# Comparison Study on Coarseness Index and Maximum Diameter of Rock Fragments by Linear Cutting Tests
## 1 Introduction  
Mechanical excavation equipment, such as tunnel-boring machines (TBMs) and road-headers, are widely used for underground construction in the civil and mining engineering fields, and the demand is continuously increasing. In mechanical excavation, excavation efficiency is an important factor, and specific energy (\(SE\)) is a representative indicator for this purpose. The \(SE\) refers to the energy consumed to excavate a unit volume, and it has an inverse relationship with excavation efficiency. The SE is affected by cutting conditions, such as the penetration depth (\(p\)) and spacing (\(s\)). Moreover, the \(SE\) decreases as the cutting depth increases, reaching a constant value at a specific depth (Figure 1a) [1; 2; 3]. At the same penetration depth, if the spacing is too narrow, the \(SE\) increases because of overcrushing. However, if the spacing is too wide, the \(SE\) increases because no interaction occurs between the cutting grooves (Figure 1b) [4; 5]. Generally, the effect of spacing is greater than that of penetration depth [6]. The rock fragments generated by excavation are also affected by the cutting conditions. [PERSON] [8] reported that the rock fragment size increases with spacing and excavation efficiency. [PERSON] [9] found that size of the rock fragments follows a Poisson distribution, and rock chips are limited by penetration depth and spacing. [PERSON], et al. [10] reported that the excavation efficiency increases as the size of the rock fragment increases and that the rock chips become long and flat as the thrust increases. [PERSON], et al. [11] found that the size of a rock chip depends on the space between the two adjacent cutting grooves. [PERSON], et al. [12] reported that size of the rock fragments follows a normal distribution and increases with the penetration depth. Therefore, a considerable number of studies have been conducted to obtain the excavation efficiency from rock fragments, primarily using the particle size distribution of rock fragments. [PERSON] [1] conducted a rock-cutting test using a drag-type cutting tool and analyzed rock fragments using the coarseness index (_CI_), a nondimensional value representing the size distribution of rock fragments. The results showed that the _CI_ increased slowly with narrow spacings and rapidly with wide spacings as the penetration depth increased. [PERSON], et al. [13] analyzed rock fragments generated by conical and chisel picks with respect to spacing. The _CI_ value increased as the spacing increased. [PERSON], et al. [14] performed a linear cutting test using a disc cutter and a chisel pick. Regardless of the rock type, _CI_ and _SE_ had an inverse relationship, and _CI_ reached the maximum value at the specific ratio of spacing to penetration depth (\(s/p\) ratio) where the _SE_ was the minimum. Recently, studies have been conducted to obtain excavation efficiency based on particle size parameters obtained by mathematical calculations. [PERSON] and [PERSON] [15] found that the size distribution of rock fragments conformed to the Rosin-Ramler distribution, and the absolute particle size (\(d^{\prime}\)) of Rosin-Ramler was related to the size of the rock chip. [PERSON], et al. [16] analyzed the rock fragments of dry and saturated sandstone cut using a disc cutter. Their results indicated that _CI_ and \(d^{\prime}\) had an inverse relationship with _SE_, and the _CI_ and \(d^{\prime}\) of dry rock were always higher than those of saturated rock. [PERSON] and [PERSON] [17] performed a linear cutting test using a pick cutter. The \(d^{\prime}\) value had a linear relationship with the median particle size (\(d_{50}\)) and the midpoint of the distribution size, _CI_ had a linear inverse relationship with _SE_, and the cutting force increased as the size of the rock chip increased. [PERSON], et al. [18] found that \(d^{\prime}\), \(d_{50}\), and mean particle size (\(d_{\text{MPS}}\)), which is the arithmetic average of all particle sizes in a sample, had similar relationships with SE.