# To the Calculation of Coal Pillars between In-seam Workings

Annotation:

Based on the fundamental methods of solid mechanics, the model is built related to the geomechanical state of the rock mass containing the coal bed and two workings passed through it. The model takes into account that the strength characteristics of the layer is inferior to the strength characteristics of the solid mass, but higher than the strength characteristics on the contact of the layer with the solid mass.

The problem of the layer state in the extremely stressed zone is reduced to the nonlinear differential equation of hyperbolic type. This equation is solved by the method of characteristics based on resolving a number of boundary value problems of the layer limit state. Strength calculation of the coal pillar is made by calculating its safety factor.

Breaking load on the coal pillar is determined by the integration of the expression of vertical normal stresses in its roof. Actual load on the coal pillar is determined in two ways. The first method is the integration of the expression of the vertical component of normal stresses along the roof of the pillar obtained from the solution of the elastoplastic problem. At the second method the actual load is calculated as the weight of the rock mass located between axes of the workings.

The values of the actual load on the coal pillar, as well as the safety factors obtained by each of two above methods, differ by less than 10%.

The graph of decreasing in the safety margin of the pillar with an increase in the span of the first working with a fixed value of the span of the second working and the constant width of the pillar is characterized by slightly decreasing curve. Widening of the coal pillar significantly increases its safety factor. For example, the increase in its width of the coal pillar by 2 m at the fixed safety factor allows to lengthen the span of one working several times.

References:
1. Borisov A.A. Mechanics of rocks and rock masses. Moscow: Nedra, 1980. 360 p. (In Russ.).
2. Ruppeneyt K.V. Some issues of rock mechanics. Moscow: Ugletekhizdat, 1954. 384 p. (In Russ.).
3. Turchaninov I.A., Iofis M.A., Kasparyan E.V. Fundamentals of rock mechanics. Leningrad: Nedra, 1989. 488 p. (In Russ.).
4. Walton G., Diederichs M., Punkkinen A., Whitmore J. Back analysis of a pillar monitoring experiment at 2.4km depth in the Sudbury Basin, Canada. International Journal of Rock Mechanics and Mining Sciences. 2016. Vol. 85. pp. 33–51. DOI: 10.1016/j.ijrmms.2016.03.001
5. Gao W., Xu F. Numerical simulation of overburden and surface movements for Wongawilli strip pillar mining. International Journal of Mining Science and Technology. 2016. Vol. 26. Iss. 1. pp. 71–76. DOI: 10.1016/j.ijmst.2015.11.013
6. Fisenko G.L. Limit states of rocks around the workings. Moscow: Nedra, 1976. 272 p. (In Russ.).
7. Petukhov I.M., Linkov A.M., Sidorov V.S., Feldman I.A. Theory of protective seams. Moscow: Nedra, 1976. 223 p. (In Russ.).
8. Pavlova L.D., Petrova T.V., Fryanov V.N. Mathematical modeling of the geomechanical state of the coal-bearing massif in the vicinity of mating if the mine workings. Novokuznetsk: SibGIU, 2002. 202 p. (In Russ.).
9. Pavlova L.D. Modeling of geomechanical processes in collapsible coal-bearing massif. Novokuznetsk: SibGIU, 2005. 239 p. (In Russ.).
10. Gao W., Ge M. Stability of a coal pillar for strip mining based on an elastic-plastic analysis. International Journal of Rock Mechanics and Mining Sciences. 2016. Vol. 87. pp. 23–28. DOI: 10.1016/j.ijrmms.2016.05.009
11. Li X., Kim E., Walton G. A study of rock pillar behaviors in laboratory and in-situ scales using combined finite-discrete element method models. International Journal of Rock Mechanics and Mining Sciences. 2019. Vol. 118. pp. 21–32. DOI: 10.1016/j.ijrmms.2019.03.030
12. Cherdantsev N.V., Fedorin V.A. Geomechanical state of the rock mass with weakening surfaces in the vicinity of the complex of extended horizontal workings. Vestnik Kuzbasskogo gosudarstvennogo tekhnicheskogo universiteta = Bulletin of the Kuzbass State Technical University. 2006. № 1 (52). pp. 17–19. (In Russ.).
13. Khristianovich S.A. Continuum mechanics. Moscow: Nauka, 1981. 484 p. (In Russ.).
14. Sokolovskiy V.V. Loose medium statistics. Moscow: Nauka, 1990. 272 p. (In Russ.).
15. Cherdantsev N.V. Modelling the trajectory of a fracture that moves under the influence of the fluid pressure in hard rock roofs of in-seam working. Available at: https://iopscience.iop.org/article/10.1088/1755-1315/206/1/012005/pdf (accessed: November 01, 2019).
16. 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
17. Lure A.I. Strength theory. Moscow: Nauka, 1970. 940 p. (In Russ.).
DOI: 10.24000/0409-2961-2020-1-26-30
Year: 2020
Issue num: January
Keywords : coal-rock massif in-seam working extreme stressed zones resistance characteristics coal pillars
Authors:
• Cherdantsev N.V.
Dr. Sci. (Eng.), Chief Research Associate, nvch2014@yandex.ru Federal Research Centre of Coal and Coal Chemistry of SO RAN, Kemerovo, Russia