The bearing capacity of footings on granular soils. I: Numerical analysis

The method of characteristics has been used to determine the bearing capacity of shallow foundations, in either plane-strain or axisymmetric condition. Most previous solutions for granular soils were based either on a straight (c, φ) envelope or simply on a constant angle of shearing, φ. For granular soils, sec φ usually varies linearly with the logarithm of mean effective stress. A new method of calculation permits φ to vary throughout the stress field as an arbitrary (or empirical) function of stress. This method is verified for both plane-strain and axisymmetric conditions by forcing a variation in sec φ equivalent to generating a constant-cohesion envelope, for which solutions already exist. The variable-φ analysis is used to demonstrate the highly significant effect of stress variation around and beneath a footing. Finally, it is shown that an equivalent constant value φ_m can be derived empirically, using the new solutions to identify an equivalent mean effective stress p_m. However, only the variable-φ solution can simultaneously capture the bearing capacity and the geometry of the bearing mechanism.