Bayesian Updating of Fragility Functions Using Hybrid Simulation
Publication: Journal of Structural Engineering
Volume 139, Issue 7
Abstract
The accuracy of fragility functions is critical for regional risk and loss estimations. This paper proposes a two-stage approach to generate improved fragility functions for engineering structures using field measurement and experimental data. In the first stage, the linear and nonlinear parameters of the bridge model are calibrated using measured earthquake responses and cyclic testing data; analytical fragilities are then generated with the calibrated model. In the second stage, a Bayesian updating approach is used to further update the derived fragilities using hybrid (analytical-experimental) simulation results. To illustrate the effectiveness of the proposed approach, fragility functions are generated for the Meloland Road Overcrossing Bridge considering four cases that represent an increasing level of data availability. A comparison of the four sets of fragility functions shows that appropriate calibration of bridge model is critical to the accuracy of the fragilities. In addition, hybrid simulation provides an economic and efficient way of validating and improving the accuracy of fragility functions through Bayesian updating.
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Acknowledgments
The authors gratefully acknowledge the partial support of this research by the National Science Foundation under the Grant No. CMMI-0724172 (NEESR-SD) and the China Scholarship Council, which partially supports the first author’s Ph.D. study.
References
Allemang, R. J., and Brown, D. L. (1982). “A correlation coefficient for modal vector analysis.” Proc., 1st Int. Modal Analysis Conf., Society for Experimental Mechanics, Orlando, FL, Vol. 1, 110–116.
Anderson, D. G. (2003). “Laboratory testing of nonlinear soil properties: I & II.” Rep. Prepared for Pacific Earthquake Engineering Research Center, Univ. of California at Berkeley, Berkeley, CA.
Ang, A. H., and Tang, W. H. (1975). Probability concepts in engineering planning and design: Basic principles, Vol. I, Wiley, New York.
Applied Technology Council (ATC). (1996). “Seismic evaluation and retrofit of concrete buildings.” Rep. ATC-40, ATC, Redwood City, CA.
Aviram, A., Mackie, K. R., and Stojadinovic, B. (2008). “Guidelines for nonlinear analysis of bridge structures in California.” Technical Rep. 2008/03, Pacific Earthquake Engineering Research Center, Univ. of California at Berkeley, Berkeley, CA.
Bentz, E. C. (2000). “Sectional analysis of reinforced concrete members.” Ph.D. thesis, Dept. of Civil Engineering, Univ. of Toronto, Toronto.
Bowman, A. W., and Azzalini, A. (1997). Applied smoothing techniques for data analysis, Oxford University Press, New York.
Campbell, K. W., and Bozorgnia, Y. (2008). “NGA ground motion model for the geometric mean horizontal component of PGA, PGV, PGD and 5% damped linear elastic response spectra for periods ranging from 0.01 to 10 s.” Earthquake Spectra, 24(1), 139–172.
Choe, D., Gardoni, P., and Rosowsky, D. (2007). “Closed-form fragility estimates, parameter sensitivity, and bayesian updating for RC columns.” J. Eng. Mech., 133(7), 833–843.
Der Kiureghian, A. (1999a). “A Bayesian framework for fragility assessment.” Proc., 8th Int. Conf. on Applications of Statistics and Probability (ICASP) in Civil Engineering Reliability and Risk Analysis, R. E. Melchers and M. G. Stewart, eds., A. A. Balkema Publishers, Rotterdam, Netherlands, Vol. 1, 219–226.
Der Kiureghian, A. (1999b). “Fragility estimates for electrical substation equipment.” Proc., 5th U.S. Conf. on Lifeline Earthquake Engineering, W. Elliott and P. McDonough, eds., Technical Council on Lifeline Earthquake Engineering, ASCE, Reston, VA, 643–652.
Der Kiureghian, A. (2002). “Bayesian methods for seismic fragility assessment of lifeline components.” Acceptable risk processes: Lifelines and natural hazards, C. Taylor and E. VanMarcke, eds., ASCE, Reston, VA, 61–77.
Elnashai, A. S. (2003). “Next generation vulnerability functions for RC structures.” Proc., Response of Structures to Extreme Loading, Elsevier, Toronto.
Elnashai, A. S., Papanikolaou, V., and Lee, D. (2004a). “Zeus NL—A system for inelastic analysis of structures.” Mid-America Earthquake Center CD Release 04-01, Mid-America Earthquake Center, Univ. of Illinois at Urbana-Champaign, Urbana, IL.
