While at Cornell together, Jeff Masek (now at U. Maryland, Dept. of Geography) and I developed a model to look at the evolution of mountain topography and fault systems under an assumption that crustal-scale fault paths develop so as to minimize the total work involved in shortening at a convergent boundary (see "Minimum-work mountain building", Masek & Duncan, 1998, JGR, v103, p907-17). Under the simplest of arrangements, the work terms are just the work of lifting the hanging wall and any overlying topography up any ramps in the fault path, and the work against friction in sliding the hanging wall over the footwall. Minimizing the uplift term favors development of long, shallow fault paths; minmizing frictional work favors shorter, steeper fault paths. Combining the two terms results in a competition for which there is a unique path which minimizes the total work done. In the simplest configuration, the crust is homogeneous (essentially like a layer of sand -- cohesionless and with uniform friction throughout), and fault paths at each step form in slightly different places along an approximately straight path through the crust. The small variations from step to step are in response to small variations in the topographic wedge being built. In this configuration, the system builds smooth thrust wedges and topography analagous to Coulomb wedges.
To approximate brittle crustal systems, we can add a feature analagous to strain weakening, in which friction is reduced along the path of the fault at each step. This causes previously-faulted paths to be slightly more favorable (frictionally) than other possible paths, so the system tends to stay with a particular fault path for awhile until the topographic variations are so great that it involves less work to break a new fault path and lift less material than to stay with the low-friction path. These runs display a "stickier" behavior, and produce irregular topography and occasional out-of-sequence thrusts.
Other features examined with the model include work due to bending over changes in the fault trajectory, the effects of erosion, and the effects of low-friction decollements. Stuart Hardy (U. Manchester) had incorporated this model into his model for fault kinematics, erosion, and sedimentation (see "Minimum work, fault activity, and the growth of critical wedges in fold and thrust belts", Hardy, S., Duncan, C., Masek, J., and Brown, D., 1998, Basin Research, v10, p365-373).
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