## 6 Real Data Example
obtained subsurface space information is increasing, and a reasonable target reliability level is thus defined based on the project cost, time, and the level of project risk. In this paper, the target reliability level is set to 6% and the number of initial CPT soundings \(\text{M}=5\) based on limited CPT sounding data and geophysical data provided by actual cases in the New Zealand Geotechnical Database in order to implement the data-driven adaptive fusion sampling strategy proposed for demonstration. It is worth noting that this does not indicate a final reliability level of 6%. In Step 1, \(\text{COV}_{\text{T}}=6.0\%\) for the spatial distribution assessment of liquefaction potential is determined as the threshold for the adaptive fusion sampling strategy process and the initial number of CPT soundings (\(\text{M}=5\)) is determined, and \(\text{N}=0\) at this time. In Step 2, the CPT-based liquefaction probability assessment framework is used to derive the corresponding \(\left(q_{c1N}\right)_{cs}\) sparse data points using the \(q_{c}\) and \(f_{s}\) data from five CPT soundings. The \(\left(q_{c1N}\right)_{cs}\) cross-section is then reconstructed from the sparse data using 2D BCS and MCMC. Figure 5 show the mean and standard deviation (SD) of the generated \(\left(q_{c1N}\right)_{cs}\) samples, quantifying the uncertainty associated with the reconstruction process, with vertical and horizontal resolutions of 0.125 m and 1 m for the cross-sections, respectively. In Figure 5, the black dashed line indicates the \(\left(q_{c1N}\right)_{cs}\) data along the depth direction, and the red solid line indicates the optimal locations C1 and C2 ranges for fusion sampling. The \(\left(q_{c1N}\right)_{cs}\) data points were interpreted as \(CRR\) cross-sections using Equation (2), as shown in Figure 6. Figure 7 shows the interpreted \(CSR\) cross-section based on five CPT soundings. The cross-section of the interpreted \(FS\) was generated based on the definition of \(FS\) (Figure 8). A version of the liquefaction probability developed by [PERSON] et al. [25] was used to evaluate the spatial distribution of soil liquefaction potential, as shown in Figure 9. Combined with the consolidation theory in the geotechnical field to monitor liquefaction-induced settlement, Figure 10 illustrates the \(\varepsilon_{p}\) distribution of the site after liquefaction. Figure 5: (\(q_{c1N}\))\({}_{cs}\) cross-section of five CPT soundings simulated by 2D BCS: (**a**) Mean; (**b**) SD. Figure 6: Interpreted cross-section of \(CRR\) based on five CPT soundings. In Step 3, \(\text{COV}_{5}>\text{COV}_{\text{T}}\) was obtained from the Step 1-2 process, so one fusion sampling was performed using MSF-BCS to trigger the adaptive process and combined with information entropy theory to determine the optimal location of fusion sampling in the range of C1 and C2. Figure 11 shows the mean and SD of the \(\left(q_{c1N}\right)_{\text{cs}}\) samples generated after the first fusion sampling at C1. Subsequently, the second fusion sampling was performed at C2, and the sampling was finally stopped with \(\text{COV}_{7}\leq\text{COV}_{\text{T}}\). The sampling process updates the assessment model in a systematic and quantitative manner. Figure 12 shows the mean and SD of the \(\left(q_{c1N}\right)_{\text{cs}}\) samples generated after fusion sampling at C2. It is worth noting that MSF-BCS is not required since the distances between CPT_31917 and CPT_31914, and between CPT_31913 and CPT_31918 are less than 15 m, satisfying the requirements for generating high-resolution cross sections [20,35]. Figure 8: Interpreted cross-section of _FS_ based on five CPT soundings. Figure 10: Interpreted \(\varepsilon_{v}\) distribution of the site based on five CPT soundings. Figure 7: Interpreted cross-section of _CSR_ based on five CPT soundings. Figure 4:0 Interpreted spatial distribution of soil \(P_{L}\) (%) based on five CPT soundings.