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Probabilistic Performance-Based Optimum Seismic Design Framework: Illustration and Validation

Yong Li1,*, Joel P. Conte2, Philip E. Gill3
Department of Civil and Environmental Engineering, University of Alberta, Edmonton, AB T6G 1H9, Canada.
Department of Structural Engineering, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093, USA.
Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093, USA.
*Corresponding Author: Yong Li. Email: .
(This article belongs to this Special Issue: Advances in OpenSees Applications to Civil Engineering)

Computer Modeling in Engineering & Sciences 2019, 120(3), 517-543.


In the field of earthquake engineering, the advent of the performance-based design philosophy, together with the highly uncertain nature of earthquake ground excitations to structures, has brought probabilistic performance-based design to the forefront of seismic design. In order to design structures that explicitly satisfy probabilistic performance criteria, a probabilistic performance-based optimum seismic design (PPBOSD) framework is proposed in this paper by extending the state-of-the-art performance-based earthquake engineering (PBEE) methodology. PBEE is traditionally used for risk evaluation of existing or newly designed structural systems, thus referred to herein as forward PBEE analysis. In contrast, its use for design purposes is limited because design is essentially a more challenging inverse problem. To address this challenge, a decision-making layer is wrapped around the forward PBEE analysis procedure for computer-aided optimum structural design/retrofit accounting for various sources of uncertainty. In this paper, the framework is illustrated and validated using a proof-of-concept problem, namely tuning a simplified nonlinear inelastic single-degree-of-freedom (SDOF) model of a bridge to achieve a target probabilistic loss hazard curve. For this purpose, first the forward PBEE analysis is presented in conjunction with the multilayer Monte Carlo simulation method to estimate the total loss hazard curve efficiently, followed by a sensitivity study to investigate the effects of system (design) parameters on the probabilistic seismic performance of the bridge. The proposed PPBOSD framework is validated by successfully tuning the system parameters of the structure rated for a target probabilistic seismic loss hazard curve. The PPBOSD framework provides a tool that is essential to develop, calibrate and validate simplified probabilistic performance-based design procedures.


Performance-based seismic design, optimum seismic design, forward PBEE analysis, inverse PBEE analysis, uncertainty quantification, hazard deaggregation

Cite This Article

Li, Y., Conte, J. P., Gill, P. E. (2019). Probabilistic Performance-Based Optimum Seismic Design Framework: Illustration and Validation. CMES-Computer Modeling in Engineering & Sciences, 120(3), 517–543.


This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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