SEISMIC RESISTANCE OF MULTI-SPANS PC BRIDGE UNDER

INTERNATIONAL COOPERATION ISSUE OF TRANSPORTATION – Especial Issue – No.01 125

I. INTRODUCTION

In present, many transport system constructions are now making rapidly progress accordingto social and economic development in Vietnam. Large and many bridges have beenconstructed, are underway and in planning. Vietnam does not have hist ory of large scaleearthquakes, however some small earthquake have been recorded by seismometers installed inVietnam. According to analysis of earthquake records obtained by the seismometers, Vietnam islocated moderated seismic activity area. Seismic des ign Specification in Vietnam (a part of22TCN 272-05) is established based on AASHTO LRFD 1998. Many bridges are design by thisSpecification.

Recently, some bridges have been constructed by Japanese economic support (ODA). Alsosome bridges are constructed in very soft ground or potentially liquefaction sand area.Evaluation by Japanese Specification is required for these conditions. It is necessary in order toconfirmation of seismic performance of the bridge and also to evaluate seismic performance bydynamic response analysis based on Japanese Specification. The dynamic response analysisconsidering material non-linearity can evaluate seismic performance on not only resistance ofmembers but also deformation, unseat, etc…In this paper, unseat of the girders is mainlyevaluated to secure of the existing bridge.

SEISMIC RESISTANCE OF MULTI-SPANS PC BRIDGE UNDER

EARTHQUAKE OCCUR IN VIETNAM

TRAN VIET HUNGMsc., Dept. of Civil Eng., University ofTransport and CommunicationCaugiay, Dongda, Hanoi, VietnamNGUYEN VIET TRUNGDr. of Eng., Professor, Dept. of Civil Eng.,University of Transport and Communication,Caugiay, Dongda, Hanoi, Vietnam

Abstracts: The response of bridges when subjected to seismic excitation can be evaluated

by dynamic response analysis methods. A preliminary seismic response analysis of a multi -

spans highway bridge in Vietnam was performed using d ynamic analysis procedures to

identify the potential for nonlinear response of bridge structure. In this study, a typical

concrete girder bridge (multiple frames in the longitudinal direction) in Vietnam is used to

seismic resistance evaluations. These eva luations are performed by performing nonlinear time

history analyses on FEA method. It is found that the typical bridge and structure

characteristic influence on response of the bridge during earthquake .

Keywords: Seismic analysis, non-linear analysis, bridge in Vietnam, earthquake

engineering, dynamic response analysis.

INTERNATIONAL COOPERATION ISSUE OF TRANSPORTATION – Especial Issue – No.01126

II. DYNAMIC RESPONSE ANALYSIS

The dynamic response of a structure depends on its mechanical characteristics and thenature of the induced excitation. Mechanical properties which are efficient to mi tigate thestructure’s response when subjected to certain inputs might have an undesirable effect duringother inputs. In a dynamic analysis, the number of displacements required to define thedisplaced positions of all the masses relative to their origina l positions is called the number ofdegrees of freedom (DOF). The equation of motion of an MDOF system is similar to the SDOFsystem, but the stiffness k, mass m, and damping c are matrices. The equation of motion to anMDOF system under ground motion can be written as

[M]{ u } + [C]{ u }+[K]{ u }= -[M]{B} gu (1)

The stiffness matrix [K] can be obtained from standard static displacement -based analysismodels and may have off-diagonal terms. The mass matrix [M] due to the negligible effect ofmass coupling can best be expressed in the form of tributary lumped masses to thecorresponding displacement degrees of freedom, resulting in a diagonal or uncoupled massmatrix. The damping matrix [C] accounts for all the energy-dissipating mechanisms in thestructure and may have off diagonal terms. The vector {B} is a displacement transformationvector that has values 0 and 1 to define degrees of freedom to which the earthquake loads are

applied. Value gu is ground acceleration.

For the purpose of analysis, energy absorbed by inelastic deformation in a structuralcomponent may be assumed to be concentrated in plastic hinges and yield lines. The location ofthese sections may be established by successive approximation to obtain a lower bound solutionfor the energy absorbed. For these sections, moment -rotation hysteresis curves may bedetermined by using verified analytic material models. In addition to a lin ear analysis, it iscommon practice to perform a capacity analysis associated with the desired inelastic response inwhich ductile flexural response occurs at selected plastic hinge regions within the structure. Theplastic hinge regions are detailed to en sure plastic behaviour while inhibiting nonductile failuremodes. The hysteresis properties were the Takeda hysteresis properties. The Takeda degradingstiffness (see Fig. 1) and bilinear elasto -plastic hysteresis (see Fig. 2) were considered to derivethe inelastic spectra.

