# Simple Approach for Evaluation of Abrasive Mixing Efficiency for Abrasive Waterjet Rock Cutting
## 1 Introduction  
Abrasive waterjets are used to cut target materials using high-velocity abrasives by accelerating them with high-pressure and high-velocity water. Although such waterjets are mainly used for cutting metals and ceramics, their geotechnical applications such as rock cutting, excavation, asphalt resurfacing, pavement adhesion improvement, and road stripe removal have recently increased [1, 2, 3]. In particular, since the cutting force can be controlled, it is possible to demolish concrete without damaging the internal steel reinforcement [4, 5]. In addition, abrasive waterjets are suitable for urban construction because of their low noise and vibration compared to those in mechanical excavation (e.g., rock blasting and breaking). However, the cost of the abrasive reaches approximately 60% of the total operation cost [6]. Efforts have been made to evaluate the effects of the abrasive waterjet parameters on the cost [7, 8, 9] and to recycle abrasives after recollection and drying [10, 11]. The abrasive cost can be reduced by using the optimum abrasive flow rate (AFR) and by using a system design with a high mixing efficiency. The optimum AFR has been estimated at the maximum cutting rate. If 80% of the maximum cutting rate is achieved with 50% of the optimum AFR, the economical AFR is 50% of the optimum AFR. The cutting energy of an abrasive waterjet is a function of the AFR, and the system design determines its characteristics [12, 13]. The optimum AFR is a function of the impact frequency, the terminal velocity, and the kinetic energy of the abrasive through the relationship between the mixing efficiency and energy [14, 15]. Meanwhile, optimizing the focus shape improves the mixing efficiency, where the momentum of the water is transferred to the abrasive [16]. In principle, the length and diameter of the focus at whichthe abrasive is mixed are the main mixing and acceleration variables that affect the cutting energy and the optimum AFR [17; 18; 19]. In other words, an economical system design is achieved through an optimal combination of focus length, focus diameter, and orifice diameter [20]. Therefore, evaluation of the mixing variables is required to enable mixing efficiency adjustment. The focus keeps the abrasive in the water jet during acceleration, but abrasive friction with the inner surface of the focus and abrasive particle collisions reduce the mixing efficiency [19]. Abrasive experience breakdown (i.e., disintegration) is caused by friction and collisions [21]. Abrasive breakdown increases with increasing pump pressure, AFR, or focus length [11]. These relations indicate that the abrasives are involved in the damping mechanics depending on the abrasive density in the focus [19; 22]. The water flow rate (WFR)-AFR ratio and the focus geometry (e.g., diameter and length) affect the abrasive breakdown, thereby reducing the abrasive mixing efficiency. Thus, AFR and waterjet system optimization begins by determining the characteristics of the mixing variables (e.g., WFR, AFR, and focus geometry). The orifice diameter and pump pressure determine the WFR [23], and the focus diameter and WFR are major factors affecting the cutting quality [17]. The larger the focus diameter, the larger the jet diameter, which affects the groove frequency and striation on the cutting surface, resulting in large changes in the surface profile amplitude [24]. Analysis of variance on the effects of the focus and orifice has shown that 98% of the cutting width and roughness results from the focus diameter and the AFR [18; 25; 26]. The abrasive mixing efficiency is the characteristic that is the most strongly affected by the AFR, and the larger the focus diameter, the higher the optimum AFR [15]. Moreover, the larger focus diameter reduces the energy that accelerates the abrasive [27]. As a result of evaluating the overall effects of the WFR and focus diameter, the economically optimum ratio between the orifice and focus diameter was determined to be three times [28].