Proceedings of the International Symposium on Engineering Lessons Learned fromthe 2011 Great East Japan Earthquake, March 1-4, 2012, Tokyo, JapanEVALUATION OF PERFORMANCE OF A SKEW
BRIDGE IN WENCHUAN 2008 EARTHQUAKEHua ZHANG1, Jianzhong LI2 and M. “Saiid” SAIIDI3
1

Ph.D. Student, Department of Bridge Engineering, Tongji University, Shanghai, China;
Visiting Scholar, Civil and Environmental Engineering, University of Nevada,Reno, NV, USA, dlerky.chang@gmail.com
2
Professor, Department of Bridge Engineering, Tongji University,
Shanghai, China, Lijianzh@tongji.edu.cn
3
Professor, Civil and Environmental Engineering, University of Nevada,Reno, NV, USA, saiidi@unr.edu

ABSTRACT: The 2008 Wenchuan earthquake caused substantial damage with major
consequences. Numerous buildings collapsed and thousands of lives were lost. Many
bridges were damaged to different degrees, some collapsed and some were left withlarge residual displacements making them unserviceable after the earthquake. The focusof the study presented in this article was the seismic performance of a skew bridge basedon field investigation and analytical studies. The field studies revealed that damage inmany bridge substructures was reduced because of the isolation effect of the rubber
bearings supporting the superstructure. However, since there was no connection between
the bearings and bridge girders, large residual displacements developed once the bearing
friction capacity was exceeded. The in-plane rotation effect enlarged the displacements
on acute angle and reduced it on obtuse angle, an effect that was consistent withobservations in previous strong earthquakes. Finite element method was used to model
the response of bridges using the record of Wolong station from Wenchuan earthquake.
The estimated residual displacements were reasonable at some locations but
substantially lower in other parts.. Parametric studies were conducted by replacing thebearings with different bearing types to determine the effect of the bearings on the
response and damage to the bridge. It was found that residual displacement would belower under certain combination of fixed and free bearings. In addition, theeffectiveness of cable restrainers in limiting displacement response of the bridge wasstudied. The results indicated that even nominal restrainers could reduce thelongitudinal residual displacements.
Key Words: Wenchuan earthquake, skew bridge, residual displacement, nonlinear
analysis, restrainer design,

INTRODUCTION
A great earthquake with magnitude of 8.0 struck Wenchuan, China on May 12th, 2008. The earthquake

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epicenter was located at latitude 31.021°N, longitude 103.367°E, with a focal depth of 14 km.
Numerous buildings and structures collapsed and thousands of lives were lost. Highway bridges, as animportant part of the transportation system with significant impact on the rescue operation after theearthquake, were extensively damaged to different degrees. Some bridges were buried by slope
failures or hit by rolling rocks from the mountain (e.g. Shunhe Bridge and Chediguan Bridge). Others
collapsed because of design deficiency (e.g. Baihua Bridge and Miaoziping Bridge). There were also
many bridges that did not collapse but underwent large residual displacements, which required
immediate rehabilitation to restore transportation service.
This paper presents the details of the investigation of a skew bridge that experienced large residual
displacements. To understand the response of the bridge during the earthquake, nonlinear response
history analyses were carried out subjected to acceleration records from the earthquake. In addition,
parametric studies were conducted and measures to improve the seismic performance of the bridge
were identified.

FIELD INVESTIGATION OF THE BRIDGE
The bridge that was investigated was the Duxiufeng Bridge on the national highway Route 213
spanning the Minjiang River, built on 2007, six months before the earthquake. This bridge is at about
15.3 km from the epicenter and 5.7 km from the fault. Fig. 1 shows the elevation and plan view of thebridge. The superstructure is supported on five drop cap bents each consisting of two 1.5 m diametercolumns. The heights of the columns from the top of the footing to the bottom of the cap are 8.30 m,
11.49 m, 13.01 m, 14.29 m and 14.28 m for bent 1 to 5, respectively. Each column has a 1.8 m
diameter pile as its footing and the top of the piles in each bent are linked by a transverse beam withcross section dimensions of 1.3 m by 1.5 m. The lengths of the piles are 43.25 m, 41.30 m, 38.00 m,
27.00 m and 27.30 m for bent 1 to 5, respectively. The height and width of the bent cap are 1.5 m and1.8 m, respectively. The site class of the bridge is Type II, consisting mostly of gravel and sand. The
definition of the site class used is from the Chinese Guidelines (JTG, 2008). The superstructure wasconstructed using four identical simply supported I-Shape girders in each span and continuous deck,with expansion joints at the middle bent and the abutments. The superstructure width is 8.5 m. The left
three spans are slightly curved, but the remaining spans are straight. The skew angle at the abutments
is 47°. The bearings at the abutments and bent 3 are Teflon plate rubber bearings with small friction toallow for thermal movement. The bearings on the other bents are rubber bearings supporting thegirders directly without any other connections. All the bearings allow for sliding once the friction force
between the girders and bearings are exceeded under lateral excitations such as earthquakes.

