A strict upper-bound limit analysis finite element formulation is used to estimate shape factors s_gamma and s_q for determining the bearing capacity of shallow foundations using the classic bearing capacity formula. The finite element formulation uses a quadratic approximation for the velocity field, an extension of a previously published Augmented Lagrangian formulation with a linear velocity field, and was implemented for a parallel processing environment. Results from determining the limit loads under three-dimensional conditions are presented and compared with previously published data. The results obtained allow a strict upper-bound determination of the shape factors. Furthermore, a practical proposal for these factors is made and compared with other proposals made by other authors.
This paper addresses an implementation of the upper bound limit analysis theorem using a parallel mixed finite element formulation. The intrinsic characteristics of the adopted upper bound formulation proved to be suitable to adapt it to an efficient parallelization scheme. In order to illustrate the computational power provided by the new parallel processing method, accurate upper bound collapse load estimates, for 3D problems, are produced using a cluster of common PC machines.
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