Investigating the Comprehensive Index of Acoustic Emissions and Fractal Characteristics of Damage of Red Sandstone Based on Information Entropy

In this study, the authors combine the acoustic emission (AE) technique with the Brazilian splitting test and the angled die shear test to monitor the development of cracks in red sandstone specimens under compression–tension and compression–shear conditions to identify the mechanism of propagation of tensile and shear failures during the process of damage to rock. We use this to propose a method to analyze the comprehensive index of fracture-induced AEs of red sandstone based on information entropy. A comprehensive index to characterize the tensile and shear failures of rock was obtained by quantifying the entropy weights of the characteristic parameters of AE and their laws of evolution were analyzed. Areas for the classification of different cracking mechanisms of rock were established based on the Box–Cox transform, and the fractal features of crack development under compression–tension and compression–shear conditions were analyzed by using the Grassberger and Procaccia (G–P) algorithm. The results showed differences in the entropy of the characteristic parameters of red sandstone in cases of tensile and shear damage, with the rise time and energy recording the maximum entropies, respectively, and the amplitude yielding the minimum entropy. The comprehensive evaluation indices for tensile failure \(\xi_{t}\) ${\xi }_t$ and shear failure \(\xi_{\tau }\) ${\xi }_{\tau }$ confirmed the existence of at least two mechanisms of deformation-induced damage—tensile fracture and shear slip—in the process of damage to the rock. The curve of evolution of the fractal dimensions \(D_{t}\) $D_t$ and \(D_{\tau }\) $D_{\tau }$ of compression–tension and compression–shear, respectively, followed the law of continuously decreasing dimensions, and their turning points reflected the change in crack development in the rock.