A calculational model for 3D fault complexity based on curvature analysis and fractal dimensions

Authors

YAN Junsheng, CCTEG China Coal Research Institute, Beijing 100013, China; CCTEG Xi’an Transparent Geology Technology Co., Ltd., Xi’an 712000, China; CCTEG Xi’an Research Institute (Group) Co., Ltd., Xi’an 710077, China; National Key Laboratory of Intelligent Coal Mining and Rock Stratum Control, Beijing 100013, ChinaFollow
LIU Zaibin, CCTEG China Coal Research Institute, Beijing 100013, China; CCTEG Xi’an Transparent Geology Technology Co., Ltd., Xi’an 712000, China; CCTEG Xi’an Research Institute (Group) Co., Ltd., Xi’an 710077, China; National Key Laboratory of Intelligent Coal Mining and Rock Stratum Control, Beijing 100013, ChinaFollow
FAN Tao, CCTEG China Coal Research Institute, Beijing 100013, China; CCTEG Xi’an Transparent Geology Technology Co., Ltd., Xi’an 712000, China; CCTEG Xi’an Research Institute (Group) Co., Ltd., Xi’an 710077, China; National Key Laboratory of Intelligent Coal Mining and Rock Stratum Control, Beijing 100013, China
YANG Hui, CCTEG Xi’an Transparent Geology Technology Co., Ltd., Xi’an 712000, China; CCTEG Xi’an Research Institute (Group) Co., Ltd., Xi’an 710077, China; National Key Laboratory of Intelligent Coal Mining and Rock Stratum Control, Beijing 100013, China
LIU Wenming, CCTEG China Coal Research Institute, Beijing 100013, China; CCTEG Xi’an Transparent Geology Technology Co., Ltd., Xi’an 712000, China; CCTEG Xi’an Research Institute (Group) Co., Ltd., Xi’an 710077, China; National Key Laboratory of Intelligent Coal Mining and Rock Stratum Control, Beijing 100013, China
DU Wengang, CCTEG Xi’an Transparent Geology Technology Co., Ltd., Xi’an 712000, China; CCTEG Xi’an Research Institute (Group) Co., Ltd., Xi’an 710077, China; National Key Laboratory of Intelligent Coal Mining and Rock Stratum Control, Beijing 100013, China
AN Lin, CCTEG China Coal Research Institute, Beijing 100013, China; CCTEG Xi’an Transparent Geology Technology Co., Ltd., Xi’an 712000, China; CCTEG Xi’an Research Institute (Group) Co., Ltd., Xi’an 710077, China; National Key Laboratory of Intelligent Coal Mining and Rock Stratum Control, Beijing 100013, China
LIU Chenguang, CCTEG Xi’an Transparent Geology Technology Co., Ltd., Xi’an 712000, China; CCTEG Xi’an Research Institute (Group) Co., Ltd., Xi’an 710077, China; National Key Laboratory of Intelligent Coal Mining and Rock Stratum Control, Beijing 100013, China
WANG Xiaohui, CCTEG China Coal Research Institute, Beijing 100013, China; CCTEG Xi’an Transparent Geology Technology Co., Ltd., Xi’an 712000, China; CCTEG Xi’an Research Institute (Group) Co., Ltd., Xi’an 710077, China; National Key Laboratory of Intelligent Coal Mining and Rock Stratum Control, Beijing 100013, China

