The Anisotropic Time-Dependent Properties and Constitutive Model Analysis of Carbonaceous Slate with Different Foliation Angles
In tunnel construction in western China, a vast amount of carbonaceous slate is encountered. High in situ stress and foliation structures cause the rock mass to exhibit pronounced anisotropic creep, readily inducing a series of engineering disasters like collapses and lining cracks. Investigating th...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-12-01
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| Series: | Applied Sciences |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2076-3417/15/1/236 |
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| Summary: | In tunnel construction in western China, a vast amount of carbonaceous slate is encountered. High in situ stress and foliation structures cause the rock mass to exhibit pronounced anisotropic creep, readily inducing a series of engineering disasters like collapses and lining cracks. Investigating the anisotropic time-dependent characteristics of carbonaceous slate is beneficial to the long-term stability of tunnel construction and operation. In view of this, carbonaceous slate specimens with different angles, <i>β</i>, between the foliation plane and loading direction were studied using a graded loading method through uniaxial compression creep tests. The results show that the instantaneous axial strain, <i>ε<sub>i</sub></i>, the axial creep strain, <i>ε<sub>c</sub></i>, the duration time of decelerating creep stage, <i>t<sub>d</sub></i>, and the steady creep strain rate, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mover accent="true"><mrow><mi>ε</mi></mrow><mo>˙</mo></mover></mrow><mrow><mi>s</mi></mrow></msub></mrow></semantics></math></inline-formula>, increased with the rise in the loading ratio, <i>k</i>. Their variations followed a power law relationship, with the <i>R</i><sup>2</sup> (Coefficient of Determination) values all exceeding 0.95. The value of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mover accent="true"><mrow><mi>ε</mi></mrow><mo>˙</mo></mover></mrow><mrow><mi>s</mi></mrow></msub></mrow></semantics></math></inline-formula> was observed to be less than 1.5 × 10<sup>−4</sup>/h when <i>β</i> < 45°, while it was found to exceed 1.5 × 10<sup>−4</sup>/h in the cases of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>β</mi><mo>≥</mo><mn>45</mn><mo>°</mo></mrow></semantics></math></inline-formula>. The long-term strength, <i>σ<sub>L</sub></i>, of carbonaceous slate showed a U-shaped pattern with the variation in <i>β</i>. The maximum <i>σ<sub>L</sub></i> occurred at <i>β</i> = 90° and the minimum was observed at <i>β</i> = 15°. A fractional nonlinear creep model (FNC model) was developed. The sensitivity analysis reveals that the larger the fractional order <i>n</i> is, the <i>t<sub>d</sub></i> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mover accent="true"><mrow><mi>ε</mi></mrow><mo>˙</mo></mover></mrow><mrow><mi>s</mi></mrow></msub></mrow></semantics></math></inline-formula> increase. <i>η</i><sub>2</sub> and <i>E</i><sub>2</sub> primarily affect the decelerated creep stage, while the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mover accent="true"><mrow><mi>ε</mi></mrow><mo>˙</mo></mover></mrow><mrow><mi>s</mi></mrow></msub></mrow></semantics></math></inline-formula> exhibits a rapid increase with the rise of <i>η</i><sub>1</sub>. To further validate the FNC model, a comparison is made with the traditional Nishihara model. The <i>R</i><sup>2</sup> of the FNC model is larger than 0.965, which is higher than that of the Nishihara model (<i>R</i><sup>2</sup> ≤ 0.911). The FNC model can effectively cope with the impact of the sudden increase in strain and well describe the characteristics of the decelerating, steady-state, and accelerating creep stages at any stress level and any angle. The results provide a reference for the study of the creep mechanism of layered rocks. |
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| ISSN: | 2076-3417 |