Ishihara - Liquefaction and Flow Failure During Earthquake [PDF]

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Ishihara,K. (1993). Gdotechnique 43, No. 3, 351-415



Liquefaction and flow failure during earthquakes K. ISHIHARA*



Two aspects of seismically-induced liquefaction are discussed which are of vital engineering significance: the triggering condition and the consequences of liquefaction. The triggering condition is examined with respect to liquefaction analysis, note being taken of the onset condition which is governed by cyclic strength. Consequences of liquefaction are discussed with respect to post-seismic stability analysis, in which the residual strength plays a major role. Procedures used for liquefaction analysis based on the results of in situ sounding tests are introduced, and the applicability of this method for estimating associated ground settlements is discussed. The evaluation of residual strength requires a better understanding of undrained sand behaviour. Results of extensive laboratory rests on Japanese standard sand are examined and new index parameters are proposed to quantify undrained sand behaviour better. The results of laboratory tests on silty sands are examined in the same way. All the results are presented in terms of whether sand behaviour is contractive or diltative. The laboratory-established criterion for contractive or diltative behaviour is expressed in terms of field parameters such as N value from the SPT or qe value from the CPT. This correlation permits in situ deposits to be classtied as being either able or not able to develop flow slide. The laboratory-established relationships between the normalized residual strength and the field parameters are presented. These correlations are shown to be consistent with many cases of flow failure observed in recent large earthquakes. The relationship between cyclic strength and residual strength is clarified.



L’article etudie deux des aspects de la liquefaction sismiquement induite qui sont d’une importance vitale pour les ingknieurs: les conditions de dCclenchement et les con&quences de la liqubfaction. Les conditions de di?clenchement sont examinies au travers d’une analyse de la IiquCfaction pour laquelle les toutes premiires conditions, regies par la r&stance cyclique, sont prises en compte. Les consequences de la IiquCfaction sont Btudiks P I’aide d’une analyse de stabiliti! post-sismique pour laquelle la r&stance rbiduelle joue une rSle primordial. L’on prbente les mkthodes utili&es pour I’analyse de la IiquCfaction fond&s sur les ri?sultats d’essais in-situ. L’applicabiliti! de cette mCthode i I’estimation des tassements associb est egalement discutCe. L’Cvaluation de la r&stance rCsiduelle demande une meilleure comprbhension du comportement des sables non-drain& Les rbultats d’essais extensifs de laboratoire sur des sables japonais standards sont Ctudib et de nouveaux param&res sont proposb pour amCliorer la quantification du comportement des sables non-drain&. Les rCsultats obtenus pour des sables argileux sont Ctudib de la m6me faGon. Tous ces rbultats sont p&en& diffbremment selon que le comportement du sable est contractant ou dilatant. Le criti?re Ctabli en laboratoire pour des comportements dilatant ou contractant peut s’exprimer en terme de paramitres de chantier tels que N valeurs issues du SPT ou q, valeurs issues du CF’T. CPT. Cette corrilation permet de classer les depats in-situ comme Ctant capahles ou non de dCvelopper un glissement par koulement. L’article prbente Cgalement les relations i?tablies en laboratoire entre la rbistance r6siduelle normaliske et les paramktres de chantiertels que SPT ou CPT. Ces correlations sont en accord avec de nombreux cas de rupture par &coulement observCs lors de grands sitismes r¢s. La relation existant entre r&stance cyclique et rbistance rbiduelle est clarif%e.



KEYWORDS: case history; earthquakes; fabric/structure of soils; liquefaction; sands; silts.



INTRODUCTION The phenomenon of sand changing its behaviour from solid to liquid was recognized in the early stage of soil mechanics’ development. The term



‘spontaneous liquefaction’ was coined by Terzaghi & Peck (1948) to indicate the sudden change of loose deposits of sand into flows much like those of viscous fluid, triggered by a slight disturbance. This phenomenon was considered to be the main cause of slope failures likely to occur in saturated deposits of fine silty sands. It was



* Professor of Civil Engineering, University of Tokyo. 351



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352



K.



ISHIHARA



LEVEL GROUND



settlement



( analysis



)



,SLOPING GROUND



Fig. 1. Flow chart of the problems associated with liquefaction



probably not until 1953 that a similar phenomenon was recognized (by Mogami & Kubo, 1953) to take place during earthquakes and addressed under the name of liquefaction as an issue of engineering significance. The impetus for Mogami & Kubo’s early work in the laboratory apparently emerged from the experience of the Fukui earthquake in 1948 in Japan, in which liquefaction of the ground and associated damage occurred in a widespread area in the alluvial plain. The Niigata earthquake of 1964 is regarded in Japan as a milestone in that it led to public recognition of liquefaction phenomena and of the importance of measures to mitigate the damage caused by earthquakes in general. The city of Niigata had been reduced to ashes by a large fire in 1955, but as a result of extensive restoration works the urban area had been reshaped and reborn as a new city with modern facilities and installations. Thus, the 1964 earthquake was an enormous blow, and caused unprecedented damage. The Niigata earthquake can be cited symbolically as the first event in the world where all kinds of modern infrastructure were destroyed (to the surprise of many) by what came to be well known later as soil liquefaction. Because of its engineering importance, the problems of liquefaction have received a great deal of attention among the geotechnical community and many efforts have been made to clarify the basic mechanism and various aspects of the associated problems. The progress of investigations into liquefaction and its consequences have been described in detail in state-of-the-art papers by Yoshimi, Richart, Prakash, Balkan & Ilyichev (1977), Seed (1979) and Finn (1981). When the ground is subjected to strong shaking during an earthquake, several phenomena of engineering significance can manifest themselves, from onset of liquefaction to sub-