Left

Right

Fig. 1 Elevation and plan view of Duxiufeng Bridge (Dimensions in m)
Fig. 2 shows the overview of Duxiufeng Bridge after Wenchuan earthquake. No damage was notedin the bents and abutments. The main problem caused by the earthquake was large residual
displacements at the left abutment (abutment 0 in Fig. 1) and between span 3 and 4 at the top of bent 3(Fig. 3). The transverse relative displacement (TRD) at the left side of abutment 0 (Fig. 1) was 530
mm, as seen on Fig. 3a. The TRD between span 3 and 4 at the right side was 300 mm, as seen on Fig.
3b.

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Fig. 2 Overview of Duxiufeng Bridge after the earthquakea TRD at left side of abutment 0
b. TRD at right side at bent 3
Fig. 3 Residual displacements after the earthquake
These large residual displacements were mainly caused by the in-plane rotation of the skew bridge.
By investigating the response of skew bridges in the 1971 San Fernando earthquake, Jennings(Jennings, 1971) pointed out that the skew bridge tend to rotate in a horizontal plane in the direction ofincreasing the skewness of the bridge (Fig. 4). Shear keys limiting superstructure movement in thetransverse direction of the Duxiufeng Bridge had been installed. However, these shear keys failed
during the earthquake (Fig. 5). After failure of the shear keys, the superstructure rotated in plane withlittle transverse restraint and experienced large residual displacements. Both spans 1 and 3 were
unseated because of the large transverse displacements. Sliding also occurred on other bearings,
leaving approximately 30 mm to 150 mm residual displacements. Due to the large residual
displacements, the bridge was taken out of service after the earthquake. The bearings and shear keys
were replaced, the superstructure was moved to the original position, and the bridge was opened totraffic approximately 100 days after the earthquake.

Fig. 4 In-plane rotation effect of skew bridge

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a Abutment 0
b. Bent 1
Fig. 5 Failure of shear keys of Duxiufeng Bridge

MODELING OF THE BRIDGE
Modeling of the superstructure
To better understand the response of the bridge during the earthquake, a nonlinear finite element
model was developed using computer program SAP 2000. From the results of comparative study,
Meng (Meng, et al. 2000) concluded that the effect of superstructure flexibility is important and should
not be ignored in dynamic analysis since the use of the rigid deck or stick model for the dynamic
analysis of skew bridges with large skew angles leads to inaccurate axial forces in the columns during
the earthquake. Therefore, the superstructure was modeled using a grid system representing the beamflexibility. In each span four elastic beams were used to model the I-Shape girders. The stiffness of thedeck was included by enlarging the flange of the girders. Each elastic beam was divided into six
elements. Transverse elements were assigned among the nodes in the same line and assumed to be
rigid.
Modeling of the bents
Plastic hinges were assigned to the top and bottom of the columns. The plastic hinge sections consistedof three types of fibers: confined concrete, unconfined concrete, and longitudinal bars. The Mander(Mander, et al. 1988) model was used to model the unconfined and confined concrete. The hinge
lengths were assumed to be (JTG, 2008):

