Modification of Linear Regression Method for Rock Shear Strength Parameters under Triaxial Condition

The triaxial strength envelope of rocks is usually nonlinear, and the shear strength parameters obtained by the linear regression method (LRM) are highly sensitive to confming pressure. In order to enable LRM to consider the influence of confining pressure on the estimation of shear strength parameters, the confining pressure effect coefficient of triaxial strength of rocks is defined. An exponential function is constructed to express the relationship between the coefficient and confming pressure, which is also introduced into the correction of LRM. A linear regression method considering confining pressure effects (CCPE-LRM) is proposed. At the same time, a rationality test method is proposed, and a distance coefficient is defined as an index to characterize the difference between the estimated and actual values of shear strength parameters. Through the verification and analysis of the triaxial strength data of various types of rocks in the published literature, the results show that the distance coefficients of various rocks are small, and the shear strength envelopes obtained by CCPE-LRM are all close to the Mohr circles in an approximately tangent state. It indicates that the shear strength envelope obtained by CCPE-LRM can replace the ideal shear strength envelope to a certain extent, and the shear strength parameters estimated by this method are in good agreement with the theoretical shear strength parameters. These prove that CCPE-LRM LRM has a good applicability.