# Analytical Solutions of Water Inflow for Foundation Pit in Confined Water Stratum
## 3 Analysis of Water Inflow for the Rectangular Foundation Pits  
In engineering projects, the shape of most foundation pits can be approximately regarded as a rectangle. However, for convenience, the foundation pit is equivalent to the circle according to the principle of the same area, then the water inflow is calculated by the analytical solutions which are suitable for the circular foundation pit. In order to explore the variance of water inflow for different size characteristics of rectangular foundation pits in confined water stratum, the numerical simulation is used to calculate the water inflow under different length-to-width ratios \(\rho\) based on the condition that the total area is equal. The circular foundation pit with a diameter of 20 m is selected as a criterion. The rectangular foundation pits' models are established with the length-to-width ratios \(\rho\) = 1:1, 2:1, 3:1, 5:1, and 9:1 based on the condition of equal total areas. The soil parameters and boundary conditions are the same as the above. In addition, the models of strip foundation pits with widths of 6 m and 8 m were established, respectively. Figure 5 shows the variation in water inflow with \(L/M\) for different shapes of foundation pits. It can be seen from the figure that the variation in water inflow with \(L/M\) for different shapes of foundation pits have the same trend. However, the shape characteristic has a great effect on the water inflow. Under the condition that the foundation pit area is equal, the water inflow of the strip foundation pit is much larger than that of the circular foundation pit with the same \(L/M\), the former is about twice as much as the latter when \(L/M\) = 1. The water inflow of the square foundation pit (i.e., the length-to-width ratio is 1) is the same as the circular foundation pit; the more difference between length and width, the more difference between water inflow. When the length-to-width ratio is 2, the water inflow of the rectangular foundation pits under each curtain insertion ratio is slightly larger than that of the circular foundation pits, but the difference between them is not large and the maximum difference is less than 5%, which is within the acceptable range. Therefore, the water inflow calculation formula of the circular foundation pit can still be used in that case. When the length-to-width ratio \(\rho\) = 5, 9, the water inflow of the rectangular foundation pits is basically the same as the strip foundation pits under the same \(L/M\). Therefore, for the calculation of water inflow, the rectangular foundation pits where the length-to-width ratio is greater than 5 can be regarded as strip foundation pits. When the length-to-width ratio is 3 or 4, the water inflow in that two cases is basically the same, but they are much larger than that of the circular foundation pit and much smaller than that of the strip foundation pit under the condition of equal area. The water inflow for the rectangular foundation when the length-to-width ratio is 3 or 4 can be calculated as the average value of the water inflow of the circular foundation pit and the rectangular foundation pit with a length-to-width ratio of \(\rho\) = 5.