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A remedy to mitigate tensile instability in SPH for simulating large deformation and failure of geomaterials

Tapan Jana, Subhankar Pal, Amit Shaw, L. S. Ramachandra

TL;DR

This work addresses tensile instability in SPH when simulating large deformation and failure of geomaterials by introducing a pressure-zone based adaptive SPH framework. The method employs a symmetric cubic B-spline kernel whose shape is continuously adjusted via knot positions to maintain stability under mixed stress states, guided by Swegle’s stability insights. Validation on a soil cylinder drop and slope failure demonstrates that the adaptive kernel eliminates tensile instability and stress noise, outperforming conventional SPH and artificial-stress SPH schemes. The approach enables robust, mesh-free large-deformation simulations of cohesive geomaterials with potential impact on landslide hazard assessment and geotechnical engineering analyses.

Abstract

Large deformation analysis in geomechanics plays an important role in understanding the nature of post-failure flows and hazards associated with landslides under different natural calamities. In this study, a SPH framework is proposed for large deformation and failure analysis of geomaterials. An adaptive B-spline kernel function in combination with a pressure zone approach is proposed to counteract the numerical issues associated with tensile instability. The proposed algorithm is validated using a soil cylinder drop problem, and the results are compared with FEM. Finally, the effectiveness of the proposed algorithm in the successful removal of tensile instability and stress noise is demonstrated using the well-studied slope failure simulation of a cohesive soil vertical cut.

A remedy to mitigate tensile instability in SPH for simulating large deformation and failure of geomaterials

TL;DR

This work addresses tensile instability in SPH when simulating large deformation and failure of geomaterials by introducing a pressure-zone based adaptive SPH framework. The method employs a symmetric cubic B-spline kernel whose shape is continuously adjusted via knot positions to maintain stability under mixed stress states, guided by Swegle’s stability insights. Validation on a soil cylinder drop and slope failure demonstrates that the adaptive kernel eliminates tensile instability and stress noise, outperforming conventional SPH and artificial-stress SPH schemes. The approach enables robust, mesh-free large-deformation simulations of cohesive geomaterials with potential impact on landslide hazard assessment and geotechnical engineering analyses.

Abstract

Large deformation analysis in geomechanics plays an important role in understanding the nature of post-failure flows and hazards associated with landslides under different natural calamities. In this study, a SPH framework is proposed for large deformation and failure analysis of geomaterials. An adaptive B-spline kernel function in combination with a pressure zone approach is proposed to counteract the numerical issues associated with tensile instability. The proposed algorithm is validated using a soil cylinder drop problem, and the results are compared with FEM. Finally, the effectiveness of the proposed algorithm in the successful removal of tensile instability and stress noise is demonstrated using the well-studied slope failure simulation of a cohesive soil vertical cut.
Paper Structure (17 sections, 34 equations, 14 figures, 4 tables)

This paper contains 17 sections, 34 equations, 14 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Governing equations and constitutive model
  3. Conservation Equation
  4. Constitutive relation
  5. Drucker-Prager plasticity model
  6. Stress scaling back
  7. Pressure correction
  8. deviatoric stress correction
  9. SPH discretization
  10. Pressure zone based adaptive algorithm
  11. B-spline basis function
  12. Adaptive Algorithm: Concept
  13. Pressure zone based criteria
  14. Estimation of the farthest immediate neighbour
  15. Validation of the SPH framework for elasto-plastic analysis of cohesive soil
  16. ...and 2 more sections

Figures (14)

  • Figure 1: yield surface on $p-\sqrt{J_2}$ plane
  • Figure 2: Cubic B-spline kernel function in 1-D
  • Figure 3: Stable zone in particle interaction
  • Figure 4: The kernel $W$ and gradient of kernel $W^{\prime}$ for different values of $a$ and keeping $b$ as 2
  • Figure 5: Deformed configuration along with pressure contour at $t$=0.8 s using conventional SPH and demonstration of pressure zone
  • ...and 9 more figures