Int. J. Struct. & Civil Engg. Res. 2013 Md. Basir Zisan and Hafizul Alim, 2013
EVALUATION OF PROBABILISTIC FAILUREOF BRIDGE PIER
Hafizul Alim1 and Md. Basir Zisan1*
Bridge is an essential lifeline structure, which provides an emergency link in transportation networksystem. During post-earthquake bridge should remain functioning without any collapse. But inreality, uncertainty behavior of civil engineering structures involve during service life since, actualand assumed environmental conditions during design are never coincide. The purpose of thispaper is to evaluate the probabilistic failure of bridge pier subjected to far field ground motion. Anonlinear static pushover and incremental dynamic time-history analysis have been performedusing the SeismoStruct nonlinear analysis program for 3D bridge bent. 20 far field ground motionsand their respective PGA are considered to develop fragility curve for conventional and FRPretrofitted bridge pier. The purpose of this study is to probabilistic determination of seismicvulnerability of bridge pier and help to decision making for effective retrofitting technique.
INTRODUCTIONBridges are considered to be li felinestructures, since they provide an emergencylink in a surface transportation network duringdisaster, such as Earthquakes. Hence bridgesare required higher seismic performance thanothers civil engineering structures. The failureof such structures causes claim of lives,economical loss including immeasurablesufferings. The exact performance evaluationof bridge under environmental action like wind,earthquake loading became uncertain sincesuch loadings action is unknown. The use of
ISSN 2319 – 6009 www.ijscer.comVol. 2, No. 2, May 2013
fragility curves establishes a relationshipbetween ground shaking intensity and theprobability of reaching or exceeding a certainresponse level. For assessment of seismiclosses due to earthquake, fragility, fragilitycurves become valuable tool for pre-earthquake disaster planning and post-earthquake recovery and retrofitting programs.
FINITE ELEMENT MODELINGThe analytical model of the bridge bent isapproximated as a continuous 2-D finiteelement frame using the SeismoStruct
33
Int. J. Struct. & Civil Engg. Res. 2013 Md. Basir Zisan and Hafizul Alim, 2013
nonlinear analysis program (SeismoStruct 6).Nonlinear static pushover and incremental
dynamic time-history analysis have beenperformed on the bridge bents to determine
the performances of the retrofitted bridge
bents. The program has the ability to figure outlarge displacement behavior and the collapse
load of structure under either static or dynamicloading, while taking into account both geo-
metric nonlinearities and inelasticity (Baker and
Cornell, 2006). 3D inelastic beam elementshave been used for modeling the pier. The elevation
and section of the pier is shown in Figure 1.
Figure 1: Elevation and Sectionof Pier Model
The fiber modeling approach has beenemployed to represent the distribution of thematerial nonlinearity along the length and crosssectional area of the member. Each fiber hasstress-strain relationship, which can bespecified to represent unconfined concrete,confined concrete, and longitudinal steelreinforcement. The confinement effect of theconcrete section is considered on the basisof reinforcement detailing. The distribution ofinelastic deformation and force is sampled byspecifying cross-section slices along thelength of the element. Twenty far field groundmotions and their respective Peak GroundAcceleration (PGA) are considered to developfragility curve.
To develop the analytical model Menegotto-pinto steel model (Choi et al., 2004) withFlippou et al. (1983) isotropic strain hardeningproperty is used for reinforcing steel material.The yield strength, strain hardening parameterand modulus of elasticity of steel areconsidered as 400 MPa, 0.5% and 2*105
Mpa, respectively. For concrete non linearvariable confinement model of Madas andElnashai (1992) with compressive strength of21 MPa and tensile strength 3.5 MPa has beenused. CFRP has been modeled using nonl inear FRP confined concrete modeldeveloped by Ferracuti and Savoia (2005).For compression, this model follows theconstitutive relationship and cyclic rulesproposed by Mander et al. (1999), and thosefollows the constitutive and Reinhardt (1989),for tension. FRP confined concrete modelproposed by Spoestra and Monti (1999) havebeen employed to model the effect of theconfinement introduced by the FRP wrapping.
EARTHQUAKE GROUND MOTIONTwenty Far field ground motions are used inthe analysis listed in Table 1. In this study PGAis considered as the Intensity Measure (IM) forit’s efficacy, utility and adequacy in vulnerabilityassessment. The PGA of the ground motionsrange from PGA 0.22 to PGA 0.728. In Figure2 spectral acceleration with 5% damping isshown.
CHARACTERISTICS OF DAMAGESTATEThe probability of entering a damage state aninput ground motion intensity parameter isexpressed by fragility curves. Different formsof Engineering Demand Parameter (EDPs)are used to measure the DS of the bridge
34
Int. J. Struct. & Civil Engg. Res. 2013 Md. Basir Zisan and Hafizul Alim, 2013
16 Cape Mendocino Rio Dell Overpass 22.7 0.385 43.8
17 Kocaeli, Turkey Duzce 98.2 0.312 59
18 Chi-Chi, Taiwan CHY101 32 0.353 70.65
19 Kocaeli, Turkey Arcelik 53.7 0.22 17.69
20 Chi-Chi, Taiwan TCU045 77.5 0.474 36.7
Table 1: Characteristics of Far Field Ground Motion Histories
Figure 2: Spectral Acceleration of Ground Motion
Sp
ec
tra
l A
cc
ele
rati
on
(g
)
Period (s)
35
Int. J. Struct. & Civil Engg. Res. 2013 Md. Basir Zisan and Hafizul Alim, 2013
components. Based on energy dissipationcapacity and ductility demand of structure,Park and Ang (1985) developed a damageindex while Hwang et al. (2000) used thecapacity/demand ratio of the bridge columnsas EDP to develop fragility curves. A capacitymodel to measure the damage of bridgecomponents based on prespective anddescriptive damage states in terms of EDPsHwang et al. (2000). This study on fragilityanalysis of bridge used the displacementductility as damage measure. Hwang et al.(2000) used the capacity/demand ratio as thebridge pier to develop fragility curves. Thedamage states are presented in Table 2.
