyclic triaxial tes ts . Thereby they discovered that when a triaxial spec imen of saturated sand is subjec ted to cyclic loading in an undrained tes t in such a manner that the principal s tresses pass in each cycle through a hydros tatic s tate of stress (which means that all shear s tresses disappear) , even a dense and highly dilative sand will develop cyclically high pore pressures and deformations .

A typical tes t result from the paper by Seed and Lee is reproduced in Fig. 10 . The s and specimen was placed at a relative dens ity of 78% . In the upper diagram are plotted ver tically the axial strains and horizontally the number of cycles on a log scale . The horizontal line in the middle represents zero s train . The horizontal lines above the zero line are for 5 , 10 and 15% compressive s trains; and below the zero line for 5 , 10 and 15% extens ion . In the lower diagram are p lot ted vertically the induced pore pressures and horizontally again the number of cycles on a log scale . The initial hydros tatic confining pressure vas one kg/sq cm. The axi al deviator stress was plus/minus 0 . 7 kg/sq CB; i.e • • the ver tical principal s tress was cycled between 1 . 7 and 0.3 kg/sq em, while the lateral s tress remained constan t at 1 . 0 k g/sq em. During the firs t 10 cycles the axi al strains remained negligib le , Dut the pore pressures increased and decreased with each cycle , reaching higher and hi gher values until after about 12 cycles the pore pressure reached the confining press ure of one kg/sq cm in the moment when all princ ipal s tresses were equal and all shear s tresses in the .pecimen became zero. When the pore pressure equalled the confining pressure for the firs t time. Seed and Lee de fined this as " initial liquefact ion. II With additional cycles the axial s trains kept increas ing .. 8een in the upper diagram. railure was defined in terms of the number of cycles when the strain amplitude in one complete cycle r.ached a certain magnitude. As c an be seen in Fig . 10. the pore

13

pressure dropped substantially and the specimen displayed a strong dilative response whenever the principal stress ratio rose to a maximum. But in spite of an essentially steady pattern of cyclic pore pressure increase and decrease, the cyclic peak strains of the specimen kept increasing. For example, at 20 cycles the total strain amplitude was 10%, about equally divided between compression and extension.

Prom such tests, Seed and Lee drew the following conclusions:

"1. Initial liquefaction can be produced by cyclic loading also in medium dense and dense sands and is not limited to loose sands.

"2. The liquefaction potential decreases with increasing con­fining pressure.

"3. The liquefaction potential decreases with increasing initial principal stress ratio and, therefore, sand adjacent to a slope is less susceptible to liquefaction than beneath a horizontal surface. II

At that time I did not realize that the term "liquefaction" in their paper had an entirely different meaning than the phenomena that I had always associated with that term. Therefore, these three con­clusions appeared to contradict all my past experience and also the results of Castro's investigations. Since I could not find any clues in their papers for these startling conclusions, I had no choice but to carry out such cyclic tests and observe carefully everything that was happening in these tests. I designed a simple arrangement that could be attached to Castro's triaxial apparatus, to apply cyclic loads of sinusoidal shape. Already the first few cyclic tests which Castro performed showed that the top of a specimen was getting soft and that obviously a radical redistribution of the water content developed within the specimen; that gradually the top of the specimen deformed by alternate necking and bulging, and that sometimes even a thin layer of water appeared on the top of the specimen in the moment when all shear stresses became zero and the pore pressures equalled the confining pressure. We measured this redistribution of the water content by freezing test specimens. This required that the specimen be reconsolidated under the confining pressure by opening the valves. Thereby a certain amount of water from the soft top portion was drained off and then the sample could be removed and frozen. An example of the measured redistribution of the water content, expressed in terms of relative density, is presented in Fig. 11 (from Ref. 8). During the test, the average relative density of the specimen was 72%; but when reconsolidated at the end of the test it increased to an average of 78%. The difference was due to water drained from the 80ft top portion of the specimen and, therefore, the actual relative density of the top must have been considerably smaller than 50%. The measured relative density in the lower portion had increased to 80 to 90%. This reflects the substantial increase in density of the lower half of the specimen. This radIcal redistribution of water content and of corresponding relative density is the combined result of three .ffecta: (1) the boundary effects which cause redistribution a180 in

14

monotonica lly loaded specim ens , as was measured already many years ago at the Wa terways Exper iment Station; (Ref . 11) . (2) the high pore pressure and softening which develop in the moment the specimen is cycled through the s tate of hydros tatic s tress; and (3) a kind of pumping action which seems to draw water to the top that is freed in the moments when cycling through the hydros tatic state of stress . The important question whether such redis tribution in test specimens is representative for wha t happens in an element in situ will be dis­cussed later.

A detailed inves tigation of the redis tribution of the wa ter content in cyclic triaxial tes ts, in which redis tribution is produced by superposition of several different mechanisms , would be a difficult undertaking. Therefore , I decided to tack le firs t the redistribution produced by one mechanism only , namely that produced by non-uni form s tress dis tr ibution on the spec imen boundaries . For this purpose I

. concentrated on the design of a gyratory apparatus in which we could perform gyratory as well as cyclic direct shear tes ts . The design I had in mind would permit freezing the specimen at the end of the-tes t in the apparatus. (Note: At that time I could not think of a rela tively simple design for freezing the tes t specimen inside a triaxial cell . In the meanwhile I have developed a design which ful­fills this requirement . I have submitted i t to the Waterways Experi­ment S tation, Vicksbur g , Miss. , in the hope that it will s timula te a detailed inves tigation of the redis tribution in cyclic triaxial tes ts . )

VIII. INVESTIGATIONS WITH GYRATORY SHEAR APPARATUS

Inves tiga tion o f redis tribution in reciprocating shear and gyratory shear tes ts would have the following advantages: ( 1) It would permit inves tigating the boundary effec ts more clearly than in cyclic triaxial tests in which it would be difficul t to sort out the influence of ( a) b oundary effec ts , (b) of the pumping action and (c) of cycling through the hydros tatic s tate of s tress; (2) it would be easier to freeze the tes t spec imen in the apparatus and without the need of re­consolidation; and (3) the redis tribution could probab ly be inves ti­gated with greater accuracy .

