## 2 Experimental Scheme
### Freeze-Thaw Modes and Conditions  
Different parts of the grottoes, cliff status, and other cultural relics are in different surroundings. As shown in Figure 1, the bottom of the cultural relic is immersed in water for a long time due to the influence of groundwater and surface runoff. The lower regions suffer from capillarity, while the upper regions are saturated when affected by rainfall and snowfall. Figure 1: Schematic diagram of different parts of stone cultural relics. Figure 2: Rock sampling site: Qingyang, Gansu, China. (**a**) Map of China; (**b**) map of Qingyang; (**c**) north Grottoes. On this basis, tests of three typical freeze-thaw modes can be used as follow: immersion freeze-thaw cycles, capillary freeze-thaw cycles, and periodic saturation freeze-thaw cycles. The simulation of freeze-thaw conditions is shown in Figure 3. The immersed freeze-thawed rock samples were completely immersed in water during the cycles, the capillary freeze-thaw rock samples were placed on the cotton towels filled with water in the tray, and the periodically saturated freeze-thaw rock samples were placed on the iron frame for five freeze-thaw cycles after 48 h of saturation. The times of freeze-thaw cycles were set to 0, 5, 10, 20, 40, 60, and 80 times, and there are totaling 147 rock samples, as shown in Table 1. The samples of control groups (0 cycle) of various modes were placed in the same water environment and maintained at a constant temperature of 25 \({}^{\circ}\)C.  
The freeze-thaw test is carried out in the humid heat chamber with rapid temperature change. The temperature control range is from \(-\)40 \({}^{\circ}\)C to +120 \({}^{\circ}\)C, and the allowable error is \(\pm\)1 \({}^{\circ}\)C. The heating and cooling rates are up to 10 \({}^{\circ}\)C/min, which meets the requirements of the test, the test chamber is shown in Figure 4. According to meteorological data of the North Grottoes in Qingyang, Gansu, the climatic temperature in the region in recent 10 years is 30 \({}^{\circ}\)C at the highest and \(-\)20 \({}^{\circ}\)C at the lowest. The surface temperature of the caves in summer afternoon is around 40 \({}^{\circ}\)C and in the winter the surface temperature is close to \(-\)25 \({}^{\circ}\)C, with a moderate increase on the basis of the historical true temperature. The annual trend of seasonal relative temperature in the Qingyang shows that the time period of below and above 0 \({}^{\circ}\)C is about 6 months. The present study investigates the failure characteristics and variation rules of rock mass under extreme temperature conditions. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Freeze–thaw Cycle/Times** & **0** & **5** & **10** & **20** & **40** & **60** & **80** \\ \hline Immersion freeze–thaw Capillary freeze–thaw & J0-1-J0-7 & J1-1-J1-7 & J2-1-J2-7 & J3-1-J3-7 & J4-1-J4-7 & J5-1-15-7 & J6-1–16-7 \\ Capillary freeze–thaw & B0-1-B0-7 & B1-1-B1-7 & B2-1-B2-7 & B3-1-B3-7 & B4-1–B4-7 & B5-1–B5-7 & B6-1–B6-7 \\ Periodic saturation freeze–thaw & R0-1-R0-7 & R1-1-R1-7 & R2-1-R2-7 & R3-1-R3-7 & R4-1–R4-7 & R5-1–R5-7 & R6-1–R6-7 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Grouping of rock samples with different freeze–thaw modes. Figure 3: Schematic diagram of three freeze–thaw methods test. (**a**) Immersion freeze–thaw; (**b**) capillary freeze–thaw; (**c**) capillary freeze–thaw.