Periodic Void Formation in Chevron Folds

T. J. Dodwell, G. W. Hunt

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An energy-based model is developed to describe the periodic formation of voids/saddle reefs in hinge zones of chevron folds. Such patterns have been observed in a series of experiments on layers of paper, as well as in the field. A simplified hinge region in a stack of elastic layers, with straight limbs connected by convex segments, is constructed so that a void forms every m layers and repeats periodically. Energy contributions include strain energy of bending and work done both against a confining overburden pressure and an axial compressive load. The resulting total potential energy functional for the system is minimised subject to the constraint of non-interpenetration of layers, leading to representation as a nonlinear second-order free boundary problem. Numerical solutions demonstrate that there can exist a minimum-energy m-periodic solution with m≠1. The model shows good agreement when compared with experiments on layers of paper.

Original languageEnglish
Pages (from-to)1011-1028
Number of pages18
JournalMathematical Geosciences
Issue number8
Early online date7 Oct 2014
Publication statusPublished - 28 Nov 2014


  • Delamination
  • Energy methods
  • Folding
  • Saddle reef formation


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