A closed form solution for the generalised failure envelope of a pile group

New criteria have been recently proposed to construct the failure envelopes of pile groups in the force space allowing to overcome the traditional design approach involving independent calculations of the vertical and lateral group capacities, which in reality are inherently coupled. The use of such envelopes offers undeniable advantages in the Ultimate Limit State design of pile foundations under seismic or wind load. However, current methodologies postulate a double-hinged failure mechanism for the single pile within the group, which can be unrealistic along with some load paths. Recent methodologies have addressed this problem but their use in routine design still requires numerical implementation. To overcome these issues, a new, closed form solution for interaction diagrams of piled foundations based on limit equilibrium is presented and discussed. The proposed domains fully address the interaction mechanisms between the vertical, horizontal and moment loads and are constructed through a few points, associated to specific distributions of loads upon piles at failure, whose coordinates can be easily determined by hand calculation. After demonstrating the prediction capability of the approach through a comparison with rigorous 3D finite element analyses, a straightforward design procedure is introduced to assess the safety of the foundation. Finally, an application of the proposed domain to a case study of a bridge pier is presented.