Fig 1. Takeda model Fig 2. Elasto-plastic hysteresis


III. ANALYTICAL MODELING

The bridge is multi-span continue bridges, representative of typical bridges in Vietnam,evaluated under this study. For superstructure was a continuou s hollow slab beam bridge with 8spans, a total length of 250m. Pier columns and abutments have bored cast -in-place pilefootings. The bridge arrangements are 3 rigid frame piers (P2, P3, and P4) and 4 bent piers isinstalled by rubber bearings support (P0 , P1, P5 and P6). The pier columns are all circular withspiral or circular lateral reinforcements. Elevation for bridge is shown in Fig. 3. The soilconditions are almost medium sand, fine sand and gravelly sand.

Fig 3. Profile of bridge

G ird e r ( lin e a r b e a m e le m e n t)

B e a rin g s p rin gS to p p e r

L o n g .= 0 .1 2 m

S p a c in g

A c tin g fo rc e

D is p .

K = 1 0 k N /m

H o z i.= 0 .0 5 m

8

K = 1 0 k N /m-1

C o lu n m p ie rN o n lin e a r b e a m e le m e n t

N o n lin e a r ro ta tin gP la s tic h in g e s p rin g

B e a m e le m e n tF o o tin g

s p r in g e le m e n t

F o u n d a tio n g ro u n d s p rin g

P

D is p .

k

k 1

Fig 4. Modeling of a bridge pier

In the pier column, a linear rotating spring that modeled a plastic hinge, the column bodywas a nonlinear beam element. The rubber bearing used bilinear model is a nonlinear spring inhorizontal direction. The dynamic analysis was perf ormed using the Newmark β method andintegration time interval was 0.01 second. The nonlinear behavior of the columns is presentedby the Takeda model with the potential plastic hinge zone located at bottom of the column asshown in Fig. 4. The stress vs. strain relation of reinforcing bars is idealized by an elastic perfectplastic model.


Lp = plastic hinge length (Lp = 0.2h – 0.1D; 0.1D ≤Lp ≤ 0.5D) with h = height of thecolumn pier (2)

Table 1. Plastic hinge length of pier, Lp (m)P0, P6 P1, P5 P2, P4(*) P3(*)

h (m) 3.9 4.8 5.7 5.9Lp m) 0.5 0.7 0.4 0.4 0.5 0.5

(*) The piers P2, P3, P4 have 2 locations of the plastic hinge length at bottom and top of pier

The inelastic dynamic analysis is performed by incorporating the non -linear rotationalspring (Kx, Ky, Kθ). The dynamic characteristic value of the surface ground is 0.82s , i.e. type IIIground according to the seismic design specified in Japanese Specifications for Highway Bridge(Part V Seismic design). In the analysis, the damping model used was Rayleigh damping. Thedamping of a structure is related to the amount of energy dissipated during its motion. It couldbe assumed that a portion of the energy is lost due to the deformations, and thus damping couldbe idealized as proportional to the stiffness of t he structure. Another mechanism of energydissipation could be attributed to the mass of the structure, and thus damping idealized asproportional to the mass of the structure. In Rayleigh damping, it is assumed that the damping isproportional to the mass and stiffness of the structure.

[C]= a0 [M] + a1 [K] (3)

in which [C] = damping matrix of the physical system; [M] = mass matrix of thephysical system; [K] = stiffness matrix of the system; a0 and a1 are pre -defined constants. Thegeneralized damping of the nth mode is then given by:

Cn = a0 Mn + a1Kn (4)

Cn = a0Mn + a1 ωn2Mn (5)

nn

nn M2

C

(6)

n1

n

0n 2

a1

2

a

(7)

Fig 5. Rayleigh damping variation with natural frequency


Fig. 5 shows the Rayleigh damping variation with natural fre quency. The coefficients a0and a1 can be determined from specified damping ratios at two independent dominant modes(say, ith and jth modes). Expressing Eq. (8) for these two modes will lead to the followingequations:

i1

i

0i 2

a1

2

a

(8)

j1

j

0j 2

a1

2

a

(9)

When the damping ratio at both the i th and jth modes is the same and equals ξ, it can beshown that:

ji

ji0

2a

;

ji1

2a

(10)

It is important to note that the damping ratio at a mode between the ith and jth modes isless than ξ. And in practical problems, the specified damping ratios should be ch osen to ensurereasonable values in all the mode shapes that lie between the ith and jth modes shapes. In theanalysis, the damping model used was Rayleigh damping. The Rayleigh damping coefficientwas set based on the vibration mode of the structure. We s tudy in case of natural frequencies are2.337Hz and 7.305Hz for damping ratio are 0.0322 and 0.0568, respectively. The values area0 = 0.45829 and a1 = 0.00225.

