## 1 Introduction  
Underwater rock-plug blasting is an important construction technique for resource development, flood control, and disaster reduction projects in the water conservancy and hydropower fields and is mainly applied when forming reservoirs or in lakes. Under conditions where it is not possible to empty reservoirs or build cofferdams, rock-plug blasting is a technique that can economically and safely allow construction of all kindsof tunnel inlets and outlets (Figure 1). The disposal of broken rocks is one of the key techniques for the success of rock-plug blasting. Generally, broken rocks produced in blasting are disposed by pre-setting a stone pit to avoid wearing down and causing damage to hydraulic facilities, including the downstream tunnel lining, valves, and downstream structures [1]. Therefore, studying the motion of broken rocks under blasting impacts and water scouring is important for the design of underwater rock-plug blasting. Many scholars have studied how to control fragmentation and harmful effects in underwater rock-plug blasting. From the perspective of blasting stress fields, [PERSON] et al. [2] expounded the penetration mechanism of rock-plug blasting under conditions involving single and double free faces. They found that the difference between the two conditions mainly resulted from the joint action of the clamping effect of the rock mass at the bottom of the rock plug and the reflected tensile stress waves at the free face. Based on one-dimensional transient flow theory and the thermodynamic characteristics of gas flows, [PERSON] et al. [3] established a numerical simulation model for the hydraulic transition process during air-cushion underwater rock-plug blasting. On this basis, they explored the hydraulic characteristics and influences of the blasting parameters in the blasting transition process under the action of the huge air mass and impact force after rock-plug blasting. [PERSON] et al. [4; 5] studied air-cushion underwater rock-plug blasting and conducted simulation experiments for field rock-plug blasting at the Xianghongdian pumped-storage power station. By using full-row borehole blasting and millisecond-delay blasting, [PERSON] et al. [6] were able to exert control over the harmful effects of rock-plug blasting, and they reduced the air shock pressure, shock pressure in water, and dynamic water pressure of plugs by combining the method with a water-filled air-cushion stone pit. [PERSON] et al. [7] carried out hydraulic model experiments on the motion forms of broken rocks during rock-plug blasting with different water pressures in the reservoir and inside and outside the tunnel. They also applied the experiment to the rock-plug blasting in the Changdian hydropower station expansion project. As is well-known, rock-plug blasting methods mainly employ concentrated charge blasting, the drilling blasting method, or combinations of the two. Before rock-plug blasting, it is generally necessary to conduct full-scale or half-scale prototype simulation tests near the location of the actual rock-plug blasting operations, which not only involves significant costs and difficulties in construction but also significant risks. Therefore, with the development of and improvements in software, researchers have used numerical methods to solve the problems in blasting engineering. Of course, numerical simulation also has limitations. For example, some calculation parameters need to use the results from model experiments; otherwise, simulation work cannot be carried out. In the 1980s, [PERSON] [8; 9] first proposed the numerical discontinuous deformation analysis (DDA) method for simulating the dynamic behaviors of discontinuous and blocky systems. Figure 1: Schematic diagram of rock-plug blasting. DDA can simulate the discontinuous deformation of rocks with large deformation and displacement in the blasting and throwing process. Based on the DDA algorithm, [PERSON] et al. [10] simulated the mechanical failure of a three-dimensional (3D) masonry structure under impact. [PERSON] et al.