"How do differential settlements in soil affect the structural stability of buildings, and what are the preventive measures and remedial techniques to mitigate their impact? Discuss the underlying mechanisms of settlement, factors influencing it$,$ and the design considerations for foundations in areas prone to differential settlements. Additionally, analyze case studies of notable structures affected by such settlements and evaluate the effectiveness of various remedial solutions employed to rectify the issue while ensuring the long$-$term structural integrity of the buildings."