Effect of Footing Roughness on Bearing Capacity Factor $N_{\gamma }$

The effect of interface friction angle $\left(\delta \right)$ between the footing and underlying soil mass on the bearing capacity factor $N_{\gamma }$ was examined by using the upper bound limit analysis, finite elements, and linear programming. The analysis was carried out by employing velocity discontinuities along all the interfaces of the chosen triangular elements. The development of the plastic strains within elements was incorporated by using an associated flow rule. It was clearly noted that an increase in $\delta$ leads to a continuous increase in $N_{\gamma }$ . With $\delta =\varphi$ , the magnitude of $N_{\gamma }$ becomes almost the same as that for a perfectly rough foundation, that is, when no slippage takes place between the footing and underlying soil mass. The size of the plastic zones increases with increase in $\delta$ and $\varphi$ . The obtained values of $N_{\gamma }$ , for perfectly smooth and perfectly rough footings, compare quite favorably with those reported in literature. The study demonstrates that in the case when $\delta$ is smaller than $\varphi$ , the assumption of a perfectly rough footing will lead to an unsafe prediction of the ultimate bearing capacity.