Model for nonlinear thermal effect on pavement warping stresses

Practically all current design for and analysis of thermally induced stresses in rigid pavements are based on an assumed linear temperature distribution across the thickness of the pavement slab. Actual temperature distributions across the thickness of a pavement slab are not linear, and studies have shown that the errors in the computed maximum warping stresses caused by the assumption of linear temperature distribution could be as high as 30% or more. Finite-element models have been developed to analyze the effects of nonlinear temperature distribution. These are numerical methods and are generally not user friendly, as they require skills to design the finite-element mesh and good judgment to ascertain convergence of the solutions. This paper describes a closed-form theoretical model to compute the warping stresses caused by a nonlinear temperature distribution. The model is derived based on the Reissner thick-plate theory for a concrete pavement slab with four free edges resting on either a Pasternak or a Winkler foundation. The nonlinear temperature distribution across the slab thickness is divided into three components that are analyzed separately. The filial solutions are obtained by superposition of the stresses caused by the three components of temperature distribution.