Abstract

Objective and Methods Faults are identified as one of the most threatening geological structural factors among hidden disaster-causing factors in coal mines. However, the 3D quantitative assessment of them remains challenging. Considering that existing quantitative indicators fail to fully reflect fault morphologies and there is a lack of 3D methods, this study proposed a calculational model for 3D fault complexity based on curvature analysis and fractal dimensions. This model improved the morphologies of traditional measurement volumes of fractal dimensions by employing the Delaunay tetrahedralization algorithm, thus effectively reducing the invalid values in calculating the 3D fractal dimensions of faults. Moreover, the model modified fault parameters by introducing fault plane curvatures, thereby retaining the structural characteristics of faults. To validate its effectiveness, this model was applied to the faults revealed in a coal mine in Shaanxi Province. Using this model, this study conducted a qualitative assessment of the complexity of geological structures and examined the data on the spatial distributions of the historical water inrush points in the mining face and roadways. Results and Conclusions Using this model, 75 partitioning intervals with nonzero statistics were identified in the mine field. Calculations revealed that the average 3D fractal dimension of faults and 3D fault complexity values integrated with Gaussian and mean curvatures were 0.9394, 1.1362, and 1.2199, respectively. Compared to a single fractal dimension, the fault complexity integrated with curvatures enjoyed significant advantages in revealing the differences in fault strikes and fault concentration zones. Based on the Pearson correlation coefficients calculated using the 3D fault complexity and the distance between sample points and water inrush points as two correlation indicators, water inrush points can be categorized into two types: those in the mining face and those in roadways. For water inrush points in the mining face, the average coefficients of their correlations with 3D fractal dimension of faults and 3D fault complexity integrated with Gaussian and mean curvatures were 0.7843, 0.8386, and 0.9072, respectively, while these average coefficients were 0.7718, 0.8324, and 0.8903, respectively, for water inrush points in roadways. These data indicate that fault complexity is highly correlated with water inrush points in the mining face compared to water burst points in roadways. In other words, the production activities in the mining face within the study area are more significantly affected by faults. Additionally, the Pearson correlation coefficients all exceeded 0.77 regardless of the curvature integrated, suggesting a strong correlation between the 3D fault complexity and the water hazard conditions of coal mines. The qualitative assessment reveals that the overall structural complexity of the coal mine is relatively low and is primarily affected by faults. The fault complexity values of the coal mine were determined at around 1, exceeding 2 in very few zones. This result implies the overall low fault complexity of the coal mine despite local fault concentration, aligning with the qualitative assessment results. The above methods validate the effectiveness of the proposed model, which provides a new modeling approach for the calculation of 3D fault complexity.

Keywords

fault complexity, 3D quantitative analysis, curvature analysis, Delaunay tetrahedralization algorithm, Pearson correlation coefficient, water inrush point

DOI

10.12363/issn.1001-1986.24.04.0237

Recommended Citation

YAN Junsheng, LIU Zaibin, FAN Tao, et al. (2024) "A calculational model for 3D fault complexity based on curvature analysis and fractal dimensions," Coal Geology & Exploration: Vol. 52: Iss. 12, Article 6.
DOI: 10.12363/issn.1001-1986.24.04.0237
Available at: https://cge.researchcommons.org/journal/vol52/iss12/6

Reference

[1] 齐庆新，潘一山，李海涛，等. 煤矿深部开采煤岩动力灾害防控理论基础与关键技术[J]. 煤炭学报，2020，45(5)：1567−1584.

QI Qingxin，PAN Yishan，LI Haitao，et al. Theoretical basis and key technology of prevention and control of coal–rock dynamic disasters in deep coal mining[J]. Journal of China Coal Society，2020，45(5)：1567−1584.

[2] 曾一凡，武强，赵苏启，等. 我国煤矿水害事故特征、致因与防治对策[J]. 煤炭科学技术，2023，51(7)：1−14.

ZENG Yifan，WU Qiang，ZHAO Suqi，et al. Characteristics，causes，and prevention measures of coal mine water hazard accidents in China[J]. Coal Science and Technology，2023，51(7)：1−14.

[3] 张建国，邱黎明，王满，等. 深部煤层不同类型隐伏构造致灾规律研究[J/OL]. 煤炭科学技术，2023，51(增刊2)：50−59.

ZHANG Jianguo，QIU Liming，WANG Man，et al. Study on disaster-causing law of different types of hidden structures in deep coal seam[J]. Coal Science and Technology，2023，51(Sup.2)：50−59.

[4] 毛德兵，尹希文，张会军. 我国煤矿顶板灾害防治与监测监控技术[J]. 煤炭科学技术，2013，41(9)：105−108.

MAO Debing，YIN Xiwen，ZHANG Huijun. Technology of prevention roof disasters and monitoring and controlling in China coal mines[J]. Coal Science and Technology，2013，41(9)：105−108.

[5] 袁亮. 我国煤炭主体能源安全高质量发展的理论技术思考[J]. 中国科学院院刊，2023，38(1)：11−22.

YUAN Liang. Theory and technology considerations on high-quality development of coal main energy security in China[J]. Bulletin of Chinese Academy of Sciences，2023，38(1)：11−22.

[6] 袁亮. 煤炭精准开采科学构想[J]. 煤炭学报，2017，42(1)：1−7.

YUAN Liang. Scientific conception of precision coal mining[J]. Journal of China Coal Society，2017，42(1)：1−7.

[7] 国家矿山安全监察局事故调查和统计司. 开展煤矿隐蔽致灾因素普查治理工作 坚决防范遏制煤矿重特大事故——煤矿隐蔽致灾因素普查治理工作专题总结[J]. 中国煤炭，2022，48(增刊2)：1−8.

