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

doi:10.12141/j.issn.1000-565X.230075

Abstract

Abstract:

In foundation pit engineering, groundwater seepage significantly impacts pit stability, yet current one-dimensional seepage theory doesn’t fully 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.

Key words: foundation pit, water pressure, steady seepage, analytical solution, simplified solution

CLC Number:

TU43

YU Jun, ZHENG Jingfan, ZHANG Zhizhong, et al. Analytical Solution and Simplified Solution of Two-Dimensional Steady Seepage Field in Foundation Pit[J]. Journal of South China University of Technology(Natural Science Edition), 2024, 52(5): 84-91.

Figures/Tables 12

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方法	基坑外侧	基坑内侧
有限元解	1 028.23	213.12
精确解	1 042.12	209.14
流网法	969.00	185.00
简化解	1 208.96	178.47
一维考虑渗流	643.68	189.32
一维静水	1 416.10	122.50

计算点号	深度z_i /m	精确解误差/%	流网法误差/%	简化解误差/%	一维考虑渗流误差/%	一维静水误差/%
合力		1.35	-5.76	17.58	-37.40	37.72
a	5	1.06	-2.47	10.02	-39.64	32.76
b	9	1.17	-4.74	15.40	-38.50	35.30
c	12	0.40	-8.00	17.34	-37.36	37.82
d	15	0.91	-5.86	23.87	-33.72	45.82
e	17	4.09	-1.73	37.04	-26.53	61.62

计算点号	深度z_i /m	精确解误差/%	流网法误差/%	简化解误差/%	一维考虑渗流误差/%	一维静水误差/%
合力		-1.87	-13.19	-16.26	-11.17	-42.52
d	3	0.37	-11.61	-12.19	-5.49	-38.85
e	5	-2.51	-17.78	-22.25	-17.13	-46.38

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