Originally I intended to confine the spec imens in wire-reinforced rubber membranes of the type developed by the Norwegian Geotechnica l Institute . But I s oon realized that it would b e necess ary t o des troy one membrane for each tes t , when cutting the frozen speCimen , and that such cut ting would be difficult . Then it occurred to me tha t we could support the rubber membrane by a type of flat coil spring which is used 88 a toy by the name of "slink.y" . This proved an exc ellent solution . We covered the surfaces of the flat coils wi th teflon to reduce friction; bu t principally we relied on a s light separation of the coils by temporarily inserting "spreaders" before the s tart of .hearing.

The first gyratory apparatus I designed with the help of Castro. But for a major research effor t I needed another intelligent slave . (This is wha t I called my doctoral candidates only half-jokingly . They

15

are in fact a modern kind of s l avery because they s lave for several years for the che rished Ph . D . , al though they may not have read a single b ook about philosophy . ) Jus t in time I found a sui table candidate , Franklin Rendon , a Mexican s tudent who was we l l endowed with endurance , a q uality particularly important for this project becaus e of the many changes in des i gn and in tes t ing techniques that had t o be deve loped by trial and erro r .

I will des cribe the apparatus only brie f ly . I t i s designed t o b e used f o r cyclic direct shear tes ts and for gy ratory shear tes ts . The mechanics of the gyratory tes ts is illus trated in the top of Fig . 12 .

A cons tant horizontal force is app l ied to the top of the spe cimen by a pair of negator springs mounted on a rotating arm. For b revi ty I designated this type of tes t the f ly tes t" . In the lower diagram of Fig . 12 is shown the mech ani cs of the cyclic direct shear test for which I int roduced the name "re ciprocating she ar tes t " , or b rief ly the "X tes t" . For both types of tes t the s ame sys tem is used for app lying the hori zontal force except tha t in the recip rocating tes ts i t is trans formed into a reciprocating force of s inus oidal shape .

Fig . 13 shows a s chematic c ross sec tion o f the app aratus . To the ro tating arm shown on the le f t is mounted a pai r of Ne gator s prings whi ch transmi t a cons t ant horizon tal force to the top of the specimen , i . e . , the horizontal force remains cons tant regardless of the magni tude of the hori zontal displacement . The b ushing and pis ton are mounted in a s liding plate which ( 1) for the gy ratory tes t , shown on the le f t side , glides between gy ratory ball bearings ; and ( 2 ) for the recipro­cating shear tes ts , shown on the righ t s ide , is moving b ack and forth between 3 s e ts o f bearings : s i de , top and bottom guide bearings .

The s pecimen is enclos ed in a rubber memb rane wh ich in turn is supp orted by the "slinky " s prin g . When placing the s pecimen , the coi ls of the flat sp ring are kep t separated by coil spreade rs which are remove d j us t before a test is s tarted . This ensures that the s linky wi ll not c arry any vertical load during the tes t .

I will not describe such det ai ls as the electrical disp lacement and pore p ress ure trans ducers , eq uipment for recording the output o f thes e t ransduce rs , the type o f mo tor used f o r ro tating the arm, the lines and equipment for s aturating the specimen prior to the tes t and the many important detai ls rel ated to the te chnique of free zing the s amp les , and cutting them into 64 segments . (All these de tai ls are des cribed in references 12 and 13 . )

Th e upper diagram i n Fig . 1 4 i s a plan view of the gyratory s liding plate and of the two displacement t rans ducers , one mounted on the rotating arm in the direction of the hori zon tal force , and the second one at 90 degrees to the arm. When us ing for calib ration purposes a s ili cone rubber specimen , the deflection was always s tri ctly in the di rection of the rotating arm. However , for s and spec imens the displacement vector lagged b ehind the direction of the arm, as indi cated by the la, angle A . The in te rnal fri ction in the s and causes a kind of s t i ck-s lip motion and also s l ight vibrations . The lower diagram in

1 6

F i g . 1 4 i s a p l an v i ew o f th e r e c i p r 0 c a t i n g s l i d i n g p l a t e w i t h i t s l a t e r a l and ve r t i c a l gui de b e ar L n g s .

Fi g . I S shuws typ i c a l p a t : e rn s o f thl' r e d i s t r ib u t i on t h a t deve l o p s i n s u ch te s t s . Th e s e t e s t s p e c i m e n s w e r e made ,) f a l t e rn a t in g l ay e r s o f un c o l o re d an d c u l o re d :� anJ , t ,) (!b s t' r v e t. h e de f o nna t i cfb . A t t h e s t a r t o f t h e s e t e s ts t h e re l a t ive dens i t y w as � 1% and as un � f o rT:1 as p rac t i c ab le . The a lJ p U e d ve r t i c a l :llld s h e a r f o r c e s we re the s ame i n b o th t e s t s . fhp l e f t g ,lmp l e w as s ub j e c t e d t o 30 re c i p r o c a t i n g c y c le s and the r i gh t on,' t o 35 gy r a t o ry ey e l e s . A f t e r f re e z i a g , c dc h s amp le was cut i n t o 6 4 e l e m e n t s , wh i ch h a d b ee n adop t e d as a s t an d a r d p ro ce dure f o r "!los t t e s t s i n th i s i ltve s t i g .J t i on . In F i g . 1 5 o n l y the res u l t s of a c e n t e r s 1 1 ( ' e a re s h own : ( 1 ) a t t he t op, ph o t o g r ap hs ; ( 2 ) b e l ow , t h e r e l a t ive de n s i t i e s o f e a ch e lemen t c omp u t e d f rom the

water c on t e n t s ( a f t e r add i ng the amo un t e xp e l l e d b y f re e z i n g ) ; and ( 3) in the l owe r d i a g r ams a r e i n d i c a t e d the c omp a c t e d z on e s as h a t ch e d areas and th e l oos e n e d z one s as b l ank a r e as . B o th s amp les deve l o p e d comp ac te d z o n e s adj acent to t h e c ap and t he b as e . I n t h e le f t s amp le the max imum r e l a t i ve den s i ty i n the t op l ay e r was 5 3 % . i n t h e b o t t om laye r 6 7% . I n t h e r i gh t s amp le th e maximum i n the t op w as 61% and i n the b o t t om 5 5% . Th e g re a t es t loos e n i n g o f the s an d deve l op ed in the mi dd le p l an e , w i th the lowe s t v a l ue 2 0 % in the le f t s amp le and 8% in the r i g h t s amp le . Howeve r , in t h e r i gh t upp e r c o rne r of the le f t s amp le one <� e gmen t s h owe d minus 3 3% whe r e s ome f ree w a t e r h a d ac cumu l a t e d o n t o p o f the s p ec i men and wh i ch , a f t e r f re e z i n g , w as included as p a r t o f t h a t e l e me n t .

