Effects of soil±structure interaction on longitudinal seismic response ofMSSS bridges

M.A. Saadeghvaziri*, A.R. Yazdani-Motlagh, S. Rashidi

Department of Civil and Environmental Engineering, New Jersey Institute of Technology, University Heights, Newark, NJ 07102-1982, USA

Abstract

This paper presents the results of a comprehensive study on the effects of soil±structure interaction on longitudinal seismic response of

existing bridges. FHWA's guidelines for footing foundation on semi-in®nite elastic half-space are used to determine translational and

rotational stiffnesses at the base of bridge abutments and piers. Similarly, stiffness and strength of abutment back®ll soil are determined based

on FHWA's procedures. Various stiffnesses at the abutments are then lumped (condensed) into one translational spring at the point of impact

between the abutment and the deck. Translational springs at the abutments are bilinear with their yield strength in compression determined

based on Mononobe±Okabe method. In tension it is equal to the friction force at the footing. Among the parameters considered is the case of

damaged back wall, where it is assumed that due to shear failure at the juncture of the back wall and breast wall the abutment strength and

stiffness, as well as mobilized abutment mass, have changed. Results indicate that soil±structure interaction (SSI) has a signi®cant effect on

the seismic response in the longitudinal direction. Abutment strength is the most critical parameter. Impact force, deck sliding, and SSI

affects all plastic rotations at the base of columns. Thus, it is important that analytical models used in seismic evaluation of bridge systems

explicitly consider SSI. q 2000 Elsevier Science Ltd. All rights reserved.

Keywords: Soil±structure interaction; Abutment; Seismic response of bridges; Longitudinal direction; Impact; Multi-span simply supported bridges

1. Introduction

The Northridge Earthquake of January 17, 1994 and the

Loma Prieta Earthquake of October 17, 1989, led to an

increased awareness concerning the response of highway

bridges subjected to earthquake ground motions. In 1991,

the Interim AASHTO Standard Speci®cations for Highway

Bridges [1] adopted the 1988 National Earthquake Hazard

Reduction Program (NEHRP) Horizontal Acceleration

maps. Under NEHRP maps many areas on the East Coast

of the US, including New Jersey, were placed into higher

seismic risk categories. For example the acceleration

coef®cient, A, for northern New Jersey has been increased

from 0.1 to 0.18. In response to this and FHWA's mandates,

the New Jersey Department of Transportation (NJDOT)

initiated its Seismic Retro®t Program [2] using FHWA's

Seismic Retro®tting Manual for Highway Bridges [3].

Furthermore, NJDOT uses the AASHTO's Seismic Design

Guidelines in the design of new bridges. General issues

related to seismic design and retro®t of bridges have been

reported elsewhere [4]. The main objective of this paper is

to present the results of three case studies of the effects of

soil±structure interaction (SSI) on the longitudinal seismic

response of bridges in New Jersey.

Most bridges in New Jersey are Multi-Span Simply

Supported (MSSS) slab on girder where under earthquake

ground motions there is a high possibility of impact between

adjacent spans and between the end-span and the abutment.

Impact forces due to longitudinal earthquake ground motion

can be large enough to cause damage to the steel bearings

and abutment back walls. Girder seat length is another

important and critical parameter. Proper estimate of the

capacity±demand ratio for seat length at various locations

requires accurate consideration of the SSI. Generally, the

longitudinal bridge displacement is restraint by the abut-

ments. However, should there be additional movements at

the abutments the integrity of the entire bridge system can

be compromised. Movements at the abutments may be due

to elastic deformation and/or inelastic deformation (as a

result of yielding in the soil). Therefore, essential to

accurate estimate of capacity±demand ratios for seat

lengths, is consideration to abutment±soil system (capacity

and stiffness).

The importance of including the ¯exibility and strength of

supports at the abutments and piers in dynamic analysis of

highway bridges is well recognized by various agencies such

AASHTO [1] and CALTRANS (California Department of

Soil Dynamics and Earthquake Engineering 20 (2000) 231±242

0267-7261/00/$ - see front matter q 2000 Elsevier Science Ltd. All rights reserved.

