"What are the fundamental principles governing soil$-$structure interaction $($SSI$)$ in civil engineering? Discuss how SSI influences the design and analysis of foundation systems, considering factors such as soil properties, structural behavior, and loading conditions. Explain the theoretical basis for various methods used to model SSI, including continuum and discrete element methods. Analyze the theoretical limitations and challenges in predicting real$-$world SSI behavior, and discuss current research trends aimed at improving the accuracy and reliability of SSI models. Provide examples to illustrate the practical implications of SSI theory in civil engineering practice."