Effect of Footing Width on Bearing Capacity Factor Nγ for Smooth Strip Footings

By incorporating the variation of soil friction angle (ϕ) with mean principal stress (σm), the effect of footing width (B) on bearing capacity factor Nγ 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 ϕ on σm. Two well-defined ϕ–σm curves from literature associated with Hoston and Toyora sands, corresponding to relative density of 18 and 74.5%, respectively, were used. The magnitude of Nγ 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 0.4m, it is possible to relate Nγ with B approximately in a linear fashion on a log–log scale. Further, it was seen that if an average value of ϕ along the footing–soil interface is obtained, it is possible to estimate a reasonable magnitude of Nγ for a given footing width provided the relationship between ϕ and σm is specified for the given material.