sequent ground settlements and sometimes flow failure involving extremely large movements of soil masses. The phenomena and problems associated with liquefaction can be put in perspective by considering two different conditions encountered in the field. One is the level ground condition in which the phenomenon of cyclic softening or liquefaction is of prime concern; the other is the sloping ground condition where flow failure or large lateral displacement is of major importance in addition to the cyclic softening. Fig. 1 shows the phenomena and problems of engineering significance for each of these conditions. In the level ground condition, the major factor would be the occurrence of cyclic softening or liquefaction in sandy deposits in which the ground starts to move back and forth with a large amplitude. The assessment of whether cyclic softening can or cannot occur in a given deposit would be the first important task in clarifying the level of safety of the ground against an earthquake with a given intensity of shaking. Under level ground conditions, the next problem would be the estimation of ground settlements resulting from dissipation of pore water pressures developed in liquefied sand deposits, which cause grave concerns for the integrity of lifelines buried at shallow depths where the deleterious effects of liquefaction are most predominant. In sand deposits such as under sloping grounds, levees or embankments, checks should be made in the same way as for level ground to determine whether or not cyclic softening or liquefaction is triggered. If liquefaction is identified as being triggered, the ground will at least undergo large-amplitude motions causing settlement or breakage of overlying structures, as in the case of level ground. In the worst case, the ground will start to move largely in one horizontal direction, perhaps driven by a slightly per-



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LIQUEFACTION AND FLOW FAILURE



sisting gravity-induced force, bringing about an intolerable amount of lateral deformation or flow-type failure. A second-step analysis is then necessary to determine whether the flow-type deformation will or will not occur, on the condition that cyclic softening or liquefaction has already occurred in the sand deposit being considered. This kind of evaluation is called postseismic stability analysis; the strength used in this analysis is termed residual strength or steadystate strength. If the once-liquefied ground is identified by post-seismic stability analysis as being prone to flow-type failure, the consequences will be disastrous, involving extensive movement or complete slumping of soil masses forming the ground or embankments. However, if the postseismic stability analysis indicates that the flowtype failure can be avoided, the consequent damage will remain below a tolerable level, although it may require some degree of repair work. In the first part of this Paper, recent developments in the evaluation procedures of liquefaction potential in the field are briefly summarized, together with the application of liquefaction potential to the estimation of ground settlements. In the second part, problems associated with flow-type deformation are examined in detail, with emphasis on the results of recent laboratory tests conducted at the University of Tokyo. The outcome of these considerations is examined in the light of the observed performance of sandy grounds during recent earthquakes. DEFINITION SOFTENING



OF LIQUEFACTION



OR CYCLIC



The basic mechanism of onset of liquefaction is elucidated from the observation of behaviour of a sand sample undergoing cyclic stress application in the laboratory triaxial test apparatus. Seed & Lee (1966) consolidated samples of saturated sand under a confining pressure and subjected them to a sequence of constant-amplitude cyclic axial stress under undrained conditions until they deformed to a certain level of peak-to-peak axial strain. This loading procedure creates stress conditions on a plane at 45” through the sample analogous to those produced on the horizontal plane in the ground during earthquakes. This correspondence of the laboratory sample and in situ soils is the basis on which the cyclic triaxial test is warranted as a useful procedure for producing meaningful data to assess the resistance of sands to liquefaction. In the test described above, it is generally observed that the pore water pressure builds up steadily as the cyclic axial stress is applied, and eventually approaches a value equal to the initially applied confining pressure, thereby produc-



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353



ing an axial strain of about 5% in double amplitude (DA). Such a state has been referred to as ‘initial liquefaction’ or simply ‘liquefaction’. For loose sand, the initial liquefaction can certainly be taken as a state of softening, because infinitely large deformation is produced suddenly with complete loss of strength during or immediately following the 100% pore water pressure build-up. For medium dense to dense sand, a state of softening is also produced with a pore water pressure build-up of almost lOO%, accompanied by about 5% DA axial strain. However, deformation thereafter does not increase indefinitely, and complete loss of strength does not take place in the sample even after the onset of initial liquefaction. None the less, some degree of softening takes place in the sample accompanied by a sizeable amount of cyclic strain, and it has therefore been customary to consider the state of 100% pore water pressure build-up or the development of 5% DA axial strain as a criterion by which to recognize a state of cyclic instability covering a wide range of density of sand. In silty sands or sandy silts containing some amount of fines, the pore water pressure is observed not to develop fully, but to stop building up when it has reached a value equal to about 90%-95% of the initial confining stress. However, a sizeable amount of cyclic strain is observed to develop, indicating considerable softening taking place in these soils. Thus, the occurrence of 5% DA axial strain in the cyclic triaxial test is used below as a criterion to define coherently the state of cyclic softening or liquefaction of soils, from clean sands to sands containing fines. In order to specify the onset of liquefaction or development of 5% DA axial strain, the number of load cycles must be specified in the constantamplitude uniform cyclic loading. In principle, the number of load cycles can be set as arbitrary, provided an appropriate correction factor is incorporated to evaluate the irregular nature of seismic loading, but it has been customary to consider 10 or 20 load cycles in view of the typical number of significant cycles present in many actual time histories of accelerations recorded during past earthquakes. Thus, the onset condition of liquefaction or cyclic softening is specified in terms of the magnitude of cyclic stress ratio required to produce 5% DA axial strain in 20 cycles of uniform load application. This cyclic stress ratio is sometimes referred to simply as cyclic strength.



