Seismic response analysis with spatially varying stochastic excitation

Abstract

Assessment of the seismic vulnerability of extended structures (e.g. bridges and lifelines) as well as of systems of structures covering extended areas requires to properly account for the effects of ground-motion spatial variability. Even in cases with relatively uniform soil conditions, ground motions may exhibit significant variations due to the incoherence and wave-passage effects, respectively manifested as random differences and deterministic time delays. Differential soil conditions cause additional variations in the amplitude and frequency content of the ground motions as these propagate from the bedrock to the surface level. The present chapter describes methods for the modeling of ground-motion spatial variability, the simulation of spatially varying ground-motion arrays and the evaluation of the response of multiply-supported structures to differential support excitations. The pertinent uncertainties in the characteristics of the ground motions are accounted for by employing concepts from stochastic time-series analysis. In particular, the notion of coherency is employed to describe the spatial variability of the ground-motion arrays, which are considered as realizations of a random field at the locations of interest. The statistical properties of the ground motions at separate locations are described through the respective auto-power spectral densities. A statistical characterization of linear structural response to differential support motions is obtained by means of a response-spectrum method, rooted in random vibration theory, while the non-linear response is investigated on the basis of the ‘equal-displacement’ rule. This chapter is inspired by the doctoral research of the author under the supervision of Professor Armen Der Kiureghian.