PII: S0267-7261(00)00056-7

www.elsevier.com/locate/soildyn

* Corresponding author. Tel.: 11-973-596-5817; fax: 11-973-596-5970.

E-mail address: ala@njit.edu (M.A. Saadeghvaziri).

Transportation) [5]. In design of new bridges using these

speci®cations, either an iterative process is used to estimate

the stiffness (or) and displacement at the abutments or

simpli®ed rules are employed to determine the stiffness

and strength of the boundary springs. Such procedures are

simpli®ed overly and do not consider the properties of soil

and all physical dimension of the substructure. In a study

conducted on the US 101/Painter Street Overpass [6] the

ªactualº abutment capacity and stiffness determined from

analyses of earthquake records were compared to ªdesignº

values provided by CALTRANS and AASHTO. It is

reported that the actual strength and stiffness values are

affected by SSI and are time variant, ªdecreasing signi®-

cantly as the abutment deformation increases.º It is

concluded that the CALTRANS procedure results in good

estimate of the stiffness and capacity of the abutment in the

transverse direction. However, in the longitudinal direction

the CALTRANS procedure overestimates the capacity and

stiffness by a factor of two. This indicates that the assumed

ultimate passive capacity of 368.7 kPa by CALTRANS may

be too high. It was also concluded that the AASHTO-83/

ATC-6 procedure results in large estimate of the abutment

stiffness in both directions. Other researchers have also

conducted extensive investigations on determining the

stiffness and strength of boundary springs to represent the

abutments in an analytical model used in time history analy-

sis. Such studies are based on the scienti®c knowledge of the

properties of soil and more detailed consideration of the

geometrical properties of the abutment. Among these

studies are works by Siddharthan, El-Gamal and Maragakis

[7] and Wilson and Tan [8]. In this study, the procedures

given by FHWA's Seismic Design of Highway Bridge Foun-

dations [9] are used to determine the parameters of the

boundary springs at the abutments and at the base of column

piers. This phase of the study is concentrated on the seismic

response of MSSS bridges under the longitudinal compo-

nent of ground motion. It is expected that the SSI is the most

critical factor for this direction where excessive deformation

can cause bridge failure in the form of span fall off. An

important aspect of SSI is foundation damping, which is a

complex problem. Radiation damping associated with wave

propagation between masses of the superstructure and foun-

dation-soil is one form of energy dissipation due to SSI.

Material nonlinearity in the foundation soil is another

form of damping. In this study the later form of energy

dissipation is explicitly modeled, while the radiation damp-

ing is accounted for implicitly through equivalent viscous

damping. In Section 2 the details of the analytical models

employed are described.

2. Analytical model

The three bridges considered (with 2, 3 and 4 spans) are

typical of bridges in New Jersey and more generally in the

Eastern United States. All the three bridges are MSSS slab-

on-girder decks with steel bearings, ®xed or expansion,

between the superstructure and substructures. Typical gap

between either adjacent spans or end-span and abutment

back wall is in the order of 25±76 mm. Multiple columns

are used at the internal pier bents. Columns are circular in

cross-section with varying lateral reinforcement (#3 hoops

at 305 mm to #4 spirals at 57 mm). In all of the three

bridges, footings support the abutments and the columns.

Abutments are seat-type, and an approach slab of varying

depth is used behind each abutment. A transition slab is then

placed between the approach slab and the roadway. The

abutment back®ll and foundation soils are considered

cohesionless. Typical plan and longitudinal elevation of

an MSSS bridge (Bridge #1) are shown in Fig. 1.

