seismic behavior analysis of a plate-girder bridge ...c).pdf · due to friction. in this study, a...

Steel Structures 8 (2008) 285-294 www.ijoss.org

Seismic Behavior Analysis of a Plate-Girder Bridge

Considering Abutment-Soil Interaction

Jeong-Hun Won1, Jia Xu Wu1, Ariunzul Davaadorj1, Sang-Hyo Kim1, and Ho-Seong Mha2*

1School of Civil & Environmental Engineering, Yonsei University, 134 Sinchon-dong, Seodaemun-gu, Seoul, 120-749, Korea2Department of Civil Engineering, Hoseo University, 165 Sechul-ri, Baebang, Asan, Chungnam, 336-795, Korea

Abstract

Longitudinal dynamic behaviors of a multi-span plate-girder bridge under seismic excitations are examined to see the effectof the abutment-soil interaction. The stiffness degradation due to the abutment-soil interaction is considered in the systemmodel, which may play the major role upon the global dynamic characteristics of the whole bridge system. An idealizedmechanical model is proposed, which is capable of considering pounding phenomena, friction at the movable supports, and thecorresponding simulation method is developed. The abutment-soil interaction is modeled as the one degree-of-freedom systemwith nonlinear spring and damper. Using the idealized mechanical model for the bridge system, the longitudinal responses ofstiffness degradation model are compared with those based on the linear system, which excludes the stiffness degradation.Results show that the stiffness degradation of the abutment-backfill system takes an important influence upon the global bridgemotions and the seismic responses may be underestimated in the system only with the constant stiffness considered. Hence,it is concluded that the stiffness degradation should be taken into account in the seismic analysis of the bridge system.

Keywords: Dynamic behavior, Seismic excitation, Stiffness degradation, Abutment-soil interaction, Nonlinear spring

1. Introduction

Recently, there are more earthquakes with bigger

magnitudes occurring world widely, and the report of the

corresponding damages are telling us that the earthquake

is truly shaking our lives as it is still remaining the one of

the biggest threats to human society. For those reasons,

earthquake related disasters have been asking us for the

better seismic concepts to prevent the worst scenario of

the damages. Correct predictions of the dynamic behaviors

of the structures under seismic excitations are more

desired for the better design of the systems.

Bridge systems consisting of several simple spans can

be described as the combination of multiple vibration

units, and the dynamic characteristics of the most units

are similar. However, the global dynamic behaviors of

such a bridge system become complicated to be predicted

due to many factors, which can be abutment-soil interactions,

poundings between girders, frictions at movable supports,

inelastic behaviors of RC piers, foundation motions

(rotation and translation), and so forth. It should be

noticed that the interactions between the adjacent

oscillating units have drawn the interest, since it may play

the major role of the span collapses. In order to prevent

span collapse, it is need to install special device such as

cable restrainers and energy dissipation system (Cho et

al., 2008; Won et al., 2008). Among the interactions

between vibrating units, the abutment-soil interaction

may be the most important component affecting the

global motions of the bridge particularly for bridge

systems with similar vibrating units (Shamsabadi et al,

2007).

It is highly challenging to verify the effect of the

abutment-soil interaction because of the uncertainties

included to the abutment-backfill system in addition to

the soil. The abutment-backfill system is often ignored or

at most modeled as either a linear spring system.

However, the abutment-soil interaction should be considered

in the analysis of bridge motions. An appropriate nonlinear

model corresponding to the abutment-soil interactions

should be adopted for the proper simulations.

A simple and economical way to represent the

abutment-backfill system in seismic behavior analysis is

to use a translational nonlinear spring. Siddharthan et al.

(1997) suggested the nonlinear spring which has

degradation of stiffness with the increment of abutment

movements. In this model, many important factors such

as nonlinear soil behavior, abutment dimensions,

superstructure loads, difference in soil conditions, and so

forth, are considered to determine the nonlinear spring

stiffness. Saadeghvaziri and Yazdani-Motlagh (2008)

Note.-Discussion open until May 1, 2009. This manuscript for thispaper was submitted for review and possible publication on Septem-ber 16, 2008; approved on November 27, 2008

*Corresponding authorTel: +82-41-540-5792; Fax: +82-41-540-5798E-mail: [email protected]

286 Jeong-Hun Won et al.

used the bilinear spring to consider effects of the

abutment on the global bridge response.

