Time-variant fragility analysis of the bridge system considering time-varying dependence among typical component seismic demands
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摘要
This paper presents a copula technique to develop time-variant seismic fragility curves for corroded bridges at the system level and considers the realistic time-varying dependence among component seismic demands. Based on material deterioration mechanisms and incremental dynamic analysis, the time-evolving seismic demands of components were obtained in the form of marginal probability distributions. The time-varying dependences among bridge components were then captured with the best fitting copula function, which was selected from the commonly used copula classes by the empirical distribution based analysis method. The system time-variant fragility curves at different damage states were developed and the effects of time-varying dependences among components on the bridge system fragility were investigated. The results indicate the time-varying dependence among components significantly affects the time-variant fragility of the bridge system. The copula technique captures the nonlinear dependence among component seismic demands accurately and easily by separating the marginal distributions and the dependence among them.
This paper presents a copula technique to develop time-variant seismic fragility curves for corroded bridges at the system level and considers the realistic time-varying dependence among component seismic demands. Based on material deterioration mechanisms and incremental dynamic analysis, the time-evolving seismic demands of components were obtained in the form of marginal probability distributions. The time-varying dependences among bridge components were then captured with the best fitting copula function, which was selected from the commonly used copula classes by the empirical distribution based analysis method. The system time-variant fragility curves at different damage states were developed and the effects of time-varying dependences among components on the bridge system fragility were investigated. The results indicate the time-varying dependence among components significantly affects the time-variant fragility of the bridge system. The copula technique captures the nonlinear dependence among component seismic demands accurately and easily by separating the marginal distributions and the dependence among them.
This paper presents a copula technique to develop time-variant seismic fragility curves for corroded bridges at the system level and considers the realistic time-varying dependence among component seismic demands. Based on material deterioration mechanisms and incremental dynamic analysis, the time-evolving seismic demands of components were obtained in the form of marginal probability distributions. The time-varying dependences among bridge components were then captured with the best fitting copula function, which was selected from the commonly used copula classes by the empirical distribution based analysis method. The system time-variant fragility curves at different damage states were developed and the effects of time-varying dependences among components on the bridge system fragility were investigated. The results indicate the time-varying dependence among components significantly affects the time-variant fragility of the bridge system. The copula technique captures the nonlinear dependence among component seismic demands accurately and easily by separating the marginal distributions and the dependence among them.
引文
Agrawal AK,Ghosn M,Alampalli S and Pan Y(2012),“Seismic Fragility of Retrofitted Multispan Continuous Steel Bridges in New York,”Journal of Bridge Engineering,17(4):562?575.
Akgül F and Frangopol DM(2004),“Lifetime Performance Analysis of Existing Prestressed Concrete Bridge Superstructures,”Journal of Structural Engineering,130(12):1889?1903.
AmiriHormozaki E,Pekcan G and Itani A(2015),“Analytical Fragility Functions for Horizontally Curved Steel I-girder Highway Bridges,”Earthquake Spectra,31(4):2235?2254.
Bertolini L,Elsener B,Pedeferri P,Redaelli E and Polder RB(2013),Corrosion of Steel in Concrete:Prevention,Diagnosis,Repair,Weinheim:Wiley-VCH Verlag GmbH&Co.KGaA.
Billah AHMM and Alam MS(2015),“Seismic Fragility Assessment of Highway Bridges:a State-of-the-Art Review,”Structure and Infrastructure Engineering,11(6):804?832.
Choi ES,DesRoches R and Nielson BG(2004),“Seismic Fragility of Typical Bridges in Moderate Seismic Zones,”Engineering Structures,26(2):187?199.
Cornell CA,Jalayer F,Hamburger RO and Foutch DA(2002),“Probabilistic Basis for 2000 SAC Federal Emergency Management Agency Steel Moment Frame Guidelines,”Journal of Structural Engineering,128(4):526?533.
