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

Abstract

This paper develops analytical solutions for shakedown limits of a cohesive-frictional half-space under a three-dimensional moving surface load. Melan's lower-bound shakedown theorem has been adopted as the theoretical basis for deriving shakedown limits. Rigorous lower-bound solutions are obtained for shakedown limits by establishing a self-equilibrated residual stress field that, together with the applied elastic stress fields, lies within the Mohr–Coulomb yield criterion throughout the half-space. By searching through the half-space, this study shows that the most critical location for satisfying the yield condition lies on the central plane. The analytical solutions derived in the paper can be used to benchmark numerical shakedown results, as well as to serve as a theoretical basis for the development of an analytical design method for pavements under moving traffic loads.