In this study, the idealized mechanical model for the

multi-simple span bridge system is proposed, which can

consider the abutment-soil interactions as well as the

pounding and friction and other factors. The abutment-

backfill system is modeled as a one-degree-of-freedom

system with a nonlinear spring and a nonlinear damper to

consider the stiffness degradation.

2. Modeling of Systems

2.1. Bridge model

The bridge considered is a three-span simple plate

girder bridge with 35 m span length as shown in Fig. 1.

Bent type piers, shallow foundations, and seat-type

abutments are used. The pier height is 12 m and the

diameter of a column is 1.7 m. The longitudinal and

transverse widths of pier foundations are 6 m and 14 m.

The height of foundations is 2 m. The abutment height is

6.5 m. The longitudinal and transverse widths of abutments

are 4.6 m and 17 m.

In this study, only the longitudinal motions are of

concern, so the total system can be divided into four

individual vibrating units shown as in the Fig. 1 (a); A1

unit, P1 unit, P2 unit, and A2 unit.

For better efficiency, a simplified mechanical model is

proposed using the lumped mass system, which is

depicted in Fig. 2. In the figure, m1, m5, m9 are the masses

of superstructures, m2, m6 are the masses of piers, m3, m7

are the masses of foundations, m4, m8 are the rotational

mass moments of inertia of foundations, and mA1, mA2 are

masses of abutments. K2, K6 and C2, C6 are the stiffness

and damping constants of the piers, K3, K7 and C3, C7 are

the translational stiffness and damping constants of the

foundations, and K4, K8 and C4, C8 are the rotational

stiffness and damping constants of the foundations,

respectively. KA1, KA2 and CA1, CA2 are the stiffness and

damping constants of the abutments. KA1,1, K2,5 and K6,9

are the stiffness of the fixed supports at individual

vibration units. F1,2, F5,6, and F9,A are the friction forces at

the movable supports. S1,5, S5,9, S9,A2 and C1,5, C5,9, C9,A2

are the stiffness and damping constants of the impact

elements, and L is height of pier. d1,5, d5,9, d9,A2 are the gap

distances between adjacent vibration units, and ug is the

ground displacement.

2.2. Abutment-backfill model

A simplest approach to represent the nonlinear

behavior of the abutment due to abutment-soil interaction

is to use translational nonlinear spring. The computational

procedure of this methodology is relatively simple while

the output shows great coincidence with the realistic

behavior of the abutment, as been verified through a field

test (Siddharthan et al., 1997; Goel & Chopra, 1997).

The abutment-backfill system is modeled in this study

as one-degree-of-freedom system with nonlinear spring

and nonlinear damper to consider the abutment stiffness

degradation as shown in Fig. 3. Since the abutment is

synchronized with the backfill (Siddharthan et al., 1994),

the mass of the abutment-backfill system is assumed to be

the summation of the mass of the abutment and the

backfill. In the Figure, mA is the mass of the abutment-

backfill system, ug(A) is the ground displacement, uA is the

displacement of mass mA, and KA(uA) and CA(uA) are the

translational nonlinear stiffness and damping coefficients

Figure 1. Sample bridge.

Seismic Behavior Analysis of a Plate-Girder Bridge Considering Abutment-Soil Interaction 287

of the soil surrounding the abutment, respectively.

Since the abutment undergoes rigid body movement

(Al-Homoud and Whitmann, 1999; Maroney, 1994), the

abutment displacement at any point is evaluated in terms

of δL and θ as shown in Fig. 3. The nonlinear spring

stiffness is obtained from estimation of the force, PL, for

a given displacement, δL, such that force equilibrium

equation is satisfied.

2.3. Poundings between girders

Two adjacent vibration units may produce poundings

upon the applied seismic excitations with various intensities,

and these poundings are governed by the relative

displacements between the oscillating systems. The

pounding is described in this study by placing spring-

damper elements (impact elements) between the masses

as shown in Fig. 4. The pounding condition and force are

defined as follows.

(1)

(2)

where ui, ui+4 are the displacement of mass mi and mi+4,

ugi, ug(i+1) are the ground displacement, and di,i+4 is the gap

distance between mi and mi+4. In addition, Si,i+4 and Ci,i+4

are denote the spring stiffness and damping constant of

impact element, respectively.