Coronelli D and Gambarova P(2004),“Structural Assessment of Corroded Reinforced Concrete Beams:Modeling Guidelines,”Journal of Structural Engineering,130(8):1214?1224.
Dong Y,Frangopol DM and Saydam D(2013),“TimeVariant Sustainability Assessment of Seismically Vulnerable Bridges Subjected to Multiple Hazards,”Earthquake Engineering and Structural Dynamics,42(10):1451?1467.
Duracrete(2000),Probabilistic Performance Based Durability Design of Concrete Structures:Final technical report,The European Union-Brite EuRam III.
Edwards RV(2006),Processing Random Data:Statistics for Engineers and Scientists,Singapore:World Scientific.
FEMA(2008),HAZUS-MH Estimated Annualized Earthquake Losses for the United States,Washington:Federal Emergency Management Agency.
Ghosh J and Padgett JE(2010),“Aging Considerations in the Development of Time-Dependent Seismic Fragility Curves,”Journal of Structural Engineering,136(12):1497?1511.
Ghosh J and Padgett JE(2012),“Impact of Multiple Component Deterioration and Exposure Conditions on Seismic Vulnerability of Concrete Bridges,”Earthquake and Structures,3(5):649?673.
Ghosh J and Sood P(2016),“Consideration of TimeEvolving Capacity Distributions and Improved Degradation Models for Seismic Fragility Assessment of Aging Highway Bridges,”Reliability Engineering and System Safety,154:197?218.
Goda K(2010),“Statistical Modeling of Joint Probability Distribution Using Copula:Application to Peak and
Permanent Displacement Seismic Demands,”Structural Safety,32(2):112?123.
Goda K and Tesfamariam S(2015),“Multi-Variate Seismic Demand Modelling Using Copulas:Application to Non-Ductile Reinforced Concrete Frame in Victoria,Canada,”Structural Safety,56:39?51.
Guo A,Yuan W,Lan C,Guan X and Li H(2015),“Time-dependent Seismic Demand and Fragility of Deteriorating Bridges for Their Residual Service Life,”Bulletin of Earthquake Engineering,13(8):2389?2409.
Hwang H,Liu JB and Chiu YH(2001),“Seismic Fragility Analysis of Highway Bridges,”Technical report,Center for Earthquake Research and Information,University of Memphis,Memphis,TN,USA.
Jara J,Galván A,Jara M and Olmos B(2013),“Procedure for Determining the Seismic Vulnerability of an Irregular Isolated Bridge,”Structure and Infrastructure Engineering,9(6):516?528.
Liu Y and Weyers RE(1998),“Modeling the Timeto-Corrosion Cracking in Chloride Contaminated Reinforced Concrete Structures,”ACI Materials Journal,95(6):675?681.
Mackie K and Stojadinovic B(2001),“Probabilistic Seismic Demand Model for California Highway Bridges,”Journal of Bridge Engineering,6(6):468?481.
Mander JB,Priestley MN and Park R(1988),“Observed Stress-Strain Behavior of Confined Concrete,”Journal of Structural Engineering,114(8):1827?1849.
Mazzoni S,McKenna F,Scott M and Fenves GL(2009),The OpenSees Command Language Manual,Version2.0,Pacific Earthquake Engineering Research Center,University of California at Berkeley.
Mc Neil AJ,Frey R and Embrechts P(2005),Quantitative Risk Management:Concepts,Techniques and Tools,New Jersey:Princeton University Press.
Moschonas IF,Kappos AJ,Panetsos P,Papadopoulos V,Makarios T and Thanopoulos P(2009),“Seismic Fragility Curves for Greek Bridges:Methodology and Case Studies,”Bulletin of Earthquake Engineering,7(2):439?468.
Nelsen RB(2013),An Introduction to Copulas,New York,USA:Springer Science and Business Media.
Nielson BG(2005),“Analytical Fragility Curves for Highway Bridges in Moderate Seismic Zones,”PhDThesis,Georgia Institute of Technology,Atlanta,USA.
