This paper proposes a one-dimensional non-linear model to predict the minimum and maximum crack spacings due to shrinkage in concrete pavements. The proposed model consists of two cohesive cracks and an elastic bar restrained by distributed elastic springs. The cohesive crack is characterized by an exponential softening constitutive relation. A set of non-linear equilibrium conditions are obtained. By varying the length of the elastic bar of the proposed model, the tensile forces acting on the cohesive cracks and the energy profiles are investigated. It is demonstrated that the cracking pattern varies with the length of the elastic bar (i.e. the spacing between the two possible cracks), from which the minimum and maximum crack spacings are obtained. Numerical analyses are made of a model pavement and the results indicate that it is the energy minimization principle that governs the cracking pattern. The proposed model provides physical insight into the mechanism of crack spacing in concrete pavements.
Theory of Crack Spacing in Concrete Pavements
