# The Stability and Failure of Deep Underground Structures at Potash Mining Deposits
## 2 Materials and Methods  
### Classification of the Mining Depths  
It is well known that one of the key factors affecting the stress-strain state of undermined rock masses is rock pressure or lithostatic pressure [17]. To calculate the vertical component of lithostatic pressure, \(\mathrm{P_{I}}\) expression (1) is commonly used. At the same time, the horizontal component of the rock pressure, \(\mathrm{P_{s}}\), in case of gentle bedding of the rock strata, is determined by the expression (2) [17; 18]  
\[\mathrm{P_{I}}=\rho\mathrm{gh} \tag{1}\]  
\[\mathrm{P_{s}}=\lambda\rho\mathrm{gh} \tag{2}\]  
where \(\rho\) is the average weighted density of the rock strata, \(\mathrm{g}\) is gravity acceleration, \(\lambda\) is the coefficient of lateral expansion (can be defined as a result of theoretical calculation or by experimental data). Note that in most cases, the initial lateral expansion coefficient for a rock mass with gentle bedding of geological layers is determined as the solution of the corresponding elasticity problem for a heavy quasi-homogeneous half-space and is assumed to be equal \(\lambda=\mathrm{v}/(1-\mathrm{v})\), where, in turn, \(\mathrm{v}\) is the Poisson's ratio [17]. It is generally accepted in specialized scientific and technical literature to classify the mining depths as \"small\" and \"great\" [17; 19]. The previous experience of the authors in solving problems of stability and strength of geotechnical structures located at different depths inside the rock strata with significantly different mechanical properties allows to us clarify and expand upon the classification of depths in geomechanics. In this article, we propose the classification of mining depths based on the level of rock pressure and mechanical properties of the rock strata at the considered depth:  
* Small depths at which the ratio of cohesion coefficient to lithostatic pressure is greater than unity (\(\mathrm{C}/\rho\mathrm{gH}>1\)). * Moderate depths at which the ratio of cohesion coefficient to lithostatic pressure is less than or equal to one (\(\mathrm{C}/\rho\mathrm{gH}\leq 1\)), but this ratio does not exceed the effective ultimate compressive strength of the correspondent rock strata (\(\rho\mathrm{gH}\leq\sigma_{\mathrm{c}}\)). * Great depths at which lithostatic pressure exceeds the effective ultimate compressive strength of the rock strata (\(\rho\mathrm{gH}>\sigma_{\mathrm{c}}\)). As follows from the introduced classification, the understanding of \"great\" depths depends not only on the absolute value the lithostatic pressure, but mainly on the value of the effective ultimate compressive strength of the rock mass in the considered strata. For example, according to the analysis of mechanical properties of rocks at the Starobinsky potassium salt deposit (Republic of Belarus), the mining depths of more than 900 m can be classified as \"great\", while for the Petrikovsky potassium salt deposit (Republic of Belarus) and Gremyachinskoe potassium salt deposit (Russian Federation), depths of more than 1000 m are classified as \"great\". Therefore, the proposed classification of the mining depths is relative and should be performed for each deposit separately considering mechanical properties of rocks and the level of rock pressure at the considered depth. The main peculiarity of solving strength and stability problems for underground structures at small mining depths is that the Earth's surface effects (free surface boundary conditions) should be considered. At moderate and great mining depths, the effects of the free surface are usually replaced by the action of equivalent load according to Formulas (1) and (2). At moderate depths, the vertical component of the boundary rock pressure distant from the area influenced by the underground structures can be determined by Formula (2), where \(\lambda=\mathrm{v}/(1-\mathrm{v})\). It should be noted that in the case of a layered rock mass, the effective (depth-weighted average) value of the Poisson's ratio should be used for calculation of the lateral expansion coefficient.