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Seismic vulnerability and loss assessment of an isolated simply-supported highway bridge retrofitted with optimized superelastic shape memory alloy cable restrainers

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Abstract

Restrainers, being of relatively low cost and easy to install, are often used to prevent unseating of bridge spans. The potential of using superelastic shape memory alloy (SMA) restrainers in preventing such failure has been discussed in the literature; however, the impact of such smart restrainers with optimized configurations in reducing the failure probability of bridge components and system as well as the long-term economic losses given different earthquake scenarios has not been investigated yet. This study presents a probabilistic seismic fragility and long-term performance assessment on isolated multi-span simply-supported bridges retrofitted with optimized SMA restrainers. First, SMA restrainers are designed following the displacement-based approach and their configuration is optimized. Then, seismic fragility assessment is conducted for the bridge retrofitted with optimized SMA restrainers and compared with those of the original bridge and the bridges with elastic restrainers (steel and CFRP). Finally, long-term seismic loss (both direct and indirect) are evaluated to assess the performance of the retrofitted bridges in a life-cycle context. Results showed that among three considered restrainers, SMA restrainers make the bridge less fragile and help the system lower long-term seismic loss. The design event (DE, 2475-year return period) specified in Canadian Highway Bridge Design Code (CHBDC, CSA S6-14 2014) may underestimate the long-term seismic losses of the highway bridges. Under DE, the damage probability of the bridge retrofitted with optimized SMA restrainers experiencing collapse damage is only 0.7%. Under the same situation, its expected long-term loss is approximate 17.6% of that with respect to the unretrofitted bridge.

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Abbreviations

a and b :

Regression coefficient

ADT :

Average daily traffic to detour

ADTE :

Average daily traffic remaining on the damaged link

A r :

Design area of the restrainer

c 1 :

Damping coefficient of the pier

c AW :

Average wages for car drivers per hour

c ATC :

Average wages for truck drivers per hour

c b :

Equivalent viscous damping of bearing

c goods :

Time value of goods transported in a cargo

c r :

Equivalent viscous damping of the restrainer

c reb :

Rebuilding cost per square meter

c run,car :

Average costs for running cars per kilometer

c run,truck :

Average costs for running trucks per kilometer

C DS,i :

Consequences at a certain damage state, i

C REP,i :

Repair cost of a bridge at damage state i

C RUN :

Running costs

C TL :

Monetary time lost for users and goods traveling

d i :

Duration of the detour

D l :

Detour distance

EDP :

Engineering demand parameter

f a :

Stress of restrainer at allowable displacement, ∆a

F b :

Restoring force of bearing at allowable displacement, Δa

F r :

Requied strength of restrainer

F inertia :

Inertia force of girder

h r :

Vertical distance between two anchored ends of restrainer

IM :

Intensity measure

k 1 :

Stiffness of pier

k b :

Effective stiffness of isolation bearing

k r :

Effective stiffness of restrainer

l :

Route segment containing bridge

L :

Length of bridge

L(tk):

Expected annual hazard loss at time tk

LCL :

Total life-cycle hazard loss

L i :

Loss of bridge at damage state i

L r0 :

Design length of restrainer at initial condition

L r1 :

Length of restrainer at design target displacement condition

m 1 :

Mass of bridge pier

m 2 :

Mass of bridge girder

n b :

Number of isolation bearings at each pier or abutment location

N :

Total number of simulation cases

N(tint):

Number of earthquakes that occur during the time interval

o car :

Average vehicle occupancies for cars

o truck :

Average vehicle occupancies for trucks

P[Fi]:

Failure probabilities of ith component

P DS,i|PGA :

Conditional probability of a bridge at damage state i for a given PGA

P s :

Failure probabilities of system

R rcr :

Repair cost ratio at damage state i

S :

Average detour speed

S 0 :

Average speed on intact link

SA(T, ξ0):

Design response spectra ordinate for period T and damping ratio ξ0

S c :

Median estimate of capacity

S D :

Average speed on damaged link

t int :

Investigated time interval

T 0 :

Ratio of average daily truck traffic

u 1 :

Displacement of bridge pier

u 2 :

Displacement of bridge girder

\(\ddot{u}_{g}\) :

Ground acceleration

W :

Width of bridge

Δa :

Allowable relative displacement between bridge girder and pier

Δd :

Design target displacement of restrainer

Δrd :

Relative displacement between girder and pier

Δs :

Slack of restrainer

θ 0 :

Horizontal angle of restrainer at initial condition

θ 1 :

Horizontal angle of restrainer at design target displacement condition

Ф:

Cumulative distribution function of standard normal distribution

α :

Normalized elongation ratio of restrainer

β c :

Logarithmic standard deviation of capacity

β D|IM :

Standard deviation of demand

γ :

Shear strain of isolation bearing

ε max :

Maximum applied strain of SMA

λ :

Median value of IM

ξ :

Standard deviation of IM

μ d :

Displacement ductility of pier

τ :

Monetary discount rate

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Acknowledgements

This study was financially supported by the Fundamental Research Funds for the Central Universities (Grant No. 2242019K40082), the National Natural Science Foundation of China (Grant No. 51908123), the Natural Science Foundation of Jiangsu Province (Grant No. BK20190370), and Natural Sciences and Engineering Research Council (NSERC) of Canada through Discovery Grant.

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Authors and Affiliations

  1. School of Civil Engineering, Southeast University, Nanjing, 210096, Jiangsu, People’s Republic of China

    Shuai Li & Jing-quan Wang

  2. School of Engineering, The University of British Columbia, Kelowna, BC, V1V1V7, Canada

    Shuai Li, Farshad Hedayati Dezfuli & M. Shahria Alam

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  1. Shuai Li
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  2. Farshad Hedayati Dezfuli
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  3. Jing-quan Wang
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  4. M. Shahria Alam
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Correspondence to Jing-quan Wang or M. Shahria Alam.

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Li, S., Hedayati Dezfuli, F., Wang, Jq. et al. Seismic vulnerability and loss assessment of an isolated simply-supported highway bridge retrofitted with optimized superelastic shape memory alloy cable restrainers. Bull Earthquake Eng 18, 3285–3316 (2020). https://doi.org/10.1007/s10518-020-00812-4

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