## 2 Experimental Methods
### Experimental Equipment and Procedure  
The experimental process is divided into three stages: the preparation stage, the sandstone soaking stage, and the uniaxial loading stage. (1) Preparation stage: the sandstone is processed into cylindrical specimens with dimensions of e50 mm \(\times\) 100 mm, as shown in Figure 3a. After processing, the red sandstone is placed into a drying oven, heated at a rate of 4 \({}^{\circ}\)C/min to 105 \({}^{\circ}\)C, and dried for 24 h (Shaoxing Shangcheng Instrument manufacturing Co., Ltd., Shaoxing, China), as shown in Figure 3b. Then, the specimens are cooled to room temperature at a rate of 0.5 \({}^{\circ}\)C/min. (2) Sandstone soaking stage: the mass of the red sandstone after drying, denoted as m0, is measured. The specimens are then placed into a constant temperature water tank set to the target temperatures (25 \({}^{\circ}\)C, 55 \({}^{\circ}\)C, 85 \({}^{\circ}\)C, and 95 \({}^{\circ}\)C). At each target temperature, the sandstone specimens are soaked for 0.5 h, 2 h, and 3 h, (Shaoxing Supo Instrument Co., Ltd., Shaoxing, China), as shown in Figure 3c, and the mass of the red sandstone after soaking, denoted as m1, is measured. (3) Uniaxial loading stage: the sandstone specimens, after soaking, are immediately placed into a homemade insulation device, as shown in Figure 3i. Uniaxial compression is performed using a WAW-1000B electro-hydraulic servo universal testing machine (Jinan Liangong Testing Technology Co., Ltd., Jinan, China), as shown in Figure 3e, with a loading rate of 0.2 mm/min. Real-time monitoring is conducted using an AE win Express8 acoustic emission system (Physical Acoustics Corporation of America (PAC), Beijing, China), as shown in Figure 3f, and strain data are collected using the DH3820 strain acquisition system Donghua Testing Technology Co., Ltd., Jingjiang, China), as shown in Figure 3g. The Nano 30 sensors (Physical Acoustics Corporation of America (PAC), Beijing, China), shown in Figure 3d, are arranged in two layers, with three sensors in each layer, positioned in a 90\({}^{\circ}\) staggered pattern. The distance between the probes and the top and bottom faces is 20 mm. The acoustic emission bandwidth ranges from 125 kHz to 750 kHz, and the preamplifier models are 2/4/6, with amplification factors of 20, 40, and 60, respectively, with the test set to 40 to ensure measurement accuracy. Calibration is performed before the experiment by using the lead-breaking operation to ensure that the collected signals are stable, clear, and free from noise. The specific experimental procedure is shown in Figure 3.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Numbering** & **Temperature/\({}^{\circ}\)C** & \begin{tabular}{c} **Soaking** \\ **Time/h** \\ \end{tabular} & \begin{tabular}{c} **Water** \\ **Content** \\ \end{tabular} & **Numbering** & **Temperature/\({}^{\circ}\)C** & \
\begin{tabular}{c} **Soaking** \\ **Time/h** \\ \end{tabular} &
\begin{tabular}{c} **Water** \\ **Content** \\ \end{tabular} \\ \hline H-25-0.5 & 25 & 0.5 & 1.04 & H-85-0.5 & 85 & 0.5 & 1.02 \\ H-25-1 & 25 & 1 & 1.62 & H-85-1 & 85 & 1 & 1.56 \\ H-25-3 & 25 & 3 & 2.02 & H-85-3 & 85 & 3 & 2.91 \\ H-55-0.5 & 55 & 0.5 & 1.37 & H-95-0.5 & 95 & 0.5 & 1.21 \\ H-55