## 2 Framework of Adaptive Fusion Sampling Strategy  
This study proposes an adaptive fusion sampling strategy, which is detailed in the following steps, and a simplified framework is shown in Figure 1.  
In Step 1, the target reliability level (\(\text{COV}_{\text{T}}\)) 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 (M) is determined, in this case, the number of fusion samples \(\text{N}=0\). In Step 2, the CPT-based liquefaction probability assessment framework is used to determine the sampling spacing for preliminary CPT sounding from prior knowledge in the geotechnical domain, and the corresponding \(\left(q_{\text{c1N}}\right)_{\text{cs}}\) sparse data points are derived using the measured cone penetration resistance (\(q_{c}\)) and sleeve friction (\(f_{s}\)) (sparse data along the horizontal direction). The \(\left(q_{\text{c1N}}\right)_{\text{cs}}\) cross-section is then reconstructed from the sparse data using 2D BCS and Markov chain Monte Carlo (MCMC) simulation to evaluate the spatial distribution of soil liquefaction potential using a version of liquefaction probability developed by [PERSON] et al. [25]. Liquefaction-induced settlement monitoring is performed in conjunction with consolidation settlement theory in the geotechnical domain.  
In Step 3, for the sampling strategy to automatically fuse the sampled samples of geotechnical and geophysical data in a self-adaptive manner and determine their optimal sampling locations, a reliability level \(\text{COV}_{\text{M+N}}\) that can explain \(\hat{\mathbf{\xi}}^{III}\) (\(\hat{\mathbf{\xi}}^{III}\) represents \(\left(q_{\text{c1N}}\right)_{\text{cs}}\) sample data) is defined in the process of Steps 1-3. When the obtained reliability level does not achieve the target reliability level (\(\text{COV}_{\text{M+N}}>\text{COV}_{\text{T}}\)), MSF-BCS is used to perform a fusion sampling to trigger the adaptive process, which is combined with the information entropy theory to determine the optimal locations for fusion sampling to finally achieve the target reliability level (\(\text{COV}_{\text{M+N}}\leq\text{COV}_{\text{T}}\)).  
Uncertainty in the sparse data simulated \(\left(q_{\text{c1N}}\right)_{\text{cs}}\) cross-section is quantified using information entropy. \(H\big{(}\hat{\mathbf{F}}^{III}\big{)}\) represents the information entropy of the \(\left(q_{\text{c1N}}\right)_{\text{cs}}\) cross-section obtained by 2D BCS using geotechnical data from previous CPT soundings, and \(H\big{(}\hat{\mathbf{F}}^{III}_{new}\big{)}\) represents the new information entropy of the \(\left(q_{\text{c1N}}\right)_{\text{cs}}\) cross-section obtained by fusion sampling provided by MSF-BCS. The optimal location for fusion sampling is determined to be the location that maximizes \(\Delta\) between \(H\big{(}\hat{\mathbf{F}}^{III}\big{)}\) and \(H\big{(}\hat{\mathbf{F}}^{III}_{new}\big{)}\). It is worth noting that the \(\Delta\) maximization has been computed in the process of Steps 1-3.  
In Step 4, a high-resolution \(\left(q_{\text{c1N}}\right)_{\text{cs}}\) cross-section is generated from the \(\left(q_{\text{c1N}}\right)_{\text{cs}}\) data points obtained in Step 3 that reach the target reliability level. The high-resolution spatial distribution of liquefaction potential is subsequently generated based on the liquefaction probability assessment framework of CPT. In Step 5, liquefaction-induced surface settlement is updated to quantitatively evaluate the potential for building damage for geotechnical design.  
Figure 1: Framework of adaptive fusion sampling strategy.