UC San Diego

A comprehensive and rigorous probabilistic methodology for performance-based earthquake engineering (PBEE) has been under development under the auspice of the Pacific Earthquake Engineering Research (PEER) Center over the past thirteen years. The probabilistic estimation of the seismic demand is an important part of the PBEE methodology and consists of a two-step procedure: probabilistic seismic hazard analysis (PSHA), and probabilistic seismic demand analysis (PSDA). Two shortcomings are identified in past applications of the PBEE methodology : (i) the use of a single, or scalar, ground motion intensity measure (IM) which is typically taken as the 5% damped linear spectral acceleration, Sa(T1), at the fundamental period of the structure; and (ii) the use of testbed applications based on two- dimensional (2-D) finite element (FE) models (e.g., 2-D frame models) of the considered structures, which are three-dimensional in nature and cannot always be reduced to 2-D models. Sa(T₁) represents an inefficient and insufficient predictor of the nonlinear structural response for structures with significant higher mode effects and significantly different fundamental periods in two orthogonal directions. This dissertation addresses both shortcomings. First, a simplified and computationally efficient vector-valued PSHA (VPSHA), making use of USGS scalar probabilistic seismic hazard maps results, is proposed. Second, a PSDA of an advanced 3-D nonlinear FE model of the 13-story National Earthquake Hazards Reduction Program (NEHRP) reinforced-concrete frame-wall building design example is performed based on the simplified VPSHA for a specific site located in Berkeley, California. Nonlinear dynamic time-history analyses (NDTHA) are performed by subjecting the 3-D nonlinear FE model to an ensemble of 90 bi-directional (horizontal) historical earthquake ground motions. The FE model was developed in OpenSees and results of the FE analyses are used to establish a statistical model between the IMs and different EDPs (e.g., roof drift ratio, interstory drift ratios, and floor absolute accelerations). Based on the computational results from NDTHA, it is found that, for the building structure considered, a vector-valued IM consisting of multiple spectral accelerations at different periods of interest is a sufficient and more efficient predictor of the structural response, and therefore provides for more reliable and mode accurate PSDA results