Elnashai, A. S., Spencer, B. F., Kuchma, D., Ghaboussi, J., Hashash, Y., and Quan, G. (2004b). “Multi-axial full-scale sub-structured testing and simulation (MUST-SIM) facility at the University of Illinois at Urbana-Champaign.” Proc., 13th World Conf. on Earthquake Engineering, International Association for Earthquake Engineering, Tokyo.
Frankel, A. D., and Leyendecker, E. V. (2001). “Seismic hazard curves and uniform hazard response spectra for the United States.” Open-File Rep. 01–436, U.S. Geological Survey, Menlo Park, CA.
Gasparini, D. A., and Vanmarcke, E. H. (1976). “Simulated earthquake motions compatible with prescribed response spectra, evaluation of seismic safety of buildings.” Rep. No. 2, Massachusetts Institute of Technology, Cambridge, MA.
Gardoni, P., Der Kiureghian, A., and Mosalam, K. M. (2002). “Probabilistic capacity models and fragility estimates for reinforced concrete columns based on experimental observations.” J. Eng. Mech., 128(10), 1024–1038.
Gardoni, P., Mosalam, K. M., and Der Kiureghian, A. D. (2003). “Probabilistic seismic demand models and fragility estimates for RC bridges.” J. Earthquake Eng., 7(1), 79–106.
Hart, C. R., Kuchma, D. A., Lowes, L. N., Lehman, D. E., Marley, K. P., and Birely, A. C. (2008). “Testing of RC walls using advanced load-control and instrumentation methods.” Proc., 14th World Conf. on Earthquake Engineering, China Earthquake Administration Ministry of Construction, Beijing.
Hashash, Y., Groholski, D. R., Phillips, C. A., and Park, D. (2009). DEEPSOIL v3.5beta, user manual and tutorial, Univ. of Illimois at Urbana-Champaign, Urbana, IL.
Holub, C. J. (2005). “Similitude considerations for small scale distributed hybrid simulation of reinforced concrete structures.” M.S. thesis, Dept. of Civil and Environmental Engineering, Univ. of Illinois at Urbana-Champaign, Urbana, IL.
Holub, C. J. (2009). “Interaction of variable axial load and shear effects in RC bridges.” Ph.D. thesis, Dept. of Civil and Environmental Engineering, Univ. of Illinois at Urbana-Champaign, Urbana, IL.
Huang, Q., Gardoni, P., and Hurlebaus, S. (2010). “Probabilistic seismic demand models and fragility estimates for reinforced concrete highway bridge with one single-column bent.” J. Eng. Mech., 136(11), 1340–1353.
Izzuddin, B. A., Karayannis, C. G., and Elnashai, A. S. (1994). “Advanced nonlinear formulation for reinforced concrete beam-columns.” J. Struct. Eng., 120(10), 2913–2934.
Jang, S., Li, J., and Spencer, B. F., Jr. (2013). “Corrosion estimation of a historic truss bridge using model updating.” J. Bridge Eng., 18(7), 678–689.
Kempton, J. J., and Stewart, J. P. (2006). “Prediction equations for significant duration of earthquake ground motions considering site and near-source effects.” Earthquake Spectra, 22(4), 985–1013.
Koutsourelakis, P. S. (2010). “Assessing structural vulnerability against earthquakes using multi-dimensional fragility surfaces: A Bayesian framework.” Probab. Eng. Mech., 25(1), 49–60.
Kwon, O., and Elnashai, A. S. (2007). “Probabilistic seismic assessment of structure, foundation and soil interacting systems.” NSEL Rep. Series 004, Univ. of Illinois at Urbana-Champaign, Urbana, IL.
Kwon, O. S., Nakata, N., Elnashai, A., and Spencer, B. (2005). “A framework for multi-site distributed simulation and application to complex structural systems.” J. Earthquake Eng., 9(5), 741–753.
Lee, D. H., and Elnashai, A. S. (2001). “Seismic analysis of RC bridge columns with flexure-shear interaction.” J. Struct. Eng., 127(5), 546–553.
Ljung, L. (1999). System identification: Theory for the user, 2nd Ed., Prentice Hall, Englewood Cliffs, NJ.
Loh, C., and Wu, T. (2000). “System identification of Fei-Tsui arch dam from forced vibration and seismic response data.” J. Earthquake Eng., 4(4), 511–537.
