Probabilistic Push-Over Analysis of Structural and Soil-Structure Systems
Publication: Journal of Structural Engineering
Volume 136, Issue 11
Abstract
In this paper, the mean-centered first-order second-moment (FOSM) method is employed to perform probabilistic push-over analysis (POA) of structural and/or soil-structure systems. Approximations of first and second statistical moments (FSSMs) of engineering demand parameters (EDPs) of structural and/or geotechnical systems with random material parameters are computed based on finite-element (FE) response and response sensitivity analysis (RSA) results. The FE RSA is performed accurately and efficiently by using the direct differentiation method (DDM) and is employed to evaluate the relative importance (RI) of the various modeling material parameters in influencing the variability of the EDPs. The proposed approximate methodology is illustrated through probabilistic POA results for nonlinear inelastic FE models of: (1) a three-story reinforced-concrete (RC) frame building and (2) a soil-foundation-structure interaction system consisting of a RC frame structure founded on layered soil. FSSMs of EDPs computed through the FOSM method are compared with the corresponding accurate estimates obtained via Monte Carlo simulation. Results obtained from “exact” (or “local”) and “averaged” (or “global”) response sensitivities are also compared. The RI of the material parameters describing the systems is studied in both the deterministic and probabilistic sense, and presented in the form of tornado diagrams. Effects of statistical correlation between material parameters are also considered and analyzed by the FOSM method. A simple approximation of the probability density function and cumulative distribution function of EDPs due to a single random parameter at a time (while all the other parameters are fixed to their mean values) is also proposed. Conclusions are drawn on both the appropriateness of using local RSA for simplified probabilistic POA and on the application limits of the FOSM method. It is observed that the FOSM method combined with the DDM provides accurate estimates of FSSMs of EDPs for low-to-moderate level of inelastic structural or system behavior and useful qualitative information on the RI ranking of material parameters on the structural or system response for high level of inelastic behavior.
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Acknowledgments
The writers gratefully acknowledge support of this research by: (1) the Pacific Earthquake Engineering Research (PEER) Center's Transportation Systems Research Program under Award No. UNSPECIFIED00006493, and (2) the Louisiana Board of Regents through the Pilot Funding for New Research (Pfund) Program of the National Science Foundation Experimental Program to Stimulate Competitive Research (EPSCoR) under Award No. UNSPECIFIEDNSF(2008)-PFUND-86. Any opinions, findings, conclusions, or recommendations expressed in this publication are those of the writers and do not necessarily reflect the views of the sponsors.
References
Applied Technology Council (ATC). (1996). “Seismic evaluation and retrofit of concrete buildings.” Rep. No. ATC-40, Redwood City, CA.
Applied Technology Council (ATC). (2005). “Improvement of nonlinear static seismic analysis procedures.” Rep. No. ATC-55, Redwood City, CA.
Barbato, M. (2007). “Finite-element response sensitivity, probabilistic response and reliability analyses of structural systems with applications to earthquake engineering.” Ph.D. dissertation, Dept. of Structural Engineering, Univ. of California at San Diego, La Jolla, CA.
Barbato, M., and Conte, J. P. (2005). “Finite-element response sensitivity analysis: A comparison between force-based and displacement-based frame element models.” Appl. Mech. Eng., 194(12–16), 1479–1512.
Barbato, M., and Conte, J. P. (2006). “Finite-element structural response sensitivity and reliability analyses using smooth versus non-smooth material constitutive models.” Int. J. Reliab. Saf., 1(1–2), 3–39.
Barbato, M., Gu, Q., and Conte, J. P. (2006). “Response sensitivity and probabilistic response analyses of reinforced concrete frame structures.” Proc., 8th National Conf. on Earthquake Engineering (CD-ROM).
Barbato, M., Zona, A., and Conte, J. P. (2007). “Finite-element response sensitivity analysis using three-field mixed formulation: General theory and application to frame structures.” Int. J. Numer. Methods Eng., 69(1), 114–161.
Bjerager, P. (1990). “On computation methods for structural reliability analysis.” Struct. Safety, 9(2), 79–96.
Bolotin, V. V. (1968). Statistical methods in structural mechanics, Holden-Day, Inc., San Francisco.
Chinese Building Press (CBP). (2001). “Code for seismic design of buildings.” GB 50011-2001, Beijing (in Chinese).
Conte, J. P., Barbato, M., and Spacone, E. (2004). “Finite-element response sensitivity analysis using force-based frame models.” Int. J. Numer. Methods Eng., 59(13), 1781–1820.
Conte, J. P., Jagannath, M. K., and Meghella, M. (1995). “Earthquake response sensitivity analysis of concrete gravity dams.” Proc., 7th Int. Conf. on Applications of Statistics and Probability, 395–402.
Conte, J. P., Vijalapura, P. K., and Meghella, M. (2003). “Consistent finite-element response sensitivity analysis.” J. Eng. Mech., 129(12), 1380–1393.
Crandall, S. H. (2006). “A half-century of stochastic equivalent linearization.” Struct. Control Health Monit., 13(1), 27–40.
Der Kiureghian, A., and Ke, B. -J. (1988). “The stochastic finite-element method in structural reliability.” Probab. Eng. Mech., 3(2), 83–91.
