Evaluation of shallow foundation bearing capacity in the case of a two-layered soil and spatial variability in soil strength parameters

In this study, a probabilistic approach for evaluating the bearing capacity of surface footings is discussed. The evaluation is based on a kinematic approach. The considered substrate consists of two different layers of soil: a top layer formed of medium or dense sand followed by a layer of soft clay. The sand layer is assumed to be homogenous, whereas the undrained shear strength of the soft clay layer is assumed to be spatially variable, described by a log-normal random field. The random field is discretized according to Vanmarcke's spatial averaging along dissipation regions in the considered failure mechanism. The mechanism utilizes plane strain conditions; however, due to consideration of the soil spatial variability in three dimensions, the impact of the length of the foundation on the random bearing capacity evaluation is considered in this study. As a result of the discretization procedure, a set of correlated random variables is obtained (each associated with an individual dissipation region in the failure mechanism). A series of numerical analyses are performed for two thicknesses of the first layer and a set of anisotropic correlation structures for the spatial variability of the undrained shear strength. The proposed method is computationally efficient and allows consideration of three-dimensional spatial variability in soil strength properties. The results are discussed and compared with those obtained by other methods.