152152152152152 QR of RTRI, Vol. 40, No. 3, Oct. ’99

PAPERPAPERPAPERPAPERPAPER

Seismic Design of Pile FoundationSeismic Design of Pile FoundationSeismic Design of Pile FoundationSeismic Design of Pile FoundationSeismic Design of Pile Foundation

Naoki TNaoki TNaoki TNaoki TNaoki TAKASE Masaki IKEGAME Shiro TAKASE Masaki IKEGAME Shiro TAKASE Masaki IKEGAME Shiro TAKASE Masaki IKEGAME Shiro TAKASE Masaki IKEGAME Shiro TANAMURAANAMURAANAMURAANAMURAANAMURAEngineer Engineer Manager

Foundation Engineering G., Structure Technology Development Dept.

Akihiko NISHIMURAAkihiko NISHIMURAAkihiko NISHIMURAAkihiko NISHIMURAAkihiko NISHIMURAGeneral Manager

Structure Technology Development Dept.

Masahiro KONDOUMasahiro KONDOUMasahiro KONDOUMasahiro KONDOUMasahiro KONDOUEngineer

Osaka Construction Office,West Japan Railway Company

In seismic design of pile foundation, it is important to evaluate the deformation prop-erty of soil and the damage process of a pile member suffering large deformation, since thedesign for earthquake motions in the new design code is larger than those in the old one.Moreover, as stipulated in the new code, dynamic analysis methods should be used forevaluating structure responses induced by earthquakes. This paper outlines the new seis-mic design method of pile foundation, the model used in push-over analysis for large de-formation and the hysteresis rule of soil-pile system.

KeywordsKeywordsKeywordsKeywordsKeywords : Foundation, Seismic Design, Pile Foundation, Group pile, Hysteresis Rule

1. Introduction1. Introduction1. Introduction1. Introduction1. Introduction

Since the Hyogoken-Nanbu Earthquake, design forearthquake motions have become larger and the conceptof the old design code became unreasonable in whichfoundations are designed with an excessive margin toobtain a sufficient capacity to resist seismic forces. Anew design concept is how to make structures safe byproperly evaluating the deformation of the total systemunder a precondition to allow damage to some degreeduring an intense earthquake. To realize this idea, animportant task is to correctly assess the deformationbehavior of soil and the damage process of pile memberswithin a large deformation scope.

Recently, the RTRI has drawn up a new seismic de-sign code, ‘Seismic Design Code for Railway Structures’(called ‘the seismic design code’ in short). According tothis seismic design code, the deformation property of pilefoundation in a large deformation scope is grasped mainlyby the push-over analysis method. Therefore, it is im-portant to perform static nonlinear analyses precisely byadequately evaluating the non-linearity of soil and pilemember. Moreover, the response of structure should beanalyzed by a dynamic analysis method in principle. Sincethere is a possibility to obtain different results by thedynamic analysis method, it is necessary to well under-stand the basic rules in the new code.

In this paper, the authors give an outline of seismicdesign for pile foundations, and the contents of the dis-cussions of the adequacy of seismic design methodadopted in the seismic design code.

2. Outline of seismic design for pile foundations2. Outline of seismic design for pile foundations2. Outline of seismic design for pile foundations2. Outline of seismic design for pile foundations2. Outline of seismic design for pile foundations

2. 1 Seismic performance of pile foundation2. 1 Seismic performance of pile foundation2. 1 Seismic performance of pile foundation2. 1 Seismic performance of pile foundation2. 1 Seismic performance of pile foundation

The basic concept of the seismic design method

adopted in the seismic design code is to define the seis-mic performance needed for structures first, and thenmake the structure satisfy the objective performancewhen it is subjected to the design earthquake motion(level 1 ground motion and level 2 ground motion).

The design seismic ground motions and the seismicperformance are established first, and it is confirmedthat structures satisfy the seismic performance. Theseismic performance of pile foundation is confirmed bythe stability level of pile foundation. The stability levelof pile foundation is determined by considering thestrength and deformation properties of soil and pile mem-bers. Table 1 shows the concept of the state of pile foun-dation corresponding to the seismic performance. Gen-erally, the seismic performance Ⅰ corresponds to the sta-bility level 1; the seismic performance Ⅱ to the stabil-ity level 2; and the seismic performance Ⅲ to the stabil-ity level 3.

