Group of Earthquake Engineering and Structural Dynamics ... · Lumped Plasticity Models: Ruaumoko,...

29.August.2006

Post-earthquake residual deformations and seismic performance assessment of buildingsPost-earthquake residual deformations and seismic performance assessment of buildings

Ufuk Yazgan and Alessandro DazioGroup of Earthquake Engineering and Structural Dynamics

Institute of Structural Engineering, ETH-Zurich

229.August.2006 Ufuk Yazgan / Institute of Structural Engineering / yazgan@ibk.baug.ethz.ch

Motivation

The need to reduce the uncertainties in the assessment of seismic performance after an earthquake

The need for a direct consideration of post-earthquake residual displacements in the seismic design of structures

Management of EarthqaukeRisks using Condition Indicators

Post-Earthquake Residual Displacements

0 5 10 15 20 25 30Time (s)

Displacement (m)

-0.06 -0.04 -0.02 0 0.02 0.04 0.06Displacement (m)

Force (kN)

Maximum Displacement

Residual Displacement

Residual Deformations at the Component Level

(Source: Lestuzzi P., Wenk. T & Bachmann T., (1999), “DynamischeVersuche an Stahlbetontragwänden auf dem ETH-Erdbebensimulator”, IBK IBK Bericht Nr. 240, April 1999 )

Courtesy National Information Service for Earthquake Engineering, University of California, Berkeley.

Residual Displacements at the Structural Level

Residual Displacements due to Ground Deformations

Post-Earthquake Assessment

A Seismic Performance Assessment Method for buildings based on residual displacements is being developed.

Damaged Building

Reconnaissance Survey

Recorded Ground Motion FEM Model

Measured Residual Displacements

Estimates of Maximum

Displacements

PostPost--Earthquake Earthquake VulnerabilityVulnerability

0 2 4 6 8 10 12 14Spectral Displacment - Sd (cm)

P(D>DC0)P(D>DC1)P(D>DC2)P(D>DC3)P(D>DC4)

Performance-Based Design

Provide essential information about the the post-earthquake:- Reparability/Usability- Vulnerability

Estimates of Maximum

Displacements

0.01 0.1 1 10T [s]

Se [m/s2]

Estimates ofResidual

Displacements

PSH Model

Seismic Performance

FE Model

Known to be well correlated with the attained damage

Lumped Plasticity Models: Ruaumoko, DRAIN-2DX, OpenSees, SeismoStructMoment, M (kNm)

0 0.1 0.2 0.3 0.4

Curvature, 8 (m-1)

400 8 φ 16

φ 8 / 100

-0.06 -0.04 -0.02 0 0.02 0.04 0.06

Displacement (m)

Force (kN)

RuaumokoSeismoStruct (Lump.Plast.)DRAIN-2DXOpenSees (Lump.Plast.)

…… are practically the same. are practically the same.

Simulated largeSimulated large--cycle responses cycle responses ……

2.0=′

=cg fA

Nn %1=gρ

Difficulties related to simulation of response

Results: Lumped Plasticity ModelsPractically, the maxima are the samePractically, the maxima are the same

However, the residual displacements are significantly differentHowever, the residual displacements are significantly different

Maximum Displacement, um (m)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Ground Motion

Mean StandardDeviation

Ruaumoko(26/10/04)

SeismoStruct(v.3.9.5)

DRAIN-2DX(v.1.10)

OpenSees (1.6.2e)

Residual Displacment , ur (m)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Ground Motion

Residual Displacement, ur (m)

Ry = 4T = 0.5 [s] ζζ == 5%

Fiber Models: OpenSees, SeismoStruct, Rechenbrett-2D

100140

Stress (MPa)

0 0.01 0.02 0.03 0.04 0.05

Strain

OpenSees(Steel02)SeismoStruct(stl_mp)

Stress (MPa) -40

0-0.03 -0.02 -0.01 0

Strain

Reinforcement:Reinforcement: Concrete:Concrete:

-0.06 -0.04 -0.02 0 0.02 0.04 0.06

Displacement (m)

Force (kN)

SeismoStruct (Fiber)

OpenSees (Fiber)

Rechenbrett-2D

OpenSees (Concrete02)SeismoStruct(con_cc)

Simulated largeSimulated large--cycle responses cycle responses ……

…… practically the samepractically the same

Results: Fiber ModelsAgain Again …… Practically, the maxima are the samePractically, the maxima are the same