Zon e s w i th r e l a t i v e dens i t i e s o f l e s s t h an 30 % , f o r t h i s typ e o f

s and , we r e p rob ab ly li q ue f i e d , at l e as t i n p a r t . I n any c as e , the mob i l i ty of the s e s p e c imens w as ob v i ous ly ce n t e re d in t h e l oo s e ne d zone s . Th i s i s a l s o re f le c t e d b y t h e de f o rma t i ons of the s and l ay e rs , s ee n i n the ph o t o g r ap h s at t h e t op , wh i ch are mos t p r onoun c e d t h r ough­out th e mi dd le o f t h e s p e c imen ; and i n the r e c i p r o c a t i n g t e s t , in the le f t ph o t o g r aph , a l s o a l ong the s i de s whe re we o f ten f ound the l oo s e s t s e gmen t s . In gy r a t o ry t e s t s the l oo s e s t s e gmen t s w e r e o f t e n

ob s e rved a l o n g t h e m i d- p l ane .

Th e p a t t e rn o f l'e d i s t r ib u t i on i s p rob ab ly c ons t an t ly c h an g i n g , even w i t h i n a s i n g l e c y c l e , e x ce p t i n the c omp ac t e d t op an d b o t t om z ones th a t remain e s s en t i a l l y s t ab le i n s h ap e , b u t b e c ome more c omp a c t w i th i n cre as ing n umb e r o f cy c l e s . T h e r e i s a r a d i c a l d i f fe rence i n re dis t r ib u t i on wh i ch deve l o p s i n r e c i p r o c a t i n g and gy r a t o ry te s t s as comp are d to cy c l i c t r i ax i a l t e s t s . I n the l a t te r the g re a t e s t w a t e r con ten t a c c umul a t E: s i n t h e t o p o f i n i t i a l l y un i f o rm tes t s p e c imens .

In F i g . 16 are s h own t y p i c al h i s t o g r ams o f the d i s t r i b u t i on o f the wate r c o n t e n t and re l a t i ve den s i t y of s p e c imen s ( 1 ) as p la ce d ; and ( 2 ) a t the end o f re c i p r o c a t i n g t e s t s . The l e f t upp e r one is a typ i c a l dis t r i b ut i on i n a tes t s p e c imen a s p rep a re d , b u t n o t s h e a re d . I n t h i s s amp le t h e w a t e r con t e n t r an ge d b e tween 2 3 . 2 and 2 4 . 6 % , c o r r e s p ond ing t o a ran ge of re l a t i ve de n s i t y b e tween 5 0 and 6 2 % . The d i s t r i b u t i on app roxima t e d a n o rm a l d i s t r i b u t i on curve . A l l f o u r s p e c imens we r e p laced a t ab o u t th e s ame r e l a t ive dens i t y , s l i gh t ly g r e a t e r t h a n 5 0 % .

l1li ( :.

I ,

I � ;

1 7

In the l ower le f t , a tes t w i th on ly two cycles o f reciprocating shear deve l op ed s ub s tan ti a l re d i s t r ibu t i on as comp ared to the o r i ginal p lace­men t . Th e upper r i gh t d i agram shows the redi s t r ibu t ion a f te r 2 5 cyc le s , w i th a range o f relat ive dens i ty f rom 3 1 t o 76% . In the lowe r right the redi s t ribut i on o f re l a t i ve dens i tv a f t e r 6 4 cyc ies ran ge d from 29 to 74% , and the shape o f the h is to gram no longer resemb les a normal dis t r ib u t i on curve .

Fi g . 1 7 s ummar i zes the red i s t r ib u t ion measuremen ts o f a l l 6 4 e lements f o r a t e s t af ter 25 cycles o f re c i p rocating s he ar . Visua l ly the redis t r ibut ion i s i ll us t ra t e d b y us ing t h ree ranges o f re lat ive dens i ties : ( 1 ) b lank areas for the loos e s t zone s , wi th re l a t ive dens i t ie s less than 48% ; ( 2 ) the d o t ted are as for the ran ge b e tween 48 and 5 9 % ; and ( 3 ) the hat ched areas f o r the dens e s t zones w i th re lat ive dens i t i e s g re ate r than 5 9 % . The t o tal ran ge of red i s t ribution in th is t e s t was b e tween 33 and 74% r e l a tive dens i t y .

Pore p ress ure and disp lacemen t trans ducer records are reproduced in Fig . 18 for a re c ip roca t ing shear tes t on dense s and with an ave rage relat ive densi ty o f 7 3 % wh i ch change d i n 7 1 cyc les to a range of 5 7 t o 8 7% . In the top diagram the p o re p re s s ure g radual ly in­creased , reach ing a maximum i n 2 1 cycles ; and after th at a lmo s t the s ame pat t e rn repeated i t s e l f in all c y c les , w i th the peak p o re pressure in each c y c le reaching ab out 9 5% o f the 2 . 0 k g / sq cm ve r tical confining p ress ure . Only three s e gmen t s o f the total record are rep roduce d : the f i rs t 2 3 cycle s , cy c les 30 to 34 and cyc les 6 8 to 71 . In the lower record i t can b e s een tha t th e horizontal def l e c t i ons increased much more s low ly than the pore p re s sures . I� fac t , when the pore p re s s ure reached i ts maximum af ter 21 cy c les , the def le c t i ons we re on ly ab out one mm in each d i rec t i on ; b u t they kep t increas ing al mos t th roughout the tes t and deve lop ed reas onab ly s teady de f le c t i ons only during the las t 10 cyc les of about 7 mm in each di rec t i on . In this tes t the in i t ia l e ff ec t ive confining p re s sure was 2 . 00 k g / s q cm and the shear s t res s cycled b e tween ± 0 . 2 2 kg/sq cm w i th a frequency o f 0 . 12 cyc les / sec .

