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

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School of Engineering | Doctoral thesis (article-based)
Degree programme
80 + app. 86
Aalto University publication series DOCTORAL THESES, 2/2023
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.
Supervising professor
Sołowski, Wojciech Tomasz, Assoc. Prof., Aalto University, Department of Civil Engineering, Finland
Thesis advisor
Korkiala-Tanttu, Leena, Assoc. Prof., Aalto University, Department of Civil Engineering, Finland
granular flow, continuum mechanics, material point method, constitutive modelling, computational geomechanics
Other note
  • [Publication 1]: S. Seyedan and W. T. Sołowski, “Enhancing Constitutive Models for Soils: Adding the Capability to Model Nonlinear Small Strain in Shear”, Advances in Civil Engineering, vol. 2019, pp. 1–11, Apr. 2019.
    Full text in Acris/Aaltodoc:
    DOI: 10.1155/2019/6016350 View at publisher
  • [Publication 2]: S. Seyedan and W. T. Sołowski, “From solid to disconnected state and back: Continuum modelling of granular flows using material point method”, Computers and Structures, vol. 251, p. 106545, Jul. 2021.
    Full text in Acris/Aaltodoc:
    DOI: 10.1016/j.compstruc.2021.106545 View at publisher
  • [Publication 3]: W. T. Solowski and S. Seyedan, “Granular Material Point Method: unsaturated soil modelling”, Geomechanics for Energy and the Environment, July 2021, Revised according to the major revision requests and awaiting the decision
  • [Publication 4]: S. Seyedan and W. T. Sołowski, “Continuum modelling of the granular flows in gaseous states using material point method”, 2nd International Conference on the Material Point Method for Modelling Soil-Water-Structure Interaction, 2019.
    Full text in Acris/Aaltodoc:
  • [Publication 5]: S. Seyedan and W.T. Sołowski, “A coupled constitutive model for modelling small strain behaviour of soils”, Numerical Methods in Geotechnical Engineering IX, Volume 1, 2018, pp. 637–642