Bearing capacity factor $N_{\gamma}$ for ring footings using the method of characteristics

The bearing capacity factor $N_{\gamma}$ was determined for both smooth and rough ring footings using the method of stress characteristics. The analysis was based on the assumption that for a rough footing the friction angle (\delta) between the footing base and underlying cohesionless material increases gradually from zero along the axis of symmetry to \phi along the outer edge of the footing. The value of $N_{\gamma}$ was found to decrease significantly with an increase in $r_{i}/r_{o}$, where $r_{i}$ and $r_{o}$ are the inner and outer radii of the ring,respectively. For larger values of \phi, the magnitude of $N_{\gamma}$ for a rough footing was seen to be significantly higher than that for a smooth footing. The obtained results were compared with those available in the literature