Numerical Simulation of the Seismic Behaviour of RC Bridge Populations for Defining Optimal...

July 03-04 2014

OpenSeesDays PortugalUniversity of Porto, Portugal

Claudia Zelaschi, UME School, IUSS Pavia, [email protected]

NUMERICAL SIMULATION OF THE SEISMIC BEHAVIOR OF RC BRIDGE POPULATIONS FOR DEFINING OPTIMAL INTENSITY MEASURES

Ricardo Monteiro, Faculty of Engineering, University of Porto, Portugal, [email protected]

Mário Marques, Faculty of Engineering, University of Porto, Portugal,[email protected]

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WHY BRIDGES?Risk assessment of a road network

Claudia Zelaschi et al [2014], Numerical simulation of the seismic behaviour of reinforced concrete bridge populations for defining optimal intensity measures

ROAD NETWORK IMMEDIATE AFTERMATH OF AN EARTHQUAKE

RELEVANT ASPECTSBridge

Critical building

(e.g. school)

Critical building

(e.g. hospital)

Severe

damage

Slight

damage

Moderate

damage

Roads with different level of importance

Post-event emergency phase management

Fragility assessment as function of seismic demand of

bridges (nodes of a road network)

Social and economical consequences

Vulnerability of existing bridges to seismic events

Structural vulnerability � fragility curves

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CASE STUDYItalian RC bridges


Collection of bridge material and geometrical information

Information of about 450 reinforced concrete bridges

Identify classes of bridges within bridge populations,

corresponding to a relevant number of structural

configurations, that could represent a real bridge network

CHALLENGE

Most bridges, of which information was collected, are

located in Molise region

OBJECTIVE

Characterize RC bridge seismic response

Assess the correlation between traditional and

innovative IMs and nonlinear structural response of

bridges

ITALIAN RC BRIDGES DATASET

HOW

Statistical investigation

Nonlinear dynamic analysis

Relationship between EDP and IMIM = Intensity measure EDP = Engineering demand parameter

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FRAMEWORK OF THE STUDYMain steps


Statistical investigation+

Sampling method

Hazardcharacterization

Seismic RC bridge responseNonlinear Dynamic analyses

Input recordsIMs

Bridgepopulation

EDPs

IM = Intensity measure IML = Intensity measure level r = record c = configuration EDP = Engineering demand parameter

IMs – EDPsrelationships

MATLABOPENQUAKE OpenSees

…

IML1

IMLi

…

IML7

r 1

r 2

r i

r 30

7 IML, 30 RECORDS FOR EACH,20 IMs

100 BRIDGE CONFIGURATIONS

…

c 1

c i

c 100

c 2

30 DYNAMIC ANALYSES FOR7 IML AND 100 BRIDGES

5 EDPs from each analysis

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STATISTICAL TREATMENT OF DATAGoodness-of-fit tests for assigning a statistical distribution to each parameter


Normal Lognormal Exponential Gamma Weibull

Real set of data Fitted distribution

TYPICAL TESTED STATISTICAL DISTRIBUTION

for i = 1:#parameters

end

Geometrical parameters

Material properties

Possible distributions:• Normal• Lognormal• Exponential• Gamma• Weibull

Data To be tested Statistical tests

• Chi-square• Kolmogorov-Smirnov

α : 1%, 5%, 10%

• Selection of the most appropriate distribution

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STATISTICAL TREATMENT OF DATAGoodness-of-fit tests for assigning a statistical distribution to each parameter


L

1 2 nn-1

a

b

b

aa

Hmax

Hmin

Others… Others…

dmin; dmax dmin; dmax

Bearings/abutments (springs) Lumped masses Fixed end Information statistically characterized

Pier height

Total bridge length

Span length

Section diameter

Superstructure width

Reinforcement yield strength

Longitudinal reinforcement ratio

Transversal reinforcement ratio

Reinforcement Young Modulus

Concrete compressive strength

Lognormal

Lognormal

Normal

Normal

Lognormal

Normal

Lognormal

Lognormal

Normal

Normal

Number of spans = round(1.5+0.03 Total length)

GEOMETRICAL PROPERTIES MATERIAL PROPERTIES

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GENERATION OF BRIDGE POPULATIONSLatin Hypercube Sampling: main concept


Stratification is the process through which the cumulative distribution curve is subdivided into equal intervals; samples are then randomly extracted from each interval, retracing the

input probability distribution

Latin Hypercube sampling (LHS) uses a technique known as “stratified sampling without replacement” (Iman et al., 1980).

i-th interval

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BRIDGE MODELLINGModelling assumptions


