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

Shaohan Zhao, Ha H. Bui, Vincent Lemiale, Giang D. Nguyen, Felix Darve

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30 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1005-1031
Number of pages27
JournalInternational Journal for Numerical and Analytical Methods in Geomechanics
Issue number5
Publication statusPublished - 10 Apr 2019


  • confining boundary
  • smoothed particle hydrodynamics (SPH)
  • strain localisation

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