Abstract
The purpose of this study is to examine in more detail under what conditions would spatial averaging over some prescribed region be sufficient to reproduce the response statistics arising from a spatially varying field. The spatially variable undrained shear strength will be first simulated by a random field. The "actual" response of a spatially variable soil mass in three problems (laboratory specimen, retaining wall, shallow foundation) is computed using the random finite element method. This actual response is the actual response exhibited by the spatially variable soil when it is subjected to the boundary conditions in the problems listed above. This actual response is compared to the response of a homogeneous soil mass whose shear strength equal to the spatial average over a prescribed area/line of interest. Based on these numerical studies, it is observed that the spatially random undrained shear strength can be converted into an equivalent homogeneous spatial average over an influence zone only for the last two problems where the critical slip curve is constrained by the location of the edge of the shallow foundation or base of retaining wall. The actual response (a random variable) and the spatial average response (a second random variable) are at most equal in " distribution", but not "almost everywhere".