## 4 Freeze-Thaw Test Results and Analysis  
### Porosity Variation Characteristics of Unloaded-Damaged Samples after Freeze-Thaw  
The freeze-thaw cycling action causes changes in rock microstructure, and the most direct result is an increase in porosity. The process of porosity change with the number of freeze-thaw cycles can directly reflect the evolution of freeze-thaw damage and the use of porosity deformation as the damage variable makes the determination and calculation of freeze-thaw damage more convenient. By measuring the porosity of the unloaded-damaged samples after each freeze-thaw cycle, the average change in porosity with the increase in the number of freeze-thaw cycles was obtained. The average porosity of the unloaded-damaged samples after \(n\) and 0 freeze-thaw cycles are set as \(P_{n}\) and \(P_{0}\), respectively. The average porosity change is shown in Equation (3), and the calculation results are shown in Table 1.  
\[\Delta P_{n}=P_{n}-P_{0} \tag{3}\]  
Figure 9 shows that the evolution of the average change in porosity of the three groups of unloaded-damaged samples is roughly the same, and the average change in porosity increases with the increase in the number of freeze-thaw cycles. The main reason is that the three-phase medium (water, ice, and rock) in the rock body has different thermophysical properties. When freezing, the uneven contraction of mineral-particle volume and the expansion of pore water freezing occur, causing the particle boundary and pore wall to be subjected to freeze-swelling force, expanding the pore volume and causing local damage  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Number of Freeze-Thaw Cycles**} & \multicolumn{3}{c}{**Average Change of Porosity (\%)**} \\ \cline{2-4}  & **Group A** & **Group B** & **Group C** \\ \hline
0 & 0.00 & 0.00 & 0.00 \\
1 & 0.12 & 0.13 & 0.12 \\
2 & 0.19 & 0.20 & 0.20 \\
3 & 0.24 & 0.25 & 0.23 \\
4 & 0.32 & 0.30 & 0.31 \\
5 & 0.38 & 0.38 & 0.39 \\
6 & 0.47 & 0.48 & 0.48 \\
7 & 0.56 & 0.58 & 0.59 \\
8 & 0.68 & 0.69 & 0.72 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Average change in porosity after freeze-thaw cycles for three groups of unloaded-damaged samples.  
Figure 8: Uniaxially loaded stress-strain curves of unloaded-damaged samples and original samples.  
inside the rock sample. When room temperature ablation occurs, the pore ice melts into water, and the freeze-swelling force gradually dissipates, accompanied by the continuous migration of water. After this freeze-thaw cycle, the porosity of the unloaded-damaged sample gradually increases. The freeze-thaw damage inside the rock sample accumulates with the increase in freeze-thaw cycles and develops from local damage to overall damage and even sprouts macroscopic fissures.  
The three groups of unloaded-damaged samples have different initial confining pressures, but the average change in porosity with the number of freeze-thaw cycles is approximately the same, indicating that the degree and trend of fine structure deterioration after freeze-thaw cycles are largely the same for unloaded-damaged samples with different initial confining pressures. The unloading quantity is used to define the degree of unloading damage, and the unloading damage state is the same, so the response to freeze-thaw cycles is also largely the same. This shows that the above definition of unloading quantity as the damage classification criterion can distinguish the degree of unloading damage, and the average change of porosity can be used to measure the freeze-thaw deterioration characteristics of unloaded-damaged samples.