Fragility Assessment for Seismically Retrofitted Skewed Reinforced Concrete Box Girder Bridges

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Fragility Assessment for Seismically Retrofitted Skewed Reinforced Concrete Box Girder Bridges

Behzad Zakeria, Jamie E. Padgettb, A.M.ASCE, Gholamreza Ghodrati Amiric

a Iran University of Science and Technology,PO Box 16765-163, Narmak, Tehran 16846, IRAN.

Correspondence to: Behzad Zakerti. E-mail: [email protected] bRice University, 6100 Main Street, MS-318, Houston, TX, USA 77005. E-mail: [email protected] c Iran University of Science and Technology,PO Box 16765-163, Narmak, Tehran 16846, IRAN. E-

mail: [email protected]

Abstract Skewed bridges are susceptible to seismic damage due to their complicated dynamic

responses. A range of potential retrofit strategies have been implemented to mitigate damages

in seismically deficient bridges. However, since the seismic responses of skewed bridges

often differ from straight bridges and the efficiency of each retrofit measure may vary from

one class to another, a comprehensive study with a wide range of retrofit options among

skewed bridges is needed. This paper assesses the impacts of ten different retrofit strategies

on the fragility of skewed single frame concrete box girder bridges with seat type abutments

in two common sub classes termed single and two-column bent. Fragility curves

corresponding to four damage states at both the component and system levels are developed

for various skew angles. The results show that while no single retrofit measure can solely

contribute to decreasing all component and system vulnerabilities in highly skewed bridges,

combinations of retrofit measures can be used to enhance the desirable level of skewed bridge

performance. The level of effectiveness of a retrofit option is highly dependent on bridge

class and skew angle.

Keywords: skewed bridges; retrofit; fragility; concrete box girder.

Introduction

Skewed bridges without adequate seismic detailing are often susceptible to significant

damage or collapse in comparison to straight bridges during earthquake events (Fung et al.

Journal of Performance of Constructed Facilities. Submitted January 17, 2013; accepted July 22, 2013; posted ahead of print July 24, 2013. doi:10.1061/(ASCE)CF.1943-5509.0000502

Copyright 2013 by the American Society of Civil Engineers

J. Perform. Constr. Facil.

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1971, Buckle 1994, Anderson et al. 1996, Hsu and Fu 2004, Okuyucu et al. 2011). The

inherent complexity, as well as irregularity, of skewed bridges has resulted in significant

vulnerabilities in this class of bridges. Shear and flexural failure of columns, deck unseating,

shear key failure and abutment rotation are among the most relevant failure modes in skewed

bridges (Shamsabadi et al. 2006, Schroeder 2006). According to recent research conducted

on the fragility of skewed concrete box girder bridges (Zakeri et al. 2013), pre 1971 box

girder bridges are found to be vulnerable to column damage due to limited seismic detailing,

deficiencies in bearings and shear keys and high potential of deck unseating at the abutments

particularly in two-column bridges.

Many retrofit programs have been initiated in the United States of America (USA),

particularly in West Coast states after 1971 San Fernando and 1994 Northridge earthquakes.

Various retrofit strategies have been implemented in practice and recently recommended by

different researchers based on the vulnerabilities in different components of bridge classes

(simply supported, continues, concrete or steel) (Robinson et al. 1979, Robert 1998, Priestly

and Seible 1991, Ethiopia 2003, FHWA 2006).

Since skewed bridges have unique responses and vulnerabilities as a result of coupled

longitudinal and transverse responses, it is important to identify appropriate retrofit strategies

for these classes of structures, which may differ from their straight bridge counterparts.

Seismic performance assessment of skewed simply-supported bridges retrofitted by friction

type rubber bearings was performed by Liu et al. (2008). They determined that rubber

bearings without any anchor bolts provide a fuse-like mechanism for rubber bearings to slide

on the bearing pad and therefore reduce the force demand of the columns. However, the

increase in bridge deck displacement for the case of higher skew angles results in wider deck

seat requirements. Sevgili and Cancer (2009) conducted a study on the seismic performance

of multi-span simply supported skewed bridges retrofitted by link slabs. Their results showed




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that adding link slabs can lead to a decrease in deck displacement in both the longitudinal and

transverse directions particularly in higher skew angles. Link slabs also decrease the tendency

for span separation and seismic force transfer to the substructure. Watanabe and Kawashima

(2004) compared the efficiency of three different configurations of restrainer cables for

mitigating the rotation of skewed bridge decks. One similarity of the above mentioned studies

is that they are all deterministic studies, which neglect uncertainties in the retrofit assessment,

such as those which stem from the hazard or bridge response and performance modeling.

Several studies have modeled the conditional probability of bridge damage with and

without retrofit through the development of fragility curves. Most of the studies have

developed fragility curves for non-retrofitted bridges (Shinozuka 1998, Hwang et al. 2000,

Choi et al. 2004, Mackie and Stojadinovic 2004, Nielson and DesRoches 2007) and only a

few of them have focused on retrofit. For example, Yang et al. (2009) conducted fragility

analyses for non-skew typical California box girder bridges retrofitted with steel jacketing

and elastomeric isolation bearings. Comparison of bridge fragility curves before and after

retrofit showed that even though the steel jacketing reduces the fragility slightly, the use of

elastomeric isolation bearings can lead to a significant reduction in the fragility for different

damage states. Other studies have also explored the fragility of retrofitted bridges in the

Central and Southeastern United States (CSUS) (Choi 2002, Padgett and DesRoches 2009)

and Northeastern United States (NUS) (Agrawal et al. 2011). The results suggest that the

most effective retrofit may differ by bridge type and damage state, or performance objective

of interest, but skew was not considered. In spite of such efforts to explore retrofitted bridge

performance probabilistically during earthquake events, the effect of retrofit on skewed

bridges, such as classes of box girder bridges, is needed to uncover viable retrofit options to

mitigate the adverse effects of both deficient seismic detailing and complex dynamic

behavior from skew considering uncertainty in the performance assessment.