The t rans duce r records o f a gyratory tes t on a specimen w i th a relative dens i ty o f 50% is shown in F i g . 19 ; and the redis t ributi on re cord is s ummar ized i n F i g . 2 0 . The e ffec tive ver t i cal s t re s s a t the s ta r t o f the t e s t was 2 . 0 k g/ sq cm and the gy ra tory she ar s t ress 0 . 22 kg/sq cm; thus , T /O c = 0 . 11 . The f requency wa s f = 0 . 10 cycles /

sec .

At the top of Fig . 19 one can s ee that the induc ed p o re p re ssure rose s tead i ly to a maximum equal to about 2 / 3 of the ini t i a l e f fe c tive confin in g p ressure and then i t remained f ai rly c ons tan t . This i s typical of a l l gyra tory tes t s perf orme d . I n s p i t e of t h i s resp onse , which di ffers rad i cally from the rec i p rocatin g tes t s (and even mo re so f rom cyclic tr i axia l tes ts in which the pore p re s sure rises even tual ly t o the confining p res s ure du ring the moment when the cyc l i c deviator s t ress passes thro ugh zero ) , we observe in gyr a t o ry te s t s a t leas t as effec t ive redi s t r ibution and severe s o f tening o f the tes t spec imens as in rec iprocating she ar and cyc l i c t riaxial t e s ts .

" I

18

In gy ra t o ry t e s t s , the d e f l ect i o n mus t b e measured i n two di rec tion s , to de f ine the de f le c t i on ve c t o r . In Fi g . 19 are repro duce d the reco rds o f the two d i s p l acement t r:1Ds duce rs wh i ch me as ure de­f le c t i ons i n t he p l ane of the ro t a t i n g a rm and norma l t o the a rm . For th is tes t the l a g an g l e , \ = 84 de g re e s , is unus ua l ly gre a t . For much denser specimens t h e l a g angl e i s gene ral ly sma l l e r wh ich I f ind s t range .

The red i s t ri b u t i on a t the end o f th is te s t , afte r 10 cycles , is shown in F i g . 20 . Th e pattern of red is t ribut i on is s omewha t s imi lar to tha t in re c ipro ca ting tes t s , pa r t icu l a r ly the compacted zone s adj acent t o the b as e and the c ap ; b u t the ve ry loose z'.me s concent rate in this tes t chi e f ly along the s id e s and the edges of the spec imen . The h is togram o f r e d i s t ribu t i o n i s c l e a r ly unsymme t rical . The s tandard deviat ion i s 0 = 7 . 7 % .

If the deve lop ment of pore p res sure equal to the con f inin g p ressure were used a s a c r iterion for t h e ons e t of cyc lic li que fa ction , we would be fo rce d to the c onc lus ion tha t one canno t ach ieve cy c l i c l iquefac t i on i n rec iproca t ing shear and i n gy rat ory shear tes ts . Never thel e s s , radi cal redi s t rib u t i on o f the water con ten t and s eve re sof tening o f the t e s t spe c imen s deve lop not only in cycli c t riaxial tes t s but als o in reciproc a t ing shear and e specia l ly in gyratory shear tests . The gyratory mo tion seems to be particularly e ff e c t ive in p ro­duc ing red is t ribu t ion of wa te r c onten t and den s i ty in conj unc t i on with re lative ly h i gh e f f e c t ive s t resses .

A s t at i s t ical ana lys is of the redi s t rib u t i on in a l l re ciprocating and gy ratory tes t s on B anding S and sh owed tha t the s tandard deviat i on dec reases wi th incre asing re la t ive dens i ty ; and approxima tely in the s ame pattern for b o th types of t e s t s when o the r var iab les a re kep t un­chan ged . The t o t a l ran ge of the s tandard devia ti on ranges be tween 2 and 10% . Spe c i mens as p repared , not s ubj ected to shea r , fal l into the narrow ran ge o f 2 to 3% ; and dense specimens had only s ligh t ly greater s t anda rd devi ations , even after 100 cyc les .

IX. COMPARI SON OF CYCL IC STRE SSES INDUCED IN S ITU AND IN LABORATORY TESTS

The s tres s e s in an e lement in s i t u , b eneath a level ground surface in a no rmal ly cons o lidated sand s t ra tum , are i l lust rated in F i g . 2 1 . Ini tially , the p rinc ipal s t re s s e s are ve r t i ca l and horizontal , w i t h a p rincipal s t res s ra t io o f ab ou t 2 . 0 , as shown by e lement (A) in the left upper c orner and in the Moh r diagram by the s t ress c i r cle "A" . Now we s uperpose earthq uake-induced h o rizontal cyc lic shear force s , as shown in the e lement des i gnated (B&C) . This causes ,th e princ ipal s t resses to swing l ike a pendulum b e tween the pos i t ions shown in the inc lined e lemen t s (B) and (C ) . The co rres p onding s t re s s c i rc le s coincide i n the si ngle s t ress c i rcle des i gnated "B&C" which i s large r than circ le i tA" and concentric . During each cyc le , all s t resses a re rep resented by a l l c oncen t ri c c i r cles b e tween these two c i r c les , progres s in g f rom A to B to A t o C t o A . Th e s t resses in the e lement never approach a hydros tat i c s t ate of s t res s , i . e . , a s tate in which

19

shear s t resses on all p lane s s i mul t ane ous ly are re duced to ze ro .

In Fi g . 2 2 we c ons ide r an e lement i n s i tu wh i c h is s ub j e c t e d also i n i t i a l ly to s t a t i c shear s t r e s s e s on h o r l z on t a l p l anes , as e . g . , in a dam or in the f o un d a t i o n o f a s t ruct u re . The s u p e rp o s i t i on o f th e cy clic she a r s tre s s e s on the s ta t i c she a r s t re s s c a u s e s t h e in i t i a l

s tres s c i rc l e t i l " t o cyc l e b e twe en t h e c i r c le s " I I " , " I I I " and " IV" . As in the p re ce d i n g case , t b e s t re s s e s in the e le me n t wi l l never app roach a h y d r o s t a t i c s tate of s t res s .

In an e lement in s i t u , w i th the d i mens i on s of a sma l l l ab o ra t o ry test specimen , a t any given moment a l l s t res s e s on the s u r fa c e s o f the elemen t and in i ts interior are for a l l p r ac t i ca l p u rp oses un i formly dis t rib uted and the s t ress grad i en t s w i th i n th e specimen are zero . Even in a s t ra t i fi e d sand wi th l ayers of d i f fe rent c omp os i t ion , the no rmal and she ar s t res se s that are t ransmi t te d a long the int erface of two l ayers w i l l be uni f o rmly d i s t rib u t e d ove r an area of a few squa re inches at any given moment during cy c l i c loading .

