A ground motion selection and modification method preserving characteristics and aleatory variablity of scenario earthquakes

In performance-based seismic design of civil infrastructure, earthquake ground motion is one of the primary sources of uncertainty in assessing the seismic performance of the civil system. It is critical to develop systematic methods to select and modify from current ground-motion databases to provide a group of earthquake motions that can realistically represent important aspects of the design motion that control the nonlinear response of civil engineering facilities. The paper presents a new ground-motion selection and modification (GMSM) method that preserves the characteristics and alteatory variability of scenario earthquakes. The resulted ground motions sets realistically represent the statistical distribution (mean, standard deviations) and correlations of the response spectra, with other selection criterion to incorporate ground motion characteristics such as earthquake magnitude, distance and site conditions etc. Numerical analyses of a 20-story RC frame structure were performed using generated record sets of different sizes. The proposed GMSM method has demonstrated excellent capacity to generate “scenario-compatible” groundmotion sets that can accurately predict the full distribution of the engineering demand parameters under the earthquake scenario. The proposed method shows great potential in performance-based earthquake design of nonlinear civil systems. Introduction In recent years, performance-based seismic design of civil infrastructure has become more and more important in preventing human losses and structural damages from earthquakes. Researchers and practitioners generally agree that earthquake ground motion is one of the primary sources of uncertainty in assessing the seismic performance of the civil system. Due to the lack of recorded data for the design-level earthquakes (which are usually rare events), it is critical to develop systematic methods and useful tools to select and modify from current ground-motion databases to provide a group of earthquake motions that can realistically represent important aspects of the design motion that control the nonlinear response of civil engineering facilities. 1 Assistant Professor, Dept. of Civil and Environmental Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong Although many ground-motion selection and modification (GMSM) methods exist, there is no consensus as to the accuracy and performance of these methods. Since traditionally the seismic hazard at a site for design purposes has been represented by a design spectrum, most existing ground-motion selection and modification (GMSM) models are mainly focused on developing time history sets that, in aggregate, have response spectra that “resemble” a single target response spectrum. Sometimes, modifications to exiting ground-motion time histories are necessary to achieve a desirable spectral shape, including “simple-scaling” approach that scales the amplitude of time histories to achieve an average fit to the spectrum (eg. Wang et. al, 2009). “Spectrum-matching” approaches adjust the ground-motion time history in frequency content so that the modified one is a very close match to the design spectrum, and the modification can be made either in the time domain (eg. Abrahamson 1992) or in the frequency domain (eg. Bolt and Gregor, 1993). Each approach has its proponents and appears to be a generally acceptable method. Besides, methods focusing on other response characteristics of the nonlinear system, such as a proxy response, or inelastic displacement, were also pursued by several researchers (eg. Watson-Lamprey and Abrahamson 2006; Shantz 2006). Current GMSM efforts are mainly focused on predicting the median response of the engineering demand parameters (EDP) under a prescribed seismic demand. Preliminary results from COSMOS 2007 workshop concluded that for a first-mode dominated structure, such as tall buildings, time histories that closely match target spectrum conditioned on the period of the first mode of the structure can yield good estimate of the median response of EDPs (eg. maximum inter-story drift ratio) for that scenario (Haselton eds. 2009). There is no guidance on GMSM regarding nonlinear response analysis of geotechnical structures, such as liquefiable soil ground, earth slopes and earth dams. The seismic responses of these facilities are significantly different from those of buildings in that under strong shaking, the soil response is a broadband phenomenon that is not controlled by a couple of spectral periods as is seen in buildings. Dynamic soil response is nonlinear, and it is affected by ground-motion amplitude and frequency contents over a broad range of periods. A GMSM procedure that incorporates the characteristics and variability of ground motion holds the key to developing predictive models to evaluate the seismic performance of these systems. To predict the full distribution of EDPs under a scenario earthquake, the aleatory variability of ground motions should be carefully incorporated in the ground-motion selection model to fully quantify the seismic demand. The importance of capturing the variability in seismic analysis is reflected in the recent ATC-58 guideline (Applied Technology Council, 2009), which recommended randomly gathering eleven ground motions from the chosen magnitude and distance bin and then scaling them to match the targeted spectrum value at the fundamental period of the structure. However, the randomness nature in the selection procedure makes it difficult to represent the true variability of ground motions. In this paper, we present a new GMSM method that preserves the intrinsic characteristics and variability of the scenario earthquakes. The method will be useful to the study the full distribution of engineering demand parameters under a scenario earthquake, particularly, for the broadband nonlinear systems whose seismic response is controlled over a large range of periods, such as liquefiable ground, the deformation in earth structures and slope-retaining wall system etc. Aleatory Variability of Ground Motions Statistical analysis shows that the probability distribution of ground-motion spectral acceleration at individual periods can be well approximated by lognormal distributions, given a certain magnitude and distance etc. Ground-motion attenuation models (eg. Chiou and Youngs, 2008, Campbell and Bozorgnia, 2008) usually provide the mean value of log spectral acceleration ln a S μ and the standard deviation of log spectral acceleration ln a S σ of a scenario earthquake based on regression analysis of a large ground-motion dataset. The correlation between spectral values at different periods is an intrinsic property of ground motions (Baker and Cornell 2006). Based on regression analysis of the PEER-NGA strong motion database, the theoretical correlation coefficients were given by Baker and Jayaram (2008). The formulation is valid over a period of range (0.01 – 10 sec), and more importantly, the resulted covariance matrix is a symmetric positive semi-definite matrix that allows the random sample generation, as a sample covariance matrix should be always at least positive semidefinite. The spectral correlation is one of the most important properties in quantifying the variability of ground motions, since it describes the correlation of the seismic demands over frequency content. The correlation coefficient can be calculated from a set of response spectra using the following formulation: ( )( ) ( ) ( ) ∑ ∑ ∑