Automated procedure to derive convex failure envelope formulations for circular surface foundations under six degrees of freedom loading

Failure envelope formulations are typically employed to assess the ultimate capacity of foundations under combined loading and for incorporation in macro-element models. However, complex interaction between each load component, especially six degree freedom (6DoF) loading, means that determining satisfactory is often a process. Previous researchers have identified this difficulty as an obstacle adoption failure approach foundation engineering applications. To address issue, paper describes systematic procedure deriving globally convex formulations; applied circular surface foundation, bearing on undrained clay, 6DoF space. The shown closely represent combinations determined from finite element analyses variety conditions, including non-planar horizontal-moment loading. An example model based proposed formulation described; provides close representation behaviour separate analysis. A key aspect it demonstrates automated process determine well-behaved formulations. nature has considerable advantages over manual procedures previously been