Shear Stress Distribution in Rock-Cemented Discontinuities under Direct Shear: Theoretical Analysis and Numerical Validation

Abstract

To better understand the shear stress distribution in rock-cemented discontinuities, such as bedding planes and mineral-filled natural fractures (NFs), subjected to direct shear, an analytical solution for shear stress was first derived on the basis of the compression and bending theories of materials. The shear stresses obtained using the analytical solution for different conditions were then verified by the numerical simulation method. Finally, the main factors that influence the shear stress distribution in cemented discontinuities were explored using the analytical solution and numerical simulation methods. The results showed that the internal moment generated by shear forces significantly affects the shear stress distribution in a cemented NF. The analytical solution which considers the internal moment can accurately predict the shear stress distribution in most cases. The shear and normal stresses are both concentrated near the ends of cemented NF; however, they are comparatively uniform in the central portion. The shear stress concentration decreases with the increasing width of cemented NF, whereas it increases with Young’s modulus of cemented NF. The nonuniformity in shear stress decreases with the specimen height, and only when the specimen height is equal to the specimen length, the error produced by the analytical solution attains a minimum. The tractions on the loading surfaces are significantly nonuniform, and the nonuniform tractions are to balance the bending moment created by shear forces. Moreover, the shear box can dramatically influence the shear stress distribution in cemented NF. Uniform normal and shear displacements which represent the normal and shear forces loaded via a rigid shear box should be used for the boundary conditions. The findings in this study can provide a theoretical foundation for the evaluation of deformation properties and shear strength of intact rocks, rock interfaces, bedding planes, or mineral-filled NFs subjected to direct shear.