# Eccentricity Effects on Bearing Capacity of Strip and Square Footings on Two-Layered Clay

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## Abstract

The undrained ultimate capacity to combined (M, V) loading of strip and square foundations on a two-layered clay deposit is investigated. Extensive two and threedimensional parametric finite element analyses are carried out in terms of the ratio of the undrained shear strength of two layers, the normalized thickness of the top layer and the normalized load eccentricity. Two basic cases are separately investigated, referring to strength ratios higher or lower than unity. The assumption of effective width of the foundations, to account for eccentricity, generally adopted for homogeneous soil, is extended for two layers. The results are mainly presented in terms of modified bearing capacity factors for strip or square footings for a wide range of dimensionless problem parameters. However, for a better visual understanding of how the bending moment affects the ultimate vertical load failure loci diagrams (“yield surfaces”) in M, V space are also presented. Emphasis is given to developing insight into the particular failure mechanisms of most examined cases.

## Keywords

Clays Bearing capacity Eccentricity Square footings Failure mechanism Numerical analysis## List of Symbols

- B
Width of footing

- B′
Effective width (B − 2e)

- e
Eccentricity of loading

- H
_{1} Thickness of upper clay layer

- H
Horizontal load

- M
Bending moment

- m
Normalized ultimate moment

- \({\text{N}}_{\text{C}} ,{\text{ N}}^{\text{ * }}_{\text{C}}\)
Bearing capacity (B.C.) factor for centric loads on strip or square footings, respectively

- \({\text{N}}_{\text{C1}} ,{\text{ N}}^{\text{ * }}_{\text{C1}}\)
Equivalent B.C. factor for centric loads on strip or square footings in case of two layered clays

- \({\text{N}}_{\text{C1,e}} ,{\text{ N}}^{\text{ * }}_{\text{C1,e}}\)
Equivalent B.C. factor for eccentric loads on strip or square footings in case of two layered clays

- q
_{u} Ultimate bearing capacity pressure

- s
_{c} Shape factor

- SR
Strength ratio (s

_{u,2}/s_{u,1})- s
_{u} Undrained shear strength

- V
Vertical load

- v
Normalized ultimate vertical load

- V
_{u,o} Ultimate centric vertical load

- V
_{u,e} Ultimate eccentric vertical load

- γ
Unit weight of the clay

- θ
Inclination of load

- \(\uplambda_{\text{N}} , \,\uplambda^{\text{ * }}_{\text{N}}\)
Ratio of bearing capacity factors for strip or square footings

- ν
Poisson’s ratio

## Notes

## References

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