2 L p  min  0.08 H  0.022 f y d s  0.044 f y d s , b 
3 


(1)

where H is the distance from the top and bottom to the point where the moment is zero; b is the lengthof the smaller side of rectangular section or the diameter of circular section; fy (MPa) is the specified
steel bar yield strength and ds is the bar diameter. The concrete grade used in the bents of Duxiufeng
Bridge is C30 with a compressive strength of 20.1 MPa (JTG, 2004). The steel grades of longitudinal
and transverse bars are HRB335 and R235, respectively. The yield strengths are 335MPa and 235 MPa,
respectively (JTG, 2004). The locations of the hinges were defined at the middle of the hinge length.
Bent caps were modeled as elastic elements.
Modeling of the rubber bearings
As stated before, the links between the girders and the bents were rubber bearings without any otherconnections. Therefore, the transfer of lateral forces takes place only through friction. No tension force
can be transmitted through the bearings. Friction Isolator link in SAP2000 was used to simulate thismechanical behavior. Friction factors can be assigned in the lateral direction to calculate lateral forces1442

based on the normal force on the bearing. The normal force is always nonlinear and is given by:kd if d  0P
0 otherwise(2)

where k is the compressive stiffness, d is the normal deformation of the bearing. In order to generate
nonlinear shear force in the element, the stiffness k must be positive, and hence normal force on the
bearing P must be negative (compressive). The sliding forces of the bearings could be different
because of the vertical input and the uneven distribution of the normal forces in the bearings. Friction
factors were set the same in lateral direction for the rubber bearings. The radius of the sliding face wasset zero because the contact face between the girders and the bearings is flat. The friction coefficient
between rubber bearings and concrete girders was taken as 0.3 from the experimental results of Huang(Huang, et al. 2010). The friction coefficient between Teflon plate rubber bearings (at the abutments
and bent 3) and concrete girders was taken as 0.02.
Modeling of the expansions joints
Gap elements were used to model the pounding effect between the superstructure segments at bent 3
and between the superstructure and the abutments. The initial gap was set 80 mm, which is thestandard expansion joint gap thickness in bridges. The girder axial stiffness was used as the gap
element stiffness in compression.
Modeling of the bents foundation and abutments
BCAD_PILE program developed at Tongji University was used to calculate the stiffness of the pilefoundation of the bents. With the arrangement of piles and soil information from the bridge site, a 6×6
stiffness matrix was derived. The springs with derived stiffness matrixes were assigned to the bottomof the columns.
According to the field investigation, the abutments did not experience any damage during theearthquake. The abutment stiffness is much larger than the bents. Therefore, in order to simplify the
analysis, the abutments were modeled as rigid elements.
Input acceleration records
The measured acceleration records from Wolong station was used to carry out nonlinear response
analysis of the bridge (Fig. 6). The site is approximately 30 km away from the bridge and has thelargest PGA among all the records from Wenchuan earthquake (Li, et al. 2008). PGAs recorded in EW,
NS and UD directions are 0.957g, 0.653g and 0.948g, respectively. 0.1HZ and 25HZ bandpass wasapplied to filter the original record. The part of the record used in the analysis was from 20 seconds
into the record to 70 seconds. All three records were applied simultaneously. The corresponding elastic
response spectra are shown on Fig. 7.

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Fig. 6 Records of different direction from Wolong station

Fig. 7 Elastic response spectrum of Wolong record

RESPONSE ANALYSIS
Modal analysis
The dynamic response of a structure is generally based on its natural modes of vibration. Therefore,
the nature vibration periods and mode shapes for the first seven modes of the bridge were calculated(Table 1). The results indicate that the fundamental mode of the bridge is in-plane rotation of thesuperstructure about the vertical axis, which is mainly due to the large skewness of the bridge andunsymmetrical column heights. Under excitations with predominant periods close to in-plane rotation
periods, the rotation response could be significant and cause relatively large displacements compared
to non skew bridges. Since the height of the columns of the right three bents is larger than that of theleft two bents, the natural periods of the bridge segment to the right of bent 3 are longer than those of
the left three spans. Out-of-plane vibration of bent 3 is similar to a cantilever beam since the Teflon
plate rubber bearings at the top of the bent only have small friction force and provide little constraint
to the bent.
Table 1 First seven natural modes of the bridge
Mode No. Periods (s) Frequency (Hz)Mode Description
1
2.462
0.406
In-plane rotation (right three spans)
2
2.087
0.479
In-plane rotation (left three spans)
3
1.754
0.570
Longitudinal vibration (right three spans)
4
1.430
0.699
Longitudinal vibration (left three spans)
5
1.329
0.752
Transverse vibration (right three spans)
6
1.108
0.902
Transverse vibration (left three spans)
7
0.645
1.551
Out-of-plane vibration of bent 3
Results of nonlinear analysis
Nonlinear response history analysis was carried out to study the seismic response of the bridge withfinite element method. The longitudinal direction of the bridge is NW 10° and the global coordinate
system of the model is as follows: X axis is along the longitudinal direction of the bridge; Y axis isalong the transverse direction of the bridge; Z axis is along the vertical direction of the bridge.

