# Shaft Wall Damage to High-Depth Inclined Ore Passes under Impact Wear Behavior
## 2 Shaft Wall Damage Model for High-Depth Inclined Ore Passes
### Influence of Ore-Pass Dip Angle \(\theta\)  
To reveal the influence of the ore-pass dip angle on the total shaft wall damage volume, the ore block size \(P\), the shaft diameter \(D\), and the inclined angle of the chute \(\alpha\) were fixed at 400 mm, 2 m, and \(60^{\circ}\), respectively, and the ore-pass dip angle \(\theta\) was set between \(50^{\circ}\) and \(89^{\circ}\). The ore passes were divided into four groups according to their depth \(H\) (60, 120, 180, and 240 m). Figure 10 presents the variation in total shaft wall damage volume \(Q_{\text{tol}}\) determined from Equations (18) and (19) with respect to the ore-pass dip angle \(\theta\) across ore-pass depths.  
Figure 9: Variation in the total shaft wall damage volume \(Q_{\text{tol}}\) with respect to ore-pass depth \(H\) across ore-pass dip angles.  
As shown in Figure 10, the ore-pass depth \(H\) has a certain influence on the \(Q_{\text{tol}}\)-\(\theta\) relation curve shape. \(Q_{\text{tol}}\) increases first and then decreases with an increase in \(\theta\), and the maximum point of the curve exists in the range of \(\theta\) from 60\({}^{\circ}\) to 80\({}^{\circ}\). The three curves for \(H\) = 120 m, \(H\) = 180 m, and \(H\) = 240 m have a maximum point in this range, and the curve for \(H\) = 60 m has two maximum points and one minimum point in this range. In addition, the greater the ore-pass depth \(H\), the greater the maximum value of the total shaft wall damage volume \(Q_{\text{tol}}\).  
Using Equations (21) and (22), it can be inferred that as \(\theta\) increases, the normal velocity of ore impacting the shaft wall decreases, while the tangential velocity increases. Additionally, based on Equations (12) and (16), as the normal and tangential velocities change, the ore indentation depth \(\delta\) decreases, and the wear length \(l\) increases. In the first half of the curve, the rate of increase in \(l\) is greater than the rate of decrease in \(\delta\). Conversely, the trend of the curve is reversed in the latter half. Therefore, \(Q_{\text{tol}}\) coupling with \(\delta\) and \(l\) manifests a tendency of initial increase followed by subsequent decrease.  
Furthermore, from Equations (19) and (20), it is evident that \(H\) influences the extremum of the \(Q_{\text{tol}}\)-\(\theta\) curve by affecting the collision frequency between the ore and the shaft wall. For the ore passes with \(H\) = 120 m, \(H\) = 180 m, and \(H\) = 240 m, the extremum points of the \(Q_{\text{tol}}\)-\(\theta\) curve correspond to \(\theta\) = 70\({}^{\circ}\) and \(\theta\) = 75\({}^{\circ}\), respectively. In the case of the ore pass with \(H\) = 60 m, as \(\theta\) changes from 65\({}^{\circ}\) to 70\({}^{\circ}\), \(Q_{\text{tol}}\) decreases due to a reduction in collision frequency. Subsequently, when \(\theta\) changes from 70\({}^{\circ}\) to 75\({}^{\circ}\), \(Q_{\text{tol}}\) increases due to an increase in \(\theta\).  
Therefore, the approach involves either minimizing the ore-pass dip angle \(\theta\) as much as possible to reduce the wear length \(l\) and, consequently, decrease the damage to the shaft wall, or approaching the ore-pass dip angle \(\theta\) of 90\({}^{\circ}\) to reduce the ore indentation depth \(\delta\), thereby diminishing the damage to the shaft wall.