Three-dimensional shakedown solutions for anisotropic cohesive-frictional materials under moving surface loads

Previous work on three-dimensional shakedown analysis of cohesive-frictional materials under moving surface loads has been entirely for isotropic materials. As a result, the effects of anisotropy, both elastic and plastic, of soil and pavement materials are ignored. This paper will, for the first time, develop three-dimensional shakedown solutions to allow for the variation of elastic and plastic material properties with direction. Melan's lower-bound shakedown theorem is used to derive shakedown solutions. In particular, a generalised, anisotropic Mohr-Coulomb yield criterion and cross-anisotropic elastic stress fields are utilised to develop anisotropic shakedown solutions. It is found that shakedown solutions for anisotropic materials are dominated by Young's modulus ratio for the cases of subsurface failure and by shear modulus ratio for the cases of surface failure. Plastic anisotropy is mainly controlled by material cohesion ratio, the rise of which increases the shakedown limit until a maximum value is reached. The anisotropic shakedown limit varies with frictional coefficient, and the peak value may not occur for the case of normal loading only.