## 2 Engineering Background
### Laboratory Tests
#### 2.2.2 Strength Experiments for Coal and Rock Mass  
An EESFMCFR is generally excavated along the floor, and the roof and two sides share an identical coal structure. Therefore, the mudstone layers of the excavated roadway roof and floor and the 8# coal seam in the LL, QD, GB and XH coal mines were sampled on-site. There were 50 coal seam, roof, and floor coal rock samples each. The physical and mechanical properties of coal and rock mass with different lithologies were tested. The testing principle is as follows:  
(1) The uniaxial compression deformation experiment of coal rock shows that there is no lateral pressure applied to the specimen, and it is only subjected to axial load. Therefore, the deformation and failure of the specimen exhibit diverse forms of failure. The calculation formula is as follows:  
\[\sigma_{c}=\frac{P}{A} \tag{1}\]  
where \(\sigma_{c}\) is the uniaxial compressive strength of coal rock, MPa; \(P\) is the failure load of the coal rock specimen, N; and \(A\) is the area perpendicular to the loading direction, mm\({}^{2}\).  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Molecular Formula** & **CO\({}_{3}\) (Substrate)** & **SiO\({}_{2}\)** & **Al\({}_{2}\)O\({}_{3}\)** & **CaO** & **S** & **Others** \\ \hline Content & 74.7\% & 12.04\% & 9.47\% & 0.961\% & 0.676\% & 2.153\% \\ \hline \hline \end{tabular}
\end{table}
Table 1: Mineral compositions.  
Figure 2: X-ray diffraction spectrum of the coal seam in the EESFMCFR.  
(2) The tensile strength of coal rock mass is generally measured indirectly using the Brazilian splitting test method. The calculation formula is as follows:  
\[\sigma_{t}=\frac{2P}{\pi DH} \tag{2}\]  
where \(\sigma_{t}\) is the uniaxial tensile strength of coal rock, MPa; \(P\) is the failure load of the coal rock specimen, N; and \(D\) and \(H\) represent the diameter and thickness of the splitting surface of the specimen, mm.  
(3) Coal rock shear strength test. The calculation formula is as follows:  
\[\left.\begin{array}{l}\sigma=\frac{P}{\alpha}(\cos\alpha+f\sin\alpha)\\ \tau=\frac{P}{\alpha}(\sin\alpha-f\cos\alpha)\end{array}\right\} \tag{3}\]  
where \(P\) is the shear load of the coal rock specimen, N; \(A\) is the shear area of the coal rock specimen, mm\({}^{2}\); \(f\) is the friction coefficient between the specimen and the upper and lower plate pressing plates; \(\alpha\) is the angle between the shear plane of the coal rock specimen and the horizontal plane, \({}^{\circ}\); \(\sigma\) is the normal stress, MPa; and \(\tau\) is the shear stress, MPa.  
According to Formula (3), the normal stress and shear stress can be substituted into Equation (4) to obtain the cohesive force and internal friction angle.  
\[\tau=c+\sigma\tan\varphi \tag{4}\]  
where \(c\) is the cohesive force of the coal rock specimen, MPa; \(\varphi\) is the internal friction angle of the coal rock specimen, in degrees.  
The experimental process is shown in Figure 3, and the results are shown in Table 2.  
Figure 3: Mechanical experiments of coal and rock mass. (**a**) Uniaxial compression test (after experiment). (**b**) Shear test (after experiment). (**c**) Brazilian splitting test (after experiment).  
The 8# coal seam has a rather low compressive strength, tensile strength and cohesion. Resultantly, the ESFFMCFR in thick seams is prone to deformation, failure and instability. In contrast, the roadway roof and floor strata are of a higher compressive strength than the 8# coal seam. Moreover, the results of the Brazilian splitting experiment show that in the initial loading and fracturing process of the mudstone samples from the roadway roof and floor, the samples are first fractured along the radial cross section, resulting in a sudden drop in load. However, the fractures are not penetrated at this moment, so the mudstone still has some bearing capacity. Such a characteristic is meaningful for analyzing the control of SR of the ESFMCFR in thick seams.