SOILS AND FOUNDATIONS DURING EARTHQUAKES

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i) Professor, Disaster Prevention Research Institute, Kyoto University, Kyoto, Japan (iai＠geotech.dpri.kyoto-u.ac.jp).ii) Associate Professor, Department of Social and Environmental Engineering, Graduate School of Engineering, Hiroshima University.

The manuscript for this paper was received for review on May 24, 2010; approved on September 29, 2010.

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SOILS AND FOUNDATIONS Vol. 50, No. 6, 937–953, Dec. 2010Japanese Geotechnical Society

SOILS AND FOUNDATIONS DURING EARTHQUAKES

SUSUMU IAIi) and KOJI ICHIIii)

ABSTRACT

This paper provides an overview of the modern understanding of the behavior of soils and foundations during anearthquake based on the papers published in Soils and Foundations over the last ˆfty years. The most fundamental is-sues in geotechnical earthquake engineering are the non-linearity of soil under cyclic loading and its implications on theseismic performance of geotechnical structures. The non-linearity of granular materials is essentially anisotropic,whereas the linear or equivalent linear model often used in conventional practices is isotropic. The non-linearity of drysoil is characterized by the diŠerence between the peak and residual strengths, and the increased awareness of the im-plications of this diŠerence over time has allowed for the development of a generalized methodology for evaluating ac-tive earth pressures. The non-linearity of saturated soil under undrained cyclic shear diŠers fundamentally from that ofdry soil, with saturated soil capable of mobilizing 100z of the shear strain in the double amplitude. The cyclic behav-ior of saturated soil under initial shear is typical of most seismic behaviors of geotechnical structures, including em-bankments, caisson quay walls, and underground structures. The liquefaction-induced ‰ow failure of geotechnicalstructures is associated with the steady state of sand in the order of 10 kPa. However, the challenge in the coming de-cades will be to evaluate the combined eŠects due to cyclic loading and the steady state. Moreover, the eŠects of porewater migration are signiˆcant in the case of highly permeable geotechnical materials when evaluating settlement of theground or addressing inter-layered structures of clay and sand. Although current research is elucidating the mechanicsof partially saturated sands, the new challenge is to understand combined hazards, such as a combination of earth-quake motions and tsunamis. Thus, new approaches and technologies need to be developed.

Key words: cyclic shear, dynamic interaction, earthquake, liquefaction, nonlinear, pore water pressure, residualstrength, stress path, stress-strain relation, undrained (IGC: D7/E8/H0)

INTRODUCTION

Inertia and gravity govern the seismic performance ofgeotechnical structures. If the combination of inertia andgravity exceeds the resistance capability in the primaryportion of soils and/or the structural components of geo-technical structures, then residual deformation is inducedin geotechnical structures. Moreover, if the degree ofresidual deformation exceeds the acceptable limit in en-gineering practices, then the geotechnical structures aredeemed to be in a state of failure.

Conventionally, the seismic stability of geotechnicalstructures has been evaluated based on a simpliˆed ap-proach, which conceptually divides the soil-structure sys-tem into a structure model and actions on the model fromthe surrounding soil mass. For example, the gray area inFig. 1(a) is an idealized model of a caisson quay wall withthe arrows indicating the forces acting on this model, in-cluding the equivalent inertia force, seismic earth, andhydrodynamic pressures. This simpliˆed analysis assumesfailure modes such as sliding, overturning, or bearingcapacity failure.

Figure 1(b) shows a detailed dynamic analysis of a cais-son quay wall. The model is deˆned for an entire geo-technical structure system, including the caisson, backˆllsoil, seawater, and foundation soil. The forces acting onthis soil-structure model are the input earthquake mo-tions at the boundary of the domain, and these are denot-ed by solid arrows. This model diŠers from the simpliˆedanalysis in that the seismic earth pressures and hydro-dynamic pressures acting upon the caisson wall, as indi-cated by the dotted arrows, are computed from theresponse analysis.

``A long history of confusion'', which is brilliantly ex-plained in ``Fifty Years of Lateral Earth Support'' (Peck,1990) may be interpreted as the confusion caused byproblems associated with the (incorrect) assumptionsmade in the failure mode or soil-structure interaction foruse in the simpliˆed model. Due to the highly non-linearresponse of soil-structure systems during strong earth-quake motions recorded in recent years, it may well bethat researchers will have to return to the basics of themechanisms of soil-structure interactions ``as is'' ratherthan continue on the path of sticking with a simple

938

Fig. 1. Models of analysis for a caisson quay wall

Fig. 2. Schematic ˆgure for total stress, eŠective stress, and pore water pressure

938 IAI AND ICHII

method and tempering the model parameters in an ad-hoc manner to make this simple model ˆt recorded casehistories.

The objective of this paper is to provide an overview ofthe modern understanding of the behaviors of soils andfoundations during earthquakes based on papers pub-lished in Soils and Foundations, Japanese GeotechnicalSociety, over the course of the last ˆfty years. Instead ofan all inclusive overview, in this paper, our focus is on themost fundamental issues in the discipline of geotechnicalearthquake engineering: i.e., the non-linearity of soil un-der cyclic loading and its implications on the seismic per-formance of geotechnical structures. The discussionsherein form the basis of a consistent framework, and willhopefully lead to further advances in mitigating seismichazards in the coming decades. The paper also discussesthe new challenge posed by combined hazards such as thecombination of earthquake motions and tsunamis duringthe Sumatra, Indonesia, earthquake of 2004, which urgethe development of new approaches and technologies inthe near future.

