## 4 Discussion
### Undrained Shear Strength (\(C_{u}\))  
To develop this study, the Equation (5), proposed by [PERSON], was used to start the analysis, because it related the undrained shear strength with the vertical effective stress and the \(K_{D}\), considering that the \(I_{D}\) must be less than 1.2.  
\[C_{u}=0.22\sigma^{\prime}{}_{vo}(0.5K_{D})^{1.25},\;I_{D}<1.2 \tag{5}\]  
In this way, the following parametric Equation (6) was used to determine the appropriate regression:  
\[C_{u}=A*\sigma^{\prime}{}_{vo}(B*K_{D})^{C},\;I_{D}<1.2 \tag{6}\]  
In Figure 22, it should be noted that the data found were scattered among themselves. However, a trend was found between meter 2 and meter 10. Consequently, the regression was performed based on the data corresponding to meter 2 and meter 10. In addition, these data provide consistent values of undrained shear strength for the type of soil that was relevant to this study.  
Furthermore, as shown in Figure 22, the zone marked between meters 2 and 10, \(C_{u}\) and \(K_{D}\) had values that were close to each other. It must be considered that the \(C_{u}\) value had a directly proportional relationship with depth. Therefore, the equation to be obtained must consider this effect. Using the Minitab program, the correlation coefficients between variables and the regression that provided the equation for the calculation of the undrained shear strength were obtained.  
Figure 22: Undrained shear distribution, \(K_{D}\), and vertical effective stress about depth.  
Figure 23 shows the relationship between each variable. According to [PERSON], [PERSON], and [PERSON] (2014) [37], the \(K_{D}\) and \(C_{u}\), as well as the \(\sigma^{\prime}v\) and \(K_{D}\), were inversely proportional; whereas, \(C_{u}\) and \(\sigma^{\prime}v\) were directly proportional. Hence, an equation was obtained based on the structure proposed by [PERSON] (Equation (6)) and using the data between meter 2 and meter 10, the equation is presented below.  
\[C_{u}=0.262\sigma^{\prime}v_{0}K_{D}^{-0.221},\;I_{D}\leq 1 \tag{7}\]  
Figure 24 shows that the undrained shear strength results obtained in the laboratory decrease with increasing depth, presenting a potential tendency with an R\({}^{2}\) equal to 0.4784.  
This equation was useful to obtain the undrained shear strength of very soft soils, such as organic soils. Therefore, it was limited by \(I_{D}\) values less than 1. With the previous equation, Figure 25 shows that the undrained shear strength values were close to those found by laboratory tests; however, these differ from those obtained using the Marchetti equation.  
Figure 23: Relationship between variables (\(C_{u}\), \(K_{D}\), and \(\sigma^{\prime}v\)).  
Figure 24: Correlation equation based on test results and depth for undrained shear strength.  
The tendency assumed by the values calculated with the equation obtained was notorious, because it kept \(C_{u}\) values in the order of 2 to 10 kPa, and they increased with depth. Although this equation could provide acceptable values for soft soils, it was not useful for more consistent soils. For example, in the first meter, where we had no organic soils, the \(C_{u}\) calculated from Equation (7) was less than the values obtained from the laboratory tests.  
In addition, it was possible to observe that the trend generated from the laboratory results and depth (Equation (8)) presented higher values than those obtained in Equation (3) in meters 2, 3, and 4. However, from meter 5 to meter 10, it adapted better to the results obtained by the equation as a function of \(K_{D}\) and \(\sigma^{\prime}{}_{vo}\), as shown in Figure 25.  
\[C_{u}=19.548z^{-0.523} \tag{8}\]  
where:  
\(z\): depth, m.