A New Perspective on the Constant mi of the Hoek–Brown Failure Criterion and a New Model for Determining the Residual Strength of Rock

The constant mi is a fundamental parameter required in the Hoek–Brown (H–B) failure criterion for estimating rock strength. Triaxial tests for the calculation of this constant are time-consuming and expensive. In this paper, a new perspective is presented for the physical meaning of the parameter mi of the H–B model in consideration of the contact friction coefficient. A correlation between the contact friction coefficient and mi is established using published data. A practical approach is proposed to determine the value of the parameter mi. In addition, previously proposed methods of estimating the residual strength of rock are reviewed. A novel method based on the H–B failure criterion is established to predict the residual strength of rock. The single model parameter used in the new model controls the residual strength nonlinearity. The strengths predicted by the proposed method for limestone, granite, slate, and sandstone are in good agreement with those measured during laboratory tests. The corresponding errors are within a range of 15%. This method is applied to an actual rock mass around a tunnel in the Hanjiang to Weihe River Project of China.