Performance Modeling Strategies Performance Modeling Strategies

for Modern Reinforced Concrete for Modern Reinforced Concrete

Bridge ColumnsBridge Columns

Michael P. Berry

Marc O. Eberhard

University of Washington

Project funded by the

Pacific Earthquake Engineering Research Center (PEER)Pacific Earthquake Engineering Research Center (PEER)

UWUW--PEER Structural PEER Structural

Performance DatabasePerformance Database

• Nearly 500 Columns– spiral or circular hoop-reinforced columns (~180)

– rectangular reinforced columns (~300)

• Column geometry, material properties,

reinforcing details, loading

• Digital Force-Displacement Histories

• Observations of column damage

• http://nisee.berkeley.edu/spd

• User’s Manual (Berry and Eberhard, 2004)

Objective of ResearchObjective of Research

Develop, calibrate, and evaluate column modeling strategies that are capable of accurately modeling bridge column behavior under seismic loading.

–Global deformations

–Local deformations (strains and rotations)

–Progression of damage

Advanced Modeling StrategiesAdvanced Modeling Strategies

F

Force-Based Fiber

Beam Column Element (Flexure)

Lumped-

Plasticity

Force-Based Fiber

Beam Column Element (Flexure)

Fiber Section at each integration point with

Aggregated Elastic Shear

Zero Length Section (Bond Slip)

Elastic Portion of Beam

(A, EI )

to Plastic Hinge

eff

Lp

Distributed-

Plasticity

CrossCross--Section ModelingSection Modeling

CrossCross--Section Modeling ComponentsSection Modeling Components

• Concrete Material Model

• Reinforcing Steel Material Model

• Cross-Section Discretization Strategy

Concrete Material ModelConcrete Material Model

Popovic’s Curve with Mander et. al. Constants and

Added Tension Component (Concrete04)

Reinforcing Steel Material ModelsReinforcing Steel Material Models

Giufre-Menegotto-Pinto

(Steel02)

0 0.05 0.1 0.150

0.5

1

1.5

σσ σσ/f

y

εεεεs

Bilinear

Measured

Es * b

0 0.05 0.1 0.150

0.5

1

1.5

εεεεs

σσ σσ/f

y,

Measured

Kunnath

Mohle and Kunnath

(ReinforcingSteel)

Section Fiber Section Fiber DiscretizationDiscretization

• Objective: Use as few fibers as possible to eliminate the effects of discretization

Cover-Concrete

Fibers

Core-Concrete

Fibers

Longitudinal Steel Fibers

0 1 2 3 4

x 10-4

0

1

2

3

4

5

6

7

8x 10

5

φφφφ (1/mm)

Mo

men

t (K

N-m

m)

Radial

Unilateral

φy Ratio

M5 ε

y

Ratio M10 ε

y

Ratio

CrossCross--Section Fiber Section Fiber DiscretizationDiscretization

Uniform (220 Fibers)

10

20

r

c

t

c

n

n

=

=

1

20

r

u

t

u

n

n

=

=

Confined Unconfined

Reduced Fiber Reduced Fiber DiscretizationDiscretization

Uniform (220 Fibers)

Nonuniform Strategies

CrossCross--Section Fiber Section Fiber DiscretizationDiscretization

5

20

2

10

r

fine

t

fine

r

coarse

t

coarse

n

n

n

n

=

=

=

=

1

20

r

u

t

u

n

n

=

=

Confined Unconfined

Uniform (220 Fibers) Reduced (140 Fibers)

10

20

r

c

t

c

n

n

=

=

1

20

r

u

t

u

n

n

=

=

Confined Unconfined

r/2

Modeling with DistributedModeling with Distributed--

Plasticity ElementPlasticity Element

Model ComponentsModel Components

Force-Based Fiber

Beam Column Element

(Flexure)

Fiber Section at each

integration point with Aggregated Elastic

Shear

Zero Length Section

(Bond Slip)

• Flexure Model (Force-Based

Beam-Column)

– nonlinearBeamColumn

– Fiber section

– Popovics Curve (Mander constants)

– Giufre-Menegotto-Pinto (b)

– Number of Integration Points (Np)

• Anchorage-Slip Model

– zeroLengthSection

– Fiber section

– Reinforcement tensile stress-

deformation response from Lehman

et. al. (1998) bond model (λ)

– Effective depth in compression (dcomp)

• Shear Model

– section Aggregator

– Elastic Shear (γ)

Model OptimizationModel Optimization

• Objective: Determine model parameters such that the error between measured and calculated global and local responses are minimized.

