This document summarizes a study that used numerical simulation to analyze the seismic behavior of reinforced concrete bridge populations in Italy. Statistical analysis was used to characterize the geometric and material properties of over 450 bridges. Nonlinear dynamic analyses were performed on 100 bridge configurations generated through Latin Hypercube sampling, varying properties. Intensity measures and engineering demand parameters were computed from the analyses to identify optimal intensity measures through regression analysis. The study demonstrated OpenSees' ability to model bridges, perform large-scale automated analysis, and interface with other software for pre- and post-processing.

1. July 03-04 2014
OpenSeesDays Portugal
University of Porto, Portugal
NUMERICAL SIMULATION OF THE SEISMIC BEHAVIOR OF RC BRIDGE
POPULATIONS FOR DEFINING OPTIMAL INTENSITY MEASURES
Claudia Zelaschi, UME School, IUSS Pavia, Italy
claudia.zelaschi@umeschool.it
Ricardo Monteiro, Faculty of Engineering, University of Porto, Portugal,
ricardo.monteiro@fe.up.pt
Mário Marques, Faculty of Engineering, University of Porto, Portugal,
mariom@fe.up.pt

2. ROAD NETWORK IMMEDIATE AFTERMATH OF AN EARTHQUAKE
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WHY BRIDGES?
Risk assessment of a road network
RELEVANT ASPECTS
Bridge
Critical building
(e.g. school)
Critical building
(e.g. hospital)
Severe
damage
Slight
damage
Moderate
damage
Roads with different level of importance
Fragility assessment as function of seismic demand of
bridges (nodes of a road network)
Vulnerability of existing bridges to seismic events
Structural vulnerability fragility curves
Post-event emergency phase management
Social and economical consequences
Claudia Zelaschi et al [2014], Numerical simulation of the seismic behaviour of reinforced concrete bridge populations for defining optimal intensity measures

3. | 2
CASE STUDY
Italian RC bridges
Collection of bridge material and geometrical information
Information of about 450 reinforced concrete bridges
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
CHALLENGE
Identify classes of bridges within bridge populations,
corresponding to a relevant number of structural
configurations, that could represent a real bridge network
ITALIAN RC BRIDGES DATASET
HOW
Statistical investigation
Nonlinear dynamic analysis
Relationship IM = Intensity measure EDP = Engineering demand parameter between EDP and IM
Claudia Zelaschi et al [2014], Numerical simulation of the seismic behaviour of reinforced concrete bridge populations for defining optimal intensity measures

4. OPENQUAKE MATLAB OpenSees
IMs – EDPs
relationships
7 IML, 30 RECORDS FOR EACH,
…
IML1
IMLi
…
IML7
20 IMs
r 1
r 2
r i
r 30
100 BRIDGE CONFIGURATIONS
…
c 1
c 2
c i
c 100
30 DYNAMIC ANALYSES FOR
7 IML AND 100 BRIDGES
5 EDPs from each analysis
IM = Intensity measure IML = Intensity measure level r = record c = configuration EDP = Engineering demand parameter
| 3
FRAMEWORK OF THE STUDY
Main steps
Statistical investigation
+
Sampling method
Hazard
characterization
Seismic RC bridge response
Nonlinear Dynamic analyses
Input records
IMs
Bridge
population
EDPs
Claudia Zelaschi et al [2014], Numerical simulation of the seismic behaviour of reinforced concrete bridge populations for defining optimal intensity measures

5. | 4
STATISTICAL TREATMENT OF DATA
Goodness-of-fit tests for assigning a statistical distribution to each parameter
Data To be tested Statistical tests
Geometrical parameters
Material properties
for i = 1:#parameters
Possible distributions:
• Normal
• Lognormal
• Exponential
• Gamma
• Weibull
TYPICAL TESTED STATISTICAL DISTRIBUTION
• Chi-square
• Kolmogorov-Smirnov
α : 1%, 5%, 10%
• Selection of the most
appropriate distribution
Normal Lognormal Exponential Gamma Weibull
Real set of data Fitted distribution
end
Claudia Zelaschi et al [2014], Numerical simulation of the seismic behaviour of reinforced concrete bridge populations for defining optimal intensity measures

6. | 5
STATISTICAL TREATMENT OF DATA
Goodness-of-fit tests for assigning a statistical distribution to each parameter
L
1 2 n-1 n
a
b
b
Hmin
a a
Hmax
Others… Others…
dmin; dmax dmin; dmax
Bearings/abutments (springs) Lumped masses Fixed end Information statistically characterized
GEOMETRICAL PROPERTIES MATERIAL PROPERTIES
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)
Claudia Zelaschi et al [2014], Numerical simulation of the seismic behaviour of reinforced concrete bridge populations for defining optimal intensity measures

7. |6
GENERATION OF BRIDGE POPULATIONS
Latin Hypercube Sampling: main concept
Latin Hypercube sampling (LHS) uses a technique known as “stratified sampling without
replacement” (Iman et al., 1980).
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
i-th interval
Claudia Zelaschi et al [2014], Numerical simulation of the seismic behaviour of reinforced concrete bridge populations for defining optimal intensity measures

