## 1 Introduction  
Investigating deep coal seams and rock formations typically involves in situ sampling followed by transportation to the laboratory for subsequent processing and the experimental analysis of rock mechanical properties. In the actual sampling, obtaining real cores of all rock formations is difficult and limited in number. Therefore, analogical methods are frequently employed to fabricate rock-like specimens for investigating the mechanical properties of rocks [1; 2; 3]. The material for making rock-like specimens is cheap and easy to obtain, and the material properties are stable. Consequently, it finds extensive application in the field of geotechnical mechanics [4; 5; 6; 7]. The production materials of rock-like specimens are generally composed of aggregate and cementing agents. Different proportions of aggregate and cementing agents are mixed and cast into standard specimens, and specimens with similar mechanical properties to coal rock are selected to replace coal rock [8; 9; 10; 11]. Currently, extensive experimental research has been conducted by domestic and international experts and scholars on rock-like specimens. [PERSON] et al. [12] prepared rock-like samples usingPortland pozzolana cement, mica sheet, and water. They carried out experimental and numerical studies on the mechanism of the micro-crack merging process of rock-like materials. [PERSON] et al. [13] studied the influence of particle size on the failure mechanism and fracture toughness of rock-like specimens. [PERSON] et al. [14] prepared rock-like specimens with different flaw configurations by 3D printing technology. They obtained the bearing capacity of rock-like specimens with single and double flaws and the mechanism of crack initiation and propagation. [PERSON] et al. [15] fabricated rock-like specimens with different proportions and conducted indoor uniaxial compression experiments to investigate the influence of the water-cement ratio and cement-sand ratio on the mechanical properties and failure modes of the specimens. [PERSON] et al. [16] investigated the impact of different thickness ratios of soft and hard interbedded layers, as well as different lithology combinations, on the mechanical properties of specimens subjected to diverse static loading rates. [PERSON] et al. [17] produced two kinds of transversely isotropic rock-like samples and compared the mechanical differences between the two kinds of rock materials by conventional triaxial compression experiments. Many scholars [18; 19; 20] have also used cement, gypsum, and other basic raw materials to prepare rock-like specimens with similar properties to the original rock by adjusting the ratio of different materials. As a non-destructive testing technology [21], acoustic emission (AE) is widely used to detect concrete, masonry, and rock [22]. [PERSON] et al. [23] monitored the acoustic emission signals of different kinds of concrete in the bending process and proposed some AE indices. [PERSON] et al. [24] proposed an innovative method for the structural health monitoring of metal components, based on the information entropy evaluation of AE data. [PERSON] et al. [25] studied the energy evolution and AE characteristics of rock under different cyclic loading and unloading paths. [PERSON] et al. [26] and [PERSON] et al. [27] carried out cyclic loading and unloading experiments on rock materials and discussed the Kaiser and Felicity effects. [PERSON] et al. [28] conducted uniaxial compression experiments on different types of rocks and conducted AE monitoring simultaneously. It was found that the AE response of rocks is closely related to the damage and fracture process. [PERSON] et al. [29] analyzed the AE generated during the compression fracture process of brittle rocks in detail and calculated the improved b value. [PERSON] et al. [30] combined the digital image correlation (DIC) method and AE technology to study the evolution law of rock deformation localization. In laboratory studies, it is usually impossible to obtain an unlimited number of rock samples.