Abstract
Using spline interpolation to select proportions of similar materials, a comparative analysis of the fracturing behavior of sandstone specimens and similar material specimens was conducted through Brazilian splitting tests under multi-path loading. The study revealed that during stepwise loading, both sandstone and similar materials exhibited memory effects and plastic deformation. However, under constant velocity loading, the relationship between force and displacement in sandstone showed linearity after compaction. Employing MATLAB optimization algorithms for the inversion of acoustic emission event information, the distribution of fracture points, and the evolution of cracks were analyzed. The findings indicated that under stepwise loading, both sandstone and similar materials exhibited banded distribution of peak frequencies, with sandstone concentrated in the mid-low-frequency range and similar materials leaning towards the low-frequency range. The amplitude-frequency characteristics of acoustic emission signals suggested that initially, sandstone produced low-frequency, low-amplitude signals. As cracks developed, these signals gradually transformed into high-frequency, high-amplitude signals, ultimately leading to macroscopic failure. The ringing counts and b-values of sandstone displayed an approximate "W" shape distribution, with a subsequent decrease in b-values during final failure. In contrast, the acoustic emission counts were inversely related to b-values. Similar materials exhibited slightly more acoustic emission counts than sandstone, with relatively lower b-values. The crack development process of both sandstone and similar materials was confirmed through these observations. From the perspective of section initiation and local damage, sandstone and similar materials exhibited similar failure characteristics. The proportions of quartz sand: cement: water = 9:1:0.9 in similar materials demonstrated the most similar characteristics to sandstone in terms of mechanical loading, acoustic emission features, and failure morphology. This suggests that these similar materials can be used as substitutes for sandstone in analogous simulation experiments. The study provides theoretical support for understanding rock fracture mechanisms, offers guidance for the selection and proportioning of similar materials, and holds significance for predicting and controlling rock fracture behavior in engineering applications.