ARTICLE IN PRESS

Influence of soil–structure interaction on the response of seismicallyisolated cable-stayed bridge

B.B. Soneji�, R.S. Jangid

Department of Civil Engineering, Indian Institute of Technology Bombay, Mumbai 400 076, India

Abstract

Soil conditions have a great deal to do with damage to structures during earthquakes. This paper attempts to assess the influence of

dynamic soil–structure interaction (SSI) on the behavior of seismically isolated cable-stayed bridge supported on a rigidly capped vertical

pile groups, which pass through moderately deep, layered soil overlying rigid bedrock. In the present approach, piles closely grouped

together beneath the towers are viewed as a single equivalent upright beam. The soil–pile interaction is idealized as a beam on nonlinear

Winkler foundation using continuously distributed hysteretic springs and viscous dashpots placed in parallel. The hysteretic behavior of

soil springs is idealized using Bouc–Wen model. The cable-stayed bridge is isolated by using high-damping rubber bearings and the

effects of SSI are investigated by performing seismic analysis in time domain using direct integration method. The seismic response of the

isolated cable-stayed bridge with SSI is obtained under bi-directional earthquake excitations (i.e. two horizontal components acting

simultaneously) considering different soil flexibilities. The emphasis has been placed on assessing the significance of nonlinear behavior of

soil that affects the response of the system and identify the circumstances under which it is necessary to include the SSI effects in

the design of seismically isolated bridges. It is observed that the soil surrounding the piles has significant effects on the response of the

isolated bridge and the bearing displacements may be underestimated if the SSI effects are ignored. Inclusion of SSI is found essential for

effective design of seismically isolated cable-stayed bridge, specifically when the towers are very much rigid and the soil condition is soft

to medium. Further, it is found that the linear soil model does not lead to accurate prediction of tower base shear response, and nonlinear

soil modeling is essential to reflect dynamic behavior of the soil–pile system properly.

Keywords: Cable-stayed bridge; Soil–structure interaction; Pile group; Nonlinear springs; Earthquake; Isolation system

1. Introduction

Significant damage of bridges due to partial or completecollapse of piers has been observed in every major seismicevent. The 1994 Northridge earthquake, 1995 Kobe earth-quake and 2001 Gujarat earthquake have demonstratedthat the strength alone would not be sufficient for thesafety of bridges during the earthquake. For the pastseveral years, the research is focused on finding out morerational and substantiated solutions for protection ofbridges from severe earthquake attack. Seismic isolationis a strategy that attempts to reduce the seismic forces to ornear the elastic capacity of the member, thereby eliminating

or reducing inelastic deformations. The main concept inisolation is to reduce the fundamental frequency ofstructural vibration to a value lower than the predominantenergy-containing frequencies of earthquake. The otherpurpose of an isolation system is to provide means ofenergy dissipation, which dissipates the seismic energytransmitted to the system. The isolation device, whichreplaces conventional bridge bearings, decouples thebridge deck (which alone is responsible for majority ofthe tower base shear) from bridge substructure duringearthquakes thereby significantly reducing the deck accel-eration and consequently the forces transmitted to thetowers or piers.Though the technique of seismic isolation has been

successfully implemented world wide for buildings andshort to medium span highway bridges [1–4], very limited

246

amount of work has been done on the use of seismicisolation for seismic response control of cable-stayedbridges. Ali and Abdel-Ghaffar [5] investigated theeffectiveness of elastomeric (elastic and hysteretic typeboth) bearings for seismic isolation of cable-stayed bridges.Wesolowsky and Wilson [6] examined the efficacy of usingseismic isolation to favorably influence the seismic responseof cable-stayed bridges subjected to near-field earthquakeground motions. It is to be noted that in these studies onisolated cable-stayed bridges, the foundation of the bridgetowers is assumed as rigid (embedded in solid rock) andthere has not been any attempt to investigate the effects ofSSI on the response of the bridges.

