Stability-enhanced smoothed particle hydrodynamics for geomaterials : methods and applications

Abstract

Geomaterials, such as soils and rocks, play a critical role in natural disasters like landslides, debris flows, and rockfalls, posing significant threats to infrastructure and human safety. Understanding their mechanical properties and interactions with environmental (trees, rainfall, etc) and structural factors (buildings, barriers, etc) is essential for designing effective mitigation strategies. However, the inherent complexity of geomaterials and the high cost of physical experiments necessitate advanced numerical methods for accurate modeling. Traditional methods like finite element method grapple with large deformations, while discrete element method is computationally expensive. In this context, smoothed particle hydrodynamics (SPH) has emerged as a promising alternative, offering robust capabilities for simulating large deformation and complex geotechnical problems efficiently. Despite significant progress in applying SPH to the simulation of elastic, elastoplastic materials, and fluids, numerical instabilities—such as tensile instability and hourglass modes—remain critical challenges. This research aims to enhance the numerical stability of SPH and extend its application to the simulation of various materials in geotechnical engineering, including elastic solids, elastoplastic particulate materials, and fluids. The goal will be achieved through four objectives: (1) investigating the causes of numerical instabilites in updated Lagrangian SPH (ULSPH) when simulating elastic and plastic materials, and proposing a general solution based on existing compensation strategies; (2) improving SPH performance in large-deformation simulations of granular materials and developing a fine grain-coarse grain coupling algorithm within SPH framework; (3) addressing tensile instability in SPH simulations of cohesive granular materials; and (4) developing a stable surface tension modeling algorithm in SPH to lay the foundation for investigating erosive processes involving particle detachment and transport in soil-water interactions. Chapter 4 investigates numerical instabilities in ULSPH simulations of elastic materials, such as particle clustering and non-physical fractures. To address these, an essentially non-hourglass formulation is proposed using a Laplacian-based shear force. Chapter 5 further develops a generalized non-hourglass formulation for both elastic and J2 plasticity models by introducing a penalty force. For the second objective, Chapter 6 develops a low-dissipation Riemann-based SPH method for simulating large deformations in granular materials. Subsequently, Chapter 7 introduces a fine-grain and coarse-grain coupling algorithm within the SPH framework to model binary granular mixtures. Chapter 8 investigates the issue of tensile instability, a common numerical instability in the simulation of cohesive granular materials. A unified transport-velocity formulation is proposed to resolve tensile instability in free-surface granular flows. To address the final objective, Chapter 9 develops a multiphase SPH framework to model surface tension effects between fluids with high density and viscosity ratios. The surface tension force is calculated as the divergence of surface stress and discretized in a momentum-conserving form. Furthermore, a penalty term is introduced to resolve the long-standing issue of zero-surface-energy modes at fluid interfaces, enhancing simulation stability and accuracy. This work establishes a robust foundation for advancing SPH in geotechnical engineering. By addressing key numerical instabilities and developing novel algorithms, it extends SPH's applicability to complex geomaterial simulations, paving the way for future research and practical applications in natural disaster modeling and mitigation strategies.