Extended stress field analysis of surface strip footing on sand

Abstract

Maksimovic's non-linear failure envelope and the consistent model of footing roughness provide the backdrop to the development of a comprehensive extension of the stress field method, which is applied to the analysis of surface footings on sand in plane strain. The note derives governing non-dimensional equations and discusses issues pertinent to the extended stress field method: modelling of the shear strength in the ultra-low stress range; internal lengths that produce scale-dependent bearing capacity factors; and the relation between slip-lines and characteristics. For constant friction angles the note produces scale-independent solutions that perfectly match already published results. For friction angles degrading with pressure, the note numerically quantifies and theoretically explains the scale dependence of the bearing capacity factor Nγ. The note shows why friction models with finite shear strength at ultra-low stresses produce Nγs ranging from Nγ(φB + ∆φ) for very small to Nγ(φB) for very large surface footings, and identifies the internal length parameter, γB/pN, as the controlling factor. Theoretical bearing capacity factors are shown to match well with experimentally obtained factors.