Limit-Equilibrium Analysis Using a Lateral Force as Functional
Publication: International Journal of Geomechanics
Volume 23, Issue 5
Abstract
A variational method, using a lateral force as a functional and incorporating equilibrium in-the-small, is proposed for limit equilibrium analysis, in which a conventional safety functional in the form of a quotient and the need to use the method of slices or Lagrange multipliers can be avoided. The lateral force is a real force acting on a retaining wall, but is a fictitious force in slope stability analysis. Furthermore, the fictitious force is related to the factor of safety. The force is a push, pull, or null when the slope is unstable, stable, or critical. By setting this lateral force to zero, a critical stability state can be obtained. The proposed variational method is capable of reproducing the classical solutions and yielding new useful analytical results. The proposed method can be a viable alternative technique, because of its effectiveness and ease of use is comparable to the conventional variational approaches.
Practical Applications
The limit-equilibrium analysis technique is widely adopted in the practice of slope stability and earth pressure on retaining walls. Among the existing techniques in limit-equilibrium analysis, the variational calculus method from a mathematical perspective is more accurate than traditional techniques. However, this method was greatly limited due to the cumbrous solution on the quotient form functional. The proposed method uses a lateral force as functional, incorporating equilibrium in-the-small. It can simplify the solution significantly and the assumption of slip surface or relation of forces can be avoided. Results obtained from the proposed method can be used in the design of clay slopes, seismic stability of cohesionless slopes, lateral earth pressure on retaining walls under seismic conditions, and lateral earth pressure on rough retaining walls. The charts can be used to conveniently assess the stability of slopes or earth pressure on retaining walls under certain conditions in the preliminary design. The suggested method can also be further developed into a broader range of practical applications.
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Acknowledgments
The research for this paper was supported, in part, by the National Natural Science Foundation of China (NSFC) and the Natural Sciences and Engineering Research Council of Canada (NSERC).
Notation
The following symbols are used in this paper:
- c
- cohesion of soil;
- disturbance force;
- functional which is a lateral force acting on the free surface of slope or retained soil mass;
- factor of safety;
- safety functional;
- h
- height of a slope or a retained soil mass;
- hcr
- critical height of a slope or a retained soil mass;
- m
- slope of the critical failure surface, m = tanβ;
- resistance force;
- s
- function of slope surface, s = s(x);
- y
- function of a slip surface, y = y(x);
- seismic coefficient applied in the horizontal direction;
- seismic coefficient applied in the vertical direction;
- β
- angle of inclination of the critical failure surface in soil mass;
- γ
- unit weight;
- δ
- angle of friction between retaining wall and backsoil;
- θ
- angle of inclination of slope;
- μ
- coefficient of internal friction of soil, μ = tanφ;
- coefficient of friction between retaining wall and backsoil, ;
- σ
- normal stress;
- τ
- shear stress acting along slip surface; and
- φ
- angle of internal friction of soil.
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Published In
International Journal of Geomechanics
Volume 23 • Issue 5 • May 2023
Copyright
© 2023 American Society of Civil Engineers.
History
Received: Apr 21, 2022
Accepted: Dec 6, 2022
Published online: Feb 28, 2023
Published in print: May 1, 2023
Discussion open until: Jul 28, 2023
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