The stiffness of spring, which is typically large and

highly uncertain, and the damping constant, which determines

the amount of energy dissipated, can be obtained by

references (Anagnostopoulos, 1988; Kim et al., 1999).

2.4. Friction of movable supports

The frictions between the superstructures and the

δi ui ui 4+– ugi ug i 1+( )– di i 4+,–+ 0≥=

Fi i 4+, Si i 4+, δi Ci i 4+, δi'+= for δi 0>

Fi i 4+, 0= for δi 0>

Figure 2. Simplified mechanical model of the bridge.

Figure 3. Abutment-backfill model.

Figure 4. Idealization of pounding.


movable supports are usually neglected in the bridge

dynamic analysis. However, this may not yield the

appropriate results since it ignores the energy dissipation

due to friction. In this study, a modified bilinear coulomb

friction model is utilized (Kim et al., 2000). The

relationship between the friction force and relative

velocity between the adjacent oscillators can be depicted

as shown in Fig. 5. In stick condition, the friction force

increases up to a given value, ε of the relative velocity

and then sustains a constant friction force multiplying

vertical force with friction coefficient (µ). The friction

forces, Fi,i+1 of the stick and sliding conditions are

expressed as follows.

(3)

where ∆i is the relative distance between vibration units

which are connected by movable supports.

2.5. Pier and foundation motions

The nonlinear pier motion is simulated by adopting the

hysteresis loop function (Kim et al., 2000). The foundation

motions are modeled as a two DOF system with

translational and rotational springs and dampers. The

values of springs are determined by the guideline of

FHWA (1986).

3. Longitudinal Abutment Stiffness Evaluation

The longitudinal abutment stiffness varies with types

and conditions of soil surrounding the abutment. The

rational evaluation of longitudinal stiffness degradation

due to abutment-soil interaction is required. This study

evaluates the nonlinear stiffness of abutment following

the procedure suggested by Siddharthan (1997).

For the considered abutment with 6.5 m height, the

longitudinal stiffness (passive state) of abutments can be

obtained as

(4)

(5)

where SL is the secant stiffness (kN ⋅ m−1 ⋅ m−1) per width

of an abutment wall, DL is the dimensionless stiffness

coefficient, xL is the abutment displacement (mm), H is

the abutment height (m), γ is the unit weight of soil (kN/

m3), and B is the abutment width in longitudinal direction

(m).

Considering the surrounding soil condition and the

dimension of abutments (γ=20 kN/m3, H=6.5 m, B=3 m,

and DL=7000), the nonlinear stiffness curve is plotted in

Fig. 6 (Nonlinear model in the figure), where the width of

the abutment in transverse direction (17 m) is included. It

is assumed that the stiffness is constant to the movement

of 1 mm. Then, the longitudinal abutment stiffness

decreases rapidly as the displacement increases when the

displacement is small.

In order to investigate the effects of stiffness degradation

on the global bridge motion, the linear stiffness of the

abutment is also considered. First, the linear model with

the initial constant stiffness of nonlinear model, which is

the stiffness at 1 mm movement of the abutment, is

considered as a linear model (Linear model-Case 1 in Fig.

6).

In addition, the linear model with the initial stiffness

suggested by Caltrans (2001) is considered (Linear

model-Case2 in the Fig. 6) since this method can easily

simulate the longitudinal abutment response. The

constant stiffness is

(6)

(7)

where w is the abutment width in transverse direction and

H/1.7 is the height proportionality factor.

Considering the abutment width in transverse direction

(17 m) and the abutment height (6.5 m), the constant

stiffness of linear model-Case2 is evaluated as 747,500

Fi i 1+,

1

2---µm

ig1

ε---∆

i= for ∆

iε<

Fi i 1+,

1

2---= µm

ig for ∆

iε≥

SL

DLE

L

xL

H-----⎝ ⎠⎛ ⎞

0.96–

=

EL

γB3

H2

--------=

Kabut

SL

Kiw

H

1.7-------⎝ ⎠⎛ ⎞

= =

Ki

11.5 103kN m⁄m

-------------×=

Figure 5. Friction force-relative displacement relationship.

Figure 6. Applied abutment stiffness (passive stiffness).


kN/m. This value is same to the stiffness of nonlinear

model at the abutment movement of 13.6 mm.

