Thrust dip and thrust refraction in fault-bend folds: Analogue models and theoretical predictions

Analogue models made of two layers of loose sand separated by a thin layer of micro glass beads were shortened by a rigid emerging ramp dipping at either 30° or 45° and possessing a high, intermediate, or null surface friction. Shortening resulted in formation of closely spaced back thrusts in the sand layers. The dips of the back thrusts vary within a range of 30° depending on the ramp friction, and 7° depending on its dip. An increase in ramp friction, or, to a lesser extent, in ramp dip, decreases the thrust dips in the model. The second important observation is that, when friction is greater along the ramp than along the layer of glass beads, then the glass beads layer acts as a separate upper ramp above which the back thrusts steepen. The theory proposed to explain these observations predicts the thrust dips through a two-step procedure: first, global equilibrium of forces in the two layers is required to yield the mean forces at stake along the ramps and thrusts, second, the total dissipation is minimized with respect to the dips of the back thrusts. The relevant frictional properties of our analogue materials have been measured in stress conditions as close as possible to the experimental ones (below 1 kPa), and used with the theory to yield optimal back thrust dips that are all within 3° of the measured dips. This is a surprisingly good fit when considering that we did not take into account geometric changes, strain-softening, and dilatancy or compaction, due to slip on the thrusts. We conclude that this general two-step theoretical procedure is validated in the context of analogue frictional materials. We also propose a possible mechanism for thrust refraction and top-to-the-foreland sense of shear observed in the hanging walls of lower-flat to ramp transition in sedimentary piles that is based on the triggering of secondary upper ramps. Finally, this mechanical approach can also be seen as complementary to the kinematic models of fold-thrust structures which, by definition, cannot grasp the strong effects of friction on the kinematics.