The modification of Mohr-Coulomb criteria based on shape function and determination method of undetermined parameters

Abstract

Rock strength criteria is a key step to estimate the stability of rock engineering, especially, the effect of intermediate principal stress on rock failure should be considered in formation at great depth. However, the mostly used Mohr-Coulomb criterion don't consider the effect of intermediate principal stress, besides, most rock mechanics laboratories do not have the ability to do true triaxial strength, the strength parameters in poly-axial strength criteria are difficult to be determined. In order to solve these problems, based on the least absolute deviation method, the square of the correlation coefficient, absolute difference and mean difference are adopted to verify the fitting effect of 10 strength criteria on 32 groups of true triaxial strength data. On this basis, the elliptical Lode angle shape function, hyperbolic Lode angle shape function, and the Lode angle shape function based on spatial slip plane are used to establish the modified MC strength criteria, which not only meets the requirements of smoothness and convexness, but also can be used widely in many geomaterials. Besides, strength parameters of the established criteria can be decided by conventional triaxial strength experiment, and the prediction accuracy of the modified MC strength criteria for the 32 groups of true triaxial strength data is better than or close to the lowest fitting error of the existing poly-axial strength criteria.