Numerical study of granular flow impacting hemi-spherical structures on steep terrains by a two-phase model with μ(I) rheology closure

Granular flow is prevalent in natural disasters such as landslides and avalanches. Investigating the impact characteristics and load variations of granular flows on structures is vital for disaster prevention and mitigation. This study employs a three-dimensional continuum model combined with the Volume of Fluid method, treating the particle phase as a non-Newtonian fluid based on the μ(I) constitutive model. A numerical solver for non-Newtonian two-phase flow capable of describing granular flows on complex terrains has been implemented. Through simulations of a typical laboratory-scale three-dimensional granular column collapse problem, we present spreading processes and deposition distributions which agree with the experimental results, thereby validating the effectiveness of our numerical approach. Using this model, we examine the dynamic interactions between granular flows and single hemispherical obstacles on steep terrains. The predictions regarding depth-time curves at several critical probes and final deposition profiles demonstrate superior accuracy compared to previous forecasts based on depth-averaged models. Additionally, an analysis of the evolution of impact forces exerted by granular flows on obstacles reveals that shoulder obstacles can significantly mitigate impact forces within primary flow regions. We also give the plugging characteristics of the granular flow near the front of the obstacles. In contrast to traditional depth integration models, our methodology offers enhanced insights into three-dimensional flow dynamics and loading characteristics, providing valuable references for disaster prediction and assessment in practical engineering.