## 3 Results and Discussion
### Properties of Clays and the Database  
The data used in this study were derived from the FI-CLAY/14/856 dataset in the TC304 database, made up of laboratory test data of clay parameters in 33 regions in Finland [50; 51]. In this study, 11 parameters of 202 Finnish clay samples were selected for research, including organic content (_Org_), clay content (_C_I), void ratio (_e_), natural water content (_W_), liquid limit (_LL_), plastic limit (_PL_), effective overburden pressure (\(\sigma^{\prime}_{vi}\)), preconsolidation pressure (\(\sigma^{\prime}_{v0}\)), overconsolidation ratio (_OCR_), compression index (_C_c), sensitivity (_S_t), and undrained shear strength (_S_u); the statistical results of this data set are as follows (Table 1 [51], Figure 4).  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Parameters** & **Symbol** & **Min** & **Max** & **Std** & **Mean** & **COV** & **Unit** \\ \hline Organic content & \(Org\) & 0.00 & 7.10 & 1.48 & 1.23 & 1.20 & \% \\ Clay content & \(CI\) & 12.70 & 95.00 & 20.61 & 58.99 & 0.35 & \% \\ Void ratio & \(e\) & 0.81 & 3.88 & 0.69 & 2.13 & 0.32 & - \\ Natural water content & \(W\) & 28.00 & 155.00 & 25.52 & 77.45 & 0.33 & \% \\ Liquid limit & \(LL\) & 24.40 & 166.00 & 24.73 & 76.78 & 0.32 & \% \\ Plastic limit & \(PL\) & 17.70 & 42.00 & 4.90 & 27.68 & 0.18 & \% \\ Effective in situ stress & \(\sigma^{\prime}_{yi}\) & 4.00 & 130.00 & 27.31 & 41.68 & 0.66 & kPa \\ Preconsolidation pressure & \(\sigma^{\prime}_{c0}\) & 13.00 & 198.00 & 37.89 & 69.35 & 0.55 & kPa \\ Overconsolidation ratio & \(OCR\) & 0.46 & 20.00 & 1.81 & 2.12 & 0.85 & - \\ Compression index & \(C_{c}\) & 0.10 & 4.22 & 0.86 & 1.29 & 0.67 & - \\ Sensitivity & \(S_{t}\) & 1.69 & 163 & 19.97 & 24.26 & 0.84 & - \\ Undrained shear strength & \(S_{u}\) & 5.21 & 240.00 & 31.32 & 28.95 & 1.08 & kPa \\ \hline \hline \end{tabular} Std: Standard deviation.  
\end{table}
Table 1: Statistical analysis of dataset.  
Figure 3: Flow chart of CatBoost–Bayesian adaptively coupled modified theoretical equations.  
Figure 5 shows the normal distribution and fitting effect of organic content (\(Org\)), clay content (\(CI\)), void ratio (\(e\)), natural water content (\(W\)), liquid limit (\(LL\)), plastic limit (\(PL\)), effective overburden pressure (\(\sigma^{\prime}_{vi}\)), preconsolidation pressure (\(\sigma^{\prime}_{v0}\)), overconsolidation ratio (\(OCR\)), compression index (\(C_{c}\)), and undrained shear strength (\(S_{u}\)), and an analysis of the abnormal value of clay undrained shear strength.  
Figure 5: \(Cont.\)  
Considering the abnormal value of clay undrained shear strength to reduce its influence on the fitting, a simple linear fitting can be performed to obtain the empirical equation of clay undrained shear strength parameters (Figure 5). It could be observed that between the single parameters of clay, the linear relationship is obvious, but the fitting error is large. At the same time, the empirical equation could not be verified. There is a certain particularity, and the constitutive relationship of the clay could not be obtained. Therefore, further research on the relationship between the multi-parameters of the clay is needed.  
Figure 5: Visualization of normal distribution of 11 clay parameters. (**a**) Fitted relationship of \(S_{u}\), \(Org\), \(CI\). (**b**) Fitted relationship of \(S_{u}\), \(e\), \(W\). (**c**) Fitted relationship of \(S_{u}\), \(LL\), \(PL\). (**d**) Fitted relationship of \(S_{u}\), \(\sigma^{\prime}_{vir}\), \(\sigma^{\prime}_{z0}\). (**e**) Fitted relationship of \(S_{u}\), \(OCR\), \(C_{c}\). (**f**) \(S_{u}\) abnormal value analysis.