2.1. Footing and abutment wall stiffnesses

FHWA's procedure [9] for rigid footing foundation on

semi-in®nite elastic half-space is used to determine transla-

tional and rotational stiffnesses for abutment and pier

foundations. The procedure considers all six degrees of

freedom, resulting in a 6 £ 6-stiffness matrix. Due to

space limitation the details of the procedure and its imple-

mentation for the bridges considered would not be discussed

here and the reader is referred to [9±10]. The relevant foot-

ing stiffnesses for a typical abutment in the longitudinal

direction are shown in Fig. 2a. In the determination of the

stiffness of the abutment wall-back®ll system, the FHWA's

procedure considers the nature of pressure/displacement

distribution when the wall is displaced (pushed) into the

back®ll by longitudinal seismic forces from the bridge

deck [9]. This is achieved by employing the appropriate

pressure diagrams/pro®les for translational and rotational

mode of displacement. The resultant stiffnesses for long-

itudinal translational and rotational (tilting) modes of the

abutment wall are also shown in Fig. 2a. They are located

at 0.37 of the height of the wall from the base.

2.2. Equivalent foundation spring

Shown in Fig. 2 are also the schematic diagrams of resul-

tant foundation springs at an abutment as well as the ®nal

simpli®ed model or equivalent abutment foundation spring.

In arriving at the ®nal simple model, it is assumed that the

abutment deforms as a rigid body and translational stiffness

of the system at the location of impact between the abutment

and the bridge deck is determined. It should be noted that

the experimental investigation [11] has shown that the abut-

ment movement is indeed a rigid body movement.

As shown in Fig. 2b, the rotational and translational stiff-

ness springs from various footings and back wall are moved

to the center of stiffness located at a height x above the base

of the footing. The resultant translational stiffness is simply

equal to the algebraic sum of all translational stiffnesses,

that is:

KT � Kf1 1 Kf2 1 Kw

M.A. Saadeghvaziri et al. / Soil Dynamics and Earthquake Engineering 20 (2000) 231±242232

M.A. Saadeghvaziri et al. / Soil Dynamics and Earthquake Engineering 20 (2000) 231±242 233

Fig

.1.

Pla

nan

dlo

ngit

udin

alel

evat

ion

of

typic

alM

SS

Sbri

dge

(Bri

dge

#1).

where Kf1 is the stiffness for the back wall footing, Kf2 is the

stiffness for wing wall footings (sum of the two), and Kw is

the stiffness of the back wall. The resultant rotational

stiffness is equal to:

KR � Krw 1 Kr1 1 Kr2 1 Kw�0:37Hw 1 tf 2 x�2

1 �Kf1 1 Kf2�x2

where Krw is rotational stiffness for the back wall, Kr1

rotational stiffness for the back wall footing, Kr2 rotational

stiffness for the wing wall footings (sum of the two), Hw is the

height of the back wall, and tf is the depth of the footing, and

x � �Kw=KT��0:37Hw 1 tf�Continuing on the assumption of rigid body movement of

the abutment, the model of Fig. 2b is simpli®ed further into

an equivalent translational stiffness, Kh, equal to:

Kh � �KRKT�=�KTh2 1 KR�As an example, using the above procedure, the equivalent

translational stiffnesses at the abutments of Bridge #1 (one

of the three cases studied) are 47.6 and 49.0G kN/m. G, the

shear modulus of soil, is in kN/m2. For a typical value of

G� 27.6 MPa the abutment longitudinal stiffness is

1330 MN/m. For the same bridge, CALTRANS' simpli®ed

procedure, which in this case only depends on the width of

the bridge, will result in a value of 3009 MN/m. The more

than a factor of two difference is consistent with the results

reported by Goel and Chopra [6].

Similarly, the mobilized abutment mass is lumped at the

point of impact between the deck and abutment, forming a

simple spring±mass system as shown in Fig. 2c. Note that

the point of impact is assumed to be at the centroid of the

deck. As it will be discussed later, the deck is modeled using

line (beam) elements.

For the columns, the translational and rotational stiff-

nesses in the longitudinal direction are placed at the base.

Unlike abutment springs, these springs are assumed to

remain elastic.

