## 3 Results and Discussion
### Estimation of Clay Undrained Shear Strength  
#### 3.3.1 Uncertainty Analysis of Equation Parameters  
Under the Bayesian framework, the CatBoost algorithm (CatBoost-Bayesian) based on a Bayesian optimization algorithm was developed to obtain the feature importance level of soil parameters affecting the undrained shear strength of clay, so as to adaptively couple the theoretical equation of undrained shear strength of \(K_{0}\) consolidated clay, which was derived from the modified Cambridge model; then, the theoretical equation of undrained shear strength of isotropically consolidated clay was established from the critical state of the overconsolidation ratio (\(OCR\)) and overburden effective pressure (\(\sigma_{vi}^{\prime}\)). Considering the constitutive relation of clay, the calculation results of the established undrained shear strength theoretical equation of isotropically overconsolidated clay were used for inversion calculation. The equation parameter \(\gamma\) of the clay in the overconsolidated state is affected by \((1-C_{s}/C_{c})\), \(\gamma=m=0.88\cdot(1-C_{s}/C_{c})\pm 0.06\cdot SD\), and the equation constant parameter is affected by the plasticity index, \(\alpha=2+0.5\cdot I_{p}\). For the measured parameters of clay that are difficult to obtain, it is recommended that when the clay depth is \(1.9\) m \(<D<17\) m, the calculation parameters of undrained shear strength should be computed according to the following recommended values \((\alpha)_{\text{OCI}}=2.246\), \((\beta)_{\text{OCI}}=0.490\); the value range of the correction coefficient of \(\sigma_{vi}^{\prime}\) is \(0.441<(\beta)_{\text{OCI}}<0.539\), and the average value is \((\beta)_{\text{OCI}}=0.490\). The theoretical equation is \((S_{u})_{\text{OCI}}=2.246\cdot\left(\sigma_{vi}^{\prime}\right)^{0.490}\cdot \left(OCR\right)^{0.770}\). This results in a stable estimate of the undrained shear strength of isotropically consolidated clays (Figure 7a,d). \[(S_{u})_{\text{OCI}}=2.246\cdot\left(\sigma_{vi}^{\prime}\right)^{0.490}\cdot \left(OCR\right)^{0.770} \tag{25}\]  
In the normally consolidated state, the fitting parameter ranges were \(0.988<\left(\alpha\right)_{\text{NCI}}<1.910,0.619<(\beta)_{\text{NCI}}<0.786\), and \(-0.993<\left(\gamma\right)_{\text{NCI}}<0.309\) in this study (Figure 7d). There  
Figure 7: Limit state functions of clay with different consolidation. (**a**) Limit state function of overconsolidated clay. (**b**) Limit state function of normally consolidated clay. (**c**) Limit state function of underconsolidated clay. (**d**) Parameter analysis of equation of state for different consolidations. is a relatively stable estimation result when the clay depth is \(1.9m<D<22m\). Therefore, for the calculation of the parameters of undrained shear strength, it is recommended to take the means \(\left(\alpha\right)_{\text{NCI}}=1.376\), \(\left(\beta\right)_{\text{NCI}}=0.703\) and \(\left(\gamma\right)_{\text{NCI}}=-0.342\) (Figure 6b). \[\left(S_{u}\right)_{\text{NCI}}=1.376\cdot\left(\sigma_{vi}^{\prime}\right)^{0. 703}\cdot\left(OCR\right)^{-0.342} \tag{26}\]  
In the underconsolidated state, the parameter ranges \(0.895<\left(\alpha\right)_{\text{UCI}}<3.589\), \(0.386<\left(\beta\right)_{\text{UCI}}<0.777\), and \(0.386<\left(\beta\right)_{\text{UCI}}<0.777\) were fitted in this study (Figure 7d). When the clay depth was \(2.5\) m \(<D<17\) m, the undrained shear strength has a relatively stable estimation result. It is recommended to take the means \(\left(\alpha\right)_{\text{UCI}}=1.793\), \(\left(\beta\right)_{\text{NCI}}=0.581\) and \(\left(\gamma\right)_{\text{NCI}}=-0.423\) for calculation (Figure 7c). The underconsolidated state of clay is the result of the interaction between the strength characteristics of the soil itself and excess pore water pressure, and its undrained shear resistance exhibits structural properties [55]. Therefore, it cannot be verified by the previous results, and it needs to be verified by the relationship between the measured value and the estimated value.