# Dewatering-Induced Stratified Settlement around Deep Excavation: Physical Model Study
## 3 Materials and Methods  
### Artificial Assumption Boundary  
A hydraulic connection between a confined aquifer and an adjacent aquitard is observed in the MAMA system for general soil layers in Shanghai. During dewatering in the confined aquifer, the pore water pressure of the overlying strata changes correspondingly. In the dewatering process, the pore water pressure in the confined aquifer decreases and breaks the original stress balance. According to the principle of effective stress, the decrease in pore water pressure in the confined aquifer is equivalent to the application of negative pore water pressure inside the MAMA system, which is an axisymmetric funnel with the center of the pumping well or deep excavation. Therefore, to simulate this physical and mechanical process in the physical model tests, the similarity ratio (prototype/physical model) of the basic physical parameter force (\(F\)), length (\(L\)), and time (\(T\)) are defined as \(\alpha_{L}=150\):1, \(\alpha_{F}=150^{3}\):1, and \(\alpha_{T}=15\):1, respectively. According to the _FLT_ dimensional analysis method, the similarity ratio of other physical parameters in the MAMA deformation system is shown in Table 2.  
Quaternary strata in middle and shallow portions can be simplified into five layers, namely, 1 + 2 of artificial filled soil, 3 + 4 of mutck clay, 5 of silty clay, 7 of fine sand, and 3 of medium-coarse sand. According to long-term hydrological observation data of Shanghai, the depth of the natural groundwater level of the first and second confined aquifers is 3.0-11.0 m and 5.0-12.0 m, respectively. Given that two layers (e.g., layers 2 and 3) of confined water were connected in this test, the natural depth of the groundwater level in the prototype and in the physical model is set as 3.0 m and 20.0 mm, respectively. To meet the similar requirements of the physical model test, natural clay (taken from layer 4) \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Parameters** & **Symbol** & **Dimensional Analysis** &
\begin{tabular}{l} **Similarity Ratio** \\ **(Prototype/Physical Model)** \\ \end{tabular} \\ \hline Stratum’s thickness & \(H\) & \(H=L\) & 150:1 \\ Weight & \(\gamma\) & \(\gamma=\rho\delta=\frac{FT^{2}}{L^{4}}\frac{L}{T^{2}}=\frac{F}{L^{5}}\) & 1:1 \\ [PERSON]’s modulus & \(E_{s}\) & \(E_{s}=\frac{F}{L}\) & 150:1 \\ Hydraulic conductivity & \(K\) & \(K=\frac{K}{9L}=\frac{L}{T}\frac{T}{L^{4}}L^{2}=\frac{L}{T}\) & 10:1 \\ Groundwater level drawdown & \(\Delta h\) & \(\Delta h=L\) & 150:1 \\ Pore water pressure & \(u\) & \(u=\frac{F}{L^{5}}\) & 150:1 \\ Settlement & \(\Delta H\) & \(\Delta H=L\) & 150:1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Dimensional analysis of main parameters in physical model tests. Figure 1: Typical geological structure of shallow strata in Shanghai (satellite images cited from Google Maps). is selected as the base material after drying and crushing by adding different proportions of water, fine sand, and sponge to meet the similarity ratio of weight \(\gamma\), Young's modulus \(E_{s}\), and hydraulic conductivity \(K\) (Table 3). ### Artificial Assumption Boundary  
In the prototype, the horizontal influence range of dewatering-induced groundwater level changes can reach several kilometers [31; 32], which cannot reappear in a physical model test with limited size. Therefore, the variable hydraulic boundary is adopted in the model to eliminate the lateral boundary effect, and the groundwater level in the lateral boundary can be determined by numerical calculation. During the test, the groundwater levels in the lateral boundary and inside the deep excavation are reduced simultaneously, and a funneled groundwater level is formed around the deep excavation. This method can reduce the constraint effect of groundwater boundary conditions in the lateral boundary effectively and simulate the true funneled groundwater level to the greatest extent. The size of the model test area is 3.0 m long, 3.0 m wide, and 1.5 m high.