Nielson BG and DesRoches R(2007),“Seismic Fragility Methodology for Highway Bridges Using a Component Level Approach,”Earthquake Engineering and Structural Dynamics,36(6):823?839.
Padgett JE and DesRoches R(2007),“Sensitivity of Seismic Response and Fragility to Parameter Uncertainty,”Journal of Structural Engineering,133(12):1710-1718.
Padgett JE,Nielson BG and DesRoches R(2008),“Selection of Optimal Intensity Measures in Probabilistic Seismic Demand Models of Highway Bridge Portfolios,”Earthquake Engineering and Structural Dynamics,37(5):711?725.
Pang YT,Dang XZ and Yuan WC(2014),“An Artificial Neural Network Based Method for Seismic Fragility Analysis of Highway Bridges,”Advances in Structural Engineering,17(3):413?428.
Park C,Kim N and Haftka R(2015),“The Effect of Ignoring Dependence Between Failure Modes on Evaluating System Reliability,”Structural and Multidisciplinary Optimization,52(2):251?268.
Ramanathan KN(2012),“Next Generation Seismic Fragility Curves for California Bridges Incorporating the Evolution in Seismic Design Philosophy,”PhD Thesis,Georgia Institute of Technology,Atlanta,USA.
Ramanathan KN,Padgett JE and DesRoches R(2015),“Temporal Evolution of Seismic Fragility Curves for Concrete Box-Girder Bridges in California,”Engineering Structures,97:29?46.
Satorra A and Bentler PM(2001),“A Scaled Difference Chi-Square Test Statistic for Moment Structure Analysis,”Psychometrika,66(4):507?514.
Seo J and Linzell DG(2013),“Nonlinear Seismic Response and Parametric Examination of Horizontally Curved Steel Bridges Using 3D Computational Models,”Journal of Bridge Engineering,18(3):220?231.
Shafei B and Alipour A(2015),“Estimation of Corrosion Initiation Time in Reinforced Concrete Bridge Columns:How to Incorporate Spatial and Temporal Uncertainties,”Journal of Engineering Mechanics,141(10):04015037.
Shayanfar MA,Barkhordari MA and Ghanooni-Bagha M(2016),“Effect of Longitudinal Rebar Corrosion on the Compressive Strength Reduction of Concrete in Reinforced Concrete Structure,”Advances in Structural Engineering,19(6):897?907.
Shinozuka M,Feng MQ,Lee J and Naganuma T(2000),“Statistical Analysis of Fragility Curves,”Journal of Engineering Mechanics,126(12):1224?1231.
Shome N,Cornell CA,Bazzurro P and Carballo JE(1998),“Earthquakes,Records,and Nonlinear Responses,”Earthquake Spectra,14(3):467-500.
Simon J,Bracci JM and Gardoni P(2010),“Seismic Response and Fragility of Deteriorated Reinforced Concrete Bridges,”Journal of Structural Engineering,136(10):1273?1281.
Siqueira GH,Sanda AS,Paultre P and Padgett JE(2014),“Fragility Curves for Isolated Bridges in Eastern Canada Using Experimental Results,”Engineering Structures,74:311?324.
Sklar A(1959),Fonctions de Répartitionàn Dimensions et Leurs Marges,Paris:UniversitéParis.
TB10002.5-2005(2005),Code for Design on Subsoil and Foundation of Railway Bridge and Culvert,The Professional Standards Compilation Group of People’s Republic of China,Beijing,China.(in Chinese)
Thoft-Christensen P,Jensen F,Middleton C and Blackmore A(1996),“Assessment of the Reliability of Concrete Slab Bridges,”In:7th IFIP WG 7.5 Working Conference,Boulder,Colorado,USA,April 2-4,1996,Aalborg:Dept.of Building Technology and Structural Engineering.
Tuutti K(1982),Corrosion of Steel in Concrete Swedish,Stockholm:Cement and Concrete Research Institute.