CYCLIC RESISTANCE OF RECONSTITUTED CLEAN SAND The potential for liquefaction of saturated sands under seismic loading conditions has been



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K. ISHIHARA



extensively investigated by many workers by means of cyclic triaxial tests, cyclic simple shear tests and cyclic torsional tests in the laboratory. The outcome of these studies has generally confirmed that the resistance to liquefaction of the samples of clean sand reconstituted in the laboratory is influenced primarily by factors such as initial confining stress, intensity of shaking (as represented by the amplitude of cyclic shear stress), number of cyclic stress applications, and void ratio or relative density. As a result of comprehensive laboratory studies, it has been recognized as reasonable and become customary to consider the combined effect of cyclic shear stress and initial confining stress in terms of the cyclic stress ratio defined as ad2a,’ for the triaxial loading condition in which e,, denotes the single amplitude of cyclic axial stress and ue’ is the initial confining stress. Thus, it has become a routine practice to take the cyclic stress ratio required to cause 5% DA axial strain under 20 load cycles as a factor quantifying the liquefaction resistance of sands under a given state of packing as represented by void ratio or relative density. This cyclic stress ratio is represented by C~dlo~o’)l*o>and is sometimes referred to as the cyclic strength. It has also been observed that the resistance to liquefaction as quantified above tends to increase in proportion to the relative density at which the sample is prepared for the laboratory tests. Although relative density has been recognized as a dominant factor influencing the cyclic strength, studies by Ladd (1974), Mulilis, Seed, Chan, Mitchell & Arulanandan (1977) and Tatsuoka, Ochi, Fujii & Okamoto (1986) have indicated that, even when the relative density is the



0



I



I



I



same, samples prepared by different methods can show different resistances to liquefaction. Fig. 2 shows the results of cyclic triaxial tests performed by Mulilis et al. (1977) on saturated samples of Monterey No. 0 sand prepared by two different methods. In one method, called air pluviation, oven-dry sand was continuously poured into the sample-forming mould, and after saturation and consolidation the sample was subjected undrained to cyclic axial stress until it softened to develop a significant amount of cyclic strain. In another method, called moist tamping, sand with 8% moisture content was spread in the mould and compacted in layers with a tamping rod so as to attain a desired density. Of several methods employed by Mulilis et al. (1977), these two were shown to produce the samples of lowest or highest resistance to liquefaction. Fig. 2 shows that the cyclic resistance of sand can vary over a fairly wide range, depending on the nature of fabric structure created by different methods of sample preparation. The study described has shown that it is important to specify a method of sample preparation if cyclic tests are to be run on reconstituted samples. In addition, it has been considered almost mandatory to conduct tests on undisturbed samples if the cyclic resistance of in situ sand deposits is to be evaluated with a reasonable level of confidence. In view of the variability due to the sample preparation described above, and because of the diversity of test results due to other testing details, Silver, Chan, Ladd, Lee, Tiedemann, Townsend, Valera & Wilson (1976) attempted to implement a co-operative testing programme in the USA in which eight organizations were requested to conduct a series of cyclic triaxial



I,,/11



1



I



I



I11111



10 Number



of cycles



to



/ 100



5 %



D.A. axial



Strain



Fig. 2. Effects of sample preparation on cyclic shear strength of sand



(Mulilis et al., 1977)



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LIQUEFACTION



AND FLOW



FAILURE



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355



between tes.t results wth



Boundary



I



01



I 10 Nvmber oi-cycles- to 5% D.A. stro,”



I 100



I



Fig. 3. Results of the co-operative tests in the USA on cyclic strength of sand (Silver ef al., 1976)



tests under specified conditions of equipment, test performance and data presentation. Monterey No. 0 sand with D,, = 0.36 mm, U, = 1.5, e max = 0.85 and emin = 0.56 was used to prepare test specimens of a relative density 60% by means of moist tamping as described above. The samples were consolidated to a confining stress of (ra’ = 100 kPa and subjected undrained to cyclic loading. The results of this programme are summarized in Fig. 3 in terms of the cyclic stress ratio plotted against the number of cycles required to produce 5% DA axial strain. The test data lie in a rather narrow band, indicating reasonable consistency of the cyclic strength between laboratories. From the average curve shown in Fig. 3, the cyclic stress ratio causing 5% DA strain in 20 cycles of loading is read as 0.31. If this cyclic stress ratio is assumed to change in proportion to the relative density, the cyclic stress ratio correas sponding to D, = 50% can be evaluated 0.31 x 50/60 = 0.26. This is the value of cyclic strength that can be compared to the value in Fig. 2 obtained by Mulilis et al. (1977). For the sample formed by the moist tamping, the cyclic stress ratio causing 5% DA strain in 20 cycles of loading is read from Fig. 2 as being 0.28. If allowance is made for the difference in initial confining stress, the cyclic strength obtained by the cooperative tests can be considered to agree well with that obtained by Mulilis et al. (1977). A similar effort at co-operative tests was undertaken by the Research Committee of the Japanese Society of Soil Mechanics and Foundation Engineering (JSSMFE), in order to diffuse the use of some concerted testing procedures among many organizations involved in geotechnical testing. Detailed accounts of this programme are given by Toki, Tatsuoka, Miura, Yoshimi, Yasuda & Makihara (1986) and Tatsuoka et al. (1986). Five laboratories participated; each was requested to perform a series of tests on samples of Toyoura sand (D,, = 0.164 mm, U, = 1.46) prepared at relative densities of 50% and 80% by



