Role of bending in gravity-driven overthrusts

Abstract

The decrease in potential energy of gravity-driven overthrusts due to change in position can be equated to the sum of strain energy required for deformation, the work done against friction, and the kinetic energy. An analytical model based on this relationship allows the strain energy in pure bending to be expressed as a function of displacement. The model applies to an elastic material, and assumes frictionless slip for the multilayered case. Minimization of potential energy leads to an estimate of the minimum initial length required for gravitational sliding, and to the apparent coefficient of friction, displacements, and velocities for given slide geometries and properties. An example problem is worked out for the case of the Heart Mountain detachment of Wyoming, U.S.A. Minimum initial length for frictionless sliding is about 5.9 km, ignoring the effect of bending, and 8.5 km for a case of multilayered bending. Blocks of this size would move only a short distance as the increase in potential energy experienced in the riser prevents further sliding. But multilayered bending seems to have been necessary for sliding, compared to bending of the overthrust sheet as a single layer. Kinetic energy relationships suggest that the apparent coefficient of sliding friction for the 45 km long block was less than 0.031; e.g., for a friction coefficient of 0.025, a velocity of 19 m/sec is predicted at a characteristic displacement of 7 km. The model thereby illustrates the need for drastic friction reduction, but does not attempt to address the question of mechanism by which friction was reduced. The energy required to deform the slide mass is thought to be small compared to the decrease in potential energy due to changing position.