TTTTTable 1 State of foundation corresponding to the seismicable 1 State of foundation corresponding to the seismicable 1 State of foundation corresponding to the seismicable 1 State of foundation corresponding to the seismicable 1 State of foundation corresponding to the seismicperformanceperformanceperformanceperformanceperformance

SeismicStability

performancelevel of pile State of pile foundationfoundation

Seismicperformance Level 1 Pile foundation do not yield. Ⅰ

Seismic Although pile foundation yield,performance Level 2 they maintain a sufficient bearing Ⅱ capacity.Seismic Although pile foundation reachperformance Level 3 the limit state, super structures do Ⅲ not collapse.

2. 2 Response calculation method for pile foundations2. 2 Response calculation method for pile foundations2. 2 Response calculation method for pile foundations2. 2 Response calculation method for pile foundations2. 2 Response calculation method for pile foundations

To check the stability level of pile foundation, theresponse values of pile foundation due to the designearthquake motion should be calculated first. Then the

153153153153153QR of RTRI, Vol. 40, No. 3, Oct. ’99

stability level can be determined by comparing the re-sponse values with the indexes of ductility, damage leveland response displacement. The response analysis shouldbe conducted by using the dynamic analysis method whichis chosen by the designer out of the following by takinginto account the ground and structure conditions.① Non-linear spectra method② Analysis method with springs supporting foundation③ Analysis method considering the soil-pile-structure

interactionThe nonlinear spectra method calculates response

values by using a nomogram (strength demanded spec-tra). The strength demanded spectra are made by usinga dynamic analysis method for different ground typesbeforehand. This method suits the cases where the vi-bration mode is comparatively simple and the plastichinge is clear, just like that of bridge piers.

The analysis method with springs supporting thefoundation is based on the dynamic analysis model wheresuper structures and pile foundations are separated. Itis proper in normal cases where the conditions of groundand structures are not complicated.

The analysis method that considers the soil-pile-structure interaction is used for cases of complicatedground condition and structure.

3. Push-over analysis3. Push-over analysis3. Push-over analysis3. Push-over analysis3. Push-over analysis

3. 1 Structural analysis model3. 1 Structural analysis model3. 1 Structural analysis model3. 1 Structural analysis model3. 1 Structural analysis model

In the seismic design of pile foundation, except thecases where the analysis method taking into account thesoil-structure interaction is applied, the plastic degreeof surged and damage process of pile members should begrasped by the push-over analysis method. Moreover,since the skeleton curves used for supporting springs aredetermined by the results of push-over analysis, calcu-lation models with high precision are needed.

In the push-over analysis, super structures and pilefoundations are modeled as a total system (Fig. 1), whichincludes the non-linear properties of both the ground andstructures. The springs in the ground are attached to

the nodal points, and the parts connecting the pile tothe spread footing and the pile to the embedded beamsare assumed to be rigid.

3. 2 Modeling of ground resistance3. 2 Modeling of ground resistance3. 2 Modeling of ground resistance3. 2 Modeling of ground resistance3. 2 Modeling of ground resistance

3. 2. 1 Characteristics of ground resistance of pilefoundation

The property of ground resistance of pile foundationis assumed to be represented by an elasto-plastic model(bilinear type). Figure 2 shows an example of a groundresistance model that becomes plastic when the subgradereaction of each ground resistance reaches the upperlimit. The methods to calculate various ground resis-tances refer to “Design Code for Foundation of RailwayStructure”. (called “the design code for foundation” inshort).

