Investigate the theoretical underpinnings of soil-structure interaction in geotechnical engineering, elucidating the complex mechanisms governing the behavior of soils under load and their interaction with structural foundations. Delve into classical and modern theories, such as Terzaghi's principle of effective stress and the finite element method, to elucidate the factors influencing soil-structure interaction, including soil properties, loading characteristics, and foundation design parameters. Explain how advanced computational techniques facilitate the analysis and prediction of soil-structure interaction phenomena, offering insights into optimizing foundation design for stability, settlement, and bearing capacity considerations.