# Simple Approach for Evaluation of Abrasive Mixing Efficiency for Abrasive Waterjet Rock Cutting
## 5 Conclusions  
The purpose of this study was to evaluate the mixing characteristics of abrasive waterjet rock cutting. The dependence of the rock cutting performance on the mixing variables, such as the abrasive flow rate, the water flow rate, and the focus geometry, was experimentally tested. To evaluate the mixing variables comprehensively, the chances of abrasive-abrasive and abrasive-focus inner surface collisions were defined in terms of the DBP in the focus. In addition, as the cutting energy and experimental results were expressed as functions of the DBP, the characteristics of the mixing variables were assessed. The results of this study can be used for geotechnical application such as improved abrasive waterjet rock excavation. The following are the major findings and contributions of this study:  
* The abrasive mixing characteristics were derived based on the mixing variables, such as the WFR, the AFR, and the focus geometry. To express the complex effects of the variables, a mixing efficiency model was developed considering the chance of collision  
Figure 12: Effect of the focus diameter on the cutting depth owing to WFR.  
Figure 13: Effects of the focus diameter on the cutting depth owing to the AFR.  
by defining the concept of the DBP, which represents the abrasive density in the focus. This model comprehensively considers the WFR, the AFR, the focus diameter and length, and the abrasive mass and diameter.
* As a result of the effects of the mixing variables, the cutting depth was experimentally obtained. It was found that using a large focus diameter or water flow rate, a higher mixing efficiency yields a greater cutting depth. The AFR affects the terminal velocity and mixing efficiency, so excessive input reduces the cutting depth. The higher the mixing efficiency, the higher the optimum AFR.
* By expressing the relationships between the experimental results and input energy as functions of the DBP, the effects of the mixing efficiency on abrasive waterjet rock cutting could be calculated. The smaller the DBP, the higher the energy required to cut a unit depth of the rock. In other words, a high energy input was required owing to the low mixing efficiency.
* The developed model demonstrated that, with a high water flow rate, the cutting efficiency was low compared to the energy input. In addition, high water flow rates indicated the optimum AFR at small DBPs. At water flow rates of over 50 mL/s, the optimum AFR was estimated to occur with a DBP of less than 0.6 mm.
* The cutting depth model was proposed based on the empirical relationship between the experimental cutting results and the mixing variables. The mixing efficiency was considered by indicating the chance of collision in terms of the DBP. The proposed model also demonstrates the effects of the mixing variables. In particular, the changes in the optimum AFR according to changes in the focus diameter are revealed. By using this model, it is possible to estimate the optimum AFR and cutting performance with minimal experimentation.  
Conceptualization, G.-C.C. and Y.C.; formal analysis, Y.C. and T.-M.O.; investigation, Y.C. and H.-J.H.; writing-original draft preparation, Y.C. and H.-J.H.; writing--review and editing, Y.C. and T.-M.O.; supervision, G.-C.C. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
This work was supported by a National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) (No. 2017R1A5A1014883) and the Basic Research Project of the Korea Institute of Geoscience and Mineral Resources (KIGAM, GP 2020-010) funded by the Ministry of Science and ICT, Korea.  
The authors declare no conflict of interest.