# Shaft Wall Damage to High-Depth Inclined Ore Passes under Impact Wear Behavior
## 2 Shaft Wall Damage Model for High-Depth Inclined Ore Passes
### 3 Engineering Case
#### 3.1.2 Parameter Selection  
Four ore passes, No. 9, 2, 3, and 1, were selected and labeled, respectively, as operating conditions 1, 2, 3, and 4 for comparative analysis. According to the engineering geological data of the mine, the physical and mechanical parameters of the ore and shaft wall rock mass are reported in Table 1. Due to the construction of ore passes in the case study having been carried out in the deep hard rock of the mine, the effect of soil layers is not basically considered [32; 33]. In addition, based on the design blueprint of the ore-pass system of the mine, it can be calculated that the vertical height of the ore discharge port \(h_{1}\), the inclined chute height \(h_{2}\), and the ore bin height \(h_{3}\) of the four ore passes are 4.4 m, 1.0 m, and 19.6 m, respectively. The other structural parameters are shown in Table 2. The block size of the ore in the ore passes is set to be 400 mm. After calculation and analysis, it was determined that the kinetic energy of an ore significantly decreases after the initial collision with the shaft wall, rendering it unable to maintain contact with the ceiling side of the shaft wall. Therefore, this paper only considers the impact wear effect on the ore pass's bottom wall. Moreover, it has been reported that the ore kinetic energy and the shaft wall damage volume decrease greatly with an increase \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Type**} & **Elastic** & **Poisson** & **Volumetric** & **Initial Yield** & **Friction** & **Cohesion** & **Coefficient of** \\  & **Modulus** & **Ratio** & **Weight** & **Strength** & **Angle** & _c/(MPa)_ & **Sliding Friction** \\  & **_E/(GPa)_** & _v/(-)_ & _v/(KN-m-3)_ & _c\({}_{\alpha}\)_/(MPa)_ & _c\({}_{\beta}\)_/(\({}^{\circ}\))_ & _v/(\({}^{\circ}\))_ & _v/(\({}^{\circ}\))_ & _v/(\({}^{\circ}\))_ \\ \hline Shaft wall rock mass & 16.80 & 0.26 & 27.80 & 59.52 & 42 & 10.60 & 0.40 \\ Ore & 14.09 & 0.25 & 40.80 & — & — & — & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Physical and mechanical parameters of ore and shaft wall rock mass. Figure 3: An ore pass drilled using a raise-boring machine. in collision frequency; thus, the shaft wall damage volume after more than three collisions is negligible [8; 9; 10; 14]. In this paper, the first three collision positions are taken, and the shaft wall damage volume calculated using Equation (18) is accumulated to obtain the total shaft wall damage volume \(Q_{\text{tol}}\). The collision points in a high-depth inclined ore pass of a deep mine are shown in Figure 4.  
Considering the structural characteristics of high-depth inclined ore passes, the total shaft wall damage volume \(Q_{\text{tol}}\) is related to the number of collisions between the extracted ore and the shaft wall. The prerequisite for the \(k\)-th collision is that the vertical total displacement of the ore from the inclined chute into the shaft section must be less than the total height of the shaft section. Hence, the total shaft wall damage volume \(Q_{\text{tol}}\) can be expressed as follows:  
\[Q_{\text{tol}}=\left\{ \begin{array}{l}0,y_{1}>H-(h_{1}+h_{2}+h_{3})\\ \sum\limits_{k=1}^{n}Q_{k},\sum\limits_{k=1}^{n}y_{k}<H-(h_{1}+h_{2}+h_{3}) \end{array} \right. \tag{19}\]  
where \(k\) is the number of collisions, and \(y_{k}\) is the vertical displacement of the ore relative to the shaft wall from the (\(k-1\))-th collision to the \(k\)-th collision. Based on the kinematic principle and the geometrical structure of an ore pass, the relation between the ore vertical displacement and the structural parameters of the ore pass can be derived as follows:  
\[y_{k}=\left\{ \begin{array}{l}\frac{D}{\cos\theta}+\frac{\xi v_{0} ^{2}\cos^{2}\tan\theta}{g},k=1\\ \frac{2v_{(k-1)n}}{g}[v_{(k-1)n}\tan^{2}\theta+v_{(k-1)t}\sin^{2}\theta\tan \theta+v_{(k-1)t}\sin\theta\cos\theta],k=2,3\end{array} \right.