2.3. Abutment strength

A nonlinear load±deformation characteristic is employed

for the translational spring that models abutment in the long-

itudinal direction. The nonlinearity includes yielding of the

spring as well as unequal strength under compressive and

tensile loads on the soil.

Under compressive load the established Mononobe±

Okabe (M±O), pseudostatic approach for passive force is

employed to determine the yield strength in compression,

Cy, [9]. Typical values for the bridges analyzed are given in

Section 2.4. Tensile yield strength at the abutment, Ty, is

assumed to be equal to frictional sliding capacity. That is:

Ty � N tan d

where d is the angle of friction between abutment footing

and foundation soil. It is assumed to be equal to f /2, where

f is soil angle of friction. N is the total normal force at the

interface, which is equal to the dead load of the superstruc-

ture and the entire abutment system (wing walls, back wall,

footings) including ®ll soil over footings.

2.4. Damaged back wall

The actual geometry of seat-type abutment consists of

two segments. One portion, which is narrower, is the back

of the seat, which is slightly longer than the depth of the

superstructure and is referred to as the back wall. The

second segment, which extends from the seat to the top of

the footing, is called the breast wall. It is quite possible for

impact forces in the longitudinal direction to cause shear

failure of the abutment at the juncture of these two

segments, normally called back wall failure. It is even

recommended in seismic design to use such a mode of fail-

ure as a fuse since it is much easier to ®x the upper portion

of the abutment rather than lower portion. As a parametric

M.A. Saadeghvaziri et al. / Soil Dynamics and Earthquake Engineering 20 (2000) 231±242234

Fig. 2. Abutment foundation springs: (a) springs for various components; (b) equivalent springs at the center of stiffness; (c) simpli®ed model.

study in this investigation special attention is devoted to

such highly possible mode of failure. For this purpose, the

stiffness of the abutment in the longitudinal direction is

determined based on mobilizing only the soil height equal

to the depth of the superstructure. Two different load trans-

fer mechanisms control the capacity of the section at the

juncture of the back wall and breast wall, namely: (i) shear

resistance provided by the concrete; (ii) shear friction,

which is a post-failure behavior and follows the ®rst

mechanism. The strength of the latter mode is actually

larger and will be used. In accordance with AASHTO

LRFD [12] the following equation can be used to determine

the nominal shear capacity, Vn:

Vn � mAvfFy

where m is the friction coef®cient between two sliding

surfaces and here is assumed to be equal to one for concrete

placed against hardened concrete, Avf is the sum of areas of

vertical rebars at the juncture, and Fy is yield strength of the

rebars.

If time history analysis indicates that this shear capacity is

exceeded, the model is modi®ed such that the back wall

stiffness and compressive strength are determined using

only the height of the back wall (i.e. total abutment height

less the breast wall height). The strength of the abutment in

tension is also reduced since only the weight of the back

wall is used in calculating the frictional resistance when the

abutment is under tensile load.

2.5. Other modeling considerations

Similar to abutments and foundations, other components

of the bridge system and parameters of response were

modeled and/or analyzed employing FHWA's Seismic

Retro®t Manual [3] and/or established principles. It is not

within the scope of this paper to present details of modeling

for these components and the reader is referred to reference

[10]. However, a brief description of the procedures

employed is presented in this section.

Columns: All three bridges analyzed under this study

have round columns. Con®nement effect is considered in

evaluation of column curvature ductility and plastic rotation

capacity per FHWA's guidelines. The effects of column

curvature ductility and lateral reinforcement on shear capa-

city are also considered. The exact moment±curvature

relationship and moment±axial load interaction for column

cross-sections are determined. This is achieved by dividing

the cross-section into a number of ®bers and satisfying

compatibility and equilibrium using commonly used

stress±strain relationships for concrete and steel materials.

The moment±curvature, axial load±moment interaction,

and shear capacity for a typical column are shown in

Fig. 3. The column is then modeled using elasto-plastic

beam elements with an initial stiffness based on the effective

moment of inertia determined using FHWA's guidelines.

