# The Stability and Failure of Deep Underground Structures at Potash Mining Deposits
## 1 Introduction  
The problem of strength and stability of geotechnical structures, such as mining excavations and underground cavities and chambers, for a given period, is one of the most important and crucial problems in geotechnics and geomechanics, since the effective and precise solution of such problems ensures safety and efficiency of underground construction, tunneling, and mining operations [1, 2]. This task becomes especially challenging when deep underground structures are considered [3]. Even though the general algorithm for solving such problems was developed a long time ago, the solution of this problem is still widely discussed in scientific publications [2, 4, 5]. In particular, many works are devoted to numerical simulations of the rock mass behavior in the vicinity of mining excavations in various mining, geological, and geotechnical conditions [4, 6, 7]. In addition, a number of works deal with stochastic and probabilistic models for predicting the stability of underground structures based on the processing of experimental data (e.g., [8, 9]). Furthermore, a significant number of publications are related to the improvement and development of new approaches and techniques for solving the problems of strength and stability of underground structures and excavations as well as to the development of new analytical solutions of such problems and evaluation of rock mass properties using various techniques [10, 11, 12, 13]. Current work considers several important issues related to the solution of a common relevant problem of the development of mathematical and computer-aided models, whichdescribe the behavior of rock masses in the vicinity of underground structures at great depths. In addition to this, the article presents a specific method, which allows for prediction of the block-like fracture of rock masses in the vicinity of underground structures directly. This problem has a significant status in the mining industry and geotechnical construction, since it is directly related to prediction of the operation period of underground structures and the safety of mining operations. One of the main points of this article is to show that the computational algorithms for the stress-strain state of rock masses in the vicinity of underground structures at great, moderate, and small depths should significantly differ. To achieve this goal, a number of numerical experiments are conducted using a specific coupled FEM-DEM technique. This technique includes series of FEM and DEM [14] simulations, the results of which are combined to obtain the forecasts of the rock mass stress-strain state and its subsequent block-like fracture. Note that there is another commonly used geomechanics method, which is also abbreviated as DEM--the discrete element method. However, this method is mainly used to describe the behavior of granular materials, such as sands and, therefore, is not used to describe the behavior of hard and ductile rocks. Therefore, in this article we use the abbreviation of DEM referring to the distinct element method, not discrete element method. The main peculiarity of the distinct element method is that the rock mass can be represented as a set of deformable blocks with specific connections between them [13]. This connection can be broken due to correspondent internal stress and, therefore, this method allows simulation of the block fracture of the rock mass. Both FEM and DEM are commonly used verified methods in rock mechanics [12]; therefore, there is no debt regarding the validity of coupled-algorithm application. However, the use of pure DEM for the problems of strength, stability, and durability of rock masses is limited, since the determination of the block structure formulation in the rock mass is a nontrivial task. Usually, this issue is solved by random generation of blocks or by the analysis of the experimental data, which are very limited in terms of industrial applications.