## 3 Results and Discussions  
### Cutter Force  
When a disc cutter cuts rock, three directional cutter forces (i.e., normal, rolling, and side forces) act on the disc cutter. The normal and rolling forces are considered as main force components to evaluate the required thrust and torque of TBM during rock excavation. It has been proven that cutter forces are affected by rock strengths [31; 36; 37]; therefore, UCS and BTS are basic input parameters used to estimate cutter forces in the empirical TBM performance prediction model. Figures 3 and 4 show the relationship between cutter forces (MNF (mean normal force) and MRF (mean rolling force)) and rock strengths (UCS and BTS). The origins of the rocks are marked with different colors. The results show that the cutter forces slightly increased with increasing UCS and BTS, regardless of the rock origin. This trend is consistent with the results of previous studies [31; 36; 37]; however, the relationships shown in Figures 3 and 4 were somewhat scattered. Because the dataset included cutter forces from different penetration depths and cut spacings, it was reasonable for this study to show the effects of cutting conditions on cutter forces. This fact is supported by previous studies [30; 31; 36; 37; 38]. Figure 3: Relationship between mean normal force and rock strengths: (**a**) UCS; (**b**) BTS. Figure 2: The Cechar abrasivity test system used in this study: (**a**) photo; (**b**) schematic drawing (1 is weight, 2 is pin guide, 3 is steel pin, 4 is specimen, 5 is vice sled, 6 is hand crank) (after [35]). To diminish the effect of the penetration depth, the boreability index (BI) can be used for the quantitative analysis of the relationship between rock strengths and cutter forces. The BI is usually called the field penetration index (FPI). The BI is calculated as the ratio of the normal force to the penetration depth, while the FPI is calculated as the ratio of the thrust per each cutter to the penetration depth per revolution [37, 39]. Figure 5 shows the relationship between the BI and cutter forces. The results show that significant linear relationships were found in the case of the normal force, as shown in Figure 5a. However, the rolling force had a poor correlation with the BI, as shown in Figure 5b. The rolling force is usually estimated based on the empirical relationship between the normal force and the rolling force. This relationship can be expressed as the concept of the cutting coefficient (CC), which is defined by the ratio of the rolling force to the normal force. As shown in Figure 6a, the average CC for the Korean rock types included in this study was 8% on average, and the CC range was consistent with the findings of previous studies [30, 37]. However, as shown Figure 6b, there are no significant relationships between CC and rock strengths in the database. The result is not consistent with the finding from the previous study [37]. Figure 4: Relationship between mean rolling force and rock strengths: (**a**) UCS; (**b**) BTS. Figure 5: Relationship between cutter forces and boreability index: (**a**) normal force; (**b**) rolling force. Based on these relationships, we attempted to find correlations between the normal forces and brittleness indices. Figure 7 shows that the brittleness indices were correlated with the normal cutter force, and that the prediction bands (upper and lower bounds) were also obtained under a 95% confidence level. Further, the results show that B1 had the best correlation with the MNF compared to the other brittleness indices. The R2 values of B1, B2, B3, and B4 were 0.50, 0.37, 0.41, and 0.18, respectively. It was presumed that the differences in these correlations were affected by the Brazilian tensile strength of the rock types; in the case of B2, the effect of the tensile strength on the brittleness values were not significant compared to B1 because the UCS was usually 10-20 times larger than the BTS. Otherwise, B5 was inherently different from B1, according to the definition.