## 6 Real Data Example
The best estimates of \(\left(q_{c1N}\right)_{cs}\) data at \(\mathrm{z}=3.375\,\mathrm{m}\) and at \(\mathrm{z}=5.750\,\mathrm{m}\) are shown in Figure 13a,b, respectively, and the best estimates along the horizontal coordinates are within the 90% confidence interval. Figure 14 shows that the initial reliability level of \(\mathrm{COV_{M+N}}\) in the sparse data model is \(\mathrm{COV_{5}}=8.8\%\), and \(\mathrm{COV_{7}}=6.0\%\) after two fusion sampling in a self-adaptive manner, which meets the condition of stopping the fusion sampling. The adaptive fusion sampling process continuously increased the reliability level of the interpreted liquefaction assessment results, and the interpolation uncertainty and soil spatial variability continued to decrease. It is worth noting that additional sampling can be performed using CPT soundings during the multi-stage process of the project when the reliability level does not meet the specific engineering requirements, which is a routine tool in practical engineering [19]. Figure 4:1 Simulated high-resolution \((q_{c1N})_{cs}\) cross-section after the first fusion sampling: (**a**) Mean; (**b**) SD. Figure 4:2 Simulated high-resolution \((q_{c1N})_{cs}\) cross-section after the second fusion sampling: (**a**) Mean; (**b**) SD. The statistical results corresponding to 1D cross-sections a1-a2 and a3-a4 along the horizontal coordinates are shown in Figure 4:3 (\(q_{\text{C1N}}\))\({}_{\text{cs}}\) measured values are in the confidence interval range [CI\(-\), CI+] of the computed values of MSF-BCS, which indicates that the proposed strategy is very effective and robust in performing sampling with small computational errors. In addition, the MSF-BCS method retains valuable information about the sampled data, with 90% confidence intervals encompassing most of the local variation in the data and providing a more reasonable average profile. In Step 4, a high-resolution \(CRR\) cross-section is generated from the \(\left(q_{\text{C1N}}\right)_{\text{cs}}\) data points obtained in Step 3 that achieve the target reliability level, as shown in Figure 4:4 The corresponding high-resolution \(FS\) cross-sections and spatial distribution of liquefaction potential are subsequently generated, as shown in Figures 16 and 17, respectively. The results indicate that most of the areas of the updated spatial distribution of liquefaction potential would have been liquefied during the \(M_{w}=6.2\) earthquake, which is consistent with the liquefaction observed at the field site during the earthquake [44; 45]. In addition, the above process verifies the feasibility of the adaptive sampling strategy. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \multirow{2}{*}{ \begin{tabular}{c} **Horizontal** \\ **Coordinate (m)** \\ \end{tabular}  } & \multicolumn{6}{c}{**a1–a2**} & \multicolumn{6}{c}{**a3–a4**} \\ \cline{2-9}  & **Measured** & **Computed** & **Value** & **CI–** & **CI+** & **Measured** & **Computed** & **CI–** & **CI+** \\ \hline
0 & 103.51 & 103.67 & 96.07 & 111.27 & 83.62 & 84.33 & 77.88 & 90.79 \\
15 & 132.33 & 132.15 & 124.55 & 139.74 & 85.97 & 87.29  
In Step 5, the liquefaction-induced surface settlement monitoring result is updated to quantitatively evaluate the potential for building damage. Figure 18 illustrates the \(\varepsilon_{v}\) distribution for the subsurface space (A-A\({}^{\prime}\)) soil using Equations (1)-(11). The updated \(\varepsilon_{v}\) was then integrated to estimate the liquefaction-induced \(S_{v}\), and the monitoring results updated by the adaptive fusion sampling strategy are shown in Figure 19. The results indicate that significant differential settlement occurs at horizontal coordinates 12.9-43.8 m and 50.9-82.0 m. The maximum settlement variations (\(\
abla S_{v}\)) achieve 81.5 mm and 93.4 mm, respectively, and the estimated \(S_{v}\) after using the adaptive fusion sampling strategy can judge the local area variations more accurately and provide reference for geotechnical engineering design. Figure 16: High-resolution _FS_ cross-section.