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Therefore, NS record with an angle of 10° to X axis was taken as longitudinal input and EW record
with an angle of 10° to Y axis was taken as transverse input. The vertical motion was also applied.
Nonlinear static pushover analysis was carried out first to determine the performance of the bents.
The results are listed on Table 2. The results show that the yield displacements increased as the bentheight increased, while the lateral load capacity dropped. The out-of-plane ductility and displacement
capacities are larger than those of the in-plane direction. This could mean that the bents are more
vulnerable for loading in the transverse direction of the bridges.
Table 2 Pushover results of the bents
Bent No.
1
2
3
4
5

Yield Displacement (mm)Out-of-plane In-plane
40
10
60
15
80
20
100
25
100
25

Ductility Capacities
Max Shear Force (kN)Out-of-plane In-plane Out-of-plane In-plane
6.90
2.67
1022
1025
7.00
3.05
765
767
7.48
3.17
653
654
5.88
2.79
619
619
6.40
2.88
608
608

The displacement histories of bent 2 and 4 for both directions are illustrated on Fig. 8. The
responses indicate that the displacement of bent 2 (a relatively short bent) in the in-plane direction was
smaller than the out-of-plane displacement. However, this trend was reversed in the taller bents (bent4). Since the yield displacements in the out-of-plane and in-plane directions of bent 2 and 4 are 60 mm
and 15 mm, 100 mm and 25 mm, respectively, it can be seen that in the out-of-plane direction thebents remained elastic, but they yielded in the in-plane direction with displacement ductility demandsof 2.22 and 2.78 for bent 2 and 4, respectively. The ductility demands were smaller than thecorresponding calculated capacity for both bent 2 and 4. Also note in Fig. 8 that there was no residual
displacement in neither direction.

a Displacement histories for bent 2b Displacement histories for bent 4
Fig. 8 Nonlinear displacement response of the bents
Fig. 9 compares the displacement ductility demands and calculated ductility capacities for all thebents, where μD is the ductility demand and μC is the calculated ductility capacity. The bents remain
elastic if μ≤1. It can be seen that all the bents remained elastic in the out-of-plane direction, while in
the in-plane direction all the bents yielded but the ductility demands were all smaller than thecorresponding calculated ductility capacities. It is interesting to note that even though the friction
coefficient of the bearings on bent 3 was small and little friction force could be transferred from thesuperstructure to the bent through the bearing, the displacement ductility demands in both directions ofbent 3 were almost the same as other bents. This result can be explained from the elastic response
spectrum (Fig. 7). As stated above, there is almost no constraint at the top of bent 3 and it can vibrate
as a cantilever system. The first two natural modes of bent 3 are out-of-plane and in-plane modes withthe periods of 0.64s and 0.33s, respectively. It can be seen from the elastic response spectrum that thecorresponding accelerations of these periods are relative large. The other bents are constrained to thesuperstructure through friction of the rubber bearings and the natural vibration periods are 2s or more1445

(in-plane rotation period of the bridge, Table 1). The spectral accelerations are much smaller at these
periods. Therefore, displacements generated with large accelerations and small mass (bent 3) wereapproximately the same as those generated with small accelerations and large masses (other bents).