(a) Model of bridge pier (b) Model of rigid frame viaduct(a) Model of bridge pier (b) Model of rigid frame viaduct(a) Model of bridge pier (b) Model of rigid frame viaduct(a) Model of bridge pier (b) Model of rigid frame viaduct(a) Model of bridge pier (b) Model of rigid frame viaductFig. 1 Structure analysis modelFig. 1 Structure analysis modelFig. 1 Structure analysis modelFig. 1 Structure analysis modelFig. 1 Structure analysis model

Fig. 2 Model of ground resistanceFig. 2 Model of ground resistanceFig. 2 Model of ground resistanceFig. 2 Model of ground resistanceFig. 2 Model of ground resistance

3. 2. 2 Upper limit of horizontal resistance of ground.(1) Case of sandy soil

From the results of the simulated loading tests ofmodel piles1), it is understood that the effective resistanceearth pressure used in the design code for foundationunderestimates the deformation property of pile founda-tion in the large deformation area, at the shape coeffi-cient of pile front (α ) of 2 in the expression (1). So themodel pile and true pile results from the load test werereviewed to examine the relation between the shape coef-ficient of pile front and deformation2)3). As a result, itwas confirmed that the value of the shape coefficient ofpile front was generally 3 to 4, see Fig. 3.

From the examination result, the resistance earthpressure was calculated at the shape coefficient of pilefront of 3, as shown by the expression (1).

pe (z) = frp α Kp γ e z ･････････････････････(1)

pe (z) : Effective resistance earth pressure per unit area

154154154154154 QR of RTRI, Vol. 40, No. 3, Oct. ’99

at depth z (kN/m2)α : Shape coefficient of pile front

(Generally to be set at 3)K p : Coefficient of passive earth pressure

Kp = tan2(45 + φ )φ : Angle of internal friction at depth z (degree)γe : Average effective unit weight at depth z (kN/

m3)z : Depth to calculate the effective resistance earth

pressure (m)frp : Coefficient of soil resistance

(Generally to be set at 1.0)

when the upper limit value is 9 times the cohesion. Ac-cordingly, as shown by the expression (2), the upper limitvalue of effective resistance earth pressure power of co-hesive soil was determined as 9 times the cohesion.

pe (z) = frc 1 + z / 2D γe z + 2c ≤ 9c ････････････(2)

D : Pile diameter (m) c : Cohesion of cohesive soil (kN/m2) frc : Coefficient of soil resistance (Generally to be set at 1.0)Other signs are the same as those in the expression

(1).

Fig. 3 Relation between Fig. 3 Relation between Fig. 3 Relation between Fig. 3 Relation between Fig. 3 Relation between ααααα and displacement in and displacement in and displacement in and displacement in and displacement in load test load test load test load test load testresultsresultsresultsresultsresults

Fig. 4 AnalysisFig. 4 AnalysisFig. 4 AnalysisFig. 4 AnalysisFig. 4 Analysismodelmodelmodelmodelmodel

(2) Case of cohesive soilThe method to calculate the effective resistance earth

pressure power of cohesive soil has an upper limit value.The design code sets the upper limit value at six timesthe cohesion ( c ). The proposal of Broms4) stipulatesthat the mean of the ultimate lateral subgrade reactionof cohesive soil in the deep domain is nine times the co-hesion, while considering a safety factor. Accordingly, itcannot evaluate the behavior of large deformation com-pletely due to the safety factor. So load test results ofsingle pile5) were simulated to examine the upper limit

0.5D

interval

1.0D

interval

P

1/

(b) Load-displacement curve of T2 pile(b) Load-displacement curve of T2 pile(b) Load-displacement curve of T2 pile(b) Load-displacement curve of T2 pile(b) Load-displacement curve of T2 pileFig. 5 Analysis result of load test by single pileFig. 5 Analysis result of load test by single pileFig. 5 Analysis result of load test by single pileFig. 5 Analysis result of load test by single pileFig. 5 Analysis result of load test by single pile

value of effective resistance earthpressure.

Load tests were performed on co-hesive soil with an N value of around2 which contained a silt ingredient.Table 2 shows the shape of the testpile. A simulation was performed forthe upper limit values of effective re-sistance earth pressure power atabout 9 and 6 times the cohesive.The length between two nodal pointsof the analysis model was 0.5D (D :pile diameter) within the range 1 / β( Kh D / 4EI4 ), and 1.0D outside it. Anon-linear property was assumed forpile member. (Fig. 4)

