## 3 Results
### Resonant Column Test  
The resonant column tests can measure rotational displacement and acceleration by the use of proximitors, an accelerometer that registers coil current. The resonant column measures resonant frequency and acceleration. Based on these measurements, we could calculate the modulus and strain levels during the tests. This type of test was performed in a fixed-free device, and excitations were imposed, as well as measurements were taken from a free end of the sample. The current that flowed through the coil provided the torque. The function generator and power amplifier devices were able to  
Figure 5: Soil compressibility characteristics (red line, empty points) with the method of work for preconsolidation pressure determination (red diamonds) in moisture content \(m\) equal to: (**a**) \(m\) = 4.6%, (**b**) \(m\) = 6.1%, (**c**) \(m\) = 8.1%, (**d**) \(m\) = 9.4%, (**e**) \(m\) = 10.8%, and (**f**) \(m\) = 12.9%. impose harmonic signals even at high torque levels. The measurements were conducted in order to find the resonant frequency \(\omega_{n}\) data, which later led to calculating the shear modulus \(G\) based on the shear wave velocity as in the following Equation (7):  
\[G=\rho\cdot v_{s}=\rho\cdot\frac{\omega_{n}\cdot l}{\beta}, \tag{7}\]  
where \(l\) is the length of the sample and \(\beta\) is a device constant calculated based on the specimen mass and geometries. We calculated the damping from the resonant column test with the use of the logarithmic decrement method in which two acceleration maxims were used to calculate the damping based on Equation (8):  
\[D=\frac{\delta ec}{\sqrt{4\pi^{2}+\delta ec^{2}}} \tag{8}\]  
where \(\delta ec\) is the logarithmic decrement calculated as (9):  
\[\delta ec=ln\left(\frac{u_{n}}{u_{n}+1}\right) \tag{9}\]  
where \(u\) is the amplitude of acceleration of the \(n\) and \(n+1\) maxims. The damping ratio can be presented as a dimensionless parameter or as a percentage [40]. Figure 7 presents the normalized shear modulus characteristics versus shear strain \(\gamma\), and in Figure 8, the damping \(D\) characteristic is presented. The shear modulus change had close characteristics. These characteristics could be easily modeled if the \(G_{0}\) modulus value were calculated. We could observe that the initial shear modulus also responded to the compaction curve. For samples prepared in moisture content equal to 10.8% (Figure 7c), the initial shear modulus \(G_{0}\) had the highest values. The impact of consolidation pressure on the \(G_{0}\) value was clear. With the rise of \(\sigma_{3}\), the \(G_{0}\) also increased. The top value of shear modulus was equal to 164.08 MPa for \(\sigma_{3}\) equal to 150 kPa. The lowest value of \(G_{0}\) was equal to 82.02 MPa for the sample confined with a pressure equal to 30 kPa in moisture content \(m=12.9\%\). Figure 6: Void ratio change in different moisture and consolidation effective stress conditions for compacted sandy silt samples from odometer tests. The soil samples were prepared in moisture contents equal to 8.1%, 9.4%, 10.8%, and 12.9%, which corresponded to the Proctor test results. Table 2 presents the soil parameters' values during the resonant column test. The compaction caused the preconsolidation state, and therefore, the overconsolidation ratio (OCR) could be calculated for the resonant column samples. The modeling of shear modulus degradation could be conducted with the application of the [PERSON] et al. (2014) modulus reduction curve (10):  
\[\frac{G}{G_{0}}=\frac{1}{1+\left(\frac{\gamma}{\gamma_{2}}\right)^{\alpha}} \tag{10}\]  
Figure 7: Modulus reduction curves with the normalized shear modulus \(G/G_{0}\) for different moisture contents: (**a**) \(m=8.1\%\), (**b**) \(m=9.4\%\), (**c**) \(m=10.8\%\), and (**d**) \(m=12.9\%\). where \(\alpha\) is a curvature parameter (usually \(\alpha\approx 0.92\)) and \(\gamma_{\rm t}\) is called the pseudo-reference strain corresponding to \(G/G_{0}=0.5\).