Minimum work, fault activity and the growth of critical wedges in fold and thrust belts

Many studies of critical wedges treat the interior of the wedge as continuous and do not address the manner in which it grows from the undeformed state to a typical imbricate wedge. In this paper we present a 2D kinematic–mechanical model which attempts to explain the development of a critical wedge in a fold and thrust belt in terms of both gravitational and frictional work. In the undeformed model a series of thrust faults are defined which have the potential to take up an external displacement. The active fault at a given time is that which minimizes gravitational and frictional work as a result of displacement. Displacement on the active fault causes a change in topography and deformation of other faults which may favour an alternative fault at the next time step. The model is a mixed Lagrangian–Eulerian scheme in which the upper surface, in addition to being deformed, is also subject to erosion, transport and sedimentation. The model predicts propagation of thrust fault activity towards the foreland through time as a result of increasing topographic (gravitational) loads and frictional work on deformed hinterland faults. As the zone of fault activity progresses through the developing critical wedge several faults are active over time-scales of ≈1 Myr. However, a simple chronology or sequence of fault activity cannot be assumed as out-of-sequence thrusting occurs during this overall foreland propagation. The detailed spatial and temporal activity of faults is complex and reflects the interaction between the development of topography, the contrast between basal (décollement) and internal coefficients of friction and the effects of erosion and sedimentation. In particular, rates of erosion and sedimentation are found to be important controls on fault activity both spatially and temporally. Erosion, by locally removing topography above a fault, reduces gravitational and frictional work enabling continued fault activity or reactivation. Sedimentation, conversely, acts to increase gravitational and frictional work on a fault, and therefore has the potential to blanket faults and render them inactive. Model results illustrate the complex feedbacks that can exist between tectonic and surficial mass transport processes.