## 1 Introduction  
The mechanical excavation method has been used in many civil and mining projects. It is becoming increasingly popular due to its numerous advantages over the drill and blasting method in terms of safety, stability, high advance rate, and less environmental impact. The important design parameters of mechanical excavators are the arrangement of cutting tools, thrust, torque, and rotational speed of the cutterhead. These design parameters should be estimated carefully by considering the effect of the cutting conditions (i.e., penetration depth (\(p\)), cut spacing (s), and cutting angle) on the cutting force, cutting efficiency, and mechanical stability of a machine [1; 2]. The linear cutting machine (LCM) test is well-known as an accurate and reliable method for evaluating the design parameters of mechanical excavators [3; 4; 5; 6; 7; 8]. The LCM has the advantage that it can apply a realistic range of cutter loads without any scale effect during testing. Although the full-scale LCM test is the most reliable method for determining the design parameters of different machines, it usually requires full-size specimens of rock, which makes the test expensive and time-consuming [9; 10; 11]. Regarding these limitations, numerical simulation is a useful tool for estimating the cutting performance of a cutting tool and for understanding the rock-cutting mechanisms. A numerical simulation can provide information concerning the fragmentation of a rock, and it can be used to estimate the cutting performance of a cutting tool more quickly and less expensively than the LCM test. In addition, in a numerical simulation, it is possible to efficiently evaluate the effects of the different factors on the cutting performance of different cutting tools (e.g., roller disc and pick cutters). As shown in Figure 1, the finite element method (FEM) is one of the most commonly used methods for solving rock cutting problems [9; 12; 13]. However, in the FEM, the meshes are distorted significantly by the indentation and penetration processes, and excessive distortion and large deformation of the mesh may cause the simulation to miscarry [14; 15]. Erosion (element deletion) and re-meshing techniques have been used to prevent these problems. However, re-meshing is a time-consuming process [15], and the use of the erosion is challenging because it causes losses in the internal energy, strength, and mass of the numerical model [16], which can lead to decreasing the accuracy of the calculations [17; 18]. Hence, the erosion option has a significant effect on the results of a numerical simulation. Setting a certain erosion criterion requires calibration with experimental results, because the erosion criterion is not a material property or physics-based phenomenon, and it cannot be calculated quantitatively [17; 19]. Therefore, it may be useful to simulate a certain behavior or event with experimental observation, but the value is limited without experimental observation. Despite this weakness, the erosion option is an essential part of the Lagrangian (FEM) analysis. The discrete element method (DEM) provides more realistic simulation results than FEM does for the cracking behavior of rock (Figure 2). However, it is well-known that the DEM usually requires the use of a large number of elements, which leads to long computation time [20]. In addition, in order to determine the mechanical properties of rocks, it is necessary to determine the micro-parameters of the particles through repetitive preliminary analysis. Nevertheless, previous studies have simulated the rock cutting process successfully using the DEM [21; 22; 23; 24; 25]. [PERSON] et al. [20] introduced an FEM-DEM coupled numerical model to simulate the rock cutting process with a disc cutter to reduce the computation time of the DEM. Figure 1: Finite element method (FEM) simulation of a rock cutting by pick cutter. Specific energy (SE) is one of the most important factors in determining the efficiency and optimum condition of a cutting system and in estimating the cutting rate [7].