Thermal Damage Constitutive Model and Brittleness Index Based on Energy Dissipation for Deep Rock
In deep underground engineering, rock usually encounters a high temperature problem. The stress–strain relationship of rock under high temperatures is the basis of engineering excavation. Based on the Lemaitre’s equivalent strain hypothesis and energy dissipation theory, the thermal damage constitut...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/3/410 |
| _version_ | 1827660007785627648 |
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| author | Xiaoli Xu Changqi Yue Liqi Xu |
| author_facet | Xiaoli Xu Changqi Yue Liqi Xu |
| author_sort | Xiaoli Xu |
| collection | DOAJ |
| description | In deep underground engineering, rock usually encounters a high temperature problem. The stress–strain relationship of rock under high temperatures is the basis of engineering excavation. Based on the Lemaitre’s equivalent strain hypothesis and energy dissipation theory, the thermal damage constitutive model of rock is established. The results show that the peak stress, ultimate elastic energy and dissipated energy at the peak all decrease with the increase of temperature in a logistic function, which indicates that the increase of temperature aggravates the deterioration of rock’s mechanical properties. Compared with rock’s constitutive model that is established on strength criterion, the thermal damage constitutive model based on energy dissipation better reflects the phenomenon of stress drop after the peak and well describes the whole stress-strain curve of rock failure, which verifies the rationality of the model. The damage model further improves the theoretical system of the rock damage constitutive model and makes up for the defect in that the traditional damage model cannot reasonably explain the nature of rock failure. The brittleness index, defined based on the energy drop coefficient, shows a logistic function with the increase of temperature, which has good physical meaning. Analyzing the phenomenon of the rock stress drop from the perspective of energy is of great significance for deeply understanding the brittle fracture mechanism of rock. |
| first_indexed | 2024-03-09T23:32:11Z |
| format | Article |
| id | doaj.art-76fb97d3ca9745c8a3ef2b0fe45f498e |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T23:32:11Z |
| publishDate | 2022-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-76fb97d3ca9745c8a3ef2b0fe45f498e2023-11-23T17:07:05ZengMDPI AGMathematics2227-73902022-01-0110341010.3390/math10030410Thermal Damage Constitutive Model and Brittleness Index Based on Energy Dissipation for Deep RockXiaoli Xu0Changqi Yue1Liqi Xu2School of Transportation and Civil Engineering, Nantong University, Nantong 226000, ChinaSchool of Transportation and Civil Engineering, Nantong University, Nantong 226000, ChinaSchool of Transportation and Civil Engineering, Nantong University, Nantong 226000, ChinaIn deep underground engineering, rock usually encounters a high temperature problem. The stress–strain relationship of rock under high temperatures is the basis of engineering excavation. Based on the Lemaitre’s equivalent strain hypothesis and energy dissipation theory, the thermal damage constitutive model of rock is established. The results show that the peak stress, ultimate elastic energy and dissipated energy at the peak all decrease with the increase of temperature in a logistic function, which indicates that the increase of temperature aggravates the deterioration of rock’s mechanical properties. Compared with rock’s constitutive model that is established on strength criterion, the thermal damage constitutive model based on energy dissipation better reflects the phenomenon of stress drop after the peak and well describes the whole stress-strain curve of rock failure, which verifies the rationality of the model. The damage model further improves the theoretical system of the rock damage constitutive model and makes up for the defect in that the traditional damage model cannot reasonably explain the nature of rock failure. The brittleness index, defined based on the energy drop coefficient, shows a logistic function with the increase of temperature, which has good physical meaning. Analyzing the phenomenon of the rock stress drop from the perspective of energy is of great significance for deeply understanding the brittle fracture mechanism of rock.https://www.mdpi.com/2227-7390/10/3/410deep rockenergy characteristicsthermal damageconstitutive modelbrittleness index |
| spellingShingle | Xiaoli Xu Changqi Yue Liqi Xu Thermal Damage Constitutive Model and Brittleness Index Based on Energy Dissipation for Deep Rock Mathematics deep rock energy characteristics thermal damage constitutive model brittleness index |
| title | Thermal Damage Constitutive Model and Brittleness Index Based on Energy Dissipation for Deep Rock |
| title_full | Thermal Damage Constitutive Model and Brittleness Index Based on Energy Dissipation for Deep Rock |
| title_fullStr | Thermal Damage Constitutive Model and Brittleness Index Based on Energy Dissipation for Deep Rock |
| title_full_unstemmed | Thermal Damage Constitutive Model and Brittleness Index Based on Energy Dissipation for Deep Rock |
| title_short | Thermal Damage Constitutive Model and Brittleness Index Based on Energy Dissipation for Deep Rock |
| title_sort | thermal damage constitutive model and brittleness index based on energy dissipation for deep rock |
| topic | deep rock energy characteristics thermal damage constitutive model brittleness index |
| url | https://www.mdpi.com/2227-7390/10/3/410 |
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