Self-similar voiding solutions for a single layered model of folding rocks

T.J. Dodwell, M.A. Peletier, C.J. Budd, G.W. Hunt

Research output: Book/ReportReportAcademic

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Abstract

In this paper we derive an obstacle problem with a free boundary to describe the formation of voids at areas of intense geological folding. An elastic layer is forced by overburden pressure against a V-shaped rigid obstacle. Energy minimization leads to representation as a non-linear fourth-order ordinary diffrential equation, for which we prove their exists a unique solution. Drawing parallels with the Kuhn-Tucker theory, virtual work, and ideas of duality, we highlight the physical significance of this differential equation. Finally we show this equation scales to a single parametric group, revealing a scaling law connecting the size of the void with the pressure/stiffness ratio. This paper is seen as the first step towards a full multilayered model with the possibility of voiding.
Original languageEnglish
Place of PublicationEindhoven
PublisherTechnische Universiteit Eindhoven
Number of pages20
Publication statusPublished - 2011

Publication series

NameCASA-report
Volume1120
ISSN (Print)0926-4507

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