## 4 Results  
### PSD under Different Freezing Durations at \(-20\)\({}^{\circ}\)C  
The freezing process has a complex relationship with thermal, hydraulic, and mechanical transformation [48], which could be investigated by analyzing the subtle changes in PSD for different freezing durations.  
When the temperature drops below the freezing point of the soft clay, the free water and part of the weak bound water in the soft clay gradually begin to freeze. Free water with a small intermolecular force freezes quickly, while free water with a large van der Waals force and some weak bound water freezes at a slow rate. Due to the interaction between the water and the soft clay surface, a part of the water in the soft clay is difficult to freeze [49]. The water content in the soft clay measured under different freezing durations can reflect the icing sequence of the water in the soft clay, and the freezing duration can affect the icing process of the soft clay so that affect the final damage of the soft clay. Pore water cannot be detected by nuclear magnetic resonance after freezing, so the PSD of soft clay after freezing for a certain period only reflect the distribution of unfrozen water.  
The unfrozen water is a key component that determines a soft clay's physical change [49; 50]. However, the frozen water is the key reason for microstructural damage. To explain the rationale behind the destructive effect of freezing, the percent change by volume at different freezing durations is plotted in Figure 11. It can be seen from Figure 11a that the water in the mesopores froze firstly and the water in the smaller pores froze later. The PSD of frozen soft clay at different freezing durations after thawing for 24 h is shown in Figure 11b. At this time, all the ice in the soft clay has melted into water, and all signals from water can be detected. In the case of freezing for 1 h and freezing for 2 h, the distribution of pores in the soft clay changes greatly. After freezing for 2 h, the peak proportion of small pores decreased by nearly 0.5%, and the peak proportion of mesopores increases by nearly 0.5%. The change in soft clay pores within 2-18 h of freezing is the same as the two hours before freezing. This indicates that during the entire freezing process, the freezing speed of water decreased.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Sample No.**} & **Sample Size** & **Freezing Duration** & **Gap Time** & **Thawing Temperature** \\  & **/mm** & **/h** & **/h** & \(f^{\circ}\)C \\ \hline A1 & \(38\times 38\) & 1 & - & 25 \\ A2 & \(38\times 38\) & 2 & - & 25 \\ A3 & \(38\times 38\) & 3 & - & 25 \\ A4 & \(38\times 38\) & 4 & - & 25 \\ A5 & \(38\times 38\) & 6 & - & 25 \\ A6 & \(38\times 38\) & 12 & - & 25 \\ A7 & \(38\times 38\) & 18 & - & 25 \\ B1 & \(38\times 38\) & 24 & 1 & 25 \\ B2 & \(38\times 38\) & 24 & 2 & 25 \\ B3 & \(38\times 38\) & 24 & 3 & 25 \\ B4 & \(38\times 38\) & 24 & 4 & 25 \\ B5 & \(38\times 38\) & 24 & 6 & 25 \\ B6 & \(38\times 38\) & 24 & 12 & 25 \\ B7 & \(38\times 38\) & 24 & 18 & 25 \\ B8 & \(38\times 38\) & 24 & 24 & 25 \\ C1 & \(38\times 38\) & 24 & - & 5 \\ C2 & \(38\times 38\) & 24 & - & 10 \\ C3 & \(38\times 38\) & 24 & - & 15 \\ C4 & \(38\times 38\) & 24 & - & 20 \\ C5 & \(38\times 38\) & 24 & - & 25 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Freezing plan.  
After six hours of freezing, the freezing duration is no longer the main cause of the soft clay microstructure damage. Pores from 0 to 0.3 \(\upmu\)m increased with freezing duration and the freezing stage was mostly completed in the first four hours, as demonstrated by the near overlap of the 6 h and 18 h curves.