American Society of Civil Engineers

Probabilistic Push-Over Analysis of Structural and Soil-Structure Systems

by Michele Barbato, A.M.ASCE, (Assistant Professor, Civil and Environmental Engineering, Louisiana State Univ. and A&M College, Baton Rouge, LA 70803. E-mail:, Q. Gu, (corresponding author), A.M.ASCE, (Associate Professor, School of Architecture and Civil Engineering, Xiamen Univ., Xiamen, Fujian, P.R. China 361005; formerly, Postdoctoral Researcher, Civil and Environmental Engineering, Louisiana State Univ. and A&M College, Baton Rouge, LA 70803 E-mail:, and J. P. Conte, M.ASCE, (Professor, Dept. of Structural Engineering, Univ. of California at San Diego, La Jolla, CA 92093. E-mail:

Journal of Structural Engineering, Vol. 136, No. 11, November 2010, pp. 1330-1341, (doi:

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Document type: Journal Paper
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.

ASCE Subject Headings:
Finite element method
Sensitivity analysis
Soil structures

Author Keywords:
Nonlinear finite-element model
Finite-element response sensitivity
Random parameter
First-order second-moment method
Engineering demand parameter