PSI - Issue 84

Luca Vené et al. / Procedia Structural Integrity 84 (2026) 544–551

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1. Introduction The design of piled foundations requires a balanced assessment of both safety and performance, ensuring adequate resistance against failure while controlling settlements and rotations that may compromise structural functionality. Traditional design methods commonly assume that the capacity of a pile group is governed by the attainment of ultimate resistance in the most heavily loaded pile. Although this assumption provides a straightforward and conservative criterion, it neglects the inherent redundancy and progressive mobilisation of resistance within pile groups, often leading to unnecessarily conservative designs (Di Laora et al., 2022). In recent years, significant progress has been achieved through analytical approaches capable of describing pile group behaviour under combined loading. Closed-form solutions for interaction domains under eccentric vertical loading were proposed by Di Laora et al. (2019) and subsequently extended to account for horizontal forces and multi axial loading conditions (Di Laora et al., 2022; Gorini and Callisto, 2022). While these formulations provide a comprehensive description of ultimate resistance, they are predominantly framed within an Ultimate Limit State (ULS) perspective. However, the design of piled foundations for many engineering applications is frequently controlled by Serviceability Limit State (SLS) criteria. In these cases, performance requirements related to allowable displacements and rotations are more restrictive than ultimate capacity considerations. Performance-based interaction domains, defined in terms of prescribed settlement or rotation limits, therefore offer a more meaningful basis for design. Although this concept has been successfully applied to other deep foundation systems, such as caissons (Rosati et al., 2020), its implementation for pile groups remains relatively underdeveloped. Recent contributions include the design oriented charts proposed by Franza and Sheil (2021) and the analytical framework introduced by Cesaro et al. (2024) for combined vertical loading and bending moments. Within this context, the present study develops performance-based interaction domains for pile groups subjected to eccentric vertical loading, with specific focus on the Q–Mx (or Q-My) load space. The proposed domains are primarily intended for serviceability assessment. The resulting methodology provides a rational and computationally efficient tool to support the preliminary design and evaluation of both new and existing piled foundations. Nomenclature pile–pile interaction coefficient between piles and pile diameter distance of the -th pile from the rotation axis Young’s modulus of the pile material initial axial stiffness of the pile–soil system pile length number of discretization elements along the pile shaft

number of computational nodes total number of piles in the group bending moment about the x-axis resultant of the base pressure vertical load acting on the pile group axial load in the -th pile lim ultimate axial capacity of a pile in compression lim,t ultimate axial capacity of a pile in tension resultant of the shaft shear stresses acting on the -th pile segment residual associated with the -th pile s center-to-center pile spacing 0 vertical settlement of the pile cap vertical settlement of the -th pile target, prescribed vertical displacement at the head of the -th pile rotation of the pile cap