The plastic moment capacity is determined by ®tting the

bilinear model to the actual moment±curvature relationship.

The actual moment±curvature relationship along with the

equations given by FHWA for plastic hinge rotation and

plastic hinge length are used to determine the plastic

hinge capacity.

Bearings: Steel bearings are used to transfer the vertical

and horizontal forces from the superstructure to the

substructure. Typically four 22-mm diameter A325 steel

bolts are used to connect the bearing to the girder, and

two 64-mm diameter A615 steel anchor bolts are used to

connect the bearings to the abutments and cap beams. These

elements are the weak links in the load transfer from the

superstructure to the substructure through the bearings, and

impact forces can easily exceed the shear capacity of these

bolts. Therefore, post-failure behavior of the bearings

(Coulomb friction) is also investigated. It is modeled

using a bilinear force±deformation relationship with yield

strength equal to coef®cient of friction times the normal

gravity force per bearing. The coef®cient of friction is

taken to be in the range of 0.2±0.6 as a parameter.

Damping: Rayleigh's damping proportional to both stiff-

ness and mass matrices is assumed. The coef®cients of

proportionality are determined such that the damping matrix

will correspond to 5% damping in the ®rst and second

modes. This is consistent with AASHTO's response spectra

and is a commonly used value in time history analysis of

structural systems. This level of damping can be looked

upon as radiation damping at the foundations, because,

there is no other source of viscous damping in the long-

itudinal direction due to high rigidity of the deck in the

axial direction. Note that, as mentioned before, energy dissi-

pation through nonlinear phenomena such as plasticity in the

columns and friction at the bearings are modeled explicitly.

Input motions: Three different ground acceleration

records are used as input motion. These are the El Centro

S00E record from the Imperial Valley Earthquake of May

18, 1940, in California; the Cholame±Shandon Array No. 2

N65E record from the Park®eld Earthquake of June 27,

1966 in California; and the Nahanni record from the

Saguany Earthquake of December 23, 1985 in eastern

Canada. Nahanni record is assumed to be a good represen-

tative of intraplate earthquakes in eastern North America.

Two peak ground accelerations (PGA) of 0.18 and 0.4 g are

considered. The former is the maximum ground acceleration

in New Jersey as per AASHTO and the latter is for regions

of higher seismicity such as California.

3. Computer model

The bridges are analyzed using DRAIN-2DX [13] where

beam±column elements are used to model the columns and

simple connection elements are employed in modeling of

bearings and soil springs. Link elements are used to model

the gap and impact between adjacent spans and between an

end-span and the abutment.

M.A. Saadeghvaziri et al. / Soil Dynamics and Earthquake Engineering 20 (2000) 231±242 235

Three bridges were analyzed. Several parameters were

investigated for each bridge. This included type of soil,

back wall condition (intact and broken), and bearing perfor-

mance (intact and failed with two different coef®cients of

friction, 0.2 and 0.6). Variation in type of soil was achieved

through changing the shear modulus, and values assumed

were 2.7, 27, and 270 MPa. Furthermore, special cases of

no impact at the abutment and/or column piers, pinned

M.A. Saadeghvaziri et al. / Soil Dynamics and Earthquake Engineering 20 (2000) 231±242236

Fig. 3. Capacity of typical column.

abutment and ®xed columns, and high-mobilized mass at

the abutments were also investigated. As discussed before,

three ground motion records and two PGAs were consid-

ered. This will result in a large number of cases to simulate

with large volume of data per simulation to process. There-

fore, to be more effective, cases not deemed important were

not considered. For example, since every response parameter

for Park®eld record with 0.18 g PGA was consistently higher

than the other two records, those two records were not

considered for all cases with PGA of 0.4 g. The total number

of simulations was therefore reduced to about 200 cases.

The analytical model for Bridge #1, which is a three span

bridge, is shown in Fig. 4. Due to symmetry only half of the

width in the transverse direction is considered. Based on the

procedures discussed in the previous sections the values for

different parameters are as follows. The translational stiff-

ness, Kh, is equal to 23.8 and 24.5 G kN/m at the left and

right abutments, respectively. Translational stiffnesses at the

left and right piers are 25.7 and 27.8 G kN/m, respectively.

