Terrain surface depressions as a function of cohesion as well as unconfined compressive strength and indirect tensile strength of rocks in terms of modelling the deformation of rock mass in construction in mining areas

Abstract The results of approximation of the settlement function of two known theories, i.e. the Knothe-Budryk theory and the Chudek-Stefański theory, have been presented. They concern the effects of under-ground mining on the surface and rock mass. The depression function, determined in these theories with the use of integral formulas, has been approximated to the algebraic form, in such a manner so that it was not necessary to take advantage of the integral calculus, at the same time taking into account the mean geomechanical values of the rock mass. Empirical data obtained from 34 types of rocks acquired from 16 drilling and research holes of the same rock mass allowed creating a correlation between the radius of the main influences and cohesion, unconfined compressive and indirect tensile strength of rocks, as well as the mean volumetric weight of rock mass. The obtained mathematical dependencies allow calculating the depression of land surface on the basis of the known geometry of excavations as well as their depth of deposition, and the already mentioned rock mass parameters. The differences between the results obtained from integral formulas and the obtained approximation formulas have been compared. The presented solutions are used in modelling land surface de-formations due to underground exploitation of deposits resulting from the needs of conducting analyses concerning construction in mining areas, without the need to use an integral calculus.