AgainAgain…… the residual displacements are significantly differentthe residual displacements are significantly different

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Ground Motion

OpenSees (1.6.2e)

SeismoStruct(v.3.9.5)

Rechenbrett-2D

Residual Displacement , ur (m)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Ground Motion

Results: Fiber vs Lumped Plasticity

0 0.005 0.01 0.015 0.02Model with lumped plasticity elements

ith fi

0 0.01 0.02 0.03 0.04 0.05 0.06Model with lumped plasticity elements

ith fi

Maximum DisplacementsMaximum Displacements Residual DisplacementsResidual Displacements

Residual displacements are significantly influenced by the Residual displacements are significantly influenced by the adopted modeling approachadopted modeling approach !!

Comparison with the experimental dataDescription of the shake table test

Lestuzzi, P., T.Wenk, H. Bachmann (1999), “Dynamische Versuche an Stahlbetontragwänden auf dem ETH-Erdbebensimulator”, IBK Bericht Nr.240, Institut für Baustatik und Konstruktion, ETH Zürich

Rotation - z = 0.25 [m]

-0.005

0 4 8 12 16 20

Time [s]

Bending Moment [kNm]

-0.01 -0.005 0 0.005 0.01 0.015Rotation - z=0.25 [m]

-0.005

0 4 8 12 16 20

Time [s]

-0.01 -0.005 0 0.005 0.01 0.015Rotation - z=0.25 [m]

-0.005

0 4 8 12 16 20

Time [s]

-0.01 -0.005 0 0.005 0.01 0.015Rotation - z=0.25 [m]

Response history

Peak deformations

Points of unloading

-0.005

0 4 8 12 16 20

Time [s]

-0.01 -0.005 0 0.005 0.01 0.015Rotation - z=0.25 [m]

Residual deformation

0 2 4 6 8 10 12 14 16 18

Time [s ]

Moment [kNm ]

Measured

Simulated

FE model is subjected to the measured rotation history

-0.01 -0.005 0 0.005 0.01 0.015

Rotation

0 2 4 6 8 10 12 14 16 18 20-60

Time(s)

ExperimentOpenSees

Example applicationLocated in a region of high seismicityMw7.4 Kocaeli, Turkey 1999 EarthquakeAround ~7000 buildings - mostly RC - MRF Three decision alternatives:

strengthening the frame by structural wallsno actionpreventing liquefaction by stone columns

0 400 800100[m]

1234567

Number of Stories

Adapazari, Turkey

Performance of the structural stock subjected to a range of seismic events needs to be assessed.

(Bayraktarli Y., U. Yazgan, A. Dazio A. and M. Faber, 2006)

Example applicationSet of representative RC frame buildings

Yield ground story drift, θyPriestley (1998)

•Fundamental mode shape, φ1

•Yield displacement at roof, Δy,roof

Nstory=1,2,3,…,7

hstory = 2.4 [m]Lbay = 6 [m] εsy = 2.1 [%]

Astory=300 [m2]

•Modal participation factor, Γ1Mstory= 0.6 [t/m2]

0 0.2 0.4 0.6 0.8 1T [s]

Sa [g]Elastic spectrum

Design spectrum

TEC-98, ζ=5%, Z1, R=8

Yield displacement, Δ*y

Base shear capacity, V*y

Yield displacement, Δ*y

Base shear capacity, V*y

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35D [m ]

V [kN ]

Nstory

Equivalent SDOF Systems for RC - MRF's

Dazio(2000)Modal Analysis

Example applicationRepresentative models for retrofitted buildings

H/L ≅ 4ρ = 1%

• Yield curvature, φy

• Yield displacement at the top, Δy,w

• Flexural yield strength, My

• Base shear at yielding Vy

Added Structural Walls

• Yield displacement, Δy,roof

• Base shear at yielding Vy

Wall +Frame System Dazio(2000)

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

V [kN]

Nstory

Equivalent SDOF Systems for RC MRF + Wall

Example applicationGround Motions

T, ζ, Ry

Substitute SDOF System

Simulated Response

Maximum Displacement, Δmax

Residual Displacement, Δres

Performance State

Vision2000(1995)

Which Δres ?

10-8 10-6 10-4 10-2 1000

1nstory=4

ures[m]

FOOLSNCC

Δres [m]

ConclusionsResidual displacements are significantly influenced by the adopted modeling approach

It is possible to establish a performance assessment strategy taking into account residual displacements to update the uncertainties

Further study is needed to identify:- Which deformations would provide an effective measure?