It should be noted that the stiffness in Fig. 6 are passive

stiffness. Since the active condition in a soil deposit can

be mobilized with a much lower abutment movement

than the passive condition (Clough and Duncan, 1991;

Barker et al., 1991), the active stiffness of the abutment

is assumed to be ten times smaller than the passive

stiffness. It is also assumed that once the degradation is

started, the degraded stiffness cannot be recovered and

that the stiffness after the critical displacement is reached

remains constant afterwards regardless of the displacement.

4. Results and Observation

Dynamic responses of the bridge under earthquakes

with various magnitudes of peak ground accelerations are

evaluated to see the effects of the longitudinal stiffness

degradation due to abutment-soil interaction. Three types

of analysis models according to the abutment models are

selected to examine the dynamic responses of the bridge

under earthquakes to see the effect of the stiffness

degradation due to the abutment-soil interaction. Two

linear models are employed, which consist of the constant

abutment stiffness (linear systems) and one model consist

of the nonlinear stiffness considering the abutment

stiffness degradation (nonlinear system). The simulated

bridge models are described in Table 1.

For the input ground motions, artificial seismic excitations

are generated by using the well-known SIMQKE code

(Gasparini, 1976), which is compatible to the design

response spectra specified in the Korean code (MOCT,

2005). An example of the simulated seismic excitation is

shown in Fig. 7.

Since seismic excitations can be indicative by stochastic

processes, the responses of a bridge system exhibit

probabilistic characteristics. Therefore, in this research to

evaluate the fluctuation of response by artificial seismic

excitations, the probabilistic characteristics of maximum

responses are estimated by the mean value and Gumbel

Type-I probability distribution (for each acceleration, the

number of samples is 10).

The equations of motions corresponding to the simplified

mechanical model are derived using the Lagrange equation.

The dynamic responses of a bridge system are then

simulated by adopting the direct integral method (4th

order Runge-Kutta method). The time step size is 2×10−5.

The exact time of pounding is obtained by the Newton

method. The 5 cm-gap distance between adjacent vibration

units is selected, and the friction coefficient for movable

support is assumed to be 0.05.

4.1. Displacements of each vibration unit

Relative displacements of each vibration unit to the

ground motion are evaluated in order to see the effects of

the stiffness degradation. For the seismic excitations with

various magnitudes of peak ground acceleration (PGA)

from 0.1 g to 0.6 g, the maximum displacements are

investigated. Table 2 shows the mean values and 90%

extreme values of Gumbel type-I for maximum displacements.

Fig. 8 represents the comparison results of the extreme

values according to the abutment models.

First, the relative displacements of A2 unit, which is

consisting of the abutment only, are observed. Under

earthquakes with PGA less than 0.3 g, the displacement is

quiet small. Consequently, the results from the linear

model (linear case 1: L-C1) and the nonlinear model are

showing the similar trends, while the other linear model

with smaller stiffness (linear case 2: L-C2) showing the

biggest responses. In the case with the PGA above 0.3 g,

the nonlinear model begins to show the bigger responses

than the other linear models, since the relative displacements

become large enough for the stiffness to dramatically

degrade.

The effect of the stiffness degradation can be seen more

clearly in the results from the A1 abutment unit, which

consists not only of the abutment itself, but also of the

superstructure. The difference between the results from

Table 1. Considered abutment models

Abutment model Description

Nonlinear model- Nonlinear spring according to the Eq. (4)- Nonlinear damper (damping ratio of 5%)

Linear model-Case 1- Linear spring with the stiffness at 1 mm movement of the nonlinear model - Linear damper (damping ratio of 5%)

Linear model-Case 2- Linear spring with the stiffness according to the Caltrans- Linear damper (damping ratio of 5%)

Figure 7. Example of simulated seismic excitation.


linear and nonlinear system becomes larger.

Secondly, the relative displacements of P1 and P2 units,

which consist of piers and superstructures, are observed.

Under weak earthquakes (PGA<0.3 g), the similar results

are obtained regardless of the types of the abutment

models, since the displacements are quite small, and the

effect of the interactions between the adjacent vibration

units is not big enough to initiate the stiffness degradation.

Under stronger earthquakes (PGA>0.3 g), the pier units

starts to show the influence from the abutment units, and

the largest displacement naturally occur from the

nonlinear system due to the stiffness degradation.

