## 3 Results and Discussion
### Analysis of Numerical Simulation Results
#### 3.2.4 Analysis of Damage Patterns of Specimens  
Figure 20 visualizes the damage characteristics of sandstone after cyclic loading and unloading applied under different freeze-thaw cycles. The following features can be  
Figure 19: Cumulative Strain Difference variation curve. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Simulated** & **Measured** & **Simulated** & **Measured** & **Stress Differ-** & **Strain** & **Single-Axis** & **Uniaxial** & **Cumulative** \\
**Feak** & **Feak** & **Stress/Mpa** & **Strain/\%** & **Strain/\%** & **ence/Mpa** & **Relief/\%** & **Strain** & **Strain** & **of Peak** \\  & & & & & & & **Differential/\%** & **Stress/Mpa** & **Difference/\%** \\ \hline
4.40 & 4.80 & 0.001 & 0.075 & 0.40 & 0.074 & & & 36.20 \\
8.40 & 7.50 & 0.0025 & 0.10 & 0.90 & 0.0975 & & & 21.20 \\
12.40 & 12.70 & 0.0026 & 0.053 & 0.30 & 0.0504 & & & 32.87 \\
16.40 & 17.25 & 0.004 & 0.15 & 0.85 & 0.146 & & & 33.61 \\
20.40 & 21.80 & 0.005 & 0.175 & 1.40 & 0.17 & & & 23.76 \\
24.40 & 25.80 & 0.006 & 0.21 & 1.40 & 0.204 & & 28.51 \\
28.40 & 32.50 & 0.007 & 0.23 & 4.10 & 0.223 & & 10.64 \\
32.20 & 36.125 & 0.0075 & 0.275 & 3.925 & 0.2675 & & & 13.33 \\
36.40 & 41.10 & 0.0085 & 0.30 & 4.70 & 0.2915 & & & 12.13 \\
40.40 & 49.00 & 0.01 & 0.34 & 8.60 & 0.33 & & & 7.51 \\
44.40 & 48.40 & 0.0105 & 0.38 & 4.00 & 0.3695 & & & 18.07 \\
48.40 & 40.00 & 0.0107 & 0.40 & 8.40 & 0.3892 & & & 9.07 \\  & & & & & & & 20.57 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Cumulative strain differential data. observed by comparing the measured damage images with the simulation results. For the sandstone without freeze-thaw, the damage cracks are generated at the ends of the prefabricated crack. Then, it gradually extended to the top and bottom ends of the specimen. During this process, the region with the most considerable deformation appears near the prefabricated crack. The overall deformation of the sandstone specimens freeze-thawed 20 cycles was close to that of the specimens without freeze-thaw, and the expansion patterns of the cracks were macroscopically similar. The difference is that after 20 freeze-thaw times, the sandstone formed a crack through the specimen's top left and bottom right surfaces. The inclination of this crack remained the same as that of the prefabricated crack. In sandstone of 40 freeze-thaw cycles, cracks first appeared on the top right surface of the specimen. Then, it penetrated the prefabricated crack and expanded toward the bottom right surface. Then, cracks began to develop on the top left surface, expanding towards and penetrating the prefabricated crack and then expanding toward the bottom left surface, forming an X-shaped crack. The maximum deformation of the sandstone with 40 cycles of freeze-thaw was concentrated on the bottom left and top right surfaces. Figure 20: _Cont._  
Figure 20: Rock damage diagram for different freeze–thaw cycles. (**a**) 0, (**b**) 0, (**c**) 20, (**d**) 20, (**e**) 40, (**f**) 40, (**g**) 60, (**h**) 60, (**i**) 80 times, (**j**) 80 times. The cracks first appeared on the top left surface of the sandstone after 60 freeze-thaw cycles, expanding towards the prefabricated crack to form a through crack. Cracks then began to appear on the top right surface of the specimen, expanding towards the center to form a through crack with the prefabricated crack. Then, the left side cracks expanded to the bottom of the specimen until the specimen was destroyed. In the sandstone with 80 freeze-thaw cycles, cracks first appeared on the right surface of the specimen and did not penetrate the central prefabricated crack. Instead, it developed in the right surface area, causing small block spallings to form on the right surface. A similar situation occurred on the left surface of the specimen with large block spalling, but it occurred slightly later relative to the right side. Finally, a distinct, wide crack was formed on the right surface. It started at the top right corner, crossed the center of the specimen, and extended to the bottom right corner.