BACK TO THE BASICS: SOIL NON-LINEARITY

Subjecting medium-density or ˆrm ground to moderateearthquake motions causes the soil to behave like a linearmaterial with a reduced shear modulus and an increaseddamping factor (Tatsuoka et al., 1978; Kokusho, 1980).In these cases of mild non-linearity, which are associatedwith the strain level on the order of magnitude less thanabout one percent, the equivalent linear model has oftenbeen used in research as well as in seismic hazard analysis.

Isotropic linear elastic material, which plays a centralrole in seismology and soil dynamics with mild non-linearity, can be described by a linear relationship be-tween the stress tensor s (extension positive) and thestrain tensor e (extension positive), using the second ord-er identity tensor I, and can be expressed as

s＝－pI＋q (1)

Using bulk modulus K and shear modulus G with thedouble dot symbol denoting double contraction, thehydrostatic (i.e., compression positive) and deviatorcomponents of stresses are given by:

p＝－KI:e, q＝2GØe－ 13

I〇×I:e» (2)

In the equivalent linear model, the shear modulus G,which can be generalized as a complex number to incor-porate hysteretic damping, is modiˆed as a function ofthe shear strain amplitude. However, the materialremains isotropic.

The non-linearity in soil originates from two sources:the non-reversible stress strain behavior induced by thepartial or total failure of the material and the eŠect ofpore water. Soil is an assembly of soil particles that forma porous structure called the soil skeleton. The pores inthe soil skeleton are ˆlled with water if the soil is belowthe ground water table. In the discipline of soil mechanics(Terzaghi, 1943), the total stress s, which acts upon anarbitrary plane within the soil, is partitioned into eŠectivestress s?, which is carried by the soil skeleton, and porewater pressure uI (compression positive) (Fig. 2):

s＝s?－uI (3)

The overall equilibrium equation of soil is satisˆed fortotal stress s, but the deformation of soil is governed bythe non-linear relation between eŠective stress s? and

939

Fig. 3. Contact normal n, tangential direction t and contact force Pdeˆned at particle contact (left) and local co-ordinate ãx, ãy, ãz fordeˆning the virtual two dimensional mechanisms (right)

939EARTHQUAKE GEOTECHNICS

strain e. In the mechanics of granular materials, stress ingranular materials, which are considered to exist in a con-tinuum, is given by a certain average of contact forces be-tween the particles. In a spherical particle assembly, thecontact force P can be partitioned into the direction ofcontact normal (or along the branch connecting the parti-cle centers) n and tangential direction t as (Fig. 3):

P＝Fn＋St (4)

Taking the average over the contact forces within therepresentative volume elements with volume V (Oda,1974; Oda et al., 1985), the macroscopic stress can be ex-pressed as

s?＝1V S l(Fn〇×n＋St〇×n) (5)

where l denotes length of the branch.Prior to determining the average of all the contacts

with a random orientation, a structure can be identiˆedby systematically grouping the contacts according to theirorientation. As depicted in Fig. 3, the ˆrst level of struc-tures is identiˆed by choosing pairs of contact force andcontact normal parallel to the plane speciˆed by the localco-ordinates ãx, ãy, ãz where ãz is the axis normal to theplane. Assembling those pairs on the plane constitutes avirtual two-dimensional mechanism. The direction n wi-thin the plane is measured relative to the local coordinateãx with angle v/2. The average of these two-dimensionalmechanisms over the surface of a unit sphere with respectto solid angle V deˆnes the macroscopic stress.

Systematically sorting the isotropic and deviator com-ponents of the second order tensors in Eq. (5) and usingthe number of summation to inˆnity, Eq. (5) can be re-written as (Iai, 1993):

s?＝－pI＋14pff(qF〈n〇×n〉＋qS〈t〇×n〉) dv dV (6)

〈n〇×n〉＝n〇×n－t〇×t, 〈t〇×n〉＝t〇×n＋n〇×t (7)

where p denotes the eŠective conˆning pressure (com-pression positive), and qF, qS denote micromechanicalstress contributions to macroscopic deviator stress due tonormal and tangential components of contact forces, re-

spectively.Equation (6) represents the mechanisms with a combi-

nation of biaxial shear〈n〇×n〉and simple shear〈t〇×n〉.However, once these mechanisms are idealized in termsof the second order tensors, they become indistinguisha-ble, except for the diŠerence in the orientation with anangle of p/4 in terms of v/2 ( see APPENDIX). Thus,Eq. (6) can be rewritten as:

s?＝－pI＋14pffq〈t〇×n〉dv dV (8)

The direct stress strain relationship is derived by relat-ing the macroscopic strain tensor e to the macroscopiceŠective stress s? through the structure deˆned by Eq.(8). By deˆning the volumetric strain e (extension posi-tive), the virtual simple shear strain g, and eŠective volu-metric strain e? to consider the eŠect of the volumetricstrain due to dilatancy ed as:

e＝I:e, g＝〈t〇×n〉:e, e?＝e－ed, (9)

then isotropic stress p and virtual simple shear stress q inEq. (8) are deˆned through path dependent functions as:

dp＝－KL/U de?, dq＝GL/U dg (10)

where the subscripts L and U respectively denote loadingand unloading, which are determined in accordance withthe signs of de? and dg for volumetric and virtual simpleshear mechanisms.