02



0.5



1



1



2 5 IO 20 50 100 200 Number of cycles to 5% DA axial strain



500



Fig. 4. Results of the co-operative tests in Japan on cyclic strength of sand (Toki ez al., 1986)



use of its own cyclic triaxial test equipment. It was stipulated that the samples be prepared by the method of air pluviation, where dried sand was poured into the sample-forming mould from a funnel in a specified manner. All the samples were consolidated isotropically under a confining pressure of (rO’= 98 kPa and cyclic loads were applied undrained until they produced a state of cyclic softening with attainment of the DA axial strain of 10%. The outcome of the co-operative tests is shown in Fig. 4, where the cyclic stress ratio is plotted against the number of cycles required to produce 5% DA axial strain. Figure 4 shows that the data from several sources fall within a relatively narrow band, indicating a reasonable degree of coincidence among the values of cyclic strength from various laboratories. There is a tendency, however, for the smaller-size specimens to show slightly greater resistance to cyclic softening than the larger samples. This is attributed to the effects of system compliance arising from membrane penetration, sample seating or tubing in the test apparatus. The curve in Fig. 4 sets an approximate boundary between the two groups of data from different sample sizes, and may be taken as indicating an average of the data from various laboratories. The cyclic stress ratio causing 5% DA strain in 20 cycles of loading is read from Fig. 4 as being 0.14 for the samples of relative density D, = 50%. Since all the samples were prepared by the air pluviation method, this value of cyclic strength can be compared with the corresponding test data of Mulilis et al. (1977) shown in Fig. 2, which indicate a similarly defined cyclic strength of 0.21. Such a large difference cannot be explained fully, but Toyoura sand of much finer grain size appears to exhibit less resistance to liquefaction. The interpretation of the test results on reconstituted samples is discussed below with reference to its practical application.



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356



K. ISHIHARA



Moist placement and dry deposition are introduced below as methods to prepare samples in laboratory tests. The moist tamping used here is roughly the same procedure as moist placement, but the air pluviation differs from the dry deposition procedure in that the sand is air pluviated from a certain height, whereas the sand is placed from zero height in dry deposition.



CYCLIC RESISTANCE OF IN SITU DEPOSITS OF SAND In view of the diversity of cyclic strength of sand samples reconstituted by different methods of preparation, it has been recognized that deposits of sands in the field may exhibit varying resistance to seismic load application. Thus, there have been increasing efforts to recover samples as perfectly undisturbed as possible from in situ sand deposits and to test them in the laboratory under conditions representative of those in the field. The in situ techniques used to recover samples of sands from below the groundwater table are divided into two groups: tube sampling and ground freezing. The tube-sampling technique has been shown to be useful for the recovery of undisturbed samples from loose deposits of sands, but adverse effects due to sample disturbance become with increasing sand density pronounced (Ishihara, 1985). The ground-freezing method has been developed instead, and used successfully to recover high-quality undisturbed samples even from dense deposits of sands. In a comprehensive investigation by Yoshimi, Tokimatsu, Kaneko & Makihara (1984) and Yoshimi, Tokimatsu & Hosaka (1989), undisturbed samples were recovered by the freezing technique from in situ sand deposits in Niigata. At the same time, a manmade fill was provided in a large bin 4 m wide, 6 m long and 5 m deep by letting the sand sediment underwater. Undisturbed samples were also obtained from this freshly deposited fill by means of the freezing method. A series of cyclic triaxial tests were conducted on the undisturbed samples thus obtained (Yoshimi et al., 1989). The outcome of the test programme is shown in Fig. 5: for clean sands with relative densities of about 50% and 80%, the cyclic resistance of undisturbed samples from the in situ deposit is about twice as great as the cyclic resistance of the sample from the newly deposited sand fill. The cyclic strength of in situ deposits is thus considered to vary greatly, depending on ageing and inherent fabric structure of sands created under different depositional conditions. The test results on reconstituted samples should therefore be considered not to reflect the true behaviour of in situ sands, and tests on high-quality undisturbed samples are



G



0.1



u”



1 Number



10 of cycles



100 to 5% DA cwol



lO( strain



Fig. 5. Cyclic strength of undisturbed samples of sand (Yoshimi et al., 1989)



always needed in order to evaluate precisely the performance of in situ deposits of sands during earthquakes. CYCLIC RESISTANCE OF SILTY SANDS Liquefaction is a state of particle suspension resulting from release of contacts between particles of sands constituting a deposit. Therefore, the type of soil most susceptible to liquefaction is one in which the resistance to deformation is mobilized by friction between particles under the influence of confining pressure. When the soil is fine-grained or contains some amount of fines, cohesion or adhesion tends to develop between fine particles, making it difficult to separate them. Consequently, a sand containing some fines generally shows a greater resistance to liquefaction. However, this tendency depends on the nature of the fines contained in the sand. If the fines comprise minerals with a dry surface texture free from adhesion, individual particles will separate readily, therefore the sand containing such fines will show as great a potential to liquefaction as clean sand. A typical example of such fines is the tailings materials produced as residue in the concentration process of ore in the mining industry. Since the tailings essentially comprise ground-up rocks, they preserve the hardness of parent rocks with dry surface. Therefore, the rock flour, in its water-saturated condition, does not possess significant cohesion and behaves as if it were clean sand. Thus, tailings have been shown to exhibit as low a resistance to liquefaction as clean sand (Ishihara, 1985). The degree of liquefiability of sand containing more or less cohesive fines such as those found in fluvial deposits has been investigated in laboratory tests by Ishihara, Sodekawa & Tanaka (1978), who showed that with increasing content of fines, the cyclic resistance of sand tends to increase to a certain extent in its normally con-