8. | 7
BRIDGE MODELLING
Modelling assumptions
Bearings/abutments Lumped masses Fixed end
PIER DECK
• Circular cross section
• Force based fiber element
• No element discretization
• Fiber discretization
according to moment-curvature
convergence
TYPICAL BRIDGE CONFIGURATION
• Deck assumed elastic
• No plastic hinge formation is
expected
• Pier-deck connections
through rigid links and stiff
bearings
ABUTMENTS
• ‘TwoNodeLink’ element with
zero length
• Springs with high stiffness
and bilinear response along
horizontal directions
• Restrained at the ground
Claudia Zelaschi et al [2014], Numerical simulation of the seismic behaviour of reinforced concrete bridge populations for defining optimal intensity measures

9. | 8
NONLINEAR DYNAMIC ANALYSIS OF BRIDGE POPULATION
Running OpenSees through Matlab script (Pre-processing phase 1)
MATLAB OpenSees
Statistical characterization
Goodness of fit tests
Generation of 100 bridges using
Latin Hypercube Sampling
Varying material and geometrical properties
Moment curvature analysis
(check until convergence)
Update section characteristics
For each bridge sample
Generate tcl files:
Assign_geometry.tcl
Assign_materials.tcl
Assign_restraints.tcl
…
Exit.tcl
Run eigenvalue analysis
(iterate varying eigensolver untill solution)
for i=1:100
(If error occurs substitute string in tcl
file related to eigen solver)
Extract transverse fundamental period of vibration
of each bridge
end
Claudia Zelaschi et al [2014], Numerical simulation of the seismic behaviour of reinforced concrete bridge populations for defining optimal intensity measures

10. | 9
NONLINEAR DYNAMIC ANALYSIS OF BRIDGE POPULATION
Numerical simulation analysis framework (Pre-processing phase 2)
OPENQUAKE MATLAB OpenSees
Hazard model
Seismic source
zones of Italian
zonation (ZS9)
Disaggregation
Get
intensity measures
(IM)
Record selection
Conditional
spectrum method
(Jayaram et al.,2011)
for i=1:100
Check transverse T1 of bridge
Select proper ground motion
record suite, based on scaling
end
(Sa(T1))
Engineering demand parameters
IML1
IMLi
…
IML7
Get
(EDPs)
Record 1
Record 2
…
Record 30
NTHA
NTHA
NTHA
NTHA
IML=Intensity measure level NTHA=Nonlinear time history analysis Sa(T1)=spectral acceleration conditioned at fund. period
Claudia Zelaschi et al [2014], Numerical simulation of the seismic behaviour of reinforced concrete bridge populations for defining optimal intensity measures

11. | 10
SELECTION OF OPTIMAL INTENSITY MEASURES
Relationship between seismic demand and seismic response (Post-processing phase)
MATLAB OpenSees
Get
Intensity measures
(IM)
Get
Engineering demand parameters
(EDPs)
20 scalar IMs 5 EDPs
e. g. Fajafar index (Iv) – PGA – PGV – PGD
Root mean square acceleration (aRMS)
Root mean square displacement (dRMS)
Spectral acceleration (Sa) – Arias Intensity (Ia) - …
e. g. [Sa,PGV] – [Iv,PGA] – [RT1_1.5T1,Np]
EDP01 – Equivalent SDOF maximum displacement
EDP02 – Maximum mean top displacement
EDP03 – Maximum displacement
EDP04 – Maximum column ductility
EDP05 – Maximum displacement of the shortest pier
Regression analysis
(2D, 3D)
Root mean square velocity (vRMS)
3 vector IMs
Evaluation of efficiency, proficiency, 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

12. | 11
REGRESSION ANALYSIS
Multivariate and single regression between IMs and EDP
BRIDGE LEVEL
R2=0.739 R2=0.599
ln(EDP03)
ln(Iv) ln(PGA)
GLOBAL LEVEL
R2=0.718 R2=0.426
R2=0.793
ln(Iv) ln(PGA)
R2=0.655
ln(EDP03)
ln(EDP03)
ln(EDP03)
ln(EDP03) ln(EDP03)
ln(Iv) ln(PGA)
ln(Iv) ln(PGA)
Iv = Fajfar index EDP03 = Maximum displacement PGA = peak ground acceleration
Claudia Zelaschi et al [2014], Numerical simulation of the seismic behaviour of reinforced concrete bridge populations for defining optimal intensity measures

13. | 12
RESULTS
IMs property: efficiency
Efficiency is represented by the dispersion around the relationship between the IM and the
estimated demand, obtained from nonlinear dynamic analyses
Claudia Zelaschi et al [2014], Numerical simulation of the seismic behaviour of reinforced concrete bridge populations for defining optimal intensity measures

14. | 13
RESULTS
IMs properties: practicality and Product-Moment Correlation Coefficient (PMCC)
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:
ln(EDP) = b.ln(IM) + ln(a)
Pearson Product-Moment Correlation Coefficient (PMCC) describes how robust the correlation between
structural demand and the considered IM. The closer PMCC is to one, the strongest is the correlation.
Claudia Zelaschi et al [2014], Numerical simulation of the seismic behaviour of reinforced concrete bridge populations for defining optimal intensity measures

15. | 14
CONCLUSIONS
OpenSees 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
Claudia Zelaschi et al [2014], Numerical simulation of the seismic behaviour of reinforced concrete bridge populations for defining optimal intensity measures