Prediction of stresses in concrete pavements subjected to non-linear gradients

Abstract

This paper presents a technique for analyzing the residual stresses in concrete pavements subjected to non-linear (stress or strain) gradients throughout the slab thickness. The analysis is separated into two parts. In the first part, an expression is presented for calculating the self equilibrated stresses within a cross-section due to internal restraints (i.e. satisfying equilibrium conditions and continuity of the strain field within the cross-section). These stresses are independent of slab dimensions and boundary conditions. In step two, the stresses due to external restraints (i.e. self-weight and subgrade reaction) are calculated using an equivalent linear temperature gradient obtained from the first part and using existing closed form solutions by Westergaard [Westergaard, H. M., Computation of stresses in concrete roads. In Proc. of the 5th Annual Meeting, Vol. 5, Part I, Highway Research Board, 1926, pp. 90–112] or Bradbury [Bradbury, R. D., Reinforced Concrete Pavements. Wire Reinforcement Institute, Washington D.C., 1947.]. The solution to this step includes slab length and boundary conditions. Total internal stresses due to non-linear gradients are obtained using the superposition principle. The proposed method has been applied to field data from another study for varying temperature profiles within a 24 h period and compared to results from conventional analysis assuming linear gradients. Significant differences were found between the two methods for night-time and early-morning conditions. A linear gradient solution sometimes underestimates tension in the bottom of a slab prior to vehicle loading by a factor of three.