# Evaluation Method for Rock Burst Hazards in Strip Filling of Working Faces in Deep Coal Mines
## 3 Impact Hazard Evaluation Method
### Indicators and Membership Functions Determination
#### 3.1.1 Stress State of Coal
After mining on both sides, the strip coal pillar is formed and produces a certain range of plastic area under abutment pressure. When the strength and size of the strip coal pillar (the width of the elastic area is sufficient) can support the load transmitted by the overlying strata, the lateral abutment pressure distribution of the strip coal pillar shows a pattern of increasing from the boundary of the coal pillar to the center, then decreasing and finally stabilizing, and the overall distribution of the abutment pressure is similar to the \"saddle-shape\", as shown in Figure 2a. In the process of roadway excavation, a large number of large-diameter boreholes were constructed inside the strip coal pillar. The peak lateral abutment pressure shifted to the center of the coal pillar with a saddle shape, as shown in Figure 2b. Along with the continuous roof subsidence caused by the mining of the working face, the coal at the edge of the elastic area of the strip coal pillar changed into plastic. It leads to an increase in the plastic area and a decrease in the elastic area, which eventually causes a decrease in the overall bearing capacity. At this time, the abutment pressure distribution appeared to be in a 'platform'. The bearing capacity of the strip coal pillar shows obvious regional differences, which could be divided into five regions. Each region is in a relatively balanced stress state, as shown in Figure 2c. The bearing capacity of the strip working face is closely related to the working face width, coal pillar width, elastic area, and pressure relief boreholes. The coal pillar is affected by the lateral abutment pressure of the adjacent goat, the coal fracture is developed, and the bearing capacity is weak. The coal in the pressure relief area is subject to plastic damage due to large-diameter boreholes, resulting in a weak bearing capacity. The coal in the elastic area is structurally intact and is subject to three-dimensional stresses from the roof, floor, and coal bodies in the pressure relief areas on both sides, making it the main load-bearing for transmitting loads to the overlying strata. A simplified mechanical model of the coal stress is established, as shown in Figure 3.  
According to the principle of energy conservation, the load distribution relationship of each part of the coal is as follows:  
\[\delta_{z}=\delta_{\rm e}+2\delta_{\rm d}+2\delta_{\rm p} \tag{4}\]  
where \(\delta_{\rm e}\) is the load borne by the coal in the elastic area; \(\delta_{\rm d}\) is the load borne by the coal in the pressure relief area; and \(\delta_{\rm p}\) is the load borne by the coal pillar. The bearing load of coal in the pressure relief area can be expressed as follows:  
\[\delta_{\rm d}=\int_{0}^{l_{\rm d}}\sigma_{\rm d}(x)dx \tag{5}\]  
where \(l_{\rm d}\) is the width of the pressure relief area and \(\sigma_{\rm d}(x)\) is the abutment pressure distribution function of coal in the pressure relief area, which is affected by factors such as the depth of pressure relief borehole, the characteristics of coal-rock mass, and the stress monitoring threshold. The load of the coal pillar can be expressed as follows:  
\[\delta_{\rm p}=\int_{0}^{l_{\rm p}}\sigma_{\rm p}(x)dx \tag{6}\]  
where \(l_{\rm p}\) is the width of the coal pillar and \(\sigma_{\rm p}(x)\) is the abutment pressure distribution function of the coal pillar, which is affected by factors such as the coal pillar width and the characteristics of coal-rock mass. The size relationship of each part of the strip coal pillar is as follows:  
\[L_{0}=2l_{\rm p}+2l_{\rm r}+2l_{\rm d}+l_{\rm e} \tag{7}\]  
where \(l_{\rm r}\) is the width of the roadway and \(l_{\rm e}\) is the width of the elastic area.