Vidal T,Castel A and Fran?ois R(2004),“Analyzing Crack Width to Predict Corrosion in Reinforced Concrete,”Cement and Concrete Research,34:165?174.
Vo?echovskyM(2015),“Hierarchical Refinement of Latin Hypercube Samples,”Computer-Aided Civil and Infrastructure Engineering,30(5):394?411.
Vu K and Stewart MG(2000),“Structural Reliability of Concrete Bridges Including Improved Chloride-Induced Corrosion Models,”Structural Safety,22(4):313?333.
Wang Q,Wu Z and Liu S(2012),“Seismic Fragility Analysis of Highway Bridges Considering MultiDimensional Performance Limit State,”Earthquake Engineering and Engineering Vibration,11(2):185?193.
Xiao Q(2014),“Evaluating Correlation Coefficient for Nataf Transformation,”Probabilistic Engineering Mechanics,37:1?6.
Xu Y,Tang XS,Wang JP and Kuo-Chen H(2016),“Copula-Based Joint Probability Function for PGAand CAV:a Case Study from Taiwan,”Earthquake Engineering and Structural Dynamics,45(13):2123?2136.
Zhang Y,Fan J and Fan W(2016),“Seismic Fragility Analysis of Concrete Bridge Piers Reinforced by Steel Fibers,”Advances in Structural Engineering,19(5):837?848.
Akgül F and Frangopol DM(2004),“Lifetime Performance Analysis of Existing Prestressed Concrete Bridge Superstructures,”Journal of Structural Engineering,130(12):1889?1903.
AmiriHormozaki E,Pekcan G and Itani A(2015),“Analytical Fragility Functions for Horizontally Curved Steel I-girder Highway Bridges,”Earthquake Spectra,31(4):2235?2254.
Bertolini L,Elsener B,Pedeferri P,Redaelli E and Polder RB(2013),Corrosion of Steel in Concrete:Prevention,Diagnosis,Repair,Weinheim:Wiley-VCH Verlag GmbH&Co.KGaA.
Billah AHMM and Alam MS(2015),“Seismic Fragility Assessment of Highway Bridges:a State-of-the-Art Review,”Structure and Infrastructure Engineering,11(6):804?832.
Choi ES,DesRoches R and Nielson BG(2004),“Seismic Fragility of Typical Bridges in Moderate Seismic Zones,”Engineering Structures,26(2):187?199.
Cornell CA,Jalayer F,Hamburger RO and Foutch DA(2002),“Probabilistic Basis for 2000 SAC Federal Emergency Management Agency Steel Moment Frame Guidelines,”Journal of Structural Engineering,128(4):526?533.
Coronelli D and Gambarova P(2004),“Structural Assessment of Corroded Reinforced Concrete Beams:Modeling Guidelines,”Journal of Structural Engineering,130(8):1214?1224.
Dong Y,Frangopol DM and Saydam D(2013),“TimeVariant Sustainability Assessment of Seismically Vulnerable Bridges Subjected to Multiple Hazards,”Earthquake Engineering and Structural Dynamics,42(10):1451?1467.
Duracrete(2000),Probabilistic Performance Based Durability Design of Concrete Structures:Final technical report,The European Union-Brite EuRam III.
Edwards RV(2006),Processing Random Data:Statistics for Engineers and Scientists,Singapore:World Scientific.
FEMA(2008),HAZUS-MH Estimated Annualized Earthquake Losses for the United States,Washington:Federal Emergency Management Agency.
Ghosh J and Padgett JE(2010),“Aging Considerations in the Development of Time-Dependent Seismic Fragility Curves,”Journal of Structural Engineering,136(12):1497?1511.
Ghosh J and Padgett JE(2012),“Impact of Multiple Component Deterioration and Exposure Conditions on Seismic Vulnerability of Concrete Bridges,”Earthquake and Structures,3(5):649?673.
Ghosh J and Sood P(2016),“Consideration of TimeEvolving Capacity Distributions and Improved Degradation Models for Seismic Fragility Assessment of Aging Highway Bridges,”Reliability Engineering and System Safety,154:197?218.