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In order to provide new insight on the influence of retrofit on the performance of skewed

bridges, this paper explores the effects of various common retrofit measures such as steel

jacketing, restrainer cables, shear keys, seat extenders and combinations of these measures on

the fragility of single and two-column skewed box girder bridges at both the component and

bridge system levels.

Overview of fragility methodology, bridge class and retrofits

Seismic fragility methodology for retrofitted bridges

Fragility curves for retrofitted bridges offer a means of comparing the influence of various

retrofit strategies on the potential damage, and are conditional probabilistic statements of

damage that depend on the intensity of the ground motion (Padgett and DesRoches 2008).

Only an overview of the fragility methodology is presented here since the detailed approach

can be found elsewhere (Padgett and DesRoches 2008). According to the basic definition of a

fragility, as presented in Equation 1, the probability of the seismic demand (D) exceeding the

capacity (C) is assessed for given a level of hazard intensity measure (IM).

|fP P D C IM

(1)

This basic formulation of the reliability assessment indicates the need to estimate both the

seismic demand and the capacity to develop fragility curves for different retrofitted bridges.

The fragility is evaluated at both the bridge component and system levels, in order to evaluate

the effect of different retrofit strategies on the fragility of skewed bridges.

In this study, peak component responses from time history analyses of bridges under

seismic shaking are monitored along with a ground motion intensity measure, selected as

peak ground acceleration (PGA), since it has been found to be an effective predictor of the

demand of the bridge portfolios, while limiting the uncertainty introduced in the model,

among other ideal characteristics (Padgett et al. 2008). Following the demand model




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proposed by Cornell et al. (2002), the median value of the seismic demand placed on a given

component (SD) can be represented by a power model, which can be lognormally transformed

in the form of:

ln ln ln DS a b IM

(2)

Where the parameters a and b are estimated from a regression analysis. The conditional

seismic demands are modeled using a lognormal distribution as shown in Equation 3:

ln lnP D d|IM 1 Φ D

D

d S

(3)

where Φ( ) ) is the standard normal cumulative distribution function, SD is the median value

of the seismic demand (Equation 2) and ßD is the lognormal standard deviation (dispersion)

of the demand, which is also estimated from the regression analysis.

The estimation of the limit state capacities associated with damage states for different

bridge components (DC) and the bridge system (DS) are developed based on HAZUS-MH

(FEMA 2005) damage states descriptions for slight, moderate, extensive and complete

damage. The limit state capacity models adopted for the as-built and retrofitted components

are shown in Table 2, where Sc is the median value and βC is the dispersion of the

lognormally distributed capacity. Box girder bridge columns in their as-built condition are

assumed to have strength degrading behavior and their related limit states in terms of

displacement ductility are adopted as 1.0, 1.2, 1.76 and 3 according to Hwang et al. (2000)

and the Seismic Retrofitting Manual for Highway Bridges (FHWA 2006). Passive and

transverse limit states of the abutments are taken as a function of ultimate displacement of

soil on the back bone curve. Complete damage is related to ultimate deformation of the soil

while slight through extensive damages are defined as half of the first yield point, the first




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yield point and the second yield point of the soil back bone curve, respectively according to

Choi (2002). As built elastomeric bearings limit states are taken as 100%, 150%, 200% and

300% (Zakeri et al. 2013, Padgett 2007) of shear strain since they are assumed to be dictated

by shear in all damage states. Limit states of the shear keys are identified according to the

mechanical model proposed by Megally et al. (2001). Shear key limit states are taken as

a function of the displacements corresponding to first yield of the shear key backbone

curve, which is defined as the slight damage. Moderate through complete limit states are

assumed as the second yield point, half of the third yield point and the third yield point of

shear key backbone curve respectively

Regarding retrofitted components, limit state capacities for steel jacketed columns are

developed based on experimental studies on steel jacketed circular columns conducted by

Chai et al. (1991) and Priestley et al. (1994a, 1994b). The limit states are taken as 3.1, 5.2,

7.2 and 8.3 for the slight through complete damage states in terms of displacement ductility.

Increasing the shear key capacity and strength, up to 75% of ultimate shear capacity of the

abutment piles (Aviram et al. 2008), is one of the retrofit measures included in this study

(Zakeri et al. 2013). The limit states for retrofitted shear keys are derived based upon yield

points of the shear key backbone curve--similar to the as-built shear keys; however, their

capacities are increased to 75% of shear capacity of the abutment piles. It should be noted

that, the yield points of the shear key backbone curves vary by changing the capacity of the

shear key, the number of piles and the strength of materials. The seat extender retrofit

provides an additional 200 mm of seat width resulting in an assumed median seat width of

600 mm. The logarithmic standard deviations of component capacity, βC, of 0.25 and 0.46 for

lower and higher damage states, respectively are defined in this study according to Nielson

(2005).




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Given lognormal demand and capacity models, fragility curves for meeting or

exceeding each component damage level j follow the typical closed form:

ln ln lnP |

2 2

IM S a bCjDCj IM

bD Cj

(4)

where the median value of demand, SD, was substituted with Equation 2 prior to

rearrangement and thus a and b are the parameters of the demand model; SCj is the median

value of the capacity at component damage level j, βCj is the logarithmic standard deviation

for the capacity at level j, from the regression analysis, and IM is the intensity measure that

the exceedance probability is conditioned upon.

