The implementation of the Laplace equation in a slope stability analysis: the streamline method

The Laplace equation satisfies the principle of the minimum potential energy, which means that groundwater flows through soil in an optimized path of minimal energy under a given condition. The essential idea of the proposed method is to convert a pure optimization problem into a boundary value prob...

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Bibliographic Details
Published in:Acta geotechnica 2021-03, Vol.16 (3), p.937-958
Main Authors: Luo, G. Y., Cao, H., Pan, H.
Format: Article
Language:English
Subjects:
Boundary conditions
Boundary value problems
Complex Fluids and Microfluidics
Dimensions
Engineering
Foundations
Geoengineering
Geotechnical Engineering & Applied Earth Sciences
Groundwater
Groundwater flow
Hydraulics
Laplace equation
Mathematical analysis
Optimization
Permeability
Potential energy
Research Paper
Safety factors
Seepage
Slip
Slope stability
Soft and Granular Matter
Soil permeability
Soil Science & Conservation
Solid Mechanics
Stability analysis
Streamlines
Tensors
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Summary:The Laplace equation satisfies the principle of the minimum potential energy, which means that groundwater flows through soil in an optimized path of minimal energy under a given condition. The essential idea of the proposed method is to convert a pure optimization problem into a boundary value problem by solving an anisotropic Laplace equation. A virtual seepage field is constructed to compute streamlines based on a dedicated permeability tensor. The permeability tensor is deduced according to the slope stress state. The magnitude of the tensor is determined by the stress failure ratio (SFR), and the major principal direction of the tensor is determined by the orientation of the maximum SFR. The boundary conditions can be applied as the entry and exit method used widely in the limit equilibrium method. The most critical slip surface is the streamline with the minimal safety factor. The proposed method is based on an elastic finite element stress and a confined virtual seepage field. Neither iterations nor assumptions about the slip surface shape and the interslice force are required in the proposed method. The major advantage of the proposed method is the optimization dimension reduction. This approach converts a 2D slope stability optimization problem into a 1D problem and greatly increases the efficiency of critical slip surface searching.
ISSN:1861-1125
1861-1133
DOI:10.1007/s11440-020-01047-y