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This paper is an attempt to understand implications of the applicability of the principle of superposition to limit analysis based on the upper bound theorem of plasticity theory with Tresca's yield criterion. One application of this analysis is in the design of offshore foundations on undrained clay subjected to combined loading. It is shown that in this type of plasticity problem, superposition can be applied to the dissipation of work, subject to certain conditions satisfied by many conventional mechanisms. However, from a practical point of view, cases where superposition cannot be applied have much greater importance. For these cases it is shown that a combination of the velocity fields from two arbitrary kinematically admissible velocity fields allows the upper bound value of surface traction to be reduced below the values calculated from the separate fields. This finding may be used in the calculation of interaction diagrams for combined loading, not only to improve the upper bound, but also to provide a smooth transition between the different mechanisms. This helps to eliminate sharp corners in the interaction diagrams, so that directions of the incremental plastic displacement vectors can be defined uniquely.
Authors:Puzrin, Alexander and Randolph, M.F.
Index Terms:geomechanics; GeomechanicsGroup; Puzrin, Alexander; Randolph, M.F.
Further Information:Date published: 2001