## 4 Results and Discussion
### Stress-Strain Evolution
The dome-shaped damage of seam 3's roof is concentrated in the left part of panel 1 closer to roadway I. Such a distribution is logical since the roof of the seam has much greater support near the protective pillar than near roadway I due to the inclination. Notably, this asymmetry of the inelastic strain distribution is due to the enhanced influence of slip planes oriented along the strike direction. Based on the obtained distribution of the inelastic strain and damage, we can draw a conclusion that the aero and hydro interconnections with the undermined seam 1 are formed, which is generally treated as a negative phenomenon, since it allows for the enhanced migration of water and gas through the developed network of cracks. The formation of several largescale inclined surfaces of damaged rocks after state c generally causes the worsening of the geotechnical conditions. Figure 6a illustrates the distribution of the inelastic strain in the vertical cross-section of the model in the plane close to roadway I. Measuring the length of the first dome along the strike direction gives the value of the first caving step. In the considered case, the value is \(\approx\)50 m, which is typical of the south Kuzbass mines [24]. Finally, after the extraction of panel 1, we obtain a distribution of the vertical stress in the seam horizon illustrated in Figure 6b. It can be noted that the stress distribution has a pronounced asymmetry relative to the center of the extracted panel. This is due to the dip angle of the coal seam. The following step of the numerical modeling is associated with stress recovery in the gob of panel 1. We take account of this step explicitly by transferring the data on the damaged elements from the previous step and once again solve the gravity stress field problem. In this step, we assume that the overburden subsidence is completed, and the stress field almost recovers its gravitational state. Let us further trace the stages of inelastic  
Figure 5: Stages of inelastic deformation development in the course of the gob increase from panel 1: (**a**) 136 m, (**b**) 178 m, (**c**) 203 m, and (**d**) surface subsidence state. strain distribution in the course of the gob increase in panel 2. Figure 7 illustrates the damage distribution in the rock mass for different instants of the panel 2 gob increase. The model is again rotated by 180\({}^{\circ}\) relative to the view given in Figure 6b, since this view better illustrates the regularities of damage accumulation. Once we have obtained the distribution of the damage and inelastic strain in the rock mass after the extraction of two adjacent panels, we can further move towards the analysis of the stress distribution in and around the protective pillar between the panels. The vertical stress tensor component \(\sigma_{yy}\) and equivalent stress \(\tau\) are only used in the stress analysis below. Let us first discuss the change in the vertical stress \(\sigma_{yy}\) in characteristic time instants, namely, after the extraction of panel 1, after the stress recovery in the gob of panel 1, and after the extraction of panel 2. Figure 8 illustrates the vertical stress distributions along the line drawn through the center of the model in the dip direction of seam 3. Shortly after the extraction of panel 1 (wherein the face retreat reaches the boundary of the computational domain), the vertical stress values (gray dash-dot line) are strongly amplified in the vicinity of the pillars on the left and right sides of panel 1. The extraction of panel 1 also affects  
Figure 6: Distribution of inelastic strain in vertical cross-section of the model in plane close to roadway I (**a**); resultant \(\sigma_{yy}\) distribution in the seam 3 plane (**b**). Figure 7: Stages of damage development in the course of the gob increase in panel 2: (**a**) 136 m, (**b**) 178 m, (**c**) 203 m, and (**d**) surface subsidence state. the stress amplification in the edge section of the undisturbed panel 2.