How do different soil types affect the design and construction of foundations for civil engineering structures? Discuss the principles behind selecting appropriate foundation types for varying soil conditions, considering factors such as bearing capacity, settlement, and lateral stability. Furthermore, analyze the role of site investigation methods in determining soil properties and their significance in ensuring the long$-$term performance and safety of structures. In your answer, delve into the complexities of soil$-$structure interaction, including the influence of soil mechanics theories on foundation design and the importance of incorporating geotechnical considerations into the overall engineering process.