A probabilistic study on impedances and kinematic response factors of square pile groups in homogeneous soils

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 is also largely influenced by uncertainties related 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 the fact that uncertainties related to the intrinsic variability of soil parameters are widely 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 related to (i) the frequency-dependent impedance functions and (ii) the kinematic response factors. Above quantities are required 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 some results are presented to show and discuss the variability of the results. In addition, a sensitivity analysis is performed to assess the influence of each variable uncertainty on the system response. Overall, response quantities are found to be very sensitive to shear wave velocity, although soil density and pile elastic modulus may often play a significant role.