Now we cons ider in Fi g . 2 3 the s tresses on the b oundaries and in the interior o f a t riaxial tes t spec imen which is f i rs t i s o t rop ica11y cons olidated and then s ub j e c t e d in undrained s tate to posi tive and negative ve r t i cal deviator s t re sses . The s t res s c i r c le for the ini t ial s t resses i s the pOint H o n the ho r i zontal axis in the Moh r diagram . S uperpos i tion o f devia t o r s t resses ranging b e tween + �o and - �o causes s t res s c i rcles to eme rge on b o th s i des of p o int H , w i th a maximum diame te r �o . H ow wi ll a dense s and res pond to such cy cli c loading? Al though the s and i s s t rongly d i l ative , neve rtheless eve ry t ime i t i s cycled through the hydros tatic s tate o f s t ress , it deve lops a s l i gh t ly con t ractive response ove r a s mall range of devi ator s t ress and s li gh t p o re p ress ures wil l b e induced . Pumping ac t i on of the ver ti cal cycli c forces tends to move the excess water toward the top of the spec imen . Thi s a c t i on , comb ined wi th the e ffec ts of in te rnal s t ress gradients induced by non-un i f orm dis t r ib u t ion of s t resses on the b oundaries . causes red i s t rib ut i on o f water content and s o f tening o f the t op of the spec imen . The cyclic peaks of the pore p ress ures keep in­creas ing and finally rise moment ari ly to the c onfining pressure 0 c eve ry time the s t resses cyc le th rough the hyd ros tatic s t ate ; o r , to use the t e rm now gene rally us ed in l i terature for th is phenomenon , the specimen suf fe rs " l ique fac t ion" . As already exp lained in the in t ro­duc t ion , thi s respons e bears no rel a t i onship to ac tual l iq ue fa c t i on of s and ; and t o di s t inguish b e tween thes e two fund amen tally d i f feren t phenomena I am us ing i n th i s p a p e r " cy c l i c l ique fact ion" when referring t o the phenomenon o f redi s tribut ion and s o f tening in a lab o ratory specimens and when the cyc l i c p o re p r e s s u re momen t arily equa l s th e con f in ing p ress ure . Exactly how cy cling through the hy dros t a t i c s t ress , the pump ing a c t i on and the c y c l i c in te rnal s t res s gradi en ts comb ine t o ach ieve cy clic l iquefac t ion i n such tes t s remains t o b e inve s t iga ted .

The me chan i c s o f red is tr ibution in recip rocating direct shear tes t s is much eas ie r to comp rehend . In Fi g . 2 4 are shown th e non-uni form s t resses th at are gene rated in such tes ts . For compari s o n , in the upp e r l e f t hand corner are sh own again the s t res s e s in an el emen t in situ in whi ch app l i cat ion o f cy c l i c hori z on tal shear s t resses

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20

automati cally mob ilize the same shear s t ress e s on vertical p l anes . All s t resses on these f i c t i tious boundaries of the element , as wel l as in the inte rior of the elemen t , are uni form a t any given moment . In s tark cont ras t , the b oundaries o f eve ry tes t spec imen are cause for non-uni form s t ress dis tributions on th e boundaries and s tress gradien ts in the interior . The rubbe r memb rane transmi ts to the cy lindrical b oundary o f the specimen only normal s t resses . Because the shear s tresses on th is ve rt ical b oundary are zero , the shear s tresses along the edges on the hori zontal faces of cap and b ase are als o ze ro . There fore , the app lied shear force i s dis tribu ted app roxima tely p ara­bolically , as shown in Fi g . 2 4 . But the over turning moment o f these shear forces is not balanced by a countermoment produced by shear forces on the ver t i cal b ound aries . There fore , to maintain equilib ri um , the cente r o f gravi ty o f the normal s t resses transmi t ted b y the cap and the bas e mus t be excent ric ; and th is excentri ci ty mus t cy cle back and forth . This highly non-uni form and cy clically changing pattern o f b oundary s tres ses and the resul t ing severe inte rnal s tress gradients tend t o comp act the sand adj acent to the cap and the b ase and p roduces the type of redis tribution th at we have measured in many reciprocating and gyratory shear tests ; (Ref . 12 and 1 3) .

X. COMPARISON OF RESPONSE TO CYCLIC LOADING OF DENSE SANDS IN S ITU AND IN LABORATORY TESTS

Dep ending on the type of cy clic tes t , one or more o f the following th ree mechanisms are the maj or causes of redist rib ution of water content and development of cy clic pore p ress ures and cy clic s t rains in laboratory tes ts on dense s ands :

1) Cycl ing through hydros tatic s tate of s t ress .

2) Pumping act i on by verti cally app lied cy clic loads .

3) S tress gradien ts wit hin th e test specimen generated by non­uni form s t ress dis t rib uti on on the specimen boundaries . This me chanism is prob ab ly aggrava ted by the small s i ze of the tes t s pecimens in conven tional tes ts .

In addi t ion , a s l i gh t rearrangemen t of grains , generated by b reaking of edges and corners of grains , may make a minor cont ribution to th e development of pore pressures and s t rains in l aborat ory tes ts . This mechanism is normal ly the only one th at p roduces p ore p ressures and s trains wi thin an e lement o f dense s and in s i t u . But in lab oratory tes ts this mechanism is comple tely overshadowed by the effe c ts of the three p rincipal mechanisms listed ab ove .

Because o f the bas i c differences b etween the mechanisms th at produce cy clic pore p ress ures and s t rains in the laboratory and in s i tu, I cons ider it virtually an impos s ib le task to extrap olate or es t ima te from such laboratory tes ts , wi th the help of empirical relationships , how cyclic pore press ures and s trains will deve lop in s i tu .

