Vertical stress distribution in isotropic half-spaces due to surface vertical loadings acting over polygonal domains

Abstract

By integrating the classical Boussinesq expression we derive analytically the vertical stress distribution induced by pressures distributed with arbitrary laws, up to the third order, over polygonal domains. Thus, one can evaluate in closed form either the vertical stress produced by shell elements, modelling raft foundations by finite elements, acting over a Winkler soil or those induced by a linear pressure distribution simulating axial force and biaxial bending moments over a pad foundation. To this end we include charts and tables, both for rectangular and circular domains, which allow the designer to evaluate the vertical stresses induced by linear load distributions by hand calculations. The effectiveness of the proposed approach is witnessed by the comparison between the analytical results obtained with the proposed formulas and the numerical ones of a FEM discretization of the soil associated with the loading distribution induced by a foundation modeled by plate elements resting on a Winkler soil.