A Simple 3D Hoek and Brown Failure Criterion

Abstract

The paper presents a simple three dimensional Hoek and Brown failure criterion which considers intermediate principal stress (σ2). An asymmetric sinusoidal expression between the principal stress σ1 and σ2 has been proposed and incorporated into the generalized 2D Hoek and Brown failure criterion (1980). The proposed expression has two strength parameters a and b. Statistical analysis of the results of eight true triaxial tests on different type of rocks, collected from the literatures, have been carried out for determining the strength parameters (a, b) at mean misfit. It has been observed from the analysis that these parameters (a, b) are independent of Hoek and Brown strength parameters (i.e. σc, m, s). The observed ranges of parameters a and b for different rock types are 0.1–0.25 and 0.7–1.6 respectively. Another set of analysis was also carried out by considering the values of strength parameters a and b equal to 0.2 and 1.2 respectively. It was observed from the analysis that the mean misfit is almost close to the previous analysis. Thus, one can reasonably consider these values for representing simple 3D Hoek and Brown failure criterion.