# Calculation of Blasting Damage Zone Radius of Different Charge Structures in Burnt Rock
## 1 Introduction
[14] studied the radius of the crushing ring and fracture ring under the conditions of coupled and uncoupled charges in blasting on the basis of considering the actual three-dimensional complex stress state in rock and obtained the corresponding radius calculation formula. On the basis of cavity expansion theory, [PERSON] et al. [15] used the Mohr-Coulomb strength criterion as the constitutive model of rock near the blasting area, modified the velocity field relationship in cavity expansion theory and established the mechanical control equation of cylindrical charge blasting in rock. Combined with the quasi-static solution of the blasting elastic zone, the theoretical calculation formulas of the radius of the blasting cavity, crushing zone and radial crack zone were given. [PERSON] et al. [16] derived the stress time history expression on the rock-blasting failure interface based on the rock-blasting failure partition model [17]. [PERSON] et al. [18], in order to study the failure mechanism of the rock around the blast hole and accurately predict the range of the crushing zone, proposed an improved model for calculating the range of the crushing zone of borehole blasting. [PERSON] et al. [19] proposed a modified model for the size of the crushing zone around the hole in borehole blasting by considering the effect of ring compressive stress and cavity expansion. However, in the above research, the research  
Figure 1: Three stages of blasting process. was mostly based on conventional and homogeneous sandstone and conglomerate. In addition, the main way to perform the analysis and calculation of blasting engineering is to design and preview the blasting scheme by means of computer numerical calculation and image presentation [20; 21; 22; 23; 24]. At present, SHOTPlus (Suite 2023), JKSimBlast (2023), ANASYS (2022)/LS-DYNA (R14.0, FLAC (Fast Lagrangian Analysis of Continua, 1.3.3), PFC (Particle Flow Code, 6.0), CDEM (Continuum Discontinuum Element Method) and so on are the most classic and widely used blasting software at home and abroad. At present, PFC (6.0), ANASYS (2022)/LS-DYNA (R14.0) and FLAC (1.3.3) are the most widely used numerical simulation software in the field of blasting research. These three are based on three numerical simulation methods: the discrete element method, finite element method and finite difference method. Due to the different methods, there are advantages and disadvantages in the study of mine blasting [25; 26; 27]. However, in actual open-pit coal mine blasting engineering, there are often a large number of joint fissures, faults, bedding, schistosity and other weak structural planes in the rock mass. Under the influence of these weak structural planes, the blasting theory studied under ideal conditions (homogeneous rock) has deviations in practical blasting applications and cannot play a precise guiding role in engineering practice. With the deepening of the research, it has become accepted that the influence of the actual joint cracks in the rock mass on the propagation of stress waves must be considered. Given that the research object of this study was burnt rock, the influence of joints and fissures in the blasting process was obvious. Compared with the blasting process of a homogeneous rock mass, the expansion of radial cracks after burnt rock blasting is affected by joints and fissures, which cannot be better extended, resulting in a smaller range of fracture zone and no damage to the rock mass in the vibration zone [28]. When the stress wave propagates to the joint fissure, reflection and refraction occur, which increases the reflection of the stress wave, and, at the same time, aggravates the attenuation of the stress wave and the energy of the detonation gas, which leads to a large degree of fragmentation of the burnt rock in the area near the explosion source. When the stress wave cannot cause the radial movement of the rock, the rock will not be damaged again.