Method for determining the trajectories of particle movement in the undermined rock mass

Abstract

A method for determining the coordinates of particles displaced as a result of undermining a rock mass is considered, which makes it possible to pre-calculate displacements and deformations of a rock mass and the earth's surface. When compiling a model, a rock mass is considered as a discrete layered medium of a block structure. The mined seam is divided into elementary sections, which generate zones of displacement of rocks and the earth's surface. As a result of their addition, a common area of displacement is formed due to whole working area, and particles of rocks or the earth's surface move, forming displacement vectors. The direction and value of these vectors can be used to define changes in the position of the original line or surface and corresponding deformations caused by these changes. Mathematical modeling of the displacement process makes it possible to establish the patterns of spatial movement of points. Comparison of the calculated trajectories of points with the results obtained during mining operations relevealed their similarity. The proposed method can be used to predict the displacements of points in the undermined rock mass during the movement of the longwall face.