On Earthquake Ground Motion and Structural Response
in Alluvial Valleys
Jacobo Bielak, Jifeng Xu, and Omar Ghattas
Computational Mechanics Laboratory
Department of Civil and Environmental Engineering
Carnegie Mellon University
Pittsburgh, Pennsylvania 15213
This paper is concerned with the problem of soil amplification 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
finite 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 different sites; these accelerograms are then used to
determine the amplification ratios of the surface response with respect
to that of the free-field motion of the rock outcrop, for different
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
differences 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 finite width; (c) due to these additional
resonances the ground amplification 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 different structures located essentially on the same site can
be subjected to significantly different 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 effects caused by the
finite lateral extent of a valley must be taken into consideration in
order to model satisfactorily seismic behavior.
Paper available through the URL http://www.cs.cmu.edu/~quake-papers/armenia.ps.gz
BibTeX entry:
@techreport{armenia97,
author = {Jacobo Bielak and Jifeng Xu and Omar Ghattas},
title = {On Earthquake Ground Motion and Structural Response
in Alluvial Valleys},
institution = {Computational Mechanics Laboratory, Carnegie Mellon
University},
number = {CMU-CML-97-101},
month = jun,
year = 1997
)