In recent years, several cable-stayed bridges have beenconstructed on relatively soft ground, which results in agreat demand to evaluate the effects of soil–structureinteraction (SSI) on the seismic behavior of the bridges,and properly reflect it in their seismic design. During theseyears, some studies have been conducted to comprehend theeffects of SSI on the seismic behavior of non-isolatedbridges [7–11]. Also, the studies have been carried out toinvestigate the seismic response of isolated reinforcedcement concrete bridges considering SSI [12–14]. Thesestudies have demonstrated that SSI generally tends toprolong the natural periods of bridge–foundation–soil

Hin

T

De

1 1 2 2 4 4 4 4 4 4 3 3 2 2

134.00 m 274.00 m

C

Part 2

6 @2.75m

5.5 m

13.5 m

13.5 m

17.0 m

Part 1

Part 3

Part 4

4.7 m

Fig. 1. Details of the semi-harp-type cable-stayed bridge model. (a) The brid

(non-isolated) and (d) tower–deck connections (isolated).

systems, and may significantly affect the internal forces instructural members and displacement response of bridges.It has also been recognized that the way in which SSI affectsthe seismic behavior of bridges depends on the conditions ofthe bridge–foundation–soil system [15], suggesting a neces-sity to perform many detailed case studies.In this paper, influence of dynamic SSI on the seismic

response of cable-stayed bridge isolated by elastomericbearings is investigated. The soil–pile interaction isidealized as a beam on nonlinear Winkler foundation(BNWF) using continuously distributed nonlinear springsand dashpots. The specific objectives of the study are: (i) toinvestigate the influence of flexibility of layered soil on theresponse of seismically isolated cable-stayed bridge; (ii) toassess the significance of nonlinearity in soil on the seismicresponse of the isolated bridge by comparing the results ofSSI considering and ignoring nonlinearity and (iii) toidentify the circumstances under which it is necessary toinclude the SSI effects in the design of seismically isolatedcable-stayed bridges.

2. The cable-stayed bridge model

The bridge model used in this study is the Quincy Bay-View Bridge crossing the Mississippi River at Quincy, IL.

Tower

Isolator

Deck

ge support

ower

ck

134.00 m Roller support

17 m

5

3.7

m

z

y

x

ge model, (b) finite element model of towers, (c) tower–deck connections

247

The bridge consists of two H-shaped concrete towers,double plane semi-harp-type cables and a compositeconcrete-steel girder bridge deck. The detailed descriptionof the bridge is given in Wilson and Gravelle [16]. Here, asimplified lumped mass finite element model of the bridgedeveloped for the investigation is as shown in Fig. 1(a). Thefinite element model of the towers is separately shown inFig. 1(b). There are 28 cable members, 14 supporting themain span and 7 supporting each side spans. The cablemembers are spaced at 2.75m c/c at the upper part of thetowers and equally spaced at the deck level on the side aswell as main spans. The relevant properties of the bridgedeck (for equivalent steel area) and towers are given inTable 1 while those of the cables are given in Table 2. Thebridge deck is assumed to be a continuous beam rigidlyconnected to the towers such that the deck moment will notbe transferred to the tower through the deck–towerconnection. For implementing seismic isolation, the isola-tion bearings are placed at each four supports of the deckreplacing conventional bearings (refer Fig. 1(c) and (d)).The bridge towers are supported on rigidly capped verticalpile groups passing through moderately deep, layered soiloverlying rigid bedrock. When piles are closely groupedtogether, the piles and soil work like a single rigid unit, andthe problem becomes of the group working like a large pier[17,18]. Hence in present approach, piles closely groupedtogether beneath the towers are viewed as a singleequivalent upright beam with second moment of areaabout x–x-, y–y- and z–z-axis equal to 82.72, 1057.726 and189.74m4; respectively, and cross-sectional area equal to20.49m2. The piles are spaced at three pile diameters, andthe properties of the single equivalent beam include groupeffects.

It is worth mentioning that a cable-stayed bridge, inthe rigorous sense, behaves nonlinearly when loaded.However, the research on ambient vibration survey of the

Table 1

Properties of the deck and the towers of the cable-stayed bridge

Part of the

structure

Cross-sectional

area (m2)

Moment of inertia about

z–z-axis (m4)

Moment of iner

y–y-axis (m4)

Deck 0.827 0.341 19.760

Tower part 1 14.120 28.050 531.580

Tower part 2 14.120 28.050 670.970

Tower part 3 17.540 30.620 1239.400

Tower part 4 35.390 32.750 1422.420

Table 2

Properties for the stay cables of the cable-stayed bridge

Cable no. Cross-sectional area (m2)

1 0.0180

2 0.0135

3 0.0107

4 0.0070

cable-stayed bridge carried out by Wilson and Liu [19] hasdemonstrated that a completely linear model was sufficientto get reasonably accurate results for the Quincy Bay-ViewBridge. Hence, no attempts are made to introducenonlinearity into the model in this investigation.Regarding modeling of the bridge components, the deck

and the tower members are modeled as space frameelements. The cables are modeled as linear elastic spacetruss elements. The stiffness characteristics of an inclinedcable can exhibit a nonlinear behavior caused by cable sag.This nonlinear behavior can be taken into account bylinearization of the cable stiffness using an equivalentmodulus of elasticity that is less than the true materialmodulus [20]. For the analysis of the bridge underconsideration, Wilson and Gravelle [16] found the valueof equivalent modulus essentially equal to the true modulusof elasticity. Hence, here nonlinearity due to cable sag isneglected and cables are treated as having a completelylinear force–deformation relationship described by the truematerial modulus of elasticity. Moreover, cables areassumed to be capable of bearing tension as well ascompression assuming that the pretension in the cables willtake care of the compression induced in the dynamicanalysis.