The system is considered as a series system given the damage state descriptions from

HAZUS that indicate the system damage level assignment in the event that any of the

relevant component damages occur. In this study bridge components are classified into

primary and secondary components based upon the components’ importance in bridge

stability under traffic or subsequent seismic event. Only the primary components, such as the

columns or deck that has reached its unseating limit state, are assumed to contribute to the

complete damage state of the bridge system (DS4). Since the loss of primary components

affects the bridge load carrying capacity and overall bridge stability, the limit states of

primary components map directly to the bridge system limit states. On the other hand the

secondary components such as shear keys, bearings and abutments, whose complete failure

will not have a similar consequence as that of the primary components, are assumed to

contribute only to the earlier system damage states (DS1, DS2, DS3 for slight, moderate and

extensive). In order to distinguish between component and system limit states, the four

damage levels for the bridge system and corresponding descriptions of component level




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damage assigned to each system damage state are presented in Table 1. Therefore the system

fragility for damage state j is evaluated as:

_1

_ sec _ 11 1

| for j 4

[ | ]

| | for j 3

N

primary i ji

j N M

primary i j ondary m ji m

P E DC IM

P DS IM

P E DC IM P E DC IM

E DCprimary iE DCprimary iE DC_primary i_

| |E DC | |||||1primary sec |1E DC |primary i j | secsecE DC | |1secse ||_ sec _ 1 |1primary _ sec __sec

(5)

where N indicates the total number of primary components and M is the total number of

secondary components. A Monte Carlo simulation is conducted to compare the capacity and

demand models with component correlations to assess failure probability at each PGA

interval based on Equation 5. Lognormal distributions of the bridge system fragility are then

estimated by the expression:

ln lnP | sys

sys

PGA medDS PGA

(6)

where medsys is the median value of the system fragility (PGA in units of g) and ζsys is the

dispersion, or logarithmic standard deviation, of the system fragility.

Description of case study skewed bridge class for retrofitting study

This study considers skewed pre-1971 two span prestressed concrete box girder bridges with

seat type abutments due to their commonality in California and significant deficiencies in

various components at the system level. Two separate sub classes termed single column and

two-column bridges are defined based on their unique base boundary conditions. According

to typical Caltrans design and modeling practice, the two-column bridges are considered to

have a pin connection between the columns and their foundation bent cap while single

column bridges enable moment transfer. The columns and deck are monolithic in most of the




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bridges belonging to this bridge class. The seat type abutment with expansion joins between

the deck and the back wall render them susceptible to pounding. The foundation systems at

the bents and abutments, include pile supported footings consisting of precast (reinforced or

prestressed concrete), driven or CIDH piles (Ramanathan 2012). The number of piles varies

by changing the bridge geometry based upon a review of bridge plans as well as personal

communication with Caltrans design engineers conducted by Ramanathan (2012). For each

bridge class, a Latin-hypercube sampling (LHS) technique (Ayyub and Lai 1989) is adopted

to sample ten representative geometries of bridges constructed prior to 1971 from the

National Bridge Inventory (NBI 2010) database in order to capture geometric variability such

as span length, deck width and column height. In order to develop bridge samples in such a

way that the samples are consistent with real word projects, design details based on a

thorough bridge plan review in California as reported in Ramanathan (2012) are implemented

in finite element models. The geometric configurations for each bridge class can be found in

Table 3 and Table 4. Four different skew angles (0°, 15°, 30° and 45°) are selected to explore

the effect of skewness on the performance of retrofitted bridges.

Description of the retrofits to address vulnerability of skewed bridges

The ten retrofit strategies implemented in this study are based on common retrofit practice

in the US including past reviews of seismic retrofit in the West Coast (Robinson et al. 1979,

Robert 1998, Priestly and Seible 1991, Ethiopia 2003, FHWA 2006) as well as recent trends

in the Central and Southeastern United States (CSUS) (Padgett and DesRoches 2009, Wright

et al. 2011). The retrofit strategies which are comprised of individual retrofits or their

combinations are listed in Table 5. For each retrofit measure, a basic design approach is

adopted, as well as uncertainties in modeling and performance assessment. Since most of the

columns in pre-1971 bridges have limited seismic detailing (Caltrans 2007), the full height

circular column jackets are considered in this study as a common retrofit practice for




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columns with flexural, shear or lap splice deficiencies. Steel restrainer cables placed at the

abutments are evaluated to limit deck displacements to mitigate unseating. The large deck

displacements coupled with lack of sufficient resistance to transverse movements,

particularly in skewed bridges, increase deck shifting or unseating as well as the demand on

other components. Therefore shear keys are considered in the transverse direction, and are

designed to limit the force transferred to the abutment to approximately 75% of the

transverse capacity of the piles at the abutments (Aviram et al. 2008). To avoid deck

unseating and collapse of the bridge spans, which are high potential threats in the skewed

bridges with significant deck rotation tendency, the seat extenders are assumed to provide

additional 200 mm length of support for the bridge decks at the abutments.

Retrofitted bridge analytical models, bridge sampling and simulations

Analytical modeling approaches for as-built and retrofitted skewed bridges

Three-dimensional nonlinear finite element models are developed in OpenSees (McKenna et

al. 2010) for use in the fragility analyses. The deck is modeled with linear beam-column

elements (the superstructure is assumed to remain elastic during seismic excitations).

Translational and rotational mass moments of inertia of are assigned as lumped masses to

bridge deck nodes in the finite element model. These nodes are placed along the longitudinal

bridge centerline and also transverse to the centerline to capture the response of skewed

bridges, in contrast to the commonly adopted spline models. Discretized fiber sections are

defined for the columns with unique models assigned to the concrete and steel fibers. The

reinforcing steel of longitudinal bars is modeled using the Steel 02 material provided by

OpenSees to include isotropic strain hardening which uses the Menegotto and Pinto model

(1973) later modified by Filippou et al. (1983). Reinforced concrete behavior is modeled

using Concrete 07 provided by OpenSees. This material used the Chang and Mander’s model

(1994) to define the monotonic stress strain curves for confined and unconfined concrete.




