Analytical Solution and Simplified Solution of Two-Dimensional Steady Seepage Field in Foundation Pit

In foundation pit engineering, groundwater seepage significantly impacts pit stability, yet current one-dimensional seepage theory doesnt́fully meet safety standards for seepage calculation. This study addresses these gaps by analyzing two-dimensional seepage in isotropic soil layers under suspended support, disregarding retaining wall thickness. The water head in each of the four regions was expressed in the form of a series solution by using the superposition principle and the separation of variables method, and the analytical solution of the seepage field was obtained by combining the continuity conditions between the regions and the orthogonality of the series solution. Comparing this analytical solution with PLAXIS 2D software results, it finds that a series term of 20 provides convergence, while a single term still maintains accuracy, representing exact and simplified solutions respectively. The simplified solution offers easy calculation, providing quick determination of water head at any point in the pit. Comparing the calculation results of one-dimensional water pressure, one-dimensional water pressure considering seepage, flow network method, simplified solution, exact solution and numerical solution, it is found that the exact solution is in better agreement with the numerical solution and has higher accuracy than the flow network method, and the simplified solution has higher accuracy than one-dimensional hydrostatic pressure and one-dimensional water pressure considering seepage. Parameter analysis reveals that relative error between accurate and simplified solutions for resultant water pressure is influenced by inner water level and distance from retaining wall to impermeable layer. The simplified solution is suitable for foundation pits of small dimensions, especially when the distance from the inner water level to the bottom of the retaining wall is greater than 7 meters and the distance from the bottom impermeable layer to the retaining wall is less than 30 meters. The calculation of the point of application of the retaining wall water pressure resultant force is suitable for foundation pits of any size. Compared with the accurate solution, the error of the simplified solution mainly occurs at the bottom of the retaining wall, while at other locations, the head error is less than 5% for small-sized foundation pits. © 2024 South China University of Technology. All rights reserved.