# Random Forest-Based Stability Prediction Modeling of Closed Wall for Goaf
## 2 Experimental Data Description
### Experimental Data Contents
#### 2.1.2 Input Factors  
The closed wall plays an important protective role in the process of roof fall, as it mitigates the impact of a shock wave and guarantees the safety of both the engineering structures and personnel. The compressive strength and shear strength of the closed wall are chosen as the important indices for evaluating the damage to the surrounding rock and its equipment caused by the shock wave generated from the roof slab fall. Assuming there is no water accumulation situation in the mined-out area, the calculation of the closed wall thickness focuses on the roof plate of the mined-out area, which generates the shock wave pressure. According to the calculation formula of two different design strengths, the thickness of the closed wall in different mined-out areas can be calculated, taking C\({}_{20}\) concrete as an example. The specific formula is shown below:  
(1) Calculated by compressive strength. \[B=\left\{\left[(a+b)^{2}+4 pab/f_{c}\right]^{1/2}-(a+b)\right\}/(4\tan\alpha) \tag{4}\]  
where \(B\) is the thickness of the closed wall, in m; \(a\) is the width of the roadways where the closed wall is located, taking the value of 2.4 m; \(b\) is the height of the roadways where the closed wall is located, taking the value of 2.6 m; \(p\) is the hydrostatic pressure on the closed wall, with the air shock wave pressure being 10 times, in MPa; \(f_{c}\) is the value of the compressive strength of concrete, taking the value of 9.5 MPa; and \(\alpha\) represents the angle of shock wave propagation, and its specific value depends on the specific conditions of the goat. (2) Calculated by shear strength. \[B\geq pab/2(a+b)f_{v} \tag{5}\]  
where \(f_{v}\) is the shear strength of C\({}_{20}\) concrete, taking the value of 2.369 MPa. The data presented above are derived from the actual conditions of the mining area where the dataset was collected, as well as the \"Code for Design of Concrete Structures\" (GB 50010-2010) [38]. Specifically, the dimensions of the roadway (\(a\) = 2.4 m; \(b\) = 2.6 m) are determined based on the statistical average of actual engineering design cases in mines. The compressive strength (\(f_{c}\) = 9.5 MPa,) and shear strength (\(f_{v}\) = 2.369 MPa) of C20 concrete are cited from the \"Code for Design of Concrete Structures\" (GB 50010-2010). Based on the organization and analysis of the existing database, combined with the current prediction model, the following three characteristic parameters were finally identified as inputs for predicting the shock wave speed (m/s, where the symbol is SPEED), the compressive strength (MPa, where the symbol is \(\sigma\)bc), and the shear strength (MPa, where the symbol is \(\tau\)). The damage level of the closed wall was classified as no damage, slight damage, or severe damage. Figure 2 presents the pairwise relationships of the input parameters, illustrating the relationships between the three variables (SPEED, \(\sigma\)bc, and \(\tau\)) in a pairwise manner, and color-coded according to the \"Damage\" level. The plots on the diagonal show the distribution of each variable, using kernel density estimation (KDE) plots. Different colors \begin{table}
\begin{tabular}{c c c} \hline
**Shock Wave Overpressure/MPa** & **Degree of Damage** & **Injuries** \\ \hline
0.02–0.03 & minor & contusion \\
0.03–0.05 & medium & organ damage \\
0.05–0.1 & serious & possible death \\ \textgreater{}0.1 & extremely serious & deaths \\ \hline \end{tabular}
\end{table} 
Table 1: Human injury from shock wave overpressure. represent different damage levels, allowing for the observation of the distribution of each variable under different damage levels. For example, \"SPEED\" exhibits a more dispersed distribution at damage level 1, while it is more concentrated and has larger values at damage level 3. The off-diagonal plots display the scatter plot relationships between two variables. The color coding also indicates the damage level.