Goda K(2010),“Statistical Modeling of Joint Probability Distribution Using Copula:Application to Peak and
Permanent Displacement Seismic Demands,”Structural Safety,32(2):112?123.
Goda K and Tesfamariam S(2015),“Multi-Variate Seismic Demand Modelling Using Copulas:Application to Non-Ductile Reinforced Concrete Frame in Victoria,Canada,”Structural Safety,56:39?51.
Guo A,Yuan W,Lan C,Guan X and Li H(2015),“Time-dependent Seismic Demand and Fragility of Deteriorating Bridges for Their Residual Service Life,”Bulletin of Earthquake Engineering,13(8):2389?2409.
Hwang H,Liu JB and Chiu YH(2001),“Seismic Fragility Analysis of Highway Bridges,”Technical report,Center for Earthquake Research and Information,University of Memphis,Memphis,TN,USA.
Jara J,Galván A,Jara M and Olmos B(2013),“Procedure for Determining the Seismic Vulnerability of an Irregular Isolated Bridge,”Structure and Infrastructure Engineering,9(6):516?528.
Liu Y and Weyers RE(1998),“Modeling the Timeto-Corrosion Cracking in Chloride Contaminated Reinforced Concrete Structures,”ACI Materials Journal,95(6):675?681.
Mackie K and Stojadinovic B(2001),“Probabilistic Seismic Demand Model for California Highway Bridges,”Journal of Bridge Engineering,6(6):468?481.
Mander JB,Priestley MN and Park R(1988),“Observed Stress-Strain Behavior of Confined Concrete,”Journal of Structural Engineering,114(8):1827?1849.
Mazzoni S,McKenna F,Scott M and Fenves GL(2009),The OpenSees Command Language Manual,Version2.0,Pacific Earthquake Engineering Research Center,University of California at Berkeley.
Mc Neil AJ,Frey R and Embrechts P(2005),Quantitative Risk Management:Concepts,Techniques and Tools,New Jersey:Princeton University Press.
Moschonas IF,Kappos AJ,Panetsos P,Papadopoulos V,Makarios T and Thanopoulos P(2009),“Seismic Fragility Curves for Greek Bridges:Methodology and Case Studies,”Bulletin of Earthquake Engineering,7(2):439?468.
Nelsen RB(2013),An Introduction to Copulas,New York,USA:Springer Science and Business Media.
Nielson BG(2005),“Analytical Fragility Curves for Highway Bridges in Moderate Seismic Zones,”PhDThesis,Georgia Institute of Technology,Atlanta,USA.
Nielson BG and DesRoches R(2007),“Seismic Fragility Methodology for Highway Bridges Using a Component Level Approach,”Earthquake Engineering and Structural Dynamics,36(6):823?839.
Padgett JE and DesRoches R(2007),“Sensitivity of Seismic Response and Fragility to Parameter Uncertainty,”Journal of Structural Engineering,133(12):1710-1718.
Padgett JE,Nielson BG and DesRoches R(2008),“Selection of Optimal Intensity Measures in Probabilistic Seismic Demand Models of Highway Bridge Portfolios,”Earthquake Engineering and Structural Dynamics,37(5):711?725.
Pang YT,Dang XZ and Yuan WC(2014),“An Artificial Neural Network Based Method for Seismic Fragility Analysis of Highway Bridges,”Advances in Structural Engineering,17(3):413?428.
Park C,Kim N and Haftka R(2015),“The Effect of Ignoring Dependence Between Failure Modes on Evaluating System Reliability,”Structural and Multidisciplinary Optimization,52(2):251?268.
Ramanathan KN(2012),“Next Generation Seismic Fragility Curves for California Bridges Incorporating the Evolution in Seismic Design Philosophy,”PhD Thesis,Georgia Institute of Technology,Atlanta,USA.
