## 6 Conclusions  
The indoor testing method to characterize the shear behavior of frozen-thawed soil-structure interfaces often demands specialized equipment and controlled environments, making it costly, time-consuming, and sometimes unavailable. Hence, leveraging the direct shear test, we developed a CART-based integrated learning model. Through cross-validation, optimal hyperparameters of the CART-based model were determined, and subsequent comparison of the model's prediction performance was discussed. The key findings of this study can be summarized as follows:  
* With the increasing thawing degree of frozen soil, the shear stress-strain curves of the frozen-thawed soil-structure interfaces evolve from exhibiting characteristics of strain  
Figure 8: Regression performance of the CART-AdaBoost algorithm, CART-RF algorithm, and CART (**a**) training set; (**b**) testing set.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Model** & \begin{tabular}{c} **Normal** \\ **Stress** \\ \end{tabular} & \
\begin{tabular}{c} **Thawing** \\ **Temperature** \\ \end{tabular} & **Roughness** & **Shear Rate** & **Strain** &
\begin{tabular}{c} **Vertical** \\ **Stress** \\ \end{tabular} \\ \hline CART-RF & 0.5751 & 0.0674 & 0.0005 & 0.0000 & 0.1706 & 0.1864 \\ CART-AdaBoost & 0.5994 & 0.0846 & 0.0004 & 0.0000 & 0.2316 & 0.0840 \\ CART & 0.5764 & 0.0678 & 0.0004 & 0.0000 & 0.1694 & 0.1860 \\ \hline \hline \end{tabular}
\end{table}
Table 8: The _VIM_ of input variables.  
softening with distinct shear stress peaks to demonstrating ideal plasticity and strain hardening traits.
* While the prediction accuracy of a single decision tree proved ineffective, the integrated algorithm models (CART-RF and CART-AdaBoost) adeptily simulated the nonlinear shear behavior of a high-stress frozen-thawed soil-structure interface, successfully predicting entire shear stress-strain curves.
* Importance ranking of the influence parameters revealed that normal pressure and thawing temperature emerged as significant influencing factors for the shear behaviors of frozen-thawed soil-structure interfaces under high stress conditions.  
This study represents an initial endeavor to utilize data obtained from direct shear tests. A scientifically grounded interpretation of shear stress-strain relationships, particularly employing modern machine learning technology, offers valuable insights for practitioners lacking access to testing facilities to directly simulate the mechanical behavior of thawing soil-structure interfaces. Furthermore, the pursuit of more accurate results necessitates additional experimental data, which will be addressed in subsequent research endeavors.  
Conceptualization, F.Z.; methodology, B.W.; validation, F.Z. and B.W.; formal analysis, B.W.; investigation, Z.L.; resources, Z.L.; data curation, F.Z.; writing--original draft preparation, F.Z. and B.W.; writing--review and editing, Z.L. and B.W.; supervision, Z.L.; project administration, Z.L.; funding acquisition, Z.L. All authors have read and agreed to the published version of the manuscript.  
This work was funded by the Natural Science Foundation of China (51408595 and 51874286), the Natural Science Foundation of Jiangsu Province of China (BK20140203), and Jinhua Science and Technology Research Project (2023-4-046).  
Not applicable.  
Data Availability StatementData will be made available on request. The data are not publicly available due to further studies will be conducted based on the data.  
We are thankful for the support of the China University of Mining and Technology for providing the database in this study.  
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.