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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2024-12-01
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| author | Yuanguang Zhu Xuanyao Wang Bin Liu Haoyuan Xue |
| author_facet | Yuanguang Zhu Xuanyao Wang Bin Liu Haoyuan Xue |
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| description | 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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| spelling | doaj-art-89b6c0b8d631404e8cee8a26abb1b18a2025-01-10T13:14:53ZengMDPI AGApplied Sciences2076-34172024-12-0115123610.3390/app15010236The Anisotropic Time-Dependent Properties and Constitutive Model Analysis of Carbonaceous Slate with Different Foliation AnglesYuanguang Zhu0Xuanyao Wang1Bin Liu2Haoyuan Xue3State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, ChinaState Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, ChinaState Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, ChinaState Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, ChinaIn 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.https://www.mdpi.com/2076-3417/15/1/236carbonaceous slatecreep behaviorengineering sustainabilityanisotropy |
| spellingShingle | Yuanguang Zhu Xuanyao Wang Bin Liu Haoyuan Xue The Anisotropic Time-Dependent Properties and Constitutive Model Analysis of Carbonaceous Slate with Different Foliation Angles Applied Sciences carbonaceous slate creep behavior engineering sustainability anisotropy |
| title | The Anisotropic Time-Dependent Properties and Constitutive Model Analysis of Carbonaceous Slate with Different Foliation Angles |
| title_full | The Anisotropic Time-Dependent Properties and Constitutive Model Analysis of Carbonaceous Slate with Different Foliation Angles |
| title_fullStr | The Anisotropic Time-Dependent Properties and Constitutive Model Analysis of Carbonaceous Slate with Different Foliation Angles |
| title_full_unstemmed | The Anisotropic Time-Dependent Properties and Constitutive Model Analysis of Carbonaceous Slate with Different Foliation Angles |
| title_short | The Anisotropic Time-Dependent Properties and Constitutive Model Analysis of Carbonaceous Slate with Different Foliation Angles |
| title_sort | anisotropic time dependent properties and constitutive model analysis of carbonaceous slate with different foliation angles |
| topic | carbonaceous slate creep behavior engineering sustainability anisotropy |
| url | https://www.mdpi.com/2076-3417/15/1/236 |
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