Conventional triaxial strength criteria are important for the judgment of rock failure. Linear, parabolic, power, logarithmic, hyperbolic, and exponential equations were, respectively, established to fit the conventional triaxial compression test data for 19 types of rock specimens in the Mohr stress space. Then, a method for fitting the failure envelope to all common tangent points of each two adjacent Mohr’s circles (abbreviated as CTPAC) was proposed in the Mohr stress space. The regression accuracy of the linear equation is not as good as those of the nonlinear equations on the whole, and the regression uniaxial compression strength (σc)r, tensile strength (σt)r, cohesion cr, and internal frictional angle φr predicted by the regression linear failure envelopes with the method for fitting the CTPAC in the Mohr stress space are close to those predicted in the principal stress space. Therefore, the method for fitting CTPAC is feasible to determine the failure envelopes in the Mohr stress space. The logarithmic, hyperbolic, and exponential equations are recommended to obtain the failure envelope in the Mohr stress space when the data of tensile strength (σt)t are or are not included in regression owing to their higher R2, less positive x-intercepts, and more accurate regression cohesion cr. Furthermore, based on the shape and development trend of the nonlinear strength envelope, it is considered that when the normal stress is infinite, the total bearing capacity of rock tends to be a constant after gradual increase with decreasing rates. Thus, the hyperbolic equation and the exponential equation are more suitable to fit triaxial compression strength in a higher maximum confining pressure range because they have limit values. The conclusions can provide references for the selection of the triaxial strength criterion in practical geotechnical engineering.
Skolem's conjecture confirmed for a family of exponential equations, III
