Failure criterion with intermediate stress and two friction angles

For many rock types, Mohr-Coulomb (MC) failure criterion is a reasonable approximation to strength data, featuring a linear relation with two principal stresses and two material parameters that describe a stress intercept (e.g. uniaxial compression or uniform triaxial tension) and pressure sensitivity (e.g. internal friction angle φ). A criticism of MC is the absence of the intermediate principal stress. Paul-Mohr-Coulomb (PMC) criterion removes that limitation by including three principal stresses. PMC has the advantage over other multi-axial stress criteria in that three material constants, such as one stress intercept and two friction angles, one for compression φ_c and one for extension φ_e, are readily identified. PMC failure criterion is reviewed and data from a series of conventional triaxial compression and extension experiments on Indiana limestone are analyzed. The extension friction angle is larger than the compression friction angle, a sufficient but not necessary condition of the intermediate stress effect. To capture the behavior of the rock in multi-axial loading, PMC is extended to include the results of plane strain compression experiments through the construction of two planes with six parameters.