aftershock seismic vulnerability and time-dependent risk ... · • conduct aftershock seismic...

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


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 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


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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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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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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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)


SelectedBridgeCases



ModelingofBridgeStructures



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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AftershockFragilityAnalysis

Sa1-0.s

P[D

>C

|Sa1

-0s]

Main shock and Aftershock fragilities of a bridge designed in Era 1112


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


CompleteLimitStateProbabilityunderAftershocksfordifferentmainshocklimitstatesandBridgeE3

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20% reduction in 𝑆𝑎


AftershockTransitionProbabilityconditionedondifferentlimitstatesundermainshock

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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


Service–lifeprobabilityofCompletedamagestateunderMSandMS‐ASscenarios

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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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aftershock seismic vulnerability and time-dependent risk ... · • conduct aftershock seismic...

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