Analytical Solution for Shear Stress Distribution on the Interface between Different Rocks under Direct Shear

This study attempted to improve the understanding of the effect of mechanical mismatch on the shear behavior of an interface or discontinuity between different rocks under direct shear. First, general and simplified analytical solutions for the shear stress (τ) distribution on a rock interface or discontinuity were determined. Subsequently, the τ distributions on the rock interface that were acquired from the analytical solutions were demonstrated via numerical simulations. Finally, the effect of mechanical mismatch between the rocks on τ distribution, shear strength, and potential location of crack initiation at the interface was investigated. The results indicated that it was difficult to widely use and promote the developed general solution. This is due to the lengthy expression for the solution and the complexity that was involved in the determination of the integration constants. The simplified solution omits the coupling effect between the interfacial τ and normal stresses (σ). In addition, it could accurately describe τ on a rock interface. The internal moment that was produced by shear forces (P) could significantly affect the τ distribution on a rock interface. Nonuniformly distributed τ is observed on the interface between different rocks and thicknesses. Furthermore, the nonuniformity increased with the increase in the mechanical or thickness mismatch. The τ and its concentration result from the loading of P. The noncoaxial P could produce compression and bending effects. The τ primarily results from the compression effect, and the bending effect affects the τ concentration. Cracks would not initiate simultaneously from both ends of the interface due to the dissimilar τ concentrations. For the sinistral sense of shear, cracks would first initiate from the right interface end if Young’s modulus of the upper rock (E₁) is smaller than that of the lower one (E₂). The results could guide a profound understanding of the shearing behavior of the rock interfaces or discontinuities between different rocks.

This study presented general and simplified analytical solutions to calculate the τ distribution on the interface or discontinuity between different rocks that were subjected to direct shear. The accuracy and reliability of the analytical solutions were validated against a series of two-dimensional (2D) finite-element models (FEM) of direct shear. The τ was distributed nonuniformly and concentrated asymmetrically on the interface between different rocks. The τ concentrations were different at both ends of the interface. The difference increased with the increase in the mismatch in Young’s modulus (E) between the rocks on either side of the interface. The mechanical mismatch between the rocks could influence the τ distribution, shear strength, and potential crack initiation location at the interface. The results could be important to better understand the shear behavior, strength characteristics, and fracture morphology of the interfaces between different rocks. Furthermore, these could further guide disaster prevention and stability evaluation of rock engineering.