From results, it can be said that the effects of stiffness

degradation upon the displacements relative to the ground

are relatively larger under moderate and strong excitations

with PGA>0.3 g. It should be noticed that the results

using the stiffness obtained by the method suggested by

Caltrans (linear case 2: L-C2) can give the similar results

under PGA below 0.3 g, but that under PGA over 0.3 g,

nonlinear model should be employed for the better

prediction of the bridge motions.

Typical time histories of these displacements are

depicted in Fig. 9-12 for both cases with linear and

nonlinear abutment models. At the level of the peak

ground acceleration (PGA) of 0.3 g, A1 unit shows the

increment of displacement in nonlinear model, while A2

units shows the bigger displacements in linear model-

case 2. In addition, P1 and P2 unit shows the similar time

histories in all considered abutment models. With regard

to the PGA of 0.6 g, the nonlinear model clearly shows

the increased time histories for all vibrating units.

Figure 8. Comparison of displacements for each vibration unit (Gumbel type-90%).

Table 2. Maximum displacements of each vibration unit (unit: cm)

PGAA1 vibration unit P1 vibration unit P2 vibration unit A2 vibration unit

L-C1c L-C2d N-Le L-C1 L-C2 N-L L-C1 L-C2 N-L L-C1 L-C2 N-L

0.1 gMeana 0.04 0.43 0.04 2.62 2.76 2.62 2.40 2.56 2.40 0.03 0.24 0.03

Gumbelb 0.05 0.50 0.05 3.00 3.22 3.00 2.78 2.96 2.79 0.05 0.27 0.05

0.2 gMean 0.18 0.94 0.55 6.45 6.67 6.68 6.17 6.32 6.20 0.13 0.54 0.17

Gumbel 0.26 1.10 0.90 7.88 7.75 8.01 7.02 7.00 6.99 0.26 0.75 0.40

0.3 gMean 0.38 1.51 2.70 8.82 9.88 9.65 8.15 8.72 8.69 0.25 1.00 0.67

Gumbel 0.53 1.75 4.00 10.57 12.30 12.23 9.99 10.33 10.89 0.35 1.36 1.03

0.4 gMean 0.58 2.22 6.13 10.42 11.54 11.80 9.02 9.62 10.13 0.35 1.33 2.38

Gumbel 0.72 2.77 8.61 13.47 13.34 14.38 10.82 11.57 12.21 0.46 1.77 3.13

0.5 gMean 0.82 3.00 9.99 12.79 13.87 14.25 10.31 10.74 12.30 0.46 1.68 4.67

Gumbel 1.09 3.86 12.80 16.72 17.34 19.28 12.90 13.42 15.56 0.69 2.22 6.44

0.6 gMean 0.98 3.82 12.10 14.54 15.75 16.07 10.95 11.70 13.43 0.59 2.10 6.94

Gumbel 1.36 5.06 15.35 19.24 21.18 20.54 14.33 14.09 16.56 0.87 2.85 8.79

a)Mean value of relative displacements of each vibration unitb)90% extreme value of Gumbel Type-Ic)Abutment model with linear spring and dashpot (case 1)d)Abutment model with linear spring and dashpot (case 2)e)Abutment model with nonlinear spring and dashpot


4.2. Relative distances between vibration units

The relative distance between the adjacent vibration

units are investigated in this section to see the effects of

the stiffness degradation more clearly under the seismic

excitations with various magnitudes of PGAs from 0.1 g

to 0.6 g. The mean values and 90% extreme values of

Figure 9. Time histories of displacement relative to ground (A1 unit).

Figure 10. Time histories of displacement relative to ground (A2 unit).

Figure 11. Time histories of displacement relative to ground (P1 unit).

Figure 12. Time histories of displacement relative to ground (P2 unit).


maximum relative distances are obtained. The results are

tabulated in Tables 3. The comparison of the maximum

relative distances is represented in Fig. 13 according to

the abutment model types.

The maximum relative distances are observed to occur

between the abutment and pier units. At the location

between A1 and P1 units, where the largest maximum

relative distances occur, the nonlinear case shows the

largest relative distances among three models due to the

stiffness degradation. As PGA increases, this trend

becomes clearer. The relative distances between P2 and

A2 units are similar to each other in the most PGA, but

the nonlinear case shows a little larger distances than the

linear cases under PGA over 0.3 g.