TTTTTable 2 Shape of test pileable 2 Shape of test pileable 2 Shape of test pileable 2 Shape of test pileable 2 Shape of test pileTest Shape and measurement (mm) LoadPile Pile Thickness Pipe Point

diameter of pile length (GL + m)T1 100 1.6 2350 3.0T2 100 1.6 2350 0.5

3. 2. 3 Correction coefficient of group pilesThe lateral resistance of group pile does not increase

in proportion to the number of single piles with respectto the initial incline and the upper limit value3). And itis confined that the allotment rate changes according tothe arrangement of piles as displacement increases. Theprevious foundation design code considers the influenceof group piles by eg for the initial incline as shown bythe expression (3). But it does not consider influence ofgroup piles for the upper limit value. So, on the basis ofthe model piles and true piles load test results2)3), theinfluence of the pile arrangement and the number ofgroup piles on the upper limit value of the lateral resis-tance of pile were examined.

eg = [1 – 5{1 – (0.6 – 0.25k) d (0.3 + 0.2k)}× {1 – m– 0.22 n– 0.09}]4 / 3 ････････(3)

eg : Coefficient of horizontal resistance in group pilek : Ratio of fixed pile tops (Generally to be set at 0.6)d : Coefficient of pile interval

(a) Load-displacement curve of T1 pile(a) Load-displacement curve of T1 pile(a) Load-displacement curve of T1 pile(a) Load-displacement curve of T1 pile(a) Load-displacement curve of T1 pile

Figure 5 shows the load-displacement curve. It suffi-ciently simulates load test result of large displacement

155155155155155QR of RTRI, Vol. 40, No. 3, Oct. ’99

d = L / D L : Pile interval (m) D : Pile diameter (m)m : Number of piles in the direction of horizontal load exertedn : Number of piles in the right angle direction of horizontal load exerted

Based on the above discussions, the effective resis-tance earth pressure for the pile group is defined by thefollowing expression.

peg (z) = ηm ηn pe (z) ≦ pe (z) ･･･････････(7)

peg (z) : Effective resistance earth pressure of pilegroup (kN/m2)

ηm : Allotment coefficient of subgrade reaction dueto the pile line. See table 3

ηn : Correction coefficient of subgrade reaction dueto pile number (expression (6))

pe (z) : Effective resistance earth pressure per singlepile (kN/m2)

Figure 7 shows the comparison of the results of pilegroup effect between loading experiments and calcula-tions using expression (7). Although sufficient data isnot available, the adequacy of the correction coefficientis confirmed by the good agreement between experimentsand calculations.

m

n

No.1 No.2 No.3line number

Direction of horizontal load exerted

m : Number of pile in the direction of horizontal load exerted n : Number of right angle in the direction of horizontal load exerted

Fig. 6 Pile Line number of group pilesFig. 6 Pile Line number of group pilesFig. 6 Pile Line number of group pilesFig. 6 Pile Line number of group pilesFig. 6 Pile Line number of group piles

TTTTTable 3 Allotment coefable 3 Allotment coefable 3 Allotment coefable 3 Allotment coefable 3 Allotment coefficients of subgrade reaction dueficients of subgrade reaction dueficients of subgrade reaction dueficients of subgrade reaction dueficients of subgrade reaction due

to pile lines (to pile lines (to pile lines (to pile lines (to pile lines (ηm )))))

(2) Correction coefficient of subgrade reaction due to pilenumber (ηn )The effect due to the number of piles at the right angle

to the direction of horizontal load is considered by takinginto account the number of piles (n) and the pile-intervalcoefficient (d). From the expression (3), the pile-groupeffect due to the number of piles at the right angle to thedirection of horizontal load exerted and due to the inter-val coefficient can be reflected by the expression (4) and(5), respectively.

N(n) = n – 0.09 ････････････････････(4)

F(d) = (0.6 – 0.25k)d (0.3 + 0.2k)

= 0.45d 0.42 (k = 0.6) ････････････(5)

Furthermore, multiplying the expression (5), normal-ized by the general interval coefficient (d = 3), by the ex-pression (4), the correction coefficient (ηn ) due to thenumber of piles at the right angle to the direction of hori-zontal load can then be derived as follows.

ηn = F(d) / F(3) × N(n) = (d / 3)0.42 n – 0.09 ････(6)

However, ηn =1.0 is adopted, in the case of clay.

