A strain-hardening macro-element model for pile groups under vertical–horizontal-moment loading

Pile foundations supporting wind turbines, silos, elevated water tanks or bridge piers are frequently subjected to multi-component loads, which may lead to significant rotations and settlements compromising the safe operation of the structure. The prediction of these displacements is of major concern and can be easily carried out using force-resultants plasticity models, also referred to as 'macro-elements', stemming from the idea of describing the foundation behaviour by a single upscaled constitutive relationship between generalized forces and displacements. When properly formulated, they can reproduce key aspects of the mechanical response of the foundation at low computational cost as compared to numerical analysis. To this end, a new macro-element for pile groups formulated in the classical framework of strain-hardening elasto-plasticity is presented and discussed. The required model parameters can be calibrated by closed-form equations and additional few data of numerical and/or experimental nature. The proposed mathematical framework is finally validated against the results of centrifuge tests and 3D finite element analyses.