## 4 Discussion
### Density  
Although [PERSON] does not have a defined equation to obtain the density of soils, there is a nomogram that relates \(\mathrm{E_{D}}\) and \(\mathrm{I_{D}}\) and provides the relationship between soil density and water density (\(\gamma_{\mathrm{s}}/\gamma_{\mathrm{w}}\)). The nomogram presented in Figure 17 established that materials whose \(E_{D}\) value was less than 12 bar (1.2 MPa) are MUCK/PEAT, and regardless of the value taken by \(I_{D}\), the ratio \(\gamma_{\mathrm{s}}/\gamma_{\mathrm{w}}\) would be 1.5. Assuming that the density of water was 1 g/cm\({}^{3}\), all soft material would have a density of 1.5 g/cm\({}^{3}\); however, this was not true.  
Figure 11 showed that density values ranged from 1 to 1.30 g/cm\({}^{3}\) for this material of study. In addition, the soil \(E_{D}\) data did not reflect the density value that would be provided by the Marchetti plot. Considering all the previously mentioned parameters, it was decided to correlate the density values of the soil with its corresponding \(I_{D}\), obtaining the following results.  
\[\rho=0.874+0.453I_{D}\ \mathrm{with}\ I_{D}\leq 1 \tag{9}\]  
The regression shown in Figure 26 was performed using Minitab and presents an R\({}^{2}\) of 0.552, which means that the association has a strong degree of relationship [37]. The linear relationship presents that as the density increases, the value of \(I_{D}\) increases. In addition,  
Figure 25: Comparison between different undrained shear strengths.  
Figure 26 shows that most of the data are grouped in the expected values of both density and \(I_{D}\).  
Additionally, the equation did not allow finding values lower than 1 g/cm\({}^{3}\), since this would be practically the density of water; however, for materials with an \(I_{D}\) lower than 0.278, the equation would provide values lower than 1 g/cm\({}^{3}\) since within the data contemplated in the regression, 2 samples presented this characteristic. However, it was necessary to develop new research for materials that have a density less than water's density.  
Furthermore, Figure 27 shows that the density results obtained in the laboratory decrease with an increasing depth, presenting a potential tendency with an R\({}^{2}\) equal to 0.4018.  
Figure 27: Correlation equation based on test results and depth for density.  
In addition, as with the other two parameters, the density obtained in the laboratory, the density obtained with the Marchetti nomogram, considering a water density of 1 g/cm\({}^{3}\), and the density obtained with Equations (9) and (10) are compared in Figure 28.  
The difference in the data obtained was notorious; the Equation (9) presented data as a function of \(I_{D}\), which was close to the real density values. In this case, the use of [PERSON]'s method provided data that were not following the material that was obtained.  
Moreover, it can be observed that the trend generated from the laboratory results and depth (Equation (10)) presented higher values than those obtained in Equation (3) in meter 2. However, from meter 3 to 10, it presented intermediate results, with respect to the results obtained by the equation as a function of the \(I_{D}\), as shown in Figure 28.  
\[\rho=1.413z^{-0.127} \tag{10}\]  
where:  
\(z\): depth, m.