Determination of the minimum number of specimens required for laboratory testing of the shear strength of rock joints

Abstract

The shear strength of rock joints is critical in determining rock mass stability. However, the reliability of shear strength determined by testing only a few rock joint specimens is questionable due to the inherent heterogeneity of rock joints. This study aimed to investigate shear strength heterogeneity and determine the required minimum number of specimens (RMN) for obtaining reliable values. Specimens were extracted from various positions within a natural rock joint, and their roughness and shear strength variations were examined. A significant correlation between shear strength heterogeneity and joint roughness was found. Monte Carlo simulation was used to simulate engineering practice sampling procedures. The effectiveness of specimen numbers under different normal stresses was evaluated using relative error and corresponding probability. Results showed that the RMN depended on acceptable relative error, specified probability, and normal stress. For acceptable relative errors of 5% to 10% and corresponding probabilities of 85–95%, the RMN exhibits a decrease with an increase in normal stress, while it demonstrates an increase when considering acceptable relative error and probability requirements. A smaller RMN was needed under high normal stress for the same rock joint, demonstrating a decrease in shear strength heterogeneity with increasing normal stress. However, commonly used specimen numbers like 3 or 5 did not always align with the recommended RMN. The results also emphasize the significance of considering rock material properties when determining the RMN. The proposed method provides a quantitative and reliable tool for determining the RMN, considering the heterogeneity of rock joints.