Cyclic constitutive equations of rock with coupled damage induced by compaction and cracking
In this paper, the cyclic constitutive equations were proposed to describe the constitutive behavior of cyclic loading and unloading. Firstly, a coupled damage variable was derived, which contains two parts, i.e., the compaction-induced damage and the cracking-induced damage. The compaction-induced...
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Format: | Article |
Language: | English |
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Elsevier
2022-09-01
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Series: | International Journal of Mining Science and Technology |
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Online Access: | http://www.sciencedirect.com/science/article/pii/S2095268622000684 |
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author | Chonghong Ren Jin Yu Xueying Liu Zhuqing Zhang Yanyan Cai |
author_facet | Chonghong Ren Jin Yu Xueying Liu Zhuqing Zhang Yanyan Cai |
author_sort | Chonghong Ren |
collection | DOAJ |
description | In this paper, the cyclic constitutive equations were proposed to describe the constitutive behavior of cyclic loading and unloading. Firstly, a coupled damage variable was derived, which contains two parts, i.e., the compaction-induced damage and the cracking-induced damage. The compaction-induced damage variable was derived from a nonlinear stress–strain relation of the initial compaction stage, and the cracking-induced damage variable was established based on the statistical damage theory. Secondly, based on the total damage variable, a damage constitutive equation was proposed to describe the constitutive relation of rock under the monotonic uniaxial compression conditions, whereafter, the application of this model is extended to cyclic loading and unloading conditions. To validate the proposed monotonic and cyclic constitutive equations, a series of mechanical tests for marble specimens were carried out, which contained the monotonic uniaxial compression (MUC) experiment, cyclic uniaxial compression experiments under the variable amplitude (CUC-VA) and constant amplitude (CUC-CA) conditions. The results show that the proposed total damage variable comprehensively reflects the damage evolution characteristic, i.e., the damage variable firstly decreases, then increases no matter under the conditions of MUC, CUC-VA or CUC-CA. Then a reasonable consistency is observed between the experimental and theoretical curves. The proposed cyclic constitutive equations can simulate the whole cyclic loading and unloading behaviors, such as the initial compaction, the strain hardening and the strain softening. Furthermore, the shapes of the theoretical curves are controlled by the modified coefficient, compaction sensitivity coefficient and two Weibull distributed parameters. |
first_indexed | 2024-04-13T21:51:18Z |
format | Article |
id | doaj.art-d049274368ef46b0a2dbb55896b94206 |
institution | Directory Open Access Journal |
issn | 2095-2686 |
language | English |
last_indexed | 2024-04-13T21:51:18Z |
publishDate | 2022-09-01 |
publisher | Elsevier |
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series | International Journal of Mining Science and Technology |
spelling | doaj.art-d049274368ef46b0a2dbb55896b942062022-12-22T02:28:25ZengElsevierInternational Journal of Mining Science and Technology2095-26862022-09-0132511531165Cyclic constitutive equations of rock with coupled damage induced by compaction and crackingChonghong Ren0Jin Yu1Xueying Liu2Zhuqing Zhang3Yanyan Cai4Fujian Research Center for Tunneling and Urban Underground Space Engineering, Huaqiao University, Xiamen 361021, ChinaFujian Research Center for Tunneling and Urban Underground Space Engineering, Huaqiao University, Xiamen 361021, China; Corresponding author.Fujian Research Center for Tunneling and Urban Underground Space Engineering, Huaqiao University, Xiamen 361021, ChinaXiamen Rail Transit Group Corporation Limited, Xiamen 361021, ChinaFujian Research Center for Tunneling and Urban Underground Space Engineering, Huaqiao University, Xiamen 361021, ChinaIn this paper, the cyclic constitutive equations were proposed to describe the constitutive behavior of cyclic loading and unloading. Firstly, a coupled damage variable was derived, which contains two parts, i.e., the compaction-induced damage and the cracking-induced damage. The compaction-induced damage variable was derived from a nonlinear stress–strain relation of the initial compaction stage, and the cracking-induced damage variable was established based on the statistical damage theory. Secondly, based on the total damage variable, a damage constitutive equation was proposed to describe the constitutive relation of rock under the monotonic uniaxial compression conditions, whereafter, the application of this model is extended to cyclic loading and unloading conditions. To validate the proposed monotonic and cyclic constitutive equations, a series of mechanical tests for marble specimens were carried out, which contained the monotonic uniaxial compression (MUC) experiment, cyclic uniaxial compression experiments under the variable amplitude (CUC-VA) and constant amplitude (CUC-CA) conditions. The results show that the proposed total damage variable comprehensively reflects the damage evolution characteristic, i.e., the damage variable firstly decreases, then increases no matter under the conditions of MUC, CUC-VA or CUC-CA. Then a reasonable consistency is observed between the experimental and theoretical curves. The proposed cyclic constitutive equations can simulate the whole cyclic loading and unloading behaviors, such as the initial compaction, the strain hardening and the strain softening. Furthermore, the shapes of the theoretical curves are controlled by the modified coefficient, compaction sensitivity coefficient and two Weibull distributed parameters.http://www.sciencedirect.com/science/article/pii/S2095268622000684Cyclic constitutive equationsRockCoupled damageCompactionCracking |
spellingShingle | Chonghong Ren Jin Yu Xueying Liu Zhuqing Zhang Yanyan Cai Cyclic constitutive equations of rock with coupled damage induced by compaction and cracking International Journal of Mining Science and Technology Cyclic constitutive equations Rock Coupled damage Compaction Cracking |
title | Cyclic constitutive equations of rock with coupled damage induced by compaction and cracking |
title_full | Cyclic constitutive equations of rock with coupled damage induced by compaction and cracking |
title_fullStr | Cyclic constitutive equations of rock with coupled damage induced by compaction and cracking |
title_full_unstemmed | Cyclic constitutive equations of rock with coupled damage induced by compaction and cracking |
title_short | Cyclic constitutive equations of rock with coupled damage induced by compaction and cracking |
title_sort | cyclic constitutive equations of rock with coupled damage induced by compaction and cracking |
topic | Cyclic constitutive equations Rock Coupled damage Compaction Cracking |
url | http://www.sciencedirect.com/science/article/pii/S2095268622000684 |
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