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]
| 1
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
| 2
CASE STUDYItalian RC bridges
Claudia Zelaschi et al [2014], Numerical simulation of the seismic behaviour of reinforced concrete bridge populations for defining optimal intensity measures
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
| 3
FRAMEWORK OF THE STUDYMain steps
Claudia Zelaschi et al [2014], Numerical simulation of the seismic behaviour of reinforced concrete bridge populations for defining optimal intensity measures
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
| 4
STATISTICAL TREATMENT OF DATAGoodness-of-fit tests for assigning a statistical distribution to each parameter
Claudia Zelaschi et al [2014], Numerical simulation of the seismic behaviour of reinforced concrete bridge populations for defining optimal intensity measures
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
| 5
STATISTICAL TREATMENT OF DATAGoodness-of-fit tests for assigning a statistical distribution to each parameter
Claudia Zelaschi et al [2014], Numerical simulation of the seismic behaviour of reinforced concrete bridge populations for defining optimal intensity measures
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
|6
GENERATION OF BRIDGE POPULATIONSLatin Hypercube Sampling: main concept
Claudia Zelaschi et al [2014], Numerical simulation of the seismic behaviour of reinforced concrete bridge populations for defining optimal intensity measures
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
| 7
BRIDGE MODELLINGModelling assumptions
Claudia Zelaschi et al [2014], Numerical simulation of the seismic behaviour of reinforced concrete bridge populations for defining optimal intensity measures
• 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
| 8
NONLINEAR DYNAMIC ANALYSIS OF BRIDGE POPULATIONRunning OpenSees through Matlab script (Pre-processing phase 1)
Claudia Zelaschi et al [2014], Numerical simulation of the seismic behaviour of reinforced concrete bridge populations for defining optimal intensity measures
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
| 9
NONLINEAR DYNAMIC ANALYSIS OF BRIDGE POPULATIONNumerical simulation analysis framework (Pre-processing phase 2)
Claudia Zelaschi et al [2014], Numerical simulation of the seismic behaviour of reinforced concrete bridge populations for defining optimal intensity measures
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
| 10
SELECTION OF OPTIMAL INTENSITY MEASURESRelationship between seismic demand and seismic response (Post-processing phase)
Claudia Zelaschi et al [2014], Numerical simulation of the seismic behaviour of reinforced concrete bridge populations for defining optimal intensity measures
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
| 11
REGRESSION ANALYSISMultivariate and single regression between IMs and EDP
Claudia Zelaschi et al [2014], Numerical simulation of the seismic behaviour of reinforced concrete bridge populations for defining optimal intensity measures
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)
| 12
RESULTSIMs property: efficiency
Claudia Zelaschi et al [2014], Numerical simulation of the seismic behaviour of reinforced concrete bridge populations for defining optimal intensity measures
Efficiency is represented by the dispersion around the relationship between the IM and the
estimated demand, obtained from nonlinear dynamic analyses
| 13
RESULTSIMs properties: practicality and Product-Moment Correlation Coefficient (PMCC)
Claudia Zelaschi et al [2014], Numerical simulation of the seismic behaviour of reinforced concrete bridge populations for defining optimal intensity measures
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.
| 14
CONCLUSIONSOpenSees capabilities
Claudia Zelaschi et al [2014], Numerical simulation of the seismic behaviour of reinforced concrete bridge populations for defining optimal intensity measures
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