The influence of traffic moving speed on shakedown limits of flexible pavements

Shakedown theory is often used to analyse elastic–plastic responses of structures subjected to variable or repeated loads. In pavement engineering, it has been used to predict the maximum admissible load (termed as ‘shakedown limit’) against excessive rutting in flexible pavements. Pavement shakedown analysis, which involves the calculation of the pavement shakedown limit, usually utilised elastic stresses induced by a static wheel load and therefore neglected any possible dynamic responses. This paper will, for the first time, evaluate the dynamic effect of the moving load on the shakedown limit of flexible pavement. A numerical approach is developed based on a recent lower bound method for solving the pavement shakedown problem. The dynamic responses of elastic stresses to the moving traffic loads are computed using finite element method in which infinite elements are used for boundaries. Shakedown limits for a single subgrade layer and a pavement-subgrade system under traffic loads at various speeds are investigated. It is found that the shakedown limit is consistent with the static solution when the load moving speed is very low and it is reduced as the load moving speed is changed towards the speed of Rayleigh wave propagation. In the layered system, the shakedown limit increases with rising strength ratio and layer thickness until a maximum value is reached. The rise of stiffness modulus ratio can either increase or decrease the shakedown limit of the first layer due to the negative effect of stress redistribution and the positive effect of rising Rayleigh speed. When the stiffness modulus ratio is relatively small, the latter effect overwhelms the former one, or vice versa.