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Abutment passive soil pressure is modeled with a hyperbolic backbone curve using the

model recommended by Shamsabadi et al. (2010). In the transverse direction the same

passive model is used by altering the backbone curve to include the wing walls based on the

length and the wing wall participation factors (Aviram et al. 2008). Piles at the abutments or

foundation of the columns are modeled with tri-linear springs according to Choi (2002).

External shear keys which are the most relevant types of shear keys in the box girder bridges

are modeled following the recommendations of Megally et al. (2001). Pounding between the

abutment and the deck is a critical phenomenon in skewed bridges and is captured using a

multi-linear element normal to the face of the deck according to Muthukumar and DesRoches

(2006). Elastomeric bearings are assumed as elastic perfectly plastic elements whose

behavior is dominated by shear. It is assumed that the bearings reach their ultimate capacity

before sliding due to their low shear capacity and deterioration expected during long ages

(Zakeri et al. 2013). The bearing slides if the force transferred by the deck is more than the

normal force. It should be noted that in addition to relying upon the recommendations of past

researchers, including models derived based on experimental test data, the above analytical

bridge modeling approach was also validated using field data. Specifically the results of

NLTHA were compared with recorded sensor data from seismic excitation of a skewed

bridge (Painter Street Overpass located on Highway 101 in Rio Dell, California). Further

details of the deterministic model validation are reported elsewhere for comparison with

curved and straight bridges (Ramanathan et al., in review).

Although the properties of the retrofit measures change for each bridge sample and

analytical model due to the variation of the bridge geometry and uncertainties in the

realization of the retrofit measure properties, a common modeling strategy is adopted for each

retrofit measure. Steel jackets are modeled by altering the fiber section of the concrete

column. The compressive strength and ultimate strain of the un-confined concrete of the




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cover and low confinement concrete of the core are improved due to confinement caused by

the jacketing. The compressive strength of the concrete was estimated from Chai et al. (1991)

as presented in following equations.

' '' '

' '

7.94 2 2.254 1 1.254

f l f lf cc f c

f c f c (7)

' 2 j yj

j j

t ff l

D t

(8)

In these models, tj (meter) is the jacket thickness, Dj (meter) is the column diameter after

jacketing and fyj (MPa) is the yield strength of jacket. Defining the thickness of jacket based

on the flexural performance of the column requires a trial and error or iterative process,

which is impractical for this study due to the number of samples. The Seismic Retrofitting

Manual for Highway Bridges (FHWA 2006) presents a conservative solution to calculate the

jacket thickness based on the performance of lap splices, which inherently also satisfies the

requirements for improved flexural performance. In many old bridges, the lack of ductility in

the columns is not only related to flexural capacity but also can be as a result of insufficient

lap splices performance (Caltrans 2007); therefore the steel jacket thicknesses should be

accompanied by improving both the flexural and splice performances. The corresponding

conservative estimation of the jacket thickness following the FHWA Seismic Retrofitting

Manual is given by:

400l

j

ft

(9)

This equation can be simplified by considering that fl is approximately equal to 2.07 MPa, as

considered in the development of this method (Chai et al. 1991), providing satisfactory

performance where volumetric ratios of longitudinal reinforcement are less than 2.5% and




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axial load, P, less than 0.15f’cAg. All bridge samples in this study are assumed to have 1.5%

longitudinal reinforcement and the axial load ratios in columns are less than 0.15. The

ultimate strain of concrete after jacketing is taken as:

'

5.60.004 yj su

cuj cc

f

D fj su0.004cu 0.004 (10)

where susu can be taken as 0.1 for A36 steel.

Restrainer cables are considered to be 19 mm diameter cables with an effective area of 143

mm2 and a length between 1.5 m and 6.1 m (Saiidi et al. 2001, Padgett 2007). The elastic

modulus of the cables is E= 69000 MPa and the yield force is Fy=174 kN. The cables are

modeled as tension only elements with an initial slack that may vary between 0 mm and 19

mm (Padgett 2007). The restrainer cables are designed to carry half of the weight, w, of

superstructure as a simplified design adopted to promote life safety and collapse prevention

(Padgett 2007). According to the FHWA Seismic Retrofitting Manual, restrainer cables

should be installed normal to the deck and the design force of cables in skewed bridges is

2 cos( )

w

, where θ is the skew angle of the bridge.

Pre-1971 bridges have low strength shear keys which are not qualified to control the deck

transverse and rotational deformations during seismic excitations (Caltrans 2007). As

mentioned above, as-built abutment shear keys experience significant damage before they can

control the deck displacement during earthquakes due to their insufficient capacity (Zakeri et

al. 2013). Increasing the shear key capacity up to 75% of the pile capacity (Aviram et al.

2008) at the abutments is implemented in this study as a retrofit measure. The enhanced

higher capacity shear keys considered as retrofits are also modeled according to test results

and suggestions of Megally et al. (2001). The only effect of the seat extenders is to increase




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the limit state capacity for deck unseating; however, they do not require any specific

analytical modeling. The analytical model associated with each retrofit is shown in Figure1.

Uncertainties treatment in bridges and retrofit measures

A total of 100 statistical bridge samples of each class of as-built and retrofitted bridges are

developed and paired with 100 ground motions for the fragility analysis. In order to account

for the uncertainties related to bridge modeling such as variations in material and component

properties in both the non-retrofitted and retrofitted bridges, a Quasi-Monte Carlo sampling

strategy (Morokoff and Caflisch 1995) is used. The modeling parameters for the retrofitted

skewed bridges vary due to uncertainties in material and component modeling, and also differ

due to geometric variation considered in the bridge class. Thus the probabilistic analysis

conducted herein considers the different sources of uncertainty such as ground motion

characteristics, bridge modeling parameters (e.g. concrete strength, soil or pile stiffness, yield

strength of steel jackets), or geometric parameters. Those uncertainties which are common in

as-built bridges can be found in Table 6.

