Coupled Elastic–Plastic Damage Modeling of Rock Based on Irreversible Thermodynamics
Shale is a common rock in oil and gas extraction, and the study of its nonlinear mechanical behavior is crucial for the development of engineering techniques such as hydraulic fracturing. This paper establishes a new coupled elastic–plastic damage model based on the second law of thermodynamics, the...
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2024-11-01
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| author | Xin Jin Yufei Ding Keke Qiao Jiamin Wang Cheng Fang Ruihan Hu |
| author_facet | Xin Jin Yufei Ding Keke Qiao Jiamin Wang Cheng Fang Ruihan Hu |
| author_sort | Xin Jin |
| collection | DOAJ |
| description | Shale is a common rock in oil and gas extraction, and the study of its nonlinear mechanical behavior is crucial for the development of engineering techniques such as hydraulic fracturing. This paper establishes a new coupled elastic–plastic damage model based on the second law of thermodynamics, the strain equivalence principle, the non-associated flow rule, and the Drucker–Prager yield criterion. This model is used to describe the mechanical behavior of shale before and after peak strength and has been implemented in ABAQUS via UMAT for numerical computation. The model comprehensively considers the quasi-brittle and anisotropic characteristics of shale, as well as the strength degradation caused by damage during both the elastic and plastic phases. A damage yield function has been established as a criterion for damage occurrence, and the constitutive integration algorithm has been derived using a regression mapping algorithm. Compared with experimental data from La Biche shale in Canada, the theoretical model accurately simulated the stress–strain curves and volumetric–axial strain curves of shale under confining pressures of 5 MPa, 25 MPa, and 50 MPa. When compared with experimental data from shale in Western Hubei and Eastern Chongqing, China, the model precisely fitted the stress–strain curves of shale at pressures of 30 MPa, 50 MPa, and 70 MPa, and at bedding angles of 0°, 22.5°, 45°, and 90°. This proves that the model can effectively predict the failure behavior of shale under different confining pressures and bedding angles. Additionally, a sensitivity analysis has been performed on parameters such as the plastic hardening rate <i>b</i>, damage evolution rate <i>B</i><sub>ω</sub>, weighting factor <i>r</i>, and damage softening parameter <i>a</i>. This research is expected to provide theoretical support for the efficient extraction technologies of shale oil and gas. |
| format | Article |
| id | doaj-art-9b8d90d3e720499fa566676046ce1586 |
| institution | Kabale University |
| issn | 2076-3417 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj-art-9b8d90d3e720499fa566676046ce15862024-12-13T16:22:11ZengMDPI AGApplied Sciences2076-34172024-11-0114231092310.3390/app142310923Coupled Elastic–Plastic Damage Modeling of Rock Based on Irreversible ThermodynamicsXin Jin0Yufei Ding1Keke Qiao2Jiamin Wang3Cheng Fang4Ruihan Hu5State Key Laboratory for Tunnel Engineering, China University of Mining and Technology (Beijing), Beijing 100083, ChinaSchool of Mechanics and Civil Engineering, China University of Mining and Technology (Beijing), Beijing 100083, ChinaSchool of Mechanics and Civil Engineering, China University of Mining and Technology (Beijing), Beijing 100083, ChinaAcademy of Deep Earth Sciences, Chinese Institute of Coal Science, Beijing 100013, ChinaState Key Laboratory for Tunnel Engineering, China University of Mining and Technology (Beijing), Beijing 100083, ChinaSchool of Aerospace Engineering, Xi’an Jiaotong University, Xi’an 710049, ChinaShale is a common rock in oil and gas extraction, and the study of its nonlinear mechanical behavior is crucial for the development of engineering techniques such as hydraulic fracturing. This paper establishes a new coupled elastic–plastic damage model based on the second law of thermodynamics, the strain equivalence principle, the non-associated flow rule, and the Drucker–Prager yield criterion. This model is used to describe the mechanical behavior of shale before and after peak strength and has been implemented in ABAQUS via UMAT for numerical computation. The model comprehensively considers the quasi-brittle and anisotropic characteristics of shale, as well as the strength degradation caused by damage during both the elastic and plastic phases. A damage yield function has been established as a criterion for damage occurrence, and the constitutive integration algorithm has been derived using a regression mapping algorithm. Compared with experimental data from La Biche shale in Canada, the theoretical model accurately simulated the stress–strain curves and volumetric–axial strain curves of shale under confining pressures of 5 MPa, 25 MPa, and 50 MPa. When compared with experimental data from shale in Western Hubei and Eastern Chongqing, China, the model precisely fitted the stress–strain curves of shale at pressures of 30 MPa, 50 MPa, and 70 MPa, and at bedding angles of 0°, 22.5°, 45°, and 90°. This proves that the model can effectively predict the failure behavior of shale under different confining pressures and bedding angles. Additionally, a sensitivity analysis has been performed on parameters such as the plastic hardening rate <i>b</i>, damage evolution rate <i>B</i><sub>ω</sub>, weighting factor <i>r</i>, and damage softening parameter <i>a</i>. This research is expected to provide theoretical support for the efficient extraction technologies of shale oil and gas.https://www.mdpi.com/2076-3417/14/23/10923shaleirreversible thermodynamicsdamage constitutive modelelastic–plasticnumerical simulation |
| spellingShingle | Xin Jin Yufei Ding Keke Qiao Jiamin Wang Cheng Fang Ruihan Hu Coupled Elastic–Plastic Damage Modeling of Rock Based on Irreversible Thermodynamics Applied Sciences shale irreversible thermodynamics damage constitutive model elastic–plastic numerical simulation |
| title | Coupled Elastic–Plastic Damage Modeling of Rock Based on Irreversible Thermodynamics |
| title_full | Coupled Elastic–Plastic Damage Modeling of Rock Based on Irreversible Thermodynamics |
| title_fullStr | Coupled Elastic–Plastic Damage Modeling of Rock Based on Irreversible Thermodynamics |
| title_full_unstemmed | Coupled Elastic–Plastic Damage Modeling of Rock Based on Irreversible Thermodynamics |
| title_short | Coupled Elastic–Plastic Damage Modeling of Rock Based on Irreversible Thermodynamics |
| title_sort | coupled elastic plastic damage modeling of rock based on irreversible thermodynamics |
| topic | shale irreversible thermodynamics damage constitutive model elastic–plastic numerical simulation |
| url | https://www.mdpi.com/2076-3417/14/23/10923 |
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