Self-similar voiding solutions of a single layered model of folding rocks
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 nonlinear fourth-order ordinary differential 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.
Keywords
Cite
@article{arxiv.1101.5325,
title = {Self-similar voiding solutions of a single layered model of folding rocks},
author = {Timothy Dodwell and Mark Peletier and Christopher Budd and Giles Hunt},
journal= {arXiv preprint arXiv:1101.5325},
year = {2015}
}