Extreme-Value Problems of Limiting Equilibrium

by Michael Garber, Lect.; Soil Sci. Dept., Faculty of Agr. Engrg., Technion-Israel Inst. of Technology, Haifa, Israel,
Rafael Baker, Sr. Research Fellow; Soil Mechanics Dept., Faculty of Civ. Engrg., Technion-Israel Inst. of Technology, Haifa, Israel,

Serial Information: Journal of the Geotechnical Engineering Division, 1979, Vol. 105, Issue 10, Pg. 1155-1171

Document Type: Journal Paper


A unified formulation of extreme-value problems in soil mechanics is presented. The unified problem includes among others the conventional slope stability, bearing capacity, and limiting loads (active and passive) problems. The solution to this unified problem is obtained within the framework of the limiting equilibrium approach. The most important result is a basic theorem of limiting equilibrium which states that the critical value of the extremization parameter is independent of the normal stress distribution along the critical slip line. The variational analysis establishes the existence of two alternative (rotational and translational) modes of failure. Two differential equations, which control the shape of the potential slip lines in each of these modes, are derived. The critical value of an extremization parameter follows from the extremiztion of a function W, the form of that varies from one particular problem to another. The extremization of W is carried out over three variables in the case of rotational mode and over two variables in the case of translational mode.

Subject Headings: Equilibrium | Load bearing capacity | Parameters (statistics) | Stress distribution | Failure analysis | Rotation | Case studies | Soil mechanics

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