Solving large deformation problems in geotechnical and geo-environmental engineering with the smoothed particle hydrodynamics: a state-of-the-art review of constitutive solutions

Coupled fluid-solid phase continuum problems associated with large deformation as geotechnics experts encounter in slope stability problems have been extensively reviewed. This has been done with a view to exploring the most efficient numerical approach to solving them for the sake of our environment. Decades ago, analytical solutions known as the limit equilibrium methods (LEM), e.g., Navier-Stokes and the likes were celebrated with the level of mathematical solutions they offered. To overcome the limitations of the LEM in handling more complex slope failure problems, numerical solutions were born, which solved these problems by method of mesh discretization. However, mesh discretization suffered distortions as these mesh-based numerical solutions like finite element method, finite difference method, material point method, discrete element method, and boundary element method were deployed to solve large deformation problems encountered in slope failures like steep watersheds, road embankments, landslides, debris flow, etc. Future developments were made in this line and the birth of the mesh-free approach to solving these largely proportional geophysical flows known as the smoothed particle hydrodynamics (SPH) took place. In this extensive review, previous works have been studied and explored the limitations of the LEM and the mesh-based numerical solutions. Also, the superiority and the use of the SPH in efficiently solving large deformations environmental geotechnics problems, especially those related to slope failure have been proposed despite the environmental conditions of the watershed. However, it has been remarked that the SPH interface is yet to integrate the intergranular force and the slope angle into its framework but maintains its superiority over the other methods.

Automated summary

This article extensively reviews coupled fluid-solid phase continuum problems associated with large deformation encountered by geotechnics experts in slope stability problems. The most efficient numerical approach to solving these problems for the sake of the environment is explored. Limit equilibrium methods (LEM) provided celebrated mathematical solutions in the past, but numerical solutions were born to overcome their limitations in handling more complex slope failure problems. The mesh-based numerical solutions suffered from distortions, leading to the development of the mesh-free smoothed particle hydrodynamics (SPH) approach which has been proposed as an efficient method for solving large deformation environmental geotechnics problems.