## 1 Introduction  
The development of geotechnical constructions such as roads, railways, levees, and foundations around the globe forces engineers to build road constructions on so far unsuitable subgrades for such purposes [1; 2; 3; 4; 5]. One of the easiest ways to improve soil properties is compaction. The traffic or railway loadings and industrial activities are connected to dynamic and cyclic excitations, which result in other soil responses in comparison to monotonic ones. The engineering constructions such as shallow foundations usually settle at an average strain equal to 1% [6]. Recently, the scientific focus of dynamic soil properties has turned from earthquake events to anthropogenic ones, which are characterized by low amplitude and low strain ranges. Soils, which are the subgrade of the foundation or road construction base, usually are compacted intentionally or unintentionally by machines such as heavy trucks. Therefore, the change in the original structure of the soil due to static and repeated loads impacts the subgrade soil parameters, which forces engineers to have proper information about the differences between natural and compacted soil. The repeating loading and excitations due to cyclic and dynamic loads can be characterized by a small strain characteristic to solve the boundary value problem [7]. The research conducted by [PERSON] et al. [8] was focused on silty soils' laboratory investigations into the main factors affecting the dynamic soil properties with the application of the resonant column technique. The materials in this study were the undisturbed specimens (from three boreholes located in southern Greece), as well as two additional remolded ones for the resonant column and cyclic simple shear tests. The soil was composed of sand and silt fractions. After a series of tests, the authors concluded that the low amplitude shear modulus (\(G_{0}\)) increased with confining pressure (\(\sigma_{0}\)), when material damping (\(D_{0}\)) was slightly decreasing. The authors also observed that the high amplitude shear modulus (\(G\)) and material damping (\(D\)) could be normalized in terms of the \(G\)/\(G_{0}\) and \(D\)/\(D_{0}\) versus the \(\gamma\)/\(\gamma_{0}\) relationship. The empirical relationship was proposed for estimation of the \(G_{0}\) parameter, based on the proposition of [PERSON] and [PERSON] [9] concerning the influence of the relative density described by coefficient \(K_{2,max}\), which is a function of the void ratio (\(K_{2,max}\) = 0.345(1000-430\(e\))) at very low strains (\(\gamma\) \(\leq\) 10\({}^{-3}\)%) (1):  
\[G_{0}=345(1-0.43e)\cdot(\sigma_{0})^{0.5}. \tag{1}\]  
where \(G_{0}\) and \(\sigma_{0}\) are in MPa and \(e\) is the void ratio. Studies of the dynamic properties of Piedmont residual soils [10] were done by performing resonant column and torsional shear tests. The residual soils tested in this research project were saprolites, which are micaceous sandy silts and silty sands obtained from depths from 0.9 m to 5.3 m. The results of the resonant column tests showed that the low amplitude shear modulus increased with confining pressure, which was also observed by [PERSON] et al. [8]. The maximum shear modulus varied by a power of less than 0.5 to confining pressure. The authors also observed that the shear modulus decreased with an increase in shear strain in the range of 0.001% to 0.002%. Factors such as the frequency or number of cycles have no significant influence on the shear modulus and damping ratio value. Further studies on Piedmont residual silty soils extended the laboratory tests with an in situ test [11] with the conclusion that \(G_{0}\) increased with increasing confining pressure. The article reported a general tendency of the normalized shear modulus G/\(G_{0}\) characteristics to increase with the increase in confining stress. The research also showed that the overconsolidation ratio did not affect the G/\(G_{0}\) relationship.