Probability-based practice-oriented seismic behaviour assessment of simply supported RC bridges considering the variation and correlation in pier performance
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摘要
Probability-based seismic performance assessment of in-service bridges has gained much attention in the scientific community during the past decades. The nonlinear static pushover analysis is critical for describing the seismic behaviour of bridges subjected to moderate to high seismicity due to its simplicity. However, in existing analysis methods,the generation of pushover curve needs tremendous amount of computational costs and requires skills, which may halter its application in practice, implying the importance of developing practice-oriented analysis method with improved efficiency. Moreover, the bridge pier performance has been modelled as deterministic, indicating that the variation associated with the pier material and mechanical properties remains unaddressed. The correlation in the performance of different piers also exists due to the common design provisions and construction conditions but has neither been taken into account. This paper develops a simplified pushover analysis procedure for the seismic assessment of simply supported RC bridges. With the proposed method, the pushover curve of the bridge can be obtained explicitly without complex finite element modelling. A random factor is introduced to reflect the uncertainty in relation to the pushover curve. The correlation in the pier performance is considered by employing the Gaussian copula function to construct the joint probability distribution. Illustrative examples are presented to demonstrate theapplicability of the method and to investigate the impact of variation and correlation in bridge pier behaviour on the seismic performance assessment.
Probability-based seismic performance assessment of in-service bridges has gained much attention in the scientific community during the past decades. The nonlinear static pushover analysis is critical for describing the seismic behaviour of bridges subjected to moderate to high seismicity due to its simplicity. However, in existing analysis methods,the generation of pushover curve needs tremendous amount of computational costs and requires skills, which may halter its application in practice, implying the importance of developing practice-oriented analysis method with improved efficiency. Moreover, the bridge pier performance has been modelled as deterministic, indicating that the variation associated with the pier material and mechanical properties remains unaddressed. The correlation in the performance of different piers also exists due to the common design provisions and construction conditions but has neither been taken into account. This paper develops a simplified pushover analysis procedure for the seismic assessment of simply supported RC bridges. With the proposed method, the pushover curve of the bridge can be obtained explicitly without complex finite element modelling. A random factor is introduced to reflect the uncertainty in relation to the pushover curve. The correlation in the pier performance is considered by employing the Gaussian copula function to construct the joint probability distribution. Illustrative examples are presented to demonstrate theapplicability of the method and to investigate the impact of variation and correlation in bridge pier behaviour on the seismic performance assessment.
Probability-based seismic performance assessment of in-service bridges has gained much attention in the scientific community during the past decades. The nonlinear static pushover analysis is critical for describing the seismic behaviour of bridges subjected to moderate to high seismicity due to its simplicity. However, in existing analysis methods,the generation of pushover curve needs tremendous amount of computational costs and requires skills, which may halter its application in practice, implying the importance of developing practice-oriented analysis method with improved efficiency. Moreover, the bridge pier performance has been modelled as deterministic, indicating that the variation associated with the pier material and mechanical properties remains unaddressed. The correlation in the performance of different piers also exists due to the common design provisions and construction conditions but has neither been taken into account. This paper develops a simplified pushover analysis procedure for the seismic assessment of simply supported RC bridges. With the proposed method, the pushover curve of the bridge can be obtained explicitly without complex finite element modelling. A random factor is introduced to reflect the uncertainty in relation to the pushover curve. The correlation in the pier performance is considered by employing the Gaussian copula function to construct the joint probability distribution. Illustrative examples are presented to demonstrate theapplicability of the method and to investigate the impact of variation and correlation in bridge pier behaviour on the seismic performance assessment.
引文
Applied Technology Council(ATC), 1996. Seismic Evaluation and Retrofit of Concrete Buildings. SSC 96-01. Applied Technology Council, Redwood City.
Aydinoglu, M.N., 2003. An incremental response spectrum analysis procedure based on inelastic spectral displacements for multimode seismic performance evaluation. Bulletin of Earthquake Engineering 1(1), 3-36.
Borzi, B., Pinho, R., Crowley, H., 2008. Simplified pushover-based vulnerability analysis for large-scale assessment of RC buildings. Engineering Structures 30(3), 804-820.
