Asymmetric function of distribution of mining exploatation influences in the medium with changing properties

Author: S. Knothe

The model elaborated in the fifties (Knothe, 1951, 1953, 1957) for prediction of rock mass (surface) displacements, based on the normal distribution of mining exploitation influences [1], allows to achieve the theoretical profile of a subsidence trough with a satisfactory accuracy for practice [2].

This profile as well as the distributions of displacements and deformations of a terrain, determined at the assumption (4), reveal the symmetry in relation to the origin of coordinate system or to the ordinate axis (Fig. 1 and 2a).

The real profile of the trough is usually asymmetric (Fig. 2b). The approach of the predicted (theoretical) profile of the trough to the real one can be obtained by introduction of the asymmetric curve of mining exploitation influences to the mathematical model (Fig. 3) taking into consideration the changes of rock mass properties caused by mining.

For construction of the asymmetric curve two functions of normal distribution [...] and [...] were assumed.

These functions have different parameters of the influences dispersion r1 and r2 in outer and inner part of the subsidence trough (Fig. 5). The function (13) describing asymmetric profile of subsidence trough gives the better compatibility of the theoretical subsidence trough profile (Fig. 6) with the real one and allows for prediction of more accurate values of displacements and deformations.