Where does the intersection of structural dynamics and geotechnical engineering present significant challenges in civil engineering operations? Discuss the theoretical framework and methodologies involved in analyzing the dynamic response of structures founded on soil, emphasizing the complexities arising from the interaction between soil behavior and structural dynamics. Elaborate on how these challenges influence the design and construction processes, including the selection of appropriate foundation types, seismic retrofitting strategies, and dynamic analysis techniques. Additionally, explore the theoretical underpinnings of soil$-$structure interaction models and their applications in predicting the dynamic behavior of civil engineering structures subjected to various loading conditions, such as seismic events and dynamic machinery$-$induced vibrations. Evaluate the significance of theoretical advancements in this interdisciplinary field for improving the resilience and sustainability of civil engineering infrastructures in dynamic environments.