Theoretical research of Hoek - Brown empirical strength criterion

By adopting the Griffith hypothesis of micro-crack distribution and taking an angle to describe the density of micro-fracture in rock, we have deduced the relation between the angle and load according to the relative principle about composite crack in linear and elastic fracture mechanics in this paper.Then according to mesoscale phenomenon in the course of rock compression, we choose acos /a ∑1 (the change rate of cos with axial stress) as the damage characteristic value of rock under triaxial compression test and deduce a theoretical strength criterion. The result perfectly coincides with Hoek-Brown Empirical Strength Criterion in mathematical expression. We prove that Hoek-Brown Empirical Strength Criterion is reasonable,and the physical coefficient m is related to the ratio between axial compression strength a, and extension strength σ1.