Analytical Solution for a Steady Seepage Field of a Foundation Pit in Layered Soil
Publication: International Journal of Geomechanics
Volume 22, Issue 10
Abstract
To reduce the negative influence of groundwater on foundation pit excavation and the surrounding environment, an analysis of seepage fields has become very important in deep excavation projects. However, the current studies on the seepage fields of foundation pits lack in-depth theoretical research, partly because the theoretical solution is complex and obscure, and the solution is limited to single-layer soil, which is difficult to apply to engineering practice. By using orthogonality and boundary conditions to construct nonhomogeneous equations, this study deals with the development of an explicit analytical solution for predicting stable seepage around a foundation pit in layered soil underlain by an impervious barrier and a constant water head maintained inside and outside the foundation pit. The validity of the analytical solution is checked by first reducing the proposed multilayered solution to that of a single-layered solution by treating the conductivity of the layers as the same and then comparing this solution with the hydraulic seepage situations predicted by the reduced model with corresponding values obtained from other analytical works. A numerical model is established using FLAC2D software to verify the solution proposed in this study and to obtain strong consistency. The solution is of a general nature and can account for the foundation pit width, the distance of the retaining wall from the impervious layer, the head difference, and the permeability variation in the layers of the soil. The study shows that flow to a multilayered foundation pit is sensitive to the width of the foundation pit, the embedded depth of the waterproof curtain, the thickness of the completely saturated soil up to the impervious barrier, and the total head difference. Furthermore, this study proves that the distribution of the conductivity in the layers plays an important role in determining the water head and the distribution of the streamlines. The results of this research could be considered in foundation pit design and water conservancy engineering practice.
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Data Availability Statement
All data, models, and code generated or used during the study appear in the published article.
Acknowledgments
We thank LetPub for its linguistic assistance during the preparation of this manuscript.
Notation
The following symbols are used in this paper:
- d1
- thickness of the soil up to the impervious barrier;
- d2
- excavation base level of the foundation pit;
- thickness of a layered soil in Zone I;
- thickness of a layered soil in Zone II;
- thickness of a layered soil in Zone III;
- hydraulic head distribution function for the j-th layer in Zone I (j = 1 to J);
- hydraulic head distribution function for the l-th layer in Zone II (l = 1 to L); and
- hydraulic head distribution function for the r-th layer in Zone III(r = 1 to R);
- h
- hydraulic head difference for the inside and outside of the foundation pit;
- ie
- exit hydraulic gradient at the bottom of the excavation
- J
- total number of soil layers in Zone I;
- hydraulic permeability coefficient of the j-th layer in Zone I (j = 1 to J);
- hydraulic permeability coefficient of the l-th layer in Zone II (l = 1 to L); and
- hydraulic permeability coefficient of the r-th layer in Zone III (r = 1 to R);
- L
- total number of soil layers in Zone II;
- L
- half width of the foundation pit;
- Le
- influential scope of seepage of the foundation pit;
- R
- total number of soil layers in Zone III;
- S
- embedded depth of a waterproof curtain outside the excavation;
- x
- horizontal coordinate;
- z
- vertical coordinate;
- α
- ratio of the horizontal permeability to the vertical permeability;
- stream function for the first layer in Zone I;
- stream function for the second layer in Zone I;
- stream function for the first layer in Zone II; and
- stream function for the first layer in Zone III.
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Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 22 • Issue 10 • October 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Aug 11, 2021
Accepted: Mar 30, 2022
Published online: Jul 20, 2022
Published in print: Oct 1, 2022
Discussion open until: Dec 20, 2022
ASCE Technical Topics:
- Construction engineering
- Construction methods
- Engineering fundamentals
- Engineering profession
- Excavation
- Foundations
- Geomechanics
- Geotechnical engineering
- Head (fluid mechanics)
- Hydraulic engineering
- Hydraulic models
- Hydraulics
- Layered soils
- Models (by type)
- Practice and Profession
- Seepage
- Soil analysis
- Soil mechanics
- Soil properties
- Soils (by type)
- Water and water resources
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