Ditlevsen, O., and Madsen, H. O. (1996). Structural reliability methods, Wiley, New York.
Dong, W. M., Chiang, W. L., and Wong, F. S. (1987). “Propagation of uncertainties in deterministic systems.” Comput. Struct., 26(3), 415–423.
European Committee for Standardization (ECS). (2005). “Eurocode 8—Design of structures for earthquake resistance.” EN1998, Brussels, Belgium.
BSCC. (1997). “NEHRP recommended provisions for seismic regulations for new buildings and other structures.” FEMA 302-303, Washington, D.C.
Ghanem, R. G., and Spanos, P. D. (1991). Stochastic finite elements: A spectral approach, Springer, New York.
Grigoriu, M. (2000). “Stochastic mechanics.” Int. J. Solids Struct., 37(1–2), 197–214.
Gu, Q., Barbato, M., and Conte, J. P. (2009a). “Handling of constraints in finite-element response sensitivity analysis.” J. Eng. Mech., 135(12), 1427–1438.
Gu, Q., Barbato, M., and Conte, J. P. (2010). “Probabilistic push-over response analysis of structural and/or geotechnical systems.” Rep. No. SSRP-2010/01, Dept. of Structural Engineering, Univ. of California, San Diego, San Diego.
Gu, Q., Conte, J. P., Elgamal, A., and Yang, Z. (2009b). “Finite-element response sensitivity analysis of multi-yield-surface J2 plasticity model by direct differentiation method.” Comput. Methods Appl. Mech. Eng., 198(30–32), 2272–2285.
Haftka, R. T., and Gurdal, Z. (1993). Elements of structural optimization, Kluwer, Dordrecht, Germany.
Haukaas, T. (2006). “Efficient computation of response sensitivities for inelastic structures.” J. Struct. Eng., 132(2), 260–266.
Haukaas, T., and Der Kiureghian, A. (2004). “Finite-element reliability and sensitivity methods for performance-based engineering.” Rep. No. PEER 2003/14, Pacific Earthquake Engineering Research Center, Univ. of California, Berkeley, Berkeley, CA.
Haukaas, T., and Der Kiureghian, A. (2005). “Parameter sensitivity and importance measures in nonlinear finite-element reliability analysis.” J. Eng. Mech., 131(10), 1013–1026.
Kleiber, M., Antunez, H., Hien, T. D., and Kowalczyk, P. (1997). Parameter sensitivity in nonlinear mechanics: Theory and finite-element computation, Wiley, New York.
Liu, J. S. (2001). Monte Carlo strategies in scientific computing. Springer series in statistics, Springer, Berlin.
Lupoi, G., Franchin, P., Lupoi, A., and Pinto, P. E. (2006). “Seismic fragility analysis of structural systems.” J. Eng. Mech., 132(4), 385–395.
Mazzoni, S., McKenna, F., and Fenves, G. L. (2007). OpenSees command language manual, Pacific Earthquake Engineering Research Center, Univ. of California at Berkeley, CA, ⟨http://opensees.berkeley.edu/OpenSees/manuals/usermanual/OpenSeesCommandLanguageManual.pdf⟩ (August 2010).
Mirza, S. A., and MacGregor, J. G. (1979). “Variability of mechanical properties of reinforcing bars.” J. Struct. Div., 105(5), 921–937.
Mirza, S. A., MacGregor, J. G., and Hatzinikolas, M. (1979). “Statistical descriptions of strength of concrete.” J. Struct. Div., 105(6), 1021–1037.
Phoon, K. K., and Kulhawy, F. H. (1996). “On quantifying inherent soil variability.” Proc., ASCE GED Spec. Conf. on Uncertainty in the Geologic Environment: From Theory to Practice, Vol. 1, ASCE, Reston, VA, 326–340.
Porter, K. A., Beck, J. L., and Shaikhutdinov, R. V. (2002). “Sensitivity of building loss estimates to major uncertain variables.” Earthquake Spectra, 18(4), 719–743.
Saltelli, A., Chan, K., and Scott, E. M. (2000). Sensitivity analysis, Wiley, Chichester, U.K.
Scott, B. D., Park, P., and Priestley, M. J. N. (1982). “Stress-strain behavior of concrete confined by overlapping hoops at low and high-strain rates.” J. Am. Concr. Inst., 79(1), 13–27.
To, C. W. S. (2001). “On computational stochastic structural dynamics applying finite elements.” Arch. Comput. Methods Eng., 8(1), 3–40.
Zona, A., Barbato, M., and Conte, J. P. (2005). “Finite-element response sensitivity analysis of steel-concrete composite beams with deformable shear connection.” J. Eng. Mech., 131(11), 1126–1139.
Zona, A., Barbato, M., and Conte, J. P. (2006). “Finite-element response sensitivity analysis of continuous steel-concrete composite girders.” Steel Compos. Struct., 6(3), 183–202.
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Information
Published In
Journal of Structural Engineering
Volume 136 • Issue 11 • November 2010
Pages: 1330 - 1341
Copyright
© 2010 ASCE.
History
Received: Jul 16, 2009
Accepted: Apr 5, 2010
Published online: Apr 10, 2010
Published in print: Nov 2010
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