An automated procedure to build failure envelopes and model the Mohr-Coulomb criterion in the three-dimensional principal stresses space from polyaxial test data

The construction of behaviour laws in rock mechanics applications relies mainly on the choice of a theoretical failure envelope (or criterion) to fit experimental data, and therefore, the representation of this surface in the stress space is a major step.
Various criterions have been developed in order to model the failure envelopes of rocks. The Mohr-Coulomb failure criterion, which is one of the most used, is based on a shearing physical mechanism which supposes that the shear strength on a plane depends on the cohesion and the internal friction angle of the material.
In this paper, our aim is to use data from a polyaxial device to represent the failure envelope of a rock in the tridimensional stress space and model it with the Mohr-Coulomb failure criterion. Therefore, the method developed by Tshibangu (1994) is automated using MatLab, a matrix computing software. We present results of tests performed on Soignies Limestone in octahedral planes and in the principal stress space. The Mohr-Coulomb criterion is then computed and compared to the experimental data.
From a set of data expressed in terms of three principal stresses at failure, this automated method allows thus to represent easily the failure envelope of a material and gives the parameters of the Mohr-Coulomb failure criterion, for various confining states.