Bearing Capacity Equation for Shallow Foundations on Unsaturated Soils

Abstract

For shallow foundations resting on unsaturated soils, matric suction increases effective stresses, resulting in enhanced bearing capacity. However, this boost in bearing capacity is ignored in practice for the sake of simplicity, thus compromising economy. That is why this study aims to consider the beneficial effect of unsaturated conditions on bearing capacity. This is achieved by applying limit analysis using the finite element method on unsaturated soils and investigating the problem parametrically for shallow foundations. The suction effect is taken into account in the formulation of the limit analysis based on effective stress principle. The numerical outcomes are verified by comparing them with available experimental data from the literature. The findings from the parametric study emphasize that the influence of suction on bearing capacity is determined by the friction angle. Moreover, the effects of a varying suction profile are contingent on the foundation width. Based on the results derived from the numerical analyses, a modified bearing capacity equation is introduced. This equation showcases a very good coefficient of determination, effectively encompassing the effects of the soil suction profile. Consequently, the proposed procedure can be considered as a convenient yet precise tool for estimating bearing capacity in engineering practice.

Keywords

• bearing capacity
• limit analysis
• unsaturated soil
• matric suction
• finite element limit analysis

References

1. Terazaghi, K., Theoretical soil mechanics. John Wiley and Sons, 1943.
2. Meyerhof, G., The ultimate bearing capacity of foudations. Geotechnique. 2(4), 301-332, 1951.
3. Vesić, A.S., Analysis of ultimate loads of shallow foundations. Journal of the Soil Mechanics and Foundations Division. 99(1), 45-73, 1973.
4. Hansen, J.B., A revised and extended formula for bearing capacity, in Bulletin No.28. Danish Geotechnical Institute: Copenhagen. 5–11, 1970.
5. Sloan, S., Lower bound limit analysis using finite elements and linear programming. International Journal for Numerical and Analytical Methods in Geomechanics. 12(1), 61-77, 1988.
6. Lysmer, J., Limit analysis of plane problems in soil mechanics. Journal of the Soil Mechanics and Foundations Division. 96(4), 1311-1334, 1970.
7. Bottero, A., R. Negre, J. Pastor, and S. Turgeman, Finite element method and limit analysis theory for soil mechanics problems. Computer Methods in Applied Mechanics and Engineering. 22(1), 131-149, 1980.
8. Sloan, S., Upper bound limit analysis using finite elements and linear programming. International Journal for Numerical and Analytical Methods in Geomechanics. 13(3), 263-282, 1989.

9. Kim, J., R. Salgado, and H. Yu, Limit analysis of soil slopes subjected to pore-water pressures. Journal of Geotechnical and Geoenvironmental Engineering. 125(1), 49-58, 1999.
10. Jennings, J.E.B. and J.B. Burland, Limitations to the Use of Effective Stresses in Partly Saturated Soils. Géotechnique. 12(2), 125-144, 1962.
11. Matyas, E.L. and H.S. Radhakrishna, Volume Change Characteristics of Partially Saturated Soils. Géotechnique. 18(4), 432-448, 1968.
12. Fredlund, D.G. and N.R. Morgenstern, Stress state variables for unsaturated soils. Journal of the geotechnical engineering division. 103(5), 447-466, 1977.
13. Khalili, N., F. Geiser, and G.E. Blight, Effective Stress in Unsaturated Soils: Review with New Evidence. International Journal of Geomechanics. 4(2), 115-126, 2004.
14. Loret, B. and N. Khalili, A three‐phase model for unsaturated soils. International journal for numerical and analytical methods in geomechanics. 24(11), 893-927, 2000.
15. Rojas, J.C., L.M. Salinas, and C. Seja. Plate-load tests on an unsaturated lean clay. in Experimental unsaturated soil mechanics. 2007. Springer.
16. Li, X., Laboratory studies on the bearing capacity of unsaturated sands. University of Ottawa (Canada), 2008.
17. Wuttke, F., B. Kafle, Y. Lins, and T. Schanz, Macroelement for statically loaded shallow strip foundation resting on unsaturated soil. International Journal of Geomechanics. 13(5), 557-564, 2013.
18. Vanapalli, S.K. and F.M. Mohamed, Bearing capacity and settlement of footings in unsaturated sands. GEOMATE Journal. 5(9), 595-604, 2013.
19. Ajdari, M. and A. Esmail Pour, Experimental evaluation of the influence of the level of the ground water table on the bearing capacity of circular footings. Iranian Journal of Science and Technology Transactions of Civil Engineering. 39(C2+), 497-510, 2015.
20. Fredlund, D.G., N.R. Morgenstern, and R.A. Widger. The shear strength of unsaturated soils. Canadian Geotechnical Journal. 15(3): 313-321, 1978.
21. Oloo, S.Y., D. Fredlund, and J.K. Gan, Bearing capacity of unpaved roads. Canadian Geotechnical Journal. 34(3), 398-407, 1997.
22. Oh, W.T. and S.K. Vanapalli, Interpretation of the bearing capacity of unsaturated fine-grained soil using the modified effective and the modified total stress approaches. International Journal of Geomechanics. 13(6), 769-778, 2013.
23. Vahedifard, F. and J.D. Robinson, Unified method for estimating the ultimate bearing capacity of shallow foundations in variably saturated soils under steady flow. Journal of Geotechnical and Geoenvironmental Engineering. 142(4), 04015095, 2016.
24. Akbari Garakani, A., H. Sadeghi, S. Saheb, and A. Lamei, Bearing capacity of shallow foundations on unsaturated soils: analytical approach with 3D numerical simulations and experimental validations. International Journal of Geomechanics. 20(3), 04019181, 2020.
25. Vo, T. and A.R. Russell, Bearing capacity of strip footings on unsaturated soils by the slip line theory. Computers and Geotechnics. 74, 122-131, 2016.
26. Martin, C., ABC–Analysis of bearing capacity. University of Oxford 77, 2004.
27. Tang, Y., H.A. Taiebat, and K. Senetakis, Effective stress based bearing capacity equations for shallow foundations on unsaturated soils. Journal of GeoEngineering. 12(2) 2017.
28. Ghasemzadeh, H. and F. Akbari, Determining the bearing capacity factor due to nonlinear matric suction distribution in the soil. Canadian Journal of Soil Science. 99(4), 434-446, 2019.
29. Jahanandish, M., G. Habibagahi, and M. Veiskarami, Bearing capacity factor, Nγ, for unsaturated soils by ZEL method. Acta Geotechnica. 5(3), 177-188, 2010.
30. Optum-G2. Finite Element Program for Geotechnical Analysis. 2020; Available from: www.optumce.com.
31. Bishop, A.W., The principal of effective stress. Teknisk ukeblad. 39, 859-863, 1959.
32. Khalili, N. and M. Khabbaz, A unique relationship for χ for the determination of the shear strength of unsaturated soils. Geotechnique. 48(5), 681-687, 1998.