Modified true triaxial Hoek-Brown criterion considering intermediate principal stress effect

In order to improve the Hoek-Brown strength criterion not considering the influence of intermediate principal stress on rock strength, the evolutions of rock strength were investigated according to the results of the rock true triaxial compression test. The intermediate principal stress coefficient was introduced to quantify the effect on rock strength. Considering the relationships between the parameter of the Hoek-Brown strength criterion and the rock stress levels, the modified Hoek-Brown strength criterion for the true triaxial stress was then established with the Lagrange interpolation method. The spatial envelope characteristics of the modified strength criterion were analyzed. The best-fitting errors of seven rocks with true triaxial test results were finally compared with the three other three-dimensional strength criteria to verify the rationality of the modified strength criterion. The research results indicate that the rock strength increases gradually with the increase of minimum principal stress, and increases first and then decreases with the increase of intermediate principal stress, which presents a significant interval effect. The modified strength criterion not only has the advantage of the Hoek-Brown strength criterion in the nonlinear characteristics of the meridian plane but also describes the basic characteristics of rock strength in stress space. The spatial envelope surfaces for the modified strength criteria with the linear and quadratic interpolation are the non-equilateral hexagonal pyramidal surfaces and conical surfaces, which can meet the requirement of continuous smoothness in the tension-compression meridian plane interval. The modified strength criterion can better predict the true triaxial strength of rocks and reasonably reflect the influence of intermediate principal stress on the rock strength. The modified strength criterion with the quadratic interpolation improves the prediction accuracy of rock strength by about 1.2 to 2.0 times compared to the criterion with linear interpolation. The modified strength criterion has good agreement with the true triaxial test results of different hard and brittle rocks compared with other true triaxial strength criteria, which shows the applicability and reliability of the modified strength criterion.