The introduction of the retrofit measures themselves also introduces additional material

and modeling uncertainties. Retrofitted random variables and their related probabilistic

models are presented in Table 7. In steel jacketed columns, the jacket yield strength with

lognormal distribution (Hess et al. 2002, Galambos and Ravindra 1978), the gap between

steel shell and column with uniform distribution and the increase the amount of stiffness of

the column due to jacketing with uniform distribution are assumed as random variables

(Priestley et al. 1996). For the restrainer cables, the random variables include the cable slack

(Saiidi et al. 1996), the yield stress of the cables (Caltrans 1997 and Hess et al. 2002) and the

cable length (Saiidi et al. 1996 and Padgett 2007). The yield strength of reinforcements with

lognormal distribution (Ellingwood and Hwang 1985) and the concrete strength with normal

distribution (Choi 2002) are defined as uncertainties in the shear key modeling.




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Ground motion records and characteristics

In order to construct probabilistic seismic demand models, the results of nonlinear time

history analysis with four bins of twenty typical non-near fault records identified by

Krawinkler et al. (2003) from the PEER Strong Motion Database and one bin of 20 near fault

California records from the SAC project data base are used. The scope of this study is limited

to studying the effect of horizontal ground motion (dominant components for the majority of

the ground motions adopted which are primarily non-near fault) and the vertical component

of earthquake is not considered. In order to adequately capture aleatoric randomness for

bridge fragility analysis, a total of 100 ground motions are adopted to exceed the

recommended minimum range of ground motions suggested by Nielson and Mackie (2009).

The peak ground accelerations (geometric mean of two horizontal components) in the first 80

ground motions varies from 0.032 g to 0.449 g, while for the SAC motions, the peak ground

accelerations (geometric mean of two horizontal components) vary from 0.265 g to 1.087 g.

Each set of orthogonal ground motions is randomly paired with a bridge sample producing a

total of 100 nonlinear dynamic analyses for each skewed and retrofitted bridge sub class.

Component and system assessment of retrofitted skewed bridge through fragility

analysis

Component fragility pre- and post-retrofit

To evaluate the effectiveness of different retrofit strategies on skewed bridges and

potential reasons for system impacts, the fragility curves of critical components before and

after retrofit are developed. Figure 2 shows the impact of retrofit on the moderate damage

state of the column, shear key, transverse bearing and abutment components in the skewed

two-column bridge sub class relative to the as-built bridge class with a 45° skew angle. Seven

of the ten retrofit strategies are shown--the remaining three retrofit strategies with seat

extenders are not shown since they are only effective in the complete damage state.




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Combinations of retrofit measures are used only for highly skewed bridges (skew angle no

less than 30°). The results in terms of effects of retrofit on the fragility of components in two-

column bridges are similar for single column bridges. It can be concluded from Figure 2a that

the use of steel jackets as a retrofit measure significantly reduces the column vulnerability,

while it has no considerable impact on the fragility of any other component. Since the

vulnerability of skewed box girder bridges is dominated by the columns, steel jacketing can

be an ideal selection for a retrofit measure. Restrainer cables on one hand decrease the shear

key and bearing vulnerability (see Figures 2b and 2c) but on the other hand increase abutment

fragility in the transverse and active directions due to additional force transfer to the abutment

as a result of restrainer engagement in tension and rotation of the skewed bridge deck (Figure

2d). Shear keys are important components in bridges, particularly in skewed ones, to control

the transverse displacement of deck during seismic excitations. Adding or increasing the

capacity of existing shear keys at the abutment can decrease the bearing, shear key and

abutment passive vulnerability, yet considerably increase abutment vulnerabilities in the

active and transverse directions as a result of the additional force transfer to the abutments.

Since highly skewed bridges are much more vulnerable than straight bridges,

combinations of retrofit measures are also considered to enhance their effectiveness in

improving bridge fragility at least up to equivalent performance of a non-skewed bridge

retrofitted by single retrofit measure. As shown in Figure 2, although jacketing does not have

any effect on the vulnerability of other components, the combination of this retrofit measure

with shear keys or restrainer cables leads to a considerable decrease in bearing and shear key

as well as column fragilities. In spite of the notable decrease in the bearing and shear key

vulnerability using a combination of restrainers and high capacity shear keys, this retrofit

strategy cannot decrease the column fragility in a considerable way. However, adding steel




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jacketing to the combination of restrainer and shear key (SJ+RC+SK) results in effective

improvement in various component vulnerabilities.

System level fragility curves of retrofitted bridges in various skew angles

To assess the effectiveness of each retrofit strategy on the overall seismic performance of

skewed bridge systems, a comparison of median PGA values (the PGA corresponding to 50%

probability of meeting or exceeding a particular damage state) for single column bridges with

various retrofit strategies is also illustrated in Figure 3 for different skew angles. It should be

noted that the PGA depicted is the geometric mean of the PGA in both the longitudinal and

transverse directions (longitudinal direction is considered to be along the length of the bridge

where traffic flows while transverse is in the perpendicular direction). As mentioned in the

previous section, combinations of retrofit measures are included for highly skewed bridges

(skew angle no less than 30°) in order to evaluate their effectiveness on decreasing bridge

fragility up to a non-skewed bridge retrofitted by single retrofit measure (e.g. steel jacketing).

Since columns dominate the bridge fragility in this class of bridges due to significant

curvature ductility demands, the use of steel jacketing leads to a significant increase in the

median value of bridge system fragility (decrease in bridge vulnerability). This result is

consistent with Chai et al. (1991) findings on six large-scale columns tests. According to their

findings, steel jackets increase the column ductility considerably and inhibit bond failures in

lap splices. This study suggests that such impacts are critical in affecting the system level

fragility of skewed bridges. Also, due to initial slack and transferring inertia forces

throughout the bridge (Saiidi et al. 2001), the cable restrainers are not alone effective in this

class of bridge. Experimental tests of shear keys conducted by Megally et al. (2001) have

revealed that accurate design of sacrificial shear keys results in deck unseating prevention as

well as avoiding additional inertial forces transfer to substructure components. In this study,




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shear keys, which are fuse-like components to control deck transverse displacements, also

improve the fragility of the bridge system, particularly for the higher damage states.

