## 4 Calculation of Primary and Secondary Settlement  
Based on the mechanics of soil consolidation, the ground settlement is composed of instant settlement (\(S_{i}\)), primary consolidation settlement (\(S_{p}\)), and secondary consolidation settlement (\(S_{s}\)) caused by creep. Therefore, the final settlement by the consolidation method is presented. The final settlements (\(S_{\infty}\)) of two improved regions are also analyzed by the consolidation model method proposed by:  
\[S_{\infty}=S_{i}+S_{p}+S_{s}\,\ S_{t}=S_{i}+S_{pt}+S_{st} \tag{1}\] \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Monitoring Items**} & \multicolumn{2}{c}{**Vacuum Preloading**} & \multicolumn{2}{c}{**Surcharge Preloading**} \\  & **Number** & **Sequence** & **Number** & **Sequence** \\ \hline Ground settlement & 20 & BC001-BC020 & 30 & BC101-BC130 \\ Excess pore water pressure & 4 & KY001-KY004 & 6 & KY101-KY106 \\ Stratified settlement & 6 & FC001-FC006 & 8 & FC101-FC108 \\ Horizontal displacement & 6 & WY001-WY006 & 4 & WY101-WY104 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Monitoring points for vacuum preloading and surcharge preloading. where \(S_{t}\) is average ground and strata consolidation settlement at time of \(t\), and \(S_{pt}\) and \(S_{st}\) are the primary consolidation settlement and secondary consolidation settlement caused by creep at time \(t\). During the primary consolidation settlement stage, \(S_{st}\) is very small and is therefore ignored. Then:  
\[S_{pt}=S_{t}-S_{i} \tag{2}\]  
The primary consolidation settlement and its rate are written as:  
\[S_{pt}=\overline{U}_{t}S_{p}\,\ \dot{S}_{pt}=\overline{\dot{U}}_{t}S_{p} \tag{3}\]  
where \(S_{pt}\) and \(\dot{S}_{pt}\) are the primary consolidation settlement and its rate, respectively. \(\overline{U}_{t}\) is the average of consolidation degree by \(\overline{U}_{t}=\sum_{i=1}^{1}\frac{\dot{q}_{i}}{\sum\Delta p}[(T_{i}-T_{i-1 })-\frac{\dot{a}}{\beta}e^{-\beta t}\big{(}e^{\beta T_{i}}-e^{\beta T_{i-1}} \big{)}]\), where \(\dot{q}_{1}\) is the loading rate of 80/20 and 80/30 kPa/d for vacuum and surcharging preloading, respectively; \(\sum\Delta p\) is the cumulative loads (80 kPa); and \(T_{1}\) and \(T_{0}\) are the start time and end time for load No.1, respectively. When the conditions of vertical and inward radial drainage are applied, \(\alpha=\frac{8}{\pi^{2}}\), \(\beta=\frac{8}{F(n)}\frac{\dot{C}_{b}}{d_{c}^{2}}+\frac{\pi^{2}}{4}\frac{C_{p} }{H^{2}}\), where \(n=d_{e}/d_{w}=19.09\), \(n=F(n)=\frac{n^{2}}{n^{2}-1}\ln n-\frac{3n^{2}-1}{4n^{2}}\). \(C_{h}\) and \(C_{v}\) are the horizontal and vertical consolidation coefficients (cm\({}^{2}\)/s), respectively. \(C_{v}=k(1+e)/a_{1-2}Y_{w}\), where \(k\), \(e\), \(a_{1-2}\) and \(\gamma_{w}\) are listed in Table 1. In the paper, \(C_{h}=C_{v}\). Substituting \(\overline{U}_{t}\) in Equation (3), the following can be obtained:  
\[\dot{S}_{pt}+\beta S_{pt}=\sum_{i=1}^{1}\frac{\dot{q}_{i}}{\sum\Delta p}(T_{i} -T_{i-1})S_{p} \tag{4}\]  
Equation (4) is the first order differential equation of \(S_{pt}\), proposed by [PERSON] [27]. Then, substituting \(S_{pt}\) in Equation (4) with Equation (2), the following is obtained:  
\[\dot{S}_{t}+\beta S_{t}=\sum_{a=1}^{1}\frac{\dot{q}_{i}}{\sum\Delta p}(T_{i}-T _{i-1})S_{p}+\beta S_{i} \tag{5}\]  
Equation (5) shows that the average ground settlement rates (\(\dot{S_{t}}\)) is liner to the \(S_{t}\) with the slope (\(-\beta\)) and intercept (\(b_{c}\)) fitted by least square method. Where \(\dot{S}_{t}=0\), \(S_{t}\) is the sum of \(S_{p}\) and \(S_{i}\), and is denoted as \(S_{pi}\).