Between pier units, the nonlinear case shows the largest

relative distances when the PGA is over 0.3 g. The

biggest difference in the relative distances obtained from

the linear and nonlinear cases can be found at the location

between pier units.

Time histories of relative distances between the

abutment unit and the pier unit are plotted in Fig. 14 and

Fig. 15. The positive value means that two units are

facing, while the negative values represent that two units

are retreating. The initial distance gap between adjacent

units is 5 cm. Thus, the positive value of the relative

distance cannot exceed this value due to the pounding.

For the time histories between A1 unit and P1 unit (Fig.

14), it is clearly shown that nonlinear model gives the

increased relative distances, which can cause the span

collapse of the simply supported bridges. With regard to

the relative distances between P2 unit and A2 unit (Fig.

15), the small increment of relative distances is shown in

the nonlinear model.

Summarizing the above results, the stiffness degradation

due to the abutment-soil interaction plays the important

role upon the global dynamic characteristics of the whole

Figure 13. Comparison of relative distance between vibration units (90% extreme value of Gumbel type-I).

Table 3. Maximum relative distances between vibration units (unit: cm)

PGAA1-P1 P1-P2 P2-A2

L-C1c L-C2d N-Le L-C1c L-C2d N-Le L-C1c L-C2d N-Le

0.1 gMeana 3.00 3.20 3.00 0.10 0.15 0.10 2.40 2.53 2.40

Gumbelb 3.32 3.81 3.32 0.17 0.27 0.17 2.82 2.97 2.82

0.2 gMeana 7.07 7.40 7.27 3.97 3.78 3.61 5.91 6.06 5.96

Gumbelb 8.55 8.62 8.89 5.55 5.82 5.65 7.24 7.43 7.29

0.3 gMeana 9.62 11.04 11.32 5.29 5.26 5.32 8.08 8.49 8.58

Gumbelb 11.99 13.73 14.08 5.53 5.39 5.49 10.44 10.61 11.01

0.4 gMeana 11.83 13.42 15.02 5.91 5.54 8.12 9.32 9.85 10.25

Gumbelb 15.92 16.23 19.86 7.21 6.16 11.44 11.68 11.99 12.56

0.5 gMeana 14.58 16.28 17.65 6.53 5.56 9.46 10.86 11.21 13.03

Gumbelb 19.91 21.86 25.03 8.83 5.70 12.62 14.48 14.67 15.18

0.6 gMeana 16.96 19.35 20.72 6.37 5.93 11.37 11.84 12.31 14.04

Gumbelb 24.09 26.59 29.85 8.35 6.71 15.33 15.96 16.26 16.32

a)Mean value of relative displacements of each vibration unitb)90% extreme value of Gumbel Type-Ic)Abutment model with linear spring and dashpot (case 1)d)Abutment model with linear spring and dashpot (case 2)e)Abutment model with nonlinear spring and dashpot


bridge system. Thus, the seismic responses may be

underestimated in the system only with the constant

stiffness considered. Therefore, the stiffness degradation

should be accommodated in the analysis of seismic

responses of the bridges.

5. Conclusions

The effect of the stiffness degradation due to the

abutment-soil interactions upon the dynamic behaviors of

a multi-span plate-girder bridge under seismic excitations

are investigated by observing the relative displacements

to ground and relative distances between the adjacent

vibration units. The abutment-soil interaction is modeled

as the one degree-of-freedom system with nonlinear spring

and nonlinear damper. By comparing results obtained

from those systems with linearly modeled abutment-soil

interaction, the following trends are observed.

(1) The longitudinal abutment stiffness is found to

dramatically decrease at the onset of seismic

excitations. The relative motions to both grounds

and adjacent units are found to be larger in the case

with consideration of the stiffness degradation of

the abutment-backfill system than in the case

without consideration of the stiffness degradation

under moderate and strong seismic excitations with

PGA over 0.3 g.

(2) The effects of the stiffness degradation of the

abutment-backfill system become much larger

when relative distances between pier units are

compared. As PGA increases, this trend becomes

more noticeable. The stiffness degradation of the

abutment-backfill system is found to take an

important influence upon the global bridge motions.

The response motions may be underestimated if

only the linear system is considered. Hence, it is

concluded that the stiffness degradation should be

taken into account in the seismic analysis of the

bridge system especially in the case of strong

seismicity.

