Strip loads on a non-linear heterogeneous half-space

Abstract

A non-linear heterogeneous half-space is considered as being defined by one modulus and two exponents to describe the increase of stiffness with depth and the degree of non-linearity. This ‘parabolic’ half-space contains the linear elastic models of Boussinesq, Gibson and Booker et al. as subsets. If the parameters are selected appropriately the material turns into a hardening plastic-like material. Differential equations are established for plane deformation of a half-space consisting of such material. An exact solution is presented for the half-surface load. This and the existing line-load solution are used to calculate approximate solutions for strip loads and the rigid strip footing. The differential equations established are used for accuracy assessment. The ‘parabolic’ half-space of this type is applicable to problems with predominantly plastic soil deformation if monotonically loaded rigid structures are considered. Although ultimate failure cannot be modelled, the influence of stiffness increase with depth on bearing capacity and on displacements of footings can be better described using this model than by other simple methods.