Granular Material Point Method: a numerical approach based on continuum mechanics for modelling granular flows

This doctoral thesis investigates and models the flows of granular materials numerically. It focuses on flows with low shear rates and replicates quasi-static, moderate and disconnected states of granular flows and the transition between them. The study employs the continuum mechanics based material point method, develops a constitutive framework for the different behaviours of granular flows, and enhances the algorithm of the material point method for modelling different states of granular flows. The constitutive framework of the thesis employs the simple linear elastic-perfect plastic Mohr-Coulomb model. It enhances the constitutive model with the highly nonlinear small strain shearing behaviour in the initial stage of flow, the dependency between the shear rate and the shear stress,and a simple stress-free behaviour during the disconnected state of the flow. It also uses the density of material points to switch to stress-free behaviour and back. The thesis employs this constitutive framework for replicating triaxial tests on Ham River sand, Toyoura sand flows and impact forces.The material point method's algorithm calculates excessive volume increases in modelling the moderate flow and deals with unphysical interactions in modelling the disconnected state. The study modifies the moderate flow material points with a density lower than critical to prevent excessive volume increases. In addition, it employs parallel grids and assigns material points to these different grids to prevent unphysical interactions. This work introduces the Granular material point method, an enhanced material point method algorithm that employs these solutions and significantly improves the material point method's capability to model the granular material's behaviour. The Granular material point method can replicate the rather unchanged density of moderate flows and prevent interactions with disconnected material points. It can recover the initial state of granular flows, lower the grid dependency when replicating the disconnected state,and employ advanced versions of the material point method. The work shows several Granular material point method simulations, including silo filling, Toyoura sand flow and impact force.Finally, the thesis extends Granular material point method to modelling flows of unsaturated granular materials. It modifies the developed framework to estimate the intergranular forces among the grains of unsaturated material. In addition, it enhances the Granular material point method's algorithm to update the suction of material points in each timestep. The thesis employs this extended Granular material point method to model the unsaturated flows of silo discharge and granular avalanche.