Line No. 1 Line No. 2 Line No. larger then 31.0 0.5 0.4

Notes : 1) In the case of clay, ηm = 1.0 for all lines 2) Number of pile lines, See Fig. 6

3. 3 Modeling pile member3. 3 Modeling pile member3. 3 Modeling pile member3. 3 Modeling pile member3. 3 Modeling pile member

Generally, the nonlinear property for each crossingsection of pile members is modeled by the relation be-tween bending moment and curvature, because the dis-tribution of bending moment along the pile length ischangeable. Moreover, the influence of axial force onthe plastic deformation of pile members is also takeninto account in the model. An example of nonlinear prop-erty model for a cast-in-place pile is shown in Fig. 8where a common axial force is exerted.

In this Figure, φ y , φm and φn represent the yield-strength curvature, the maintaining-maximum-strengthcurvature and the maintaining-yield-strength curvature,respectively. Generally, the corresponding relations be-

(1) pile number 3(1) pile number 3(1) pile number 3(1) pile number 3(1) pile number 3 ××××× 3 (2) pile number 33 (2) pile number 33 (2) pile number 33 (2) pile number 33 (2) pile number 3 ××××× 33333d = 2.5 d = 3.0d = 2.5 d = 3.0d = 2.5 d = 3.0d = 2.5 d = 3.0d = 2.5 d = 3.0Fig. 7 Comparison of pile group efFig. 7 Comparison of pile group efFig. 7 Comparison of pile group efFig. 7 Comparison of pile group efFig. 7 Comparison of pile group effectfectfectfectfect

Fig. 8 Example of non-linearity model for a pile memberFig. 8 Example of non-linearity model for a pile memberFig. 8 Example of non-linearity model for a pile memberFig. 8 Example of non-linearity model for a pile memberFig. 8 Example of non-linearity model for a pile member(cast-in-place pile)(cast-in-place pile)(cast-in-place pile)(cast-in-place pile)(cast-in-place pile)

(1) Allotment coefficient of subgrade reaction due to pileline (ηm )The effect of pile group due to the horizontal load

can be obtained by substituting n = 1 into the expres-sion (3) which indicates the number of piles at the rightangle to the direction of horizontal load (Fig. 6). Sincethe upper limit values of the horizontal subgrade reac-tion change according to the pile line, the allotment co-efficients (ηm ) are determined in Table 3 by referring tothe results of experiment and computation (expression(3)) which include the allotment ratios of pile lines andthe effect coefficients of pile group.

156156156156156 QR of RTRI, Vol. 40, No. 3, Oct. ’99

tween the limit values of curvature and the damage lev-els are defined as follows.

φ y to level 1 ; φm to level 2 ; φn to level 3.Furthermore, this nonlinear property of pile mem-

ber is established under the precondition that no sheardamage occurs. Otherwise, it is necessary to check theshear damage by another method.

3. 4 Y3. 4 Y3. 4 Y3. 4 Y3. 4 Yield point of a pile foundationield point of a pile foundationield point of a pile foundationield point of a pile foundationield point of a pile foundation

Yield point of a pile foundation is established accord-ing to the load-displacement curve of an overall struc-ture, where the displacement increases rapidly mainlybecause of the subgrade reaction reaching the upper limitvalues or the stiffness of pile members decreasing dueto the strength yielding. However, the yield point wherethe displacement rapidly increases in the load-displace-ment curve varies for different types of foundations. Thismakes it difficult to judge the yield point from a) thedegree to which the subgrade reaction exceeds the up-per limit values and b) the number of members dam-aged over the total number of members.

In order to investigate the causes of yield point, somecommon prototype pile foundations were chosen for trialdesigning. As a result, it was confirmed that the yieldpoint appears when a) the subgrade reaction yields atthe outermost edge of the indentation in side of pile groupand b) half of the total number of pile members yields 6).

