## 3 Results and Discussion
### Estimation of Clay Undrained Shear Strength
#### 3.3.2 Verification of the Feasibility of the Theoretical Equation  
The Bayesian framework concept is an effective means of correcting the original judgments using the new information collected. Based on the new information of the \(S_{u}\) and \(OCR\) ofthe Finnish clay database, as well as the \(\sigma_{vi}^{\prime}\) test index, priori equations are corrected so that the generated posterior equations are more realistic and have fewer errors. The mean and standard deviation of \(S_{u}\) are also calculated to verify the distribution form of the posterior equation. The form of the probability distribution of \(S_{u}\) for the posterior equation was performed to verify the rationality of the Bayesian framework. By testing, the posterior equation estimated the undrained shear strength with small standard deviation and low variability (Figure 8). The results visualized in Figure 9 were computed by the theoretical equation mentioned above. The measured and theoretically computed values of the undrained shear strength of clay were compared, in which the abscissa is the measured value, and the ordinate is the theoretical computed value. For the underconsolidated state of clay (Figure 9a),  
Figure 8: Test of probability distribution of undrained shear strength. (**a**) Test of prior and posterior probability distribution. (**b**) Test of Finnish clay and posterior probability distribution. since there was no previous result to verify, Equation (10) of [PERSON] and [PERSON] et al. was selected to better estimate the undrained shear strength of clay. The theoretically computed value is in good agreement with the measured value. For the normally consolidated state of clay (Figure 9b), the theoretically computed results in this study are slightly larger or smaller than the measured values; meanwhile, for the overconsolidated state of clay (Figure 9c), the theoretically computed results in this study are in good agreement with the measured values, and the computed values of [PERSON] and [PERSON] et al. are obviously larger. It is found that the \(R^{2}\) values in the underconsolidated state, the normally consolidated state and the overconsolidated state are 0.88, 0.91 and 0.97, respectively. Under the double logarithmic coordinate, the undrained strength ratio \({S_{u}}/{\left({\sigma_{vi}^{\prime}}\right)^{\beta}}\), corrected by \(\beta\), and the overconsolidation ratio \(OCR\) both show an obvious linear relationship, which verifies the theory proposed by our predecessors. \({S_{u}}/{\left({\sigma_{vi}^{\prime}}\right)^{\beta}}\) increases linearly with the increase in \(OCR\) in the overconsolidated state (Figure 10a), and \({S_{u}}/{\left({\sigma_{vi}^{\prime}}\right)^{\beta}}\) decreases linearly with the increase in \(OCR\) in the underconsolidated state and normally consolidated state (Figure 10b). The reliability of the theoretical equation proposed in this study is further verified. It is not difficult to find that the gap between the theoretical computed value and the experimental point in this study is significantly smaller than the gap between the theoretically computed value and the measured value studied by [PERSON] and [PERSON] et al. (Figure 10a). This study found that \({\left({S_{u}}\right)_{\text{NCI}}}\) has a stable estimation result when the clay depth is \(1.9\text{ m}<D<22\text{ m}\), and \({\left({S_{u}}\right)_{\text{OCI}}}\) has stable estimation result when the clay depth is \(1.9\text{ m}<D<17\text{ m}\). When the clay depth is \(0\text{ m}<D<1.9\text{ m}\), the estimated value of \({\left({S_{u}}\right)_{\text{OCI}}}\) fluctuates greatly. The smaller the compressibility index (\(C_{c}\)) value, the lower the compressibility of the soil, and the \(C_{c}\) value of the low compressibility soil is generally  
Figure 10: The relationship between \({S_{u}}/{\left({\sigma_{vi}^{\prime}}\right)^{\beta}}\) and OCR. (**a**) Overconsolidated state. (**b**) Underconsolidated and normally consolidated state. Figure 9: Comparison between the theoretically computed and measured values of \({S_{u}}\).