Effect of Footing Width on Bearing Capacity Factor $N_\gamma$ for Smooth Strip Footings

By incorporating the variation of soil friction angle $\phi$ with mean principal stress $\sigma_m$ the effect of footing width (B) on bearing capacity factor $N_\gamma$ was examined for a smooth strip footing placed on a granular medium without any surcharge pressure. The analysis was performed by means of a numerical lower bound limit analysis in conjunction with finite-elements and linear programming. An iterative computational procedure was framed to account for the dependency of $\phi$ on $\sigma_m$. Two well-defined $\phi-\sigma_m$curves from literature associated with Hoston and Toyora sands, corresponding to relative density of 18 and 74.5%, respectively, were used. The magnitude of $N_\gamma$ was obtained for different footing widths, covering almost the entire range of model and field footing sizes. It was noted that for B greater than about 0.4 m, it is possible to relate $N_\gamma$ with B approximately in a linear fashion on a log–log scale. Further, it was seen that if an average value of $\phi$ along the footing–soil interface is obtained, it is possible to estimate a reasonable magnitude of $N_\gamma$ for a given footing width provided the relationship between $\phi$ and $\sigma_m$ is specified for the given material