Accident Investigation and Statistics Department of National Mine Safety Administration. Carrying out the general survey and treatment of hidden disaster-causing factors and resolutely preventing and containing majoraccidents in coal mines—Special topic summary of the general survey and treatment of hidden disaster-causing factors in coal mines[J]. China Coal，2022，48(Sup.2)：1−8.

[8] 袁亮. 我国深部煤与瓦斯共采战略思考[J]. 煤炭学报，2016，41(1)：1−6.

YUAN Liang. Strategic thinking of simultaneous exploitation of coal and gas in deep mining[J]. Journal of China Coal Society，2016，41(1)：1−6.

[9] 康红普，张镇，黄志增. 我国煤矿顶板灾害的特点及防控技术[J]. 煤矿安全，2020，51(10)：24−33.

KANG Hongpu，ZHANG Zhen，HUANG Zhizeng. Characteristics of roof disasters and controlling techniques of coal mine in China[J]. Safety in Coal Mines，2020，51(10)：24−33.

[10] 赵军利，王文元，杨威. 基于地质构造角度的煤与瓦斯突出机理研究进展[J]. 煤矿安全，2022，53(10)：197−204.

ZHAO Junli，WANG Wenyuan，YANG Wei. Research progress of coal and gas outburst mechanism based on geological structure[J]. Safety in Coal Mines，2022，53(10)：197−204.

[11] 刘泽威，刘其声，刘洋. 煤层底板隐伏断层分类及突水防治措施[J]. 煤田地质与勘探，2020，48(2)：141−146.

LIU Zewei，LIU Qisheng，LIU Yang. Classification of hidden faults in coal seam floor and measures for \rwater inrush prevention[J]. Coal Geology & Exploration，2020，48(2)：141−146.

[12] 李鹏，蔡美峰，郭奇峰，等. 煤矿断层错动型冲击地压研究现状与发展趋势[J]. 哈尔滨工业大学学报，2018，50(3)：1−17.

LI Peng，CAI Meifeng，GUO Qifeng，et al. Research situations and development tendencies of fault slip rockburst in coal mine[J]. Journal of Harbin Institute of Technology，2018，50(3)：1−17.

[13] B. B. 鲁基诺夫，袁崇孚. 为确定煤层突出危险性对构造条件的综合评定[J]. 中州煤炭，1992(3)：47.

[14] 曹代勇，周云霞，魏迎春. 矿井地质构造定量评价信息系统的开发及应用[J]. 煤炭学报，2002，27(4)：379−382.

CAO Daiyong，ZHOU Yunxia，WEI Yingchun. Development of the quantitative evaluation information system of mining geology structure[J]. Journal of China Coal Society，2002，27(4)：379−382.

[15] 王建国，王海凤，刘见宝. 矿井断层复杂程度系数的几何方法评价[J]. 煤炭科学技术，2015，43(5)：115−117.

WANG Jianguo，WANG Haifeng，LIU Jianbao. Assessment on geometric method for complexity degree coefficient of mine fault[J]. Coal Science and Technology，2015，43(5)：115−117.

[16] 施龙青，刘捷，邱梅，等. 断层定量化在突水危险性评价中的应用[J]. 中国科技论文，2020，15(1)：100−104.

SHI Longqing，LIU Jie，QIU Mei，et al. Application of fault quantification in risk assessment of water inrush[J]. China Sciencepaper，2020，15(1)：100−104.

[17] YANG Binbin，YUAN Junhong，DUAN Lihong，et al. Using GIS and fractal theory to evaluate degree of fault complexity and water yield[J]. Mine Water and the Environment，2019，38(2)：261−267.

[18] 郭强，成文举，杨廷军，等. 基于博弈论组合赋权的断层定量评价模型及应用[J]. 煤矿安全，2023，54(6)：199−206.

GUO Qiang，CHENG Wenju，YANG Tingjun，et al. Fault quantitative evaluation model and application based on game theory combination weighting[J]. Safety in Coal Mines，2023，54(6)：199−206.

[19] 夏玉成，胡明星，陈练武. 矿井构造的GMDH–BP评价预测方法及其应用[J]. 煤炭学报，1997，22(5)：466–470.

XIA Yucheng，HU Mingxing，CHEN Lianwu. GMDH-BP method and its application in evaluation and prediction of mine structure[J]. Journal of China Coal Society，1997，22(5)：466–470.

[20] 汪吉林，姜波. 模糊人工神经网络在矿井构造评价中的应用[J]. 中国矿业大学学报，2005，34(5)：609−612.

WANG Jilin，JIANG Bo. Using fuzzy artificial neural network to evaluate the mine structure[J]. Journal of China University of Mining & Technology，2005，34(5)：609−612.

