Linear fractal evolution characteristics of rock crack distributions during loading process
To investigate the fractal characteristics of rock crack distributions during the loading process, discrete element method was used to make rock samples with joints and record the crack propagation. The Box-counting method was used to quantitatively analyze the fractal dimension of the crack distrib...
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| Published in | Scientific reports Vol. 14; no. 1; pp. 18303 - 15 |
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| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
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Nature Publishing Group UK
07.08.2024
Nature Publishing Group Nature Portfolio |
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| Abstract | To investigate the fractal characteristics of rock crack distributions during the loading process, discrete element method was used to make rock samples with joints and record the crack propagation. The Box-counting method was used to quantitatively analyze the fractal dimension of the crack distribution at each moment, and the relationship between the crack fractal dimension and strain ratio was established based on fractal theory. The results indicated that the relationship between the fractal dimension of the crack distribution and strain ratio showed a strong linear characteristic. By transforming this linear relationship into a linear function, the slope of the function was found to be linked to the failure patterns of the sample, and a refinement coefficient (damage-fracture reduction factor) was identified from the slope as an effective basis for determining the degree of sample damage and fracture. The damage-fracture reduction factor can be categorized: 0.25–0.5 (spilt and fracture), 0.5–0.9 (synergy between fracture and damage), 0.9–1 (microcrack asymptotic damage). Owing to the linear fractal characteristics, an expression for the damage variables influenced by failure patterns can be established from the geometric aspect. In addition, the linear fractal characteristics of the cracks were verified in other acoustic emission and crack extension experiments. |
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| AbstractList | Abstract To investigate the fractal characteristics of rock crack distributions during the loading process, discrete element method was used to make rock samples with joints and record the crack propagation. The Box-counting method was used to quantitatively analyze the fractal dimension of the crack distribution at each moment, and the relationship between the crack fractal dimension and strain ratio was established based on fractal theory. The results indicated that the relationship between the fractal dimension of the crack distribution and strain ratio showed a strong linear characteristic. By transforming this linear relationship into a linear function, the slope of the function was found to be linked to the failure patterns of the sample, and a refinement coefficient (damage-fracture reduction factor) was identified from the slope as an effective basis for determining the degree of sample damage and fracture. The damage-fracture reduction factor can be categorized: 0.25–0.5 (spilt and fracture), 0.5–0.9 (synergy between fracture and damage), 0.9–1 (microcrack asymptotic damage). Owing to the linear fractal characteristics, an expression for the damage variables influenced by failure patterns can be established from the geometric aspect. In addition, the linear fractal characteristics of the cracks were verified in other acoustic emission and crack extension experiments. To investigate the fractal characteristics of rock crack distributions during the loading process, discrete element method was used to make rock samples with joints and record the crack propagation. The Box-counting method was used to quantitatively analyze the fractal dimension of the crack distribution at each moment, and the relationship between the crack fractal dimension and strain ratio was established based on fractal theory. The results indicated that the relationship between the fractal dimension of the crack distribution and strain ratio showed a strong linear characteristic. By transforming this linear relationship into a linear function, the slope of the function was found to be linked to the failure patterns of the sample, and a refinement coefficient (damage-fracture reduction factor) was identified from the slope as an effective basis for determining the degree of sample damage and fracture. The damage-fracture reduction factor can be categorized: 0.25–0.5 (spilt and fracture), 0.5–0.9 (synergy between fracture and damage), 0.9–1 (microcrack asymptotic damage). Owing to the linear fractal characteristics, an expression for the damage variables influenced by failure patterns can be established from the geometric aspect. In addition, the linear fractal characteristics of the cracks were verified in other acoustic emission and crack extension experiments. To investigate the fractal characteristics of rock crack distributions during the loading process, discrete element method was used to make rock samples with joints and record the crack propagation. The Box-counting