## 3 Results and Discussion
### Estimation of Clay Undrained Shear Strength
#### 3.3.3 Comparative Analysis of Estimation Results  
Considering the effect of clay depth (\(D\)), the combination of the feature importance of the CatBoost-Bayesian hybrid model and the calculation of the theoretical equation derived from the modified Cambridge model can well estimate the undrained shear strength of clay, and the theoretical computed value is in good agreement with the measured value (Figure 12a,b). The computed average properties of the clay at different consolidation states were \(\text{R}^{2}=0.92,\text{ Evar}=0.92,\text{ RMSE}=0.19,\text{ MAE}=0.03\). This indicated that the uncertainty of the theoretical equation is significantly reduced when the overconsolidation ratio was combined with the preconsolidation pressure or the effective overburden pressure.  
Figure 11: Error analysis of undrained shear strength of clay.  
Figure 12: Comparison of \(S_{u}\) computed results. (**a**) Recommended equation: \(R^{2}=0.91\). (**b**) Recommended equation: \(R^{2}=0.97\).  
The computed results of the test set of the CatBoost-Bayesian hybrid model under five-fold cross-validation are within the 95% confidence interval, and the computed average performance is training set \(R^{2}=0.91\), \(\text{Evar}=0.91\), \(\text{RMSE}=0.30\), \(\text{MAE}=0.12\); test set \(R^{2}=0.86\), \(\text{Evar}=0.86\), \(\text{RMSE}=0.37\), \(\text{MAE}=0.20\). Only a very small number of undrained shear strength estimates at K3 in the test set exceed the 95% confidence interval, proving the reliability of the computed results [58]. In the five-fold cross-validation, there is a gap between the computed value of a small amount of undrained shear strength and the real value, which leads to the large value of RMSE and MAE, and the fitting effect is not significant enough (Figure 13a-d).  
As shown in Figure 14, UCI_S\({}_{u}\), NCI_S\({}_{u}\), and OCI_S\({}_{u}\) demonstrate the performance of CatBoost-Bayesian hybrid model for estimating the undrained shear strength of clay in different consolidation states of clay, as well as the overall CatBoost-Bayesian hybrid model performance, which is subsequently compared with LightGBM-Bayesian, XGBoost-Bayesian hybrid model for comparison. The training and test set performance evaluations are shown in Table 3.  
Figure 14: Estimation performance visualization.  
Figure 13: Comparison of quantitative evaluation indicators. (**a**) \(R^{2}\). (**b**) Evar. (**c**) RMSE. (**d**) MAE.  
On the R\({}^{2}\) and Evar curves explaining the variance score of the model, the CatBoost-Bayesian hybrid model has the strongest ability to explain the variance in the undrained shear strength under five-fold cross-validation, which could explain almost 86% of the 202 undrained shear strengths of clay. The sample variability shows that the hybrid model has a better effect; RMSE and MAE evaluate the closeness of the predicted clay undrained shear strength to its experimental value, and the smaller the value, the better the model fitting effect. It could be observed that the estimated results for clays in different isotropically consolidated states could explain almost 92% of the 202 sample variability in the undrained shear strength of clays. The RMSE and MAE of this study are all lower than other intelligent mixed models, and the results show that the combination of CatBoost-Bayesian feature importance and theoretical formula has the best fitting effect (Figure 14).  
The estimated performance results in Table 3 show that the theoretical equations of UCL_Su, NCI_Su and OCI_Su derived by combining the CatBoost-Bayesian importance parameters are better than other models in different consolidation states of clay. Among the models of the same type, the estimation performance of the CatBoost-Bayesian hybrid model in the training set and test set is better than other models.