Why is it critical to consider soil$-$structure interaction $($SSI$)$ in the design of civil engineering projects, particularly for large$-$scale structures such as high$-$rise buildings, bridges, and dams? Explain the underlying principles of SSI, including the key factors that influence this interaction and how it affects the overall stability and performance of structures. Discuss the methods and tools used by civil engineers to analyze and mitigate the potential adverse effects of SSI, and elaborate on the theoretical implications of neglecting SSI in structural design. Consider the role of material properties, soil type, and foundation design in your explanation, and address how SSI considerations might evolve with advancements in engineering technology and materials. What are the theoretical challenges faced in accurately modeling SSI, and how can these challenges be addressed through both analytical and empirical approaches?