# Stability Analysis of the Exploitation System with Room and Pillar by Analytical Methods
## 4 Results  
Stability Analysis of a Rock Salt Mining System with Rooms and Pillars Based on the Limit Equilibrium Theory  
Based on the methods of the limit equilibrium principle, the stability of the exploitation system is due to the degree of stress, the dimensions of the geometric elements of the system (pillar, floor), and the exploitation depth. According to the geomechanical, technical, and mining conditions of the salt mine considered in this work [11; 12; 42], this statement is also highlighted by the results obtained for the four situations that were considered in the study (Figure 5):  
* Case 1: \(\mathrm{I}_{\mathrm{room}}=16\) m, \(\mathrm{I}_{\mathrm{pillar}}=14\) m, \(\mathrm{\SIUnitSymbolMicro}\mathrm{\SIUnitSymbolMicro}\mathrm{\SIUnitSymbolMicro} \mathrm{\SIUnitSymbolMicro}\mathrm{\SIUnitSymbolMicro}\mathrm{\SIUnitSymbolMicro}  
Figure 5: Stability evaluation of the operating system according to the equilibrium principle limits: (**a**) the variation in the effective stress; (**b**) the variation in load degree; (**c**) the deformation variation over a period of 100 days. The effective load that belongs to some pillars depends not only on the size of \(\gamma_{\rm A}\)H but also on the \(\rm l_{r}/\rm l_{p}\) ratio (room width/pillar width), the way of distributing the stress, and the qualitative variation in the salt of the pillars. At exploitation depths of 200-250 m and values of the geometric dimensions of the room and pillar of 14 m and, respectively, 16 m, the load degree is 0.23-0.25. The extraction coefficient has a value of 35.7%, and the required height of the pillar is 8 m. The effective stress respects the condition (2) of stability (15.05 MPa < 30.55 MPa). When increasing the depths up to 350 m and the values of the geometric dimensions of the room and pillar (\(\rm l_{r}=13\) m and \(\rm l_{p}=17\) m), the condition of stability is respected. The load degree is 0.28 < 0.3, the effective stress does not exceed 20 MPa, and the required height of the pillar becomes 9 m (the value of the extraction coefficient being 31.9%). At depths of 800 m and dimensions of \(\rm l_{r}=11\) m and \(\rm l_{p}=19\) m, the load degree varies within 0.33-0.35, and the effective stress does not exceed 50% of the value of the limit stress. Under these conditions, for an extraction coefficient of 24%, the  
Figure 6: Extraction coefficient variation (**a**) and load degree variation (**b**) depend on depth \(\rm H_{0}\) and room–pillar geometry (\(\rm H_{max}=500\) m). required height of the pillar should be 12 m. In fact, rheological research [42; 49] showed that in terms of creep behavior, for the conditions of this mine salt, the pillars are located in the estimated stability field (0.3-0.45)\(\sigma_{\rm c}\) (\(\sigma_{\rm c}\) being uniaxial compressive breaking strength). Figure 7: The variation in the effective stress and the limit stress (**a**), the extraction coefficient (**b**), and the load degree (**c**) depends on the operating depth H\({}_{0}\) and the geometry of the room and pillar (H\({}_{\rm max}\) = 800 m). It results that, according to the theory of limit equilibrium, with the increase in exploitation depth, the stress state in the room-pillar system also changes, emphasizing the inelastic, plastic deformation character of rock salt. In such a context, to ensure the stability and reliability of the system, it is required that within a given network of rooms and pillars, the dimensions of the pillars increase at the expense of reducing the opening of the rooms. This fact leads to a significant decrease in the extraction coefficient. Stress State in the Pillar Based on the Principles and Theories of the Mechanics of the Continuous Medium  
For the proposed analytical model to evaluate the stress state in the pillar based on the theories of the mechanics of the continuous environment, the coefficients A\({}_{0}\), B\({}_{0}\), and C\({}_{0}\) were determined. These were obtained for ratio values h/b: 0.1 \(-\) 3; 0.01 \(-\) 1 and \(\lambda\) = 0.05 \(-\) 0.4 (Table 1).