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Aftershock Seismic Vulnerability and Time-dependent Risk Assessment of Bridges
Sujith Mangalathu, Ph.D.
Research teamProf. Henry Burton, UCLA
Prof. Jonathan Stewart, UCLADr. Sujith Mangalathu, UCLAMehrdad Shokrabadi, UCLA
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Motivation
Aftershock Vulnerability and Time dependent Risk Assessment of Bridges
• Caltrans uses the following table to relate bridge seismic damage to post-earthquake functionality and repair priorities
Mangalathu, S., Jeon J-S., Padgett, J. E., DesRoches, R., "ANCOVA-based Grouping of Bridge Classes for Seismic Fragility Assessment", Engineering Structures, Vol. 123, 2016, pp 379-395. 2
Aftershock Vulnerability and Time dependent Risk Assessment of Bridges
Goals/OverallObjective
• Conduct aftershock seismic vulnerability and time-dependent risk assessment of typical California bridges
• Evaluate the effect of seismic design philosophy on the time-dependent risk
• Use results from vulnerability and risk assessments to inform decisions regarding the appropriateness and timing of inspections and post-event closure (partial and complete)
• The extent to which ‘residual structural capacity’ and ‘time-dependent aftershock hazard and risk’ inform these damage-functionality and inspection priority relationships is unclear.
Motivation
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Mainshocks AftershocksDamaged Bridge
Aftershock Vulnerability and Time dependent Risk Assessment of Bridges
Aftershock fragility
Steps involved in proposed framework• Select mainshock-aftershock ground motions
• Create structural models of bridge structures
• Conduct mainshock and mainshock-aftershock fragility analysis
• Quantify time-dependent hazard (APSHA) and risk (Markov Chain Models) assessment
• Establish time-dependent risk and functionality/inspection relationships
Time-dependent hazard and risk
Time-dependent risk and decision-making
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Emergency
Vehicle only
Limited traffic
No heavy trucks
All vehicles
Time
Func
tiona
lity
Aftershock Vulnerability and Time dependent Risk Assessment of Bridges
Selectionofgroundmotions
Past studies have reported non-negligible differences in frequencycontent of mainshock (MS) and aftershock (AS) records
Therefore, MS-AS sequences in response history analysis
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Aftershock Vulnerability and Time dependent Risk Assessment of Bridges
Mainshock‐aftershockgroundmotionsforbridge‐specificriskanalysis
Selected based on high-seismicity zones in California
Set of 34 record-pairs from Class 1 and Class 2 events in PEER-NGA West2 database
5.8 𝑀 , 7.6
4.0 𝑀 , 6.5
𝜀~1.3Mainshocks Aftershocks
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Aftershock Vulnerability and Time dependent Risk Assessment of Bridges
Mainshock‐aftershockgroundmotionsfornetworkriskanalysis
10-1 100
Period (s)
10-4
10-2
100
Median
Set of 33 record-pairs
Selected based on a hypothetical scenario event
𝑀 , 7.3
6.2 𝑀 , 7.1
10-1 100
Period (s)
10-4
10-2
100
MedianMainshocks Aftershocks
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Aftershock Vulnerability and Time dependent Risk Assessment of Bridges
SelectedBridgeCasesforvariousdesigneras
Mangalathu, S (2017). Performance based grouping and fragility analysis of bridges in California. Ph.D. Thesis. Georgia Tech, USA8
• More than 24,000 bridges in California
• Mangalathu (2017): based on design
philosophy, bridges in California can be
grouped into three
• Era 11 (constructed before 1970)
• Era 22 (Between 1970-1990)
• Era 33 (Constructed post 1990)
Aftershock Vulnerability and Time dependent Risk Assessment of Bridges
SelectedBridgeCases
Mangalathu, S (2017). Performance based grouping and fragility analysis of bridges in California. Ph.D. Thesis. Georgia Tech, USA9
Aftershock Vulnerability and Time dependent Risk Assessment of Bridges
ModelingofBridgeStructures
Mangalathu, S (2017). Performance based grouping and fragility analysis of bridges in California. Ph.D. Thesis. Georgia Tech, USA10
Aftershock Vulnerability and Time dependent Risk Assessment of Bridges
AftershockFragilityAnalysis
Aftershock fragility: A conditional probability that determines the likelihood that a damaged structure will meet or exceed a specified level of damage, given an aftershock intensity measure and an initial damage state associated with the mainshock [mainshock-damage-dependent aftershock fragility].
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Aftershock Vulnerability and Time dependent Risk Assessment of Bridges
AftershockFragilityAnalysis
Sa1-0.s
P[D
>C
|Sa1
-0s]
Main shock and Aftershock fragilities of a bridge designed in Era 1112
Aftershock Vulnerability and Time dependent Risk Assessment of Bridges
AProbabilisticFrameworkforQuantifyingMSandMS‐ASSeismicRisk
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Π
𝑃 𝑃 ⋯ 𝑃0 𝑃 ⋯ 𝑃⋮ ⋮ ⋱ ⋮0 0 ⋯ 𝑃
𝑃
𝑃 , 𝐸𝐷𝑃 𝑒𝑑𝑝 |𝐼𝑀 𝑃 , 𝐸𝐷𝑃 𝑒𝑑𝑝 |𝐼𝑀 𝑑𝜆 𝑖𝑚
Probability of transition between limit states at time step 𝑘 after
mainshock
𝑖: damage state under 1st event𝑗: damage state 2nd event
APSHA curve at time step 𝑘 after mainshock
0 0.5 1 1.5 2 2.50
0.2
0.4
0.6
0.8
1P[
Com
plet
e|D
S MS
]
IntactSlightExtensive
Aftershock Vulnerability and Time dependent Risk Assessment of Bridges
CompleteLimitStateProbabilityunderAftershocksfordifferentmainshocklimitstatesandBridgeE3
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20% reduction in 𝑆𝑎
Aftershock Vulnerability and Time dependent Risk Assessment of Bridges
AftershockTransitionProbabilityconditionedondifferentlimitstatesundermainshock
15
0 2 4 6Time elapsed since mainshock (days)
10-8
10-7
10-6
10-5
10-4
P[C
ompl
ete
| Mod
erat
e]
Era 1Era 2Era 3
Daily 𝑃 𝐶𝑜𝑚𝑝𝑙𝑒𝑡𝑒
0.23% in 50 years
0.12% in 50 years
0.03% in 50 years
All motor vehicle accidents0.6% in 50 years
0 10 20 30 40 50Time (years)
10-6
10-4
10-2
100
Era 1Era 2Era 3
Only mainshockMainshock-aftershock
Aftershock Vulnerability and Time dependent Risk Assessment of Bridges
Service–lifeprobabilityofCompletedamagestateunderMSandMS‐ASscenarios
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Aftershock Vulnerability and Time dependent Risk Assessment of Bridges
Conclusions
Performed aftershock probabilistic seismic hazard analysis (APSHA)to quantify time-dependent post-mainshock hazard.
Implemented Markov Chain Model that integrates time-dependenthazard curves and mainshock-damage-dependent-fragilities toquantify time-dependent risk
Suggested a time-dependent risk outcomes to inform bridgefunctionality and inspection priorities
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