### Assessment of Soil Stiffness at Small Strains  
The soil stiffness or shear modulus \(G\) at small to large strains generally results from the material properties of the soil (grain characteristics, plasticity, void ratio, cementation), the stress state or stress history (overconsolidation ratio, mean effective stress) and the dynamic loading characteristics (frequency, number of cycles, drained/undrained conditions). However, factors that significantly influence \(G\) are the engineering shear strain amplitude \(\gamma\), soil plasticity index \(PI\) and effective stress \(\sigma^{\prime}\)[8; 9]. The initial shear modulus \(G_{0}\) is defined at an infinitesimally small shear strain, typically \(\gamma=10^{-6}\), and can be measured in the laboratory using the BE and RC tests. According to the studies, the BE technique provides \(G_{0}\) similar to that obtained with the RC technique (e.g., [10; 11; 12; 13]). In addition, [PERSON] et al. [14] found that performing BE and RC tests separately may lead to a possible discrepancy in the determination of \(G_{0}\). Nonetheless, the behavior of materials in practice may differ from laboratory test results due to factors such as sample disturbance and variations in assessment methods [15]. In the past, numerous researchers have formulated empirical relationships for estimating \(G_{0}\) derived from laboratory tests. In general, these empirical equations follow the form proposed by [PERSON] and [PERSON] [16], in which \(G_{0}\) is expressed as a function of the material constant \(S\), void ratio \(e\), overconsolidation ratio \(OCR\), and effective stress \(\sigma^{\prime}\):  
\[G_{0}=S\cdot f(e)\cdot g(OCR)\cdot h\big{(}\sigma^{\prime}\big{)} \tag{1}\]  
[PERSON] and [PERSON] [17] have shown that \(G_{0}\) for normally consolidated soils (\(OCR=1\)) is not influenced by \(PI\). However, for overconsolidated soils (\(OCR>1\)), \(G_{0}\) increases with higher \(PI\). For practical applications, it is sometimes suggested that the effects of \(OCR\) on \(G_{0}\) can be completely neglected [18]. Due to advances in measurement technology, direct measurement of \(G_{0}\) is now widely used in various laboratory or field tests, as it provides more reliable and cost-effective measurements compared to empirical relationships [19]. Usually, laboratory measurements of the secant shear modulus \(G\) are normalized with respect to \(G_{0}\) as a function of \(\gamma\). The shape of the \(G/G_{0}\) curve for cohesive soils is notably influenced by factors such as \(PI\), \(\sigma^{\prime}\) and the void ratio \(e\)[20; 21; 22]. In cohesive soils, however, \(e\) is closely related to \(\sigma^{\prime}\) and \(OCR\)[6]. Therefore, most research focuses on studying the effects of \(PI\), while the influence of \(\sigma^{\prime}\) and \(OCR\) on the \(G/G_{0}\) curves is only occasionally considered. [PERSON] and [PERSON] [21] formulated \(G/G_{0}\) curves with hyperbolic stiffness reduction in the form of a normalized reference engineering shear strain \(\gamma_{ref}\). After modification by [PERSON] and [PERSON] [23], the modulus reduction model is expressed as follows:  
\[\frac{G}{G_{0}}=\frac{1}{1+0.385\cdot\left(\frac{\gamma}{\gamma_{07}}\right)} \tag{2}\]  
where \(\gamma_{ref}=\gamma_{0.7}\) is the reference engineering shear strain at which the shear modulus \(G_{0}\) decreases to about \(70\%\). Numerical modelling software usually requires inputs for \(G_{0}\) and \(\gamma_{0.7}\) to construct the \(G/G_{0}\) curve, as is the case with the HSS model. In addition, such a formulation of the \(G/G_{0}\) curve is characterized by a lower susceptibility to numerical errors [6]. For cohesive soils, it was shown that the \(\gamma_{0,7}\) increases with \(PI\), \(\sigma^{\prime}\) and \(OCR\). This effect is more pronounced in soils with lower \(PI\), while it decreases with increasing \(PI\)[24; 25]. Many studies have shown that the \(G/G_{0}\) curve is generally not affected by \(OCR\) (e.g., [17; 26]). Nevertheless, [PERSON] et al.