Ramanathan KN,Padgett JE and DesRoches R(2015),“Temporal Evolution of Seismic Fragility Curves for Concrete Box-Girder Bridges in California,”Engineering Structures,97:29?46.
Satorra A and Bentler PM(2001),“A Scaled Difference Chi-Square Test Statistic for Moment Structure Analysis,”Psychometrika,66(4):507?514.
Seo J and Linzell DG(2013),“Nonlinear Seismic Response and Parametric Examination of Horizontally Curved Steel Bridges Using 3D Computational Models,”Journal of Bridge Engineering,18(3):220?231.
Shafei B and Alipour A(2015),“Estimation of Corrosion Initiation Time in Reinforced Concrete Bridge Columns:How to Incorporate Spatial and Temporal Uncertainties,”Journal of Engineering Mechanics,141(10):04015037.
Shayanfar MA,Barkhordari MA and Ghanooni-Bagha M(2016),“Effect of Longitudinal Rebar Corrosion on the Compressive Strength Reduction of Concrete in Reinforced Concrete Structure,”Advances in Structural Engineering,19(6):897?907.
Shinozuka M,Feng MQ,Lee J and Naganuma T(2000),“Statistical Analysis of Fragility Curves,”Journal of Engineering Mechanics,126(12):1224?1231.
Shome N,Cornell CA,Bazzurro P and Carballo JE(1998),“Earthquakes,Records,and Nonlinear Responses,”Earthquake Spectra,14(3):467-500.
Simon J,Bracci JM and Gardoni P(2010),“Seismic Response and Fragility of Deteriorated Reinforced Concrete Bridges,”Journal of Structural Engineering,136(10):1273?1281.
Siqueira GH,Sanda AS,Paultre P and Padgett JE(2014),“Fragility Curves for Isolated Bridges in Eastern Canada Using Experimental Results,”Engineering Structures,74:311?324.
Sklar A(1959),Fonctions de Répartitionàn Dimensions et Leurs Marges,Paris:UniversitéParis.
TB10002.5-2005(2005),Code for Design on Subsoil and Foundation of Railway Bridge and Culvert,The Professional Standards Compilation Group of People’s Republic of China,Beijing,China.(in Chinese)
Thoft-Christensen P,Jensen F,Middleton C and Blackmore A(1996),“Assessment of the Reliability of Concrete Slab Bridges,”In:7th IFIP WG 7.5 Working Conference,Boulder,Colorado,USA,April 2-4,1996,Aalborg:Dept.of Building Technology and Structural Engineering.
Tuutti K(1982),Corrosion of Steel in Concrete Swedish,Stockholm:Cement and Concrete Research Institute.
Vidal T,Castel A and Fran?ois R(2004),“Analyzing Crack Width to Predict Corrosion in Reinforced Concrete,”Cement and Concrete Research,34:165?174.
Vo?echovskyM(2015),“Hierarchical Refinement of Latin Hypercube Samples,”Computer-Aided Civil and Infrastructure Engineering,30(5):394?411.
Vu K and Stewart MG(2000),“Structural Reliability of Concrete Bridges Including Improved Chloride-Induced Corrosion Models,”Structural Safety,22(4):313?333.
Wang Q,Wu Z and Liu S(2012),“Seismic Fragility Analysis of Highway Bridges Considering MultiDimensional Performance Limit State,”Earthquake Engineering and Engineering Vibration,11(2):185?193.
Xiao Q(2014),“Evaluating Correlation Coefficient for Nataf Transformation,”Probabilistic Engineering Mechanics,37:1?6.
Xu Y,Tang XS,Wang JP and Kuo-Chen H(2016),“Copula-Based Joint Probability Function for PGAand CAV:a Case Study from Taiwan,”Earthquake Engineering and Structural Dynamics,45(13):2123?2136.
Zhang Y,Fan J and Fan W(2016),“Seismic Fragility Analysis of Concrete Bridge Piers Reinforced by Steel Fibers,”Advances in Structural Engineering,19(5):837?848.
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