The article presents the stages of numerical modeling of the stress-strain and strength state of a rock mass in the area of a ventilation drift during the mining of flat seams. The problem is solved by the finite element method, taking into account the physical and mechanical properties of coal, host rocks of the roof and soil of the seam and their changes over time of mining. The technique also takes into account the influence of adjacent waste lava. To assess the strength state of the host rocks, the Mohr criterion was used, and to assess the strength state of the coal seam, the criterion of rock strength under volumetric compression was used. The dependences of changes in the values of deformation characteristics of rocks over time were specified by rock creep equations, which made it possible to use the variable modulus method. An example is given of calculating the distribution of the stress-strain state of a rock mass, the convergence of the roof and soil, and soil heaving along the length of a ventilation road. A significant influence of the creep of the immediate soil on the amount of heaving of the roadway soil is shown.

The study delves into the elastoplastic deformation of a frozen wall (FW) with an unrestricted advance height, initially articulated by S.S.Vyalov. It scrutinizes the stress and displacement fields within the FW induced by external loads across various boundary scenarios, notably focusing on the inception and propagation of a plastic deformation zone throughout the FW's thickness. This delineation of the plastic deformation zone aligns with the FW's state of equilibrium, for which S.S.Vyalov derived a formula for FW thickness based on the strength criterion. These findings serve as a pivotal launchpad for the shift from a one-dimensional (1D) to a two-dimensional (2D) exploration of FW system deformation with finite advance height. The numerical simulation of FW deformation employs FreeFEM++ software, adopting a 2D axisymmetric approach and exploring two design schemes with distinct boundary conditions at the FW cylinder's upper base. The initial scheme fixes both vertical and radial displacements at the upper base, while the latter applies a vertical load equivalent to the weight of overlying soil layers. Building upon the research outcomes, a refined version of S.S.Vyalov's formula emerges, integrating the Mohr - Coulomb strength criterion and introducing a novel parameter -the advance height. The study elucidates conditions across various soil layers wherein the ultimate advance height minimally impacts the calculated FW thickness. This enables the pragmatic utilization of S.S. Vyalov's classical formula for FW thickness computation, predicated on the strength criterion and assuming an unrestricted advance height.