It is evident from the figures that although some retrofit measures such as steel jacketing

can decrease bridge vulnerability, the skew angle still has significant effect on increasing

bridge fragility in these retrofitted bridges. Practical bridge retrofit decision-making for a

highly skewed bridge necessitates a retrofit strategy that can decrease bridge vulnerability up

to a non-skewed bridge retrofitted with single retrofit measure. However, the combinations of

retrofit measures are included for highly skewed. Figures 3 shows that the combination of

restrainer cable and shear key is not an ideal retrofit strategy since it does not have a

considerable effect on decreasing the ductility demand of vulnerable columns. The

combination of steel jackets with shear keys can be a desirable retrofit measure for highly

skewed bridges by increasing the median value of the fragility for all damage states. This

combination reduces the vulnerability of the skewed bridge system to a level on part with the

fragility of an equivalent straight bridge. Although the combination of restrainer cables and

steel jacketing can be effective, this strategy only has a significant impact on the system

fragility in the moderate and extensive damage states. The combination of shear keys, steel

jacketing and restrainer cables (SK+SJ+RC) is more effective in shifting the fragility than the

other retrofit strategies when the skew angle is high, particularly for the moderate and

extensive damage states. The effect of seat extenders can be found in the complete damage

state due to the considerable increase in the unseating capacity limit (200 mm additional seat

width). Since the combination of shear keys and steel jackets is already an effective retrofit

strategy for decreasing the fragility of highly skewed bridges, the combination of this set of

retrofit measures with seat extenders (SK+SJ+SE) becomes the most effective retrofit

strategy in avoiding the complete damage state.




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A comparison of the median PGA values for this class of bridge and various retrofit

strategies in different skew angles is shown in Figure 4 for all damage states. As a single

retrofit measure, steel jacketing has significant effect on shifting the bridge fragility,

particularly in lower skewed (not more than 30°) two-column bridges. Although restrainer

cables have the least impact at the lower damage states as a result of initial slack which

postpones restrainer engagement leading to damage in low capacity components (e.g.

columns, bearings or shear keys), in higher damage states cable restrainers become more

effective particularly for bridges with higher skew angles. The effects of restrainers in higher

skew angles are much more significant because they decrease longitudinal displacements of

the bridge as well as transverse displacements; therefore components in both directions

experience lower demands. Converse to single column bridges, Figure 4 shows that the

combination of restrainer cables and steel jacketing is more effective than the combination of

shear keys and steel jackets in all damage states. Since two-column bridges are prone to have

higher displacement in both longitudinal and transverse directions because of the pin

connection between bottom of column and pile cap, the restrainer cables become more

effective in this sub class of bridges. It can be concluded from the figures that the most

effective retrofit measure in higher skew angles for all damage states is the combination of

shear keys, steel jacketing and restrainer cables (SK+SJ+RC) which can reduce the column,

bearing and shear key vulnerabilities simultaneously. The least effective combination of

retrofit measures for highly skewed two-column bridges is the combination of shear keys and

restrainers, particularly in the lower damage states.

Overall, although the least effective retrofit strategy is similar in highly skewed single and

two-column bridges, the most effective retrofit strategy is different in two sub classes of

bridges. It also can be concluded from Figure 3 and Figure 4 that the retrofit strategies are

more effective in shifting the fragility of the as-built bridge in single column bridges than the




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two-column bridges. This result is attributed in difference to the column bottom boundary

conditions and dynamic responses in two bridge sub classes which results in the as-built two-

column bridge sub class having more initial vulnerability. The effectiveness of retrofit

strategies varies depending upon the damage state of interest. The results show that choosing

an appropriate retrofit measure for a bridge, depends on the bridge class and performance

objective of the bridge.

Conclusions

This paper develops fragility curves for different retrofit strategies for two single frame

concrete box girder bridge sub classes typical in California named single and two-column

bridges. Emphasis is placed on uncovering the effectiveness of each retrofit strategy for

skewed bridges by assessing the fragility of multiple components as well as the bridge

system. The results have shown that although retrofit strategies tend to be targeted at

individual component fragility, other components might be affected indirectly in either a

positive or a negative way. It is found that while individual retrofit measures do not provide a

significant improvement in the bridge fragility, particularly for vulnerable highly skewed

bridges, combinations of retrofit measures can result in considerable improvements in

performance. Comparison of the fragility of bridges in different skew angles has revealed that

the most effective retrofit strategy for a straight bridge might not always be the most effective

retrofit strategy for a highly skewed bridge, due to the complex dynamic response of skewed

bridges. Since columns in pre-1971 concrete box girder bridges are the most vulnerable

components for the skewed bridges, steel jacketing can be an ideal selection for a retrofit

measure in low skew (less than 30°) bridges. By combining steel jacketing with shear keys

and restrainer cables, the system fragility further improves by mitigating the damage induced

by longitudinal and transverse deck displacements common in skewed bridges. Overall, the

results show that the impact of skew in worsening the seismic performance may be more




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significant than the effect of a single retrofit measure in improving bridge performance for

highly skewed bridges. In such cases, a combination of retrofits particularly including steel

jacketing can overcome the impact of skew and improve the performance of highly skewed

bridges to a level that is even less vulnerable than straight bridges retrofitted with a single

retrofit measure. The findings from this study suggest viable retrofit options for this class of

bridges and can form the basis for detailed cost-benefit analysis of seismic retrofits selected

in practice. Additional future research opportunities include the need to consider the effect of

the vertical component of earthquakes on the fragility of bridges and selection of retrofits.

