"Discuss the interplay between soil mechanics and foundation engineering in the context of constructing a high$-$rise building on a site with challenging soil conditions. Begin by explaining the fundamental principles of soil mechanics, including soil classification, compaction, and bearing capacity analysis. Delve into the complexities of site investigation and soil testing techniques necessary to assess soil properties accurately. Subsequently, explore the critical role of foundation engineering in ensuring the stability and safety of structures, considering factors such as types of foundations $($e$.$g$.,$ shallow, deep$),$ load distribution, and settlement analysis. Additionally, analyze the potential geotechnical challenges posed by the site's soil composition, such as expansive clay or loose sands, and propose suitable foundation solutions to mitigate these challenges effectively. Furthermore, discuss the importance of ongoing monitoring and risk management strategies throughout the construction process to address unforeseen soil$-$related issues and ensure the long$-$term structural integrity of the building. Illustrate your answer with relevant case studies or real$-$world examples to demonstrate the practical application of soil mechanics principles in foundation engineering for high$-$rise construction projects."