Mathematical Modeling of the Amplitude Dynamics of Saturated Sludge in a Landslide Wave Surge

Mathematical model is formulated using Partial differential equations, and analyzed to describe the dynamics of wave propagation with application to landslide. Its occurrence leads to loss of lives of people and their properties. This study aims at understanding the dynamics of landslide wave propagation, in order to make adequate projection in an attempt to mitigate the risks involved in the occurrence. The objective of this study is; to develop a mathematical model to describe the dynamics of a landslide wave propagation. Numerical solutions were carried out using Runge-Kutta algorithm’s inbuilt in MATLAB, to simulate the current and future dynamics of the model. The mathematical model was used to simulate and analyze landslide wave propagation phenomena in affected areas. The results of this study showed that the maximum amplitude of 0.49m is achieved at an inclination of 50° and gradually drops down to 0.45m at a slope of 19.2°. This defines the region where inhabitants should be relocated to avoid loss of lives and destruction of property during the occurrence of landslide. The high amplitude occurs in the wave propagation region, necessitating the implementation of control strategies along the same region.