# Experimental and Modeling of Residual Deformation of Soil-Rock Mixture under Freeze-Thaw Cycles
## 3 Experimental Results
### Residual Deformation Analysis  
The soil-rock mixture specimens will alternately produce freezing expansion and thawing settlement during the freeze-thaw cycle, and the superposition of the two is the residual deformation of the specimens. The residual deformation of each group of specimens is shown in the Figure 8.  
As can be seen from the Figure 8, almost all of the soil-rock mixture specimens produced thawing and sinking after the freeze-thaw cycles. The initial residual deformation of the specimens is larger than the later residual deformation, but with the increase of the number of freeze-thaw cycles, the residual deformation gradually stabilizes. The residual deformation decreases and then increases with the increase in the rock content in the specimens, and reaches the minimum residual deformation in the S2 group specimen with 80% rock content.  
According to the freeze-thaw change curves of the soil-rock mixture specimens as shown in the Figure 9, the residual deformation of each specimen is shown as settlement deformation. When the rock content of the specimens is between 70% and 80%, the freeze-swelling and thawing changes of the specimens in the S2 and S3 groups are smaller than those in the S1 group with 90% rock content and the S4 group with 60% rock content, or the blocks in the specimens in this rock content range can provide the best skeletal support. The freeze-swelling and thawing changes of the specimens in the other two groups are larger, with a maximum deformation of about 12%, and thus eventually also produce larger residual changes.  
Figure 6: Freeze–thaw cycle temperature of samples in group S1.  
Figure 7: Frost heave amount of each group of samples.  
The final residual deformation produced by each specimen is shown in Table 2. When the rock content of the soil-rock mixture specimen is 60-80%, the residual deformation is all settlement deformation. With the increase of the lumpy rock content in the specimens, the settlement amount gradually decreased and reached the minimum settlement amount of 2.54 mm in the specimens of group S2 with 80% rock content, which was only 48.29% and 25.81% of the settlement amount in the specimens of groups S3 and S4, while the specimens of group S1 produced the maximum settlement amount, which was almost six times of the settlement amount in group S2.  
It can be inferred that there is an optimal rock content in the range of 80% to 90%, and until this content is reached, the increase of the boulder content can make the skeleton effect of the boulders in the soil-rock mixture specimens more and more obvious, so that they can resist the deformation caused by the freeze-thaw cycles. However, the S1 group specimens with the highest rock content showed the largest settlement, either because the boulder content was too high or the soil could not completely fill the pores between them, thus producing a larger amount of melting and settlement under the freeze-thaw cycles.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Number** & **S1** & **S2** & **S3** & **S4** \\ \hline Residual Deformation (mm) & \(-\)14.62 & \(-\)2.54 & \(-\)5.26 & \(-\)9.84 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The final residual deformation of each sample.  
Figure 8: The residual deformation of each group of samples.  
Figure 9: The distribution of freezing and thawing.