The rotational stiffnesses are equal to 28.2 and

47.2 G kN m/rad at the left and right piers, respectively.

The yield strengths are in the range of 4.5±20 MN depend-

ing on soil-type, abutment dimensions, and PGAs [9]. Abut-

ment tensile strength, which is taken to be equal to friction

at the foundation and again depends on soil-type, is in the

range of 3034±6430 kN. In the case of damaged (broken)

back wall for both abutments the compressive strength is

equal to 0.9±2 MN and tensile strength is marginal at

384 kN. The translational stiffness for this case is equal to

15.6 G kN/m. Note that for the two cases of intact abutment

and damaged abutment the reduction in stiffness is not as

much as the reduction in strength. This is due to the fact that

for intact abutment the rigid body movement of the entire

abutment reduces the stiffness at the location of impact

while for the case of damaged abutment the soil resistance

is provided more or less at the point of impact. The columns

are 1.2 m in diameter and the effective moment of inertia

determined based on FHWA's guidelines is 0.0412 m4,

which is 38% of gross moment of inertia. The nominal

moment capacity of the columns under gravity load of

2969 kN is 3516 kN m and their shear capacity ranges

from 1400 to as low as 591 kN depending on ductility

demand. Due to the difference in column heights at the

two interior bents, the plastic rotation capacity and plastic

hinging shear force are different. They are equal to 0.015 rad

and 511 kN for the left column, and 0.0173 and 413 kN for

the right column. Fig. 4 shows the gravity load acting on

each bearing that is used in determining the frictional resis-

tance at these locations. The available edge distance is 200 and

250 mm at the abutments and column bents, respectively.

4. Pushover analysis

Before discussing the results of the time history analyses,

it is instructive to compare the relationship between the

M.A. Saadeghvaziri et al. / Soil Dynamics and Earthquake Engineering 20 (2000) 231±242 237

Fig. 4. Analytical model for Bridge #1.

pseudostatic response and demand based on design guide-

lines. A graphically useful method for such comparison is to

plot the pushover load±deformation behavior of the bridge

along with AASHTO's response spectrum. This is shown in

Fig. 5. AASHTO's response spectra for 0.18 and 0.4 g are

plotted in an alternative manner. It is assumed that stiffness

is equal to load divided by displacement and then, using the

weight of the bridge, the response spectrum is transferred

from acceleration vs. period space to load vs. displacement.

Thus, on this diagram lines radiating from the origin will

show systems with different periods (e.g. x-axis is a system

with in®nite period and y-axis a system with zero

period). The load±deformation for the bridge is obtained

by applying an increasing force at the level of the deck in

the longitudinal direction. The load±deformation relation-

ship, in general, is highly nonlinear and originally of

stiffening nature as the gaps close and other elements of

the bridge system get involved. As seen from these curves,

the stiffness and strength of the foundations signi®cantly

in¯uence the load±deformation behavior of the system.

Comparison of the load±deformation curves indicates that

abutment strength would have more effect on the seismic

response of the bridge system than abutment stiffness.

Shown in this ®gure is also the bridge response using

CALTRANS approximate approach, where the maximum

strength is based on the maximum soil-strength of 368.7 kPa

and stiffness is equal to 114.8 MN/m per unit width of the

deck in meter.

Based on CALTRANS approach the displacement of

the bridge in the longitudinal direction is limited due to

high stiffness and strength at the abutment. Actually,

using this method there is not much difference in long-

itudinal deck displacement between the two seismic

coef®cients (0.18 and 0.4). Depending upon SSI at the

base of piers there is no or only a slight level of yield-

ing in the columns. Note that pushover analysis is direc-

tion dependent if the gap sizes are not identical at the

abutments and at the top of the piers. The maximum

displacement is limited by the sum of the gap openings

at the left pier and the left abutment plus deformation in

the left abutment. In this example the maximum displa-

cement is 120 mm plus the slight elastic deformation in

the abutment. The abutment deformation is small due to

high stiffness and this is the reason for the small differ-

ence between seismic coef®cient of 0.18 and 0.4. As

seen from Fig. 6, at this level of deformation (i.e.

about 130 mm) the plastic rotation in the columns of

pier #2 (right pier) is well below the plastic rotation

capacity.

