PSI - Issue 84

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

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3. Validation of the Numerical Procedure This section validates the proposed method by comparison with literature results. The case study refers to the idealized pile foundation in Cesaro et al. (2024), where an explicit nonlinear incremental procedure was used to derive performance-based interaction domains. Their results provide a benchmark to assess the reliability of the developed numerical approach. A direct comparison is performed between the interaction domains obtained here and those reported by Cesaro et al. (2024). The reference configuration is a 3×3 pile group subjected to vertically eccentric loads, with dimensionless parameters: , = 3 4 , = 3, =80, =0. where the parameter denotes the inclination angle of the external moment vector measured with respect to the -axis; the value =0 therefore corresponds to a bending moment acting about the -axis. To ensure proper alignment and comparability, the axes were normalized using the same dimensionless ratios adopted in the reference study, namely Q/Q lim and M/(sQ lim ) . The performance-based domains were obtained by considering different limit values for the normalized settlement w/D or rotation θ at the pile cap. Figure 2 compares the performance-based interaction domains reported by Cesaro et al. (2024) with those obtained through the proposed procedure. Figure 2a refers to limit conditions defined by prescribed values of the normalised settlement ratio w/D, with w/D = 3%, 5%, and 10%, while Figure 2b refers to limit conditions defined by prescribed rotation angles θ = 0.25°, 0.50° and 1.00°.

Figure 3 illustrates the combined condition, where both rotation and settlement constraints are simultaneously enforced (w/D = 5% and θ = 0.5°), allowing a direct assessment of the coupled rotational –translational behavior. Figure 2: Comparison between the performance-based interaction domains reported by Cesaro et al. (2024) and those obtained with the proposed numerical procedure: (a) prescribed normalised settlement ratios / = 3% , 5% , and 10% ; (b) prescribed rotation angles =0.25 ∘ , 0.5 ∘ , and 1 ∘ .

Figure 3: Comparison between the performance-based interaction domains reported by Cesaro et al. (2024), and the corresponding domains obtained through the proposed numerical procedure. The comparison refers to case with w/D = 5%, and θ =0.5°.