Generalization of the n–k influence function to predict mining subsidence

Abstract

Within the context of mining subsidence simulation, this paper proposes a generalization of the n–k influence function, considering two physical concepts: the first is gravity, which characterizes the forces acting on the ground, and the second, the convergence of the roof and floor of the mine workings due to the stress state of the ground. Caving in of the roof generates direct subsidence, and the swelling of the floor, indirect subsidence, which allows us to better carry out the shape of the expected subsidence trough. These physical concepts are fundamental to mathematically implement the n–k influence function, permitting the interpretation of this function on the basis of physical and geometric concepts that may be evaluated more directly by the expert who has to perform the calibration, validation and sensitivity analysis of the phenomenon of subsidence. They likewise allow the scope of application of influence functions to be extended to non-horizontal seams, as well as taking into account the quality of the rock mass and the presence of preferential sliding directions, in both the roof and the floor of the seam. In the development of this work, we shall first define a new generalized influence function ( n–k–g), introducing the aforementioned geometric and physical concepts. The parameters n and k characterize the ground and g is related to the gravity. We shall then go on to justify their interpretation and see their application in the simulation of non-horizontal seams. Finally, we shall present the results obtained in a particular case, comparing these results with modeling previously carried out using FLAC.