The size effect of a conical footing on Nγ

By incorporating the diameter (size) effect of a conical footing, the factor Nγ has been computed. The analysis has been performed by using the lower bound theorem of limit analysis in combination with finite elements and linear optimization. By using an iterative procedure, the dependency of peak friction angle (ϕ) on mean stress (σm) has been incorporated to obtain Nγ for various cone apex angles (α) with several cone diameters (B) covering almost entire possible ranges of model and field cone footing sizes. Three different ϕ–σm curves reported from literature, associated with Hostun and Toyoura sands, were chosen. For the value of B approximately greater than (i) 0.45 m for a smooth footing, and (ii) 0.85 m for a rough footing, the magnitude of Nγ decreases almost linearly with an increase in B on a log–log scale. For the value of B greater than about 8.0 m, the factor Nγ shows only a little change with an increase in the footing diameter. The results from the analysis compare well with the data reported in literature.