## 2 Extended Pick Failure Probability Assessment Approach  
### A Typical Cutting Cycle  
Figure 1 shows a schematic view of a typical cutting cycle in underground roadway development with a continuous miner. As an example, Figure 2 shows the locus of a pick tip on the cutting drum of a continuous miner over such a cutting cycle. A drum is normally equipped with a large number of picks which are attached to the drum on the external surface. The reason that only a pick is shown in Figure 1 is to make the figure clear. The roadway face can be divided into three sections: the roof rock, the floor rock and the coal seam. The cases where coal exists inside a rock section or rock bands are included inside the coal seam are not considered in this study. A 'full cutting cycle' is the complete process for cutting these three  
Figure 1: A schematic view of a typical cutting cycle in underground roadway development. sections sequentially. In this cycle, the drum first cuts into the face along the roof for a half of the drum to form the roof, then shears down to the floor, and finally cuts back to clear the floor. Therefore, a full cutting cycle can be divided into three stages: sump-in (cutting-into), shearing-down and cutting-back. In Figure 2, \(h_{t}\), \(h_{r}\) and \(h_{f}\) are respectively the height of the roadway, the thickness of the rock removed to form the roadway roof (roof rock) and the thickness of the rock removed to form the roadway floor (floor rock). The thickness of the roof rock and that of the floor rock are measured from the roadway roof and the roadway floor respectively. The parameters used to develop Figure 2 are shown in Table 1. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Unit** & **Value** \\ \hline Roadway height & mm & 3000 \\ Drum’s tip-to-tip diameter & mm & 1000 \\ Drum rotational speed & rpm & 50 \\ Drum advance speed & m/min & 3 \\ Drum sump-in depth & mm & 500 \\ Drum cutting-back distance & mm & 150 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters used to draw Figure 2.  
Figure 2: Locus of a typical pick tip in a typical cutting cycle in underground roadway development. Other information used to draw Figure 2 is as follows:  
A full cutting cycle involves multiple drum revolutions which are depicted by the locus of a pick tip in Figure 2. In order to show the drum advance directions more clearly, the locus of the pick tip in one drum revolution is divided into two equal parts: the half involving rock/coal cutting is marked in red and the other half is marked in green. The black line represents the face profile before this cutting cycle. The two blue curves respectively indicate the interface between the roof rock and the coal seam, and that between the coal seam and the floor rock. At the beginning of the face cutting cycle, i.e., the initial position, the circle formed by the cutting tips of the drum just touches the face profile before this cutting cycle and the pick tip in consideration is located at the top most position, which is the start point to measure the angular position of the pick in the sump-in stage. The aim of this study is to estimate the failure probability of a pick over a full cutting cycle. The pick failures in the following analysis have the same meaning as those defined in [11], that is, the sudden failure of the tip and/or body of a pick due to excessive bending or impact force acting on the pick tip. Other failure modes such as tip fatigue failure will be studied in the future. In this study, it is assumed that rock breakout is effective. When a pick is installed on a drum, it is randomly selected from a given batch of picks. Once being installed on the drum, the pick will be in service continuously until it has failed. From [11], it is known that the failure of a pick is a combination of its tip failure and body failure.