Representative sampling method for laboratory testing on shear strength of rock joints

The direct shear test is commonly used to determine the shear strength of rock joints. The measured shear strength, however, varies greatly with specimen positions due to the heterogeneity of rock joints. As a result, selecting specimens that represent the overall properties of rock joints is usually difficult. This paper aims to investigate the heterogeneity of rock joints and propose a new sampling method for selecting representative specimens. The roughness and shear strength variations of specimens taken from different positions of a natural rock joint were analyzed, and it was discovered that the heterogeneity of rock joint roughness is responsible for the heterogeneity of shear strength. The limitations of the traditional sampling method based on visual judgment were extensively investigated, revealing that shear strength parameters acquired by the traditional method contain large coefficient of variation (COV) values. To acquire trustworthy shear strength parameters, we proposed a representative sampling method based on the maximum likelihood estimation of the overall properties of rock joints. The number of determined representative specimens increases with the increase of normal stress. Representative specimens determined under low normal stresses can likewise exhibit the overall properties of the rock joint when subjected to high normal stresses. The Mohr-Coulomb and a nonlinear criterion were used to validate the derived representative specimens, demonstrating that the proposed method can produce reliable shear strength parameters and shear strength envelopes. Particularly, the determined representative specimens could derive shear strength parameters with relative errors less than 10% and COV values less than 0.1. The proposed method provides a quantitative and reliable tool for determining representative specimens to obtain reliable shear strength of rock joints.