## 3 Results and Discussion  
Within the scope of this study, using the stress-strain relationship obtained from monotonic triaxial tests as a result of the laboratory studies presented in detail, above and whole test curves of resonant column and monotonic triaxial tests were generated, as given in Figure 5. It should be noted that in the monotonic triaxial experiments conducted in this study, E\({}_{\rm ur}\) could not be measured. Instead, the values of E\({}_{0}\) and E\({}_{50}\) were determined by evaluating the stress-strain curves given in Figure 6a. E\({}_{\rm dyn}\) is derived from G\({}_{0}\) obtained from resonant column tests considering the [PERSON]'s ratio range (\(\upsilon\) = 0.2, 0.3 and 0.4) by using E\({}_{\rm dyn}\) = 2G\({}_{0}\)(1 + \(\upsilon\)) relation. Figure 5 shows that the shear modulus (G\({}_{0}\)) values obtained from resonant column tests for five different sand samples (S1-S5) increase with increasing confining stress. The specimens appear to be confined within a narrow range under similar stress conditions; however, the S5 specimen consistently exhibits higher G\({}_{0}\) values compared to the others. This difference can be attributed to the fact that S5 is clean sand, since the grain-to-grain contact is more direct and the stiffness properties are generally higher in sands without fine grains. The initial elastic modulus (E\({}_{0}\)) and secant elastic modulus (E\({}_{50}\)) obtained from monotonic triaxial compression tests were evaluated for five different sand specimens at varying relative densities (D\({}_{\rm R}\) = 0.45 and 0.70). As shown in Figure 5, both modulus values increase with increasing confining stress. In specimens with high relative density (D\({}_{\rm R}\)\(\geq\) 0.70), E\({}_{0}\) and E\({}_{50}\) values are significantly higher, especially specimen S5, which exhibited higher modulus of elasticity values compared to other sands under the same confining stress. Figure 4: RCT equipment and stages: (**a**) placing the specimen and dimension control; (**b**) adjusting the cell pressure and vacuum by servo-system; (**c**) testing stage. Figure 3: MTX test equipment: (**a**,**b**) placing the specimen with the vacuum; (**c**) applying cell pressure and shearing; (**d**) specimen at the end of test. Figure 5: Test curves of resonant column tests (**left column**) and monotonic triaxial tests (**right column**). In this study, special emphasis was placed on defining the static stiffness of the tested soils in accordance with the conceptual framework proposed by [3]. Therefore, it becomes important which of the modules E\({}_{0}\), E\({}_{ur}\) and E\({}_{50}\) in Figure 6a is E\({}_{stat}\). To understand this,  
\[\mathrm{R_{sec}}=\frac{\mathrm{E_{stat}}}{\mathrm{E_{50}}} \tag{3}\]  
relation was defined. Here, R\({}_{sec}\) is the ratio between static elastic modulus (E\({}_{stat}\)) and the secant modulus (E\({}_{50}\)). R\({}_{sec}\) will be 1.0 when E\({}_{stat}\) is assumed as E\({}_{50}\). On the other hand, [13] suggests R\({}_{sec}\) = 3.0 by using the E\({}_{stat}\) = E\({}_{ur}\) for HS and HSsmall constitutive models. Ref. [3] probably used the notation Ei as the static modulus of elasticity and defined it as shown in Figure 6b. This issue was discussed by [7; 14] as to which of the static moduli of elasticity (E\({}_{0}\), E\({}_{ur}\), E\({}_{50}\)) defined in Figure 6a is E\({}_{stat}\). As a result, they stated that the relationship E\({}_{stat}\) = E\({}_{ur}\) = 3E\({}_{50}\) is more appropriate for E\({}_{stat}\). In other words, considering \(\upsilon\) = 0.2, they obtained R\({}_{sec}\) = 3. Figure 7 illustrates the relationships between elastic moduli and their respective ratios, as calculated for five distinct sand specimens under varying assumptions of Poisson's ratio (\(\upsilon\) = 0.2, 0.3, 0.4). The [3] correlation posits that an increase in the static elastic modulus corresponds to a decrease in the E\({}_{dyn}\)/E\({}_{stat}\) ratio.