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

- 50 Downloads

## 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.

## References

- Bowles JE (2004) Foundation analysis and design. Translated by Tong Xiaodong et al. China Building Industry Press, Beijing, pp 185–233Google Scholar
- Frydman S, Burd HJ (1997) Numerical studies of bearing-capacity factor
*N*_{γ}. J Geotechn Geoenviron Eng 123(1):20–29. https://doi.org/10.1016/j.sandf.2014.06.013 CrossRefGoogle Scholar - Fu HL, Xing XS, Peng WX, Wang J (2015) Theoretical solution of bearing capacity of shallow circular broken rock-mass foundation according to limit equilibrium analysis. J Railway Sci Eng 4:801–805Google Scholar
- Hansen JB (1970) A revised and extended formula for bearing capacity. Bull Dan Geotechn Inst 28:5–11Google Scholar
- Helin FU, Xing X, Peng W, Wang J (2015) Theoretical solution of bearing capacity of shallow circular broken rock-mass foundation according to limit equilibrium analysis. J Railway Sci Eng 21(2):897–906Google Scholar
- Hu ZP, Wang R, Xia XB, Wang X, Chen Y (2015) Modifying the formula of the ultimate bearing capacity of a shallow circular foundation. J Highway Transport Res Dev 9(4):9–15. https://doi.org/10.1061/JHTRCQ.0000419 CrossRefGoogle Scholar
- Jiang YP, Xiong JH (2005) Analysis of ultimate bearing capacity of square and circular foundations. Rock Soil Mech 26(12):1991–1995Google Scholar
- Kumar J, Khatri VN (2015) Bearing capacity factors of circular foundations for a general c–ϕ soil using lower bound finite elements limit analysis. Int J Numer Anal Methods Geomech 35(3):393–405. https://doi.org/10.1002/nag.900 CrossRefGoogle Scholar
- Liu Y, Wang G (2008) Stability analysis and evaluation of cave foundation under the role of groundwater in Karst Area. J Mt Sci 26(4):453–458Google Scholar
- Liu SQ, Lu KL, Zhu DY, Jiang ZF (2015) Calculation of ultimate bearing capacity of circular footing. J Eng Geol 23(5):1005–1012Google Scholar
- Luo H, Lee V (2014) Soil-structure interaction on a shallow rigid circular foundation: SH wave source from near-field excitations. J Earthq Eng 18(1):67–89CrossRefGoogle Scholar
- Merifield RS, Lyamin AV, Sloan SW (2006) Limit analysis solutions for the bearing capacity of rock masses using the generalised Hoek–Brown criterion. Int J Rock Mech Min Sci 43(6):920–937. https://doi.org/10.1016/j.ijrmms.2006.02.001 CrossRefGoogle Scholar
- Meyerhof GG (1951) The ultimate bearing capacity of foundations. Geotechnique 2(4):301–332. https://doi.org/10.1680/geot.1951.2.4.301 CrossRefGoogle Scholar
- Peng XQ (1999) Ultimate bearing capacity of purely cohensive null-gravity soil on a circular foundation. J Huaqiao Univ (Natural Science) 26(12):1991–1995Google Scholar
- Terzaghi K, Peck RB (1948) Soil mechanics in engineering practice, vol 48. Wiley, New York, pp 149–150Google Scholar
- Vesic AS (1973) Analysis of ultimate loads of shallow foundations. J Soil Mech Found Div 99(11):45–73. https://doi.org/10.1016/0148-9062(74)93043-5 CrossRefGoogle Scholar
- Yang JS, Zhang J, Zhang QS, Zhang JS (2005) Finite element analysis of ultimate bearing capacity of circular footing above karst cave. Chin J Rock Mech Eng 24(2):276–301Google Scholar
- Ying YF, Pan WF (2002) Nonlinear finite element analysis of strength and settlement of soft soil foundation under circular plank. Rock Soil Mech 23(2):250–256Google Scholar
- Zhang QY (2013) Ultimate bearing capacity of circular footing with six-degree-of-freedom under combined loading. Chin J Geotech Eng 35(3):559–566Google Scholar
- Zhou Z, Fu HL, Li L (2002) Theoretical solution of bearing capacity of shallow circular foundation. J Railway Sci Eng 20(3):12–16Google Scholar