3. Modeling of the soil–pile system

In the last two decades, several numerical and analyticalmethods have been developed to compute the dynamicstiffness and seismic response factors of pile foundationsaccounting for soil–pile interaction. Most of these methodsassumed linear viscoelastic response of the surroundingsoil. Nevertheless, under moderate and strong seismicloading, pile foundations undergo significant displacementsand the behavior of the soil–pile system can be nonlinear.

tia about Moment of inertia about

x–x-axis (m4)

Young’s

modulus (MPa)

Mass density

(kg/m3)

0.027 205,000 7850

15.390 30,787 2400

15.390 30,787 2400

19.760 30,787 2400

27.640 30,787 2400

Young’s modulus (MPa) Cable weight (N/m)

205,000 1765.80

205,000 1324.35

205,000 1049.67

205,000 686.70

248

Studies on the nonlinear dynamic response of piles havebeen conducted with the finite element method [21]. Thefinite element method, which requires discretization of thepile and the surrounding soil, although powerful, iscomputationally very expensive. In contrast, the BNWFmodel is a versatile and economical approach. Trochaniset al. [22] have carried out the most comprehensive studyon the nonlinear response of piles using a BNWF modelutilizing a model of viscoplasticity, better known as theBouc–Wen model [23,24], to describe the force–displace-ment relation of distributed nonlinear springs that approx-imate the soil reaction on the pile. Their study concentratedon the static and quasi-static (zero-frequency limit) loadingof piles, and for this type of loading it was shown that theBouc–Wen model predicts well the response of a variety ofsoil–pile systems.

Herein, the soil–pile interaction is idealized as a BNWFusing continuously distributed nonlinear springs andviscous dashpots placed in parallel (Fig. 2(a)). The presenceof the damper makes the model very efficient for theprediction of the pile response under dynamic loads since itaccounts realistically for the energy that radiates outward.The response of the superstructure is investigated underthree different types of soil surrounding the pile founda-tion, namely, soft, medium and firm. The soils areconsidered in layers of different thickness resting on rock(Fig. 2(b)), with increasing stiffness and decreasing damp-ing with depth. Assuming that the rigid bedrock isavailable at a depth of 25m, soil springs are distributedat 2.5m centers. Thus, the discretization of pile into 11segments by using 10 springs is enough to achieve sufficientaccuracy in the analysis. The spring coefficients have beencomputed by method suggested in Specification for

cs

ks

1.25

m

2.5

m

1.25

m

9@ 2

.5 m

= 2

2.5

m

Pile

cs

ks

cs

ks

Nodal mass

Fig. 2. Schematic of dynamic BNWF model in layered

Highway Bridges issued by Japan Road Association [25].In the suggested method, reference soil reaction coefficientk0 is first computed using Eq. (1), where Es is Young’smodulus of soil. The soil reaction coefficient per unit area,kr, is obtained using Eq. (2), where Be is the width of thefoundation perpendicular to the direction considered:

k0 ¼1:2Es

30, (1)

kr ¼ k0

ffiffiffiffiffiBe

30

�3=4

r. (2)

Young’s modulus can be evaluated using the relation

Es ¼ 2Gsð1þ msÞ, (3)

where Gs is the shear modulus and ms is Poisson’s ratio forthe soil.It should be mentioned that, when using Eqs. (1) and (2),

the units of Be and Es must be in centimeters and kg/cm2,respectively. The horizontal spring coefficients (ks) for eachpart of foundation are obtained by multiplying kr by thearea of its surface perpendicular to the excitation direction.The horizontal spring coefficients are evaluated by takingthe widths of foundation perpendicular to the longitudinaland transverse directions of the bridge as 21 and 9m,respectively. Although it has been recognized that springcoefficients are frequency dependent, the spring coefficientscomputed using the method suggested in Japan RoadAssociation [25] are frequency independent for practicaluse.The second key parameter for soil is damping. Two

fundamentally different damping phenomena are asso-ciated with soil, namely material damping and radiation

5 m

10

m5

m

5 m

soil strata. (a) BNWF model and (b) layered soil.

