Slope stability analysis using smoothed particle hydrodynamics (SPH) method

Abstract

In conventional deformation analysis of geomaterials, the infinitesimal and the finite deformation theories have been widely used. These theories have been successfully implemented in several numerical methods, such as finite element method (FEM). As a result, it is now possible to predict a wide variety of deformation behaviors of geomaterials. However, when dealing with large deformation problems using the framework of the FEM, excess distortion of the FEM mesh may lead to instability of the calculation.In this study, in order to solve large deformation problem of geomaterials, the smoothed particle hydrodynamics (SPH) method is used. The method is a kind of particle method based on the mesh-free Lagrangian scheme, and is one of the promising numerical methods in the field of geotechnical engineering. The method can solve large deformation problems without mesh distortion. Moreover, it can handle the governing equations and existing constitutive models for geomaterials based on a continuum mechanics. Therefore, this method can represent the entire deformation process of a geomaterial from the small strain region to the large deformation region.In this paper, first, basic theory and formulation of the SPH method based on solid mechanics are summarized. Then, the result of a simple calculation is shown to verify the accuracy of the spatial derivatives based on the theory of the SPH method. Also, simulations of simple shear tests of both an elastic and elasto-plastic material are carried out and the obtained results are compared with theoretical solutions. Based on the obtained results, calculation accuracy of the method is discussed. Finally, a series of slope stability analyses are carried out. The numerical results obtained from the SPH method and the safety factors obtained from the Fellenius method are compared. The results indicated that the SPH method is able to express the same tendencies of safety factor obtained from the conventional circular slippage calculations. Moreover, the SPH method can evaluate both the deformation and stability simultaneously. Based on the series of validations and simulations, the effectiveness of the SPH method is discussed from the point of view of geotechnical engineering.