Explore the concept of soil$-$structure interaction $($SSI$)$ in geotechnical engineering, emphasizing its significance in the design and performance evaluation of foundation systems. Describe the mechanisms through which soil properties influence the behavior of structures, and vice versa, highlighting key parameters such as soil stiffness, bearing capacity, and settlement. Evaluate different analytical approaches for modeling SSI effects, such as empirical methods, numerical simulations, and experimental techniques, discussing their applicability and limitations in practical engineering scenarios.