Acknowledgment

This work has been supported by Yonsei University,

Center for Future Infrastructure System, a Brain Korea 21

program, Korea.

References

Al-Homoud, A.S. and Whitman, R.V. (1999). “Seismic

analysis and design of rigid bridge abutments considering

rotation and sliding incorporating non-linear soil

behavior”, Soil Dynamics and Earthquake Engineering,

18 (4), pp. 247-277.

Anagnopoulos, S.A. (1988). “Pounding of buildings in series

during earthquakes”. Earthquake Engineering and

Structural Dynamics, 16, pp. 443-456.

Barker, R.M., Duncan, J.M., Rojiani, K.B., Ooi, P.S.K., Tan,

C.K. and Kim, S.G. (1991). Manuals for the design of

bridge foundations. Transportation Research Board,

Washington, D.C., NCHRP Report 343.

Figure 14. Time histories of relative distances between A1 and P1.

Figure 15. Time histories of relative distances between P2 and A2.


Caltrans (2001). Cartrans seismic design criteria, California

Department of Transportation, CA, USA.

Cho, K-I., Kim, S-H., Choi, M-S., and Lim, J-Y. (2008). “A

study on seismic performance of girder bridges equipped

with bi-directional energy-dissipating sacrificial devices”,

International Journal of Steel Structures, 8 (1), pp. 59-65.

Clough, G. W. and Duncan, J. M. (1991). Foundation

Engineering Handbook. 2nd edition: New York: 223-235.

Federal Highway Administrations (FHWA) (1986). Seismic

design of highway bridge foundation. Vol II. Design

Procedures and Guidelines, Report FHWA-RD-86-102.

Gasparini, D. A. and Vanmarcke, E. H. (1976). Evaluation of

Seismic Safety of Buildings Simulated Earthquake

Motions Compatible with Prescribed Response

Spectra,Massachusetts Ins. of Technology: Report No. 2.

Goel, R.K. and Chopra, A.K. (1997). “Evaluation of bridge

abutment capacity and stiffness during earthquake”.

Earthquake Spectra, 13(1), pp. 1-23.

Kim, S-H., Lee, S-W and Mha, H-S. (2000). “Dynamic

behaviors of the bridge considering pounding and friction

effects under seismic excitations”. Structural Engineering

and Mechanics, 10(6), pp. 621-633.

Kim, S-H., Mha, H-S and Won, J-H. (1999). “Dynamic

behavior analysis of bridges considering pounding

between adjacent girders under seismic excitations”.

Journal of Computational Structural Engineering

Institute of Korea, 12(3), pp. 509-518 (in Korean).

Maroney, B., Kutter, B., Romstad, K., Chai. Y.H. and

Vanderbilt, E. (1994). “Interpretationof large scale bridge

abutment test results”. Proceedings of the 3rd Annual

Seismic Research Workshop, California Department of

transportation, Sacramento, CA.

Ministry of Construction and Transportation(MOCT).

(2005). Korean Design Code for Highway Bridges (in

Korean), Korea.

Saadeghvaziri, M.A. and Yazdani-Motlagh, A.R. (2008).

“Seismic behavior and capacity/demand analyses of three

multi-span simply supported bridges”, Engineering

Structures, 30 (1), pp. 54-66.

Shamsabadi A., Rollins, K.M., and Kapuskar, M. (2007).

“Nonlinear soil-abutment-bridge structure interaction for

seismic performance-based design”, Journal of

Geotechnical and Geoenvironmental Engineering, 133

(6), pp. 707-720.

Siddharthan, R. V., El-Gamal, M., and Maragakis, E. A.

(1994). “Investigation of performance of bridge abutment

in seismic regions”, Journal of Structural Engineering,

120 (4), pp. 1327-1346.

Siddharthan, R. V., El-Gamal, M., and Maragakis, E. A.

(1997). “Stiffness of abutments on spread footings with

cohesionless backfill”, Canadian Geotechnical Journal,

34 (5), pp. 686-697.

Won, J-H., Mha, H-S., Cho, K-I., and Kim, S-H. (2008).

“Effects of the restrainer upon bridge motions under

seismic excitations”, Engineering Structures, 30 (12), pp.

3532-3544.

seismic behavior analysis of a plate-girder bridge ...c).pdf · due to friction. in this study, a...

Documents