Although soil non-linearity is complex, its formulationhas similarities with isotropic linear elastic material. Thiscan be understood by comparing Eqs. (1) and (2) (linearisotropic materials) to Eqs. (8) and (10) (non-lineargranular materials). However, diŠerences are also recog-nized; soil non-linearity is essentially anisotropic (i.e.,direction dependent), and merely adjusting the elasticshear modulus G in Eq. (2) does not approximate theanisotropy.

GEOTECHNICAL STRUCTURES WITH DRY SOIL

The seismic behavior of geotechnical structures de-pends on the soil-structure-foundation interaction. Thisinteraction is generally complex due not only to the geo-metry of the problem but also to the highly non-linear be-havior of soil during strong earthquake motions. Evenprior to earthquake shaking, the stress state of soil in thevicinity of a geotechnical structure may be close to theshear failure condition, which poses an additionalchallenge when attempting to characterize the seismicresponse and stress/strain state of the soil.

As shown in Fig. 4, the stress-strain relationship of soilduring cyclic shear under dry conditions is typicallyrepresented by a hysteresis loop (Kokusho, 1980). Thehysteresis loop depends on the shear strain level becausethe loop is bound by upper and lower limits, which arespeciˆed by the soil strength. The behavior of soil dis-cussed here, for example, explains the hysteretic subgradereaction on an embedded foundation such as a buriedwall being forced into cyclic motion, as illustrated in Fig.

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Fig. 4. Sand behavior under drained cyclic shear

Fig. 5. Hysteretic subgrade reaction in drained cyclic shear condition

Fig. 6. Stress-strain behavior of sand in plane strain cyclic loadingtests (Masuda et al., 1999)

Fig. 7. Wall displacement and active earth pressure coe‹cient, modi-ˆed from Koseki et al. (1998)

940 IAI AND ICHII

5. The upper and lower limits of the subgrade reactioncorrespond to the active and passive earth pressures, re-spectively. Both of these limits play important roles in theconventional design practices of retaining structures.

The subgrade reaction schematically shown in Fig. 5 isunrealistic in regard to two aspects. One is that the con-ˆning stress in the soil changes as the embedded founda-tion moves in or away. A more realistic subgrade reactionpresented in terms of the ratio over the vertical eŠectivestress is shown in the upper ˆgure in Fig. 6, whose shapediŠers from the lower ˆgure in terms of the ratio over themean eŠective stress (Masuda et al., 1999).

The other aspect is that there is a signiˆcant diŠerencebetween the peak and residual internal friction angles ofsand. Typical values for dense sand are qpeak＝509, qres＝309. As shown in Fig. 7, this diŠerence can signiˆcantlyaŠect the earth pressures. In the conventional simpliˆedanalysis, the earth pressures on the wall from the drybackˆll are typically estimated using the Mononobe-

Okabe equation (Mononobe, 1924). In the uniform ˆeldof horizontal and (downward) vertical accelerations khgand kvg, where g denotes acceleration of gravity, thebody force vector, originally pointing downward due togravity, is rotated by the seismic inertia angle c deˆnedby

c＝tan－1 « kh

1－kv$ (11)

The Mononobe-Okabe equation is obtained by rotatingthe geometry of Coulomb's classical solution through theseismic inertia angle c. A complete set of equations maybe found in the design codes and manuals. The ratio inthe right hand side of Eq. (11) represents the net eŠects of

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Fig. 8. Multi-stage active failure, modiˆed from Koseki et al. (1998)

Fig. 9. Typical test result on medium loose Toyoura sand (Dr＝49.6%) (Kiyota et al., 2008)

941EARTHQUAKE GEOTECHNICS

seismic inertia on the backˆll soil behind the wall andgoverns the onset condition of active failure plane.

Referring to Fig. 7, ˆrst, the onset of failure shouldcoincide with the full mobilization of the peak internalfriction angle rather than the residual one. Once a failureplane is formed, the sliding along this plane reduces theinternal friction angle to the residual one, which causesthe sliding to be trapped in the same failure plane until

the eŠective seismic inertia exceeds the threshold valuefor the onset of another failure plane, which also cor-responds to the peak internal friction angle. Figure 8schematically depicts the onset conditions of the initialand second failure planes among multiple choices ofpotential failure planes. This line of reasoning has led tothe proposal of a generalized method to estimate activeearth pressures for dry backˆll (Koseki et al., 1998). Thisgeneralized method is advantageous over the convention-al Mononobe and Okabe equation (Mononobe, 1924) fordesigning geotechnical structures for strong earthquakemotions.

Applications, i.e., the distinction between the peak andresidual strengths of soil, to other types of geotechnicalstructures have yet to be made, but the initiative de-scribed above has potential.