Therefore, the yield point of pile foundation with acommon shape can be determined as the point when itreaches one of the states shown in Table 4. If a pilefoundation has too many piles, it is difficult to deter-mine the yield point by the criterion in Table 4. In thiscase, the yield point can be determined by taking intoaccount the causes which intensify the displacement rap-idly in the load-displacement curve.

mined by the load-displacement curves which representthe relationship between the load and displacement inthe central axial of the pile group head. These load-dis-placement curves are obtained by the static nonlinearanalysis of the total structural system. Moreover, the cou-pling effect between swaying and rocking movements isalso included in these skeleton curves, where the 1st vi-bration mode is presumed as the predominant mode. Fig.9 shows an example of modeling the skeleton curve. Gen-erally, the bilinear type behavior is used in the modelwhere the yield point is determined by the criterion Table4 and only the 2nd incline of stiffness is taken into ac-count. In the case of rigorous analysis, the tri-linear typebehavior should be applied.

Fig. 9 Example of skeleton curve for supporting springsFig. 9 Example of skeleton curve for supporting springsFig. 9 Example of skeleton curve for supporting springsFig. 9 Example of skeleton curve for supporting springsFig. 9 Example of skeleton curve for supporting springs

4. Modeling supporting springs4. Modeling supporting springs4. Modeling supporting springs4. Modeling supporting springs4. Modeling supporting springs

When analyzing a pile foundation by replacing it withsupporting springs, it is important that the influence ofpiles and ground on the super structures should be re-flected in the model of supporting springs. In generalcases, there are three kinds of supporting springs neededfor a pile foundation: horizontal, vertical, and rockingsupporting springs. The model of skeleton curves andhysteresis behavior used for these springs are describedas follows.

4. 1 Skeleton curves of support springs4. 1 Skeleton curves of support springs4. 1 Skeleton curves of support springs4. 1 Skeleton curves of support springs4. 1 Skeleton curves of support springs

The skeleton curves of supporting springs are deter-

TTTTTable 4 Yable 4 Yable 4 Yable 4 Yable 4 Yield point definition for pile foundationield point definition for pile foundationield point definition for pile foundationield point definition for pile foundationield point definition for pile foundationSubgrade in the indenta-tion - in side of pile group

Subgrade in the pulling -out side of pile group

Pile members

When the vertical resistance of pile headin the outermost edge reach the upperlimit value of design vertical capacityWhen the vertical resistance of the headof a half (ignoring fractions) of total pilesreach the upper limit of design pull-outresistanceWhen the strength of a half (ignoringfractions) of the total piles yield

4. 2 Hysteresis behavior of supporting spring4. 2 Hysteresis behavior of supporting spring4. 2 Hysteresis behavior of supporting spring4. 2 Hysteresis behavior of supporting spring4. 2 Hysteresis behavior of supporting spring

The hysteresis behavior of the supporting spring isaffected by the characteristics of pile members, and hori-zontal and vertical subgrade reactions. By simulatingthe loading experiment cases of single piles, it is con-firmed that the horizontal subgrade reaction contributesthe most to the hysteresis behavior of supporting spring,within the scope where the damage of pile members isnot so severe. Moreover, the hysteresis behavior of hori-zontal subgrade reaction changes due to the degree of‘standing-alone-property’ (SAP) of soil. With a soil of thelow-degree SAP (like non-cohesion dry sand), the shapeof its hysteresis behavior looks like a spindle, and with asoil of high-degree SAP (like clay) the shape of its hyster-esis behavior is a slip type7).

As to the effect of pile member on the hysteresis be-havior of supporting spring, it is confirmed that there islittle difference of hysteresis behavior between the lin-earity and non-linearity of pile member. By analyzing

Fig. 10 Example of hysteresis behavior for pile foundationFig. 10 Example of hysteresis behavior for pile foundationFig. 10 Example of hysteresis behavior for pile foundationFig. 10 Example of hysteresis behavior for pile foundationFig. 10 Example of hysteresis behavior for pile foundation

157157157157157QR of RTRI, Vol. 40, No. 3, Oct. ’99

Limit values of ductility factor μ L

Stability Stability Stabilitylevel 1 level 2 level 3

cast-in-place pile 1 5 8

prototype pile foundations, it is understood that the hys-teresis behavior between a single pile and a pile group isalmost the same.

In general cases, most pile foundations are built inthe soil with low degree of SAP and high level of under-ground water. From the discussions above, it is appro-priate to assume the hysteresis behavior of supportingspring as the Clough model shown in Fig. 10, where theeffect due to decaying can be considered.

