PSI - Issue 84

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

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2. Methodological Framework for Performance-Based Interaction Domains The response of a pile group is commonly governed by admissible limits on settlement and rotation at the pile cap. In this study, a numerical framework is proposed to derive performance-based interaction domains in the Q–Mx (or Q-My) space associated with prescribed limit states defined in terms of settlement, rotation, or their combination. The methodology accounts for the nonlinear axial load–displacement behaviour of individual piles and incorporates pile– pile interaction effects, enabling a consistent representation of the global response of the pile group. The pile cap is assumed to be infinitely rigid, with piles connected through spherical hinges, so that bending moments at the pile heads are neglected while displacement and rotation compatibility is enforced, in line with widely adopted modelling approaches. The load-settlement curve of each pile is first characterised through single-pile analysis and, in the absence of load-test data, represented by a nonlinear hyperbolic relationship. Group effects are then introduced using the interaction-factor method of Poulos and Davis (1980), with coefficients derived from Boundary Element Method analyses of equally loaded pair of piles and assumed to be load-independent, such that nonlinearities are fully concentrated at the pile–soil interface, i.e. pile-pile interactions are considered linear (Caputo and Viggiani, 1984). For a prescribed performance limit at the pile cap, a set of admissible rigid-body motion scenarios is generated. For each scenario, the pile axial forces are determined through a bounded nonlinear least-squares optimisation, and the corresponding values of Q and Mx (or My) are computed, thereby defining the performance-based interaction domain in the Q–Mx (or Q-My) plane. 2.1. Load–Settlement Behaviour of a Single Pile The nonlinear response of the pile–soil system is represented by a hyperbolic load–settlement relationship. Under this assumption, the axial behaviour of an isolated pile is fully characterised by K s , Q lim and Q lim,t . Accordingly, for each pile i , the relationship between Q i and w i is expressed by Eq. (1) and is schematically illustrated in Figure 1a. In the absence of pile load-test data, K s is evaluated through a BEM–based procedure. As shown in Figure 1b, the pile is discretised into n vertical uniform blocks of height d v =L/n, resulting in n v =n+1 computational nodes. Values of d v

Figure 1: a) Hyperbolic load–settlement relationship of the single pile–soil system. b) Pile discretisation into elements of height .