method was used to quantitatively analyze the fractal dimension of the crack distribution at each moment, and the relationship between the crack fractal dimension and strain ratio was established based on fractal theory. The results indicated that the relationship between the fractal dimension of the crack distribution and strain ratio showed a strong linear characteristic. By transforming this linear relationship into a linear function, the slope of the function was found to be linked to the failure patterns of the sample, and a refinement coefficient (damage-fracture reduction factor) was identified from the slope as an effective basis for determining the degree of sample damage and fracture. The damage-fracture reduction factor can be categorized: 0.25-0.5 (spilt and fracture), 0.5-0.9 (synergy between fracture and damage), 0.9-1 (microcrack asymptotic damage). Owing to the linear fractal characteristics, an expression for the damage variables influenced by failure patterns can be established from the geometric aspect. In addition, the linear fractal characteristics of the cracks were verified in other acoustic emission and crack extension experiments.To investigate the fractal characteristics of rock crack distributions during the loading process, discrete element method was used to make rock samples with joints and record the crack propagation. The Box-counting method was used to quantitatively analyze the fractal dimension of the crack distribution at each moment, and the relationship between the crack fractal dimension and strain ratio was established based on fractal theory. The results indicated that the relationship between the fractal dimension of the crack distribution and strain ratio showed a strong linear characteristic. By transforming this linear relationship into a linear function, the slope of the function was found to be linked to the failure patterns of the sample, and a refinement coefficient (damage-fracture reduction factor) was identified from the slope as an effective basis for determining the degree of sample damage and fracture. The damage-fracture reduction factor can be categorized: 0.25-0.5 (spilt and fracture), 0.5-0.9 (synergy between fracture and damage), 0.9-1 (microcrack asymptotic damage). Owing to the linear fractal characteristics, an expression for the damage variables influenced by failure patterns can be established from the geometric aspect. In addition, the linear fractal characteristics of the cracks were verified in other acoustic emission and crack extension experiments. |
| ArticleNumber | 18303 |
| Author | Zheng, Zaimin Zuo, Jianping Su, Xiaopeng Huang, Jingyi Wei, Xu |
| Author_xml | – sequence: 1 givenname: Jingyi surname: Huang fullname: Huang, Jingyi organization: School of Civil Engineering, Chongqing Jiaotong University – sequence: 2 givenname: Xu surname: Wei fullname: Wei, Xu email: wxwish@cqjtu.edu.cn organization: School of Civil Engineering, Chongqing Jiaotong University, State Key Laboratory of Mountain Bridge and Tunnel Engineering – sequence: 3 givenname: Zaimin surname: Zheng fullname: Zheng, Zaimin organization: School of Mathematics & Statistics, Chongqing Jiaotong University – sequence: 4 givenname: Xiaopeng surname: Su fullname: Su, Xiaopeng organization: School of Civil Engineering, Chongqing Jiaotong University – sequence: 5 givenname: Jianping surname: Zuo fullname: Zuo, Jianping organization: State Key Laboratory of Coal Resources and Safe Mining, China University of Mining and Technology (Beijing) |
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| Keywords | Rock damage Fractal dimension Damage-fracture reduction factor Crack propagation |
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Rep.202111130712021NatSR..1113071S1:CAS:528:DC%2BB3MXhsF2hs7jI10.1038/s41598-021-92277-x341585498219689 69121_CR34 Z Liu (69121_CR22) 2024; 10 YP Li (69121_CR33) 2005; 42 B Sun (69121_CR4) 2021; 11 69121_CR17 AR Ingraffea (69121_CR30) 1980; 4 H Xie (69121_CR11) 1988; 20 J Petit (69121_CR31) 1988; 7 Y Yin (69121_CR24) 2020; 262 PF Yin (69121_CR29) 2023; 40 HCM Chan (69121_CR32) 1990; 45 G Chen (69121_CR36) 2018; 18 Q Ren (69121_CR26) 2007; 38 J Carrillo (69121_CR23) 2017; 46 69121_CR20 X Liu (69121_CR37) 2016; 35 J Zhou (69121_CR15) 1997; 18 Y Lai (69121_CR21) 2023; 33 L Yang (69121_CR2) 2007; 5 YY Li (69121_CR6) 2018; 11 69121_CR8 69121_CR1 JP Zuo (69121_CR28) 2020; 125 69121_CR3 J Li (69121_CR13) 1992 Y Yin (69121_CR10) 2024; 296 BB Gao (69121_CR7) 2015; 11 Y Chen (69121_CR35) 2018; 18 ZX Zhang (69121_CR18) 2001; 34 MN Bagde (69121_CR16) 2002; 63 C Zhu (69121_CR5) 2019 SL Passman (69121_CR25) 1980; 51 L Xia (69121_CR27) 2021; 42 S Zamen (69121_CR9) 2020 H Xie (69121_CR12) 1989; 21 H Xie (69121_CR14) 1997; 22 Y Zhao (69121_CR19) 2018; 26 |
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| SubjectTerms | 704/2151 704/2151/2809 Acoustic emission Crack propagation Damage-fracture reduction factor Fractal dimension Fractals Humanities and Social Sciences multidisciplinary Rock damage Rocks Science Science (multidisciplinary) |
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| Title | Linear fractal evolution characteristics of rock crack distributions during loading process |
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