Orientational Analysis of the Vesic’s Bearing Capacity of Shallow Foundations

L. F. dos Santos, A.C.de Freitas


Soils and Rocks, São Paulo, 43(1): 3-9, January-March, 2020 | PDF


The determination of the bearing capacity of shallow foundations can be considered as a complex elasto-plastic deformation problem, which is often studied phenomenologically. The phenomenological equations are naturally constructed based on the typical dimensions of the variables involved (unit weight, foundation size, etc.) – all physical laws must guarantee the principle of dimensional balance. Nevertheless, there is another requirement physical laws must obey that is less often explored: all equations must be orientationally balanced. While this requirement is obvious for vectorial equations, the laws of continuum mechanics often mix tensors, vectors and scalar quantities. Moreover, not all scalar quantities are considered orientationless (for instance, areas and angles define an orientation determined by the unit vector normal to the plane). Here, the main equations found in the literature for the bearing capacity of soils will be analyzed, testing the orientational balance of the phenomenological equations. It will be shown that not all equations are well balanced – in particular the critical rigidity index for the generalized failure of soils determined by Vesic (1973) is not balanced. Perhaps not surprisingly, the equations that are well balanced lead to a good agreement with experimental data from the literature, while the critical rigidity index fails systematically when compared to tests in model foundations on sand.

Submitted on October 1, 2017; Final Acceptance on February 13, 2020; Discussion open until August 31, 2020.
DOI: 10.28927/SR.431003