# The Stability and Failure of Deep Underground Structures at Potash Mining Deposits
## 3 Results  
### FEM Simulation of the Rock Mass State in the Vicinity of Single Mining Excavations  
This section presents the results of model studies aimed at assessing the state of rock mass in the vicinity of single mining excavations located in a potassium salt strata at moderate and great depths. The results of FEM simulation of mechanical behavior of the rock mass in the vicinity of long horizontal excavation of various cross-sections are presented below. In particular, rectangular and arched cross-sections are considered (see Figure 1). Figure 2 below shows the distribution of the Nadai-Lode coefficient (4) in the vicinity of the mining excavations at moderate and great depths. The analysis of Figure 2 shows that the type of stress-strain state of the rock mass in the vicinity of mining excavations significantly differs depending on the considered mining depths. At the same time, the shape of the cross-section does not have a significant impact on the type of stress-strain state. In addition to that, the stress-strain state of the rock mass at moderate and great depth changes is not only quantitative and nonlinear but also qualitative when the great depth is reached. Thus, at moderate depth, the rock mass in the vicinity of excavations is mainly in the state of generalized compression, while at a greater depth, it is in the state of generalized shear (Figure 2). At a moderate depth, generalized shear zones are also formed in the roof and bottom of excavations, but these zones have only a local pattern. At greater depth, zones of generalized tension are formed  
Figure 2: Distributions of the Nadai–Lode coefficient in the vicinity of mining excavations of different cross-sections at moderate and significant mining depths. Red color—zones of generalized compression; green color—zones of generalized shear; and blue color—zones of generalized tension. at the bottom of excavations, which leads to significant displacements of rock masses in the area of the excavated space due to the soil heaving effect. The numerical experiments show that by using various failure criteria, the evaluations of the limit state zones in the rock mass can be absolutely different by the size, shape, and localization at the outline of mining excavations [15]. Therefore, Figure 3 below shows the estimates of limit state zones in the rock mass in the vicinity of mining excavations according to the complex limit state criterion (3). This figure demonstrates that at a great depth the entire rock mass in the vicinity of the mining excavation is in the limit state and the size of the limit state zone exceeds the double cross-section size. In addition, Figure 3 shows the formation of rock pressure vaults in the vicinity of the excavation roof. As follows from the simulation results, the effect of pressure vaulting is most pronounced for excavations located at great depths. Moreover, Figure 3 illustrates the collapse vaults at the roof of the considered excavations, which are especially important at great depths. Figure 4, in turn, proves the fact that at great depths, the cross-section of the excavation does not have a significant effect on the stress-strain state of the rock mass in the vicinity of excavations. The size of the cross-section has less influence on the size and shape of limit state zones at great depths than at small and moderate depths. At great depths, the shape of the cross-section has an increasingly localized effect on the limit state zones in the rock mass. Figure 3: Limit states of the rock mass in the vicinity of mining excavations of different cross-sections at moderate and great mining depths according to complex limit state criterion (3). Red color—limit state zones; black lines—pressure vaults. The next important conclusion is that at greater depths, the shape and size of the limit state zones in the rock mass become less and less dependent on the geological structure of the enclosing rock mass and more dependent on the equivalent mechanical properties of the rock mass.