Abstract
In the process of underground mining, steeply inclined rocks or coal seams are often encountered, forming the openings of right-angle trapezoid. According to the geological conditions of a mining project in China, an analytical elastic solution of stress and displacement around right-angle trapezoidal opening in a homogeneous, isotropic, and linear elastic geomaterial is presented, which is based on the evaluation of the conformal mapping representation by an appropriate numerical calculation and the complex potential functions. The different results from other shaped openings are shown as follows. In a right-angle trapezoidal opening, the maximum displacements of roof falling occur on the low side, while the most horizontal displacements on the low side are around the roof and the most horizontal displacements on the high side are around the middle of the high side in this opening. These results are also compared with the numerical calculations in FLAC software, illustrating that the solution may be easily applied to rock mechanics or rock engineering for understanding the deformation of floor heave and roof falling down. The solution is also suitable for optimum design of bolt supporting in a right-angle trapezoidal opening, which is different from the traditional concept of symmetrical bolt supporting. Finally, a methodology is proposed for the estimation of conformal mapping coefficients for a given cross-sectional shape of an opening without symmetrical axis.
Highlights
Received: 10 November 2021Underground openings in rocks and coal seams are excavated in a wide range of geometries, such as circle [1,2,3,4], ellipse [5], ovaloid [6], rectangle [7], etc
The engineer can analyze the correctness of numerical calculations because of the simplification of numerical modeling; the analytical solution provides a basis for grasping the correctness
The excavation-induced as right-angle trapezoidal shapes in steeply inclined rocks or coal seams in China, and asymmetrical elastic deformation in surrounding rock or coal seam is a difficult problem some numerical calculations are carried out as shown in references from [15,16]
Summary
Underground openings in rocks and coal seams are excavated in a wide range of geometries, such as circle [1,2,3,4], ellipse [5], ovaloid [6], rectangle [7], etc. The excavation-induced as right-angle trapezoidal shapes in steeply inclined rocks or coal seams in China, and asymmetrical elastic deformation in surrounding rock or coal seam is a difficult problem some numerical calculations are carried out as shown in references from [15,16]. The excavation-induced asymmetrical elastic deformation in surrounding rock trapezoidal should be for given to obtain stress or on the or coal seam openings is a difficult problem the stability of the supporting thedisplacement openings. The deformation on the boundary of opening is obtained and analyzed, a theoretical solution of right-angle trapezoidal opening in elastic, isotropic, and homogewhich coal mayseam bringisabout a better insight topowerful the stability of opening in underground rock neous proposed based on the conformal mapping method. Quently, the deformation on the boundary of opening is obtained and analyzed, which may bring about a better insight to the stability of opening in underground rock (coal seam)
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