# Experimental Study of Material Proportioning for Similar Modeling of Brittle Rocks
## 5 Proportioning and Validation of Brittle Rock Analogs
### Failure Modes and Acoustic Emission Characteristics  
In the proportioning tests for analogous materials for brittle rock, it was essential not only to consider the material's physical and mechanical parameters but also to ensure that the specimen's failure mode and acoustic emission characteristics reflected the typical deformation behavior of brittle rock. The mechanical tests were conducted on the analogous material specimens prepared, and the final failure modes of the specimens under different loading conditions are shown in Figure 12. Under uniaxial compression, two prominent macroracks formed along the loading direction in the specimen. In the initial loading phase, no microcracks appeared on the specimen's surface. As loading approached the specimen's peak strength, microcracks began to nucleate and cluster in the upper-mid portion of the specimen, rapidly propagating to trigger a sudden failure. The specimen primarily exhibited tensile fracturing, with pronounced brittle characteristics. Axial splitting failure is a typical fracture mode of brittle rocks under uniaxial compression, indicating that the prepared specimen exhibited fracture behavior consistent with that of brittle rock. In the Brazilian splitting test, a macroscopic crack formed along the specimen's diameter in the loading direction, initiating at the specimen center and rapidly extending toward the loading points at each end. This behavior aligns with the fundamental assumptions of the Brazilian splitting test. The fracture surface displayed a rough texture without any frictional scoring, indicating that tensile failure occurred in the specimen. The stress-strain curve and acoustic emission characteristics of the analogous material specimens under uniaxial compression conditions are shown in Figure 13. In the initial loading stage, a small number of acoustic emission (AE) events occurred due to the compaction effect. As the axial load increased, at around 342 s, a cluster of AE events appeared, indicating the initiation and coalescence of internal microcracks. At this point, both the number of AE events and the AE energy showed a significant increase. As the stress approached the peak load, the number of AE events increased exponentially, indicating the rapid propagation and nucleation of internal cracks. Eventually, the specimen underwent instability failure. For comparison, the typical stress-strain curve, acoustic emission characteristics, and failure mode of Jinping marble under uniaxial compression [34] are shown in Figure 14. During the pre-peak stage, the Jinping marble exhibited two concentrated bursts of acoustic emission (AE) events. The first AE burst corresponded to the initiation and nucleation of microcracks within the rock, while the second AE burst corresponded to macroscopic failure, displaying a distinct exponential growth trend. Acoustic emission monitoring is an effective method for analyzing the evolution of microfractures within specimens. Before reaching the peak load, both types of specimens exhibited similar concentrated bursts of AE events, indicating that the analogous material specimens and the natural Jinping marble underwent comparable processes of microcrack initiation, propagation, and nucleation during loading. Ultimately, both types of specimens experienced axial splitting failure, demonstrating that the analogous material specimens effectively replicate the fracture behavior of the natural Jinping marble. This suggests that the two materials share a similar brittle fracture mode. Figure 12: Failure mode of the analogous material specimens: (**a**) uniaxial compression test and (**b**) Brazilian splitting test. Figure 13: Uniaxial compression test of the analogous material specimens: (**a**) stress–strain curve and (**b**) acoustic emission characteristics.