## 3 Results and Discussion  
### Rock Fragmentation  
In this numerical analysis, the crack propagation and fragmentation behavior of rock were represented by the damage level of each particle. In rock cutting, damage and fragmentation of the rock occur in the area between adjacent cutters and in the area of contact with the cutters. At the point of contact with the pick cutter, the rock fragmentation and stress distribution are affected by the penetration depth, whereas the rock fragmentation pattern between adjacent cutters depend on the cut spacing. Figure 11 shows the changes in the fragmentation pattern associated with different cut spacings (at the penetration depth of 9 mm). The figures clearly show that the size of the fragmented area was affected by the cut spacing, and the fragmented area became larger as the cut spacing increased for the  
Figure 10: Rock cutting model used in this study. same penetration depth. The area was maximized at a specific cut spacing. The optimum spacing is defined as the point where the rock can be chipped to the maximum extent for a given penetration depth. The numerical simulations showed that the optimum cut spacings were found to be 20 mm (\(p\) = 5 mm), 21 mm (\(p\) = 7 mm), 27 mm (\(p\) = 9 mm), and 22 mm (\(p\) = 11 mm). Figure 12 shows the damage of rock particle that was accumulated by the interaction of adjacent cutters at the optimum cut spacing (i.e., in the relieved mode). The area between the two cutters, which was damaged by the first cutter, fails when it is damaged again by the second cutter. However, if the cut spacing was larger than the optimum cut spacing (unrelieved mode), the damage was limited to a certain range. Figure 13 shows the difference in the fragmentation pattern of the two cutting modes. Although the rock between adjacent cutters was cut completely by the interaction of the cutters in the relieved mode, a ridge remained between the adjacent cutters at the optimum cut spacing in the unrelieved mode, which means that the interaction between the cutters was inefficient to cut all of the rock particles between the adjacent cutters. Figure 11: The rock fragmentation pattern at different cut spacings. Figure 12: The damage accumulation due to interaction of adjacent cutters. Figure 14 shows the contour of damage of the cut surface for the rock model at different heights (\(p\) = 5 mm and \(s\) = 20 mm). The term \"height\" refers to the distance from the surface of a rock model. The crack in the vertical direction propagated up to 10 mm from the surface (as represented by the range of the damaged particles) when the pick cutter penetrated 5 mm. The cracks ranged from 10 mm to 24 mm with changes in penetration depth. [PERSON] et al. [11] noted that the FEM numerical models might need improvements in terms of the reality and accuracy; in the traditional FEM simulations, the rocks beneath the cutter tip usually cut off excessively in the vertical direction, while the chipping of the rocks between the cut spacing is usually less than real situation. This may be because that the plastic hardening and failure in different parts of the rock specimen are usually considered the same by assigning one function of the equivalent stress versus plastic strain for elastic-plastic mechanics of continuous materials. In this study, as described in Figure 8, the rock was modelled to behave according to different functions under compression (beneath the cutter tip) and tensile (chipping between adjacent cut lines) stresses. The results of rock fragmentation in numerical simulation indicated that the different behavior of the rock under compression and tensile stress was adequately simulated. It is noteworthy that the extent of cracking might depend on the both penetration depth of the pick cutter and the particle size of the rock model. Figure 14: Distribution of damage extent in vertical direction after cutting (cutting condition: \(p\) = 5 mm, \(s\) = 20 mm). Figure 13: The interaction between the adjacent cutters in numerical simulation at different cutting modes.