Level Set Methods for Multilayer Geological Folding

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• Level Set Methods for Multilayer Geological
  Folding
• Jonathan Boon, Chris Budd Giles.Hunt

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Motivating Examples
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Experiments
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Experiments on layers of paper (courtesy of
Ahmer Wadee, Rorie Edmunds, Jonathan Boon)
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In-between States
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Model 1

• Euler strut
• Energy
• Critical Load depends on length of strut.

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Model 2

• Strut on a linear elastic foundation more
  realistic
• Critical load
• Wavelength

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Model 3

• Viscous foundation
• Biot Dominant wavelength
• Valid for small deflections.
• Wavelength does not agree well with reality.

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P
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Multilayer models

• Two layer model developed (Budd et al. 2003).
• Addition of friction to elastic foundation model.
• Can not accurately extend to n layer model
  because outer layers become non-sinusoidal
• Use level set method to model the multilayer
  geometry.

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Swallowtail
Lagrangian formulation
Eulerian formulation
Serial folding
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LSM applied to parallel fold
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Comparison of model with experiment

• Reformulate mechanical model in terms of the
  geometry

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Conclusion

• Singularity formation in multilayers can be
  predicted by the geometry.
• Nonlinear bending energy provides a mechanism of
  restabilising a fold.
• Serial folds form most naturally from the
  reactive end.
• Further work needed to verify results and to
  check the effects of unmodelled behaviour