# Calculation of Blasting Damage Zone Radius of Different Charge Structures in Burnt Rock
## 1 Introduction  
Quantitative blasting technology, careful blasting construction and fine blasting management can effectively control the process of explosive energy release and rock crushing, as well as meet the requirements of open-pit mines for controllable, safe, and economical blasting processes and effects. At the same time, the application of blasting technology in open-pit mines efficiently reduces the labor intensity of workers and accelerates the advancement of engineering tasks. It is an important measure to realize the rapid development of open-pit mines and even all economic mining constructions. The blasting of a rock mass in an open-pit mine is a complex dynamic process, which involves the high-speed detonation of explosives, dynamic expansion of the explosion cavity, nonlinear deformation of rock under the explosion load and so on [1]. Taking the explosive explosion in an infinite rock mass as an example, the dynamic process of rock-blasting failure can be divided into three stages: the explosion shock wave action stage, explosion stress wave action stage and explosion gas action stage. The first stage is the stage of explosion shock wave action. The rapid reaction of explosives propagates detonation waves in explosive materials, and the detonation velocity of most high-energy explosives is 1500-9000 m/s [2]. The explosion pressure caused by an explosive's explosion is usually between 1 GPa and 1 GPa [3], which is far beyond the compressive strength of the surrounding rock, resulting in the large nonlinear deformation and failure of surrounding rock similar to a fluid, and then forming a crushing zone with a range of about 1.5 to 4 times the radius of the explosive [4]. The second stage is the stage of the explosion stress wave. When the explosion shock wave attenuates into a stress wave, the radiallypropagating compressive stress wave propagates outward, and the associated tensile stress is generated in the tangential direction. Because the dynamic tensile strength of rock is much lower than the dynamic compressive strength, the tangential tensile stress can form radial cracks. With the further propagation of the explosion stress wave, when the intensity of the stress wave produced by the blasting is attenuated to the point where the rock cannot form permanent deformation, a far-field elastic vibration zone is formed [5]. The vibration wave propagating in this zone is measured to have a constant wave velocity, which is considered to be elastic [6]. The third stage is the stage of detonation gas action. The gas product produced by the explosion of the explosive expands dynamically and penetrates into the initial crack formed by the stress wave, which makes the crack expand further. Some studies suggest that the detonation gas forms a quasi-static stress field similar to the stress wave action [7]. The explosive blasting process is described in the three stages shown in Figure 1 below. According to the different characteristics of rock failure, [PERSON] and [PERSON] [8] first proposed in 1971 that after the explosion of explosives, a rock-blasting failure zoning model with a crushing zone, usually divided into a crushing zone, fracture zone and vibration zone, will be formed around the blast hole, as shown in Figure 2. This model has been recognized by the majority of scholars and has been continuously developed and improved [9; 10; 11]. The typical partition model of rock-blasting failure is shown in Figure 1[12]. The quantitative calculation of the crushing zone and fracture zone is of great significance and function for the study of the blasting fracture mechanism, explosive performance and blasting technology. Many scholars carried out a lot of fruitful research work: [PERSON] et al. [13] proposed a new formula for calculating the radius of the fracture zone by considering the effect of the shock wave and the existence of a crushing zone. [PERSON] et al.