## 3 Single-Hole Column Charge Blasting Crater Test for Coal and Rock
### Analysis of Blast Crater Test Results
#### 3.2.3 Blasting Crater Throwing and Crushing Energy Distribution and Parameter Analysis  
A non-linear relationship analysis was conducted between the charge burial depth ratio \(K_{\text{b}}\) and the crater volume under various burial depths to determine the optimal charge burial depth and the corresponding specific explosive consumption for coal and rock benches. In addition, the energy distribution law of charge burial depth and rock fragmentation was explored. Based on the blasting crater theory [39], the following are the calculation formulas for the critical explosive burial depth \(L_{\text{e}}\left(\text{m}\right)\), the optimal burial depth \(L_{\text{j}}\left(\text{m}\right)\), and the rock strain energy coefficient \(E_{\text{b}}\):  
\[L_{\text{e}}=E_{\text{b}}\cdot\sqrt[3]{Q} \tag{3}\]  
\[L_{\text{j}}=\Delta_{\text{j}}\cdot E_{\text{b}}\cdot\sqrt[3]{Q} \tag{4}\]  
where \(Q\) is the charge mass, kg; \(\Delta_{\text{j}}\) is the best depth ratio, \(\Delta_{\text{j}}=L_{\text{j}}/\left(E_{\text{b}}\cdot\sqrt[3]{Q}\right)\), and \(E_{\text{b}}=L_{\text{e}}/\sqrt[3]{Q}\). Figure 6: Statistical diagram of geometric parameters of rock bench crater. Based on similarity criteria, the main influencing factors of the blasting crater fragmentation volume \(V\) are the charge amount \(Q\) and depth \(W\), i.e.,  
\[V=f(Q,W) \tag{5}\]  
The relationship between the charge amount \(Q\), depth \(W\), and blast crater fragmentation volume \(V\) is simplified to more clearly describe the non-linear relationship between the charge proportion depth \(E_{\text{b}}\) and the crater volume of coal and rock under different burial depths as follows:  
\[Y^{\prime}=f(X^{\prime}) \tag{6}\]  
where \(Y^{\prime}\) is the unit explosive rock breaking volume, \(Y^{\prime}=V/Q\), m; \(X^{\prime}\) is the charge proportion depth, \(X^{\prime}=W/Q^{1/3}\), m/kg\({}^{-3}\); \(W\) is the charge depth, m, \(W=L_{1}+L_{0}/2\); \(L_{1}\) is the stemming length, m; \(L_{0}\) is the charge length, m.  
Based on the statistical results of the coal and rock blast crater tests in Table 3 and subsequent supplementary rock step blasting test data, a non-linear fitting analysis of the charge proportion depth (\(W/Q^{1/3}\)) and unit explosive rock-breaking volume (\(V/Q\)) was performed using Equation (6). The characteristic curves of the coal and rock bench blast craters are depicted in Figure 7.  
The fitting formula for the coal bench blast crater can be obtained from the characteristic curve: \(Y^{\prime}=5.07{X^{\prime}}^{3}-25.79{X^{\prime}}^{2}+34.24{X^{\prime}}-8.14\). The fitting formula for the characteristic curve of the rock bench blasting crater is \(Y^{\prime}=21.88{X^{\prime}}^{3}-63.42{X^{\prime}}^{2}+57.62{X^{\prime}}-13.55\). In addition, based on the fitting curve, the charge depth ratios for coal and rock benches during blasting are 0.91 and 0.74, respectively, where the corresponding volume ratios are maximized. This indicates that these values are the optimal charge depth ratios for coal and rock, which will yield the best rock-breaking effect. The fitting results show that when the charge depth ratio is less than optimal, the volume ratio increases with the charge depth. However, the volume ratio decreases rapidly when it exceeds the optimal charge depth ratio. This indicates that a reasonable charge amount and depth significantly impact the blasting effect. Based on the extrema and zero points of the curve, the strain energy coefficient \(E_{\text{b}}\) for #3 coal-rock is 1.74, the optimal depth ratio is 0.91/1.74 = 0.523, and the maximum rock-breaking volume per charge is 5.47 m\({}^{3}\), with a corresponding fragmentation-specific consumption of 0.18 kg/m\({}^{3}\). For the overlying rock layer (sandstone) of #3 coal, the strain energy coefficient is 2.60, the optimal depth ratio is 0.74/2.60 = 0.285, and the maximum rock-breaking volume per charge is 3.16 m\({}^{3}\), with a corresponding fragmentation-specific consumption of 0.32 kg/m\({}^{3}\).