249

damping. Material damping can be thought of as ameasure of the loss of vibration energy resulting primarilyfrom hysteresis in the soil. The radiation damping is ameasure of energy loss from the structure throughradiation of waves away from the foundation. Expressionsfor damping coefficients are available in literature [26,27],on the basis of which the following simple approximation isderived [28]:

cs ¼ Qs6a�1=40 rsV sd þ 2xs

ks

os, (4)

where xs and rs are the damping ratio and mass density ofthe soil, d is the pile diameter, shear wave velocity,V s ¼

ffiffiffiffiffiffiffiffiffiffiffiffiGs=rs

p, os ¼ pV s=2df , df is the thickness of soil

layer and a0 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiosd=V s

p. The coefficient Qs is given by the

expression

Qs ¼ 2 1þ3:4

pð1� msÞ

� �1:25 p4

� �0:75. (5)

The dynamic properties of the soils such as shearmodulus, mass density, Poisson’s ratio, damping ratio,shear strength, etc. that vary with the depth are given inTable 3 [29,30].

The force resulting from the nonlinear spring alone isgiven by

F s ¼ aksq0 þ ð1� aÞksqZ, (6)

where q0 is the pile deflection at the location of the spring, ais a parameter that controls the post-yielding stiffness, q isthe value of pile deflection that initiates yielding in thespring and Z is a hysteretic dimensionless quantity that isgoverned by the following equation:

q _Z ¼ A _q0 þ bj _q0jZjZjn�1 � g _q0Z

n. (7)

In the above equation b, g, n and A are dimensionlessquantities that control the shape of the hysteretic loop. Thehysteretic model of Eq. (7) was originally proposed byBouc [23] for n ¼ 1, and subsequently extended by Wen[24], and used in random vibration studies of inelasticsystems. It can be easily shown that when A ¼ 1 in Eq. (7),parameter ks in (6) becomes the small-amplitude elastic

Table 3

Dynamic properties of different types of layered soils

Depth, h (m) Shear modulus, Gs (MN/m2) Mass density, rs (Mg/m3) P

Soft Medium Firm Soft Medium Firm S

0

80 400 900 2 2 2.1 0

5

125 625 1350 2 2.1 2.1 0

10

245 1225 2550 2 2.2 2.3 0

20

550 2750 6500 2.2 2.2 2.5 0

25

distributed stiffness, and parameter a becomes the ratio ofthe post- to pre-yielding stiffness [31]. Based on thisobservation, all the subsequent analysis is carried outtaking A and n equal to 1. The other parameters, whichdo not affect much the peak response, are kept constant(i.e. b ¼ g ¼ 0.5). The plastic soil behavior (no hardening)at large pile deflections indicated that the ultimate post-yielding stiffness of the soil is zero and, therefore, theparameter a in Eq. (6) is set equal to zero.The value of q (pile deflection at which yielding initiates

in the soil spring) in Eq. (7) at depth h is provided by

qðhÞ ¼ lðhÞtðhÞdks=S

, (8)

where S is the spacing between two adjacent springs, t(h) isthe shear strength of the soil at depth h and l(h) is adimensionless quantity. Considerable research has beendone to quantify l [32,33]. l values between 9 and 12 maybe appropriate at depths where plane strain conditions arevalid. At shallow depths, plane strain conditions are notvalid due to vertical deformation of the soil during lateralmotion of the pile. Hence, l values of 2 or 3 have beensuggested. The following expression for the variation of lwith depth is recommended [33]:

lðhÞ ¼ 3þsz

tðhÞþ J

h

d; ho

6d

gs=tðhÞ þ J, (9)

lðhÞ ¼ 9; hX6d

gs=tðhÞ þ J, (10)

where sz is the overburden pressure and gs ¼ rsg is thespecific weight of the soil. The value of parameter J inEq. (9) must be determined empirically. In the absence ofsuch data, the recommended value of J ¼ 0.5 may be used.

