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

Abstract

Summary In this paper, a new approach to applying confining stress to flexible boundaries in the smoothed particle hydrodynamics (SPH) method is developed to facilitate its applications in geomechanics. Unlike the conventional SPH methods that impose confining boundary conditions by creating extra boundary particles, the proposed approach makes use of kernel truncation properties of SPH approximations that occur naturally at free‐surface boundaries. Therefore, it does not require extra boundary particles and, as a consequence, can be utilised to apply confining stresses onto any boundary with arbitrary geometry without the need for tracking the curvature change during the computation. This enables more complicated problems that involve moving confining boundaries, such as confining triaxial tests, to be simulated in SPH without difficulties. To further enhance SPH applications in elasto‐plastic computations of geomaterials, a robust numerical procedure to implement Mohr‐Coulomb plasticity model in SPH is presented for the first time to avoid difficulties associated with corner singularities in Mohr‐Coulomb model. The proposed approach was first validated against two‐dimensional finite element (FE) solutions for confining biaxial compression tests to demonstrate its predictive capability at small deformation range when FE solutions are still valid. It is then further extended to three‐dimensional conditions and utilised to simulate triaxial compression experiments. Simulation results predicted by SPH show good agreement with experiments, FE solutions, and other numerical results available in the literature. This suggests that the proposed approach of imposing confining stress boundaries is promising and can handle complex problems that involve moving confining boundary conditions.

Comparison of SPH boundary approaches in simulating frictional soil–structure interaction

“…The following two approaches can be used to express the momentum equation for movement of particle i [2,55]:…”

“…A viscous damping term is also introduced to the SPH momentum equation to damp out unphysical oscillations in an alternative approach by Bui and Fukagawa [3] and Zhao et al [55]. This viscous damping term needs to be used with cautions as high damping values can unphysically damp out the energy.…”

“…In the past decades, continuum-scale meshless methods suitable for problems involving large deformation have been developed and utilized; these methods include the smoothed particle hydrodynamics (SPH) method [2,37,38], material point method (MPM) [14,25], and the particle finite element method (PFEM) [13,54]. Among these methods, SPH is the oldest and truly mesh-free technique, whereas the other methods are still, to certain extents, based on a computational background mesh and, hence, have drawbacks such as the instability due to particles grid crossing [9], difficulties in implementing accurate 3D boundary conditions in MPM [47,55], and issues with re-meshing in PFEM [54].…”

Applications of micropolar SPH in geomechanics

“…4.2 where the simulations of biaxial compression are conducted, a method to handle stress boundary condition is required. The approach suggested by Zhao et al [69] is adopted to model the flexible confined boundary condition, but a new criterion is proposed herein to determine which particles should be treated with this procedure. By doing so, Eq.…”

Simulation of mixed‐mode fracture using SPH particles with an embedded fracture process zone

“…The problem can be severe when it comes close to the boundary where the kernel approximation is truncated by the boundary, although this is also an advantage of SPH that allows the method to automatically handle free-surface boundary conditions in many applications. 73 To address this issue, the SPH corrective technique originally developed by Chen et al 63 is adopted in this study. The approach allows both the kernel and its gradient approximations to be corrected by means of the Taylor series expansion.…”