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LIQUEFACTION



AND FLOW



n:Loam



FAILURE



I



.: Undisturbed



0



10



20 Plasticity



30 index



40



, Ip



50



60



Fig. 6. Effects of plasticity index on the cyclic strength of fines-containing sand



solidated state, but to a greater extent if overconsolidated. This tendency is expected, because adhesion between fine particles tends to prevent the separation of individual particles when the sand is about to liquefy. Thus, sand containing such somewhat plastic fines generally exhibits a higher resistance to liquefaction. However, since the effects of fines are manifested in various ways, depending on the nature of the fines, it would be very useful to have a key parameter capable of specifically quantifying the liquefaction characteristics of fines-containing sands. It is commonly observed that relative density fails to be an appropriate index parameter if the fines content is greater than about 50%. Compilation of several series of laboratory tests has shown that the most important index property influencing the cyclic strength is the plasticity index of the fines contained in the sand (Ishihara & Koseki, 1989). This is clearly demonstrated in the results summarized in Fig. 6, where the cyclic strength is plotted against the plasticity index I, of the materials used in the tests. The cyclic strength does not change much for the low plasticity range, below I, = 10, but increases thereafter with increasing plasticity index.



EVALUATION RESISTANCE



OF BY



DURING



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EARTHQUAKES



One method to accomplish this is to take advantage of the penetration resistance of the standard penetration test (SPT), which has found worldwide use in the investigation of in situ characteristics of soil deposits. There are basically two approaches for establishing the correlation of the blow count value N of the SPT with the cyclic strength of soils in the field. The first approach is based on investigation of whether or not in situ soil deposits have actually developed liquefaction during past earthquakes. With an intensity of shaking estimated by some appropriate procedure, values of cyclic stress ratio believed to have occurred in in situ soil deposits during an earthquake can be estimated and compared with the penetration resistance of a sandy soil at any depth of an in situ deposit. Since it is known whether or not liquefaction-induced ground damage has occurred, it is possible to establish a threshold relation between the cyclic stress ratio and the N value of the SPT test. Such an approach was developed by Seed (1979) on the basis of a vast number of field performance data on sand deposits exposed to strong shaking during recent earthquakes. The relation derived by Seed, Idriss & Arango (1983) based on more comprehensive data is shown in Fig. 7, which plots the cyclic stress ratio causing initial lique-



LIQUEFACTION SPT



AND



CPT



Recovery of high-quality undisturbed samples and laboratory testing is the most reliable procedure for accurate evaluation of the cyclic strength of sand. However, obtaining sand samples from deposits below the groundwater table is a costly operation, and can be justified only for an important construction project. Therefore, a simpler and more economically feasible procedure to assess the cyclic resistance of sand needs to be established.



0



10 Normolized



20 N-value



30



40



, Nt=0833(N~)60



Fig. 7. Summary chart for evaluation of tbe cyclic strength of sands based OIIthe normalized SPT N value



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358 faction kinds based ratios



K.



ISHIHARA



against the normalized N value. The three of stress ratio are shown on the y-axis, on past studies indicating these three stress to be approximately equal



bridge design (Tatsuoka, Iwasaki, Tokida, Yasuda, Hirose, Imai & Kon-no, 1980) is =



O.O676JN,



+ 0.225 log,,



for 0.04 mm < D,, < 0.6 mm where ~~~is the amplitude of average shear stress taken over the time history of seismic motions. the amplitude of maximum &lax,JcrV’ denotes shear stress required to cause liquefaction. The N, value plotted on the x-axis is obtained by correcting a measured N value to that corresponding to an overburden pressure of 1 kgf/cm* = 98 kPa. is used to indicate explicitly the In Fig. 7, Vi),, blow count value obtained with a driving energy 60% of the theoretical free-fall energy of the SPT hammer. The SPT practice in the USA is considered to employ this level of energy on average. Rate of energy transmission in Japanese practice is considered to be 1.2 times as great as in US practice, therefore the relation N, z 0.833 (N,),, can be used to convert the N value of SPT between the two practices as indicated on the x-axis of Fig. 7. The second method to establish a correlation between the cyclic strength and N value is to collect a large number of laboratory test data on the cyclic strength of undisturbed soil samples recovered from deposits of known penetration resistance. An empirical correlation between these two quantities can easily be established: one of the relations incorporated in the Japanese code of



Normolized



cone



= O.O676JN,



(2a)



