The performance-based earthquake engineering (PBEE) approach, developed at the Pacific Earthquake Engineering Research Center (PEER), aims to robustly decompose the performance assessment and design process into four logical stages that can be studied and resolved in a systematic and consistent manner. However, the PBEE approach faces two key challenges: (1) an accurate seismic structural analysis and (2) the selection and modification of ground motions (GMs). This report addresses these two challenges with application to reinforced concrete (RC) bridge systems.
In nonlinear structural dynamics, the most accurate analytical simulation method is the nonlinear time history analysis (NTHA). It involves the use of different types of direct integration algorithms and nonlinear equation solvers where their stability performance and convergence behaviors are of great significance. Lyapunov stability theory, the most complete framework for stability analysis of dynamical systems, is introduced in this study. Based on this theory, a new nonlinear equation solver is developed and its convergence performance theoretically formulated and verified by several examples. Stability is one of the most important properties of direct integration algorithms to consider for efficient and reliable NTHA simulations. Two Lyapunov- based approaches are proposed to perform stability analysis for nonlinear structural systems. The first approach transforms the stability analysis to a problem of existence, which can be solved via convex optimization. The second approach is specifically applicable to explicit algorithms for nonlinear single-degree-of-freedom and multi-degree-of-freedom systems considering strictly positive real lemma. In this approach, the stability analysis of the formulated nonlinear system is transformed to investigating the strictly positive realness of its corresponding transfer function matrix.
Ground motion selection and modification (GMSM) procedures determine the necessary input excitations to the NTHA simulations of structures. Therefore, proper selection of the GMSM procedures is an important prerequisite for accurate and robust NTHA simulation, and thus for the entire PBEE approach. Although many GMSM procedures are available, there is no consensus regarding a single accurate method, and many studies have focused on evaluating these procedures. This report develops a framework for probabilistic evaluation of the GMSM procedures in the context of a selected large earthquake scenario with bidirectional GM excitations.
In urban societies, RC highway bridges are key components of transportation infrastructure systems and play a significant role in transporting goods and people around natural terrains. Therefore, they are expected to sustain minor damage and maintain their functionality in the aftermath of major earthquakes, a common occurrence in California due to its many active faults. Accurate seismic structural analysis of existing and newly designed RC highway bridges is fundamental to estimate their seismic demands. As important lifeline structures, RC highway bridge systems are investigated as an application of the previously discussed theoretical developments proposed in this report to address the two key challenges in the PEER PBEE approach.
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