Analysis of the Trajectory of a Hydraulic Fracture near the Seam Working and the Conditions for its Straight-line Growth


Model of the geomechanical state of a disc hydraulic fracture propagating in the solid rocks near the seam working is based on the methods of solid mechanics and fracture mechanics.
Stress field in the coal-rock mass containing in-seam working and growing hydraulic fracture was constructed as a result of solving an elastoplastic problem, in which the area of plasticity is the extremely stressed zones of the edge parts of the seam. The stress field in the edge parts was determined in the course of the numerical solution of three boundary value problems of the seam limiting state. The criteria for the onset of the limiting state are the general criterion of the Coulomb — Mohr limiting state for the formation and a special criterion for the limiting state for its contact with the rock mass. 
By replacing the extremely stressed zones with the stresses acting on their contact with the rock mass, the elastoplastic problem is reduced to the second external boundary value problem of the theory of elasticity, which is solved by the method of boundary integral equations.
At the relatively low fluid pressures in the pumping unit, the trajectory of the hydraulic fracture is a smooth curved line of the small length with a significant deviation of its ends from the direction of the seed crack.
With increasing fluid pressure, the crack length increases, and the deviation from the direction of the seed crack decreases. There are fluid pressures at which the crack propagates in a straight line and practically does not change its original direction. The straight-line trajectory of the crack in the vicinity of the working located at different depths corresponds to a point on the graph of the dependence of the relative length of the crack on the fluid relative pressure. This graph is a straight line.

1. Klishin V.I., Zvorygin L.V., Lebedev A.V., Savchenko A.V. Safety problems and new technologies for the coal deposits underground mining. Novosibirsk: Novosibirskiy pisatel, 2011. 524 p. (In Russ.).
2. Kozyreva E.N. Opportunities to Increase Gas Emission Control Efficiency at the Extraction Section. Vestnik Nauchnogo tsentra VostNII po bezopasnosti rabot v ugolnoy promyshlennosti = Bulletin of Research Center for Safety in Coal Industry (Industrial Safety). 2017. № 3. pp 30–35. (In Russ.).
3. Huang B., Liu J., Zhang Q. The reasonable breaking location of overhanging hard roof for directional hydraulic fracturing to control strong strata behaviors of gob-side entry. International Journal of Rock Mechanics and Mining Sciences. 2018. Vol. 103. pp. 1–11. DOI: 10.1016/j.ijrmms.2018.01.013
4. Golovin S.V., Baykin A.N. Influence of pore pressure on the development of a hydraulic fracture in poroelastic medium. International Journal of Rock Mechanics and Mining Sciences. 2018. Vol. 108. pp. 198–208. DOI: 10.1016/j.ijrmms.2018.04.055
5. 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
6. Zubkov V.V., Koshelev V.F., Linkov A.M. Numerical simulation of hydraulic fractures initiation and growth. Fiziko-tekhnicheskie problemy razrabotki poleznykh iskopaemykh = Physical and technical problems of the mineral deposit development. 2007. № 1. pp. 4563. (In Russ.).
7. Chernyy S.G., Lapin V.N., Esipov D.V., Kuranakov D.S. Methods for modeling cracks initiation and propagation. Novosibirsk: Izd-vo SO RAN, 2016. 312 p. (In Russ.).
8. Cherdantsev N.V. One of the Approaches to the Construction of Trajectory of Hydraulic Fracturing in the Rock Mass Near Mine Working. Prikladnaya matematika i mekhanika = Applied mathematics and mechanics. 2020. Vol. 84. № 2. pp. 208233. (In Russ.). DOI: 10.31857/S0032823520020034
9. Cherdantsev N.V. Calculation of the parameters of disk hydraulic fracture located in the strong rocks of the seam top near the in-seam working. Naukoemkie tekhnologii razrabotki i ispolzovaniya mineralnykh resursov = Science-intensive technologies for the development and use of the mineral resources. 2020. № 6. pp. 84–89. (In Russ.).
10. Cherdantsev N.V., Presler V.T., Izakson V.Yu. Geomechaniacl state of a strength-anisotropic rock mass in the vicinity of mating tunnels. Fiziko-tekhnicheskie problemy razrabotki poleznykh iskopaemykh = Journal of Mining Science. 2010. № 2. pp. 6268. (In Russ.).
11. Sokolovskiy V.V. Loose medium statistics. Moscow: Nauka, 1990. 272 p. (In Russ.).
12. Galindo R.A., Serrano A., Olalla C. Ultimate bearing capacity of rock masses based of modified Mohr — Coulomb strength criterion. International Journal of Rock Mechanics and Mining Sciences. 2017. Vol. 93. pp. 215–225. DOI: 10.1016/j.ijrmms.2016.12.017
13. Sedov L.I. Continuum medium mechanics. In 2 volumes. Vol. 2. Moscow: Nauka, 1984. 560 p. (In Russ.).
14. Baklashov I.V. Fundamentals of geomechanics. In 2 volumes. Vol. 1. Moscow: Izd-vo Moskovskogo gosudarstvennogo gornogo universiteta, 2004. 208 p. (In Russ.).
15. Murakami Yu. Guide on the stress intensity factors. In 2 volumes. Vol. 1. Moscow: Mir, 1990. 48 p. (In Russ.).
16. 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 = RAS Izvestiya. Fluid and gas mechanics. 2011. № 4. pp. 109–118. (In Russ.).
17. Sneddon I.N., Berri D.S. The Classical Theory of Elasticity. Moscow: Fizmatgiz, 1961. 220 p. (In Russ.).
DOI: 10.24000/0409-2961-2021-5-18-23
Year: 2021
Issue num: May
  • Cherdantsev N.V.
    Cherdantsev N.V.
    Dr. Sci. (Eng.), Chief Research Associate, Federal Research Centre of Coal and Coal Chemistry of SO RAN, Kemerovo, Russia