Study on Optimal Conventional Triaxial Strength Criterion of Rock Based on Gauss-Newton Method

Conventional triaxial strength criteria are used widely to judge the rock failure states. In this paper, the nonlinear least squares method (Guass-newton method) is used to fit the regression relationships between the maximum principal stress σ 1 as well as the differential stress σ 1 -σ 3 and the minimum principal stress σ 3 by the linear, parabolic, power, logarithmic, hyperbolic and exponential equations in the principal stress space by using 1stOpt software. Results show that the linear equation has a poor fitting effect (low R 2 ), while power, logarithmic, hyperbolic, and exponential equations perform better. Nonlinear equations can approximate test uniaxial compressive strength values, and using (σ t ) t improves regression accuracy. In conclusion, different equations are recommended based on (σ t ) t inclusion. The power equation is good when (σ t ) t is excluded, and power, logarithmic, exponential, and hyperbolic equations are suitable when (σ t ) t is included. For regression tensile strength (σ t ) r , power equation fitting is closest to the test value without (σ t ) t , and all nonlinear equations work well with (σ t ) t . These four nonlinear equations are ideal for fitting triaxial failure envelopes due to high R², guiding rock engineering. The conclusions are of some significance to use the conventional triaxial strength criterion in geotechnical engineering.