Wave‐Number Domain Approach for Soil Variability Analysis

Abstract

The effect of the spatial variability of soil parameters on the calculated settlement and stresses is analyzed. The soil is taken as an elastic solid with random shear modulus and a constant Poisson's ratio. A wave‐number domain approach is proposed for the approximate solution of an elasticity problem in which the shear modulus is a random function of position. This method is based on the spectral representation of the shear modulus. The fluctuated parts of displacement and stresses are first expressed in terms of evolutionary spectra. Then, the second‐order moments of the displacement and stresses are obtained by numerical integration without the use of Monte Carlo simulation. This procedure is applied to a semi‐infinite plane strain problem with vertical variability. Results of the method are presented and compared with Monte Carlo simulation and the “stochastic integral formulation.” For large autocorrelation distance, a random variable model could be sufficient for the analysis of the variability of stresses. However, for small autocorrelation distance, the coefficient of variation of the stresses can become very large; consequently, estimation of stresses by the classical theory of elasticity could be far from reality.