GEOTECHNICAL STRUCTURES WITHSATURATED SOIL

The undrained behavior of a saturated soil under cyclicshear completely diŠers from the drained behavior dis-cussed above; the undrained behavior is strongly aŠectedby the excess pore water pressures and the correspondingchange in the eŠective stress of the soil, as shown in Fig. 9(Kiyota et al., 2008). The upper and lower limits speciˆedby the shear strength of the soil under a drained conditionare not relevant to the hysteresis loop of the soil in the un-

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Fig. 10. Deformation/failure of gravity quay wall

Fig. 11. Deformation mode of soil element under undrained cyclic loading with initial shear

942 IAI AND ICHII

drained condition because these limits are aŠected by thechange in the eŠective conˆning stress during cyclic load-ing. Another important fact is the progressive increase inthe shear strain amplitude without an increase in the cy-clic stress amplitude.

Recent laboratory results (Fig. 9) indicate that theshear strain amplitude can easily exceed 100z of shearstrain in double amplitude at the cyclic stress ratio of0.16. This ˆnding has two implications. One is that largelateral displacements, which are equivalent to 100zshear strain, may be explained solely by the mechanismsof cyclic behavior of saturated soil. During the 1964Niigata earthquake, clean sand deposits with a thicknessof about 10 m liqueˆed during an earthquake with a shearstress ratio of about 0.18, and resulted in the lateral resid-ual displacement in the order of several meters. Thus, thelarge lateral displacement of nearly level ground during1964 Niigata earthquake may be understood as beingsolely due to cyclic shear. Referring to the ‰ow failuremechanism may not be necessary to understand thisphenomena. The other is more conˆdence might beplaced on the ability to evaluate the large deformation ofgeotechnical structures associated with the shear strain ofsoil beyond the 5z range.

Figures 9(c)–(d) depict other recent ˆndings; the addi-tion of shear strength, which is likely due to the interlock-ing eŠect, and the detailed shape of the stress strain be-havior during cyclic mobility. These details can sig-niˆcantly improve the modeling of soil, especially withrespect to its capability of evaluating the deformation ofgeotechnical structures associated with the stress path

passing through the zero eŠective stress state.In a two- or three-dimensional non-linear problem,

which is the case when analyzing the seismic behavior ofgeotechnical structures, the soil stress condition is furtheraŠected by gravity. For example, the stress state of soilbehind a retaining wall, which is denoted by the letter Ain Fig. 10, may be close to the active shear failure condi-tion. The soil below the wall, which is indicated by the let-ter B, may be close to the failure condition in a compres-sion shear mode. These anisotropic stress states beforeand during an earthquake are hereafter referred to as theinitial shear, and it should be understood that they aŠectthe behavior of soils subjected to cyclic load during anearthquake.

Figure 11 provides a conceptual image of the deforma-tion of soil element B undergoing stress and strain condi-tions discussed herein. The soil gradually deforms alongthe directions of the initial principal stresses (pointingdown in this case). This cumulative increase in the axialstrain diŠerence is presumed to be an important mechan-ism for governing the movement and settlement (or up-lifting) of the structures. In terms of the stress-strainrelationships, the deformation of the soil element dis-cussed above can be represented by the computed resultsshown in Fig. 12 (Iai et al., 1998). The behavior of soil,which is represented by the gradual approach of the stresspath towards the failure line in Fig. 12(a), is associatedwith the cumulative increase in the axial strain diŠerence(Fig. 12(d)).

To account for the behavior of soil reviewed above inthe analysis of geotechnical structures, a constitutive

943

Fig. 12. Computed stress strain relationships of anisotropically consolidated soil during cyclic simple shearing: (a) stress path in t－(－s?m) plane,(b) stress path in txy－(－s?m) plane, (c) stress and strain curve in txy－gxy plane, and (d) stress and strain curve in txy－(ex－ey) plane, where t＝((sx?－sy?)/2)2＋t2

xy and (－s?m)＝－(sx?＋sy?)/2 (Iai et al., 1998)

943EARTHQUAKE GEOTECHNICS

model, which is simple, numerically robust, but sophisti-cated enough to reproduce the essential features of thesoil behavior, is necessary. The features of this model in-clude the ability to(1) Follow the stress path close to the shear failure line

such as shown in Figs. 9(a)–(c),(2) Reproduce the hysteresis loop of a hardening spring

type such as shown in Figs. 9(b)–(d),(3) Reproduce the progressive increase in the shear strain

amplitude such as shown in Figs. 9(b)–(d), and(4) Analyze the cyclic behavior of sand under an

anisotropic stress ˆeld such as shown in Fig. 12.As revealed by a series of centrifuge model tests and

eŠective stress analysis by one of the authors and his col-leagues, embankments constructed on loosely depositedsaturated sand tend to settle at the crest associated withthe lateral spreading. As shown in Figs. 13(a)–(b), this isdue to the eŠect of the initial shear caused by the gravityload from the embankments applied downward on thefoundation soil beneath the embankment. Undrained cy-clic loading induces the deformation of soil (Fig. 11), andgradually induces the deformation in the foundation soilin terms of settlements and lateral spread. The soil behav-ior described here provides the basis for developing an en-gineering methodology in the form of eŠective stressanalysis to diŠerentiate the failure mode and the degreeof deformation depending on the geotechnical conditionsand properties of foundation soil as shown in Fig.13(a)–(d). To validate the engineering methodology, acomplete set of data on the undrained cyclic behavior of

soil elements, input earthquake motions, and the behav-iors of embankments is required (Kuwano and Ishihara,1988; Matsuo et al., 2000).

