## 5 Results and Discussion  
The stress-strain dataset, which has not been introduced to the model-building process, is used to test the predictive performance of the model. The prediction results of different models for the test set are summarized in Table 7. To more intuitively illustrate the predictive effect of the model, the stress-strain curves of the test set are plotted in Figure 7.  
One can notice that the prediction effects are different between different models and the same model on different test sets. Both the ensemble algorithms, the CART-RF algorithm and the CART-AdaBoost algorithm, have good predictive performance for stress-strain curves under different test conditions, whether it is strain softening at high pressure with \(-5\)\({}^{\circ}\)C (Figure 7a) or strain hardening at high pressure with \(20\)\({}^{\circ}\)C (Figure 7c). However, it \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \(MAE\) & \(RMSE\) & \(R^{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of different hyperparameters of the CART-RF algorithm. can be seen that the prediction accuracy of the CART-AdaBoost algorithm is higher, and the predicted values were observed to essentially match the trends of the shear test results. The model can reflect the phenomenon of stress convergence in the later process of shearing. Although CART has better predictions under some experimental conditions (Figure 7b), the overall prediction performance of a single decision tree is poor. As shown in Figure 8, the accuracy of CART on the training set is \(R^{2}\) = 0.994, while the accuracy on the test set is low (\(R^{2}\) = 0.763), indicating that CART has poor generalization. It should be noted that, like other big data learning algorithms, the CART-RF algorithm and the CART-AdaBoost algorithm may not be able to accurately predict the material behavior outside the range of training data. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Dataset** & **Evaluation Index** & **CART** & **CART-RF** & **CART-AdaBoost** & **ANN** \\ \hline \multirow{4}{*}{Training set} & \(R^{2}\) & 0.994 & 0.998 & 0.999 & 0.913 \\  & \(RMSE\) & 0.090 & 0.053 & 0.034 & 0.330 \\  & \(MAE\) & 0.051 & 0.025 & 0.024 & 0.198 \\  & \(R^{2}\) & 0.488 & 0.730 & 0.786 & 0.086 \\ \multirow{4}{*}{Testing set1} & \(RMSE\) & 0.538 & 0.391 & 0.348 & 0.719 \\  & \(MAE\) & 0.440 & 0.304 & 0.286 & 0.663 \\  & \(R^{2}\) & 0.940 & 0.952 & 0.932 & 0.411 \\ \multirow{4}{*}{Testing set2} & \(RMSE\) & 0.100 & 0.090 & 0.107 & 0.314 \\  & \(MAE\) & 0.080 & 0.072 & 0.092 & 0.270 \\  & \(R^{2}\) & 0.955 & 0.969 & 0.957 & 0.950 \\ \multirow{4}{*}{Testing set3} & \(RMSE\) & 0.254 & 0.249 & 0.201 & 0.268 \\  & \(MAE\) & 0.201 & 0.182 & 0.208 & 0.200 \\ \multirow{4}{*}{Testing set4} & \(R^{2}\) & 0.882 & 0.953 & 0.982 & 0.029 \\  & \(RMSE\) & 0.427 & 0.270 & 0.168 & 1.227 \\ \multirow{4}{*}{Testing set5} & \(MAE\) & 0.231 & 0.173 & 0.109 & 1.118 \\  & \(R^{2}\) & 0.548 & 0.625 & 0.660 & 0.604 \\ \multirow{4}{*}{Testing set5} & \(RMSE\) & 0.391 & 0.356 & 0.339 & 0.366 \\  & \(MAE\) & 0.320 & 0.285 & 0.279 & 0.251 \\ \hline \end{tabular}
\end{table} 
Table 7: Prediction performance for different models. Figure 7: Comparison of prediction results under different models with experimental data: (**a**) testing set 2; (**b**) testing set 3; (**c**) testing set 4. Given the size of the training dataset used in this study, we used a shallow neural network to predict the frozen-thawed soil-structure shear stress-strain curves. As we know, artificial neural network (ANN) is one of the most commonly used prediction algorithms, consisting of an input layer, hidden layers, and an output layer. According to the number of hidden layers, it is divided into a shallow or a deep neural network (DNN). Table 6 shows the performance comparison of the ANN model and the CART-based model in the dataset. For the shear stress-strain curve, the prediction effect of ANN is generally lower than that of the CART-based model, and the accuracy of ANN on the training set is much higher than the test set.