## 3 Experimental Methods
### Experimental System
#### 3.1.2 Electrical Resistance Testing System  
Electrical resistivity is one of the inherent physical parameters that defines the resistance characteristics of a testing specimen [26]. The electrical resistivity at different loading stages could reveal the failure characteristics of a coal/rock specimen. It is significant for predicting the collapse of dynamic disasters. In the current experiments, sandwiched coal-rock specimens as a whole were viewed as an electrical resistance body.  
Generally, the electrical resistivity of a single coal/rock body is determined [27] by Equation (1):  
\[\rho=R\cdot\frac{S}{H}=R\cdot\frac{\pi r^{2}}{H} \tag{1}\]  
where \(\rho\) is the electrical resistivity of a single coal/rock body (\(\Omega\cdot\)m); \(R\) is the electrical resistance of a single coal/rock body (\(\Omega\)); \(S\) is the effective cross-sectional area of a single coal/rock body (m\({}^{2}\)); \(H\) is the height of a single coal/rock body (m); and \(r\) is the radius of a single coal/rock body (m).  
Meanwhile, the electrical resistivity is usually regarded as being equal for coal/rock elements with the same diameter and height [28]. Therefore, the electrical resistivity of a sandwiched coal-rock specimen can be calculated by the following equation:  
\[\rho_{h}=R_{h}\frac{S_{h}}{H_{h}}=(mR_{c}+nR_{r})\cdot\frac{S_{h}}{mH_{c}+nH_ {r}}=(mR_{c}+nR_{r})\cdot\frac{\pi r^{2}}{mH_{c}+nH_{r}} \tag{2}\]  
where \(\rho_{h}\) is the electrical resistivity of a sandwiched coal-rock specimen (\(\Omega\cdot\)m); \(R_{h}\) is the electrical resistance of a sandwiched coal-rock specimen (\(\Omega\)); \(S_{h}\) is the effective cross-sectional area of a sandwiched coal-rock specimen (m\({}^{2}\)); \(H_{h}\) is the height of a sandwiched coal-rock specimen (m); \(R_{c}\) is the electrical resistance of the coal element (\(\Omega\)); \(R_{r}\) is the electrical resistance of the rock element (\(\Omega\)); \(H_{c}\) is the height of the coal element (m); \(H_{r}\) is the height of the rock element (m); \(m\) is the number of coal elements in the sandwiched coal-rock specimen; \(n\) is the number of rock elements in the sandwiched coal-rock specimen; and \(r\) is the diameter of the sandwiched coal-rock specimen (m).  
To measure the electrical resistance of sandwiched coal-rock specimens, a two-electrode insulation resistance testing system was adopted in this experimental system. It was mainly composed of resistance testing holders, copper electrodes, insulation boards, a data acquisition instrument, and an analysis software. As shown in Figure 4, copper electrodes were fixed symmetrically at the upper and  
Figure 4: Experimental system for the sandwiched coal-rock specimen in the uniaxial compressive test. (1—loading plates; 2—insulation boards; 3—copper electrodes; 4—testing sandwiched coal-rock specimen).  
lower ends of the sandwiched coal-rock system. They were sandwiched between the insulation boards and the testing coal-rock specimen. Resistance testing holders were connected with the upper and lower copper electrodes, which were also linked with the data acquisition instrument. The measuring deviation was within 1%. The maximum testing resistance was \(10^{12}\Omega\) and the data acquisition frequency was 5 Hz.