Stochastic dynamic analysis of bridges subjected to spatially varying ground motions

Using response spectrum and time-history analysis methods, we perform a thorough investigation of the response of bridges subjected to spatially varying support motions. Three main causes of spatial variability are considered: the incoherence effect, which represents random differences in the amplitudes and phases of seismic waves due to reflections and refractions that occur during wave propagation in the heterogeneous medium of the ground and due to differential superposition of waves arriving from different parts of an extended source; the wave-passage effect, which describes the differences in the arrival times of waves at separate locations; and the site-response effect, which accounts for differences in the intensities and frequency contents of surface motions due to variable soil profiles underneath the supports. The multiple-support response spectrum (MSRS) method, originally developed by Der Kiureghian and Neuenhofer (1992), is generalized to allow consideration of response quantities that depend on the support degrees of freedom, and is extended to account for quasi-static contributions of truncated modes. Efficient algorithms and a computer code are developed for the implementation of this generalized and extended MSRS method. The code is used for comprehensive parametric analyses of four real bridge models with vastly different characteristics. The analyses identify cases of ground motion spatial variability and types of bridges for which the effects of spatial variability are significant. Methods are developed for simulation of spatially varying ground motion arrays incorporating the effects of incoherence, wave passage, and differential site response. The simulated motions inherit statistical characteristics of a specified acceleration record at a reference site. The conditional simulation approach preserves time-history characteristics of the specified record; however, the array of motions exhibits increasing variability with distance from the reference site. The unconditional simulation method generates an array of motions that preserve the overall temporal and spectral characteristics of the specified record and exhibit uniform variability at all locations. The simulated motions are validated by examining their physical compliance and by comparing their response spectra, coherency characteristics, and power spectral densities with corresponding target models. Sets of simulated support motions are used to investigate the effect of spatial variability on linear and nonlinear bridge response by time-history analyses. Comparisons between linear and nonlinear pier drifts are performed to assess the accuracy of the “equal displacement” rule (Veletsos and Newmark, 1960) for spatially varying ground motions. Comparisons between mean peak responses obtained from linear time-history and MSRS analyses provide information on the range of errors induced by the approximations involved in MSRS analyses. Finally, coherency analysis of a recorded array of near-fault ground motions is performed. The ability of commonly used models to describe the incoherence component of this array is assessed.