## 2 Research Methods and Means
### PFC-FLUENT Numerical Simulation of Gob Flow Field  
#### 2.2.1 Macroscopic and Mesoscopic Parameters and DEM Model Construction  
Calculation of macro- and micro-parameters  
Selecting and calculating appropriate macroscopic and mesoscopic parameters are important steps in the model construction for PFC simulation [25]. Bonded particle models are divided into contact bond models and parallel bond models. A parallel bond model can more realistically simulate coal-like materials in tension or shear fracture and, thus, is selected for simulation in this work. Referring to the mesoscopic parameters of rock materials based on the principle of particle flow measurement, the following empirical formulas were used to calculate the parameters for PFC numerical simulation.  
(1) Empirical formula of elastic modulus:  
\[E/E_{c}=a+b\ ln(k_{n}/k_{s}) \tag{1}\]  
where \(E\) is the elastic modulus, GPa; \(E_{c}\) is the [PERSON]'s modulus, GPa; \(k_{n}/k_{s}\) is the stiffness ratio; \(a=1.652\); and \(b=-0.395\).  
Figure 1: Monitoring pipeline layout in the three zones of gob (own elaboration). (**a**) Roadway layout of 31,116 fully mechanized working face. (**b**) Plan view of the three zones of gob with monitoring pipelines buried.  
[PERSON]'s ratio empirical formula:  
\[v=c\ ln(k_{n}/k_{s})+d \tag{2}\]  
where \(v\) is [PERSON]'s ratio; \(c\) = 0.209; and \(d\) = 0.111.  
Regression analysis of uniaxial compressive strength:  
\[\frac{\sigma_{c}}{\overline{\sigma}}=\left\{\begin{array}{ll}a\left(\frac{ \pi}{\overline{\sigma}}\right)^{2}+b\frac{\pi}{\overline{\sigma}},\ 0<\frac{\pi}{\overline{\sigma}}\leq 1\\ c\quad,\quad\frac{\pi}{\overline{\sigma}}>1\end{array}\right. \tag{3}\]  
where \(\sigma_{c}\) is the compressive strength, MPa; \(\overline{\sigma}\) is the normal connection strength of parallel connection, MPa; \(\tau\) is the tangential connection strength of parallel connection, MPa; \(a=-0.965\); \(b\) = 2.292; and \(c\) = 1.327.  
Regression analysis of tensile strength:  
\[\frac{\sigma_{t}}{\overline{\sigma}}=\left\{\begin{array}{ll}d\left(\frac{ \pi}{\overline{\sigma}}\right)^{2}+e\frac{\pi}{\overline{\sigma}},\ 0<\frac{\pi}{\overline{\sigma}}\leq 1\\ f\quad,\quad\frac{\pi}{\overline{\sigma}}>1\end{array}\right. \tag{4}\]  
where \(\sigma\_t\) is tensile strength, MPa; \(d=-0.174\); \(e\) = 0.463; and \(f\) = 0.289.  
The calculated macroscopic and mesoscopic parameters are shown in Table 2.  
The PFC model and boundary conditions  
The mining process of 31,116 working face in Jinjie Coal Mine was simulated and analyzed using the PCF\({}^{3\text{D}}\) software. Based on the geological histogram of the coal seam, a numerical model was established by the radius expansion method, as shown in Figure 2a. The original size of the working face leads to a very large model and a large number of particles, which makes the calculation difficult, calculation time long, and results inaccurate. Therefore, the model size was reduced in proportion to 106 m long, 67.18 m wide, and 20.51 m high, with a total of 6 floors. Because the average dip angle of the coal seam is 1\({}^{\circ}\), the upper boundary of the model is a free boundary, and the left and right boundaries are fixed. The particles are allowed to move in the vertical direction, and the bottom boundary restricts their movement in the vertical direction. The particle sizes of the model are in the range of 0.6-0.8, with reasonable size ratio. The mining process is shown in Figure 2b and is divided into 10 mining steps. Each mining step records the overlying rock collapse and porosity changes.