Analytical Solution of the Two-Dimensional Steady-State Seepage Field of a Seepage Anisotropy Pit Considering the Free Surface

An anisotropic foundation pit steady-state seepage field under a suspended waterproof curtain support considering the position of the free surface is studied analytically, and an analytical solution for the free surface position is given. The head distribution in the three zones is expressed as a se...

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Bibliographic Details
Published in:Mathematics (Basel) 2024-07, Vol.12 (13), p.2098
Main Authors: Yu, Jun, Zhang, Yang, Li, Dongkai, Zheng, Jingfan
Format: Article
Language:English
Subjects:
analytical solution
Anisotropy
Aquifers
Boundary conditions
Coordinate transformations
Engineering
Exact solutions
Finite element analysis
Finite element method
foundation pit
free surface
Free surfaces
Groundwater
Mathematical analysis
Methods
Numerical analysis
Numerical methods
Orthogonality
Permeability
Seepage
seepage anisotropy
Steady state
Two dimensional analysis
two-dimensional steady-state seepage
Vertical orientation
waterproof curtain
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Summary:An anisotropic foundation pit steady-state seepage field under a suspended waterproof curtain support considering the position of the free surface is studied analytically, and an analytical solution for the free surface position is given. The head distribution in the three zones is expressed as a series solution using the separation of variables method, and the explicit solution for the extent of the seepage field in each zone is obtained by combining the continuity condition between zones and the series orthogonality condition. The free surface position is determined according to the condition that the total head of the free surface is equal to the position head. A comparison of the calculation results of the analytical method and the indoor test and finite element analysis results verifies the correctness of the analytical solution, and the analytical method has more calculation efficiency than the finite element numerical method. Employing the aforementioned methods to analyze the influence parameters of the free surface position, the results show that drawdown increases as the ratio of the vertical permeability coefficient to the horizontal permeability coefficient increases; the greater the ratio of pit width to depth, the more significant the drawdown, but when the ratio continues to exceed 1.5, the drawdown is negligible.
ISSN:2227-7390
2227-7390
DOI:10.3390/math12132098