## 5 Connection To Numerical Modelling
### Constitutive Model Parameters
#### 5.2.2 Layers 2, 3, 4, and 5  
Layers 2, 3, 4, and 5 are modelled using the HSS model as undrained materials. For these layers, \(E_{\mathit{oed}}\) is determined as the average value from both the CPT- and \(V_{s}\)-based workflows, following Equations (59) and (60), as proposed by [42] and [37], respectively.  
\[E_{\mathit{oed}}=\alpha_{M}(q_{t}-\sigma_{\mathit{v}});\,\alpha_{M}=Q_{\mathit{ tn}};\,for\,\,I_{\mathit{cn}}\geq 2.2\,\&\,Q_{\mathit{tn}}<14 \tag{59}\]  
\[E_{\mathit{oed}}=0.00010V_{s}^{2.212}\times 1000 \tag{60}\]  
The relationships between the different stiffness parameters for layers 2, 3, 4, and 5 are defined as follows [70]: \(E_{50}^{ref}=1.25\times E_{\mathit{oed}}^{ref}\) and \(E_{uv}^{ref}=5\times E_{50}^{ref}\).  
The small-strain shear modulus, \(G_{0}\), is obtained from the \(V_{s}\)-based workflow, while the reference stiffness parameters for the HSS model were previously defined in Equations (53)-(55). The reference value of \(G_{0}\) (\(G_{0}^{ref}\)) is determined as follows:  
\[G_{0}=G_{0}^{ref}[\frac{c^{\prime}\cos\,\varphi^{\prime}+c^{\prime}_{3}\sin\, \varphi^{\prime}}{c^{\prime}\cos\,\varphi^{\prime}+p^{ref}\sin\,\varphi^{ \prime}}]^{m} \tag{61}\]  
In the HSS model, the small-strain stiffness behaviour is governed not only by \(G_{0}^{ref}\) but also by the threshold shear strain (\(\gamma_{0.7}\)), at which the secant shear modulus reduces to 0.722 \(G_{0}\). The value of \(\gamma_{0.7}\) is determined based on the plasticity index (\(PI\)) and the overconsolidation ratio (\(OCR\)) using the following relationship [74]:  
\[\gamma_{0.7}=0.0001+5\times 10^{-6}PI(OCR)^{0.3} \tag{62}\]  
The plasticity index can be calculated from the CPT measurements using the method described by [75]:  
\[PI=\frac{17.5R_{f}(1+B_{q})^{1.2}}{(0.33Q_{t})^{0.31}} \tag{63}\]  
OCR is determined as the average value from both the CPT- and \(V_{s}\)-based workflows, following the methods defined in Table 2. The coefficient of earth pressure at rest (\(K_{0}\)) is determined using the method by [76] as cited in [71]:  
\[K_{0}=(1-\sin\,\varphi^{\prime}_{\mathit{cv}})OCR^{\sin\,\varphi^{\prime}_{ \mathit{cv}}} \tag{64}\]  
where \(\varphi^{\prime}_{\mathit{cv}}\) represents the critical state friction angle. For layers 2 and 3 (clay layers), an average value of 28.6\({}^{\circ}\) was adopted, as proposed by [77]. A higher value of 32\({}^{\circ}\) was selected for layer 1 (sandy silt), while a lower value of 25\({}^{\circ}\) was used for layers 4 and 5 (sensitive fine-grained soils).  
The material sets for the five layers are presented in Table 7. [PERSON]'s ratio (\(v_{ur}\)) was set to 0.2 for all layers, while \(m\) was assigned a value of 0.7 for layer 1 and 1.0 for the remaining layers. OCR methods often yield unrealistically high values for shallow layers due to very low effective stresses. As a result, the predicted OCR value for layer 1 was deemed unrealistic. Therefore, the OCR value was manually assigned as 3, slightly higher than the value obtained for layer 2. The connection between the determined material sets and a finite element software is discussed in the following section through a simple synthetic case study.