A probabilistic investigation on the dynamic behaviour of pile foundations in homogeneous soils

Soil-structure interaction is a complex problem to address in structural design due to difficulties related to the modelling of the soil-foundation behaviour, which is frequency-dependent and affected by uncertainties. The substructure method is an efficient approach to include the soil-foundation behaviour in the superstructure response, since it allows addressing separately the soil-foundation and the superstructure analysis exploiting different tools and expertise. A deterministic approach is usually adopted for the soil-foundation system analysis selecting properties of foundation and soil based on an engineering judgment, despite uncertainties due to the intrinsic variability of soil parameters are largely recognised by both scholars and practitioners, as well as confirmed by experimental campaigns and laboratory tests. This paper presents a probabilistic perspective of the dynamic behaviour of pile foundations in homogeneous soils, focusing on the effects of the uncertainties in: (i) the frequency-dependent impedance functions; and (ii) the kinematic response factors necessary to derive the foundation input motion from the free-field motion. Single piles and square pile groups are considered. Uncertainties are described through the probabilistic distributions of parameters governing the soil-foundation dynamic response, while the samples are generated using the quasi-random sampling technique. Probabilistic analyses are performed utilizing an efficient numerical model that has been developed, and the variability of the output quantities is presented and discussed. The latter reveals to be strongly affected by frequency. In addition, sensitivity analyses are performed to investigate the influence of each variable uncertainty on the system response. The response quantities are highly sensitive to the shear wave velocity while the soil density and the pile elastic modulus may have a significant role, depending on the foundation layout.