The uplift of a light, buried structure in looselydeposited sandy ground, as shown in Fig. 14, is associ-ated with the deformation of the soil subject to undrainedcyclic loading with the direction of the initial principalstress axis pointing upward at the foundation soil beneaththe structure (Koseki et al., 1997). For uplift to continue,the surrounding soil should be continuously suppliedtowards the bottom of the structure. Thus, utilizing thevertical walls that surround a buried structure can be aneŠective measure for mitigating damage (Yoshimi, 1998).

When a geotechnical structure has a non-symmetriccross section, such as a caisson quay wall, the initial sheardue to gravity tends to push the wall towards the sea. Arelatively ideal set of data, including an in situ frozenlarge diameter sample of soil, input earthquake motion,and a detailed measurement of the deformation of thegeotechnical structure, are available as part of the casehistory of the damage to a caisson quay wall at Kobe Portduring the 1995 Hyogoken-Nambu earthquake, Japan(Inagaki et al., 1996; Iai et al., 1998). As shown in Figs.15 and 16, loosely deposited foundation soil beneath thecaisson wall signiˆcantly deformed, causing large lateralmovement and the caisson wall to tilt towards the sea.The induced axial strain diŠerence in the foundation soilafter shaking reached about 15z. The ideal data set onthis case history oŠers an opportunity for the earthquakeengineering community as it is a benchmark for testing

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Fig. 13. Deformation of embankments on saturated foundation after shaking

Fig. 14. Deformation of saturated soil around the buried structure af-ter shaking (Koseki et al., 1997)

944 IAI AND ICHII

the applicability of developed methodologies to evaluateseismic performance of a geotechnical structure (Dakou-las and Gazetas, 2005).

The eŠects of soil on the pile foundation diŠer from thebehavior of soil subject to the initial shear. In this situa-tion, the relative displacement between the soil and thestructure is the major mechanism that governs the seismicbehavior of the pile foundations. The eŠect of excess porewater is signiˆcant, and may be larger than the eŠectivestress acting on the pile (Tokimatsu and Suzuki, 2004)and dependent on the seepage condition (Uzuoka et al.,2008). Studies in this category of soil-structure interac-tions include case histories of pile damage (Tokimatsuand Asaka, 1998) and underground structures (Iida et al.,1996) as well as model tests on embedded footing(Tamura et al., 2007) and ‰exible underground structures(Tamari and Towhata, 2003).

The aforementioned soil behavior under anisotropicstress conditions has been studied and conˆrmed through

laboratory experiments by applying cyclic torsion on thesoil specimen in a triaxial loading device (Ishihara and Li,1972). This test procedure was later upgraded through theuse of a hollow cylinder testing device (Kuwano and Ishi-hara, 1988; Matsuo et al., 2000; Arangelovski andTowhata, 2004). In these test procedures, the direction ofthe initial principal stress diŠers from the direction of cy-clically applied principal stress. Another series of testprocedures taken through the course of a laboratorystudy used a triaxial testing device and applied the triaxialcyclic shear in the same direction as the initial shear (Vaidet al., 1989; Hyodo et al., 1994). Typically, the directionof the initial principal stress due to gravity in a geo-technical structure diŠers from the direction of cyclicprincipal stress applied during earthquakes; the directionof the initial principal stress depends on the geometry ofthe geotechnical structure and the relative location of thesoil element in the stress ˆeld of the geotechnical struc-ture. Soil behavior is signiˆcantly in‰uenced by the direc-tions of applied principal stress after the initial shear(Nakata et al., 1998). This is due to the anisotropic natureof granular materials as discussed earlier. Ideally, theapplicability of the constitutive model should be testedfor these general stress conditions.

LIQUEFACTION-INDUCED FLOW FAILURE

When the soil is sheared monotonically under un-drained conditions in a shear strain range beyond 20z,the steady state is eventually reached, as schematicallydepicted in Fig. 17 (Vaid et al., 1989; Yoshimine and

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Fig. 15. Deformation of a caisson quay wall at Kobe port during 1995 Hyogoken-Nambu, Japan, earthquake (Inagaki et al., 1996)

Fig. 16. Computed deformation of a caisson quay wall (Iai et al., 1998)

Fig. 17. Schematic ˆgure of undrained behavior of sand under monotonic loading (modiˆed after Vaid et al., 1989; Yoshimine et al., 1998), (a)stress strain relationships, (b) eŠective stress paths

945EARTHQUAKE GEOTECHNICS

Ishihara, 1998). When the steady state strength is lessthan the initial shear induced in the slope, earthquakes

may trigger liquefaction-induced ‰ow failure (Fig. 18)(Ishihara et al., 1990b). The steady state strength of en-

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Fig. 18. Failure of Mochikoshi, Shizuoka, Japan, tailings dam (Ishihara et al., 1990)

Fig. 19. Hollow cylinder test results on the eŠects of cyclic loading be-fore reaching the stead state (Toyoura sand with DL clay mixture)

Fig. 20. Cyclic triaxial test results directly reaching the steady state (PIMasado) (Toyota et al., 2004)

946 IAI AND ICHII

gineering interest to evaluate the liquefaction-induced‰ow failure is typically on the order of 10 kPa (Hanzawa,1980; Ishihara et al., 1990a). Although the steady state ofsand is unaŠected by the initial conˆning stress, it is verysensitive to the ˆnes content and void ratio(Papadopoulou and Tika, 2008). In the case of Masado,a decomposed granite used for reclamation in the Kobeport, the steady state strength can be about 10 kPa at avoid ratio as low as e＝0.4 (Ishihara et al., 1998;Tsukamoto et al., 1998).

