PEER 2002 PEER Annual Meeting Seismic Performance Modeling of Reinforced Concrete Bridges Stephen...

2002 PEER Annual Meeting

PPEEEERR Seismic Performance Modeling

of Reinforced Concrete Bridges

Stephen MahinByron and Elvira Nishkian Professor of Structural Engineering

Mahmoud Hachem, Brian Buckman and Colin Cook Graduate Student Reseachers

University of California at Berkeley


PEER Bridge Program

Focus on:• Monolithic reinforced

concrete bridge construction

• New rather than older construction detailing

• Representative of:– Viaducts

– Overcrossings

– Major interchanges


Many Elements Involved

• Approaches• Abutments• Foundations• Movement Joints• Columns/Piers• Superstructure• Nonstructural Features

Thrust Area 5

Structural Performance


Spirally Reinforced Column Tests

Test Matrix • Loading history

– Traditional cyclic– Pulse initiated cyclic– Variable axial load– Shaking table testing

• Loading rates: Fast and quasi-static

• Aspect ratios: Moderate and low

• Cross-sectionCircular and interlocking spirals


Discuss: Shaking Table Tests

Objectives:• Data to validate analytical models• Compare performance for near-fault

and long-duration excitations• Assess effects of multiple components

of ground motion• Assess cumulative damage models• Effect of cross-sectional geometry

•Circular sections with spirals•Noncircular with interlocking spirals


Column Performance

After Design Level Event (R=4) After First Maximum Level Event (=6)


Condition at end of tests

Fractured Spiral Fractured Bar

Buckled Bars

After sixth repetition of Maximum Run - Olive View


Long Duration Excitations

QuickTime™ and a decompressor

are needed to see this picture.

QuickTime™ and a decompressor

are needed to see this picture.

1985 Llolleo, Chile Record


Peak Displacement Response

Maximum Bottom and Top Disp. in Long and Lat directions, Test A2

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.00

A2-Run1Yield

A2-Run2Design 1

A2-Run3Max 1

A2-Run4Design 2

A2-Run5Max 2

A2-Run6Max 3

A2-Run7Design 3

A2-Run8Max 4

A2-Run9Max 5

A2-Run10Max6

Displacement [in]

Long. Column Disp Lat. Column Disp Long. Peak Ground Disp Lat. Peak Ground Disp

First Bar

Buckling

Bar

Fracture

Bi-directional input has limited effect and in the cases considered extends life of column


Bi-directional Response

- 8 - 6 - 4 - 2 0 2

- 8

- 7

- 6

- 5

- 4

- 3

- 2

- 1

0

1

2

Δl a t

( i n )

Δ

l

o

n

g

(

i

n

)

Dis

pla

cem

ent

, in

.

Displacement, in.

Ground motion characteristics have a large effect on:

• Nature of bi-directional response• Sensitivity of maximum

displacements to intensity• Residual displacements

Currently design criteria, for ideal conditions and without significant P-Δ effects or eccentric gravity loads, result in well-performing columns with significant reserve capacity


Verification of Analytical Models

Global: Displacements, Residual

Displacements, Forces, Moments

Local: 1. Curvatures, 2. Strains, 3. Slip Rotations, …4. Cumulative Damage

Response quantities: Analytical Models:• Elastic Analysis with

equivalent sectional Stiffness (EI e)

• Concentrated hinge models with equivalent plastic hinge properties

• Fiber models with distributed section properties with equivalent material properties


Elastic Models

Various assumptions for approximating “effective” section stiffness EI EIe as defined by Caltrans

gives reasonable results for maximum displacement

EIeTest

Maximum Credible


Elastic Models

EIeTest

Maximum Credible

Maximum Credible

Lateral Direction



Not always


Elastic Models



Not always

EIeTest

Maximum Credible

Design Level


Elastic Models



Not always No information on residual

displacements Other engineering demand

parameters inferred from pushover analyses

EIeTest

Residual Displacement

Maximum Credible

Design Level


Concentrated Plastic Hinge Models

• Various methods for estimating equivalent properties for concentrated plastic hinge (Lp, M-, etc.)