Table 2. Damping ratio of the members

Member Damping ratio

Bridge column – pier

(nonlinear member)2%

Bridge column – pier, footing

(linear member)5%

Girder (linear member) 3%

Bearing spring 4%

Foundation spring 10%

This analysis used two ground motion records in Japan are acceleration records in theDorokyou Shihousho (Level 1 in Japa n code) and Kushirogawa-1994 (Level 2 in Japan code)with the peak ground acceleration of ground motion records are 1.41m/s 2 (following to lowearthquake occurs in Vietnam) and 4.38m/s 2, respectively. The main seismic attack on moststructures is the set of horizontal inertial forces acting on the structural masses, these forcesbeing generated as a result of horizontal ground accelerations. For most structures, verticalseismic loads are relatively unimportant in comparison with horizontal seismic loads. T herefore,in this study the structure is excited in the horizontal (longitudinal) direction. The records have avariety of peak ground acceleration as shown in Fig. 7.


0

5000

10000

15000

20000

25000

00.0

010.0

020.0

030.0

040.0

050.0

060.0

07

φ (1/ m)

Mom

ent

(kN.

m)

P1, P5P0, P6P2, P4P3

a) Moment vs. curvature relation

0

5000

10000

15000

20000

25000

00.0

005 0.001

0.0015 0.0

020.0

025 0.003

0.0035 0.0

040.0

045

θ (rad)

Mom

ent

(kN.

m)

P1, P5P0, P6P2, P4P3

b) Moment vs. rotation relation

at the plastic hinge

Fig 6. M - and M – θ relationships of column piers

Max acc. is 1.41m/ s2

- 1.5

- 1.0

- 0.5

0.0

0.5

1.0

1.5

2.0

0 10 20 30 40 50

Time (s)

Acce

lera

tion

(m/s

2 )

a) Horizontal acc. in the Dorokyou Shihousho

(Maximum acc. is 1.41m/s2)

Max acc. is 4.38m/ s2

- 6.0

- 4.0

- 2.0

0.0

2.0

4.0

6.0

0 10 20 30 40 50 60

Time (s)

Acc.

(m/s

2 )

b) Horizontal acc. in the Kushirogawa, 1994

(Maximum acc. is 4.38m/s2)

Fig 7. The ground motion records used in this analy sis

IV. RESPONSE OF BRIDGE STRUCTURE IN A LOW -MODERATE SEISMIC ZONE

The main objective is to determine relative superstructure -substructure displacementsobtained from an dynamic analysis for typical highway bridges located in a low to moderateseismic zone. Fig. 8 shows the response of the bridge for peak magnitude of the input wave is1.41m/s2 while install stopper and non-stopper. The accelerations of girder are 1.62m/s 2 and2.47m/s2 while maximum displacements of girder are 1.4cm and 2.2cm for install s topper andnon-stopper, respectively. The small displacement of girder can result in frame rigid structure atpier P2, P3, P4. With the results shows under a poor ground excitation, the bridge structure cannot damage of girder and bearing support. In this case, stopper and no-stopper weren’t influentto safety of structure when poor earthquake occurs. Fig. 9 shows the hysteretic response at theplastic hinge of the pier P1 (rubber bearing) and pier P2 (rigid pier and girder). The maximumrotations of P1, P2 are 1.072×10-4 rad, 4.149×10-5 rad and 3.134×10 -4 rad, 2.062×10-4 rad forinstall stopper and non-stopper, respectively. The difference can be caused by piercharacteristics and typical structure. However, the possibility of the undesired behavior, such asunseating failure of the superstructure, is still low since the absolute value of the relativedisplacement is very small.


