# Random Forest-Based Stability Prediction Modeling of Closed Wall for Goaf
## 2 Experimental Data Description
### Experimental Data Contents
#### 2.1.1 Shock Wave Velocity  
The extent of damage to mine walls caused by shock waves primarily depends on their velocity; therefore, this paper collected data on shock wave velocities. During mining activities, the roof of a mined-out area can collapse due to rock damage or destabilization. The process of roof collapse is similar to the piston movement, which aligns with the pump model. In this model, the rock wall (side gang) acts as the pump, while the falling rock mass serves as the piston, as shown in Figure 1. When the roof collapses, the falling rock body releases a significant amount of energy while compressing the air inside the mined-out area, and continues along the roadway in the form of waves dramatically discharged to form a shock wave. Then, the closed wall is damaged by the pressure and amplitude of the shock wave, causing it to deform, crack, or collapse, thus affecting the stability of the closed wall. The magnitude of the shock wave generated during a roof fall in a mined-out area is typically expressed as the maximum velocity \(v_{\max}\). This velocity is influenced by factors such as the height of the mining area, the exposed area, and the total area of the roadway leading to the mined-out area. According to the \"pump\" model, the movement of the falling rock can be regarded as a free falling, and the mined-out area and the falling rock can be regarded as a cylinder and a piston, respectively. In this context, \(v_{\max}\) can be calculated using the following equation:  
\[v_{\max}=\frac{\eta S_{k}\sqrt{2 gH}}{S_{a}+(1-\eta)S_{e}} \tag{1}\]where \(\eta\) is the whole-layer disintegration coefficient of the roof plate in the mined-out area, and its value is related to the rock layer of the roof plate and the exposed area. Specifically, the stronger the surrounding rock, the larger the exposed area and the higher the value. \(S_{k}\) is an exposed area of the mined-out area, \(g\) is the gravity acceleration, \(H\) is the height of the roof plate, \(S_{a}\) is the sum of all of the broken areas of the roadway connected with the mined-out area, and \(S_{e}\) is an exposed area of the roof plate. From Equation (1), it is evident that the maximum velocity of the shock wave is positively correlated with the exposed area and the height of the roof plate in the mined-out area, while it is negatively correlated with the total cross-sectional area of all roadways connected to the mined-out area. Based on the conversion relationships between the wind speed and force (Equations (2) and (3)), and referencing the blasting safety regulation \"GB 6722-2014\" [37], the degree of injury to the human body from impact airflow is shown in Table 1 (under the standard conditions, the air gravity \(r\) = 0.01225 \(\text{kn}/\text{m}^{3}\), and the gravitational acceleration \(g\) = 9.8 \(\text{m}/\text{s}^{2}\)). \[F=\rho Q(V_{2}-V_{1}) \tag{2}\]  
\[Wp=\frac{0.5 rv^{2}}{g} \tag{3}\]  
In Equation (2), \(F\) represents the force, \(\rho\) represents the fluid density, \(Q\) represents the volumetric flow rate, \(V_{2}\) represents the outlet velocity, and \(V_{1}\) represents the inlet velocity. This formula can be used to calculate the force generated by the fluid due to the change in its velocity. Meanwhile, in Equation (3), \(Wp\) represents the pressure head, \(r\) represents the radius, \(v\) represents the fluid velocity, and \(g\) represents the acceleration due to gravity. This formula converts the fluid's velocity into a pressure head, and is used to estimate the pressure and energy loss. Figure 1: Shock wave formation mechanism (pump model). There are two types of the process in which the caving of the goal roof compresses the air to form shock waves. (**a**) The rock mass of the overall collapse of the goat roof and the rock wall of the goat are equivalent to a piston and a cylinder respectively. This process is similar to the downward movement of the piston. The compressed air is rapidly discharged through the channel below the cylinder, forming an air shock wave. This is the pump model.