• Circular cross section• Force based fiber element• No element discretization• Fiber discretization

according to moment-curvature convergence

TYPICAL BRIDGE CONFIGURATION

PIER DECK

• Deck assumed elastic• No plastic hinge formation is

expected• Pier-deck connections

through rigid links and stiff bearings

ABUTMENTS

Bearings/abutments Lumped masses Fixed end

• ‘TwoNodeLink’ element with zero length

• Springs with high stiffness and bilinear response along horizontal directions

• Restrained at the ground

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NONLINEAR DYNAMIC ANALYSIS OF BRIDGE POPULATIONRunning OpenSees through Matlab script (Pre-processing phase 1)


MATLAB OpenSees

Statistical characterizationGoodness of fit tests

Generation of 100 bridges usingLatin Hypercube Sampling

Varying material and geometrical properties

Moment curvature analysis(check until convergence)

Update section characteristics

For each bridge sampleGenerate tcl files:

Assign_geometry.tclAssign_materials.tclAssign_restraints.tcl

…Exit.tcl

Run eigenvalue analysis(iterate varying eigensolver untill solution)

(If error occurs substitute string in tclfile related to eigen solver)

Extract transverse fundamental period of vibrationof each bridge

for i=1:100

end

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NONLINEAR DYNAMIC ANALYSIS OF BRIDGE POPULATIONNumerical simulation analysis framework (Pre-processing phase 2)


MATLABOPENQUAKE OpenSees

Hazard modelSeismic source zones of Italian zonation (ZS9)

Disaggregation

Record selectionConditional

spectrum method(Jayaram et al.,2011)

Getintensity measures

(IM)

for i=1:100

end

Check transverse T1 of bridge

Select proper ground motion record suite, based on scaling

(Sa(T1))

IML1

IMLi

…

IML7

Record 1

Record 2

…

Record 30

NTHA

NTHA

NTHA

NTHA

GetEngineering demand parameters

(EDPs)

IML=Intensity measure level NTHA=Nonlinear time history analysis Sa(T1)=spectral acceleration conditioned at fund. period

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SELECTION OF OPTIMAL INTENSITY MEASURESRelationship between seismic demand and seismic response (Post-processing phase)


MATLAB OpenSees

GetIntensity measures

(IM)

GetEngineering demand parameters

(EDPs)

Regression analysis(2D, 3D)

Evaluation of efficiency, proficiency, practicality and Product Moment Correlation Coefficient (PMCC)

20 scalar IMs 5 EDPs

e. g. Fajafar index (Iv) – PGA – PGV – PGDRoot mean square acceleration (aRMS)

Root mean square velocity (vRMS)Root mean square displacement (dRMS)

Spectral acceleration (Sa) – Arias Intensity (Ia) - …

3 vector IMs

e. g. [Sa,PGV] – [Iv,PGA] – [RT1_1.5T1,Np]

EDP01 – Equivalent SDOF maximum displacementEDP02 – Maximum mean top displacement

EDP03 – Maximum displacementEDP04 – Maximum column ductility

EDP05 – Maximum displacement of the shortest pier

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REGRESSION ANALYSISMultivariate and single regression between IMs and EDP


R2=0.739 R2=0.599

R2=0.718 R2=0.426

R2=0.793

R2=0.655

Iv = Fajfar index EDP03 = Maximum displacement PGA = peak ground acceleration

BRIDGE LEVEL

GLOBAL LEVEL

ln(Iv) ln(PGA)ln(Iv) ln(PGA)

ln(E

DP

03)

ln(E

DP

03)

ln(E

DP

03)

ln(E

DP

03)

ln(E

DP

03)

ln(E

DP

03)

ln(Iv) ln(PGA)

ln(Iv) ln(PGA)

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RESULTSIMs property: efficiency


Efficiency is represented by the dispersion around the relationship between the IM and the

estimated demand, obtained from nonlinear dynamic analyses

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RESULTSIMs properties: practicality and Product-Moment Correlation Coefficient (PMCC)


ln(EDP) = b.ln(IM) + ln(a)

Practicality is an indicator based on the direct correlation between the IM and the EDP. It is quantifiable through b values of the predictive models. The closer b is to one, the more practical is the corresponding IM.

Predictive model:

Pearson Product-Moment Correlation Coefficient (PMCC) describes how robust the correlation betweenstructural demand and the considered IM. The closer PMCC is to one, the strongest is the correlation.

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CONCLUSIONSOpenSees capabilities


MODELLING AND ANALYSIS – INTERACTION WITH OTHER SOFTWARE

Capability to develop different bridge models, improving the characterization of abutments and

bearings response

Automatizing analysis procedures can be settled by means of Matlab, allowing the updating of

tcl files

PRE- AND POST-PROCESSING

Pre- and post-processing phases can be managed through external scripts, which simplifies a

large number of steps that would be needed for the treatment of input data and results

LARGE NUMBER OF ANALYSES

The present work demonstrates the possibility to handle a considerable number of analyses

Numerical Simulation of the Seismic Behaviour of RC Bridge Populations for Defining Optimal...

Engineering

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