4. Numerical study with nonlinear soil modeling

The cable-stayed bridge is isolated by using high-damping rubber bearings and the effects of SSI areinvestigated by performing seismic analysis in time domainusing direct integration method. Influence of SSI on the

oisson’s ratio (m) Damping ratio (xs) Shear strength, ts (kN/m2)

oft Medium Firm Soft Medium Firm Soft Medium Firm

.4 0.35 0.3 0.07 0.04 0.02 25 50 100

.4 0.35 0.3 0.06 0.04 0.02 50 100 150

.4 0.35 0.3 0.05 0.04 0.02 75 150 200

.4 0.35 0.3 0.05 0.04 0.02 100 200 300

250

seismic response of isolated cable-stayed bridge is investi-gated under the four real strong earthquake groundmotions, namely, (1) 1940 Imperial Valley, (2) 1995 Kobe,(3) 1989 Loma Prieta and (4) 1994 Northridge earthquakes.The first one is widely used by the researcher in the pastand the last three represent the strong motion earthquakerecords. The peak accelerations of these earthquakeground motions are shown in Table 4. The specificcomponents of these ground motions applied in thelongitudinal and transverse directions are also indicatedin Table 4. The displacement and acceleration responsespectra of the above four ground motions for 2% of thecritical damping are shown in Fig. 3. The maximumordinates of the spectral acceleration along the longitudinaldirection are 1.302g, 4.12g, 3.55g and 3.24g occurring atthe period of 0.46, 0.35, 0.64 and 0.35 s and along thetransverse directions are 0.955g, 3.559g, 2.215g and 1.967g

occurring at the period of 0.53, 0.39, 0.4 and 0.51 s for

Table 4

Peak ground acceleration of various earthquake ground motions

Earthquake Recording station Applied in longitudin

Component

Imperial Valley, 1940 El Centro N00E

Kobe, 1995 Japan Meteorological Agency N00E

Loma Prieta, 1989 Los Gatos Presentation Center N00E

Northridge, 1994 Sylmar Converter Station N00E

Note: PGA ¼ peak ground acceleration.

1.2

0.8

0.4

0.0

Spec

tral

dis

plac

emen

t (m

)Sp

ectr

al a

ccel

erat

ion

(m) 4

3

2

1

00 1 2 3 4

Time period (s)

Logitudinal

Imperial Valley, 1940Kobe, 1995Lomba Prieta, 1989Northridge, 1994

Fig. 3. Displacement and acceleration spectra of four earthquake ground mo

Imperial Valley, Kobe, Loma Prieta and Northridgeearthquakes, respectively. The spectra of these groundmotion indicate that the ground motions are recorded athard soil or rock site.As damping in the structure is very low, 2% damping is

assumed. For the HDRB, damping ratio (xb) is taken equalto 10%. Previous studies on seismic isolation of cable-stayed bridges [6,34] have shown that a small amount ofisolation is sufficient to reduce the seismically inducedforces in the bridge. Higher amount of isolation results inlarger displacement of the deck and trade-off to reductionof the base shear of the towers. Hence, herein the isolationperiod is taken equal to 2 s and is kept constant throughoutthe study. To evaluate the effects of SSI on the seismicresponse of the bridge, the evaluation criteria proposed arerelative displacement in the longitudinal (xb1) and trans-verse (yb1) directions of the isolators at the abutment,relative displacement of the isolators in the transverse

al direction of the bridge Applied in transverse direction of the bridge

PGA (g) Component PGA (g)

0.348 N90E 0.214

0.834 N90E 0.629

0.570 N90E 0.607

0.843 N90E 0.600

0 1 2 3 4

Time period (s)

Transverse

Dampling = 2%

tions applied in the longitudinal and transverse directions of the bridge.

251

direction at the deck–tower junction (yb2), absoluteacceleration of the deck in the longitudinal direction atthe left abutment ð €xdÞ and base shear response of thetowers along longitudinal (Vx) and transverse (Vy) direc-tions at the left tower normalized to the weight of the deck,Wd. Because of the symmetrical structure with anti-symmetry earthquake loading about vertical axis ofsymmetry, the results at the symmetrical nodes of thestructure are found similar in magnitude and direction.Hence, results of the response quantities are presented forleft half part of the bridge.

