How do different soil types affect the stability of structures in civil engineering, considering factors such as compaction, moisture content, and particle size distribution? Discuss the mechanisms through which clay, sand, silt, and gravel influence the bearing capacity and settlement characteristics of foundations. Furthermore, analyze the role of geotechnical investigations and laboratory testing methods in assessing soil properties and determining suitable foundation designs. Evaluate the significance of understanding soil$-$structure interaction in the context of structural stability and the prevention of issues like differential settlement and slope instability. Additionally, explore how advancements in soil mechanics and geotechnical engineering have contributed to the development of innovative foundation solutions and mitigation strategies for challenging soil conditions.