# The Stability and Failure of Deep Underground Structures at Potash Mining Deposits
## 4 Conclusions and Discussion  
In this article, a coupled FEM-DEM algorithm for stability analysis of deep underground excavations is proposed. The main idea of this algorithm is that for accurate and effective stability analysis of geotechnical systems, the discrete structure of the enclosing rock mass must be considered, since in the vicinity of underground cavities and excavations the rock mass tends to obtain a block-like structure. Therefore, to simulate the rock mass fracture efficiently, discontinuous numerical methods, like DEM, should be used. However, in the majority of applied engineering cases, it is not possible to predict the exact pattern of block structure formulation and to evaluate if such structure can be dangerous  
Figure 8: Block structure formulation at the depths of 1200 m according to the Griffith criterion. Figure 9: The results of the DEM simulation for the mining excavations at the depths of 1200 m.  
for entire geotechnical systems or excavation. In addition to that, explicit simulations of crack propagation and block-like failure requires a lot of time and computational power. In this regard, the following conclusions can be made based on the results of the research:  
(1) Full and accurate prediction of the excavation stability can be obtained using the efficient FEM-DEM coupled algorithm. Determination of the rock mass stress-strain state and limit state zones is proposed to be conducted using classic FEM based on the mentioned complex limit state criterion, while the block fracture of the rock mass and stability analysis of underground structures should be performed using further DEM simulation. To define the pattern of block structure formulation in the zones of limit states, the use of the Lade criterion has been proposed. Such approach allows one to save time and computational power, since the block structure is generated only in the limit state zones according to a certain rule and to efficiently evaluate all critical factors, which can influence the state of the considered geotechnical systems since a multicriterial approach is used. (2) The computational algorithms for calculating stress-strain state and limit state of the rock masses in the vicinity of underground structures should be different for moderate and great mining depths. (3) Classification of mining depths should be performed based on such parameters as the rock pressure at the considered depth, average cohesion coefficient of the rock mass, and the effective ultimate compressive strength of the rock mass. (4) At great mining depths the limit state zones in the vicinity of underground structures depend more on the geological structure of the rock mass and the particular depth, rather than on the shape of the cross-section of the excavation. Therefore, when conducting strength and stability calculations of geotechnical structures, the most attention should be paid to the characteristic size of the underground cavities, rather than their shape. (5) Based on the results of the model problem solution, for single mining of a 4.8 m cross-section excavation located in a salt-rock mass at moderate (H = 600 m) and great (H = 1200 m) depths, it was established that the limit state zones at a moderate depth reaches up to 2 m near the sides of the excavations, while at great depths the limit state zones reach 7.6 m at the entire outline of the excavations. However, at great depth the block structure formulates only in 0.8 m of the excavation outline according to the specific pattern. Further DEM studies have shown that the obtained blocks fail inside the excavation, but the total volume of the failed rock mass will be significantly less than the volume of the limit state zones. Future work for the development of the coupled FEM-DEM algorithms should involve creep behavior of the rock mass, since present study demonstrates stability assessment of mining excavations for a short time period (up to several months).