2 1

Whenever one makes us e of emp irical relationships , there mus t b e a common denominato r . (E . g . , the At terberg limi ts are use ful i n soil mechanics for es tab lishing emp i rical re lationships because p las ticity and various engineering prope rties are re lated t o the content s of clay par t i cles and their mine ral ogy . ) I cannot f ind a common denominator between the p rincipal mechanisms that control the cy lic response in laboratory specimens and the response of an element in s i t u . In laboratory specimens the deve l opment of p ore pressures and cy clic de formations is the result o f radi cal redis tribut ion which in turn is produced by mechanisms that normally do not exi s t in an element in s i tu . I n an e lement i n s i tu normally there i s n o redi s tribut ion and the s tress es remain homogeneous , i . e . , no s t ress gradien ts develop wi thin the specimen . In the convent ional cyclic t riaxi al tes ts cy clic lique­faction wi l l develop even in very dense s ands , when applying enough cycles ; but in s itu, cy clic liquefaction cannot deve lop , except perhap s quite local ly , adj acent to certain rigid boundaries such as p iles or p iers .

Is there a p os s ib i li ty o f develop ing a laboratory tes t wh i ch will dup l i cate the s tress es wi thin an element in s i tu? I t is conceivable tha t we could shake a large mas s of s and, e . g . , a 3 meter cube , wi th a well ins t rumented "e lement" in the cen ter of this mass , to meas ure cyclic pore p ress ures and s t rains . I t would be a cos t ly research effor t , b ut worth serious cons ideration .

Another approach would b e the app lication of the fini te elemen t me thod . T o reduce the number of variab les to a minimum , I sugges t comp aris on o f the two-dimens ional s tress dis tribution of an element in s i tu with that in a long p rismatic tes t s pecimen subj e c ted to reci­procating shear , w i th zero shear s tress on the vertical sides . This would be equivalent to ass uming that in situ a s and s t ratum cont ains ( 1) frictionless , vertical , p arallel planes which are aligned normal t o the cy clic forces , and ( 2 ) rough and inextens ib le horizontal p lanes . I t wi l l req uire experimentation wi th various assump tions of the s and properties to achieve redi s t ribut ion of water content that app roximates what we have observed in rec iprocating shear tes ts . When I firs t cons idere d this app roach , I concluded that i t is too comp licated for the availab le techniques . But th e vision of s uc cess ful treatmen t is so very attrac tive that I would l ike to pers uade the mos t resource ful spec i alis ts in this b ranch of app lied mathemat i cs to lend a hand . Success o f this app roach would not only result in a convincing demons tration of the enormous di f ferences between the response of in s i t u elements and lab oratory specimens t o cy clic l oading, but it would open up the pos s ib i lity of inves tigating the e f fects of local s tress concent rati ons produced by rigid bodies that penet rate into a sand mass , when sub j ec ted to earthquake loading .

The only clearly re alis tic approach t o th is ent i re prob lem area cons is ts of comp rehensive inve s t i gations of the full-s cale experiments whi ch nature has made and continues to perform in highly seismi c relions o f the worl d . But rel iab le in format ion wi ll not be derived from such inves tigat ions unless they are p receded by extens ive preliminary efforts , t o sharpen our tools so t o speak ; in particular to improve avai lable methods and to deve lop new methods (1 ) for conduc t ing

, '

2 2

i n s i tu meas urements o f the degree of denseness o f s ands , and ( 2 ) for de termining the re lative dens ity on small spec imens cut from un­dis turbed b lock s amples that are taken by hand after lowe ring the groundwater . Whenever pos s ible also the age of s and s t rata should be de termined be cause there are indications that young alluvi al s ands are much more sus cep tib le to actual lique fac t i on or development of large s trains than old sediment s th at have b een s ubj ec ted already to many severe earthquakes . Because o f th e great magn i tude and cos ts o f such comprehens ive inves t i gat ions and for o ther reas ons , they would best be undertaken as co operative e f forts by several countries with zones subj ect t o severe seismic act ivity .

Mos t p ub lished field inve s t igat ions on e f fects o f earthquakes on s and depos its are defi cient and make interpretation difficult . Un­warran ted re liance is p l aced on the s tandard dynamic pene trat ion tes t whi ch is far f rom a s t andard as p ract i ced t oday . (E . g . , during a comprehens ive inves ti gati on o f a rather uniform s tratum o f be ach s and deposi ts for the foundation o f a nuclear power plant , four dif ferent b oring organizations made borings independent ly at the s ame location , within a 3 m radius . When comparing their result s , the blowcount s dif fered b y as much as a fac t or of three ! ) As a b as is f o r es timating the in s i t u relative dens i ties by correl ation with b lowcounts , there is a tendency to us e the ave rage b lowcoun t for an en tire s tratum ins tead of p ay in g special at tent ion to layers or lenses wi th the lowe s t blow­coun ts . In alluvial depos i t s one o f ten encoun ters large variations in den s ities b e tween adj acent zones in the same sand stratum . Des t ructive movements at ground leve l may be caused by ac tual lique f act i on of a loose , relative ly thin layer that can be eas i ly ove rlooked in such erude s ubsurface inve s t i gations ; and then overlying , much denser layers are wrongly b lamed for having caus ed the movements . We need more de t ai le d and more accurate in s i tu measurements than is possib le by dynamic p ene t ration tes ts , perhap s con t inuous s tatic cone penetration me asure­ments , to iden t i fy the looses t zones that are respons ib le for large movements . Un for tunately the ident i f i cati on of such zones is p articularly di f fi cult or impossible when the lique fied s and has flowed out laterally or through cracks to the s urface .

St udy o f des criptive l ite rature o f e arthquake e f fects on alluvial depos i t s convinced me that large and des tructive ground movements are caused by actual lique faction or severe sof tening of contract ive s and l ayers at s ome dep th . I believe that the lique fac tion potent ial of such layers could best be iden t i fied by means of triaxial t es ts on undis turbed s amp les , us ing load control tes ts o f the type developed by Cas t ro (Re f . 8) .

