Complex Variable Solution for Stress and Displacement of Layered Soil with Finite Thickness

Abstract

The static problem of a layered isotropic elastic body is a very useful research subject in relation to the analysis and design of foundation works. Due to the complexity of the problem, there is no analytical solution to the problem so far. This study provides an efficient analytical approach to accurately calculate the displacement and stress fields of the soil. The constraints of bedrock on soil, different soil layer thickness and the shear stress of the foundation on soil were all taken into account in the analysis. In this study, each layer is regarded as an isotropic elastomer with infinite width, and the layers are in complete contact. By using conformal mapping, each layer is mapped to a unit circle, and the two complex potential functions are expanded into Taylor series with unknown coefficients. These unknown coefficients are obtained by satisfying boundary conditions and continuity conditions. The boundary and continuity conditions were verified in this paper. As a validation step, we compared the analytical results for the settlement with the results of the ANSYS numerical simulations and found good agreement. Parametric analyses were also carried out to investigate the influence of different distribution forms of base pressure on surface settlement, and the effects of layered properties on the surface settlement and stress field.