Bradley, B.A., 2013. Practice-oriented estimation of the seismic demand hazard using ground motions at few intensity levels. Earthquake Engineering&Structural Dynamics 42(14), 2167-2185.
Camara, A., Astiz, M.A., 2012. Pushover analysis for the seismic response prediction of cable-stayed bridges under multidirectional excitation. Engineering Structures 41(3),444-455.
Chopra, A.K., Goel, R.K., 2000. Evaluation of NSP to estimate seismic deformation:SDF system. Journal of Structural Engineering 126(4), 482-490.
Der Kiureghian, A., 1996. Structural reliability methods for seismic safety assessment:a review. Engineering Structures18(6), 412-424.
Der Kiureghian, A., Liu, P.L.,1986. Structural reliability under incomplete probability information. Journal of Engineering Mechanics 112(1), 85-104.
Du, X., Qiang, H., Li, Z., et al., 2008. The seismic damage of bridges in the 2008 Wenchuan Earthquake and lessons from its damage. Journal of Beijing University of Technology 34(12),1270-1279.
Fajfar, P., 2007. Seismic assessment of structures by a practiceoriented method. In:Ibrahimbegovic, A., Kozar, I.(Eds.),Extreme Man-made and Natural Hazards in Dynamics of Structures. Springer, Dordrecht, pp. 257-284.
Freeman, S.A., 1978. Prediction of Response of Concrete Buildings to Severe Earthquake Motion. American Concrete Institute,Detroit.
Freeman, S.A., Nicoletti, J.P., Tyrell, J.V., 1975. Evaluations of existing buildings for seismic risk-a case study of Puget Sound Naval Shipyard. In:1st U.S. National Conference on Earthquake Engineering, Bremerton, 1975.
Ghobarah, A., Aly, N.M., El-Attar, M., 1998. Seismic reliability assessment of existing reinforced concrete buildings. Journal of Earthquake Engineering 2(4), 569-592.
Goda, K., Hong, H.P., 2008. Estimation of seismic loss for spatially distributed buildings. Earthquake Spectra 24, 889-910.
Kalkan, E., Kunnath, S., 2004. Lateral load distribution in nonlinear static procedures for seismic design. In:Constructures Congress, Nashville, 2004.
Krawinkler, H., Rahnama, M., 1992. Effects of soft soils on design spectra. In:The 10th World Conference on Earthquake Engineering, Rotterdam, 1992.
Krawinkler, H., Seneviratna, G.D.P.K., 1998. Pros and cons of a pushover analysis of seismic performance evaluation.Engineering Structures 20(S4/6), 452-464.
Kolias, B., Fardis, M.N., Pecker, A., 2005. Design of Structures for Earthquake Resistance-Part 2:Bridges. EN 1998-2. Institution of Civil Engineers, London.
Lee, R., Kiremidjian, A.S., 2007. Uncertainty and correlation for loss assessment of spatially distributed systems. Earthquake Spectra 23, 753-770.
Li, Q., Ellingwood, B.R., 2007. Performance evaluation and damage assessment of steel frame buildings under main shock-aftershock earthquake sequences. Earthquake Engineering&Structural Dynamics 36(3), 405-427.
Li, Q., Ellingwood, B.R., 2008. Damage inspection and vulnerability analysis of existing buildings with steel moment-resisting frames. Engineering Structures 30(2), 338-351.
Li, Q., Wang, C., 2015. Updating the assessment of resistance and reliability of existing aging bridges with prior service loads.Journal of Structural Engineering 141(12), 04015072.
Ministry of Housing and Urban-Rural Development of the People's Republic of China, 2011. Code for Seismic Design of Urban Bridges. CJJ 166-2011. China Agriculture and Building Press, Beijing.
Ministry of Transport of the People's Republic of China, 1989.Code for Seismic Design of Highway Bridges. JTJ 004-89.China Agriculture and Building Press, Beijing.
Muntasir Billah,A.H.M., Shahria Alam, M., 2015. Seismic fragility assessment of highway bridges:a state-of-the-art review.Structure and Infrastructure Engineering 11(6), 804-832.
