One-dimensional models for plane and non-plane power-law flow in shortening and elongating thrust zones

Abstract

The movement of a thrust sheet, even in external parts of fold-thrust belts, occurs by deforming rocks within a zone of finite thickness. A significant fraction of thrust-zone strains may accrue slowly as viscous deformation. This contribution uses a simple one-dimensional model of power-law flow to analyse the viscous deformation in thrust zones. The model generates profiles of stress and velocity for plane and non-plane flows that shorten or elongate during shearing. These stress and velocity profiles are, in essence,’ snapshots’ of stresses and velocities in real thrust zones that sequentially shorten and elongate during thrust emplacement. A comparison of stress and velocity solutions for flows with different stress exponents gives a way to examine structural settings where a single weak layer develops and affects stresses throughout the sheet. Using data on the orientations of stress principal directions during episodes of shortening and elongation derived from the mesoscopic fault array in an external thrust zone from the southern Appalachian fold-thrust belt, the plane-flow solution suggests that differential stresses in the thrust zone did not exceed 20 MPa. Moreover, body forces due to the dipping upper surface of the sheet were apparently not the primary source of the tractions during thrust zone shortening or elongation episodes. The additional tractions that other portions of the thrust sheet exerted on this thrust-zone segment had comparable magnitudes during shortening and elongation episodes. Comparing plane and non-plane solutions indicates that (1) shearing may localize at shallower depths or occur with different orientations for principal stresses relative to the thrust-zone boundaries, and (2) shortening or elongation may occur at smaller magnitudes of in-transport compression or tension, in non-plane structural settings like the growing tips of thrusts.