Results of time history analyses under 1940 ImperialValley earthquake ground motion along longitudinaldirection are presented in Figs. 4–6 for soft, medium andfirm soil, respectively. The results obtained with andwithout SSI are plotted in the same graphs for comparisonpurpose. The trend of the results indicates that there is notmuch variation in acceleration and base shear responsewith the type of soil considered. However, for the soft soilstrata, little increase in bearing displacement is observedand the response reduces as soil becomes stiffer. Timehistory plots under 1940 Imperial Valley earthquakeground motion along transverse direction are presentedin Figs. 7–9 for soft, medium and firm soil, respectively. Itis observed that in transverse direction the deck accelera-tion and tower base shear found to be increased for softsoil, and the responses reduce as the soil becomes stiffer.However, increase in displacement response of the isolatorat the abutment is insignificant when SSI is considered. Thedynamic force–displacement loops in longitudinal as wellas transverse directions for the soil spring near pile head

0.2

0.0

-0.2

0.15

0.00

-0.15

0.15

-0.15

0.00

0 5 10

T

x d (

g)V

x /W

dx b

1 (m

)

Fig. 4. Time variation of deck acceleration, tower base shear and bearing di

Imperial Valley, 1940, earthquake motion.

under the 1995 Kobe earthquake ground motions arepresented in Fig. 10. It is to be noted that for the soft soilstrata, the displacement response is large and spring forceis less. As the soil stiffness increases, the inclination of theloop also increases with increase in spring force andreduction in displacement as expected. Thus, the plotsindicate that, by using the Bouc–Wen model for hysteresissystems, the nonlinear behavior of soil strata is adequatelycaptured.The peak values of the response quantities under

different earthquake ground motions are presented inTable 5. It can be observed from the table that the responsequantities other than tower base shear in transversedirection are not much affected by the SSI consideration.Since the deck is isolated from the tower, the increase indisplacement response due to SSI is little and is in the rangeof 3–20% in the longitudinal direction, and 3–13% in thetransverse direction with soft soil strata. With the firm soilstrata, the increase in displacement response of the deckreduces to 10%. Also, it can be observed that, for all theearthquakes except Kobe, 1995, the displacement responseof the isolator decreases as the soil stiffness increases. Thisis in agreement with the trend in displacement spectra ofthe earthquake ground motions (Fig. 3). Further, it is to benoted from Table 5 that the base shear response of thetower along longitudinal direction is not much influencedby the consideration of SSI. The reason behind this couldbe explained with the help of earthquake accelerationspectra presented in Fig. 3. The time period of the fixedbase tower (i.e. without SSI) along the longitudinaldirection comes out to be around 1.7 s and the inclusion

15 20 25 30

ime (s)

Without SSIWith SSI

splacement in the longitudinal direction of the bridge for soft soil under

0.2

0.0

-0.2

0.15

0.00

-0.15

0.15

-0.15

0.00

0 5 10 15 20 25 30

Time (s)

x d (

g)V

x /W

dx b

1 (m

)

Without SSIWith SSI

Fig. 5. Time variation of deck acceleration, tower base shear and bearing displacement in the longitudinal direction of the bridge for medium soil under

Imperial Valley, 1940, earthquake motion.

0.2

0.0

-0.2

0.15

0.00

-0.15

0.15

-0.15

0.00

0 5 10 15 20 25 30

Time (s)

x d (

g)V

x /W

dx b

1 (m

)

Without SSIWith SSI

Fig. 6. Time variation of deck acceleration, tower base shear and bearing displacement in the longitudinal direction of the bridge for firm soil under

Imperial Valley, 1940, earthquake motion.

252

of SSI further makes it more flexible. Thus, the time periodof the tower with SSI consideration falls in the zoneof more or less steady spectral acceleration resultingin insignificant influence on the base shear response.

However, the tower base shear in the transverse directionis greatly affected by the type of soil strata considered.The increase in the tower base shear is about 30–65%for soft site, and gradually approaches to the values

0.15

0.00

-0.15

0.25

0.00

-0.25

0.05

0.00

-0.05

Vy

/ Wd

y d /

(g)

0 5 10 15 20 25 30

Time (s)

Without SSIWith SSI

y b1

(m)

Fig. 7. Time variation of deck acceleration, tower base shear and bearing displacement in the transverse direction of the bridge for soft soil under Imperial

Valley, 1940, earthquake motion.

0.15

0.00

-0.15

0.25

0.00

-0.25

0.05

0.00

-0.05

Vy

/ Wd

y d (

g)

0 5 10 15 20 25 30

Time (s)

Without SSIWith SSI

y b1

(m)

Fig. 8. Time variation of deck acceleration, tower base shear and bearing displacement in the transverse direction of the bridge for medium soil under

Imperial Valley, 1940, earthquake motion.

253

of the base shear without SSI consideration as the stiffnessof the soil increases. This happens because the timeperiod of tower when fixed base is considered comes outto be equal to 0.25 s, which falls in the left side of the peak

of acceleration spectra (Fig. 3). When SSI is considered,the tower becomes little flexible and the time periodfalls in the peak range of the acceleration spectra, whichmakes the base shear response to increase significantly.

