## 3 Model Verification
### Numerical Analysis for Single Abrasive Erosion
#### 3.2.1 Numerical Model Details  
Numerical analyses were conducted for the same cases as those in the theoretical tests (Table 2). LS-DYNA provides many material models for concrete, rock, and soil, including Brittle Damage, Johnson-Holmquist concrete, Concrete Damage Rel3, and Continuous Surface Cap Model (CSCM). To simulate plastic deformation and microcrack failure of the target simultaneously, CSCM was used as the damage model. In CSCM, crack failure occurs via brittle damage when the energy exceeds the threshold, due to tensile pressure [46]. This model is suitable for high-stress, large-strain conditions such as those present in crater formations, concrete spalling, and impact-induced fracture inside concrete [47]. Therefore, microcrack generation using a conical pick in rock [48], the unloading characteristics of rock [49], and the smeared crack approach for concrete damage progression under repeated impact [50,51] have been simulated using the CSCM. The properties of the target were measured and computationally modeled via numerical analysis (unconfined compressive strength: 236 MPa; tensile strength: 11 MPa; Young's modulus: 56.5 GPa; Vickers hardness: 980 kg/mm\({}^{3}\)) (Figure 5 and Table 3). As the CSCM has many input parameters, the properties of the rock-like target were repeatedly adjusted and combined to obtain the same properties as those of the actual granitic rock specimen. To prevent breakage of the abrasive particles upon collision, an elastic model was used for modeling the abrasive particles.  
During collision between a spherical abrasive particle and a box-shaped target rock at normal incidence, the entire model is symmetrical about the \(x\) and \(y\) axes; hence, a 1/4 symmetry physical model could be used. In addition, it was possible to reduce the computation time by increasing the meshing density of the impact area and widening the gap between the nodes at the boundary (Figure 6). To reduce the boundary effect, the target geometry was established at eight times the radius of the largest abrasive particle (i.e., \(d_{p}/2=0.172\) mm), and the nonreflecting boundary condition was set on an outside surface in the model. The damage constitutive law and erosion criteria were used for evaluating nonlinear rock erosion, crack extension, and fragment formation upon contact [43,48].  
Figure 5: Tensile and compressive strengths of the granitic rock target used in the numerical analyses.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \begin{tabular}{c} **Density** \\ **(kg/m\({}^{3}\))** \\ \end{tabular} & \begin{tabular}{c} **Compressive** \\ **Strength** \\ **(MPa)** \\ \end{tabular} & \begin{tabular}{c} **Shear Strength** \\ **(MPa)** \\ \end{tabular} & \begin{tabular}{c} **Tensile** \\ **Strength** \\ **(MPa)** \\ \end{tabular} & \
\begin{tabular}{c} **Young’s** \\ **Modulus** \\ **(GPa)** \\ \end{tabular} &
\begin{tabular}{c} **Vickers** \\ **Hardness** \\ **(kg/mm\({}^{3}\))** \\ \end{tabular} \\ \hline
2650 & 236 & 23 & 11 & 56.5 & 980 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Properties of the target (granite) used in the numerical analyses.  
The \"Eroding Surface to Surface\" and \"Automatic General\" keywords were applied for erosion through segment-based contact between the abrasive and target.