## 6 Conclusions  
In this paper, the frost heave and thaw settlement induced by freezing walls in the AGF method, which are inadequately investigated in the current literature, are systematically examined by a set of state-of-the-art numerical models built by FLAC3D with the data retrieved from the literature. Similar to the results reported by [PERSON] et al. [2], for the characteristics of the freezing and thawing processes, our results show that a shrinkage stage occurs before entering the linear fast-freezing stage and the settlement becomes stable after a linear fast settlement during the thaw settlement. For temperature distribution within a freezing wall, it is found that the temperature of a certain area within the freezing wall is below freezing temperature prior to the fast-freezing stage and after the fast-thawing stage. For ground displacement, the results indicate that during the frost heave process, the displacement curve along the transverse direction of the tunnel is wider than that along the longitudinal direction of the tunnel, while that of the thaw settlement is comparatively uniform in different directions.  
In terms of the effects of the thickness of the freezing wall on the freezing and thawing characteristics, it is observed that (1) the increase in the thickness of the freezing wall gives rise to the extension of the freezing process and the fast-thawing stage; (2) similar to that pointed out by [PERSON] [13], the frost heave and thaw settlement of the ground surface might increase exponentially with growth in the thickness of the freezing wall, which can be informative when it comes to the determination of the thickness of the freezing wall; and (3) the thickness of the freezing wall is also a contributory factor to a more gentle displacement distribution of the surface ground.  
This study provided insights into the ground displacements during the freezing and thawing processes of artificial freezing methods in the construction of subway cross  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Thickness of the** & \multirow{2}{*}{**Displacement Type**} & **Direction of the** & & & & & & \\
**Freezing Wall (m)** & & **Cross-Section** & \(y_{0}\) & \(x_{c}\) & \(w\) & \(A\) & \(y_{0}+A\) & \(R^{2}\) \\ \hline \multirow{4}{*}{1.0 m} & & X-axis & 0.35 & 0.11 & 11.14 & 1.57 & 1.92 & 1.00 \\  & & Y-axis & 0.12 & \(-\)0.35 & 10.09 & 1.83 & 1.95 & 1.00 \\  & & X-axis & 0.69 & 0.04 & 11.19 & 3.88 & 4.57 & 1.00 \\  & & Y-axis & 0.48 & 0.06 & 11.19 & 4.17 & 4.65 & 1.00 \\  & & X-axis & 1.12 & 0.02 & 11.51 & 6.51 & 7.64 & 1.00 \\
2.0 m & \multirow{2}{*}{
\begin{tabular}{c} Tasur settlement \\ \end{tabular} } & Y-axis & 0.97 & 0.00 & 11.40 & 6.72 & 7.70 & 1.00 \\  & & X-axis & 1.61 & 0.10 & 11.69 & 10.08 & 11.69 & 1.00 \\  & & Y-axis & 1.63 & \(-\)0.07 & 11.43 & 10.19 & 11.82 & 1.00 \\  & & X-axis & 2.24 & 0.08 & 11.64 & 14.24 & 16.48 & 1.00 \\
3.0 m & & Y-axis & 2.38 & 0.11 & 11.50 & 14.29 & 16.68 & 1.00 \\ \hline \hline \end{tabular}
\end{table}
Table 5: _Cont._passages. However, in this study, the groundwater movement during freezing and thawing process was not considered. More research is needed to investigate the interaction of groundwater dynamics with the freezing and thawing processes.  
Methodology, Y.O.; Software, H.C.; Validation, S.Y.; Formal analysis, H.B.; Data curation, T.C.; Writing--original draft, Y.O. and L.W.; Writing--review & editing, A.S. and Q.Z. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not Applicable.  
The raw data supporting the conclusions of this article will be made available by the authors on request.  
Authors [PERSON], [PERSON], [PERSON], [PERSON], [PERSON] and [PERSON] were employed by the company China Construction Eighth Engineering Division Co., Ltd. The remaining authors declare that the re-search was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.