For typi cal alluvial s ands cont aining not more than a few pe rcent o f silt s i zes , the uppe r limit of relative dens i ty for whi ch I cons ider actual lique fact ion to be a possib i l i ty , lies in the range b e tween ab out 40 and 50% , depending on con f in ing pressure . Medium- loose sands in the range b e tween 40 and 60% may be s l ightly contractive or s l ight ly dilat ive ; and in s i tu they may resp ond to cy clic l oading with s trains of obj e c t i onab le magni tude , but rarely with act ual lique faction . In strongly dilative , aniso tropi cally conso lidated s ands in s i tu, with

·

Ij • •

I

2 3

relative dens i ties greater than ab out 70% , I cons ider i t normally impossib le for cy clic pore p ress ures to app roach or equal the conf ining p ressure be cause d i l atency w i l l au tomatically caus e the grain s tructure to offs e t loss of s trength by "b racing i tself" so to speak , requiring only minute s t rains ; and I doub t tha t induced pore press ures will normal ly ri se as high as 50% of the confining pressure . In c ontras t , in laboratory specimens of dense sand the redi s trib ution of water con tent , developmen t of s o f t zones and cyc lic l iquefaction c annot be prevented by mob i li zation of a s t rong di lat ive respons e . Spe cial condi t ions that may caus e development of high p ore pressures and excessive s t rains in dense sand in s i tu are the following: ( 1) Adj acent to rigid b oundaries where severe s t ress gradi ents can develop and produce redis tribution of water content . I t would mer i t inve s tigation whethe r such response could sub s tantially reduce the b earing capacity of p i les or p iers dur ing earthquakes . ( 2 ) I f i t were possib le to main tain in s i tu a mas s of sand in an isot ropically conso­lidated s t ate during cy clic loading (wh i ch I doub t ) , then cyclic lique­faction in dens e s and would be theore ti cally possible .

XI . LABORATORY TEST S FOR DES IGN PURPOSES - INTERIM RECOMMENDATIONS

Unt i l s uch t ime when more reliab le data wi ll be availab le on the in s i tu respons e o f di l at ive sands to cy clic loading , I have recommended in re cent years , as a tempo rary expedient , the us e of cyclic triaxial tes ts on aniso t ropically consolidated specimens cut from undis turbed s amp les . Independent ly , other inve s t igators have also tended to include cyc lic triaxi al tes ts on anisotropi cally cons ol ida ted specimens . See , e . g . , the comp rehensive report on ANALYSIS OF THE SLIDES IN THE

SAN FERNANDO DAMS DURING THE EARTH -QUAKE OF FEBRUARY 9, 1 971 , (Ref . 14) . In my recommenda t ion and interp re t at ion o f such tes ts I am now guided by the f o llowing observations and assump tions :

1) In cy clic t riaxial tes ts , redis trib ution and bui ldup o f cy clic pore pressures becomes p arti cularly severe when the peak pore press ures rise wel l ab ove 50% of the confining press ure . Therefore , I use as a test parame ter the number of cy cles , NSO ' required for the pore p ressure to reach 50% o f the confining p ress ure . At that p oint the cyclic s trains are generally s ti ll small .

2 ) I make the f ollowing arbi trary as sumptions which I cons ider to be wel l on the s afe side : ( a) that the me ch anism which causes the bui ldup of pore pressure in s i t u (breakage and minor rearrangement of grains ) is respons ib le for one-fourth of th e cy clic pore pressures induced in laboratory tes ts , with the o ther three-fourths produced by the me chanisms that cause redi s t ribution of water content and sof tening o f the tes t specimens ; and (b ) that in situ the pore pressure wi ll reach 50% of the confining pres sure wh ich in my j udgment is an upper limi t for medium dense and dense s ands unde r the wors t conditions .

3) The p ore pressure in the tes ts rises app roximately in direct p ropor t i on to the number of cy cles up to about 50% o f the conf ining pressure . When comb ining this wi th the preceding assump tion , it follows

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tha t the number o f cy cles whi ch would be required in s i tu t o reach 50r­of the confining p ressure would b e 4xN5 0 .

4) I f an e s t imate of the cy clic s trains is req uired, i t would be ne tes s ary to carry out p recise measurement s of the cy clic s t rains up to NSO and use th ese s trains as a b asis for j ud gment , keeping in mind that only a fraction of these s t rains are caused by the mechanism tha t controls the development of pore press ures and s trains in s i tu .

Again I wish t o emp hasize that t he s t rains which develop in cyc lic laboratory t e s t s when the pore pressures rise to the conf ining pressure ( i . e . when cycl ic liquefact ion is reached ) , as well as all further increase in cycl ic strains dur ing add i t ional cyc ling , b ear no relation­shi� t o the strains that develop in sit u for d i la t ive sands , in my j udgment .

I cons ider the use o f the bes t pos s ib le undis turbed samp les (preferab ly hand-cut b lock s amp les ) an essential requirement for meaningful res ul t s . I also require the use o f the type o f lub ricated ends whi ch we re deve loped by Professors P . Rowe and L. Barden (Ref . 15 ) . In general , the tes t specimens should be precons olidated to a p rincipal s t ress-ratio o f 2 . 0 .

For average alluvi al sands w i th a s i lt fract ion not exceeding a few percent , and w i th a relative densi ty in the range be tween ab out 40 and 60% , we deal with a trans i t i on range between l oose s ands that can actually lique fy and medium dense s ands tha t are s afe agains t ac tual liq uefaction . I n that range i t is pos s ible that triaxial tes ts w i th monotoni c load increas e , us ing dead l oad inc rements , will p roduce l arger s t rains than cy clic loading . Therefore , in that range I rec ommend als o performance o f mono tonic load control t e s ts on specimens that are anis o t ropi cally cons o lidated wi th a p rincipal s tress ratio o f 2 . 0 . Such tes ts also permit a bet ter di f ferentiation b e tween di lative and contract ive resp onse than cyclic tes ts . Unless the results show a well developed dilative resp ons e , I advise performance of addi tional tes ts to define the F line ; Figs . 6 and 8 .

XII . SUMMARY OF PRINCIPAL CONCLUS IONS AND RECOMMENDAT IONS

1. General - To di f feren tiate b e tween b as i cally di f ferent phenomena which are both called LIQUEFACTION in li terature , the term ACTUAL LIQUEFACTION is used in this p aper for the resp onse o f contractive ( loos e ) s and whi ch results in s ubs tantial increas e in pore press ure and loss of s treng th . that can cause a flow s lide ; and the term CYCLIC LIQUE­

FACTION is used for the resp ons e of dilative (dense) s and in cyclic triaxial tes ts when the p ore pressure rises momentarily in each cyc le t o the con fin ing p ress ure .

