1 / 15

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?

kyrene
Download Presentation

Deformation of Sediments via Grain-Scale Simulations: Variational Algorithm

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related