5. Checking the stability level of pile foundation5. Checking the stability level of pile foundation5. Checking the stability level of pile foundation5. Checking the stability level of pile foundation5. Checking the stability level of pile foundation

5. 1 Response ductility factor5. 1 Response ductility factor5. 1 Response ductility factor5. 1 Response ductility factor5. 1 Response ductility factor

In the seismic design, it is confirmed that the stabil-ity level of pile foundation is less than the limit valuecorresponding to each stability level by checking the re-sponse ductility factor. The limit values of response duc-tility factor corresponding to various stability levels forcast-in-place pile are shown in Table 5. Moreover, thelimit values of ductility factors are based on the resultsof loading experiments. If there is the sufficient strengthleft for pile members, the limit values can be determinedby other methods while taking the damage process intoaccount.

5. 2 Damage level of member5. 2 Damage level of member5. 2 Damage level of member5. 2 Damage level of member5. 2 Damage level of member

In the seismic design, it is necessary to confirm thatthe demanded damage level of each pile member is sat-isfied. Referring to some studies8), it is understood thateven when the damage level of one part of a pile groupexceeds the damage level 1 or 2, the strength remainingfor the total structural system is enough. Therefor, thelimit values for the damage level of pile member havebeen relaxed.

5. 3 Response displacement5. 3 Response displacement5. 3 Response displacement5. 3 Response displacement5. 3 Response displacement

It is confirmed that the values of response displace-ment or residual displacement should be less than thelimit values corresponding to various stability levels.

6. Conclusions6. Conclusions6. Conclusions6. Conclusions6. Conclusions

In order to establish the algorithm of seismic designfor pile foundation during an intense earthquake, theauthors proposed the following two concepts, which areexamined to be proper by a model and prototype experi-ments and analyses.a) Method to simulate the deformation performance of

pile foundation with high accuracy in a large defor-mation range.

b) Model concerning the hysteresis behavior given tosupporting spring of pile foundations.Moreover, the authors will discuss the concept of us-

ing indexes to check the seismic performance of pile foun-dation. In the future, the adequacy of these indexesshould further be examined by trial design of the pro-posed method.

ReferencesReferencesReferencesReferencesReferences

1) Nishimura, A. et al. : “Test and Analyses of LateralLoading Tests of Pile Foundation Models in LargeDisplacement Range (Single Pile)”, The 29th JapanNational Conference on Soil Mechanics And Foun-dation Engineering, 1994.6 (in Japanese)

2) Takagi, S. et al. : “Study About Simulation of LateralLoading Tests of Pile Foundation Models in LargeDisplacement Range”, The 47th Annual Conferenceof The Japan Society of Civil Engineers, 1992.9 (inJapanese)

3) Kousa, K. et al, : “Large Lateral Displacement Ex-periment of Cast-in place piles And Analytical Con-sideration”, Symposium on Limit State Design ofFoundation, 1995.5 (in Japanese)

4) Broms, B.B : “Design of laterally loaded piles”, Jour-nals of the soil mechanics and foundations division,ASCE, pp79-99, 1965

5) Hasuda, T. : “Prediction of Vibration And Structure-borne sound in Over Track Buildings”, RTRI ReportVol.7, No.10, 1993.10 (in Japanese)

6) Kuroki, T. et al. : “Study on Subgrade Rreaction inPile Foundation Suffering Large Lateral Deforma-tion (The Analytic Examination About Real Struc-ture)”, The 53th Annual Conference of The JapanSociety of Civil Engineers, 1998.10 (in Japanese)

7) Kondou, M. et al. : “Study on Property of RestoringForce of Pile Foundation-Soil in Earthquake-Resis-tant Design”, The 10th Earthquake Engineering Sym-posium, 1998.11 (in Japanese)

8) Kimura, Y. et al. : “An Experimental Study on TheDuctility of Pile Foundations”, Journal of Study En-gineering, Vol.44A, 1998.3 (in Japanese)

TTTTTable 5 Stability levels and limit values of ductility factorable 5 Stability levels and limit values of ductility factorable 5 Stability levels and limit values of ductility factorable 5 Stability levels and limit values of ductility factorable 5 Stability levels and limit values of ductility factor