Analytical Solution to Ultimate Lateral Pressure on a Vertical Plate in Undrained Soil
Publication: International Journal of Geomechanics
Volume 21, Issue 9
Abstract
For a vertical plate emerging on the surface of undrained cohesive soil, the adhesion between the plate and soil considerably impacts the lateral soil pressure on it. However, very few closed-form solutions have been published to address this seemingly simple problem; they either are restricted to certain conditions or overpredict the ultimate lateral pressure. This paper applies both the lower-bound and upper-bound methods of plasticity to develop a rigorous analytical solution to the ultimate lateral pressure, allowing for the undrained shear strength of soil to increase linearly with depth and a general adhesion on the interface. A method is presented to extend the static stress field throughout the soil mass to validate the lower-bound values. The developed solution is found to be an exact solution for homogeneous soil; the predicted results for nonhomogeneous soil fall within a narrow range bounded by the lower and upper limit values, with the range of errors mostly being within 1%. The solution reduces to the classic Bell’s relationship in the undrained condition if ignoring the adhesion on the interface. When the full active pressure behind the plate is mobilized, the upper-bound solution is rigorous but the lower-bound one is not unless examining a smooth surface. However, the predicted results are close enough to more rigorous ones to be used in engineering practice.
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Data Availability Statement
All data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The author acknowledges the support and encouragement from John Shelton and Jason Pasternak at Delmar Systems, during the course of this study. The author was also grateful to Professor Charles P. Aubeny from Texas A&M University for his constructive suggestions.
Notation
The following symbols are used in the paper:
- F
- lateral soil resistance on the plate;
- f
- reduction factor;
- H
- height of plate;
- k
- shear strength gradient with depth;
- p
- lateral soil pressure on the plate;
- su
- undrained shear strength;
- su0
- undrained shear strength on the surface;
- su-ave.
- average shear strength;
- v
- virtual velocity in the velocity field;
- v0
- virtual velocity of plate translating;
- v1 and v2
- virtual velocity components in the α′-line and β′-line directions;
- z
- depth of soil;
- α
- adhesion factor;
- ɛ, β, and η
- parameters for calculation defined in Fig. 11;
- φ
- internal friction angle;
- γ′
- submerged unit weight of soil;
- θ
- angle of the major principal stress from the x-axis in soil;
- θ0
- angle of the major principal stress from the x-axis on the plate surface;
- σz, σx, and τxz
- normal and shear stresses in soil; and
- σ1, σm, and σ2
- major, mean, and minor principal stresses in soil.
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Published In
International Journal of Geomechanics
Volume 21 • Issue 9 • September 2021
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Sep 26, 2020
Accepted: May 7, 2021
Published online: Jul 1, 2021
Published in print: Sep 1, 2021
Discussion open until: Dec 1, 2021
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