The shear resistance at the quasi-steady state, whichcorresponds to the transition over the phase transforma-tion line that can induce a large shear strain in engineer-ing sense, is highly dependent and almost proportional tothe initial conˆning stress and the direction of shear(Yoshimine et al., 1998; Nakata et al., 1998). The ques-tion of how cyclic loading during an earthquake aŠects

the stress strain behavior of soil on its way to a steadystate remains. A series of laboratory tests performed byone of the authors and his colleagues using Toyoura sandwith DL clay mixture (Fig. 19) indicates that the peakshear resistance is signiˆcantly aŠected by the cyclic load-ing, and a large shear strain can be induced due to cyclicloading before reaching the steady state. Indeed, cyclicloading can directly lead the soil to the steady statewithout going through the peak, as shown in Fig. 20(Toyota et al., 2004).

Most of the damage to river dikes and embankmentscan be analyzed without considering the eŠect of thesteady state as described earlier. However, recent ex-periences in the analysis of one particular type of riverdike, river dike No. 1 of the Shiribeshi-Toshibeshi river,Hokkaido, Japan, during the 1993 Hokkaido-Nanseiokiearthquake with a Richter magnitude of 7.8, poses a newchallenge (Matsuo et al., 2000). This river dike, whichwas constructed on loosely deposited sand with a thick-

947

Fig. 21. Cross section of the river dike

Fig. 22. Damage to a river dike at the Shiribeshi-Toshibetsu river, Hokkaido, Japan, during Hokkaido-Nansei-oki earthquake of 1993

Fig. 23. Computed deformation of river dike

947EARTHQUAKE GEOTECHNICS

ness of about 5 m (Fig. 21), was heavily damaged duringthe earthquake (Fig. 22). The results of the analysis per-

formed by the authors and their colleagues show a typicalpattern of deformation like that in Fig. 23. However, thedegree of deformation is excessively sensitive to the typeof algorithm and the details in the constitutive modelingin the vicinity of the failure line. Without considering thesteady state, the result suggests very small settlements asshown in Case A in Fig. 24. Because the shear strains in-duced in the foundation soil are on the order of severaltens percent, the eŠects of residual strength Sus have beenstudied. Table 1 and Fig. 24 show the results. The best ˆtto the measured crest settlements are given for Case D2,but the residual strengths Sus are apparently very low onthe order of 10 kPa. Cases C1 through C4 are in the rangeof those reported in the literature based on laboratorytests. However, future study in this area is considerednecessary.

When the soil enters into the regime where the shearresistance decreases with increasing shear strain (the ap-

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Table 1. Case designation for numerical analysis

Case No. Sus (kPa) for Asa Sus (kPa) for As1 Sus (kPa) for As2

A / / /

B 0.1 180 50C1 25 180 50C2 50 180 50C3 75 180 50C4 100 180 50D1 0.1 100 25D2 0.1 25 7D3 0.1 15 5

Fig. 24. Computed settlements at crest

Fig. 25. Evaluation for the eŠect of highly permeable materials (Kanatani et al., 2001)

948 IAI AND ICHII

parent strain softening regime after the peak), bifurca-tion or instability can be included in the phenomenon(Asaoka et al., 1994; Ikeda and Murota, 1996). In theory,this aspect of the phenomenon should be included in theobserved phenomena of seismic behavior of geotechnicalstructures with a very loose, sandy deposit. Another con-troversial point on the steady state is the eŠect of porewater migration during or after shaking. The migrationof pore water can change the void ratio, which can lead toa signiˆcant change in the steady state strength. Again,further study on this point will be of interest.

EFFECTS OF PORE WATER MIGRATION

As described in the previous chapter, the primary fac-tors aŠecting the seismic performance of geotechnicalstructures are the undrained behaviors of soils. However,one behavioral category of geotechnical structures is seri-ously aŠected by the migration of pore water relative to

the soil skeleton during and after an earthquake. Thiscategory can be classiˆed into three types.

One type is associated with highly permeable geo-technical materials, such as rubble stones (Fig. 25). Inthis type of geotechnical structure, the dynamic interac-tion between the ‰uid and solid particles of geotechnicalmaterials can be signiˆcant, depending on the type ofloading and materials (Kanatani et al., 2001).

The second type is associated with the pore water ‰owtowards the ground surface, and this ‰ow induces settle-ments. In practice, the order of the settlements of lique-ˆed sand typically ranges from 3 to 5z in terms of volu-metric strain (Nagase and Ishihara, 1988), but the theo-retical upper limit of the settlements should correspondto the current void ratio relative to the minimum void ra-tio (Shamoto and Zhang, 1998).

The third type is associated with the inter-layered struc-ture of clay and sand, causing a delayed failure of thegeotechnical structure due to the migration of pore water.The formation of a water ˆlm under the impermeableclay layer can trigger the ‰ow failure of the geotechnicalstructure (Kokusho, 2000).

