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 σ1 as well as the differential stress σ1-σ3 and the minim...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
EDP Sciences
2025-01-01
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| Series: | E3S Web of Conferences |
| Online Access: | https://www.e3s-conferences.org/articles/e3sconf/pdf/2025/31/e3sconf_mdoa2025_01002.pdf |
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| Summary: | 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 (σt)t improves regression accuracy. In conclusion, different equations are recommended based on (σt)t inclusion. The power equation is good when (σt)t is excluded, and power, logarithmic, exponential, and hyperbolic equations are suitable when (σt)t is included. For regression tensile strength (σt)r, power equation fitting is closest to the test value without (σt)t, and all nonlinear equations work well with (σt)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. |
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| ISSN: | 2267-1242 |