- Which are feasible to measure?

Outlook / Open QuestionsRC frame and structural wall systems are being studied

Effective intensity measures related to residual displacements are being investigated

Efficient ways to relate the seismic performance to structural response parameters needs to be identified

Methods to include nonlinear soil deformation in the seismic performance assessment needs to be investigated

Effect of ground motion record processing schemes on the simulated residual displacements needs to be studied

ThankThank youyou

Any Questions?Any Questions?

-0.04 -0.02 0 0.02 0.04 0.06

Displacement (m)

Force (kN)

0 5 10 15 20Time [s]

Lumped-plasticity model(Ruaumoko)Fiber-element model(OpenSees)

0 0.015 0.03 0.045

Displacement (m)

Force (kN)

Stiffness is updated at the Stiffness is updated at the end of each stepend of each step

Stiffness is updated within Stiffness is updated within each stepeach step

-0.015 0 0.015 0.03 0.045

Displacement (m)

Force (kN)

dt=0.01

dt=0.005

dt=0.002

dt=0.0005

dt=0.0001

ImprtanceImprtance of of ““time integration step sizetime integration step size”” and proper updating of stiffnessand proper updating of stiffness

0 0.02 0.04 0.06 0.08With late stiffness updating

0 0.005 0.01 0.015 0.02With late stiffness updating

Properly updating stiffness is crucial for Properly updating stiffness is crucial for

estimating the residual displacements estimating the residual displacements !!

Force (kN)

-0.06 -0.04 -0.02 0 0.02 0.04 0.06

Displacement (m)

1-element

3-elements

5-elements

7-elements

Force (kN)

-0.06 -0.04 -0.02 0 0.02 0.04 0.06

Displacement (m)

Stiffness-based approach

Flexibilty-based approach

Effect of mesh densityEffect of mesh density Effect of element formulationEffect of element formulation

-0.005 0 0.005 0.01 0.015 0.02

Strain

Stress (MPa)

without partial reloading

with partial reloading

26% increase in strain at the unloaded state

Partial reloading

-0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04

Displacement (m)

Force (kN)

without partial reloading

with partial reloading

25% increase in the displacement at the unloaded state

Partial reloading

Force Force -- DisplacementDisplacement Steel StressSteel Stress--StrainStrain

Limited memory problem of the steel Limited memory problem of the steel hysteresishysteresis::

Properly simulating the response of steel is Properly simulating the response of steel is

critical for estimating the residual displacements critical for estimating the residual displacements !!

Residual displacements are significantly influenced by the adopted modeling approach

Differences in the small-cycle response leads to notably different residual displacement estimates

“Time integration step size” can have a strong effect on the computed residual displacements

Meshing of the system may have a significant influence on the computed residual displacements

“Memory limitation” problem related to steel hysteresis response results inappropriate unloading paths

Limit State DriftsCalculation of limit state displacementsMaximum Displacements Hstory= 2.4 [m] - Height of a story MRF

HN FO O LS NC C FO O LS NC C φ1,1 Γ FO O LS NC Cnstory [m] < > <[m] [m] [m] [m] [m]> nstory <[m] [m] [m] [m] [m]>

1 2.4 0.002 0.005 0.015 0.025 0.025 0.0048 0.012 0.036 0.06 0.06 1 1.000 1.000 4.80E-03 1.20E-02 3.60E-02 6.00E-02 6.00E-022 4.8 0.002 0.005 0.015 0.025 0.025 0.0048 0.012 0.036 0.06 0.06 2 0.618 1.171 6.63E-03 1.66E-02 4.97E-02 8.29E-02 8.29E-023 7.2 0.002 0.005 0.015 0.025 0.025 0.0048 0.012 0.036 0.06 0.06 3 0.445 1.220 8.84E-03 2.21E-02 6.63E-02 1.11E-01 1.11E-014 9.6 0.002 0.005 0.015 0.025 0.025 0.0048 0.012 0.036 0.06 0.06 4 0.347 1.241 1.11E-02 2.78E-02 8.35E-02 1.39E-01 1.39E-015 12 0.002 0.005 0.015 0.025 0.025 0.0048 0.012 0.036 0.06 0.06 5 0.285 1.252 1.35E-02 3.37E-02 1.01E-01 1.68E-01 1.68E-016 14.4 0.002 0.005 0.015 0.025 0.025 0.0048 0.012 0.036 0.06 0.06 6 0.241 1.258 1.58E-02 3.96E-02 1.19E-01 1.98E-01 1.98E-017 16.8 0.002 0.005 0.015 0.025 0.025 0.0048 0.012 0.036 0.06 0.06 7 0.209 1.262 1.82E-02 4.55E-02 1.36E-01 2.27E-01 2.27E-01

