Coupled Bearing Capacity Factor for Strip Foundations on Cohesive-Frictional Soil Slopes under Static and Seismic Conditions
Publication: International Journal of Geomechanics
Volume 20, Issue 11
Abstract
This paper investigates the bearing capacity of strip foundations resting on a cohesive-frictional soil sloping ground under both static and seismic conditions by applying the kinematic theorem of limit analysis. With the consideration of a composite collapse mechanism involving a generalized continually deforming shear zone, analytical expressions are established by incorporating the coupled influence of the soil resistance contributed by the cohesion, angle of internal friction, and self-weight of the soil mass. The loading conditions owing to inertia forces of supporting structures and the changes in the body forces of the supporting soil medium occurred during an earthquake are included in the analysis based on a pseudostatic approach. Rigorous upper-bound solutions are presented in the nondimensional form as charts and tables for the practical range of parameters that are normally encountered in the field. Additionally, by extending the concept of slope stability, a closed-form expression is proposed for computing the limiting values of horizontal seismic acceleration coefficients beyond which the sloping ground becomes unstable. The importance of the consideration of coupling effects of the soil resistance toward evaluating the static and seismic bearing capacity of foundations on the sloping ground over conventional approaches is discussed.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request (the data in the graphs and the code generated for obtaining data).
Notation
The following symbols are used in this paper:
- c
- unit cohesion of soil medium;
- c*
- modified value of unit cohesion of soil medium;
- nondimensional coefficients;
- i
- inclination of resultant load on the foundation with vertical;
- keq
- equivalent horizontal seismic acceleration coefficient to account for kv;
- kh
- horizontal seismic acceleration coefficient;
- kh,eq
- kh or keq;
- kh,Limit
- limiting values of kh corresponding to stable slope;
- kv
- vertical seismic acceleration coefficient;
- Mn
- ratio of Qh to Qv;
- Nc(ϕ, β, kh)
- bearing capacity factor with respect to weightless cohesive soil medium;
- coupled bearing capacity factors for cohesive-frictional soil medium;
- bearing capacity factor with respect to purely frictional soil medium;
- Qh
- horizontal force (or) load on foundation;
- qu
- vertical bearing capacity of foundation;
- Qv
- vertical force (or) load on foundation;
- R0
- length of the initial radial line;
- Rξ
- length of the radial line at any angle ξ from R0;
- Sn
- stability number;
- Ti
- vector of tractions on the loaded boundary surface A;
- V0
- velocity of foundation or the underlying triangular rigid zone pqr;
- Vi
- kinematically admissible velocity field;
- VL
- velocity of the outermost end triangular rigid zone pst;
- Vξ
- velocity of any angle ξ from R0;
- Xi
- vector of distributed forces within the region Γ;
- Xn
- cohesive strength parameter;
- α, μ, and δ
- angular variables used for defining the collapse geometry;
- β
- inclination angle of sloping ground;
- γ
- unit weight of soil medium;
- ϕ
- angle of the internal friction of soil medium;
- ϕ*
- modified value of the angle of internal friction of soil medium; and
- ψ
- angle of dilatancy of soil medium.
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History
Received: Dec 5, 2019
Accepted: Jul 13, 2020
Published online: Aug 28, 2020
Published in print: Nov 1, 2020
Discussion open until: Jan 28, 2021
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