Underthrusting‐accretion cycle: Work budget as revealed by the boundary element method

Sandbox models of accretionary wedges have demonstrated that fault systems grow episodically via cycles of alternating wedge thickening, which is accommodated by slip along faults within the wedge (underthrusting), and wedge lengthening, which is accommodated by growth of new faults at the wedge toe (accretion). The transition between these two modes of deformation is controlled by the interplay of work against gravity, frictional heating, the work of deformation around faults, and the work of fault propagation and seismic/acoustic energy. Using numerical mechanical models based on the boundary element method, we have simulated the deformation observed in sandbox experiments, providing a mechanical analysis of the underthrusting/accretion transition. Our results show that the total work done by the contracting wedge increases during the underthrusting stage up to a critical value when the propagation of a new frontal thrust significantly reduces the work required for further deformation. The numerical models also predict the location of the maximum shear along the basal décollement during underthrusting as well as the energetically most viable position and vergence for the nucleation of a new thrust. These locations do not coincide, and the match of the energetically most favorable position with the experimental results suggests that the new thrust ramps develop first ahead and then link down and backward to the propagating basal décollement. The shear localization producing a new thrust ramp will occur where the energy spent by the deforming wedge is minimized due to an optimal combination of gravitational, frictional, internal, and propagation work terms.