In the heart of big cities, a less obvious challenge exists right under our feet. The everyday activities of city life, like traffic, construction, and industrial work, do more than just create noise. They send vibrations through the ground, which can be problematic, sometimes even destabilizing buildings and affecting the people who live there. This modern issue needs a modern solution. This book introduces the concept of trenches filled with a material called geofoam, an innovative method to control these ground vibrations. Mehran Naghizadeh delves into a detailed study to see how placing these trenches in specific locations can help protect against these vibrations. The book walks through various automated 2D and 3D models, demonstrating how the trenches can be effectively used to protect areas close to and far from the source of vibrations. The study goes beyond just explaining what these trenches are and how they work. It looks into the reasons behind their design, examining different trench shapes and how each shape helps in managing these underground vibrations. The challenge is more complex than it seems. The ground we walk on is not just a single layer but has different layers with various properties. This book takes you on a journey to understand how these layers influence the effectiveness of our vibration warriors. It an exploration of how every layer in the soil contributes to managing vibrations.