Mathematical model of load prediction on horizontal mine tunnel support

This paper focuses on determination of rock mass volume that exerts pressure on roof support in horizontal mine tunnels with regard to the internal friction coefficient as well as the shear and tear resistance (cohesion). The authors propose a new mathematical model to find the most probable shape of the failure surface in rock mass above a horizontal mine tunnel in case of the uniform physical and mechanical properties of rock mass in neighborhood of the mine tunnel. At the present time, the load on horizontal mine tunnel support is estimated using approximate mathematical models built in the first half of the previous century, with many various assumptions and simplifications, and updated with the data on geological conditions and heading technologies in a certain underground opening. The adopted mathematical description of arch formation in rock mass above a mine tunnel leads to the unfounded acceptance of an estimated load in determination of a load-bearing capacity of mine support and, consequently, to an invalid strength design of the support. This study aims to develop a mathematical model for the stress–strain behavior of rock mass above a horizontal mine tunnel, with regard to the physical and mechanical parameters of rocks and geometrical parameters of the mine tunnel, to find the most probable load applied to the mine tunnel support. The obtained analytical relations enable more accurate assessment of the shape of the failure surface in rock mass above a horizontal mine tunnel as against the current procedures, given that the physical and mechanical properties of rock mass above the tunnel are uniform.

Evstratov V. A., Voronova E. Yu., Lugantsev B. B., Isakov V. S., Kholodova L. A. Mathematical model of load prediction on horizontal mine tunnel support. MIAB. Mining Inf. Anal. Bull. 2025;(3):54-63. DOI: 10.25018/0236_1493_2025_3_0_54.

V.A. Evstratov¹, Dr. Sci. (Eng.), Professor, Professor, e-mail: vae602@yandex.ru, ORCID ID: 0000-0001-9531-2557,
E.Yu. Voronova¹, Dr. Sci. (Eng.), Assistant Professor, Head of Chair, e-mail: eleonora_sam_ti@mail.ru, ORCID ID: 0000-0002-4721-4570,
B.B. Lugantsev, Dr. Sci. (Eng.), Professor, Full Member of the Academy of Mining Sciences, Chairman of the Board of Directors, Shakhty Scientific Research and Design Coal Institute, 346500, Shakhty, Russia, e-mail: boris4721@mail.ru, ORCID ID: 0000-0002-8296-7922,
V.S. Isakov, Dr. Sci. (Eng.), Professor, Head of Chair, Platov South Russian State Polytechnic University, 346400, Novocherkassk, Russia, e-mail: vs.isakov@mail.ru, ORCID ID: 0000-0003-1859-6589,
L.A. Kholodova¹, Senior Lecturer, e-mail: holodova0420@yandex.ru, ORCID ID: 0009-0003-9726-399X,
¹ Shakhty Automobile and Road Construction Institute—Branch of the Platov South Russian State Polytechnic University, 346500, Shakhty, Russia.

V.A. Evstratov, e-mail: vae602@yandex.ru.

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