Closed-form solution for curling responses in rigid pavements

Closed-form expressions for calculating stresses and displacements of partially restrained concrete pavement caused by a linear temperature gradient are presented. Translational and rotational linear elastic springs along the slab edges defined the partial restraint. In addition to plate theory behavior, the model assumes linear elastic concrete and an infinitely long slab resting on a Winkler foundation. The solutions of curling stresses and displacements were validated using the finite-element (FE) method and quantified the effect of semirigid connections, slab and foundation material properties, and slab thickness and width on them. Rotational and translational restraints, which can be related to joint condition in concrete pavement, had significant influence on the magnitude and location of maximum curling stresses and deflections. In addition, Westergaard analysis, a particular case of the proposed solution when there is no restriction along the slab's edges, resulted into the largest deflections at the center of the slab and the lowest maximum curling stresses. Adjustment factors that convert the theoretical findings from an infinitely long slab to a square slab are proposed.