Noh, Y., Choi, K.K., Du, L., 2009. Reliability-based design optimization of problems with correlated input variables using a Gaussian copula. Structural and Multidisciplinary Optimization 38(1), 1-16.
Panandikar, N., Narayan, K.S.B., 2015. Sensitivity of pushover curve to material and geometric modelling-an analytical investigation. Structures 2, 91-97.
Qin, S., 2008. Static Nonlinear Analysis Methods for Estimating Seismic Performance for Bridges(PhD thesis). Dalian University of Technology, Dalian.
Stewart, M.G., Val, D.V., 1999. Role of load history in reliability based decision analysis of aging bridges. Journal of Structural Engineering 125(7), 776-783.
Vidic, T., Fajfar, P., Fischinger, M., 1994. Consistent inelastic design spectra:strength and displacement. Earthquake Engineering and Structural Dynamics 23(5), 507-521.
Vitoontus, S., 2012. Risk Assessment of Building Inventories Exposed to Large Scale Natural Hazards(PhD thesis). Georgia Institute of Technology, Atlanta.
Wang, C., Bao, Q., Li, Q., 2014. Simplified pushover analysis method for simply supported concrete bridges. Technology for Earthquake Disaster Prevention 9(3), 439-446.
Wang, C., Zhang, H., Li, Q., 2017. Time-dependent reliability assessment of aging series systems subjected to nonstationary loads. Structure and Infrastructure Engineering 13(12), 1513-1522.
Wight, J.K., MacGregor, J.G., 2012. Reinforced Concrete:Mechanics and Design, sixth ed. Pearson Education, Inc., Upper Saddle River.
Zordan, T., Briseghella, B., Lan, C., 2011. Parametric and pushover analyses on integral abutment bridge. Engineering Structures33(2), 502-515.
Aydinoglu, M.N., 2003. An incremental response spectrum analysis procedure based on inelastic spectral displacements for multimode seismic performance evaluation. Bulletin of Earthquake Engineering 1(1), 3-36.
Borzi, B., Pinho, R., Crowley, H., 2008. Simplified pushover-based vulnerability analysis for large-scale assessment of RC buildings. Engineering Structures 30(3), 804-820.
Bradley, B.A., 2013. Practice-oriented estimation of the seismic demand hazard using ground motions at few intensity levels. Earthquake Engineering&Structural Dynamics 42(14), 2167-2185.
Camara, A., Astiz, M.A., 2012. Pushover analysis for the seismic response prediction of cable-stayed bridges under multidirectional excitation. Engineering Structures 41(3),444-455.
Chopra, A.K., Goel, R.K., 2000. Evaluation of NSP to estimate seismic deformation:SDF system. Journal of Structural Engineering 126(4), 482-490.
Der Kiureghian, A., 1996. Structural reliability methods for seismic safety assessment:a review. Engineering Structures18(6), 412-424.
Der Kiureghian, A., Liu, P.L.,1986. Structural reliability under incomplete probability information. Journal of Engineering Mechanics 112(1), 85-104.
Du, X., Qiang, H., Li, Z., et al., 2008. The seismic damage of bridges in the 2008 Wenchuan Earthquake and lessons from its damage. Journal of Beijing University of Technology 34(12),1270-1279.
Fajfar, P., 2007. Seismic assessment of structures by a practiceoriented method. In:Ibrahimbegovic, A., Kozar, I.(Eds.),Extreme Man-made and Natural Hazards in Dynamics of Structures. Springer, Dordrecht, pp. 257-284.
Freeman, S.A., 1978. Prediction of Response of Concrete Buildings to Severe Earthquake Motion. American Concrete Institute,Detroit.
Freeman, S.A., Nicoletti, J.P., Tyrell, J.V., 1975. Evaluations of existing buildings for seismic risk-a case study of Puget Sound Naval Shipyard. In:1st U.S. National Conference on Earthquake Engineering, Bremerton, 1975.