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Concrete Bridge Columns for Enhanced Shear Strength-Part 2: Test Results and Comparison with

Theory.” ACI Structural Journal, 91(5), 537–551.

Priestley M. J. N., Seible F., and Calvi G. M. (1996). Seismic Design and Retrofit of Bridges. John Wiley

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Ramanathan, N.K. (2012), “Next generation seismic fragility curves for California bridges incorporating




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the evolution in seismic design philosophy,” Ph.D. thesis, Georgia Institute of Technology, Atlanta.

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Shantz T. and Roblee C. (2011), “Estimates of foundation springs, piles capacities and uncertainties for

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Watanabe G. and Kawashima K. (2004),“Effectiveness of cable-restrainers for mitigating rotation of a

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and without Protective Systems,” Proceedings of the 2009 Structures Congress, Austin, TX, April.

Wright T, DesRoches R. and Padgett J.E. (2011), “Bridge seismic retrofitting practices in the central and

southeastern United States,” Journal of Bridge Engineering; 16(1): 82-92.DOI: 10.1061/ (ASCE)

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Zakeri B., Padgett J.E. and Ghodrati Amiri G. (2013), “Fragility analysis of skewed single frame concrete

box girder bridges,” Journal of Perform. Constr. Facil. DOI: 10.1061/(ASCE)CF.1943-5509.0000435.

Figure captions list:

Figure.1. Analytical models for retrofitted components.

Figure 2. Comparison of the effectiveness of different retrofit strategies on component vulnerabilities

(column, shear key, abutment and bearing transverse) at the moderate damage state in 45° skew angle-

Two-column bridges.

Figure 3.Comparison of median value of fragility for various retrofit strategies in different skew

angles at the various damage states-Single column bridges.




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Note 1: The SK+SE, SJ+SE and SK+SJ+SE retrofit strategies are just compared in complete damage

while they are only effective in this specified damage state.

Note 2: Combination of retrofit measures are only used for bridges with skew angle more than 15°.

Figure 4. Comparison of median value of the fragility for various retrofit strategies in different skew

angles at all four damage states for two-column bridges

Note 1: The SK+SE, SJ+SE and SK+SJ+SE retrofit strategies are just compared in complete damage

while they are only effective in this specified damage state.

Note 2: Combination of retrofit measures are only used for bridges with skew angle more than 15°.

Table 1. Component damage states mapping and bridge system level damage states definitions along with

component damage states consistent with HAZUS-MH (FEMA 2005) qualitative damage states.

Limit States

Component Level Limit States

System Level

Limit States Primary

Components

Secondary

Components

Slight DC1 DC2 DS1

Moderate DC2 DC3 DS2



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Table 2: Component limit state capacities in their as-built and retrofitted conditions

Extensive DC3 DC4 DS3

Complete DC4 NA DS4



Accepted Manuscript Not Copyedited


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Component DC1 DC2 DC3 DC4

Sc βc Sc βc Sc βc Sc βc

Column As-built (μΔ) 1.0 0.25 1.2 0.466 1.76 0.46 3.0 0.25

Steel jacketed (μΔ) 3.1 0.25 5.2 0.25 7.2 0.46 8.3 0.46

Abut-p† (mm) 0.05×ymax§ 0.25 0.1× ymax 0.25 0.35× ymax 0.46 1.0× ymax 0.46

Abut-a† (mm) 18.1 0.25 36.3 0.25 108.8 0.46 217.6 0.46

Abut-t† (mm) 0.05× ymax 0.25 0.1× ymax 0.25 0.35× ymax 0.46 1.0× ymax 0.46

Brg-Long† (mm) 37.5 0.25 56.2 0.25 75.0 0.46 93.7 0.46

Brg-Trans† (mm) 37.5 0.25 56.2 0.25 75.0 0.46 93.7 0.46

Shear key As-built (mm) 1.0×dy

# 0.25 7.0× dy 0.25 14.0× dy 0.46 22.0× dy 0.46

Retrofitted (mm) 1.0×dy# 0.25 8.0× dy 0.25 17.0× dy 0.46 29.0× dy 0.46

Seat

width

As-built (mm) N/A N/A N/A N/A N/A N/A 400 0.46

Seat extender

(mm)

N/A N/A N/A N/A N/A N/A 600 0.46

† Abut-p = Abutment passive deformation, Abut-a= Abutment active deformation, Abut-t= Abutment transverse

deformation, Brg-Long= Elastomeric bearing deformation in the longitudinal direction, Brg-Trans= Elastomeric bearing

deformation in the transverse direction.

§ ymax= Maximum soil displacement capacity.

# dy= Shear key displacement corresponding to yield point in backbone curve of shear key.

Table 3: Geometric configuration for ten samples of single column bridges





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Table 4: Geometric configuration for ten samples of two-column bridges

Bridge no. Spans Span length (m) Deck width (m) Column height (m)

1 2 27.60 10.80 5.78

2 2 22.96 14.52 8.40

3 2 41.99 10.40 10.20

4 2 60.18 13.70 6.56

5 2 44.11 12.80 4.39

6 2 41.00 8.00 4.50

7 2 16.78 12.10 6.29

8 2 43.27 13.00 9.36

9 2 29.99 12.30 10.80

10 2 29.32 9.60 4.11





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Table 5: Retrofit strategies and their abbreviations

Bridge no. Spans Span length (m) Deck width (m) Column height (m)

1 2 34.42 12.90 6.14

2 2 62.68 10.40 12.59

3 2 49.41 21.00 8.98

4 2 26.02 18.10 6.03

5 2 19.11 9.10 11.42

6 2 42.62 11.60 6.83

7 2 13.97 20.30 4.21

8 2 30.66 16.20 5.47

9 2 51.67 12.20 4.88

10 2 39.57 13.10 4.27





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Retrofit Strategy Abbreviation

