Simulation and discretization of random field in the slip-line method

The paper deals with the problem of bearing capacity of a strip footing based on the random subsoil. The solution has been obtained in a framework of the slip-line method. In order to include randomness of the soil medium, a modification of the method of characteristics is proposed. In such an approach, the stochastic finite difference method based on the Monte Carlo technique has been adopted. It enables including a spatial variability of soil properties into the analysis and to determine its influence on the variance of the ultimate collapse load. It is assumed that the soil medium is purely cohesive and only its cohesion can be considered as a random field. The simulation algorithm of multi-dimensional random field, based on the diagonalisation of the covariance matrix by a transformation using a lower-triangle matrix is described. The problems of the medium discretization and stabilization of the solution are discussed