Computer modeling of fracture growth under the action of pressure applied to its surfaces

The article discusses an approach to modeling propagation of a single fracture during fluid injection in it in a uniform isotropic medium. The problem is solved in 3D formulation using the finite element method. Meshing involves the SMART method which ensures fine meshing at the tip of the fracture along the whole path of its growth. The problem formulation assumes an initial fracture of a small length (a nucleus of a future long fracture). The conditions of the fracture growth starting are based on the failure criterion and the J-integral calculated along a closed perimeter rimming the fracture tip. At the initial stage of the fracture deformation as fluid is being injected in it, the opening of the fracture increases without advance of the fracture tip and, accordingly, the J-integral increases. When the integral reaches a critical value typical of a failing material, the material starts failing with the advance of the fracture front. The stress–strain behavior of the enclosing medium of the fracture is assessed depending on the fracture propagation. When the initial fracture lies in the main plane of the actual initial stresses, the fracture trajectory represents a plane that extends the initial fracture. If the initial fracture lies in neither of the main planes, the fracture propagation is connected with the formation of a smooth surface which asymptotically approaches one of the main planes.

Trofimov V. A., Filippov Yu. A., Makeeva T. G. Computer modeling of fracture growth under the action of pressure applied to its surfaces. MIAB. Mining Inf. Anal. Bull. 2025;(8):29-44. [In Russ]. DOI: 10.25018/0236_1493_2025_8_0_29.

V.A. Trofimov¹, Dr. Sci. (Eng.), Chief Researcher, e-mail: asas_2001@mail.ru,
Yu.A. Filippov¹, Cand. Sci. (Eng.), Senior Researcher, e-mail: filippov.yury@gmail.com,
T.G. Makeeva, Cand. Sci. (Geol. Mineral.), Assistant Professor, Moscow State University of Civil Engineering (National Research University), Moscow, Russia, e-mail: makeeva13new@yandex.ru,
¹ Institute of Problems of Comprehensive Exploitation of Mineral Resources of Russian Academy of Sciences, 111020, Moscow, Russia.

V.A. Trofimov, e-mail: asas_2001@mail.ru.

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