Steel jacketing SJ

Restrainer cables RC

Shear key SK

Restrainer cable and shear key RC+SK

Restrainer cable and steel jacketing RC+SJ

Steel jacketing and shear key SJ+SK

Restrainer cable, steel jacketing and shear key RC+SJ+SK

Shear key and seat extender SK+SE

Steel jacketing and seat extender SJ+SE

Steel jacketing, shear key and seat extender SJ+SK+SE

Table 6: Random variables and distributions incorporated in the as-built bridge models





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Modeling

parameter

Probability

distribution

Distribution parameters Units Reference

1 2

Steel yield strength Lognormal λ = 6.13 ζ = 0.08 MPa Ellingwood and

Hwang (1985)

Concrete unconfined

strength Normal μ = 33.8 σ = 4.3 MPa Chio (2002)

Elastomeric bearing

shear modulus Uniform l = 0.66 u = 2.07 MPa AASHTO (1998)

Coefficient of

friction Lognormal λ = -0.92 ζ = 0.1

Mander et al.

(1996) and Dutta

(1999)

Piles translational

stiffness Lognormal λ = 1.94 ζ = 0.3 kN/mm/pile Shantz and

Roblee (2011) Piles axial stiffness Lognormal λ = 6.09 ζ = 0.3 kN/mm/pile

Abutment passive

initial stiffness Uniform l = 14.5 u = 29 kN/mm/m

Shamsabadi et al.

(2010)

Damping Normal μ = 0.045 σ =

0.0125

Fang et al. (1999)

and Bavirisetly et

al. (2000).

Abutment gap Normal μ = 40.2 σ = 19 mm Based upon

inventory review

Mass Uniform l = 0.9 u = 1.1 Nielson (2005)

Loading direction Uniform l = 0 u = 2π radians

Table 7: Random variables and distributions associated with the bridge retrofits



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Modeling parameter Probability

distribution

Distribution parameters Units Reference

1 2

Steel jacket yield strength Lognormal λ = 5.6 ζ = 0.078 MPa

Hess et al. (2002)

and Galambos and

Ravindra (1978)

Steel jacket gap Uniform l = 12.7 u = 25.4 mm Priestley et al.

(1996)

Additional column stiffness

duo to jacketing Uniform l = 20 u = 40 %

Priestley et al.

(1996)

Restrainer cable slack Uniform l = 0 u = 19 mm Saiidi et al. (1996)

Restrainer cable length Uniform l = 1.5 u = 6.1 m Saiidi et al. (1996)

and Padgett (2007)

Restrainer cable yield

strength Lognormal λ = 7.1 ζ = 0.1 MPa

Caltrans (1997)

and Hess et al.

(2002)

Shear key steel yield strength Lognormal λ = 6.13 ζ = 0.08 MPa Ellingwood and

Hwang (1985)

Shear key concrete

unconfined strength Normal μ = 33.8 σ = 4.3 MPa Chio (2002)

Note: λ, μ are mean and ζ, σ are dispersion values in lognormal and normal distributions respectively. l, u are

lower and upper limits in uniform distributions.





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0 0.25 0.5 0.75 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

PGA (g)

P[M

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ate|P

GA

]

Two−column bridges− Column− 45°

ABSJRCSKRC+SKSJ+RCSK+SJSK+SJ+RC





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0 0.25 0.5 0.75 10

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0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

PGA (g)

P[M

oder

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GA

]

Two−column bridges− Shear key− 45°






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0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

PGA (g)

P[M

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GA

]

Two−column bridges− Abutment Transverse− 45°






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0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

PGA (g)

P[M

oder

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GA

]

Two−column bridges− Bearing Transverse− 45°

ABSJRCSKSK+RCRC+SJSK+SJSK+SJ+RC





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0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

AB SJ RC SKRC+SK

RC+SJSK+SJ

SK+SJ+RC

Med

ian

PGA

(g)

Single column bridges−Slight damage

0°15°30°45°





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0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

AB SJ RC SKRC+SK

RC+SJSK+SJ

SK+SJ+RC

Med

ian

PGA

(g)

Single column bridges−Moderate damage

0°15°30°45°





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0

0.5

1

1.5

2

2.5

AB SJ RC SKRC+SK

RC+SJSK+SJ

SK+SJ+RC

Med

ian

PGA

(g)

Single column bridges−Extensive damage

0°15°30°45°





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1

1.5

2

2.5

3

3.5

4

4.5

5

AB SJ RC SKRC+SK

RC+SJSK+SJ

SK+SJ+RCSK+SE

SJ+SE

SK+SJ+SE

Med

ian

PGA

(g)

Single column bridges−Complete damage

0°15°30°45°





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0.2

0.25

0.3

0.35

0.4

0.45

0.5

AB SJ RC SKRC+SK

RC+SJSK+SJ

SK+SJ+RC

Med

ian

PGA

(g)

Two−column bridges−Slight damage

0°15°30°45°





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0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

AB SJ RC SKRC+SK

RC+SJSK+SJ

SK+SJ+RC

Med

ian

PGA

(g)

Two−column bridges−Moderate damage

0°15°30°45°





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0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

AB SJ RC SKRC+SK

RC+SJSK+SJ

SK+SJ+RC

Med

ian

PGA

(g)

Two−column bridges−Extensive damage

0°15°30°45°





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1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

AB SJ RC SKRC+SK

RC+SJSK+SJ

SK+SJ+RCSK+SE

SJ+SE

SK+SJ+SE

Med

ian

PGA

(g)

Two−column bridges−Complete damage

0°15°30°45°





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Documents

Fragility Assessment for Seismically Retrofitted Skewed Reinforced Concrete Box Girder Bridges