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- 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 | 1 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

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