Fig. 9 Calculated ductility demands
The axial displacements of most Friction Isolator links had positive values, indicating that opening
between the girders and the bearings occurred during the earthquake. Strong vertical input and uneven
distribution of axial force among the bearings caused by dynamic vibration led to unloading of the
bearings and opening at the interfaces. There was no friction force between the bearings and thegirders when opening occurred, which means the girders lost lateral constraint leading to to large
sliding displacements. All the bearings had residual displacements in both directions. The maximum
residual displacements of the bearings in the longitudinal and transverse directions were 121 mm and229 mm, respectively. The calculated residual relative displacements of the superstructure are listed inTable 3. There are some differences between the calculated and field results. According to field
investigation, the transverse residual relative displacement at abutment 0 on left side was 530 mm.
However, it was only 45.5 mm from the nonlinear analysis. The difference at bent 3 was relatively
small. These differences may be caused by the site effect. Although acceleration records from Wolong
station are the nearest records to the bridge, local site effect may change the excitations of the bridge.
The riverbed can alter the amplitude and frequency content of the seismic waves. For a more accurate
estimate of the response, measured records in the actual site are necessary. Another possible
explanation for discrepancies between the calculated and measured residual displacements is the factthat calculated residual displacements are generally very sensitive to small variations in modelingassumptions and the material properties.
Table 3 Calculated residual relative displacement of superstructure
Position
Longitudinal (mm) Transverse (mm)Right side
90.3
19.4
Abutment 0
Left side
116.1
45.5
Right side
58.0
274.0
Bent 3
Left side
82.7
250.2
Right side
31.6
62.2
Abutment 6
Left side
29.4
60.2

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The maximum axial deformation of the gap elements was 84 mm and the corresponding force was
1446 kN. This pounding occurred at left side of bent 3, due to the in-plane rotation
EFFECTS OF DIFFERENT BEARING TYPES
Neither the field investigation nor the nonlinear response history results indicated strength loss in thebridge under the Wenchuan earthquake. However, the large residual displacements led to the closureof the bridge. An analytical study was undertaken to determine if, by changing the bearings, residual
displacements could be reduced without compromising the load capacity of the bridge. Two different
types of bearings were studied. The first had pin bearings at bent 2 and 4, and roller bearings at otherbents. The roller bearings allowed for unrestrained movement of the superstructure in the longitudinal
direction but prevented movement in the transverse direction. The second type also had pin bearings at
bent 2 and 4, but allowed for unrestrained longitudinal and transverse movement of the superstructure
at other bents. To facilitate discussions in this article, the bridge model with the first bearing
combination is labeled “pin-roller bearing” and the one with the second type is labeled “pin-freebearing.” The model with the actual bearing used in the Duxiufeng Bridge is referred to as “rubber
bearing.”
Fig. 10 shows the displacement ductility demands of the bents for different bearing types. The
pin-roller bearing experienced the largest bent displacement ductility demands in the out-of-plane
direction and was the only model in which the columns in bent 1 and 3 yielded. None of the piers in
the other two models yielded in the longitudinal direction. The in-plane rotation is restrained because
the transverse movement is restrained. It appears that the transverse restraint led to large bent forces inboth directions, which increased the displacement ductility demands for the bents. The differences ofdisplacement ductility demands in the out-of-plane direction of pin-free and rubber bearing wererelatively small. Pin-roller bearing also had the largest displacement ductility demands in the in-plane
direction of all the bents, except for bent 4 and 5. In contrast, the results of pin-free bearing wereslightly larger than that of rubber bearing at pinned bents (bent 2 and 4). Therefore, the pin-free andrubber bearing models are preferred in controlling damage in the bents under the Wolong station
earthquake records.

a Out-of-plane displacement ductility demands b In-plane displacement ductility demands
Fig. 10 Displacement ductility demands of bridge models with different bearing types
The maximum relative displacement between girders and bents of different bearing types are listed
in Table 4. The results indicate that the bridge with rubber bearing had the largest relative
displacement in both the longitudinal and transverse directions. The results for pin-free bearing model
were approximately one half of the results for rubber bearing. The longitudinal residual displacementin the pin-roller bearing model was slightly smaller than that with rubber bearing, and because of
constraint against transverse movement, the transverse relative displacement was zero. The results
indicate significant reduction in both the longitudinal and transverse residual displacements in the1447

pin-free model compared to bearing types of the actual bridge labeled as “Rubber” in the table.
Therefore, pin-free bearing is recommended for the Duxiufeng Bridge to control permanent
displacements.
Table 4 Max relative displacement between Girders and Bents
Bearing type Longitudinal (mm) Transverse (mm)Rubber135
254
Pin-free
68
118
Pin-roller
121
0

