Steel ball dropped into very fine sand You
Steel ball dropped into very fine sand (You. Tube) Challenge the future 1
Simulation of sphere being shot into clay-like material (Al-Kafaji) Challenge the future 2
Stability analysis of a simplified 2 -phase formulation in Geomechanics Miriam Mieremet Thursday, 8 January 2015 Challenge the future 3
Content 1. Problem: Numerical instability with 2 -phase MPM 2. Approach: Simplifications and methods 3. Study: Stability analysis with simplified 2 -phase FEM 4. Conclusion 5. Outlook Challenge the future 4
Problem: Numerical instability with 2 -phase MPM Cone Penetration Test (myv-sg. nl) Challenge the future 5
Numerical instability with 2 -phase MPM 2 -phase continuum • Solid phase • Water phase Challenge the future 6
Numerical instability with 2 -phase MPM 2 -phase formulation Challenge the future 7
Numerical instability with 2 -phase MPM Material Point Method & Euler Cromer Method Initial configuration Calculation step Resetting the mesh Challenge the future 8
Numerical instability with 2 -phase MPM Stability Criterion 1 -phase Unexpected instability 2 -phase • High permeability: Stable • Low permeability: Unstable What is the right stability criterion? Simulation of CPT with MPM (Ceccato) Challenge the future 9
Approach: Simplifications and methods Challenge the future 10
Simplifications and methods Problem: Study: Large deformations Small deformations Three dimensions One dimension 2 -phase Simplified 2 -phase Challenge the future 11
Simplifications and methods Problem: Study: MPM FEM Tetrahedral elements Linear elements Challenge the future 12
Simplifications and methods Stability analysis Von Neumann Method Matrix Method Challenge the future 13
Study: Stability analysis with simplified 2 -phase FEM Oedometer Test Challenge the future 14
Stability analysis with simplified 2 -phase FEM Variables velocity of solid phase velocity of water phase effective stress pore pressure Challenge the future 15
Stability analysis with simplified 2 -phase FEM 2 -phase formulation Challenge the future 16
Stability analysis with simplified 2 -phase FEM Simplified 2 -phase formulation Challenge the future 17
Stability analysis with simplified 2 -phase FEM Finite Element space discretization Challenge the future 18
Stability analysis with simplified 2 -phase FEM Euler Cromer time discretization Challenge the future 19
Stability analysis with simplified 2 -phase FEM Von Neumann Method • Space discretization • Time discretization • Error equation • Fourier decomposition Challenge the future 20
Stability analysis with simplified 2 -phase FEM Amplitude equation Stability criterion Challenge the future 21
Stability analysis with simplified 2 -phase FEM Matrix Method • Space discretization • Error equation • Eigenvalue decomposition • Time discretization Challenge the future 22
Stability analysis with simplified 2 -phase FEM Error equation Stability criterion Challenge the future 23
Stability analysis with simplified 2 -phase FEM Compare analytical and numerical solution with Challenge the future 24
Stability analysis with simplified 2 -phase FEM Compare analytical and numerical solution with Challenge the future 25
Conclusion • Familiarization with geomechanical problems • Investigation of 1 - and 2 -phase formulation • Implementation in Matlab • Literature study on stability analysis Challenge the future 26
Conclusion • Stability criterion for simplified 2 -phase FEM: Challenge the future 27
Outlook • Stability analysis with 2 -phase FEM (1 D) • Stability analysis with 2 -phase FEM (3 D) • Study impact of… § Local Damping § Mass Scaling § Strain smoothening • Introduction of stability criterion into Deltares MPM code Challenge the future 28
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