Determination of "mi" in the Hoek–Brown failure criterion of rock

The m_i is an important parameter in the use of the Hoek–Brown failure criterion. It can be estimated using a triaxial compressive strength test but in many projects there is no actual test result for the parameter. An estimation of m_i comes from a reference table giving a constant value. Elsewhere some empirical equations for the value were suggested in the 1990s. Applying these equations is limited use since they are available for a few rock types and the equations are based on just uniaxial compressive strength tests of rock. In this research rocks were divided into three categories (Igneous, Sedimentary and Metamorphic) and three empirical formulas are suggested for the categories based on uniaxial compressive strength (σ_ci) and tensile strength (σ_t) of rocks by nonlinear regression. The equations have been obtained by a combination of the two independent parameters and the trial and error method was used to find the equations with the highest correlation coefficient. The data base uses data from many original international research projects and much data from Iranian tunnelling projects. The models have a high level of accuracy and have been used to describe most rock types although the authors know that the technique can be improved using a new and larger collection of data in the future.