Effect of footing width on Nγ

By incorporating the dependency of soil friction angle (ϕ) on mean principal stress (σm), the effect of footing width (B) on bearing capacity factor (Nγ) is examined for a rough strip footing. The analysis is performed by means of a numerical lower bound limit analysis in conjunction with triangular finite elements and linear programming. To account for the variation of ϕ with σm, a solution is obtained by using an iterative procedure. Two well defined ϕ–σm curves from the literature, associated with Hoston and Toyoura sands that correspond to relative densities of 18% and 74.5%, respectively, are used. The magnitude of Nγ is computed for different footing widths. It is noted that for B greater than about 0.2 m, the magnitude of Nγ varies almost linearly with B on a log–log scale. For different footing widths, a good comparison is seen between the obtained rigorous solution and that obtained by using a constant value of ϕ, which corresponds to the equivalent mean normal stress level as defined by De Beer.