EFFECTS OF RESTRAINERS
The effect of cable restrainers on reducing residual displacements of the Duxiufeng Bridge was alsostudied. Cable restrainers were assumed to be installed at the expansion joints at the abutments andbent 3. Two restrainers were symmetrically arranged at each abutment expansion joints attaching thegirders to the abutments. Another four restrainers were symmetrically arranged at the middle
expansion joint attaching span 3 and 4 to bent 3. The restrainer stiffness was assumed to be the same atdifferent locations. The minimum restrainer stiffness was calculated 2.5 kN/mm according to theminimum restrainer stiffness requirement recommended by Saiidi et al. (Saiidi, 2001). Different
stiffness values of 1.25kN/mm, 2.5 kN/mm, 5 kN/mm and 10 kN/mm were assumed to carry out aparametric study. The initial slack of the restrainers was taken as zero to account for the extreme lowtemperature and the most critical condition for restrainer loading.

a Longitudinalb Transverse
Fig. 11 Comparison of max bearing residual displacement
The comparison of the maximum bearing residual displacement with different restrainers is shownin Fig. 11, where positions 0 and 6 represent abutment 0 and 6 and positions 1 to 5 represent bent 1 to
5. It can be seen that when there was no restrainer, the max bearing residual displacements in thelongitudinal direction of position 0 to 3 were significant. Even a relatively small restrainer stiffness
can reduce these residual displacements by approximately 50%. Increasing restrainer stiffness canfurther reduce the residual displacements, but the rate of reduction becomes small when the restrainer
stiffness exceeds 5 kN/mm. Fig. 11b shows that restrainer had little effect on limiting the max bearing
residual displacement in the transverse direction when the stiffness was smaller than10 kN/mm. Thiswas expected because the restrainers acted mainly in the longitudinal direction. Meanwhile, lateralbiaxial input and rotation of the superstructure led to coupled longitudinal and transverse
displacements of the superstructure. Therefore, restrainers partly affected the transverse displacement.

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If the stiffness is sufficiently large, the effect on limiting the transverse displacement becomessignificant. The maximum elongation of the restrainers were 94 mm, 72 mm, 60 mm and 52 mm forthe stiffness of 1.25 kN/mm, 2.5 kN/mm, 5 kN/mm and 10 kN/mm, respectively. These are all smaller
than the yield displacement of the most commonly used restrainers (Saiidi, et al. 2001), which is 107
mm, indicating the restrainers can remain elastic during the earthquake.

CONCLUSIONS
Based on the field investigation and nonlinear analysis of the Duxiufeng Bridge after Wenchuan
Earthquake, following conclusions are drawn:
1. The Wenchuan Earthquake did not cause severe damage to Duxiufeng Bridge. The main issue that
led to the closure of the bridge was the large residual displacement of the superstructure and theunseating of the bearings.
2. Large sliding displacements occurred between the rubber bearings and the girders because there
were no stoppers.
3. Nonlinear dynamic analysis of the bridge based on a record that was obtained 30 km away from thebridge site provided an approximate estimate of residual displacements.
4. Parametric analytical studies revealed that by allowing unrestrained movement at most of the
bearing, the residual superstructure displacements can be reduced without imposing additional demandon the bents.
5. Parametric studies on the effect of restrainers showed that even nominal restrainers are effective in
reducing the residual displacements in the bearings. Both the longitudinal residual displacements canbe controlled with appropriate size of restrainers.

ACKNOWLEDGEMENTS
The support by the Scientific and Technical Project on Western Transportation Construction, Grant No.
2008318200098 for the project named ‘Seismic Damage Evaluation, Mechanism Analysis and
Evaluation of Seismic Fortification Criterion on Highway during Wenchuan Earthquake’ is gratefully
acknowledged. The writers wish to thank Dr. Liu Zhenyu for his field investigation materials. The study
presented in this article was conducted in the course of a visiting researcher scholarship awarded to thefirst author to conduct research under the supervision of the third author. The scholarship sponsored by
the China Scholarship Council is also gratefully thanked. The opinions and conclusions presented in thispaper are those of the authors and do not necessarily reflect the views of the sponsoring organizations.

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