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

School of Energy Science and Engineering, Henan Polytechnic University, Jiaozuo 454003, China

^a) Corresponding author: guobaohua@139.com;
^b) 15222314016@163.com;
^c) zhe991027@163.com;
^d) 19103948962@163.com;
^e) zhongpb04@163.com;

Abstract

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 σ₁ as well as the differential stress σ₁-σ₃ and the minimum principal stress σ₃ 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 R²), 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.