probabilistic seismic demand models for multi-span highway

Probabilistic Seismic DemandModels for Multi-Span Highway

Bridges

Kevin Mackie

Bozidar Stojadinovic

University of California, BerkeleyDepartment of Civil and Environmental Engineering &Pacific Earthquake Engineering Research Center

EM 2002 ConferenceColumbia University, NYJune 3-5, 2002

Session:

Seismic Response of Bridges

What is a PSDM?PSDM = Probabilistic Seismic Demand Model

Relationship of seismic Intensity Measures (IM) tostructural Engineering Demand Parameters (EDP)

log(EDP)

log(

IM)

Why a demand model?1.) Quantitative Performance Based Earthquake

Engineering tool for designers of bridges

What is probability of y, given x?

i0 5 10 15 20 25 30 35

-0.1

-0.05

0

0.05

0.1

0.15

t me [sec]

acce

lera

tion

[g] x

+

y

Intensity Measure: x Demand Measure: y

Why a demand model?2.) How do design parameters

affect performance?

Performance

Haz

ard

Performancebetter

Shorter(stiffer)

Taller(flexible)

Why a demand model?3.) Module in Pacific Earthquake Engineering

Research Center (PEER) probabilistic framework

i0 5 10 15 20 25 30 35

-0.1

-0.05

0

0.05

0.1

0.15

t me [sec]

acce

lera

tion

[g]

DemandModel

IntensityMeasures

DemandMeasures

CapacityModel

Hazard Performance

DecisionVariables

This project

PEER Performance based earthquake engineering framework

Probabilistic SeismicDemand Analysis

Æ Definemotions (IM)

Æ Define classof structures(EDP)

Æ Defineanalysismodel

Æ Nonlinearanalysis

Æ Designparametersensitivity

Æ Groundmotion binsensitivity

Æ Residualdependence(M, R)

Seismicity: Ground Motions & IMs• Period Independent Intensity Measures

• Magnitude, Distance, Strong motion duration• Cumulative absolute velocity• Cumulative absolute displacement• Arias intensity• Frequency ratios• RMS acceleration• Characteristic intensity• PGA, PGV, PGD

Ground Motion Bins

5.6

5.8

6.0

6.2

6.4

6.6

6.8

7.0

0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0

Distance R (km)

SMSR

LMSR LMLR

SMLR

• Period Dependent IntensityMeasures

• Sa, Sv, Sd• Spectral combinations• Sd,inelastic

Demand: Bridges

3-bent

Single bent

2-bent

3-bent stand-alone

Single-columnbents

Demand: EDPs• Local EDPs

• Steel stress & strain• Concrete stress & strain

• Intermediate EDPs• Column curvatureductility• Maximum columnmoment• Plastic rotation• Hysteretic energy

• Global EDPs• Displacement ductility• Drift ratio• Residual displacement index

Single column/benthighway overpasses in

California

OpenSees Bridge Model

Ground level

Soil springs

Abutmentsprings and gaps

Elastic deck

Fiber RC column

Mode 1 - Longitudinal

Mode 3 - VerticalMode 2 - Transverse

Bridge Design Parameters

• L• L/H• rs,long

• Dc/Ds• Abut

span lengthspan to column height ratiocolumn longitudinal reinforcementcolumn to superstructure dimensionsabutment mass/stiffness models

60-180 ft1.2-3.51-4%0.67-1.33various

Extending Optimal PSDMto Multi-bent bridges

100

102

103

Intensity Measure vs Demand Measure (Parameters)

Drift Ratio Longitudinal

s=0.31, 0.30, 0.28, 0.32

L2=1080L2=1440L2=2160L2=2520

Stiffness

Stif

fnes

s

Practical, effective, efficient

Period-dependent IM with Global response parameter

2-bent bridge with abutments

Extending Optimal PSDMto Multi-bent bridges

100

101

102



s=0.34, 0.37, 0.39, 0.38

L2=1080L2=1440L2=2160L2=2520

Stiffness

Con

stan

t int

ensi

ty

Practical, effective, efficient in short period range

Period-independent IM with Global response parameter

2-bent bridge with abutments

SufficiencyMagnitude dependence

Distance dependence

15 20 25 30 35 40 45 50 550.5

1

1.5

2

2.5

3

3.5

4

4.5

Residual Dependence (semilog scale)

Distance (km)

c (*E- 2)=0.04, -0.11, 0.15, 0.63

L2=1080L2=1440L2=2160L2=2520

5.8 5.9 6 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.80.5

1

1.5

2

2.5

3

3.5

4

4.5

Residual Dependence (semilog scale)

Magnitude

c (*E- 2)=7.46, 11.54, 0.19, -36.89

L2=1080L2=1440L2=2160L2=2520

Bent Configuration Comparison

100

102

103



s=0.30, 0.22, 0.25

bents=1bents=2bents=3

•Longitudinal demand Ú as bents Ò

•Transverse demand approx. same

Design Parameter Sensitivity

100 101

102

103


Maximum Displacement Longitudinal

s=0.26, 0.25, 0.19, 0.30

L2=1080L2=1440L2=2160L2=2520

Stiffness

Stif

fnes

s

Increasing stiffness lowers demand slightly

L2 large

L2 small

Intermediate Span length (L2)

3-bent bridge no abutments

L2 small, L/H constant

L2 large, L/H constant

L2

Stif

fnes

s

Seismicity• Parameter sensitivity to bins• All lines of same color should have same slope at given

intensity• Higher demand for higher magnitude bins

10-1 100102

103

Bin dependence (LMSR -) (LMLR -.) (SMSR --) (SMLR..)


Dc/Ds=0.67Dc/Ds=0.75Dc/Ds=1 Dc/Ds=1.3

Column diameter to superstructure ratio (DcDs)

Highmagnitudebins

Lowmagnitudebins

Stiffness

Transverse Irregularity RI*

100

102

103



s=0.32, 0.29, 0.29

irregular=1irregular=2irregular=3

†

RI* =1L

f (x)dx0

L

ÚÊ

Ë Á Á

ˆ

¯ ˜ ˜ *100%

vs pure transverse translation

1st transverse mode shape

No loss ofefficiency with

periodindependent IM

PSDM ExtensionsStructural Demand Hazard Curves

0 0.5 1 1.5 2 2.5 3 3.5 4 4.510-4

10-3

10-2

10-1

100

101Average Structural Demand Hazard Curve


Dc/Ds=0.67Dc/Ds=0.75Dc/Ds=1 Dc/Ds=1.3

PSDM Extensions

Æ Maximum post-earthquakefunctionality (trafficload, eg)

Æ Probability ofexceeding a givendamage state(fragility)

Functional EDPs

ConclusionsÆ PSDMs allow designers to see the effects of:Æ seismicityÆ design parameterson seismic performance of a bridge

Æ PSDMs fit into PEER performance-based designframework, Sa(T1)-D optimal PSDM reducesdemand model dispersion

Æ Optimal single-bent models remain optimal formulti-bent

Æ Transverse irregularity (RI*) adequately predictedby Sa(T1)

Thank You!ÆQuestions?

ÆFor more information contact:Æ Kevin Mackie: [email protected]

Æ Boza Stojadinovic: [email protected]

ÆVisithttp://millerbird.ce.berkeley.edu

probabilistic seismic demand models for multi-span highway

Documents