A Non-linear Three-Dimensional Failure Criterion Based on Stress Tensor Distance

The basis of engineering stability evaluation lies in the study of the relationship between rock stress and strength. However, there is no unified expression for the tensile strength and shear strength in the commonly used failure criteria, and the effect of intermediate principal stress is sometimes neglected. A three-dimensional non-linear failure criterion (3DNFC) was proposed based on the concept of tensor distance. The criterion contains only three parameters, which can be obtained through well-established uniaxial compression and tensile tests. The effect of the intermediate principal stress on the rock strength was estimated by the coefficient m. Based on the true triaxial test data of 12 rock types, the proposed 3DNFC was compared with traditional failure criteria, and the performance of the criterion was validated. The results show that the 3DNFC can be employed to characterize the influence of intermediate principal stress on rock strength. The misfits to true triaxial data are rare, and the fitting effect is better than other commonly used failure criteria. 3DNFC has a simple mathematical form and clear physical meaning. The triaxial strength of rock predicted by a uniaxial test is in good agreement with the measured value. 3DNFC can be conveniently applied to the stability analysis and evaluation of rock encountered in engineering practice when only uniaxial test data are available.