# Analytical Solutions of Water Inflow for Foundation Pit in Confined Water Stratum
## 2 Water Inflow Solutions of Circular and Strip Foundation Pits  
Only radial seepage is considered; the seepage analytical models of strip foundation pits and circular foundation pits can be regarded as two-dimensional cases. The central axis of the foundation pit is taken as the \(z\)-axis, the radial direction of the foundation pit is taken as the \(r\)-axis, and the intersection of the central axis and the bottom plate of the aquifer is selected as the origin to establish a coordinate system. The central axis and the radial direction of the foundation pit are taken as the \(z\)-axis and the \(r\)-axis, respectively. A coordinate system is established in which the origin is the intersection of the central axis and the bottom of the aquifer. According to the principle of hydraulics, the theoretical model of the foundation pit with the suspended water-proof curtain in the confined water stratum is established. As shown in Figure 1, where \(H\) is the water table of the confined water, \(r_{0}\) is the length from the central axis of the foundation pit to the excavation boundary, \(R\) is the influence radius of dewatering, \(h_{0}\) is the value of the hydraulic contour line at the bottom of the water-proof curtain, \(D(z)\) is the hydraulic head distribution function on the outer side of the water-proof curtain, \(H_{d}\) is the water table in the foundation pit, \(H_{w}\) is the hydraulic head at the maximum drawdown position of the aquifer, \(L\) is the length of the water-proof curtain inserted into the aquifer, and \(M\) is the thickness of the aquifer.  
To obtain water inflow of the foundation pit in a confined water stratum, several assumptions are made: the thickness of the water-proof curtain is ignored; there is a steady seepage process in the calculation region; the water table in the foundation pit is horizontal; only radial seepage is considered The seepage region can be divided into three parts: the outside of the foundation pit (Region 1), the region below the water-proof curtain in the foundation pit (Region 2), and the vertical seepage region in the pit (Region 3). Due to the water interception effect of the water-proof curtain, the water in Region 1 flows around into Region 2, and the water horizontally flows below the water-proof curtain, then the flow direction is turned in Region 2 and the water flows into Region 3 vertically.  
Based on the seepage continuity, the water inflow in the three regions is the same, namely:  
\[Q_{1}=Q_{2}=Q_{3}=Q \tag{1}\]  
where \(Q_{1}\), \(Q_{2}\), and \(Q_{3}\) are the water inflow in the three regions, respectively; \(Q\) is the water inflow in the foundation pit. Because only radial seepage is considered, the hydraulic head distribution in the seepage region is independent of the angle, based on the two-dimensional condition, the hydraulic head at each point in the seepage region can be expressed as \(h(r,z)\), and the boundary conditions in the seepage region are given as:  
\[\left\{\begin{array}{l}h(r,z)=H;\;r=r_{0}+R,\;z>0\\ \frac{\partial h(r,z)}{\partial z}=0;\;0\leq r\leq r_{0}+R,\;z=0\\ \frac{\partial h(r,z)}{\partial z}=0;\;r_{0}<r\leq r_{0}+R,\;z=M\\ h=h_{0};\;r=r_{0},\;0\leq z\leq M-L\\ h=D(z);\;r=r_{0},\;M-L\leq z\leq M\\ h(r,z)=H_{d};\;0<r<r_{0},\;z=H_{d}\end{array}\right. \tag{2}\]