Vertical bearing capacity factors for circular and strip footings on Mohr–Coulomb soil

Abstract

The method of characteristics is used to establish consistent factors for the vertical bearing capacity of circular and strip footings on soil which satisfies a linear [Formula: see text] Mohr–Coulomb strength criterion. This method of solution avoids the assumption of arbitrary slip surfaces, and produces zones within which equilibrium and plastic yield are simultaneously satisfied for given boundary stresses. Although similar solutions have previously been published for circular footings, their application has been hindered by errors and confusions over terminology. These are resolved, and the method of solution is explained. It is confirmed that Terzaghi's approach to the superposition of bearing terms containing Nq, Nγ, and Nc is both safe and sufficiently accurate for circular footings, as for strip footings. The values to be adopted are tabulated as functions of [Formula: see text]. Differences between the factors applicable to circular and strip footings far exceed the allowances of the empirical shape factors in common use. Some new shape factors are suggested that better represent the relationship between the limiting equilibrium of circular and strip foundations. Some current shape factors attempt to allow simultaneously for the differences in equilibrium solutions and the differences in axisymmetric (triaxial) and plane strain soil parameters. This cannot succeed, since the relationship between strength parameters depends strongly on relative density. The new bearing factors facilitate a more rational approach in which soil parameters appropriate to the geometry can first be determined and then used to find appropriate bearing capacity factors. Key words : bearing capacity, axisymmetry, method of characteristics, footings, plane strain.