- 3

- 2

- 1

0

1

2

3

0 10 20 30 40 50 60

Time (s)

Acce

larat

ion

(m/s

2 )

Stopper Non- stopper

a) Acceleration of the girder at the end girder

(A1 side)

- 0.025

- 0.020

- 0.015

- 0.010

- 0.005

0.000

0.005

0.010

0.015

0.020

0.025

0 10 20 30 40 50 60

Time (s)

Disp

lacem

ent (

m)

Stopper Non- stopper

b) Displacement of the end girder

(A1side)

0

0.005

0.01

0.015

0.02

0.025

P0 P1 P2 P3 P4 P5 P6

Horiz

onta

l Dis

plac

emen

t (m

) Non stopper Stopper

c) Displacement of top’s pier

Fig 8. Response of the bridge with wave 1.41m/s 2

- 8000

- 6000

- 4000

- 2000

0

2000

4000

6000

8000

- 0.0002 - 0.0001 0 0.0001 0.0002Rotat ion, θ (rad)

Mom

ent

(kN

.m)

Pier P1

- 8000

- 6000

- 4000

- 2000

0

2000

4000

6000

8000

- 0.0001 - 0.00005 0 0.00005 0.0001Rotat ion, θ (rad)

Mom

ent

(kN

.m)

Pier P2

Fig. 9a) Case of stopper

- 15000

- 10000

- 5000

0

5000

10000

15000

- 0.0004 - 0.0002 0 0.0002 0.0004Rotat ion, θ (rad)

Mom

ent

(kN

.m)

Pier P1

- 15000

- 10000

- 5000

0

5000

10000

15000

- 0.0004 - 0.0002 0 0.0002 0.0004Rotat ion, θ (rad)

Mom

ent

(kN

.m)

Pier P2

b) Case of non-stopper

Fig 9. Hysteretic response at the plastic hinge of pier under input wave 1.41m/s2


V. RESPONSE OF THE BRIDGE WITH STRONG GROUND EXCITATIO N

Following to 22TCN 272-05, longitudinal stoppers shall be designed for a force calculated

as the acceleration coefficient times the permanent load of the lighter of the two adjoining spans

or parts of the structure. If the stopper is at a point where rel ative displacement of the sections of

superstructure is designed to occur during seismic motions, sufficient slack shall be allowed in

the stopper so that the restrainer does not start to act until the design displacement is exceeded.

Fig. 10 and Fig. 11 shows the response of the bridge for peak ground acceleration is 4.38m/s 2

when installed stopper and non-stopper. The accelerations of girder are 38.6m/s 2 and 4.52m/s2

while maximum displacements of girder are 10.13cm and 23.91cm for install stopper and non -

stopper, respectively. The acceleration of girder in case of install stopper larger non -stopper is

caused by the sudden exchange of velocity at the time pounding. Longitudinal displacement of

girder can be restrained by stopper in the top of pier.

- 0.05

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0 10 20 30 40 50 60 70

Time (s)Horiz

onta

l disp

lacem

ent (

m)

Non stopper Stopper

Fig 10. Displacement of the end girder (abutment A1) with input wave 4.38m/s 2

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0 10 20 30 40 50 60 70

Time (s)

Disp

lacem

ent (

m)

Pier P0 Pier P1 Pier P2 Pier P3

P0P3P2P1

a) Case of stopper

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0 10 20 30 40 50 60 70

Time (s)

Disp

lacem

ent (

m)

Pier P0 Pier P1 Pier P2 Pier P3

P0

P1P2

P3


Fig 11. Displacement of top’s pier with input wave 4.38m/s2


- 40000

-30000

-20000

-10000

0

10000

20000

30000

-0.04 -0.03 -0.02 -0.01 0 0.01

Rotat ion, θ (rad)

Mom

ent

(kN.

m)

Resistance Response

Mc,θ c

Mu,θ u

Mc=6520.4kN.m θ c=8.54x10- 5rad My=20756.4kN.m θ y=9.29x10- 4rad Mu=22224.0kN.m θ u=4.18x10- 3rad Mc,θ c

My,θ y

Mu,θ u

My,θ y

PierP1

- 50000

- 40000

- 30000

- 20000

- 10000

0

10000

20000

30000

40000

- 0.04 - 0.03 - 0.02 - 0.01 0 0.01

Rot at ion, θ (rad)

Mom

ent

(kN.

m)

Resistance Response

Mc=6569.2kN.m θ c=4.92x10- 5rad My=20895.1kN.m θ y=5.34x10- 4rad Mu=22276.6kN.m θ u=2.39x10- 3rad

PierP2

Mc,θ cMy,θ y

Mu,θ u

Mc,θ cMy,θ yMu,θ u

a) Case of stopper

- 40000

- 30000

- 20000

- 10000

0

10000

20000

30000

- 0.05 - 0.04 - 0.03 - 0.02 - 0.01 0 0.01

Rot at ion, θ (rad)

