## 3 Application of APD to a Soft Clay Site
### Soil Parameters
#### 3.2.4 Stiffness Parameters  
The small-strain shear modulus (\(G_{0}\)) is determined from \(V_{s}\) using Equation (52), where \(\rho\) represents the soil density. For the CPT-based workflow, \(G_{0}\) is computed using Equation (52), with \(V_{s}\) values derived from the methods listed in Table 4. The selected methods for calculating \(G_{0}\) are presented in Table 5. \begin{table}
\begin{tabular}{l l l l} \hline
**Workflow** & **Method** & & **Author** \\ \hline \multirow{6}{*}{\(V_{s}\)} & \(0.01V_{s}^{2}\) & (22) & [35] \\  & \(\sigma_{v}^{\prime}\) & (23) & [36] as cited in [35] \\  & \(0.007691V_{s}^{2.009}\) & (24) & [37] \\  & \(\sigma_{v}^{\prime}\) & (25) & [24] \\  & \(0.1097V_{s}^{1.3575}\) & (25) & [24] \\ \hline \end{tabular} Note: \(l_{\alpha}\) = normalised soil behaviour type (SBT) index; \(Q_{t}\) = normalised cone resistance; \(B_{q}\) = pore pressure parameter ratio; \(K_{D}\)= horizontal stress index.  
\end{table} 
Table 2: _Cont._ \begin{table}
\begin{tabular}{l l l l} \hline
**Workflow** & **Method** & & **Author** \\ \hline \multirow{6}{*}{CPT} & \(\dfrac{q_{t}-\sigma_{v}}{N_{kt}}\); \(N_{kt}=12\) & (26) & [38] \\  & \(\dfrac{q_{t}-\sigma_{v}}{N_{kt}}\); \(N_{kt}=10.5-4.6\ln(B_{q}+0.1)\) & (27) & [19] \\ \cline{1-1}  & \(\dfrac{u_{2}-u_{0}}{N_{\Delta u}}\); \(N_{\Delta u}=6\) & (28) & [38] \\ \cline{1-1}  & \(\dfrac{u_{2}-u_{0}}{N_{\Delta u}}\); \(N_{\Delta u}=7.9+6.5\ln(B_{q}+0.3)\) & (29) & [19] \\ \cline{1-1}  & \(\dfrac{q_{t}-u_{2}}{N_{ke}}\); \(N_{ke}=8\) & (30) & [38] \\ \cline{1-1}  & \(\dfrac{q_{t}-u_{2}}{N_{ke}}\); \(N_{ke}=4.5-10.66\ln(B_{q}+0.2)\) & (31) & [19] \\ \hline \multirow{6}{*}{DMT} & \(0.12(P_{0}-\sigma_{v})\) & (32) & [32] \\  & \(0.09(P_{1}-\sigma_{v})\) & (33) & [32] \\ \cline{1-1}  & \(0.22\sigma_{v}^{\prime}(0.5K_{D})^{1.25}\) & (34) & [31] \\ \cline{1-1}  & \(0.018(E_{D})\) & (35) & [39] \\ \cline{1-1}  & \(0.35\sigma_{v}^{\prime}(0.47K_{D})^{1.14}\) & (36) & [39] \\ \hline \multirow{6}{*}{\(V_{s}\)} & \(0.152V_{s}^{1.142}\) & (37) & [40] \\ \cline{1-1}  & \(0.021V_{s}^{1.52}\) & (38) & [37] \\ \cline{1-1}  & \(0.016V_{s}^{1.50}\) & (39) & [24] \\ \hline \end{tabular}
\end{table} 
Table 3: Selected methods for the undrained shear strength (\(s_{u}\)). The total unit weight was determined from tube sampling, as reported in [7]. Figure 3a displays the outcomes of the three workflows based on the methods summarised in Table 1. For the CPT-based workflow, the upper limit of the predicted range (blue highlighted area) shows good agreement with the reference data in Clay 1 and Clay 3 (see Figure 2), suggesting that certain methods provided reliable estimates. Nevertheless, the majority of CPT-based methods yielded lower values than those measured, which can be attributed to the low \(f_{s}\) values and ultimately led to an underestimation in the average CPT-derived results. In contrast, the average values from the \(V_{s}\)-based workflow show good agreement with the reference values. For the DMT-based workflow, the predicted unit weight aligns well with the reference values in Clay 1 but is overestimated in Clay 2. The evaluation of OCR was based on oedometer tests [9,10], as cited in [7]. Figure 3b presents the OCR values obtained using the methods listed in Table 2. The average predictions from the three workflows align closely with the reference OCR values, demonstrating good overall agreement. The \"reference\" \(s_{u}\) values were collected from various sources, as cited in [7], with these sources highlighted in the legend of Figure 3c. The average predictions from the CPT-based workflow provided reasonable estimates of the reference values.