Ground Strain Estimation for Seismic Risk Analysis

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Abstract
Under the assumption that strong motion earthquakes result primarily from surface waves in a layered medium resting on a semi‐infinite rock formation, a method is developed to derive the expression for the Rayleigh wave that produces acceleration at the ground surface with a specified power spectral density. The Rayleigh wave characteristics are then used to obtain a corresponding free‐field normal ground strain at any depth in the medium. Other important features of this paper are as follows: (1) The ground acceleration and strain are both modeled as Gaussian stationary processes; (2) the power spectral densities used for these processes are functions of the earthquake's magnitude, epicentral distance (reflecting the attenuation effect), and the N‐values (indicating the site soil conditions); and (3) since the ground strain is modeled as a random process, and since its spectral density function involves a significantly uncertain attenuation relationship, the maximum ground strain is a random variable. The expected value of the maximum ground strain is evaluated as a function of the magnitude, epicentral distance and site soil conditions. The coefficient of variation of the maximum ground strain is also estimated.

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