Mom

ent

(kN.

m)

Resistance Response

MuMy

Mc

Mc

My Mu

Mc=6520.4kN.m θ c=8.54x10- 5rad My=20756.4kN.m θ y=9.29x10- 4rad Mu=22224.0kN.m θ u=4.18x10- 3rad

PierP1 -90000

-70000

-50000

-30000

-10000

10000

30000

-0.1 -0.08 -0.06 -0.04 -0.02 0 0.02

Rotation, θ (rad)

Mom

ent

(kN.

m)

Resistance Response

Mc=6569.2kN.m θ c=4.92x10-5rad My=20895.1kN.m θ y=5.34x10-4rad Mu=22276.6kN.m θ u=2.39x10-3rad

PierP2

McMyMu

McMyMu


Fig 12. Hysteretic response at the plastic hinge of pier under input wave 4.38m/s 2

Fig. 12 shows the hysteretic response at the plastic hinge of the pier P1 (rubber bearing)

and pier P2 (rigid pier and girder). The maximum rotations of P1, P2 are 3.15×10 -2rad, 3.67×10-

2rad and 4.06×10-2rad, 8.34×10-2rad for install stopper and non-stopper, respectively. The results

shows almost moment at the plastic hinge of pier overpass moment resistance of pier, thus crack

potential occurs in pier will happen.

VI. CONCLUSIONS

The dynamic behaviors of a multi-span highway bridge system under seismic excitations

are examined with various conditions. On the basis of the results and discussions of the current

study, the following conclusions can be made:

1. Although relative displacement superst ructure - substructure analysis and beam seat

length may be valuable in estimating seismic resistance of bridge in seismic zones, especially

for highway bridges located in a low to moderate seismic zone (i.e. acceleration coefficient,


A=0.09-0.29g) such as Vietnam. This bridge is safety during earthquake in Vietnam.

2. In conclusion, the continuous spans may remain in the elastic range without any

disruption to traffic due to the low seismic excitation such as Level 1, JRA -2002; while a partial

damage may occur due to the strong earthquake such as Level 2, JRA -2002. Thus evaluation

seismic by dynamic response analysis is very importance and needed.

3. The use of stoppers may decrease displacement of girder and prevent unseating fromsuperstructure

References

[1]. Specification of highway bridges, Part V seismic design, Japan Road Association, 2002.

[2]. 22TCN 272-05, Specification for bridge design, Ministry of Transport of Vietnam, 2005.

[3]. TCXDVN 375: 2006, Design of structures for earthquake resistance , Vietnam Ministry of

Construction, 2006.

[4]. Meterials design of bridge structure in Vietnam

[5]. AASHTO. Load and resistance factor design (LRFD) specifications for highway bridges. Washington

(DC): American Association of State Highway and Transportati on Officials (AASHTO), 1998.

[6]. AASHTO. AASHTO LRFD Bridge design specifications, 3rd Edition, Washington (DC): American

Association of State Highway and Transportation Officials, 2004.

[7]. Tongxiang An, Osamu Kiyomiya , Dynamic response analyses and mod el vibration tests on seismic

isolating foundation of bridge pier, Structural Eng./Earthquake Eng., JSCE, Vol. 23, No. 2, pp. 195s -214s,

2006.

[8]. Shigeru Miwa, Takaaki Ikeda , shear modulus and strain of liquefied ground and their application to

evaluation of the response of foundation structures, Structural Eng./Earthquake Eng., JSCE, Vol. 23, No.

1, pp. 167s-179s, 2006.

[9]. Yusuke Ogura, Shigeki Unjoh , Response characteristics of bridge abutments subjected to collision of

girder during an earthquake, Structural Eng./Earthquake Eng., JSCE, Vol. 23, No. 1, pp. 135s -141s, 2006.

[10]. Nasim K. Shattarat, Michael D . Symans, David I. McLean, William F. Cofer, Evaluation of

nonlinear static analysis methods and software tools for seismic analysis of highway bridges, Engineering

Structures, Vol. 30, Issue 5, pp. 1335-1345, 2008.

[11]. M. Ala Saadeghvaziri, A.R. Yazdani-Motlagh, Seismic behavior and capacity/demand analyses of

three multi-span simply supported bridges, Engineering Struct ures, Vol. 30, pp. 54-66, 2008

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SEISMIC RESISTANCE OF MULTI-SPANS PC BRIDGE UNDER