## 1 Introduction
Another experimental study on sandy and silty soils showed that \(G_{0}\) was related to the mean effective principal stress \(\sigma^{\prime}{}_{m}\) and void ratio [12; 13; 14; 15]. This relationship is presented by Equation (2):  
\[G_{0}=A\cdot F(e)\cdot(\sigma^{\prime}{}_{m})^{n} \tag{2}\]  
where \(A\) is an empirical constant reflecting the soil fabric formed through various stress and strain histories, \(n\) is an empirically determined exponent, equal to 0.5, and \(F(e)\) is the void ratio function defined as (3):  
\[F(e)=\frac{\left(B-e\right)^{2}}{1+e}, \tag{3}\]  
where the constant \(B\) is usually taken as 2.17 for round-grained sands [16; 17; 18]. The tests performed by [PERSON] et al. [19] on silty sands revealed the impact of fines content on the small strain stiffness and shear strength of silty sand. They performed triaxial and bender element tests on the mix of Ottawa sand and silt with a known gradation component. The results showed that the small strain shear modulus \(G_{0}\) was a function of the stress state and degree of compactness of the silty sand. The authors also noted that, although small strain stiffness dropped with finescontent, the critical-state strengths rose. The reason for that might be the freshly deposited silty sand fine particles that were not positioned in a way to provide optimum interlocking, so the small strain responses of soil resulted in low stiffness characteristics. The greater stresses would result in fine particles' rearrangement and therefore increase interlocking, dilatancy, and shear strength. The properties of soil differ even in the same layer, which is locally subjected to other stress conditions or the groundwater flow regime. Therefore, the response of soil is strongly influenced by what are generally termed local site conditions [20]. The topic of non-cohesive soil physical characteristics' impact on the dynamic properties is still under development. Recently, an effort to understand the effect of mean grain size was conducted by [PERSON] and [PERSON] [21] and by [PERSON] and [PERSON] [22]. The results of the tests showed that the increase of the coefficient of uniformity caused an increase in the non-linearity of the normalized shear modulus and damping ratio with shear strain. The normalized shear modulus and damping ratio also increased with the decrease in mean grain size. The authors employed the results of the bender element, as well as cyclic triaxial tests to derive an empirical equation for the shear modulus degradation curve based on the modified hyperbolic model [21]. The work of [PERSON] and [PERSON] [23] aimed to study the elastic moduli change in unsaturated soils. They tested a wide range of soil types in a uniaxial compression apparatus. The results of the tests showed that the volumetric water content impacted the elastic moduli values. The results also indicated that the initial state of volumetric water content, as well as the drying and wetting path, would affect the values of elastic moduli. A significant amount of knowledge concerning unsaturated non-cohesive soil response to cyclic loading was gathered recently [24; 25; 26; 27]. The reason for that was the high demand for resilient modulus characteristics. Resilient modulus \(M_{r}\) is one of the well-known parameters used in pavement engineering, which specifies the resilient strain during one cycle of loading. During cyclic loading of the soil, hysteretic behavior is observed in the shearing strain range equal to \(10^{-3}\%\). The response to such excitation in this strain range differs from this in the range \(10^{-4}\%\) and \(10^{-5}\%\), where we can observe that the elastic response and damping ratio are assumed to be equal to zero [28; 29]. The resilient strain is defined as the soil elastic response to cyclic loading during the unloading phase [30].