TU Delft - a bird

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Steel ball dropped into very fine sand (YouTube)
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Simulation of sphere being shot into clay-like
material (Al-Kafaji)
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Stability analysis of a simplified 2-phase
formulation in Geomechanics

• Miriam Mieremet
• Thursday, 8 January 2015

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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

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• Problem
• Numerical instability with 2-phase MPM

Cone Penetration Test (myv-sg.nl)
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Numerical instability with 2-phase MPM

• 2-phase continuum
• Solid phase
• Water phase

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Numerical instability with 2-phase MPM
2-phase formulation
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Numerical instability with 2-phase MPM
Material Point Method Euler Cromer Method
Calculation step
Resetting the mesh
Initial configuration
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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)
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• Approach
• Simplifications and methods

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Simplifications and methods
Problem Study Large deformations Small
deformations Three dimensions One
dimension 2-phase Simplified 2-phase
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Simplifications and methods
Problem Study MPM FEM Tetrahedral
elements Linear elements
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Simplifications and methods
Stability analysis Von Neumann Method Matrix
Method
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• Study
• Stability analysis with simplified 2-phase FEM

Oedometer Test
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Stability analysis with simplified 2-phase FEM
Variables velocity of solid phase velocity
of water phase effective stress pore
pressure
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Stability analysis with simplified 2-phase FEM
2-phase formulation
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Stability analysis with simplified 2-phase FEM
Simplified 2-phase formulation
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Stability analysis with simplified 2-phase FEM
Finite Element space discretization
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Stability analysis with simplified 2-phase FEM
Euler Cromer time discretization
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Stability analysis with simplified 2-phase FEM

• Von Neumann Method
• Space discretization
• Time discretization
• Error equation
• Fourier decomposition

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Stability analysis with simplified 2-phase FEM
Amplitude equation
Stability criterion
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Stability analysis with simplified 2-phase FEM

• Matrix Method
• Space discretization
• Error equation
• Eigenvalue decomposition
• Time discretization

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Stability analysis with simplified 2-phase FEM
Error equation
Stability criterion
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Stability analysis with simplified 2-phase FEM
Compare analytical and numerical solution with
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Stability analysis with simplified 2-phase FEM
Compare analytical and numerical solution with
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Conclusion

• Familiarization with geomechanical problems
• Investigation of 1- and 2-phase formulation
• Implementation in Matlab
• Literature study on stability analysis

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Conclusion

• Stability criterion for simplified 2-phase FEM

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Outlook

• Stability analysis with 2-phase FEM (1D)
• Stability analysis with 2-phase FEM (3D)
• Study impact of
• Local Damping
• Mass Scaling
• Strain smoothening
• Introduction of stability criterion into
  Deltares MPM code