Semianalytical Solution for Evaluating Bearing Capacity of a Footing Adjacent to a Slope
Publication: International Journal of Geomechanics
Volume 21, Issue 2
Abstract
The study of the influence of foundations, placed adjacent to slopes, on the bearing capacity is of great importance in geotechnical engineering. The available analytical and empirical methods have some limitations in considering the soil properties and the location of the footings on the top surface of the slope. To overcome these limitations, finite element analysis (FEA) is usually performed. However, FEA requires significant computational effort and, therefore, the need for an analytical solution that can consider all the effective parameters on bearing capacity of the foundation still exists. Hence, a new analysis is proposed. In this regard, the stress distribution within a slope, due to the placement of a footing on the upper surface of the slope, is evaluated in this study. Following that, the minimum value of the vertical footing load required to destabilize the slope is computed. The strength properties and unit weight of the soil, the width and location of the footing, and the slope geometry are all taken into account in the analysis. The results show good agreement with the literature, including numerical, analytical, and empirical approaches. Thus, the proposed method that is more comprehensive compared with previous solutions can help both researchers and engineers to verify the FEM model or conducting a parametric study of the ultimate bearing capacity of the footing near the slope.
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Data Availability Statement
All data, models, and code generated or used during the study appear in the published article.
Notation
The following symbols are used in this paper:
- a
- end coordinate of the footing;
- c
- cohesion;
- c
- path of complex linear integration (real part);
- E
- Young’s modulus;
- F(z)
- function of loading in complex space;
- f(r)
- function of loading in real space;
- g
- gravity;
- H
- height of the slope;
- I1, I2, I3
- first, second, and third stress invariants;
- i
- imaginary number;
- J2, J3
- second and third deviatoric stress invariants;
- p
- footing load;
- r
- radial in polar coordinate;
- u
- step function;
- X
- x-axis of Cartesian coordinate;
- X′
- local Cartesian coordinate;
- x
- footing size;
- Y
- y-axis of Cartesian coordinate;
- Z
- depth direction of slope in Goodman and Brown’s model;
- z
- complex number;
- λ
- normalized footing distance;
- θ
- angle that measured from the bisector of the wedge;
- θ
- lode angle;
- α
- half of the wedge angle;
- α
- slope angle in Goodman and Brown’s model;
- β
- polar coordinate angle in Goodman and Brown’s model;
- ϕ(r, θ)
- real Airy stress function;
- Φ(z, θ)
- complex Airy stress function;
- φ
- friction angle;
- ρ
- density;
- polar stress component;
- σij
- stress tensor;
- δij
- Kronecker delta;
- ψ
- slope angle;
- ν
- Poisson’s ratio; and
- π
- pi number.
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Published In
International Journal of Geomechanics
Volume 21 • Issue 2 • February 2021
Copyright
© 2020 American Society of Civil Engineers.
History
Received: Mar 18, 2020
Accepted: Sep 4, 2020
Published online: Dec 7, 2020
Published in print: Feb 1, 2021
Discussion open until: May 7, 2021
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