The complexity of the Soil-Structure Interaction (SSI) problem is mainly due to difficulties related to the modelling of the soil-foundation behaviour, which is not only frequency-dependent, but also largely affected by uncertainties relevant to soil properties and stratigraphic conditions. According to a sub-structuring scheme for the analysis of SSI problems, a deterministic approach is usually adopted for the analysis of the soil-foundation system assuming properties and geotechnical models based on the expert judgment, despite uncertainties related to the intrinsic variability of soil parameters are largely recognised and confirmed by experimental campaigns and laboratory tests.

This paper presents a probabilistic study on the dynamic behaviour of square pile group foundations in homogeneous soils, focusing on the effects of the uncertainties in (i) the frequency-dependent impedance functions; and (ii) the kinematic response factors. Above quantities are necessary to define compliant restraints for the modelling of the soil-foundation system in performing inertial soil-structure interaction analysis and for the definition of the foundation input motion starting from the free-field motion. Square pile groups are considered and uncertainties are described through probabilistic distributions of parameters governing the soil-foundation dynamic response. The probabilistic analyses are performed through a numerical model developed by the Authors and the variability of the results is presented and discussed. In addition, a sensitivity analysis is performed to evaluate the influence of each variable uncertainty on the system response. Response quantities are overall high sensitive to shear wave velocity, even if the soil density and the pile elastic modulus may often have a significant role.