Ghobarah, A., Aly, N.M., El-Attar, M., 1998. Seismic reliability assessment of existing reinforced concrete buildings. Journal of Earthquake Engineering 2(4), 569-592.
Goda, K., Hong, H.P., 2008. Estimation of seismic loss for spatially distributed buildings. Earthquake Spectra 24, 889-910.
Kalkan, E., Kunnath, S., 2004. Lateral load distribution in nonlinear static procedures for seismic design. In:Constructures Congress, Nashville, 2004.
Krawinkler, H., Rahnama, M., 1992. Effects of soft soils on design spectra. In:The 10th World Conference on Earthquake Engineering, Rotterdam, 1992.
Krawinkler, H., Seneviratna, G.D.P.K., 1998. Pros and cons of a pushover analysis of seismic performance evaluation.Engineering Structures 20(S4/6), 452-464.
Kolias, B., Fardis, M.N., Pecker, A., 2005. Design of Structures for Earthquake Resistance-Part 2:Bridges. EN 1998-2. Institution of Civil Engineers, London.
Lee, R., Kiremidjian, A.S., 2007. Uncertainty and correlation for loss assessment of spatially distributed systems. Earthquake Spectra 23, 753-770.
Li, Q., Ellingwood, B.R., 2007. Performance evaluation and damage assessment of steel frame buildings under main shock-aftershock earthquake sequences. Earthquake Engineering&Structural Dynamics 36(3), 405-427.
Li, Q., Ellingwood, B.R., 2008. Damage inspection and vulnerability analysis of existing buildings with steel moment-resisting frames. Engineering Structures 30(2), 338-351.
Li, Q., Wang, C., 2015. Updating the assessment of resistance and reliability of existing aging bridges with prior service loads.Journal of Structural Engineering 141(12), 04015072.
Ministry of Housing and Urban-Rural Development of the People's Republic of China, 2011. Code for Seismic Design of Urban Bridges. CJJ 166-2011. China Agriculture and Building Press, Beijing.
Ministry of Transport of the People's Republic of China, 1989.Code for Seismic Design of Highway Bridges. JTJ 004-89.China Agriculture and Building Press, Beijing.
Muntasir Billah,A.H.M., Shahria Alam, M., 2015. Seismic fragility assessment of highway bridges:a state-of-the-art review.Structure and Infrastructure Engineering 11(6), 804-832.
Noh, Y., Choi, K.K., Du, L., 2009. Reliability-based design optimization of problems with correlated input variables using a Gaussian copula. Structural and Multidisciplinary Optimization 38(1), 1-16.
Panandikar, N., Narayan, K.S.B., 2015. Sensitivity of pushover curve to material and geometric modelling-an analytical investigation. Structures 2, 91-97.
Qin, S., 2008. Static Nonlinear Analysis Methods for Estimating Seismic Performance for Bridges(PhD thesis). Dalian University of Technology, Dalian.
Stewart, M.G., Val, D.V., 1999. Role of load history in reliability based decision analysis of aging bridges. Journal of Structural Engineering 125(7), 776-783.
Vidic, T., Fajfar, P., Fischinger, M., 1994. Consistent inelastic design spectra:strength and displacement. Earthquake Engineering and Structural Dynamics 23(5), 507-521.
Vitoontus, S., 2012. Risk Assessment of Building Inventories Exposed to Large Scale Natural Hazards(PhD thesis). Georgia Institute of Technology, Atlanta.
Wang, C., Bao, Q., Li, Q., 2014. Simplified pushover analysis method for simply supported concrete bridges. Technology for Earthquake Disaster Prevention 9(3), 439-446.
Wang, C., Zhang, H., Li, Q., 2017. Time-dependent reliability assessment of aging series systems subjected to nonstationary loads. Structure and Infrastructure Engineering 13(12), 1513-1522.
Wight, J.K., MacGregor, J.G., 2012. Reinforced Concrete:Mechanics and Design, sixth ed. Pearson Education, Inc., Upper Saddle River.
Zordan, T., Briseghella, B., Lan, C., 2011. Parametric and pushover analyses on integral abutment bridge. Engineering Structures33(2), 502-515.