On numerical modeling of subsidence induced by mining

The paper contains a new approach to calculate subsidence induced by mining. Its essence consists in combining reliable empirical data with rigorous accounting for compatibility conditions in 3D multi-layered media. The mathematical tool employed is the fast Fourier transform. It serves us for efficient solution of 3D elasticity equations for tens and even hundreds of layers. Stresses at the Earth surface are zero. At the mining levels, displacement discontinuities are considered to be proportional to the extracted thickness. Low- or no-friction contacts are presumed. Normal displacements at contacts may be continuous or include contact dilation. The layers are considered to be isotropic, homogeneous and elastic. Asymptotic formulae for high and low frequencies are used to increase accuracy and decrease the time of calculations. Layers being normally thin, the accepted presumptions do not distort the subsidence picture significantly given the boundary conditions at the mining level are prescribed in terms of displacements. This allows us to introduce necessary corrections accounting for strongly nonlinear effects discussed in the paper. The corrections are made automatically in the computer program Lay-Subsid developed by the authors. Numerical results and examples are given. They show flexibility and potential of the suggested approach for subsidence prediction and for further development of the code