Sandstone damage and acoustic emission characteristics under the cyclic loading and unloading of the intermediate principal stress of the true three-axis

The work aimed to study the damage and acoustic emission (AE) characteristics of sandstone under the cyclic disturbance stress during underground engineering excavation. Graded cyclic intermediate principal stress \begin{document}$ {\sigma }_{2} $\end{document} was tested using the rock-unloading test system of the true three-axis disturbance and the AE system. The mechanical properties of sandstone were studied under \begin{document}$ {\sigma }_{2} $\end{document} to prove its damage law and AE characteristics, and the effect of intermediate principal stress under true triaxial cyclic process were revealed. The results showed that the graded cyclic loading and unloading of \begin{document}$ {\sigma }_{2} $\end{document} had a greater influence on ultimate intermediate principal stress \begin{document}$ {\varepsilon }_{{\mathrm{2max}}} $\end{document} and the smallest influence on ultimate minimum principal stress \begin{document}$ {\varepsilon }_{{\mathrm{3max}}} $\end{document}. \begin{document}$ {\sigma }_{2} $\end{document} caused \begin{document}$ {\varepsilon }_{{\mathrm{2max}}} $\end{document} and loading and unloading moduli to increase first and then decrease with increased minimum principal stress \begin{document}$ {\sigma }_{3} $\end{document}. Cyclically loading or unloading \begin{document}$ {\sigma }_{2} $\end{document} caused unstable failure to sandstone. When minimum principal stress \begin{document}$ {\sigma }_{3} $\end{document} was small, sandstone unloaded at \begin{document}$ {\sigma }_{2} $\end{document} and damaged as it approached \begin{document}$ {\sigma }_{3} $\end{document}. When \begin{document}$ {\sigma }_{3} $\end{document} was large, sandstone loaded at \begin{document}$ {\sigma }_{2} $\end{document} and damaged as it approached maximum principal stress \begin{document}$ {\sigma }_{1} $\end{document}. Growth rate \begin{document}$ \beta $\end{document} of corresponding rock-octahedron stress \begin{document}$ {\tau }_{8} $\end{document} was similar during failure (\begin{document}$ \beta $\end{document}=1.1260). Characteristic parameter RA-AF of AE signals was analyzed. The failure mode of the sandstone samples gradually shifted from tensile shear failure to shear failure with increased \begin{document}$ {\sigma }_{3} $\end{document}. Besides, the loading damage variable of sandstone increased first and then stabilized as \begin{document}$ {\sigma }_{2} $\end{document} increased. The unloading damage variable showed a significant S-shaped trend of deceleration, acceleration, and re-deceleration.