On Earthquake Ground Motion and Structural Response in Alluvial Valleys

This paper is concerned with the problem of soil ampli cation and structural damage due to local site conditions in sedimentary valleys during earthquakes. It focuses on a small valley in Kirovakan, for which one dimensional (1D) wave propagation analyses have failed to provide adequate answers for the large extent and spatial distribution of damage during the 1988 Armenia Earthquake. A more realistic two-dimensional nite element analysis is performed herein in search of an explanation for the observed behavior. Using as input an inferred rock accelerogram, the response of the valley is calculated for a vertically incident SH-wave. Synthetic accelerograms of the surface ground motion are presented for di erent sites; these accelerograms are then used to determine the ampli cation ratios of the surface response with respect to that of the freeeld motion of the rock outcrop, for di erent frequencies and for a continuous set of sites. In addition, response spectra are evaluated for simple oscillators representing structures located at various sites. Results of the 2D simulations show striking di erences with respect to those from 1D analyses. In particular, (a) while the resonant frequencies exhibited by a 1D model for a given site also appear in the 2D model, the peak ground response and structural response are almost twice as large for the 2D as for the 1D model; (b) the 2D model exhibits, in addition, a new set of resonant frequencies and concomitant \mode shapes" across the valley, which are directly related to its nite width; (c) due to these additional resonances the ground ampli cation ratio tends to oscillate very rapidly, both spatially and with frequency, leading to the observation that two identical structures located in the same vicinity or two slightly di erent structures located essentially on the same site can be subjected to signi cantly di erent seismic forces, even if the underlying soils have very similar characteristics. These results provide a meaningful explanation for the observed damage, and thus, serve to exemplify a situation in which site e ects caused by the nite lateral extent of a valley must be taken into consideration in order to model satisfactorily seismic behavior. Professor and Director, Computational Mechanics Laboratory, Department of Civil and Environmental Engineering, Carnegie Mellon University, Pittsburgh, PA 15213 Research Assistant, Computational Mechanics Laboratory, Department of Civil and Environmental Engineering, Carnegie Mellon University, Pittsburgh, PA 15213. Associate Professor and Co-Director, Computational Mechanics Laboratory, Department of Civil and Environmental Engineering, Carnegie Mellon University, Pittsburgh, PA 15213