• Various idealized hysteretic models– Bilinear vs. Stiffness

Degrading

– Coupled and uncoupled

BilinearStiffness Degrading

Maximum Credible




Maximum Credible

• Most models provide adequate estimate of maximum displacement


Design Level



• Most models provide adequate estimate of maximum displacement

• Nonlinear models provide indication of yielding and degradation on wave form and residual displacement– Estimates are often poor

– Stiffness degrading models generally better


Maximum Credible

Stiffness Degrading Bilinear

Lateral Direction




Maximum Credible

Stiffness Degrading Bilinear

Lateral Direction



• Local information on strains, bar buckling, fatigue, etc. must be inferred from detailed analysis of member– Problem under cyclic

loads?


Fiber Models

• Useful for well confined members controlled by ductile yielding

• Approximations at material level, number of fibers used to model section, manner in which member is discretized longitudinally


Maximum CredibleFiber Model

Concentrated Hinge Models


Fiber Models

• Generally, much better fidelity• Results, especially for residual displacement and local deformations

(strain) sensitive to modeling of section• Fixed end rotations due to bar pullout not yet accounted for in OpenSees

Maximum Credible

Fiber Model


Model Performance vs. Test


where 2Nf is the number of half cycles to failure at a plastic strain

Performance Evaluation

Park & Ang:

• Damage Indices:

Bar Fatigue Damage Index:

bfp Na −= )2(ε

D =1

2Nf∑

D =dmax

dult+β

dE∫

Fydult

Section Fatigue, spalling, bar buckling, residual displacement, etc.


Damage Idecies at First Bar Fracture


Parametric Study

• Design multiple columns with varying:

Dcol

P

HAspect Ratio (ar)

Axial Load (Pr)

Diameter (Dcol)


Design Procedure Used

• Given Dcol, ar, Pr

– Determine sp from BDS

– Solve iteratively for l that would result in the

required strength: Fy =mass×Sa

Z For each l value:

Perform M- analysis, determine My, EIeff, Mu and u (failure reached when εc>εcu or εs>εsu)


Column Design according to ARS

ZMass

StrengthSa =


Moment-Curvature Analysis

Also determine c (Neutral Axis Depth)


Idealized Force-displacement Model

Deformation

Force Exact BehaviorIdealized

Fy

K

Kh

dult

Fu

Also determine Lp and T


Ground Motions Used 20 LMSR motions and 50 LMLR motions

LMSR motions


Mean Results


Mean+1 SD Results


Fragility Curves

Compute Fragility curves for: Park & Ang Index (Minor and Significant

damage) Fatigue Index Spalling (|εcu| > 0.009)

0

0.01

0.02

0.03

0.04

0.05

0.06

0 0.5 1 1.5 2

Transverse Reinforcement Ratio (%)

Calculated Compressive Strain

Onset of Spalling

Onset of Bar Buckling

Assumes analysis model and preformance criteria are correct


Fragility Curves for Events with Large Magnitude at Small Distance

Spalling

Fatigue Failure

SignificantDamage

(Park&Ang)

MinorDamage

(Park&Ang)


Fragility Curves for Events with Large Magnitude at Large Distance

MinorDamage

(Park&Ang) Spalling

Fatigue Failure

SignificantDamage

(Park&Ang)


Summary

• New design and detailing criteria for circular columns generally result in performance consistent on average with performance objectives

• Ground motion characteristics effect: – Maximum response– Bi-directional response characteristics– Residual displacements


Summary

• Analytical models involve significant levels of judgement to get adequate prediction of performance

• Nearly all models with reasonable stiffness estimates can predict max. displacements– Small diameter, low aspect ratio (low periods), high loads, P-Δ

effects and gravity load eccentricities potential problems – Fiber models provide best fidelity, but need further assessment

and refinement

• Residual displacements and local deformations (spalling, bar buckling, steel fracture, etc.) sensitive to modeling


Summary

• Parametric and fragility analyses provide useful basis for understanding behavior, but integration into overall PEER assessment methodology essential

• Additional shaking table tests will be carried out along with analytical studies to:– get data on more complex bridge systems requiring

significant redistribution of load once yielding occurs

– Identify damping and strain rate effects

PEER 2002 PEER Annual Meeting Seismic Performance Modeling of Reinforced Concrete Bridges Stephen...

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