## 4 Selection of HSS Model Parameters
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Region** & **Soil Sample** & \(\mathbf{E_{\text{ood}}^{\text{ref}}/E_{\text{s}}}\) & \(\mathbf{E_{\text{50}}^{\text{ref}}/E_{\text{ood}}^{\text{ref}}}\) & \(\mathbf{E_{\text{ur}}^{\text{ref}}/E_{\text{50}}^{\text{ref}}}\) & \(\mathbf{G_{0}^{\text{ref}}/E_{\text{ur}}^{\text{ref}}}\) \\ \hline Gaoxiong [17] & Sand & - & 1 & 3 & 2.42 \\ Tongchuan [24] & Loess & 0.93 & 12.46 & 7.6 & 2.23 \\ Xi’an [25] & Loess & 1.77 & 1.61 & 5.29 & 1.73 \\ Yan’an [26] & Loess & - & 1.2 & 3 & 3 \\ Jinan [27] & Clay & 1 & 1 & 8 & 1.5 \\ Jinan [28] & Silty clay & - & 0.91 & 6.97 & 1.74 \\ Shanghai [18] & Soft clay & 0.63\(\sim\)1.06 & 1.08\(\sim\)1.2 & 6.7\(\sim\)11.6 & 0.8\(\sim\)1.2 \\ Shanghai [29] & Clay & 0.9 & 1.2 & 6–8 & 2.5\(\sim\)4.9 \\ Wuhan [30] & Silty clay & 0.7–0.8 & 0.7–1.5 & 3.7–5.8 & 2.1–3.0 \\ Hangzhou [31] & Clay & 0.92 & 1.18 & 6.53 & 2 \\ Hangzhou [32] & Silty clay & 0.73\(\sim\)1 & 1–2.22 & 5–8.97 & 1.3–3 \\ Suzhou [33] & Silty clay, Silt & - & 0.8 & 4 & 3.8–4.55 \\ Yancheng [34] & Silty clay & 0.84 & 1.5 & 5.56 & 1.57–1.73 \\ Changzhou [35] & Clay, Silty clay & - & 1.33–1.50 & 3.6–4.3 & 1.6–2.0 \\ Paris, France & Sand & - & 1 & 2.5 & 1.89 \\ London, Britain [37] & Clay & - & 2 & 5.3 & 4.16 \\ Lisbon, Portugal [38] & Stiff clay & - & 1 & 3 & 2.3 \\ Jurmala, Latvia [39] & Subglacial till & - & 1 & 3 & 2.96 \\ Incheon, South Korea [40] & Sediment & - & 1.25 & 3 & 2.65 \\ Ledsgard, Sweden [41] & Clay & - & 1 & 3 & 2.53–3.03 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The modulus ratios of HSS models in different regions. applications, it is usually calculated using empirical formulas, such as those for clay (\(K_{0}=0.95-\sin\varphi^{\prime}\)) and for sand (\(K_{0}=1-\sin\varphi^{\prime}\)). According to the theory of elasticity, it can also be calculated using [PERSON]'s ratio \(\
u\) (see Formula (9)):  
\[K_{0}=\
u/(1-\
u) \tag{9}\]  
[PERSON] et al. [19] established the relationship between \(K_{0}\) and the void ratio \(e\) based on indoor tests. For cohesive soils, the relationship is as expressed in Formula (10), while for sandy soils, it is as shown in Formula (11):  
\[K_{0}=0.049e+0.02I_{\mathrm{P}}+0.139 \tag{10}\]  
\[K_{0}=0.154e+0.224 \tag{11}\]  
In the formulas mentioned, \(I_{\mathrm{P}}\) represents the plasticity index. Since Formulas (10) and (11) are derived from the \(K_{0}\) test values of typical soils in the Shanghai area, they are subject to regional limitations. Shanghai is characterized by soft clay soil, the mechanical properties of which may differ significantly from those of loess in the Xi'an area. [PERSON] [42] obtained the fitting formula for \(K_{0}\) of loess by fitting it with the over-consolidation ratio (OCR), as in Formula (12):  
\[K_{OCR}=0.42\times OCR^{0.36} \tag{12}\]  
Due to the significant influence of water content and stress history on the \(K_{0}\) value of loess, Formulas (10) and (11), provided by [PERSON], do not account for the impact of stress history. Although Formula (12) is a fitting formula specifically for loess, it also fails to consider the effects of water content \(w\) and void ratio \(e\). Consequently, using these formulas to calculate the \(K_{0}\) value of loess may lead to some deviation. This article fits the water content \(w\), void ratio \(e\), over-consolidation ratio, and the coefficient of earth pressure at rest \(K_{0}\) for loess, resulting in Formula (13):  
\[K_{0}=1.4w+0.033e+0.11 OCR^{-0.28} \tag{13}\]  
The deviation between the \(K_{0}\) calculated using this formula and the experimental results does not exceed 15%, as shown in Figure 8. This indicates that Equation (13) is more suitable than the previous equation for calculating the \(K_{0}\) of loess. Figure 8: Comparison chart between \(K_{0}\) calculated by various formulas and test results. Other parameters can be determined based on the geological survey report and relevant research experience. \(m\) was set to 0.75.