Strip foundation on 2-D and 3-D random subsoil

The paper affords a stochastic description of a three-dimensional (3-D) soil medium and its modelling under plane strain conditions. The main aim of the paper is to work out a computational model enabling incorporation of 3-D variability of soil properties into the plane strain state analysis. First, the 2-dimensional (2-D) problem and its reduction to the uni-axial strain state is considered. Then this is extended for the 2-D schematisation of the 3-D state. The resulting standard deviations for the 3-D state of stress and strain are compared with those for the 2-D state. It is assumed that the soil medium is statistically homogeneous and its mechanical behaviour governed by the linear elasticity theory. It is also assumed that elastic parameters can be modelled as the multidimensional random fields. The strip foundation on a soil layer in the 3-D and the 2-D strain states is analysed. Stochastic 2-D and 3-D finite element methods, based on the Monte Carlo technique were used. The analysis performed enables determination of the standard deviations of components of the stress tensor and the displacement vector for the 3-D state, based on the solution for the 2-D plane strain state.