An essential aspect of civil engineering involves the analysis and design of structures to withstand various environmental forces. Consider a scenario where a team of civil engineers is tasked with designing a bridge over a river in a region prone to seismic activity. Discuss the interplay between soil mechanics and structural engineering in such a project, emphasizing the significance of soil characteristics, including but not limited to soil composition, density, and shear strength. Elaborate on the challenges associated with determining the seismic response of the bridge foundation considering the dynamic behavior of both the soil and the structure. Additionally, explore the role of geotechnical investigations and advanced analytical techniques, such as finite element analysis, in optimizing the bridge's performance under seismic loading conditions. Evaluate potential mitigation strategies to enhance the resilience of the bridge against seismic events, considering both traditional approaches and innovative solutions in civil engineering practice. Finally, assess the broader implications of incorporating soil$-$structure interaction considerations in the design of critical infrastructure, highlighting the importance of interdisciplinary collaboration between geotechnical engineers and structural engineers in addressing complex engineering challenges.