Theoretical Solutions for Static and Dynamic Shakedown of Cohesive-Frictional Materials Under Moving Loads

Shakedown theory can serve as a theoretical basis for the design of pavements and railways against long-term residual settlements. Based on the static and dynamic lower-bound shakedown theorems, this paper presents theoretical shakedown solutions for a plane strain cohesive-frictional half-space under a repeated moving load. The medium is described as a Mohr-Coulomb material. A self-equilibrated residual stress field which fully satisfies yield and boundary conditions is introduced to calculate the lower-bound shakedown limit. The dynamic effect of the moving load is considered using analytical solutions of the dynamic elastic stress fields in the half-space. It is found that the two-dimensional static shakedown limits agree with previous literatures. Surface traction has a negative influence on the shakedown limit. Particularly, when large surface sliding is considered, the shakedown limit is actually controlled by the shear stress distribution rather than the normal pressure. The dynamic shakedown limit is very close to the static solution when the load moving speed is very slow. And it is reduced as the load moving speed is increased towards the wave propagation speed in the semi-infinite medium. A material with a high friction angle is more vulnerable to the rise of the load moving speed in terms of the percentage of the shakedown limit reduction from the static solution. The theoretical results in paper can be used to benchmark numerical shakedown solutions.