The formation of a water ˆlm under the impermeableclay layer may not always trigger serious damage to thegeotechnical structure above this capping layer. Asshown in Fig. 26, depending on such conditions as theground shaking intensity and the thickness or overallstrength of the capping layer, there might not be seriousconsequences for geotechnical structures above the cap-ping clay layer (Ishihara et al., 1993; Acacio et al., 2001).Evidence from the 1999 Chi-Chi earthquake seem to sup-port this notion (Juang et al., 2005). Despite the apparentsimplicity in the proposed criterion shown in Fig. 26, thephenomenon involved in this criterion is complex, includ-ing the eŠect of water ˆlm formation and the potentialredistribution of excess pore water pressures towards theground surface. Further study on this issue will no doubtbe welcome.

A problem associated with the inter-layered structureof clay and sand can be induced through the disturbanceapplied to the clay layer. If the clay layer is an importantmechanism to support the entire geotechnical structuresystem, then a disturbance applied to this layer can causedamage to the geotechnical structure long after earth-

949

Fig. 26. EŠect of capping clay layer without evidence of subsoil liq-uefaction (Ishihara et al., 1993)

Fig. 27. Investigated coastal protection line for Osaka Bay Area,Japan

949EARTHQUAKE GEOTECHNICS

quake shaking (Noda et al., 2009).

PARTIAL SATURATION

Soil improvement techniques to mitigate seismicdamage to geotechnical structures are important, and willbe addressed in a separate paper in the same issue of Soilsand Foundations. However, the line of thought presentedin this paper clearly distinguishes between drained andundrained behaviors of soils with or without the eŠects ofpore water migration. It is worthwhile to cover brie‰y theintermediate condition of drainage, i.e., partial satura-tion. In comparison to studies on fully drained (i.e., dry)or fully saturated sands, studies on the mechanical prop-erties of partially saturated sand are relatively new andcan be considered as a generalization in understandingthe behavior of sand under cyclic loading. There are twodistinct mechanisms that aŠect the cyclic resistance ofsand (Unno et al., 2008; Okamura and Noguchi, 2009).One is the eŠect of increasing the average volume com-pressibility in a mixture of air and water as the degree ofair injection increases because the compressibility of air ismuch higher than that of water. As the average volumecompressibility increases, the soil skeleton more readilyreduces in volume as the excess pore water (and air) pres-sure increases under a constant total pressure; thus, thesoil skeleton retains a higher eŠective stress than the fullysaturated case. The other mechanism is the suction,which increases the shear resistance of the soil skeleton.Overall, these two mechanisms contribute to the increas-ing liquefaction resistance by the partial saturation ofsand.

NEW CHALLENGE: COMBINED HAZARDS

State-of-the-art earthquake engineering based on theoverview above is typically based on a site-by-site detailedanalysis. However, directly applying cutting-edge earth-quake engineering is di‹cult along a long coastal protec-tion line. Thus, there is a very real and pressing need for anew methodology to be developed. The example that isoverviewed below has been developed via the collectiveeŠorts of the authors and their associates, and has beenadopted for coastal areas in Japan.

The seismic performance of geotechnical structureswhich extend over the 70 km of coastline along the OsakaBay area has been evaluated (Fig. 27). The northern partof the coastal protection line is slightly inland from thesea because reclamation was made on the seaside of thisline to construct artiˆcial land, including man made is-lands, for industrial development after the constructionof the coastal protection line that was initially on thecoast line directly exposed to the sea. The southern partof the coastal protection line remains directly exposed tothe sea. Geotechnical conditions along the coastal protec-tion line were compiled based on boring data, which wasoriginally obtained at 100 to 500 m intervals for the con-struction of the Hanshin Bay Area Highway.

The primary objective of this assessment was to avoidcombined hazards such as those that occurred during the2004 Sumatra, Indonesia, earthquake (Fig. 28). The per-formance grades of the coastal structures re‰ect the con-sequences of failure and were based on importancecategorized by land use and the elevation of the groundrelative to the sea level. Highly industrialized zones withlow ground water level were assigned to have the highestperformance requirements for the protection of thecoastal zone.

950

Fig. 28. Coastal area of Banda Aceh, Indonesia, before (above) andafter (below) the Indian Ocean-Sumatra earthquake of 2004 (afterQuickbird)

Fig. 29. Cross sections and primary parameters used for the simpliˆeddesign charts stress analysis

Fig. 30. Results of the seismic assessment of coastal protection line

950 IAI AND ICHII

Instead of carrying out an eŠective stress analysis on asite-by-site basis, a set of design charts was developedbased on a comprehensive set of parametric studies onembankments and gravity structures, which are idealizedin Fig. 29. The design charts are incorporated into aspreadsheet format. Required input data are (1) the basicparameters deˆning the cross section of the structures, (2)the geotechnical conditions as represented by the SPT N-

values, and (3) earthquake data represented by the waveform, peak ground acceleration, or distance and magni-

951951EARTHQUAKE GEOTECHNICS

tude from the seismic source. These design charts canconveniently and e‹ciently assess the vulnerability ofcoastal geotechnical structures extending over a distanceof tens of kilometers, taking variable geotechnical andstructural conditions into consideration.