Comparison of the design spectra to the load±defor-

mation curves for the bridge where the SSI is consid-

ered, as shown in Fig. 5, indicate that the bridge

response will involve signi®cant nonlinearity at the

abutments. Depending on SSI, the ductility demand

would be different for different PGAs. Furthermore,

there would be a signi®cant difference between the

effect of the two levels of ground motion. Similarly,

bridges that may have failure in their abutment back

wall will need a much larger hysteretic energy capacity

and ductility demand at various components. Since the

design spectra are for a linear system with 5% damping,

the actual displacement demand can not be determined using

the curves of Fig. 5. This will require time history analysis,

which is described in Section 5.

M.A. Saadeghvaziri et al. / Soil Dynamics and Earthquake Engineering 20 (2000) 231±242238

Fig. 5. Pushover vs. response spectrum for Bridge #1.

5. Results of time history analyses

Many cases for the three different bridges were analyzed,

as mentioned earlier, however, for the sake of simplicity the

presentation will focus only on the response of Bridge #1.

Among the three earthquake records used, almost always

the Nahanni record caused the lowest response in all three

bridges regardless of PGA and SSI. Although, similar

conclusion can not be made about the other two records

(both from California earthquakes) responses were higher

more often for the Park®eld record.

For an input motion with PGA of 0.18 g the overall seis-

mic response in the longitudinal direction is marginal with

the lowest capacity±demand ratio (aside from bearing

performance) of 1.04 for the seat length for Bridge #1.

Impact forces between two adjacent spans or between an

end-span and the abutment are large enough to cause

damage to the bridge in the form of bearing failure. The

level of impact force depends on the soil-type and abutment

condition (intact vs. damaged back wall). When the abut-

ment is assumed intact the impact forces are increasing as

the soil-stiffness decreases. For the case of damaged back

wall the trend is reversed. For the same soil-type there is less

impact force in a damaged back wall case compared to an

undamaged (or intact) abutment. These variations are

related to the ratio of the abutment stiffness to its mobilized

mass. Depending on this ratio, the amplitude of the abut-

ment response will change, resulting in different interaction

with the bridge deck and indicating the importance of

modeling SSI. Upon failure of the bearings the coef®cient

of friction has also an effect on the response. It is dif®cult to

quantify its effect, however, results show lower number of

yield cycles in the columns for lower coef®cient of friction.

This is probably due to the fact that under lower coef®cient

of friction there is more energy dissipation through friction.

The higher the input ground motion the more signi®cant is

the effect of SSI on the response of the bridge.

Fig. 7 shows various response time histories under the

Park®eld record with 0.4 g peak ground acceleration. The

time histories represent deck sliding at the right abutment of

Bridge #1 for various SSI models. Note that the shear modu-

lus, G, of 27 MPa is assumed to be, in an average sense,

representative of typical ®ll and embankment soils used for

bridges in New Jersey. Furthermore, the case of 2.7 MPa

shear modulus is taken as the extreme lower end of the

spectrum, and may not represent actual cases. The compres-

sive strength of abutments with this very soft soil is assumed

to be equal to that for G � 27 MPa; corresponding to a

frictional angle of 208. However, the stiffnesses are differ-

ent. This will enable comparison of results with respect to

both strength and stiffness.

