# Fractal Behavior of Size Distribution and Specific Surface Area of Blasting Fragments
###### Abstract
[22] employed digital image processing techniques to study the surface texture of sediment particles, such as roundness and angularity. [PERSON] et al. [23] utilized charge-coupled device cameras and 3D laser scanners to study the angularity of coarse aggregates. As mentioned previously, the existing methods can only characterize the shape features of particles within a certain particle size range [24], whereas the particle size and shape of blasting fragments vary widely [3; 7], posing challenges to the characterization of their shape properties [25; 26]. Fractals allow the quantification of seemingly chaotic and randomly distributed phenomena and behaviors [27]. Research indicates that the defects, shapes, strength, deformation, and energy consumption of rock and soil materials all exhibit statistical self-similarity at certain scales, i.e., fractal characteristics [28]. Fractals have become important tools in rock mechanics research. The fractal dimension is the primary parameter for describing fractals [28] and has been widely used in various applications, such as mineral particle morphology analysis [29; 30], rock damage assessment [31], and fragmentation evaluation [32]. During the process of rock fragmentation, the fractal dimension can continuously change at different resolutions (different lengths of the measuring stick), allowing the target object to exhibit dual or multifractal characteristics [27]. Extensive studies on fragmentation phenomena have indicated that the fractal dimension of rock fragmentation typically falls between 2.0 and 3.0 [28]. In previous research, the fractal dimension was often fitted according to the fragment size distribution to assess the fragmentation quantitatively [33; 34]. In summary, as blasting fragments are typical irregular particles, most previous studies focused on characterizing the shape features of rock particles within a small particle size range. Limited research exists on the shape and fractal characteristics of blasting fragments across the entire particle size range. Furthermore, SSA is a useful indicator for calculating rock fragmentation energy, as it comprehensively reflects particle size and shape characteristics [3]. Neglecting the shape properties of blasting fragments would inevitably reduce the accuracy of SSA calculations along with the accuracy of evaluating the explosive energy utilization efficiency [35; 36; 37]. Thus, fractal theory must be used to study the shape characteristics of blasting fragments across the entire particle size range. In this study, seventeen field blasting tests at four quarries and indoor measurements of shape parameters of randomly collected blasting fragments were performed. Image processing techniques were employed to obtain blasting fragmentation distribution for each test. Using fractal theory, the fractal dimensions of the particle size distribution and fragmentation were calculated, revealing the multifractal characteristics of rock blasting fragmentation and clarifying the probability of rock blasting fragmentation. Moreover, a predictive formula for the SSAs of blasting fragments was established using the fragmentation fractal dimension.