## 1 Introduction
Specific energy is defined as the energy (work) required to excavate a unit volume or mass of rock, and it is estimated as shown in Equation (1) [26]. \[SE=\frac{F_{c\_mean}\times l}{V} \tag{1}\]  
where \(SE\) is the specific energy (J/m\({}^{3}\)), \(F_{c\_mean}\) is the mean cutting force of a pick cutter (kN), \(l\) is the cutting distance (mm), and \(V\) is the volume of excavated rock (m\({}^{3}\)). The specific energy is influenced by the cut spacing, and it is minimized at a specific cut spacing. In mechanical rock excavation, the breakage of rock occurs due to the interaction between the adjacent cutters. Figure 3 shows that, if the spacing between adjacent pick cutters is too small, the adjacent pick cutters cannot make significant rock chips. If the spacing between them is too large, they do not make any rock chips. The interaction between adjacent cutters determines whether the cutting mode is relieved or unrelieved. In the relieved cutting mode, the interaction occurs between the cutters, i.e., the cut spacing is small or optimum, whereas in the unrelieved cutting mode, there is no interaction between the cutters, i.e., the cut spacing is large. Figure 3: The rock cutting pattern by two adjacent pick cutters according to the cut spacing to penetration depth ratio (modified after [7]). Figure 2: Discrete element method (DEM) simulation of a rock cutting by pick cutter. It has been shown that the cutting mode or setting a cut spacing significantly affects the cutting forces and specific energy [1; 3; 7; 8; 9]. Moreover, it has been shown that the cutting forces and specific energy in unrelieved cutting mode have higher value than those in relieved cutting mode [3; 26; 27; 28]. However, previous numerical studies [12; 13; 20; 21; 22; 23; 24; 25] introduced above have been performed for simple 2D analysis or unrelieved cutting mode of a single pick cutter. In these cases, therefore, the cutter forces and specific energy are not adequately evaluated or are overestimated. As introduced above, the simulation of rock cutting has been improved over time using different numerical methods and material models. These efforts allow us to overcome the limitations of experimental research in rock cutting problems. Although the numerical simulation techniques have been improved, the simulation of rock cutting is still considered to be a difficult task because the mechanisms by which fragmentation occurs and the behaviors of rock during the cutting process are complex. Numerical simulation of actual rock cutting phenomena still require many assumptions, and it is difficult to fully explain the behavior of rocks during the cutting process. Therefore, in numerical simulation of rock cutting, it is important to apply different numerical methods and numerous material models to identify the merits and limitations of each technique. Such numerical studies allow us to substitute the rock cutting tests or reduce the number of the tests that must be used to estimate the design parameters of mechanical excavators. As parts of these efforts, this study employed the smooth particle hydrodynamics (SPH) method to improve the traditional FEM analysis in rock cutting simulation with a three-dimensional code, i.e., AUTODYN-3D. The SPH method is a gridless (mesh free or meshless) technique for solving computational continuum dynamics problems, and it has several potential advantages over the grid-based Lagrange processor. Specifically, it avoids the problems caused in the traditional FEM by the excessive deformation of the mesh. Despite the many advantages of the SPH technique, its applicability in rock cutting simulation has yet to be evaluated. In this study, the Drucker-Prager (DP) yield model was used to simulate the brittle behavior of rock. In addition, the cumulative damage (CD) model were used to define the failure of material considering distinctive behavior of rock when subjected to compressive and tensile stresses.