2 . Cri tical voi d Ra t i o - The concept of the cri t i c al void rat i o , deve loped more th an 4 0 years ago ( Fig . 1 ) had t o be modif ied on the b as is of inves tigations of the f low s lide in F t . Peck dam and Cas tro ' s investigations (Re f . 8) . During actual liquefaction the sand grains

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rearrange themse lves into a flow s t ruc ture which ensures a min imum resis tance to f l ow . By us ing dead loads in R (undrained ) triaxial tests , l iquefaction can be achieved at greater relat ive dens i t ies than with s train control tests ; and the type of test used 40 years ago gave results even more on the unsafe s ide . The same relationship be tween crit i cal void ratio and effective minor p rincipal stress is obtained with (1 ) iso tropically consolidated spec imens , ( 2 ) anisotrop ically conso lidated specimens , and ( 3 ) wi th cyclic l oad tes ts ; Fig . 6 .

3 . Redi s tri bu t i on of Wa ter Con ten t i n Cycl i c Tes ts - The pro­gressive increase of cyclic pore pressures and softening in test specimens in various types of cyclic t es ts , includ ing cyclic l iquefaction in triaxial tests , are caused by radical redistribut ion of the wa ter content which is generated by mechanisms that are normally not active in s i t u .

4 . Recommenda ti on for Fi eld Inves tiga ti ons - Because it is unlikely that a laboratory tes t can be devised which wi ll produce in tes t specimens the type of uni form s t ress dis tribut ion that exists during cyclic loading in a typi cal element in s itu , the au thor believes that c los ing the great gap between laboratory and in situ response will require primarily comp rehens ive f ield invest igations of many full-scale tests that nature has performed in highly seismic regions . Such in­ves tigations will have t o be carried out with the bes t possib le investigat ional tools and with meticulous atten tion to details , les t they wil l create mis lead ing information .

5 . In terim Recommenda ti ons for Labora tory Tes ts - For e s t imat ing the in situ response of medium dense and dense sands , i . e . , sands which are safe agains t ac tual l iquefact ion , an in terim procedure is suggested which is based on performance of cyclic t riaxial tests on anisotropically consolidated specimens cut from und is turbed samples .

Whenever a quest ion arises whether a sand stratum could experience actual l iquefact ion , it is recommended to carry out R tests wi th dead load increments , as developed by Cas tro (Ref . 8) , using the be s t poss ible undis turbed samp les .

XI I I . ACKNOWLEDGEMENTS

The doctoral research by Gonzalo Cas tro and Franklin Rendon was made pos s ible wi th assis t ance of many organizations and individuals . Detailed acknowledgement s were included in Cas tro ' s thesis (8) and will be included in Rendon ' s thesis .

I am part icularly indebt ed to Stan ley D . Wilson for his crit ical review of a draft of this paper and his many valuab le sugges t ions .

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XIV. REFERENCES

(l) Casagrande , A. , "Characteris tics of Cohesionless Soils Affecting the Stab ility of Earth Fillslf , Journal of the Bos ton Soci ety of Ci vi l Engi neers , January 1936 . Reprinted in " CONTRIBUTIONS ro SOIL MECHANICS , 1 925-1 940" , Bos ton Soci e ty of Ci vi l Engineers , October 1940 .

( 2 ) Casagrande , A . and Watson , J . D . , "Compaction Tes ts and Critical Densi ty Investigations of Cohes ionless Materials for Franklin Falls Damtl , Appendix BII in Report to the U . S . Engi neer Corps , Bos ton, 19 3 8 .

(3) Casagrande , A. , liThe Shearing Resistance of Soils and its Relation to the Stability of Earth Dams" , P roceedings , Soi ls and Founda tion Conference of the U . S . Engineer Department , Bos ton , Mass . , June 1938 .

(4) Watson , J . D . , "Stress-Deformation Characteris tics of Cohesion1ess Soils from Triaxial Compress ion Tes ts" , S c . D . TheSiS , Harvard Unive rs i ty , 1940 .

(5) Corps of Engineers , U . S . Department of the Army , "Report on the Slide of a Portion of the Upstream Face at Fort Peck Dam. " U.S. Government Printing Offi ce , Washington, D . C . , July 19 39 .

(6) Middlebrooks , T . A. , "Fort Peck S lide" , ASCE Transacti ons , Vol . 107 , 194 2 .

( 7 ) Casagrande , A. , "Role o f the Calculated Risk in Earthwork and Foundation Engineering" , Journal of the Soi l Mechanics and Founda tions Di visi on , ASCE , July 1965 .

(8) Cas tro , Gonzalo , "Liquefaction of Sands" , Harvard Soi l Mechani cs Seri es No. 8 1 , January 1969 .

(9) Cas tro , Gon za10 , "Liquefaction and Cyclic Mobility of Saturated Sands " , Journal of the Geotechni cal Engi neering Di visi on , ASCE, June 19 75 .

(lOa) Seed, H . B . and Lee , K. L . , "Liquefaction of Saturated Sands during Cyclic Loading" , Journal of the Soi l Mechanics and Founda tions Di vi s i on , ASCE , Novembe r 1966 .

( lOb) Lee , K . L. and Seed , H . B . , "Cyclic Stress Conditions Causing Liquefaction of Sand" , Journal of the Soi l Mechani cs and Founda ti ons Di vision , January 1967 .

( 11) Shockley , W . G . and Ahlvin , R. G . , '�on-Uniform Conditions in Triaxial Tes t Specimens" , Research Conference on Shear strength of Cohesi ve Soi l s , ASCE, Boulde r , Colorado , 1960 .

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(12) Casagrande , A . and Rendon , F . , "Reciprocating and Gyratory Shear Apparatus - Design , Tes ting Procedures and Tes ts on Saturated Sand , " Report to WATERWAYS EXPERIMENT STATION , Vicksb urg , Miss . , 19 7 6 .

(13) Rendon , t . , Doctoral Dissertation ( in preparation) , Harvard University , 19 76 .

( 14) Seed , H . Bolton , Lee , K . L . , Idries , I . M . and Makdisi , F. l . , "Analysis of the Slides in the San Fernando Dams during the Earthquake of Feb . 9 , 19 7 1 , " Ear thquake Engi neering Research Cen ter , Report No . EERC 7 3-2 , University of California , Berkeley , California , June 19 7 3 .

( 15) Rowe , P . and Barden , L . , "Importance of Free Ends in Triaxial Testing , " Journa l , Soi l Mechanics and Founda tions Di vi si on , ASCE , January 196 4 .

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