ANALYTICAL FRAGILITYCURVESFragility is modelled by a lognormal cumulativedistribution function where the structuraldemand and capacity are assumed to belognormally or normally distributed. In this study,probabilistic seismic demand models are usedto derive the fragility curves. The groundmotions are scaled to selective intensity levelsand an Incremental Dynamic Analysis (IDA) isconducted at each level of the intensity. Aregression analysis is carried out to obtain themean and standard deviation for each limitstate by assuming the power law function
Damage State Slight Moderate Extensive Collapse(DS=1) (DS=2) (DS=3) (DS=3) Reference
Bridge Physical Cracking and Moderate Degradation FailingComponent Phenomenon Spalling Cracking and without Leading to
(Cornell et al., 2002), which gives a logarithmiccorrelation between median EDP and selectedIM:
EDP = a(IM)b or, ln(EDP)
= ln (a) + bln (IM) ...(1)
where, a and b are unknown coefficients whichcan be estimated from a regression analysisof the response data collected from thenonlinear time history analysis. In order tocreate sufficient data for the cloud approachincremental dynamic analysis is carried outinstead of nonlinear time history analysis. Thedispersion of the demand,
EDP| IM, conditional
upon the IM can be estimated from Equation(2) (Karthik et al., 2012).
2
=1|
ln=
- 2
N b
iEDP IM
ln EDP aIM
N... (2)
With the probability seismic demandmodels and limit states corresponding tovarious damage states, it is now possible togenerate the fragilities using Equation (3),
comp
ln ln nIM IMP LS | IM ... (3)
ln - lnln = c
n
S aIM
b... (4)
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Int. J. Struct. & Civil Engg. Res. 2013 Md. Basir Zisan and Hafizul Alim, 2013
ln(IMn) is defined as the median value of the
intensity measure for the chosen damagestate (slight, moderate, extensive, collapse),a and b are the regression coefficients of thePSDMs and the dispersion component ispresented in Equation (5) (Madas andElnashai , 1992 and Mander, 1999).
| 2c+EDP
comp
IM
b...(5)
where Sc is the median and
cis the dispersion
value for the damage states of the bridge pier.The dispersion coefficient
cis used as
describe by Karthik Ramanathan et al. (2012).
RESULT EVALUATIONPSDM of two type of bridge pier are shown inFigures 3 and 4. The impact of two differentmeasures under far field earthquake groundmotions on the demand models is comparedin Table 3.
Plots of the fragility curves for two cases areshown in Figures 5 to 8, which illustratedrelative vulnerability of the retrofitted bridgebents over a range of far field Earthquakeintensities and damage states. From figures
Figure 3: PSDM of As-Build Concrete Pier
y = 1.1464x + 1.9295
R2 = 0.8224
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
-4 -3 -2 -1 0
In (Ductility)
In (
PG
A)
y = 0.9491x + 1.2629
R2 = 0.7645
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
-4 -3 -2 -1 0
ln (PGA)
ln (D
uct
ility
)
Figure 4: PSDM of Concrete Pier Retrofitted by FRP
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Int. J. Struct. & Civil Engg. Res. 2013 Md. Basir Zisan and Hafizul Alim, 2013
00.10.20.30.40.50.60.70.80.9
1
0 0.2 0.4 0.6 0.8
PGA (g)
Pro
babi
lity
of D
amag
e
FRP
As built
00.10.20.30.40.50.60.70.80.9
1
0 0.2 0.4 0.6 0.8
PGA (g)
Prob
abili
ty o
f Dam
age
FRP
As built
00.10.20.30.40.50.60.70.80.9
1
0 0.2 0.4 0.6 0.8
PGA (g)
Prob
abili
ty o
f Dam
age
FRP
As built
Column DuctilityPier Condition
ln (a) b EDP|IM
As-built 1.15 1.92 0.43
Retrofit by FRP 0.95 1.26 0.43
Table 3: PSDM for two types of Bridge Pier
Figure 5: Fragility Curve for Slight Damage
Figure 6: Fragility Curve for Moderate Damage
Figure 7: Fragility Curve for Extensive Damage
38
Int. J. Struct. & Civil Engg. Res. 2013 Md. Basir Zisan and Hafizul Alim, 2013
00.10.20.30.40.50.60.70.80.9
1
0 0.2 0.4 0.6 0.8
PGA (g)
Prob
abili
ty o
f Dam
age
FRP
As built
it is evident that retrofitted measure by FRP iseffective for different damage states in termsof reducing the probability of the damage fora given PGA.
CONCLUSIONThis study evaluates the seismic fragility ofsingle concrete pier both in as built conditionand with retrofitting stage. To investigateseismic vulnerability of the bridge pier 20 nearfield earthquake ground motion are utilized toevaluate likelihood of exceeding the seismiccapacity of the bridge pier. The result indicatesthat the retrofitted with FRP posses lessvulnerability at all damage states under far fieldearthquake.
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Int. J. Struct. & Civil Engg. Res. 2013 Md. Basir Zisan and Hafizul Alim, 2013
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