Seismic Soil$-$Structure Interaction Modeling: Describe the theory behind seismic soil$-$structure interaction $($SSI$)$ modeling and its importance in earthquake engineering. Discuss the dynamic behavior of soil$-$foundation$-$structure systems subjected to seismic loading, considering factors such as soil stiffness, site conditions, and structural damping. Explore analytical and numerical methods for simulating SSI effects, including equivalent linear analysis, frequency$-$dependent soil properties, and time$-$domain simulations. Evaluate the challenges in predicting soil amplification, foundation rocking, and structural pounding during earthquakes, and how accurate SSI modeling can improve seismic design and risk assessment for civil engineering structures.