0.15

0.00

-0.15

0.25

0.00

-0.25

0.05

0.00

-0.05

Vy

/ Wd

y d (

g)

0 5 10 15 20 25 30

Time (s)

Without SSIWith SSI

y b1

(m)

Fig. 9. Time variation of deck acceleration, tower base shear and bearing displacement in the transverse direction of the bridge for firm soil under Imperial

Valley, 1940, earthquake motion.

0.50

0.25

0.00

0.00

-0.25

-0.50

0.50

0.25

0.00

-0.25

-0.50

0.50

0.25

0.00

-0.25

-0.50

Fs

/ Wd

0.50

0.25

0.00

-0.25

-0.50

0.50

0.25

0.00

-0.25

-0.50

0.50

0.25

0.00

-0.25

-0.50

Fs

/ Wd

-0.02 -0.01

0.00

0.01 0.02 0.00-0.02 -0.02-0.01 0.01 0.02 0.00

-0.02

-0.01 0.01 0.02

0.00-0.02 -0.01 0.01 0.02 0.00-0.02 -0.01 0.01 0.02 0.00-0.01 0.01 0.02

Longitudinal LongitudinalSoft soil Medium soil

LongitudinalFirm soil

Transverse

Displacement (m) Displacement (m) Displacement (m)

Transverse TransverseSoft soil Medium soil Firm soil

Fig. 10. Dynamic force–displacement loops of nonlinear soil spring under the Kobe, 1995, earthquake motion.

254

As the soil stiffness increases, the tower base shear intransverse direction approaches to the value of shearwithout considering the SSI effects (i.e. the fixed basetower case).

5. Numerical study with linear soil modeling

In the practical design of bridges, when it becomesnecessary to conduct dynamic response analysis of bridges,

Table 5

Peak response quantity under different earthquake motions with nonlinear SSI

Earthquake Response quantity Without SSI Soft soil % Difference Medium soil % Difference Firm soil % Difference

Imperial Valley, 1940 Vx/Wd 0.176 0.168 4.55 0.150 14.77 0.159 9.66

Vy/Wd 0.275 0.456 �65.82 0.366 �33.09 0.315 �14.55

xb1 (mm) 174.628 212.071 �21.44 197.776 �13.26 192.900 �10.46

yb1 (mm) 68.749 70.718 �2.86 69.399 �0.95 69.054 �0.44

yb2 (mm) 203.702 208.905 �2.55 207.463 �1.85 204.650 �0.47

Kobe, 1995 Vx/Wd 0.434 0.439 �1.15 0.41 5.53 0.435 �0.23

Vy/Wd 0.618 0.860 �39.16 0.706 �14.24 0.665 �7.61

xb1 (mm) 357.114 347.062 2.81 350.737 1.79 353.185 1.10

yb1 (mm) 135.634 153.212 �12.96 147.437 �8.70 142.874 �5.34

yb2 (mm) 236.828 251.418 �6.16 259.283 �9.48 260.683 �10.07

Loma Prieta, 1989 Vx/Wd 0.446 0.483 �8.30 0.455 �2.02 0.450 �0.90

Vy/Wd 0.535 0.832 �55.51 0.771 �44.11 0.638 �19.25

xb1 (mm) 611.689 682.528 �11.58 655.544 �7.17 643.274 �5.16

yb1 (mm) 119.201 125.630 �5.39 121.778 �2.16 121.975 �2.33

yb2 (mm) 209.731 199.954 4.66 213.848 �1.96 217.586 �3.75

Northridge, 1994 Vx/Wd 0.644 0.605 6.06 0.628 2.48 0.635 1.40

Vy/Wd 0.715 0.958 �33.99 0.841 �17.62 0.701 1.96

xb1 (mm) 565.568 606.726 �7.28 593.451 �4.93 587.680 �3.91

yb1 (mm) 147.744 156.171 �5.70 159.439 �7.92 154.949 �4.88

yb2 (mm) 416.184 430.049 �3.33 437.847 �5.21 427.620 �2.75

Table 6

Peak response quantity under different earthquake motions with linear SSI

Earthquake Response quantity Without SSI Soft soil % Difference Medium soil % Difference Firm soil % Difference

