Lower bound shakedown analysis of layered pavements using discontinuous stress fields

Abstract

Pavements and railways are subjected to repeated wheel loads of different magnitudes. Both load magnitudes and number of repetitions of load need to be considered in order to avoid significant damages to a pavement. A conventional finite element technique is convenient for calculating static pavement responses, but the prediction of pavement performance under repeated loading is much more difficult as it needs a large number of time steps or loading cycles. Shakedown analysis with a statically admissible residual stress field offers a simple approach for predicting the maximum magnitude of repetitive load which can be allowed to act on the pavement in order to prevent excessive permanent deformation. This paper presents a lower bound shakedown formulation using a linear approximation of the Mohr-Coulomb yield criterion. The residual stress field is modelled using 3-noded triangles where stress discontinuities are allowed to occur at the edges of each triangle. Lower bound shakedown limits are obtained by insisting that both the total and the residual stress fields don't violate the yield condition everywhere in the pavement. The proposed formulation is first verified using a homogeneous isotropic half space and then applied to a two-layer pavement. The variation of shakedown limits with material properties and layer thickness are investigated. The results presented can be used to form a sound theoretical basis for pavement design.