Dynamic shakedown limits for flexible pavement with cross-anisotropic materials

Abstract

Shakedown solution is widely used to analyse the elastic-plastic behaviours of structures in pavement design. Previous studies only concerned the shakedown theorem under traffic loads for an isotropic material, although the material is usually anisotropic. This paper firstly proposed a numerical analysis for anisotropic materials under moving traffic load, based on Melan’s lower-bound shakedown theory. An anisotropic Finite Element–Infinite Element (FE–IE) model is used to calculate the dynamic stresses in the anisotropic material subjected to moving traffic loads with different speeds. Then, the shakedown limits for an anisotropic half-space and a two-layered pavement system are determined, respectively. It is found that the Rayleigh wave speed of the soil has a significant effect on the shakedown limits. For a cross-anisotropic half-space, the shakedown limits mainly depend on the stiffness ratio of the two layers and the Poisson’s ratio only has a small effect, although both of them significantly affect the Rayleigh wave speed. Furthermore, the shakedown limit increases with increasing cohesion ratio until it reaches a maximum value, and it gets rid of the control of shakedown condition when the moving speed exceeds the Rayleigh wave speed. For a two-layered anisotropic system, the results are similar to those in an isotropic system. Failure tends to occur on the top of the second layer instead of the first layer when the speed of moving load or the anisotropic Young’s modulus ratio increases, together with the decrease of shakedown limit.