Imperial Valley, 1940 Vx/Wd 0.176 0.176 0.00 0.159 9.66 0.168 4.55

Vy/Wd 0.275 0.475 �72.73 0.449 �63.27 0.422 �53.45

xb1 (mm) 174.628 212.398 �21.63 198.056 �13.42 193.22 �10.65

yb1 (mm) 68.749 70.621 �2.72 67.722 1.49 67.468 1.86

yb2 (mm) 203.702 210.77 �3.47 213.459 �4.79 206.223 �1.24

Kobe, 1995 Vx/Wd 0.434 0.449 �3.46 0.415 4.38 0.447 �3.00

Vy/Wd 0.618 0.869 �40.61 0.744 �20.39 0.876 �41.75

xb1 (mm) 357.114 347.762 2.62 351.234 1.65 353.664 0.97

yb1 (mm) 135.634 153.396 �13.10 147.719 �8.91 142.65 �5.17

yb2 (mm) 236.828 252.032 �6.42 264.561 �11.71 271.884 �14.80

Loma Prieta, 1989 Vx/Wd 0.446 0.491 �10.02 0.464 �4.04 0.452 �1.35

Vy/Wd 0.535 0.844 �57.76 0.895 �67.29 0.879 �64.30

xb1 (mm) 611.689 683.516 �11.74 657.174 �7.44 644.927 �5.43

yb1 (mm) 119.201 126.113 �5.80 125.367 �5.17 124.194 �4.19

yb2 (mm) 209.731 199.724 4.77 217.232 �3.58 224.567 �7.07

Northridge, 1994 Vx/Wd 0.644 0.611 5.12 0.667 �3.57 0.673 �4.50

Vy/Wd 0.715 0.968 �35.38 0.886 �23.92 0.885 �23.78

xb1 (mm) 565.568 606.206 �7.19 594.594 �5.13 588.857 �4.12

yb1 (mm) 147.744 156.723 �6.08 163.987 �10.99 154.294 �4.43

yb2 (mm) 416.184 429.829 �3.28 450.099 �8.15 427.617 �2.75

255

the soil is modeled with linear spring and dashpot system.Hence, here in this study, it has been tried to investigate theeffectiveness of linear soil model in seismic response ofisolated cable-stayed bridge. The peak values of theresponse quantities assuming completely linear soil modelare presented in Table 6. Similar to the nonlinear case, herealso the response quantity found affected the most is thetower base shear in the transverse direction. The results

show that no convergence (i.e. approaching the responsewith SSI to that of without SSI) in base shear response isobserved with increase in soil stiffness. To visualize thedifference in results obtained with the linear and nonlinearsoil models, the tower base shear in longitudinal andtransverse directions for firm soil are plotted in Fig. 11 inthe form of bar chart for all the four earthquakes. Thenumbers on x-axis show the sequence of earthquakes

0.60

0.45

0.30

0.15

0.00

0.8

0.6

0.4

0.2

0.0

Vx

/ Wd

Vy

/ Wd

1 2 3 4 1 2 3 4

Earthquake Earthquake

Without SSI

Nonlinear SSI

Linear SSI

Fig. 11. Comparison of tower base shear with linear and nonlinear soil models.

256

considered in this study. The large difference between theresults with nonlinear and linear soil models specifically forshear in transverse direction indicates that the considera-tion of nonlinearity in soil is essential to predict accurateresults.

6. Conclusions

Influence of SSI on seismic response of isolated cable-stayed bridge has been investigated under bi-directionalearthquake excitations. The deck of the bridge is isolatedfrom the towers by using conventional high-dampingrubber bearings. Three types of layered soil strata, namely,soft, medium and firm, have been considered for the study.The soil–pile interaction is idealized as a BNWF usingcontinuously distributed nonlinear springs and viscousdashpots placed in parallel, and Bouc–Wen model is usedto model hysteretic behavior of the soil. From the trends ofthe results of the present study, following conclusions maybe drawn:

(1)

For soft soil condition, the bearing displacement maybe underestimated if SSI is ignored, especially in thelongitudinal direction. However, no significant increasetakes place in deck displacement in transverse direction.

(2)

The tower base shear response in the longitudinaldirection is not much affected irrespective of the soiltypes.

(3)

Significant influence of soil–pile interaction is observedon tower base shear response in the transversedirection. The response is much higher as comparedto that of the bridge with fixed tower base when the soilis soft to medium. As the stiffness of the soil strataincreases the effect of SSI diminishes.

(4)

Analyzing the structure assuming linear soil model doesnot lead to accurate prediction of tower base shearresponse, and nonlinear soil modeling is essential toreflect dynamic behavior of the soil–pile systemproperly.

(5)

Inclusion of SSI is essential for effective design ofseismically isolated cable-stayed bridge, specificallywhen the towers are very much rigid and the soilcondition is soft to medium.

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