## 5 Results and Discussions
### Primary and Secondary Settlement Analysis  
Figure 4 illustrates the correlation between \(\dot{S}_{t}\) and \(S_{t}\) for both vacuum preloading and surcharge preloading. Using the slopes and intercepts of the \(\dot{S}_{t}\)-\(S_{t}\) curve in Figure 4 and Equations (8), (9), (12), and (13), \(S_{\infty}\), \(S_{i}\), \(S_{p}\), and \(S_{\rm s}\) are calculated and tabulated in Table 4. Then, \(E_{s}\), \(E_{\varphi}\), and \(K_{e}\) are calculated as 4.19 MPa, 6.83 MPa, and 4726.80 MPa/d in the surcharge preloading region, while they are 4.48 MPa, 4.67 MPa, and 3433.90 MPa/d in the vacuum preloading region. Table 4 shows that the instant settlement, \(S_{i}\), the primary consolidation settlement, \(S_{p}\) and the secondary consolidation settlement', \(S_{s}\), of vacuum preloading account for 28.2%, 44.7%, and 27.1% of the final settlements, \(S_{\infty}\), while the ones of surcharged loading do 26.7%, 55.5%, and 17.0% of \(S_{\infty}\). This means that the \(S_{s}/S_{\infty}\) during vacuum preloading is 1.6 times that during surcharge preloading. The reason for this is speculated as follows: Firstly, in Section 5.1 on the 83 rd day, the \(U_{st}\) of vacuum preloading is less than the one of surcharge preloading. In other words, \(S_{s}/S_{\infty}=1-U_{st}(t=83)\) of the vacuum preloading is greater than the one of the surcharge preloading. Secondly, the surcharge preloaded \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Vacuum Preloading** & \multicolumn{2}{c}{**Surcharge Preloading**} \\  & **Settlement** & **Settlement** & **Settlement Ratio** \\ \hline immediate & 375.4 & 28.2\%, & 400.2 & 26.7\%, \\ primary consolidation & 594.6 & 44.7\% & 804.8 & 55.5\% \\ secondary consolidation & 360 & 27.1\% & 246 & 17.0\% \\ final & 1330 & 100\% & 1451 & 100\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Ground settlements by consolidation model method. Figure 4: Curves of settlement rate and settlement: (**a**) vacuum preloading; (**b**) surcharge preloading. foundation undergoes an additional stress field by a similar loading method for preloading and service stage, while the vacuum preloaded one is subjected to a negative pressure seepage field in the preloading stage and to an additional stress field in the service stage. Figure 5 depicts the predicted curves for \(S_{i}\), \(S_{pt}\), and \(S_{st}\) plotted against time. From Figure 5 it can be deduced that after preloading, \(S_{i}\) and \(S_{pt}\) tend to stabilize within 83 days, while \(S_{st}\) is smaller. In the service after the 83 rd day, the \(S_{gs}\) is still increasing for a long time of 10 ten years and is dominated by \(S_{st}\). If the \(S_{st}\) of the preloading improved ground is over excessive, this may result in adverse settlement and settlement differences during the life of the building, reducing the serviceability of the foundations. During the primary consolidation phase, soil consolidation primarily arises from the expulsion of air and free water within the pores. Conversely, secondary consolidation chiefly occurs due to the reorganization of soil grain structure and the creep of bound water films on soil grain surfaces. As illustrated in Figure 5, the duration required for vacuum preloading consolidation to achieve settlement stability is notably longer compared to surcharge preloading consolidation. The reason for this may be that the vacuum preloading method acts on the pore water vapor fluid in the soil, and as pore water and gas dissipate, the pore space between soil particles gradually expands, inducing the rearrangement and compaction of soil particles without incurring shear damage or particle breakage. In contrast, the external load of surcharge preloading is applied directly to the soil skeleton or particles. The compression or disintegration of the skeleton prompts the translation or rotation of clay agglomerates, culminating in the internal cementing fracture of these agglomerates. Macroscopically, this process manifests as creep deformation of the soil.