Journal of South China University of Technology(Natural Science) >
Analytical Solution and Simplified Solution of Two-Dimensional Steady Seepage Field in Foundation Pit
Received date: 2023-03-01
Online published: 2023-07-12
Supported by
the National Natural Science Foundation of China(52078496)
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.
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), 2024 , 52(5) : 84 -91 . DOI: 10.12141/j.issn.1000-565X.230075
| 1 | 汤连生,黄国怡,杜赢中,等 .考虑地下水渗流的基坑水土压力计算新图式[J].岩土力学,2004,25(4):565-569. |
| TANG Lian-sheng, HUANG Guo-yi, DU Ying-zhong,et al .A new calculation chart of water-earth pressure on foundation pit considering groundwater seepage[J].Rock and Soil Mechanics,2004,25(4):565-569. | |
| 2 | ZHANG M, YAO D X, LU H F,et al .Solution of seepage field in different soil layers of concrete dam foundation by flow net method[J].IOP Conference Series:Earth and Environmental Science,2020,546(5),052053/1-7. |
| 3 | 张邦芾 .基坑工程地下水渗流场特性研究[D].北京:中国建筑科学研究院,2014. |
| 4 | 薛丽影,杨斌,刘丰敏,等 .基坑工程地下水渗流模型试验系统研究[J].岩土工程学报,2017,39(S1):126-130,11. |
| XUE Li-ying, YANG Bin, LIU Feng-min,et al .Model test system for groundwater seepage in foundation pit engineering[J].Chinese Journal of Geotechnical Engineering,2017,39(S1):126-130,11. | |
| 5 | SHI C H, SUN X H, LIU S L,et al .Analysis of seepage characteristics of a foundation pit with horizontal waterproof curtain in highly permeable strata[J].Water,2021,13(9):1303/1-26. |
| 6 | LI Y F, CHAI J R, XU Z G .Analysis of influence of seepage on stability of foundation pit[J].IOP Conference Series:Materials Science and Engineering,2017,207(1):012093/1-6. |
| 7 | SHI J J, WU B, LIU Y,et al .Analysis of the influence of groundwater seepage on the deformation of deepfoundation pit with suspended impervious curtain[J].Advances in Mechanical Engineering,2022,14(3):1-10. |
| 8 | CAO Cheng-yong, SHI Cheng-hua .Analytical procedure for massive water-sealing barriers used in deep excavations considering seepage effect and its application[J].Journal of Central South University,2022,29(6):2033-2048. |
| 9 | 罗勇,龚晓南,吴瑞潜 .考虑渗流效应下基坑水土压力计算的新方法[J].浙江大学学报(工学版),2007,41(1):157-160. |
| LUO Yong, GONG Xiao-nan, WU Rui-qian .New method for calculation of water-earth pressure on foundation pit considering groundwater seepage[J].Journal of Zhejiang University(Engineering Science),2007,41(1):157-160. | |
| 10 | FOX E N, MCNAMEE J .The two-dimensional potential problem of seepage into a cofferdam[J].Philosophical Magazine Series 7,1948,39(290):165-203. |
| 11 | BERESLAVSKII E N .The flow of ground waters around a Zhukovskii sheet pile[J].Journal of Applied Mathematics & Mechanics,2011,75(2):210-217. |
| 12 | 黄大中,谢康和,应宏伟 .渗透各向异性土层中基坑二维稳定渗流半解析解[J].浙江大学学报(工学版),2014,48(10):1802-1808. |
| HUANG Da-zhong, XIE Kang-he, YING Hong-wei .Semi-analytical solution for two-dimensional steady seepage around foundation pit in soil layer with anisotropic permeability[J].Journal of Zhejiang University(Engineering Science),2014,48(10):1802-1808. | |
| 13 | YU J, YANG X X, DENG P B,et al .Analytical solution for a steady seepage field of a foundation pit in layered soil[J].International Journal of Geomechanics,2022,22(10):04022160/1-10. |
| 14 | THUSHARA A M, NAGARATNAM S .Simple solutions for square and rectangular cofferdam seepage problems[J].Canadian Geotechnical Journal,2018,56(5):730-745. |
| 15 | 张承宗 .数学物理方法与复数特殊函数[M].北京:中国宇航出版社,2014. |
| 16 | 王钊,邹维列,李广信 .挡土结构上的土压力和水压力[J].岩土力学,2003,24(2):146-150. |
| WANG Zhao, ZOU Wei-lie, LI Guang-xin .Earth pressure and water pressure on retaining structure[J].Rock and Soil Mechanics,2003,24(2):146-150. | |
| 17 | 余俊,李东凯,胡钟伟,等 .考虑挡墙厚度基坑稳态渗流场的解析解[J].岩土工程学报,2023,45(7):1402-1411. |
| YU Jun, LI Dongkai, HU Zhongwei,et al .Analytical solution of steady seepage field of foundation pit considering thickness of retaining wall[J].Chinese Journal of Geotechnical Engineering,2023,45(7):1402-1411. |
/
| 〈 |
|
〉 |