## 4 Discussion
### Elasticity Modulus (E)  
The modulus of elasticity equation was proposed and validated by [PERSON], relating to the value of \(E_{D}\), to the value of the modulus of elasticity itself, and is limited by the value of \(I_{D}\) and \(K_{D}\)[24]. However, according to [2], the value of the elasticity modulus cannot be directly equal to \(E_{D}\) due to the absence of information about the stresses that soil  
Figure 17: Results of the DMT plotted on Marchetti’s nomogram.  
has undergone in its history. Hence, the elasticity modulus was approximately 80% of the odometric modulus or \(M_{DMT}\).  
To find a correlation between the elasticity modulus (\(E\)) and the dilatometer modulus (\(E_{D}\)), it was necessary to see how the behavior of \(E\) about \(I_{D}\) was (Figure 18), because the material index (\(I_{D}\)) was used to define the type of material.  
Figure 18 presented that the dilatometer modulus (\(E_{D}\)) was proportional directly to \(I_{D}\), presenting a lineal relationship, with R\({}^{2}\) equal to 0.873. Moreover, 85% of \(I_{D}\) values were less than 1, so the equation presented in Figure 19 has a higher degree of effectiveness for soils with an \(I_{D}\) of less than 1.  
Figure 20 shows that the modulus of elasticity results obtained in the laboratory decrease with an increasing depth, presenting a potential tendency with an R\({}^{2}\) equal to 0.4881.  
Figure 19: Correlation and regression equation to obtain the modulus of elasticity.  
Figure 18: Relationship between the \(I_{D}\) and \(E_{D}\) of all collected data.  
A comparison was also presented between the results obtained using the equations currently in force based on [PERSON]'s studies and the data obtained in the laboratory, which is presented in Figure 21.  
Figure 21 showed that Equation (3) had the best fit, with respect to the expected results, which ranged between 0.2 MPa and 0.5 MPa. Therefore, an exponential model (Figure 19) was chosen to obtain consistent values of the elasticity modulus considering the real data. Nevertheless, considering that the \(E_{D}\) depended directly on the \(I_{D}\) (Figure 17), Equation (3) was limited to \(I_{D}\) values less or equal to 1.  
\[E=0.231e^{0.326E_{D}},\quad I_{D}\leq 1 \tag{3}\]  
The results of Equation (3), which were presented in Figure 19, show the variation between the three values of elasticity modulus. The data presented by [PERSON] presented extremely high values concerning the values obtained in the laboratory tests. Equation (3)  
Figure 20: Correlation equation based on test results and depth for modulus of elasticity.  
Figure 21: Comparison between different elasticity modulus values.  
derived in this work, although it provided low results for more consistent materials, presenting a trend with more accurate values for organic soils with a low \(I_{D}\) equal to or less than 1.  
In addition, it was possible to observe that the trend generated from the laboratory results and depth (Equation (4)) presented higher values than those obtained in Equation (3) in meters 2 and 3. However, from meter 4 to meter 10, it adapted better to the results obtained by the equation as a function of \(E_{D}\), as shown in Figure 21.  
\[E=1.191z^{-0.581} \tag{4}\]  
where:  
\(z\): depth, m.