This study is devoted to the analysis of isolated straight finite-length cracks in linear field of intact rock mass. The cracks are modeled by mathematical cuts orientation of which is governed by their inclination angle relative to the vertical. The static aspect of such weakening supposes a classical approach with setting of the a priory parameters that characterize rock mass with mathematical cut. It is important that such problems and determination of stress intensity factors belong to the class of ill-posed problems as they operate infinite stresses and zero displacements at crack tips. The kinematic aspect of rock deformation in the vicinity of cracks assumes taking into account influence exerted by rock mass deadweight on the displacement of crack edges. The influence zone of mathematical cut is determined using the classical static approach. In the influence zone of crack, vertical fibers are selected and subjected to loading by deadweight of rocks. In the roof, the deadweight direction is opposite to the action of stresses on the crack edges, while in the floor, these directions coincide, which deepens dissymmetry of deformation. In any case, the computational accuracy requires taking into account deadweight of rocks, which makes it possible to obtain analytically (in the first approximation) displacements of crack edges and to refine characteristics of rocks by any program of numerical calculation. The authors use phenomenological theory to calculate displacements based on in-situ values of edges. This theory allows solution of inverse problems by identifying characteristic parameters of rock mass with weakening by successive approximations, starting from natural stresses in intact rock mass. The dynamic aspect of the problem is connected with the growth of cracks under increasing internal pressure, i.e. with failure of rocks. It is considered that crack propagation is jump-wise and connected with formation of pores in the neighborhood of the crack tip and with rock fracture in this zone. The influence of stress state of intact rock mass on deformation in the vicinity of crack and on the crack propagation direction is discussed. For each of the aspects, dissymmetry of rock deformation is determined, and its effect on selection of fracture initiation and growth point is estimated. A set of interacting hydraulic fractures and their propagation directions in the varying stress field are analyzed. Within some limits, it is possible to control propagation directions of interacting cracks considering that the width of crack opening is the largest in the middle and decreases toward the crack tips.

Acknowledgements: This study was supported by the Russian Foundation for Basic Research, Project No. 18-05-00533.

For citation: Kurlenya M. V., Mirenkov V. E. Influence of rock mass stress state on propagation direction of hydraulic fractures. Gornyy informatsionno-analiticheskiy byulleten'. 2019;3:5-13. [In Russ]. DOI: 10.25018/0236-1493-2019-03-0-5-13.


Rock mass, deadweight, fracture, edges, displacement, movement, failure.

Issue number: 3
Year: 2019
ISBN: 0236-1493
UDK: 539.3
DOI: 10.25018/0236-1493-2019-03-0-5-13
Authors: Kurlenya M.V., Mirenkov V.E.

About authors: M.V. Kurlenya, Academician, Doctor of Technical Sciences, Professor, Scientific Director of the Institute, e-mail:, V.E. Mirenkov, Doctor of Technical Sciences, Professor, Chief Researcher, e-mail:, Chinakal Institute of Mining of Siberian Branch of Russian Academy of Sciences, 630091, Novosibirsk, Russia. Corresponding author: V.E. Mirenkov, e-mail:


1. Mikhlin S. T. Rock mass stresses above coal seam. Izvestiya akademii nauk SSSR. Otdelenie tekhnicheskikh nauk. 1942, no 7—8, pp. 13—28. [In Russ].

2. Barenblatt G. I., Khristianovich S. A. Roof falls in mines. Izvestiya akademii nauk SSSR. Otdelenie tekhnicheskikh nauk. 1955, no 11, pp. 73—86. [In Russ].

3. Sher E. N., Kolykhalov I. V. Propagation of closely spaced hydraulic fractures. Fiziko-tekhnicheskiye problemy razrabotki poleznykh iskopayemykh. 2011, no 6, pp. 43—53. [In Russ].

4. Kresse O., Weng X. et al. Numerical modeling of hydraulic fractures interaction in complex naturally fractured formations. Rock Mechanics and Rock Engineering. 2013. Vol. 46, no 4. Рp. 117—128.

5. Crosby D. G., Rahman M. M. Single and multiple transvers fracture initiation from horizontal wells. J. of Petroleum Science and Engineering. 2002. Vol. 35, no 3—4. Рp. 29—36.

6. Mirenkov V. E. О некорректных задачах геомеханики. Fiziko-tekhnicheskiye problemy razrabotki poleznykh iskopayemykh. 2018, no 3, pp. 3—9. [In Russ].

7. Kurlenya M. V., Mirenkov V. E. Deformation of ponderable rock mass in the vicinity of straight finite-line crack. Fiziko-tekhnicheskiye problemy razrabotki poleznykh iskopayemykh. 2018, no 6, pp. 12—19. [In Russ].

8. Vasil'ev V. V. Singular solutions in problems of mechanics and mathematical physics. Mekhanika tverdogo tela. 2018, no 4, pp. 48—65.

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