It is well-established that the effect of the soil significantly influences the overall behaviour of structures, particularly in the presence of vibrations. The majority of the developed approaches can be categorised into two groups: the direct approach and the substructure method. The first one is based on detailed modelling of the soil, foundation and structure using FEM and is not commonly used because it is computationally expensive and thus not feasible for standard engineering practice. The second method uses the dynamic stiffness matrix of the substructure to include it in the analysis of the general structure. Due to the impracticality of the first method, various methodologies have been investigated to better address SSI through the dynamic stiffness matrix, also known as impedance functions. They provide an approximate representation of the SSI that facilitates quicker analysis and sufficiently accurate results.

These approximation techniques typically involve intricate systems composed of lumped masses, dashpots, and springs. The characteristics of these elements vary based on soil and foundation types. For instance, a circular plate laying on homogeneous soil can be modelled as a mass, spring, dashpot single-degree-of-freedom system, where the coefficients of the elements represent the SSI of the disc. Similarly, a pile embedded in soil can be modelled with springs on the side that represent the effect of the friction between the structure and the soil. Some of the existing models for these two cases will be studied in this work.

Four mechanical analogues will be computed and compared for the first SSI problem: Lysmer's, Kausel's, and two of Wolf's models. These models define the mass, stiffness, and damping coefficients differently, but yield similar responses. Additionally, the results will be compared to a finite element (FE) model with the same soil and foundation characteristics to assess their applicability. For the second SSI problem, Novak's solution for piles under vertical vibrations will be studied and compared to the response of an FE model. The relevance of these SSI problems lies in the simplicity of reproducing the analogues to use as a reference. They are suitable benchmark problems to evaluate an alternative computational approach that is proposed in this work.

This work's objective is to determine the feasibility of analysing the response of these systems using a hybrid computational approach. This method involves generating responses using an FE model with a range of soil and foundation parameters as a first step. Secondly, these results are input into a Neural Network (NN). The NN is trained to reproduce the response of any system by knowing only the geometric characteristics of the foundation, and the shear modulus, Poisson's ratio, and density of the soil. The network's output is the frequency response function (FRF) of said system, which is subsequently used in an optimisation process. The output of this second process is the values for the system's mass, stiffness, and damping characteristics. Ultimately, these values can be used to construct the dynamic stiffness matrix necessary for solving the soil-structure interaction of a particular structure.

The central question addressed in this research is: What constitutes an efficient data-driven process for translating large soil-foundation datasets into simplified mechanical analogues that provide a reduced and accurate representation of the system? After assessing its applicability, it can be concluded that a hybrid two-step computational approach is an efficient and generic method for solving SSI problems.