# An approach for calculating the vertical ultimate bearing capacity of a shallow circular foundation

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## Abstract

In this work, a new method for the vertical bearing capacity of a shallow circular foundation was proposed with the amended formula by combining the limit equilibrium method and the principle of conservation of energy. Then the vertical ultimate bearing capacity of eight different circular foundations was acquired with the above mentioned method, an empirical formula method, and the static load test to obtain comparative results. The results showed that the relative error for the proposed method was deemed as the most accurate, close to the result of Vesic method, while much less than the relative error for both Meyerhof method and Hansen method. In addition, the impact factors for vertical ultimate bearing capacity including density, cohesion, friction angle of soil, radius, and burial depth of shallow circular foundation were also discussed, indicating that the shear strength parameters and density of soil, and especially the friction angle were the main influencing factors of the bearing capacity.

## Keywords

Shallow circular foundation Vertical ultimate bearing capacity Limit equilibrium Conservation of energy Shear sliding## List of symbols

*V*_{s}The volume of shear slip zone

*q*Uniformly distributed load from soil weight above the base plane

*c*,*φ*The cohesion and friction angle of foundation soil

*h*_{q}The burial depth of circular foundation

*F*_{pbu}The ultimate minimum vertical load of circular foundation

*τ*_{N}The shear force in the direction of sliding surface

- ER
_{i} The relative error

*y*The bearing capacity according to approximated relationship of Eq. 4

*F*_{1},*F*_{2},*F*_{3},*F*_{4},*F*_{5}Lateral extrusion force, the normal force of slip surface, the shear force of slip surface, its own gravity, and additional force, respectively

- ∆
*D*, ∆*Y* The resultant displacement and vertical displacement of shear slip zone

*S*_{N},*S*_{F}A lateral surface area and an internal surface area

*σ*_{F}Extrusion force from lateral compression expansion

*h*_{c}The above mentioned effective depth of circular foundation

*γ*_{q}Soil weight

*P*_{u}Ultimate bearing capacity of shallow circular foundation

*σ*_{N,}*σ*_{τ}The normal stress and the shear stress of shear slip surface

*σ*The standard error

*δ*An evaluation index with the effect degree of impact factors on the vertical bearing capacity

- ∆
*h*, ∆*r* The vertical and horizontal deformation increments

## Notes

### Acknowledgements

The author thanks Prof. Dr. Xiuying Cao for providing many instructions in this research. This work was supported by Collaborative Research Project of China and Australia (No. 16394507D), National Natural Science Foundation of China (No. 50978022), Provincial intelligence introduction project (No. Z20180288), and Introducing High-level Overseas Talent Funding Projects (No. 201703).

### Complaince with ethical standards

### Conflict of interest

The authors declare that they have no conflict of interest.

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