- 0.05



for 0.6 mm < D,, < 1.5 mm



(2b)



where D,, is the mean particle diameter in millimetres. N, is obtained through the correction factor C, , defined as N,=C,N



c,



1.7 = ~ trV’+ 0.7



where 0”’ is the effective overburden pressure in kgf/cm*. The cyclic strength obtained from equation (2) is plotted against N, in Fig. 7 for typical grain sizes of D,, = 0.15 mm and 0.35 mm. Equation (2) was originally derived in the form of a linear correlation between the laboratory-determined cyclic strength and relative density D,. It was rewritten later in the form of equation (2) by use of the relation D, = 16,/N,. Therefore equation (2) is valid only in the range of relative density less than about 70%, where the cyclic strength is related linearly to the relative density. In terms of SPT blow count, equation (2) should be considered to hold true for the N, < 20. Similar attempts were made by Kokusho, Yoshida & Esashi (1983) on the basis of a vast body of laboratory test data on clean sands. Relations based on a large body of field performance data obtained mainly in Japan were proposed by Shibata (1981) and Tokimatsu & Yoshimi (1983), and they are also shown in Fig. 7. On the basis of recent large earthquakes in China, the criterion for identifying sandy deposits as being susceptible



reslstonce,qcl(MF’a)



Fig. 8. Summary chart for evaluation of the cyclic strength of sands based on the normalized CPT qcvalue



Fig. 9. Definition of an increment of N, value, allowing for the effects of fines



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LIQUEFACTION



AND FLOW



FAILURE



or immune to liquefaction was presented in the form of a code requirement. Through some numerical manipulation (Ishihara, 1990) the Chinese criterion can be expressed as =



75,ax I A =



6



(9.5N,



+ 0.466N12)



6”’



(4) This relation is also shown in Fig. 7. From the cluster of curves proposed by various researchers, it is apparent that the relations fall in approximately the same range for N, = 10-25, where actual data were available in abundance. In view of the increasing popularity of the cone penetration test (CPT), it has become desirable to establish a relation between CPT tip resistance qc and the cyclic strength, analogous to that developed for the SPT N value. Based on compilation of a large body of field performance data, Robertson & Campanella (1985) proposed correlations for clean sands and silty sands as shown in Fig. 8, where the cone tip resistance is expressed in the form of qcl, a value normalized to an effective overburden pressure of 0”’ = 1 kgf/cm’ (98 kPa). Similar correlations were established by Seed & De Alba (1986) and Shibata & Teparaska (1988), in which the effects of fines content are allowed for in terms of the median grain size. The correlations for the case of apparently clean sands with D,, 2 0.25 mm and for silty sands with D 5. < 0.15 mm proposed in these works are shown in two groups in Fig. 8. In most of the correlations epitomized above, effects of the presence of fines are allowed for in such a way that the penetration resistance becomes smaller with increasing fines content if soils possess equal cyclic strength. At constant penetration resistance, soils are observed to have increasing cyclic strength with increasing fines content as shown schematically in Fig. 9. Thus,



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359



given a correlation such as equation (2) in terms of a parameter associated with grading such as fines content F, or average diameter D,,, it is possible to determine the amount of the shift AN, shown in Fig. 9 as a function of fines content. The value of AN, is interpreted as a decrease in N, value for clean sands so as to have the same cyclic strength as silty sands. Thus, if the cyclic strength for fines-containing sands is f(N,, F,), the increment AN, is determined as f(N, - AN,, F,) = f(N,, 0)



(5)



Introduction of this requirement into an empirical correlation such as equation (2) gives an explicit expression for AN,, but it is also possible to read AN, directly from a family of curves such as that shown in Fig. 8 compiled for different values of fines content. The increment AN, thus obtained from the compiled data by Seed & De Alba (1986) is plotted in Fig. 10. By connection of these points, a curve is drawn in Fig. 10 that can be used for practical purposes. The same argument can be developed to obtain the increment AN, associated with residual strength. In this case, the value of AN, implies the change of N, value required by fines-containing sand to have the same residual strength as clean sand. The increment related to the cyclic strength is different from that associated with the residual strength. A curve of AN, for the residual strength was obtained from the values suggested by Seed & Harder (1990), and is shown in Fig. 10: its use is discussed below. The curves for the increment are shown in Fig. 11. Aqci similarly obtained These curves can be used to estimate the cyclic strength or residual strength based on in situ CPT data. The method of correction described above is based on the assumption that the effects of fines can be taken into account in terms of grading parameters such as fines content and mean diam-



105 -



Based on cyct,c strength



residual



/, 0



strength



i



201



/



Based on residual strength



I



I 10



20 Fines



30 content



,



40



50



FC P/J



Fig. 10. Increment AN, value as a function of fines content



0



10



20 Fines



30 content



, FC C%)



40



50



Fig. 11. Increment Aqcl as a function of fines content



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360



K.



ISHIHARA



mined. If the plasticity index of the fines is found to be greater than I,, = 10, further correction must be made for the cyclic strength by use of the chart in Fig. 12. Experience has shown that most sandy soils in alluvial deposits or manmade fills possess a plasticity index less than 15, therefore, the correction in this regard may not change the cyclic strength appreciably.



