Renormalization group study on connectivity of fracture network of overlying strata in deep coal mining

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This paper focuses on the analysis of the connectivity of fracture network of overlying strata in deep coal mining based on the renormalization group method. Firstly, the probability formula of transfixion fracture formation in fractured overlying strata is derived out. The critical probability of transfixion fracture formation presents a negative exponent relation with the Weibull shape parameter. Secondly, on the basis of geological conditions of No. 15-22060 coal mining face in No. 8 Mine of Pingdingshan Coal Mining Group, the physical model under lateral pressure is constructed. During the process of coal mining face advancement, fracture networks of different advancement distances are extracted and binarized. These fracture networks are then transformed into matrixes of “0” and “1” elements. After applying the renormalization group method to these matrixes, the in-plane, horizontal, and vertical connectivities of fracture networks in deep coal mining are studied when the coal mining face is advanced 180 m. As to in-plane fracture networks of different classes, the last four matrixes obtained with the renormalization group method are zero, indicating that these networks are not connected, which is induced by the low occupancy of fracture areas of fracture networks of different classes. The distribution shape of “1” representing fractures is consistent with that of strata-separating fractures, and it is possible that the horizontal fracture is connected only if strata-separating fractures are present in the whole area of interest. The fracture networks of different classes are not connected in the vertical direction. However, when the area of interest is decreased, the proportion of elements “1” reflecting the vertical connectivity of fracture networks in the matrix is increased, and the rank of the zero matrix is decreased. These results may serve as a reference to the reasonable methane exploitation in deep coal mining.

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  1. Carpinteri A (1994) Scaling laws and renormalization groups for strength and toughness of disordered materials. Int J Solids Struct 31(3):291–302

  2. Carpinteri A, Cornetti P, Barpi F, Valente S (2003) Cohesive crack model description of ductile to brittle size-scale transition: dimensional analysis vs. renormalization group theory. Eng Fract Mech 70(14):1809–1839

  3. Chen Z, Tham LG, Yeung MR (2002) Renormalization study and numerical simulation on brittle failure of rocks. Chin J Geote Eng 24(2):184–187

  4. Chen H, Qin S, Xue L, Yang B, Zhang K (2018) A physical model predicting instability of rock slopes with locked segments along a potential slip surface. Eng Geol 242:34–43

  5. Feng Z, Zhao Y, Wen Z (2005) A renormalization group approach to the stick-slip behavior of faults. Chin J Rock Mech Eng 24(2):236–240

  6. Gao M, Jin W, Zheng C, Zhou H (2012) Real-time evolution and connectivity of mined crack network. Journal of China Coal Society 37(9):1535–1540

  7. Han B, Ye Z, Zhou C (2000) A study on critical seepage characteristics for unsaturated flow in a single rock fracture. Adv Water Sci 11(1):1–7

  8. Hu X, Liu X, Du J, Wang B (2001) Percolation model for breakthrough pressure in unconsolidated porous media. Journal of Tsinghua University (Science and Technology) 41(6):85–88

  9. Hudson J, Fairhurst C (1969) Tensile strength, Weibull’s theory and a general statistical approach to rock failure. In: The proceedings of civil engineering materials, pp 901–904

  10. Li G, Cao S, Luo F, Li Y, Wei Y (2018) Research on mining-induced deformation and stress, insights from physical modeling and theoretical analysis. Arab J Geosci 11(5):100

  11. Lv Z, Feng Z, Zhao Y (2007) Numerical simulation of 3d percolation mechanism in porous media. Chin J Rock Mech Eng 26(Supplement 2):4019–4023

  12. Manukian N (1990) A statistical model of fractures. PhD thesis, University of California

  13. Shao P, He Y (2001) Microcosmic failure detection analysis and critical failure action for brittle rock. Coal Science and Technology 29(7):31–33

  14. Shao P, Zhang Y, He Y, Zhang D (2004) Percolation fracture behavior and fragmentation distribution in rock blasting. Journal of China University of Mining and Technology 33(6):635–640

  15. Smalley R, Turcotte D, Solla S (1985) A renormalization group approach to the stick-slip behavior of faults. J Geophys Res Solid Earth 90(B2):1894–1900

  16. Sun M (2014) Study on in-situ stress distribution law and its application in pingdingshan mining area. Master’s thesis, China University of Mining and Technology

  17. Taherynia MH, Aghda SMF, Fahimifar A (2016) In-situ stress state and tectonic regime in different depths of earth crust. Geotech Geol Eng 34(2):679–687

  18. Tu J, Sun Q, Jiang Z, Xue L, Qian H (2013) Analysis on rock resistivity variation with stress ratio at the state of critical brittle failure. Journal of China Coal Society 38(2):221–225

  19. Wang C, Zhang N, Han Y, Xiong Z, Qian D (2013a) Experiment research on overburden mining-induced fracture evolution and its fractal characteristics in ascending mining. Arab J Geosci 8(1):13–21

  20. Wang J, Chen X, Huang Y, Zhang Z (2013b) A study of stochastic generation and connectivity of fracture network in rock mass. Hydrogeology & Engineering 40(2):30–35

  21. Wei X, Gao M, Lv Y, Shi X, Gao H, Zhou H (2012) Evolution of a mining induced fracture network in the overburden strata of an inclined coal seam. Int J Min Sci Technol 22(6):779–783

  22. Xue L, Sun Q, Wang Y, Wang S, Li G (2013) Study on the critical state of brittle failure of rock based on renormalization group theory. J Basic Sci Eng 21(4):710–722

  23. Yuan L (2016) Strategic thinking of simultaneous exploitation of coal and gas in deep mining. Journal of China Coal Society 41(1):1–6

  24. Zhou H, Xie H (1998) Renormalization group research on seepage flow in rock and soil media based on the pore packing model. Journal of Xi’an Mining Institute 18(2):97–102

  25. Zhou H, Xie H (2000) Estimation of permeability of porous media by using renormalization group. Journal of China University of Mining and Technology 29(3):244–248

  26. Zhou H, Liu J, Xue D, Yi H, Xue J (2012) Numerical simulation of gas flow process in mining-induced crack network. Int J Min Sci Technol 22(6):793–799

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The authors would like to acknowledge Prof. Hongwei Zhou (China University of Mining and Technology, Beijing) for the guidance of applying renormalization group analysis.

Funding information

This work is funded by the National Natural Science Foundation of China (Grant No. 51508150), the Hebei Education Department (Grant No. QN2016115), and the Department of Housing and Urban-rural Development of Hebei (Grant No. 2018-142).

Author information

Correspondence to Jiadun Liu.

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Responsible Editor: Murat Karakus

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Li, D., Liu, J. Renormalization group study on connectivity of fracture network of overlying strata in deep coal mining. Arab J Geosci 13, 63 (2020).

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  • Deep coal mining
  • Physical model
  • Fracture network
  • Connectivity
  • Renormalization group method