Failure envelopes of rigid tripod pile foundation under combined vertical-horizontal-moment loadings in clay

The problem considered in this computational study is for the bearing capacity determination of three-dimensional (3D) rigid tripod-pile groups subjected to combined vertical (V), horizontal (H), and bending moment (M) loads. Using the adaptive 3D finite element limit analysis (FELA) coupled with lower bound, upper bound and mixed Gauss element formulations, numerical results are compared with those of the previous study under a single-component loading (V, or H, or M). The failure envelope in the 3D V–H–M loading space is then constructed, and several failure mechanisms presented to complement the discussions on the complex 3D responses. This is followed by a parametric study for the various factors such as the pile length, pile spacing, pile-soil adhesion factors as well as the loading direction angle. Finally, a closed-form design expression of failure envelopes considering the abovementioned influential parameters and the combined load are derived. Noting that the current industry-based design procedures for tripod-pile groups are rarely found, the outcome of the present study can be used with great confidence in design practice.