Vision 2000 (1995) Dazio(2000) Dazio(2000)

MRF + SW

φ1,1 Γ FO O LS NC Cnstory <[m] [m] [m] [m] [m]>

1 1.000 1.000 4.80E-03 1.20E-02 3.60E-02 6.00E-02 6.00E-022 0.321 1.197 1.25E-02 3.13E-02 9.38E-02 1.56E-01 1.56E-013 0.156 1.291 2.38E-02 5.94E-02 1.78E-01 2.97E-01 2.97E-014 0.093 1.347 3.85E-02 9.63E-02 2.89E-01 4.82E-01 4.82E-015 0.061 1.384 5.68E-02 1.42E-01 4.26E-01 7.10E-01 7.10E-016 0.043 1.410 7.84E-02 1.96E-01 5.88E-01 9.80E-01 9.80E-017 0.032 1.430 1.04E-01 2.59E-01 7.77E-01 1.30E+00 1.30E+00

Dazio(2000) Dazio(2000)

Residual Displacements MRF

HN FO O LS NC C FO O LS NC C φ1,1 Γ FO O LS NC Cnstory [m] < > <[m] [m] [m] [m] [m]> nstory <[m] [m] [m] [m] [m]>

1 2.4 0.001 0.002 0.005 0.025 0.025 0.0024 0.0048 0.012 0.06 0.06 1 1.000 1.000 2.40E-03 4.80E-03 1.20E-02 6.00E-02 6.00E-022 4.8 0.001 0.002 0.005 0.025 0.025 0.0024 0.0048 0.012 0.06 0.06 2 0.618 1.171 3.32E-03 6.63E-03 1.66E-02 8.29E-02 8.29E-023 7.2 0.001 0.002 0.005 0.025 0.025 0.0024 0.0048 0.012 0.06 0.06 3 0.445 1.220 4.42E-03 8.84E-03 2.21E-02 1.11E-01 1.11E-014 9.6 0.001 0.002 0.005 0.025 0.025 0.0024 0.0048 0.012 0.06 0.06 4 0.347 1.241 5.57E-03 1.11E-02 2.78E-02 1.39E-01 1.39E-015 12 0.001 0.002 0.005 0.025 0.025 0.0024 0.0048 0.012 0.06 0.06 5 0.285 1.252 6.74E-03 1.35E-02 3.37E-02 1.68E-01 1.68E-016 14.4 0.001 0.002 0.005 0.025 0.025 0.0024 0.0048 0.012 0.06 0.06 6 0.241 1.258 7.91E-03 1.58E-02 3.96E-02 1.98E-01 1.98E-017 16.8 0.001 0.002 0.005 0.025 0.025 0.0024 0.0048 0.012 0.06 0.06 7 0.209 1.262 9.09E-03 1.82E-02 4.55E-02 2.27E-01 2.27E-01

Vision 2000 (1995)

MRF + SW

φ1,1 Γ FO O LS NC Cnstory <[m] [m] [m] [m] [m]>

1 1.000 1.000 2.40E-03 4.80E-03 1.20E-02 6.00E-02 6.00E-022 0.321 1.197 6.26E-03 1.25E-02 3.13E-02 1.56E-01 1.56E-013 0.156 1.291 1.19E-02 2.38E-02 5.94E-02 2.97E-01 2.97E-014 0.093 1.347 1.93E-02 3.85E-02 9.63E-02 4.82E-01 4.82E-015 0.061 1.384 2.84E-02 5.68E-02 1.42E-01 7.10E-01 7.10E-016 0.043 1.410 3.92E-02 7.84E-02 1.96E-01 9.80E-01 9.80E-017 0.032 1.430 5.18E-02 1.04E-01 2.59E-01 1.30E+00 1.30E+00

Dazio(2000) Dazio(2000)

θ1st Story Δ1st Story

Δ*=Δ1stStory / ( Γφ1,1)

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