###### Abstract  
In this study, we investigated the characteristics of abrasive erosion considering the material properties of abrasives and targets. An abrasive particle erosion model considering energy transfer due to hardness differences was developed based on energy conservation using the correlation between volume removal and effective kinetic energy. To obtain the effective erosion kinetic energy of an abrasive, an acceleration model was derived for the abrasive particles, including terms describing the properties of the abrasive and fluid. The applicability of the suggested model was verified by comparing the brittle erosion results  
the volume removal rate (\(V_{r}\)) is proportional to the applied erosion energy (\(E_{e}\)). Regression models originate from independent investigations of the functions of variables (\(f(x)\)), and reaction kinetic models are based on their similarities to the kinetic parameters of reactions, including the erosion probability (\(k_{a}\)), abrasive flow rate (\(\dot{m}_{a}\)), and reaction order (\(m\)). Figure 1 shows the impact of abrasives, plastic deformation, and microcracking (microfracture, intergranular cracking) that occurs in quasibrittle materials such as granite [15; 20; 21]. Energy conservation models have the advantage of considering volume removal due to both plastic deformation and microcrack fracture. In particular, an elastoplastic model [20; 21] considering energy conservation provides clear theoretical explanations regarding brittle erosion. This model uses the plastic deformation based on the model developed using [PERSON]'s model [28; 29]: it considers the threshold velocity of the impact (\(k\)) and the energy required to remove the target volume (\(\epsilon\)). This model also defines the removal volume (\(V_{r}\)) during microcrack fracture using the equation proposed by [PERSON] [30]: it calculates \(V_{r}\) by considering the stress-wave energy factor (\(f_{w}\)), the total stress-wave energy (\(W\)), and the fracture energy per unit area (\(\gamma\)) on which the stress-wave energy acts through the following equation:  
\[V_{r}=\frac{m_{p}(v_{t}-k)^{2}}{2\varepsilon}+\frac{f_{w}aW}{6\gamma}. \tag{1}\]  
Here, \(m_{p}\) is the mass of the particle, \(v_{t}\) is the terminal velocity of the particle, and \(a\) is the flaw distribution parameter. The elastoplastic model has been used to investigate erosion in other experiments [31] as well: it has also been applied to analyze the micromechanism of material removal in polycrystalline brittle materials [32] and to develop fracture mechanics models [33]. Although this model effectively represents plastic deformation through intergranular or microcrack erosion in terms of the fracture energy, the approach used in this model is complex and difficult to use. This is because it requires estimating the specific energy for material removal (\(\varepsilon\)) through experimental and theoretical calculations; moreover, the characteristics of the abrasive particles are not considered in the theoretical representations of erosion. Therefore, this study developed a simple but robust waterjet abrasive erosion model for rock-like material considering abrasive characteristics such as density, diameter, and hardness. The developed model was verified through comparisons to the elastoplastic model developed by [PERSON] and [PERSON] [20; 21] and numerical modeling results. Then, a parametric study was performed to explore the effect of the abrasive characteristics on waterjet erosion performance. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Abrasive Waterjet Models** & **Equations** & **References** \\ \hline Volume displacement models & \(dV_{r}=dV_{D}\) & [9; 19] \\ Energy conservation models & \(dV_{r}/dt=dE_{e}/dt\) & [20; 21; 22; 23] \\ Regression models & \(V_{r}=\alpha f(x)^{\beta}\) & [16; 24; 25] \\ Reaction kinetic models & \(V_{r}=k_{a}\dot{m}_{a}^{m}\) & [26; 27] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Overview of major erosion models.