Development of new linear and nonlinear failure criteria of true triaxial stresses of rock by the critical analysis of various rocks test results

There are various failure criteria for true triaxial stresses, which have initially been developed for the fracture of solid material such as metals. These criteria are applied for the stability analysis of wellbores and some storage caverns in rock media. In this research, true triaxial failure criteria has been investigated comprehensively by a new method using 12 groups of true triaxial strength test results of rocks including granite, monzonite, amphibolite, andesite, dolomite, Limestone, trachyte, marble, sandstone and shale. The Von Mises and Murrell criteria would not fit the test results due to their particular forms. Neither, Drucker and Prager criterion would fit the test results because of non-correlation between its defined parameters and the mechanical properties such as internal friction angle (ϕ). The relationship between octahedral shear stress (toct) and octahedral normal stress (σoct) having a constant exponent is shown to fit well the various groups of test results. The coefficient of this new criterion (B) that has been obtained by functional fitting is in good correlation with the parameters of ϕ, mi and σci. The power function relationship between toct and the mean of minimum and maximum principal stresses (σm,2) is found to be have a constant exponent also showing a good correlation with the various test results. The coefficient of this criterion (B') showed a good correlation with the parameters of ϕ, mi and σci., too. The linear relationship between toct and σoct of true triaxial strength test results was analyzed. A linear failure criterion was obtained to fit the 12 groups of results, as acceptable correlations have been obtained between the constant and coefficient of this new criterion with the mechanical properties such as internal friction angle (ϕ) and cohesive strength (C). Mogi-Coulomb linear criterion (relationship between toct and σm,2) also fitted the results and an acceptable correlation has been obtained between the defined constant and coefficient parameters of this criterion with the mechanical properties. The linear failure criteria are preferred that is because of having the constant parameter which is a function of mechanical properties of internal friction angle (ϕ) and cohesive strength (C).