Quantitative approaches for assessing ground motion impact in performance based earthquake engineering

Abstract

Over the past several decades, Performance Based Earthquake Engineering (PBEE) has evolved to become a major focus in earthquake engineering research. One of the most attractive features of this philosophy is the ability to account for response uncertainty in a more explicit manner. One of the cornerstones of modern PBEE is the ability to perform nonlinear time history analysis (NLTHA) on structural systems with the aid of fast computers. This advancement in tools made the use of incremental dynamic analysis (IDA) popular. Through IDA, curves describing the relationship between peak responses of structures and seismic intensity of earthquake ground motions can be obtained and can be used to derive uncertainty metrics of the seismic responses of interest. Many critical concepts in PBEE, such as fragility, response distribution, and seismic reliability, are linked heavily to IDA. As a result, the computation of most PBEE metrics must be done numerically (empirically) through NLTHA. The fundamental understanding of ground motion (GM) impact in PBEE is not clear. In order to better understand the role of GMs in PBEE, an innovative approach was proposed in this study to quantify GM uncertainty and its impact on idealized structural system responses. The research work started at the quantification of IDA curves as a function of ground motion parameters, structural parameters and seismic intensity. This was done successfully for the elastoplastic single-degree-of-freedom (SDOF) system acceleration and then expanded to bilinear SDOF system displacement, which has direct implications for damage control in PBEE. The proposed formulas quantitatively illustrate (1) the changing of response uncertainty with seismic intensity; (2) the interaction of ground motion parameters and structural parameters on uncertainty propagation; (3) the relative contribution of ground motion uncertainty and structural parameter uncertainty with different seismic intensity. Additionally, the identified ground motion parameters in the uncertainty quantification framework can present the ground motion characteristics and then can be used to validate the ground motion suite equivalency in the context of response uncertainty. The newly developed methodology challenges the existing simplified ways to calculate seismic uncertainty, such as the assumption of constant uncertainty contribution from GMs at different intensity levels. This was then tested through specially designed shake table tests that are focused on validating seismic uncertainty propagation. Through the probabilistic shake table tests, it was validated that the response uncertainty value is dependent on the seismic intensity, and the relative contribution of ground motion uncertainty and structural parameter uncertainty is closely correlated with seismic intensity. By using the experimental response data, square-root-sum-of-squares (SRSS) method used in many simplified uncertainty estimation procedures was verified to be not exact but conservative. Through collaboration with researchers at the US Geological Survey, the relationship between seismically induced structural damage and GM response spectrum was investigated. A vector-valued damage potential indicator (DPI) including seismic intensity and spectral shape component was proposed. Through correlation analyses, a circle rule was proposed to identify the most critical period regions of the response spectrum with regard to the bilinear SDOF system damage. This approach also provided a pathway to evaluate GM impact on structures without NLTHA.