01



10



20 Plasticity



30 Index



,



40 Ip



50



69



Fig. 12. Chart for modification of cyclic strength allowing for the effects of plasticity index



eter. However, as pointed out above, the grading of soils is not necessarily an essential factor influencing the cyclic strength: the nature of the fines, as represented by plasticity index, is a more physically meaningful parameter governing the strength mobilized in cyclic loading. If this effect is to be incorporated into the cyclic strengthpenetration resistance relation, it is necessary to know how the penetration resistance is influenced by the plasticity of fines. However, there are no relevant test data. Under the circumstances described, the only way at present to elucidate this relation would be first to evaluate the cyclic strength of in situ soil deposits through the procedures described above, where effects of fines are allowed for in terms of the grading indices, and then to modify it in accordance with a relation such as that shown in Fig. 6. In utilizing this relation, it would be expedient to normalize the cyclic strength at any plasticity to the cyclic strength at low plasticity index (< 10). The curve modified in this way is shown in Fig. 12. With the background information as given above, the procedures to determine the cyclic strength of the soil in a given deposit can be summarized as follows.



(4 By means of SPT or CPT, penetration



(4



resistance (N, or s,i) is obtained, together with the fines content F, or mean diameter D,, for the soils in question, throughout the depth at a given site. If necessary, the plasticity index of the fines fraction must be determined. If the material is identified as clean sand with fines content less than 5%, the cyclic strength is determined from the chart shown in Fig. 7 or Fig. 8. If more than 5% fines is shown to exist in the soil, measured N, or qEl values should be increased based on the chart shown in Fig. 10 or Fig. 11. Then, by use of the chart in Fig. 7 or Fig. 8, the cyclic strength is deter-



ANALYSIS OF LIQUEFACTION



The cyclic shear stress induced at any point in level ground during an earthquake due to the upward propagation of shear waves can be assessed by means of a simple procedure proposed by Seed & Idriss (1971). If a soil column to a depth z is assumed to move horizontally and if the peak horizontal acceleration on the ground surface is amsx, the maximum shear stress 7mar acting at the bottom of the soil column is given by t max = amaxrd



Yt zh



rd = 1 - 0.0152



(64



(6b)



where y, is unit weight of the soil, g is the gravitational acceleration and rd is a stress reduction coefficient to allow for the deformability of the (rd < 1). Seed & Idriss (1971) soil column expressed the value of rd in a graphical form, but Iwasaki, Tatsuoka, Tokida & Yasuda (1978) recommended the use of the empirical formula given in equation (6b), where z is in metres. Division of both sides of equation (6a) by the effective vertical stress a,’ gives 7max -= , 0”



a max -‘d, 9



0” 0”



(7)



where G” = y,z is the total vertical stress. Equation (7) has been used widely to assess the magnitude of shear stress induced in a soil element during an earthquake. One of the advantages of equation (6) is that all the vast amount of information on the horizontal accelerations that has ever been recorded on the ground surface can be used directly to assess the shear stress induced by seismic shaking in the horizontal plane within the ground. Liquefaction can be analysed by a simple comparison of the seismically induced shear stress with the similarly expressed shear stress required to cause initial liquefaction or whatever level of shear strain amplitude is deemed intolerable in design. Usually, the occurrence of 5% DA axial strain is adopted to define the cyclic strength consistent with 100% pore water pressure build-up as mentioned above. The externally applied cyclic



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LIQUEFACTION SPT IO



AND FLOW



FAILURE



N-value 20



30



DURING D%



40



0.2



EARTHQUAKES



361



(mm) 0.4



0.6



Kawogishi



- cho



Fig. 13. Example of liquefaction analysis



stress ratio can be evaluated by equation (7); the corresponding strength can be obtained by any of the procedures mentioned in the previous section. Thus, the liquefaction potential of a sand deposit is evaluated in terms of factor of safety F, , defined as,



If the factor of safety is < 1, liquefaction is said to take place. Otherwise, liquefaction does not occur. A typical example of the liquefaction analysis made for a deposit at Kawagishi-cho in Niigata using the correlation in equation (2) is shown in Fig. 13, for the recorded peak horizontal acceleration of nmax = 0.169. The liquefaction is shown to have developed in the sand sediment down to a depth of about 10 m. This result is consistent with what was observed on the ground surface at the time of the 1964 earthquake. The factor of safety obtained in this way is generally used to identify the depth to which liquefaction is expected to occur in a future earthquake. This information is necessary if some countermeasure is to be implemented in an in situ deposit of sands.



SETTLEMENTS IN SAND DEPOSITS FOLLOWING LIQUEFACTION



When saturated sand deposits are subjected to shaking during an earthquake, pore water pressure is known to build up, leading to liquefaction or loss of strength. The pore water pressure then starts to dissipate mainly towards the ground surface, accompanied by some volume change of the sand deposits which is manifested on the ground surface as settlements. The volume-change characteristics of sand due to drainage of pore water pressures induced by undrained cyclic loading have been studied in laboratory tests by Lee & Albaisa (1974), Tatsuoka, Sasaki & Yamada (1984) and Nagase & Ishihara (1988). From these studies it has become apparent that the volumetric strain after liquefaction is influenced not only by the density, but, more importantly, by the maximum shear strain that the sand has undergone during the application of cyclic loads. On this basis, Tokimatsu & Seed (1987) attempted to deploy a methodology to predict the post-liquefaction settlements of the ground. An alternative procedure for estimation of the ground settlements was explored by Ishihara & Yoshimine (1991) by way of the maximum shear strain, which is a key parameter influencing the post-liquefaction volumetric strain. This



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362 2 6



K. ISHIHARA



5 Clean



sands



.



