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Deformation of Sediments via Grain-Scale Simulations: Variational Algorithm

Deformation of Sediments via Grain-Scale Simulations: Variational Algorithm. Ran Holtzman, Dmitriy Silin, Tad Patzek U.C. Berkeley holtzman@berkeley.edu. Motivation. Why micromechanics? Mechanics of granular matter is controlled by interaction of discrete grains Why numerical simulations?

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Deformation of Sediments via Grain-Scale Simulations: Variational Algorithm

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  1. Deformation of Sediments via Grain-Scale Simulations: Variational Algorithm Ran Holtzman, Dmitriy Silin, Tad Patzek U.C. Berkeley holtzman@berkeley.edu

  2. Motivation • Why micromechanics? • Mechanics of granular matter is controlledby interaction of discrete grains • Why numerical simulations? • Enable micromechanical analysis, unavailable from experiments (restricted to 2D or a single grain pair) • Existing models: • Spatially-averaged solutions (EMT1) • Dynamic grain-scale simulations (DEM2) 1 – Duffy & Mindlin, 1957 2 – Cundall & Strack, 1979

  3. Our Model of Granular Matter • 3D heterogeneous, disordered pack • Spherical grains, differ in size & properties • Bounded by a rigid container(imposing boundary conditions) • Contact forces & moments  macroscopic stress

  4. Variational Algorithm • Quasi-static model: sequence of static equilibrium configurations • Equilibrium: minimal-work path • Moduli: fit stress-strain to Hooke’s law:

  5. Normal Compression grain i P h P grain j Hertz (1882)

  6. Shear Q Q

  7. Frustrated Rotation Q Q

  8. Torsion Mtor Mtor

  9. Challenges in Modeling Friction • Loads depend on normal force and load history1 • Implementing M-D theory1 - cumbersome for multiple contacts • Simplified models • Ignoring frictional loads (zero tangential stiffness) • Ignoring partial slip (fixed stiffness)2 • Simplified treatment of partial slip (variable stiffness)3-4 1 – Mindlin & Deresiewicz (1953) 3 – Walton & Braun (1986) 2 – Jenkins & Strack (1993) 4 – Vu-Quoc & Zhang (1999)

  10. Linearized Formulation • Incremental loading, small perturbations • Shear increment decoupled from normal components current DQ ut u DQ Q0 Q0(proj) initial Q k ||Q||=mP

  11. Predicted Moduli vs. Experiments

  12. Predicted Moduli vs. Experiments

  13. Summary • Quasi-static grain-scale simulations of a deforming sediment • Physically-based model, no calibration used • Macroscopic moduli match experimental data • Application: effect of dissociation on hydrate-bearing sediments

  14. Extensions • Add cement, angular grains , and pore constituents that interact with the solid grains • Statistical and qualitative analysis of microscopic parameters – e.g. force chains • Reduce computing time by using parallel computing

  15. Thank You! Funded by the assistant secretary for fossil energy, office of Natural Gas and Petroleum Technology, N.E.T.L. D.O.E. Contract #DE-FC26-05NT42664 holtzman@berkeley.edu

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