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Seismic spectra on soil with uncertain properties
Author(s) -
Hong Han Ping,
Rosenblueth Emilio
Publication year - 1987
Publication title -
earthquake engineering and structural dynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.218
H-Index - 127
eISSN - 1096-9845
pISSN - 0098-8847
DOI - 10.1002/eqe.4290150711
Subject(s) - discretization , taylor series , mathematics , probability density function , mathematical analysis , spectral line , physics , statistics , astronomy
Expected spectral ordinates and their standard deviations are computed for ground motions produced by SH waves at the surface of a homogeneous soil formation resting on a half‐space of rock. Wave transmission is idealized as linear and one‐dimensional. Uncertainties about soil properties are taken into account using various approximations: a Taylor series expansion of the Fourier spectrum magnification factors with different numbers of terms and different intervals for numerical differentiation; discretization of the joint probability density function of the soil properties so as to match its moments up to those of third order including the crossed moments; a discretization that matches up to some fifth‐order moments; and a fine numerical integration for the marginal density function of the modulus of rigidity, discretizing the rest of the density function. The latter approach gives sufficiently accurate results for practical purposes. Effects of even moderate uncertainty about soil properties on the statistics of spectral ordinates are found to be decisive.