An improved SPH method for saturated soils and its application to investigate the mechanisms of embankment failure: Case of hydrostatic pore‐water pressure

Abstract

SUMMARYThe method of smoothed particle hydrodynamics (SPH) has recently been applied to computational geomechanics and has been shown to be a powerful alternative to the standard numerical method, that is, the finite element method, for handling large deformation and post-failure of geomaterials. However, very few studies apply the SPH method to model saturated or submerged soil problems. Our recent studies of this matter revealed that significant errors may be made if the gradient of the pore-water pressure is handled using the standard SPH formulation. To overcome this problem and to enhance the SPH applications to computational geomechanics, this article proposes a general SPH formulation, which can be applied straightforwardly to dry and saturated soils. For simplicity, the current work assumes hydrostatic pore-water pressure. It is shown that the proposed formulation can remove the numerical error mentioned earlier. Moreover, this formulation automatically satisfies the dynamic boundary conditions at a submerged ground surface, thereby saving computational cost. Discussions on the applications of the standard and new SPH formulations are also given through some numerical tests. Furthermore, techniques to obtain the correct SPH solution are also proposed and discussed throughout. As an application of the proposed method, the effect of the dilatancy angle on the failure mechanism of a two-sided embankment subjected to a high groundwater table is presented and compared with that of other solutions. Finally, the proposed formulation can be considered a basic formulation for further developments of SPH for saturated soils.

Frictional contact algorithms in SPH for the simulation of soil–structure interaction

“…For a general reference, see . Recently, it has also been successfully applied to the field of geotechnical engineering, such as simulating flow‐like landslides by treating soil as equivalent fluid [] or using velocity–pressure version of the Biot–Zienkiewicz model [], or solving large deformation and post‐failure flows by treating soil as elastoplastic material []. Compared with other numerical methods such as the finite element method (FEM) or discrete element method (DEM), SPH has several advantages.…”

An application of a cohesive fracture model combining compression, tension and shear in soft rocks

“…However, the Roscoe shear band theory [21], which is based on the critical kinematic surface and relates shear band orientation with dilation angle, proposes that the shear bands must be parallel to the no-extension lines. The no-extension line is necessary for a continuous displacement field [22]. The orientation of the no-extension line is (h r ¼ 45 À u d =2Þ with the major principle stress.…”

A generic approach to modelling flexible confined boundary conditions in SPH and its application

“…In addition, viscous damping is required in SPH to stabilise the potentially excessive stress wave propagation due to the sudden application of the confining stress vectors on the computational domain without an initial stress condition. This viscous damping can be incorporated in the SPH motion equation following the approach proposed by as follows: where is the acceleration of particle i due to internal stress and external force; ξ is a dimensionless damping coefficient chosen to be 0.1, (Nguyen et al 2017).…”