As it can be seen from Fig. 7, for the case of damaged

back wall the deck displacement can exceed the seat length

and cause fall off of the bridge deck. The maximum hori-

zontal deck displacements for different SSI models are

given in Table 1. Lower strength for the case of damaged

back wall, as it will be discussed later, is the main cause of

higher deck displacements for all three soil-types. However,

comparison of two cases of G � 2:7 and 27 MPa indicates

that abutment stiffness also has an important effect on the

seismic response (e.g. 185 vs. 246 mm, which is 33 percent

increase). Bridge displacement in the longitudinal direction

is limited by abutment deformation and stiffer soils tend to

act more like ®xed abutments.

M.A. Saadeghvaziri et al. / Soil Dynamics and Earthquake Engineering 20 (2000) 231±242 239

Fig. 6. Plastic rotation vs. right deck displacement.

The only difference between two cases of undamaged

back wall and reduced compressive strength is in their

strength. For the latter case the strength is reduced to that

of a damaged abutment with G � 27 MPa: Comparison of

these two curves indicates that abutment strength has a more

pronounced effect on the response. Mobilized mass of the

abutment and back®ll is another SSI parameter that has an

effect on the response. Higher mass will increase level of

impact forces at the abutments. Time histories of plastic

rotation at the base of the columns in both Piers 1 and 2

are shown in Fig. 8. Again SSI plays a signi®cant role on the

ductility demand at the base of the columns. However, there

is not a uniform trend with respect to soil-type. Note that

consideration of soil-type and its interaction with the bridge

includes boundary springs and masses at the base of piers,

too. In general, bridges supported on softer soil will have

larger displacements, mostly due to deformation of the abut-

ment. On the other hand, for the same bridge deck displace-

ment, ¯exibility at the base of the columns for softer soils

demands lower plastic rotation. But, as the results show, the

plastic rotation demand at the base of the columns may be

even less for stiffer soils. This is due to displacement-limit-

ing effect of abutment for stiffer soils because of its

higher strength and stiffness. These contradicting effects

of substructures on bridge response cause the highest plastic

rotation demands in the columns on moderately stiff soils

and not on the stiffest soil as shown in Table 2. This, once

again, demonstrates the need for explicit consideration of

SSI. It should be mentioned that for lower PGAs where

abutments are not signi®cantly involved, the plastic rotation

is higher for stiffer soils, as expected.

6. Conclusions

Based on a comprehensive study of three actual MSSS

bridges, the following conclusions can be made with regard

to seismic response in the longitudinal direction:

² Seismic response of this type of bridges is complicated

by the impact between adjacent spans. Generally, impact

reduces displacements, however, it signi®cantly

increases the level of forces in the bearings such that

their failure is quite possible even under a low level of

peak ground acceleration.

² SSI has a detrimental effect on seismic response in the

longitudinal direction, and such affect is more important

at the abutment than at the column piers.

² Abutment strength has more effect on longitudinal seis-

mic response (seat length demand) than abutment stiff-

ness and mass.

² Plastic rotation demand is also affected by SSI and

such demand is higher for medium than soft or stiff

soils.

² Dynamic analysis of this class of bridge system

should explicitly consider the SSI.

M.A. Saadeghvaziri et al. / Soil Dynamics and Earthquake Engineering 20 (2000) 231±242240

Fig. 7. Time histories of deck sliding for various SSI models at the right abutment.

Table 1

The maximum horizontal right deck displacements (mm) for different SSI

models

G-soil� 0.4 ksi G-soil� 4 ksi G-soil� 40 ksi

Undamaged back wall 247 185 170

Failed back wall 343 274 239

Finally, as we go towards performance-based seismic

design of structural systems including bridges, it is

important to develop realistic response spectra that

re¯ect the actual level of equivalent damping. To this

end, in order to be able to quantify the effect of SSI in

a ªdesignº format, consideration should be given to

detailed study of nonlinear systems with stiffening

load±deformation characteristics.

Acknowledgements

This research study is supported by the New Jersey

Department of Transportation/FHWA and the National

Center for Transportation and Industrial Productivity at

NJIT. The results and conclusions are those of the authors

and do not necessarily re¯ect the views of the sponsors.

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