Lynch, S. M. (2007). Introduction to applied Bayesian statistics and estimation for social scientists, Springer, New York.
Madas, P., and Elnashai, A. S. (1992). “A new passive confinement model for the analysis of concrete structures subjected to cyclic and transient dynamic loading.” Earthquake Eng. Struct. Dyn., 21(5), 409–431.
Mahmoud, H. (2011). “Seismic behavior of semi-rigid steel frames.” Ph.D. thesis, Univ. of Illinois at Urbana-Champaign, Urbana, IL.
McKenna, F., and Fenves, G. L. (2001). The OpenSees command language manual, version 1.2, Pacific Earthquake Engineering Research Center, Univ. of California at Berkeley, Berkeley, CA.
Mid-America Earthquake Center (MAEC). (2008). “MAEviz software.” MAEC, Univ. of Illinois at Urbana-Champaign, Urbana, IL, 〈http://mae.cee.illinois.edu/software_and_tools/maeviz.html〉 (Feb. 12, 2012).
Mosalam, K. M., Ayala, G., White, R. N., and Roth, C. (1997). “Seismic fragility of LRC frames with and without masonry infill walls.” J. Earthquake Eng., 1(4), 693–720.
National Institute of Buildings Sciences (NIBS). (1999). HAZUS, earthquake loss estimation technology, FEMA, Washington, DC.
Nielson, B. G. (2005). “Analytical fragility curves for highway bridges in moderate seismic zones.” Ph.D. thesis, Georgia Institute of Technology, Atlanta.
Nielson, B. G., and DesRoches, R. D. (2007). “Seismic fragility methodology for highway bridges using a component level approach.” Earthquake Eng. Struct. Dyn., 36(6), 823–839.
Padgett, J. E., DesRoches, R., and Nilsson, E. (2010). “Regional seismic risk assessment of bridge network in Charleston, South Carolina.” J. Earthquake Eng., 14(6), 918–933.
Pan, Y. (2007). “Seismic fragility and risk management of highway bridges in New York State,” Ph.D. thesis, City Univ. of New York, New York.
Pan, Y., Agrawal, A. K., and Ghosn, M. (2007). “Seismic fragility of continuous steel highway bridges in New York State.” J. Bridge Eng., 12(6), 689–699.
Reinhorn, A. M., Barron-Corvera, R., and Ayala, A. G. (2001). “Spectral evaluation of seismic fragility of structures.” Proc., Structural Safety and Reliability (ICOSSAR 2001), A. A. Balkema Publishers, Rotterdam, Netherlands.
Robert, C. P. (2007). The Bayesian choice: From decision-theoretic foundations to computational implementation, 2nd Ed., Springer, New York.
Rojahn, C., and Sharpe, R. L. (1985). “ATC-13, earthquake damage evaluation data for California.” Rep., Applied Technology Council, Redwood City, CA.
Rossetto, T., and Elnashai, A. (2003). “Derivation of vulnerability functions for European-type RC structures based on observational data.” Eng. Struct., 25(10), 1241–1263.
Shah, H. C., Mortgat, C. P., Kiremidjian, A. S., and Zsutty, T. C. (1975). “A study of seismic risk for Nicaragua, Part I.” Rep. No. 11, Dept. of Civil and Environmental Engineering, Stanford Univ., Stanford, CA.
Shinozuka, M., Feng, M. Q., Lee, J., and Naganuma, T. (2000). “Statistical analysis of fragility curves.” J. Eng. Mech., 126(12), 1224–1231.
Singhal, A., and Kiremidjian, A. S. (1996). “Method for probabilistic evaluation of seismic structural damage.” J. Struct. Eng., 122(12), 1459–1467.
Spencer, B. F., Jr., Elnashai, A., Kuchma, D., Kim, S., Holub, C., and Nakata, N. (2006). “Multi-site soil-structure-foundation interaction test (MISST).” Final Rep., Univ. of Illinois at Urbana-Champaign, Urbana, IL.
Zhong, J., Gardoni, P., Rosowsky, D., and Haukaas, T. (2008). “Probabilistic seismic demand models and fragility estimates for reinforced concrete bridges with two-column bents.” J. Eng. Mech., 134(6), 495–504.
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© 2013 American Society of Civil Engineers.
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Received: Oct 18, 2011
Accepted: Jul 24, 2012
Published online: Aug 10, 2012
Published in print: Jul 1, 2013
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