Weighting functions for the stiffness of circular surface footings on multi-layered non-homogeneous elastic half-spaces under general loading

The classic contact problem of a rigid, rough circular surface footing bearing on a multi-layered non-homogeneous elastic half space was studied, leading to a simplified methodology for footing stiffness under six degrees-of-freedom loading that makes use of approximate weighting functions. The proposed methodology considers the effects of non-homogeneity by computing weighted average elastic parameters. These are then used as inputs to the stiffness solutions for a homogeneous elastic half-space. A key benefit of the proposed model is that it can handle both continuously varying and multi-layered non-homogeneity. The accuracy of the new method was evaluated by comparing its predictions against three-dimensional finite element analyses. The results of the study show that the proposed methodology can provide excellent predictions of the footing stiffness under general loading for most cases, except when there are stiff layers overlying softer layers.