Simple prediction of the undrained displacement of a circular surface foundation on non-linear soil

Textbooks and university courses teach elasticity and plasticity as separate methods for analysing the stiffness and strength of a shallow foundation. The behaviour of real soil is neither linear elastic nor perfectly plastic. In this paper, two simple techniques for incorporating nonlinearity in routine design have been validated using finite element (FE) analysis. These two techniques - Atkinson's method and the mobilisable strength design (MSD) approach - assume that the responses of an individual soil element and the boundary value problem being considered are self-similar. Using this assumption, the soil element response can be scaled to predict the response of the boundary value problem. Atkinson's method is based on elasticity whereas MSD uses plasticity. Non-linearity has been captured in the FE analysis using a power law soil model. This approach uses minimal parameters, but is shown to capture accurately the undrained stress strain response of typical clays under monotonic loading. Comparison with elastic and plastic solutions showed that the FE analysis was accurate to within < 5% at the elastic and plastic extremes of the loading range. The responses of the soil and the boundary value problem are shown to be sufficiently self-similar up to two-thirds of the failure load for the foundation response to be predicted simply by a linear scaling of the soil response. Previously reported scaling factors for vertical loading are confirmed, and new factors for horizontal and moment loading are derived. These results show that, for this particular boundary value problem, soil non-linearity can be captured with sufficient accuracy for routine design, without recourse to sophisticated numerical analysis. These self-similarity methods are simple enough to be taught to undergraduates, and could be incorporated in textbooks alongside the core sections on elasticity and plasticity, providing guidance on the application of these techniques to real non-linear soil.