A Constitutive Model for Aggregate Interlock Shear Based on Micromechanics

A new constitutive model for interface shear in concrete is presented. The composite is treated as a single-phase medium with no distinction in the strength difference between the matrix and the inclusions. The model consists of an assemblage of springs and a triangular asperity as a statistically equivalent replacement of the rough crack surfaces. The constitutive model relates the normal and shearing stresses and displacements in terms of the interface strength, contact areas, the contact angle of the rough crack surface, and the crack closing pressure. Using the concepts of critical state soil mechanics, conditions were stipulated for dilation and contraction of the rough crack, in terms of the intensity of the applied constant normal stresses. The deformability of the asperity was mathematically described in terms of the initial angle of contact and a progression of this angle to a minimum by means of an exponential model. Using idealized test results, a mathematical model was developed for contact area as a function of the crack width and tangential displacement. The performance of the constitutive model was verified by predicting the experimental results. The comparisons appear to be very satisfactory.