To the Calculation of the Trajectory of Hydraulic Fracturing Crack in the Solid Rocks Near In-seam Working


The model of the geomechanics state of hydraulic fracture disk crack in the solid rocks near in-seam working was developed. The peculiarity of this model is the inhomogeneous stress field due to the presence of working. This field plays an important role in the calculation of crack growth trajectory, and under certain conditions significantly changes the stress of the original crack.

The problem on the stress state of the rock mass in the vicinity of the in-seam working is reduced to the second external boundary problem of the theory of elasticity for the integral singular equation. The stresses acting in the boundary zones of the formation are found in the numerical solution of three boundary problems of the limit state theory for a number of areas of the limit zone, and they are approximated by polynomial functions.

During the analysis of the results obtained, the following features in the crack propagation were determined. If the working fluid pressure in the pumping equipment is two times higher than the gravitational pressure in the massif, the hydraulic fracture sharply changes its initial direction propagating to the working circuit. When four times is exceeded, the crack trajectory is straight line and coincides with the direction of the original crack. If the ratio of the working fluid pressure to the gravitational pressure of rocks lies in the interval from three to four, then the crack trajectory has the form of a smooth, flat curve of the line, only at the very beginning slightly changing the direction relative to the initial hydraulic fracturing crack.

  1. Petukhov I.M., Linkov A.M. Mechanics of rock bumps and blow-outs. Moscow: Nedra, 1983. 280 p. (In Russ.).
  2. Shadrin A.V. Static and Dynamic Outburst Hazard of Coal Seams. Bezopasnost truda v promyshlennosti = Occupational Safety in Industry. 2018. № 4. pp. 42–48. (In Russ.). DOI: 10.24000/0409-2961-2018-4-42-48
  3. Jiang C., Xu L., Li X., Tang J., Chen Y., Tian S., Liu H. Identification model and indicator of outburst-prone coal seam. Rock Mechanics and Rock Engineering. 2015. Vol. 48. Iss. 1. pp. 409–415. DOI: 10.1007/s00603-014-0558-0
  4. Klishin V.I., Zvorygin L.V., Lebedev A.V., Savchenko A.V. Problems of safety and new technologies for the underground mining of coal deposits. Novosibirsk: ANO ID «Novosibirskiy pisatel», 2011. 524 p. (In Russ.).
  5. Chernyy S.G., Lapin V.N., Esipov D.V., Kuranakov D.S. Methods for modeling initiation and propagation of cracks. Novosibirsk: Izd-vo SO RAN, 2016. 312 p. (In Russ.).
  6. Zubkov V.V., Koshelev V.F., Linkov A.M. Numerical modeling of hydraulic fracture initiation and development. Fiziko-tekhnicheskie problemy razrabotki poleznykh iskopaemykh = Journal of Mining Science. 2007. № 1. pp. 45–63. (In Russ.).
  7. Martynyuk P.A., Pavlov V.A., Serdyukov S.V. Integrated use of hydraulic fracture and deformational measurements for permeable rock stress estimation. Gornyy informatsionno-analiticheskiy byulleten = Mining Information and Analytical Bulletin. 2013. № 2. pp. 155–163. (In Russ.).
  8. Chengzeng Y., Hong Z. A two-dimensional coupled hydro-mechanical finite-discrete model considering porous media flow simulating hydraulic fracturing. International Journal of Rock Mechanics and Mining Sciences. 2016. Vol. 88. pp. 115–128. DOI: 10.1016/j.ijrmms.2016.07.019
  9. Teodorovich E.V., Trofimov A.A., Shumilin I.D. Shape of a plane hydraulic fracture crack in an elastic impermeable medium at various injection rates. Izvestiya RAN. Mekhanika zhidkosti i gaza = Fluid Dynamics. 2011. № 4. pp. 109–118. (In Russ.).
  10. Yoshioka K., Bourdin B. A variational hydraulic fracturing model coupled to a reservoir simulator. International Journal of Rock Mechanics and Mining Sciences. 2016. Vol. 88. pp. 137–150. DOI: 10.1016/j.ijrmms.2016.07.020
  11. Xia B., Zhang X., Yu B., Jia J. Weakening effects of hydraulic fracture in hard roof under the influence of stress arch. International Journal of Mining Sciences and Technology. 2018. Vol. 28. Iss. 6. pp. 951–958. DOI: 10.1016/j.ijmst.2017.12.024
  12. Sedov L.I. Continuum mechanics: textbook. In 2 volumes. Vol. 2. Moscow: Nauka, 1984. 560 p. (In Russ.).
  13. Hellan K. Introduction to fracture mechanics. Moscow: Mir, 1988. 364 p. (In Russ.).
  14. Cherepanov G.P. Brittle fracture mechanics. Moscow: Nauka, 1974. 640 p. (In Russ.).
  15. Cherdantsev N.V., Cherdantsev S.V. Analysis of the State for a Coal Massif Enclosing in-Seam Working and a Geological Discontinuity. Izvestiya RAN. Mekhanika tverdogo tela = Mechanics of Solids. 2018. № 2. pp. 110–121. (In Russ.).
  16. Sneddon J.N., Berry D.S. The classical theory of elasticity. Moscow: Gosudarstvennoe izd-vo fiziko-matematicheskoy literatury, 1961. 220 p. (In Russ.).
  17. Cherdantsev N.V. The Results of the Numerical Solution of the Equations of the Limit State of the Seam Marginal Zone and their Approximation by the Polynoms. Bezopasnost truda v promyshlennosti = Occupational Safety in Industry. 2019. № 6. pp. 7–13. (In Russ.). DOI: 10.24000/0409-2961-2019-6-7-13 
DOI: 10.24000/0409-2961-2019-10-57-62
Year: 2019
Issue num: October
Keywords : rock mass mine working stress intensity factors crack the theory of Griffiths — Irwin hydraulic fracture
  • Cherdantsev N.V.
    Cherdantsev N.V.
    Dr. Sci. (Eng.), Chief Research Associate,, Federal Research Centre of Coal and Coal Chemistry of SO RAN, Kemerovo, Russian Federation