Figure 30 shows the results of the seismic assessment ofthe coastal protection line in the Osaka Bay Area. Thesettlements of the coastal protection facilities due toearthquake shaking ranged from 0.2 to 1.2 m (Fig.30(a)), and areas with smaller margin to the acceptablelevel of settlements are not robust. Figure 30(c) denotesareas less likely to protect the land from a tsunami thatmust be strengthened or improved as a preparatory meas-ure.

CONCLUSIONS

The modern insight of the behavior of soils and foun-dations during an earthquake is based on a deeper under-standing of the non-linearity of soil under cyclic loadingand its implication on the seismic performance of geo-technical structures. The most fundamental issues in thediscipline of geotechnical earthquake engineering, whichwill be the basis for further advances in mitigating seismichazards in the coming decades, may be summarized asfollows:(1) The non-linearity of granular material composed of

an assembly of granular particles is essentiallyanisotropic because the macroscopic stress of agranular material is given as a tensorial average of thecontact forces between the particles. The linear or e-quivalent linear model, which is typically used in con-ventional applications deals with mild non-linearity,is isotropic, and diŠers fundamentally from the non-linearity of granular materials.

(2) The non-linearity of dry soil is characterized by thediŠerence in the peak and residual strengths. The on-set of failure coincides with the full mobilization ofthe peak strength. Once a failure plane is formed,then the shear resistance mobilized along this planereduces the residual strength. Sliding planes aretrapped in the same failure plane during this process.Understanding these observations has led to the de-velopment of a general methodology to evaluate ac-tive earth pressures.

(3) The non-linearity of saturated soil under an un-drained cyclic shear completely diŠers from that ofthe dry soil and can mobilize the 100z of the shearstrain in double amplitude. The cyclic behavior ofsaturated soil under the initial shear describes most ofthe seismic behavior of geotechnical structures, in-cluding embankments, caisson quay walls, and un-derground structures. The reasonable characteriza-tion of the cyclic behavior of saturated soil will be thebasis for developing an engineering methodology inthe form of eŠective stress analysis to diŠerentiate thefailure mode and the degree of deformation depend-ing on the geotechnical conditions and properties ofthe foundation soil.

(4) Liquefaction-induced ‰ow failure of geotechnicalstructures is associated with the steady state of sandon the order of 10 kPa. Although the initial conˆningstress does not aŠect the steady state of sand, it is verysensitive to the ˆnes content and void ratio. Thesteady state strength of Masado, a decomposedgranite in Kobe, is about 10 kPa at a void ratio as lowas e＝0.4. The shear resistance at the quasi-steadystate, which corresponds to the transition over thephase transformation line capable of inducing a largeshear strain in an engineering sense, is highly depend-ent and almost proportional to the initial conˆningstress. The combination of the eŠects of cyclic load-ing and the steady state poses a challenge for the com-ing decades.

(5) The eŠects of pore water migration are signiˆcant inhighly permeable geotechnical materials, the evalua-tion of ground settlement, and also in the inter-layered structure of clay and sand. Studies to eluci-date the mechanics of partially saturated sands are inprogress, but many challenges remain for the comingdecades.

(6) A new challenge is developing new appraoches forcombined hazards, such as the combination of earth-quake motions and tsunamis observed during the2004 Sumatra, Indonesia earthquake. Thus, radicallynew approaches and technologies must be developedin the near future.

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APPENDIX

The macroscopic stress in granular materials as deˆnedfor continuum is given by a certain average of contactforces between the particles. In an assembly of plane cir-cular particles, the contact force P can be partitioned intothe direction of contact normal (or along the branch con-necting the particle centers) n and tangential direction t as( see Fig. 3)

P＝Fn＋St (12)

953

Fig. A1. Stress component in the direction of u for deˆning twodimensional mechanisms: (a) biaxial shear〈n〇×n〉; (b) simple shear

〈t〇×n〉

953EARTHQUAKE GEOTECHNICS

where

nT＝[n1 n2]t T＝[t1 t2] (13)

and

n1＝cos un2＝sin ut1＝n2＝sin ut2＝－n1＝－cos u (14)

The biaxial shear〈n〇×n〉and the simple shear〈t〇×n〉areindistinguishable except for the diŠerence in the orienta-tion with an angle of p/4 as shown in Fig. A1. Alterna-tively, the components of these tensors can be written as

〈n〇×n〉＝« n1

n2$[n1 n2]－« t1

t2 $[t1 t2]

＝« n21－t 2

1

n2n1－t2t1

n1n2－t1t2

n22－t 2

2 $＝« cos2 u－sin2 u

2 sin u cos u2 sin u cos usin2 u－cos2 u $

＝« cos 2usin 2u

sin 2u－cos 2u $ (15)

〈t〇×n〉＝« t1t2 $[n1 n2]＋« n1

n2 $[t1 t2]

＝« 2t1n1

t2n1＋t1n2

t1n2＋t2n1

2t2n2 $＝« 2 sin u cos u

sin2 u－cos2 usin2 u－cos2 u

－2 sin u－cos u $＝« sin 2u

－cos 2u－cos 2u－sin 2u $ (16)

Substitution of u＝u*－p/4 into Eq. (15) yields

〈n〇×n〉＝« sin 2u*－cos 2u*

－cos 2u*－sin 2u* $ (17)

Comparison on Eqs. (16) and (17) implies the diŠerencein the angle of p/4 where u＝v/2.

The solid angle dV is associated with the ãz axis direc-tion in Fig. 3.