Deterministic chaos in frictional wedges revealed by convergence analysis

• Published in: International journal for numerical and analytical methods in geomechanics 2013-12, Vol.37 (17), p.3036-3051
• Main Authors: Mary, B.C.L., Maillot, B., Leroy, Y.M.
• Format: Article
• Language: English
• Subjects: accretionary wedges; Chaos theory; Convergence; Deformation; deterministic chaos; Discretization; Earth sciences; Earth, ocean, space; Exact sciences and technology; Failure; fold-and-thrust belts; frictional materials; imperfection sensitivity; kinematic approach; limit analysis; Sand; Sciences of the Universe; Tectonics. Structural geology. Plate tectonics; Topography; Wedges
• ISSN: 0363-9061; 1096-9853
• DOI: 10.1002/nag.2177

SUMMARYA triangular wedge, composed of a frictional material such as sand, and accreting additional material at its front, is the classical prototype for accretionary wedges and fold‐and‐thrust belts. A simplified method is proposed to capture the internal deformation of this structure resulting from a large number of faulting events during compression. The method combines the application of the kinematic approach of limit analysis to predict the optimum thrust‐fold and a set of geometrical rules to update the geometry accordingly, at each increment of shortening. It is shown that the structure topography remains approximately planar with a slope predicted by the critical Coulomb wedge theory. Failure by faulting occurs anywhere within the wedge at criticality, and its exact position is sensitive to topographic perturbations resulting from the deformation history. The convergence analysis in terms of the shortening increments and of the topography discretization reveals that the timing and the position of a single faulting event cannot be predicted. The convergence is achieved nevertheless in terms of the statistics of the distribution of the faulting events throughout the structure and during the entire deformation history. It is these two convergence properties that are presented to justify the claim that these compressed frictional wedges are imperfection sensitive, chaotic systems. Copyright © 2013 John Wiley & Sons, Ltd.