State-of-the-Art Review of Continuum Mechanics-Based Modelling of Soil Surface Erosion

Abstract Soil surface erosion can shape the morphography of rivers and estuaries in the natural environment and induce high potential risks to structures in engineering. Numerical simulations based on continuum mechanics theory can provide reliable assessments of the evolution of surface erosion from the perspective of a large-scale view. However, current studies on continuum mechanics-based modelling are still limited. This paper comprehensively reviews such numerical simulations of soil surface erosion. This review begins by discussing the fundamental physical mechanisms of surface erosion. Subsequently, it explores the basic physics-based conservation equations controlling soils and fluids in surface erosion. Then, the empirical formulae depicting the different stages of surface erosion are presented. Building on these mathematical foundations, this paper reviews various numerical methods for surface erosion modelling from a continuum mechanics perspective. Finally, this paper discusses the advantages and limitations of the numerical methods. This work can provide researchers convenience for using numerical models on surface erosion simulations.