Mechanical and Energy Evolution Characteristics of Sandstone under True Triaxial Cyclic Loading
To study the mechanical and energy evolution characteristics of sandstone under true triaxial cyclic loading, a sandstone mechanical test with different intermediate principal stress under true triaxial loading was conducted using the rock true triaxial disturbance unloading test system. The influen...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-06-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/13/12/7230 |
| _version_ | 1797596276845445120 |
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| author | Chunliang Dong Chaotao Fan Xiaoyu Lu Guangming Zhao Minjie Qi Ruipeng Qin |
| author_facet | Chunliang Dong Chaotao Fan Xiaoyu Lu Guangming Zhao Minjie Qi Ruipeng Qin |
| author_sort | Chunliang Dong |
| collection | DOAJ |
| description | To study the mechanical and energy evolution characteristics of sandstone under true triaxial cyclic loading, a sandstone mechanical test with different intermediate principal stress under true triaxial loading was conducted using the rock true triaxial disturbance unloading test system. The influence of axial load on the deformation, energy evolution, and macroscopic failure characteristics of sandstone under different intermediate principal stress in a true triaxial test was systematically analyzed, and the damage evolution law of sandstone under true triaxial cyclic load was revealed. Results showed that the failure mode of sandstone under true triaxial compression changed from tension–shear composite failure to tension failure. Grading cyclic load <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></semantics></math></inline-formula> greatly influenced maximum principal strain <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>ε</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></semantics></math></inline-formula> and minimum principal strain <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>ε</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></semantics></math></inline-formula> but had little influence on intermediate principal strain <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>ε</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula>. Under the same <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula> condition, the input energy and elastic energy in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></semantics></math></inline-formula> directions increased nonlinearly. Under different <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula> conditions, the dissipated energy in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></semantics></math></inline-formula> directions decreased with the increase in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula>. With the increase in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula>, graded cycles <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>ε</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>ε</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></semantics></math></inline-formula> decreased considerably, and the failure mode changed from tensile failure to shear failure. When the cyclic loading rate increased, the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>ε</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>ε</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>ε</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></semantics></math></inline-formula>, and volume strain <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>ε</mi></mrow><mrow><mi>v</mi></mrow></msub></mrow></semantics></math></inline-formula> of sandstone failure decreased, but the expansion point increased. Under true triaxial grading cyclic loading and unloading, the total dissipated energy of sandstone increased exponentially. The larger <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula> was, the smaller the damage variable was. |
| first_indexed | 2024-03-11T02:48:15Z |
| format | Article |
| id | doaj.art-efd9302b47574f5e9132589f7ab18073 |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-11T02:48:15Z |
| publishDate | 2023-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj.art-efd9302b47574f5e9132589f7ab180732023-11-18T09:10:56ZengMDPI AGApplied Sciences2076-34172023-06-011312723010.3390/app13127230Mechanical and Energy Evolution Characteristics of Sandstone under True Triaxial Cyclic LoadingChunliang Dong0Chaotao Fan1Xiaoyu Lu2Guangming Zhao3Minjie Qi4Ruipeng Qin5State Key Laboratory of Mining Response and Disaster Prevention and Control in Deep Coal Mines, Anhui University of Science and Technology, Huainan 232001, ChinaState Key Laboratory of Mining Response and Disaster Prevention and Control in Deep Coal Mines, Anhui University of Science and Technology, Huainan 232001, ChinaState Key Laboratory of Mining Response and Disaster Prevention and Control in Deep Coal Mines, Anhui University of Science and Technology, Huainan 232001, ChinaState Key Laboratory of Mining Response and Disaster Prevention and Control in Deep Coal Mines, Anhui University of Science and Technology, Huainan 232001, ChinaState Key Laboratory of Mining Response and Disaster Prevention and Control in Deep Coal Mines, Anhui University of Science and Technology, Huainan 232001, ChinaSchool of Civil Engineering and Architecture, Anhui University of Science and Technology, Huainan 232001, ChinaTo study the mechanical and energy evolution characteristics of sandstone under true triaxial cyclic loading, a sandstone mechanical test with different intermediate principal stress under true triaxial loading was conducted using the rock true triaxial disturbance unloading test system. The influence of axial load on the deformation, energy evolution, and macroscopic failure characteristics of sandstone under different intermediate principal stress in a true triaxial test was systematically analyzed, and the damage evolution law of sandstone under true triaxial cyclic load was revealed. Results showed that the failure mode of sandstone under true triaxial compression changed from tension–shear composite failure to tension failure. Grading cyclic load <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></semantics></math></inline-formula> greatly influenced maximum principal strain <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>ε</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></semantics></math></inline-formula> and minimum principal strain <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>ε</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></semantics></math></inline-formula> but had little influence on intermediate principal strain <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>ε</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula>. Under the same <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula> condition, the input energy and elastic energy in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></semantics></math></inline-formula> directions increased nonlinearly. Under different <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula> conditions, the dissipated energy in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></semantics></math></inline-formula> directions decreased with the increase in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula>. With the increase in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula>, graded cycles <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>ε</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>ε</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></semantics></math></inline-formula> decreased considerably, and the failure mode changed from tensile failure to shear failure. When the cyclic loading rate increased, the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>ε</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>ε</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>ε</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></semantics></math></inline-formula>, and volume strain <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>ε</mi></mrow><mrow><mi>v</mi></mrow></msub></mrow></semantics></math></inline-formula> of sandstone failure decreased, but the expansion point increased. Under true triaxial grading cyclic loading and unloading, the total dissipated energy of sandstone increased exponentially. The larger <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula> was, the smaller the damage variable was.https://www.mdpi.com/2076-3417/13/12/7230rock mechanicstrue triaxial cycleenergydeformationdamage characteristicsdamage |
| spellingShingle | Chunliang Dong Chaotao Fan Xiaoyu Lu Guangming Zhao Minjie Qi Ruipeng Qin Mechanical and Energy Evolution Characteristics of Sandstone under True Triaxial Cyclic Loading Applied Sciences rock mechanics true triaxial cycle energy deformation damage characteristics damage |
| title | Mechanical and Energy Evolution Characteristics of Sandstone under True Triaxial Cyclic Loading |
| title_full | Mechanical and Energy Evolution Characteristics of Sandstone under True Triaxial Cyclic Loading |
| title_fullStr | Mechanical and Energy Evolution Characteristics of Sandstone under True Triaxial Cyclic Loading |
| title_full_unstemmed | Mechanical and Energy Evolution Characteristics of Sandstone under True Triaxial Cyclic Loading |
| title_short | Mechanical and Energy Evolution Characteristics of Sandstone under True Triaxial Cyclic Loading |
| title_sort | mechanical and energy evolution characteristics of sandstone under true triaxial cyclic loading |
| topic | rock mechanics true triaxial cycle energy deformation damage characteristics damage |
| url | https://www.mdpi.com/2076-3417/13/12/7230 |
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