Bearing Capacity by Variational Method

by Michael Garber, Research Fellow; Soil Sci. Dept., Faculty of Agricultural Engrg., Technion—Israel Inst. of Tech., Haifa, Israel,
Rafael Baker, Lect.; Soil Mechanics Dept., Faculty of Civ. Engrg., Technion—Israel Inst. of Tech., Haifa, Israel,

Serial Information: Journal of the Geotechnical Engineering Division, 1977, Vol. 103, Issue 11, Pg. 1209-1225

Document Type: Journal Paper


A general limit equilibrium approach has been applied to the problem of bearing capacity of foundations. The approach is completely rigorous in the sense that the critical rupture surface and the critical stress distribution along it are derived by variational methods without any a priori assumptions. The critical rupture surface has been proven to be log-spiral, which degenerates to a circular arc in the case of the frictionless soil. The superposition principle that was assumed by Terzaghi is derived by the use of variational analysis. The values of the obtained bearing capacity factors Nc(φ) and Nq(gf) corresponds closely to that obtained from the plasticity theory. The N/dγ(φ) factor obtained corresponds rather well with De Beer's and Feda's experimental results, while Terzaghi's solution for N/dγ(φ) is too low by a factor of approximately two.

Subject Headings: Load bearing capacity | Stress distribution | Distinguished engineers | Limit equilibrium | Case studies | Friction | Plasticity

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