## 1 Introduction  
In the 21 st century, with the increasing demand for human development, the burial depth of underground engineering has gradually increased, and practices and theories of underground engineering such as mining and tunnels have achieved unprecedented development. However, with the increase in burial depth, engineering disasters are also increasing, causing a large number of casualties and property losses. Engineering disasters have seriously restricted the development of underground engineering [1, 2]. The main cause of engineering disasters is rock fracture, where a large number of fractures gather and connect under engineering disturbances, ultimately forming engineering disasters. Therefore, studying the spatial evolution process of rock fractures is of great significance for preventing engineering disasters. The internal fractures in rocks often undergo a process of dimensional reduction from disorder to order. In the initial stage of loading, a small number of fractures are generated within the rock. As external forces increase, fractures continue to be generated, extended, and accumulated, forming multiple fracture clusters; with further increase in external forces, the largest fracture cluster expands and eventually forms a through-going fracture surface, leading to the failure of the specimen. Compared with other fracture clusters, the fracture cluster that forms a through-going fracture surface has a greater impact on the failure of the specimen. Currently, there is limited research that is specifically focused on the classification of fracture clusters based on spatial information. At present, there are various monitoring technologies that can monitor the evolution process of internal fractures in rocks, such as CT, AE, etc. AE is an advanced technique with proven real-time monitoring abilities. AE is not only used in laboratory research, but is also widely used in engineering practices [3; 4]. Therefore, numerous scholars have conducted research on rock failure processes based on AE studies. [PERSON] et al. [5] researched the relationships between the stress, AE and crack evolution process, and found that when white patches or macro cracks were initiated, the stress-strain curve dropped and the accumulated AE count curve increased. [PERSON] et al. [6] constructed the amplitude-frequency spectra of AE for four successive time instants to analyze the time changes in the structural parameters of the rock. [PERSON] et al. [7] analyzed multifractal characteristic of pauses between acoustic AE and the energy distribution functional forms of the AE signal. Three-dimensional AE monitoring allows to locate spatial fractures in real-time, visually display the distribution of fractures, and document the spatiotemporal evolution of fractures. Therefore, many scholars have conducted research on the evolution of internal fractures based on the spatial distribution of AE. [PERSON] et al. [8] researched the micro mechanisms of granite fracture during three-point bending and found that during three-point bending of granite, AE events are localized in the zone of formation of the future main crack. [PERSON] et al. [9] used AE to analyze sandstone and obtained the spatial distribution of micro-cracks formed due to uniaxial compression. [PERSON] et al. [10] analyzed the spatial distribution of hypocenters of AE signal sources, and revealed that the transition to correlated defect formation occurs in some regions in the case of continuous electrical exposure, despite the accumulation of almost uniform spatial defect. [PERSON] et al. [11] explored the development mechanism of cracks in the process of rock failure using AE and found that by fully analyzing the characteristics of AE signals in the time and frequency domain, the time and conditions of producing large cracks can be accurately and efficiently determined.