Soil surface erosion simulation using material point method

• Extend MPM with efficient inflow/outflow boundaries for soil surface erosion • Propose unified state-dependent constitutive model for bed- and suspended-load • Validate the model against experiments and other methods with excellent agreement • Assess model performance via systematic comparative studies • Enable accurate soil surface erosion simulation without empirical criteria Existing continuum-based soil surface erosion modeling has primarily focused on one-phase Eulerian methods, while the use of Lagrangian particle methods, particularly the Material Point Method (MPM), remains limited. Although two-phase MPM formulations for soil-water coupling have been developed, they typically employ conventional elastoplastic soil models that fail to capture the complex soil behavior involving transitions from a static bed to bed-load and suspended-load states. Furthermore, rigorous experimental validation and detailed comparative assessments of MPM for soil surface erosion remain scarce and underexplored. To address these gaps, this study applies the explicit two-phase two-point MPM algorithm to model the soil surface erosion. By employing dual sets of Lagrangian material points on a shared Eulerian grid, the approach effectively resolves soil-fluid interactions during erosion. An effective inflow/outflow boundary algorithm is proposed, enabling the addition and removal of water particles at the boundaries to achieve an efficient fluid boundary. Furthermore, a unified state-dependent constitutive framework for soil-solid is proposed, incorporating an elastoplasticity- μ ( I ) solid-to-fluid transition constitutive relation and an equation of state. The former captures the nonlinear solid-to-fluid transition behavior of bed-load particles, while the latter describes suspended-load particles. The proposed MPM model is validated against a series of benchmark problems, including dam break, water injection, wall-jet erosion, overtopping erosion, and tsunami overflow erosion scenarios. Comparative analysis demonstrates that the proposed MPM-based surface erosion model accurately captures the soil-fluid interface, bed-load, and suspended-load particle evolution in surface erosion without empirical erosion criteria.