# Roadway Backfill Mining with Super-High-Water Material to Protect Surface Buildings: A Case Study
## 3 Design for Roadway Backfill Mining under Surface Buildings  
### Reasonable Width of Segment Coal Pillar in the Working Face  
Reasonable coal pillar width should not only ensure the stability of the roadway during excavation, but also ensure the safety of the working face during the mining process. During mining progress at the adjacent working face, the basic roof breaks into the key block at the edge of the goat and forms an articulated structure with the adjacent rock blocks. The abutment pressure of the overburden transferred to the coal is divided into two parts according to the fracture line, i.e., the internal stress field between the fracture line and coal and the external stress zone in the deep region (it becomes the original stress zone beyond a certain point). Additionally, the stress in the internal stress zone is determined by the weight and movement of the overburden under the fracture line, and the whole surrounding rock is in low stress, which is beneficial to roadway maintenance, as shown in Figure 2.  
The study shows that the abutment pressure \(\sigma_{y}\) from the position of coal wall \(x\) in the relief stress zone is given by Equation (3) [34]:  
\[\sigma_{y}=G_{x}y_{x} \tag{3}\]  
where \(G_{x}\) is the stiffness of coal from the coal wall \(x\), Pa; and \(y_{x}\) is the compression of coal layer at \(x\), m.  
Figure 1: Schematic diagram of the Wangtaipu coalmine location and the key strata (KS). Stressing the development from the goat to the internal stress field, the horizontal stress in the coal increases gradually and is positively correlated with the coal stiffness, and negatively correlated with the coal compression. In order to simplify the analysis, the linearization of the \(G_{x}\) and \(y_{x}\) distribution can be obtained from Equation (4):  
\[y_{x}=\frac{y_{0}}{x_{0}}(x_{0}-x),\ G_{x}=\frac{G_{0}}{x_{0}}x \tag{4}\]  
where \(G_{0}\) is the maximum coal stiffness in the internal stress field, Pa; \(y_{0}\) is the coal compression at the edge of goat, m; and \(x_{0}\) is the width of internal stress field, m.  
Then, according to Equations (3) and (4), the abutment pressure in the internal stress field can be obtained as follows in Equation (5):  
\[\int_{0}^{x_{0}}\sigma_{v}dx=\frac{G_{0}y_{0}x_{0}}{6} \tag{5}\]  
Based on the theory of the internal and external stress field, the abutment pressure in the internal stress field on the coal seam around the stop is equal to the self-weight of the basic roof stratum during the initial pressure of the working face. Accordingly, the following equation can be obtained:  
\[\frac{G_{0}y_{0}x_{0}}{6}=LC_{0}M\gamma \tag{6}\]  
where \(L\) is the panel length, m; \(C_{0}\) is the first roof weighting pace of the adjacent working face, m; \(M\) and \(\gamma\) are the basic roof strata thickness and bulk density, respectively. Therefore, the geometric relationship between \(y_{0}\) and \(x_{0}\) is as follows:  
\[\frac{y_{0}}{x_{0}}=\frac{\Delta h}{L^{\prime}}=\frac{h-m_{z}(K_{\rm c}-1)}{L ^{\prime}} \tag{7}\]  
where \(h\) is the coal seam thickness, m; \(m_{z}\) is the immediate roof thickness, m; \(\Delta h\) is the maximum subsidence of basic roof stratum, m; \(K_{\rm c}\) is the residual expansion coefficient; and \(L^{\prime}\) is the suspension span of the rock beam, approximated to the periodic weighting step of the fully mechanized caving mining face, m.  
According to the inclusion theory [35], the expression of coal stiffness \(G_{0}\) in the plastic state is:  
\[G_{0}=\frac{E}{2(1+\
u)\xi} \tag{8}\]  
where \(E\) is the elastic modulus of coal, Pa; \(\
u\) is Poisson's ratio; and \(\xi\) is the influence coefficient, which is related to the development of fissures in coal. Figure 2: Basic roof broken structure model of gob-side entry.