[21] 朱宝龙，夏玉成. 人工神经网络在矿井构造定量评价中的应用[J]. 煤田地质与勘探，2001，29(6)：15−17.

ZHU Baolong，XIA Yucheng. Quantitative evaluation of mining structure based on the artificial neural network[J]. Coal Geology & Exploration，2001，29(6)：15−17.

[22] 薛喜成，吕自豪，倚江星，等. 基于IGA–BP的矿井构造复杂程度评价[J]. 煤矿安全，2023，54(3)：193−203.

XUE Xicheng，LYU Zihao，JI Jiangxing，HUO Gaopu. Evaluation of mine structure complexity based on IGA–BP model[J]. Safety in Coal Mines，2023，54(3)：193−203.

[23] 童仁剑，郑士田，吴燕军，等. 地面定向孔超前预注浆掩护巷道穿断层破碎带关键技术[J]. 煤炭科学技术，2022，50(6)：196−203.

TONG Renjian，ZHENG Shitian，WU Yanjun，et al. Key technology of advance pre-grouting of ground directional holes to shield roadway passing fault and broken zone[J]. Coal Science and Technology，2022，50(6)：196−203.

[24] 张子敏，张玉贵. 大平煤矿特大型煤与瓦斯突出瓦斯地质分析[J]. 煤炭学报，2005，30(2)：137−140.

ZHANG Zimin，ZHANG Yugui. Investigation into coal-gas outburst occurred in Daping Coalmine，by using theories of gas-geology[J]. Journal of China Coal Society，2005，30(2)：137−140.

[25] 张鹏，朱学军，孙文斌，等. 采动诱发充填断层活化滞后突水机制研究[J]. 煤炭科学技术，2022，50(3)：136−143.

ZHANG Peng，ZHU Xuejun，SUN Wenbin，et al. Study on mechanism of delayed water inrush caused by mining-induced filling fault activation[J]. Coal Science and Technology，2022，50(3)：136−143.

[26] WU Qiang，XU Hua，ZOU Xukai，et al. A 3D modeling approach to complex faults with multi-source data[J]. Computers & Geosciences，2015，77：126−137.

[27] 刘光伟，宋佳琛，白润才，等. 基于Morphing方法的断层面重构[J]. 重庆大学学报，2018，41(2)：69−77.

LIU Guangwei，SONG Jiachen，BAI Runcai，et al. Fault surface reconstruction based on Morphing method[J]. Journal of Chongqing University，2018，41(2)：69−77.

[28] YAN Jun，ZHANG Benyu，YAN Shuicheng，et al. A scalable supervised algorithm for dimensionality reduction on streaming data[J]. Information Sciences，2006，176(14)：2042−2065.

[29] ROMANET P，SATO D S，ANDO R. Curvature，a mechanical link between the geometrical complexities of a fault：Application to bends，kinks and rough faults[J]. Geophysical Journal International，2020，223(1)：211−232.

[30] MANDELBROT B. How long is the coast of Britain?statistical self-similarity and fractional dimension[J]. Science，1967，156(3775)：636−638.

[31] KOENDERINK J J，VAN DOORN A J. Surface shape and curvature scales[J]. Image and Vision Computing，1992，10(8)：557−564.

[32] Le Méhauté A. Fractal Geometries Theory and Applications[M]. CRC Press，1991.

[33] 张满仓，兰天伟，贾伟东，等. 断裂构造分形几何特征对冲击地压的控制作用研究[J]. 煤炭工程，2023，55(5)：103−110.

ZHANG Mancang，LAN Tianwei，JIA Weidong，et al. Effect of fractal geometric characteristics of fracture structure on rock burst control[J]. Coal Engineering，2023，55(5)：103−110.

[34] PARMAR K S，BHARDWAJ R. Water quality index and fractal dimension analysis of water parameters[J]. International Journal of Environmental Science and Technology，2013，10(1)：151−164.

[35] LIU Yongjie，LI Xuelong，LIU Shumin，et al. Study on influence of fault structure on coal mine gas occurrence regularity based on the fractal theory：A case study of Panxi Mine in China[J]. Energy Sources，Part A：Recovery，Utilization，and Environmental Effects，2022，44(2)：4917−4927.

[36] ZHANG Gaizhuo，GUO Junzhong，XU Bin，et al. Quantitative analysis and evaluation of coal mine geological structures based on fractal theory[J]. Energies，2021，14(7)：1925.

[37] FOROUTAN-POUR K，DUTILLEUL P，SMITH D L. Advances in the implementation of the box-counting method of fractal dimension estimation[J]. Applied Mathematics and Computation，1999，105(2/3)：195−210.