## 2 Cyclic Triaxial Loading and Unloading Experiments on Rock  
### Preparation of Samples  
The red sandstone utilized for the experiments was sourced from a consistent rock block, characterized by uniform textures and lacking significant structural or compositional variations. The red sandstone specimens were ground, polished, and machined to slices, of which the components and structures could be observed under a polarizing microscope. The outcomes of the experiments are presented in Figure 1. The specimen mainly contained ultra-fine-grained sand, some fine-grained sand, and a small amount of coarse-grained sand. The sandstone studied in this paper had high strength and strong cementation. The rock structure was inhomogeneous and showed low maturity and moderate weathering and alteration. The components in the rock mainly included quartz, rock debris, and a small amount of feldspar, with granular kaolinite filled between grains, which were probably formed by the alteration of argillaceous rocks. A small amount of argillaceous matrix was distributed between grains ([PERSON], 2018; [PERSON], 2018). The rock material was fashioned into cylindrical specimens conforming to standard dimensions, measuring 50 mm across and 100 mm tall, adhering to the mechanical testing standards for rock. The parallel alignment of the top and bottom surfaces was maintained to a precision of \(\pm\)0.02 mm. Prior to initiating the triaxial experiments, the specimens' longitudinal wave velocity was assessed using an RSM-SY6 ultrasonic testing device (Wuhan Sinorock Technology Co., Ltd., Wuhan, China), and the samples were further selected based on their weight. The fundamental physical properties of these specimens are detailed in Table 1.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Scheme 1**} & \multirow{2}{*}{**Serial No.**} & \multirow{2}{*}{\begin{tabular}{c} **Confining** \\ **Pressure/ (MPa)** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Longitudinal** \\ **Wave** \\ **Cycloity/\(\
u_{p}\)** \\ **(g/cm’)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Mass/** \\ **(g)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Density/** \\ **(g/cm’)** \\ \end{tabular} } & \multirow{2}{*}{**Scheme 2**} & \multirow{2}{*}{**Serial No.**} & \multirow{2}{*}{\begin{tabular}{c} **Confining** \\ **Pressure/ (MPa)** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Longitudinal** \\ **Wave** \\ **Cycloity/\(\
u_{p}\)** \\ **(m/s)** \\ \end{tabular} } & \multirow{2}{*}{**Mass/**} & \multirow{2}{*}{\
\begin{tabular}{c} **Density/** \\ **(g/cm’)** \\ \end{tabular} } \\ \hline \multirow{4}{*}{
\begin{tabular}{c} Conventional \\ triaxial \\ compression \\ tests \\ \end{tabular} } & I-1 & 1 & 4260 & 476 & 2.424 & & R-1-1 & 1 & 4369 & 475 & 2.419 \\  & I-1 & 1 & 4380 & 479 & 2.440 & R-1-2 & 1 & 4326 & 476 & 2.424 \\  & I-1-3 & 1 & 4201 & 468 & 2.384 & Triaxial & R-1-3 & 1 & 4128 & 472 & 2.404 \\  & I-2 & 5 & 4520 & 480 & 2.445 & CLU tests & R-2-1 & 5 & 4523 & 469 & 2.389 \\  & I-2 & 5 & 4432 & 481 & 2.450 & & R-2-2 & 5 & 4366 & 476 & 2.424 \\  & I-2 & 5 & 4125 & 467 & 2.378 & & R-2-3 & 5 & 4278 & 472 & 2.404 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Fundamental physical characteristics of the samples.