60 “I. 7 0 7% 8 0 “I. 90 %



0



2 Scngle



1,



6



amphtude



8 of



shear



10 strain



Fig. 14. Post-liquefaction volumetric against maximum shear strain



12



I_ 14



, k’hax (‘1.)



strain



16



plotted



methodology is based on two basic concepts derived from results of extensive laboratory tests. The first is the relation of the volume change of saturated sand and maximum shear strains. The outcome of simple shear tests performed in this context on clean sand with various relative densities is shown in Fig. 14, which plots the volumetric strain during the reconsolidation E, against the maximum shear strain Y,,, experienced by the sample during the undrained irregular loading. The developed pore water pressure became equal to the initial vertical stress when the amplitude of irregular loads was sufficiently large to produce the maximum shear strain of about 3%, as indicated in Fig. 14. This is consistent with the results of many other tests indicating that cyclic softening or initial liquefaction with 100% pore water pressure build-up occurs accompanied by maximum shear strain of the order of 2%-3%. It is important to note in Fig. 14 that, even when the maximum shear strain increases beyond 2%-3% (the value required to cause initial liquefaction), the volumetric strain during reconsolidation tends to increase significantly. In order to estimate the liquefaction-induced settlement of a sand deposit using the correlation shown in Fig. 14, it is necessary to know the maximum shear strain that the sand will undergo during the application of shaking in a future earthquake. This can be determined based on the second concept, as follows. As mentioned above, the cyclic strength has customarily been defined as the cyclic stress ratio required for a DA axial strain of 5% to be developed in the sample in the triaxial tests. In the case of very loose sand, the sand starts to deform greatly as soon as such a state of softening is encountered, and therefore whatever amount of DA strain may be used, almost the same value is obtained for the cyclic strength. However, in the case of medium dense to dense sand, this does not apply; the cyclic



stress ratio tends to increase with increasing shear-strain amplitude specified to define the cyclic softening. In other words, a larger magnitude of cyclic resistance can actually be mobilized over the nominally determined cyclic strength if more than 5% DA axial shear strain is allowed to take place in the triaxial test samples. Consequently, when the factor of safety for liquefaction is defined as indicated by equation (8) for the 5% DA axial shear strain, cases often occur where the computed factor of safety becomes less than unity. As already defined, a factor of safety of unity implies a state of cyclic softening producing a 5% DA axial strain, and a factor of safety less than unity means that the soil has been softened to a state in which more than 5% DA axial strain is produced. Thus, the factor of safety F, is considered to be a function of the DA axial strain and, conversely, if the factor of safety is known for a sand deposit at a given site, the DA axial strain developing in the sand during liquefaction can be determined. Half this shear strain, i.e. the single-amplitude axial strain, is regarded as the maximum shear strain that the sand has undergone in the course of liquefaction during earthquakes. The relation in the above context of the factor of safety and the shear strain amplitude can be established on the basis of available data obtained in laboratory tests. Simple shear test data on a clean sand obtained by Nagase (1985) were processed in this context as represented by a family of curves in Fig. 15, where the factor of safety is shown against the maximum shear strain Ymax for the sand with different relative densities. Fig. 15 shows that, at a given value of factor of safety less than unity, the larger the relative density, the smaller will be the maximum shear strain. The family of curves in Fig. 15 can be used to assess the maximum amplitude of shear strain for a known factor of safety value. If the value of



IL



0



I 2 Single



I



4



6 omplltude



a of



shear



10 strain



14 I ii , Lax (“/.I



12



Fig. 15. Relation of factor of safety and maximum shear strain



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LIQUEFACTION



AND FLOW



maximum shear strain is hence known, the postliquefaction volumetric strain can be determined through the use of the established curves shown in Fig. 14. At this stage, if the factor of safety is known by way of the conventional method of liquefaction analysis, it will be possible to circumvent the determination of the maximum shear strain and to estimate the amount of post-liquefaction volumetric strain directly. For this purpose, combinations of the factor of safety F, and the volumetric strain E, giving equal magnitude of maximum shear strain were read from each family of curves shown in Figs 14 and 15. The are combinations of F, and E, thus obtained plotted to establish a family of relations as shown in Fig. 16, where the maximum shear strain y,., is taken as a tracking parameter. If these curves are to be used for practical purposes, the axial strain in the triaxial mode should be converted to shear strain in the simple shear mode according to the relation y,,, = 1.5~~~~~. In the case of constant-amplitude axial strain in the triaxial test, &rmaxis taken to be equal to cr. The maximum shear strain yma, indicated in Fig. 16 is the one converted thus. As can be seen in Fig. 14, an upper limit exists in the reconsolidation volumetric strain for each given density, and therefore even when the



,,O~ 1.8 1.6



FAILURE



DURING



EARTHQUAKES



363



maximum shear strain becomes fairly large there is no change in the volumetric strain. This is reflected in Fig. 16 in such a way that the postliquefaction volumetric strain becomes independent of the factor of safety when it is very small. In Fig. 16, the curves for small relative densities ( p=(G;+203)/3



stress



I 0.60



(MPa)



0.96 -



Steady



0



/ 010



/



1



0.20 0.30 Effective cont,n,ng stress



I



I



0.40



I



, p’=@~‘+2d)/3



Fig. 29. Determination of the quasi-steady state (QSS)



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state



Line



050 (MPa)



0.60



LIQUEFACTION



Toyoura



0.70 II 0.02



AND



FLOW



DURING



373



EARTHQUAKES



sand



I



/IN



0.05 Effective



FAILURE



1.0 0.1 0.2 0.5 2.0 confining stress, p’:(S’+ZU b IO