( )

( )( )

2

1

2

max

n

meas calc

push

meas

F FE

F n

−=∑ ( )

( )( )

2

1

2

max

n

meas calc

strain

meas

En

ε ε

ε

−=∑

Model EvaluationModel Evaluation

. . meas

calc

KS R

K=

_ 4%

_ 4%

. .meas

calc

MM R

M=

mean 14.89 6.73 7.78 14.4 1.02 1.03

cov (%) – – – – 15 8

totalE pushE (0 / 2)D

strainE

− ( / 2 )D D

strainE

− . .S R . .M R

Optimized Model:

• Strain Hardening Ratio, b = 0.01

• Number of Integration Points, Np = 5

• Bond-Strength Ratio, λ = 0.875

• Bond-Compression Depth,

• dcomp =1/2 N.A. Depth at 0.002 comp

strain

• Shear Stiffness γ = 0.4

Modeling with LumpedModeling with Lumped--

Plasticity ElementPlasticity Element

LumpedLumped--Plasticity ModelPlasticity Model

Fiber Section assigned

to Plastic Hinge

Elastic Portion of Beam

(A, EI )

Lp

eff

• Hinge Model Formulation:

– beamwithHinges3

– Force Based Beam Column Element

with Integration Scheme Proposed by

Scott and Fenves, 2006.

– Fiber Section

• Elastic Section Properties– Elastic Area, A

– Effective Section Stiffness, EIeff

• Calculated Plastic-Hinge Length– Lp

Section Stiffness CalibrationSection Stiffness Calibration

mean 1.00 1.00

cov (%) 19 16

Stiffness Ratio Stats

effEI = sec sec

calcEIαcalc

g c gE Iα

PlasticPlastic--Hinge Length CalibrationHinge Length Calibration

Cyclic ResponseCyclic Response

Cyclic Material ResponseCyclic Material Response

• Cyclic response of the fiber-column model depends on the cyclic response of the material models.

• Current Methodologies– Do not account for cyclic degradation steel

– Do not account for imperfect crack closure

Giufre-Menegotto-Pinto (with Bauschinger Effect)Steel02

Reinforcing Steel Confined and Unconfined Concrete

Karsan and Jirsa with Added Tension Component Concrete04

Evaluation of ResponseEvaluation of Response

Lumped-PlasticityDistributed-

Plasticity

Ef orce (%) Ef orce (%)

mean 16.13 15.66

min 6.63 6.47

max 44.71 46.05

-15 -10 -5 0 5 10 15-300

-200

-100

0

100

200

300

∆∆∆∆ /∆∆∆∆y

Fo

rce

(K

N)

Lehman No.415

Measured

OpenSees

KunnathKunnath and and MohleMohle

Steel Material ModelSteel Material Model• Cyclic degradation according to Coffin and Manson Fatigue.

• Model parameters:

– Ductility Constant, Cf

– Strength Reduction Constant, Cd

Preliminary Study with Preliminary Study with KunnathKunnath Steel Steel

ModelModel• Ductility Constant, C

f=0.4

• Strength Reduction Constant, Cd=0.4

-15 -10 -5 0 5 10 15-300

-200

-100

0

100

200

300

∆∆∆∆/∆∆∆∆y

Fo

rce

(K

N)

Lehman No.415

Measured

OpenSees

-15 -10 -5 0 5 10 15-300

-200

-100

0

100

200

300

∆∆∆∆ /∆∆∆∆y

Fo

rce

(K

N)

Lehman No.415

Measured

OpenSees

Giufre-Menegotto-Pinto (with Bauschinger Effect)

Kunnath and Mohle (2006)

Giufre-Menegotto-

Pinto

Kunnath and

Mohle

Ef orce (%) Ef orce (%)

mean 16.13 11.98

min 6.63 5.15

max 44.71 29.45

Continuing WorkContinuing Work

Imperfect Crack Closure

•Drift Ratio Equations

•Distributed-Plasticity Modeling Strategy

•Lumped-Plasticity Modeling Strategy

Prediction of Flexural Damage

Key Statistics Fragility Curves Design Recommendations

Evaluation of Modeling-Strategies for Complex Loading

•Bridge Bent (Purdue, 2006)

•Unidirectional and Bi-directional Shake Table

(Hachem, 2003)

Thank you