The work budget of rough faults

• We modeled geologic faults of various fractal roughness parameters.
• We analyzed changes in work and energy during loading in relation to fault roughness.
• We found that smoother faults are more efficient than rougher faults.
• We report that faults have no energetic reason to become planar, and remain rough.

Faults in nature have measurable roughness at many scales and are not planar as generally idealized. We utilize the boundary element method to model the geomechanical response of synthetic rough faults in an isotropic, linear elastic continuum to external tectonic loading in terms of the work budget. Faults are generated with known fractal roughness parameters, including the root mean square slope (β), a measure of roughness amplitude, and the Hurst exponent (H), a measure of geometric self-similarity. Energy within the fault models is partitioned into external work (Wext), internal elastic strain energy (Wint), gravitational work (Wgrav), frictional work (Wfric), and seismic energy (Wseis). Results confirm that Wext, or work done on the external model boundaries, is smallest for a perfectly planar fault, and steadily increases with increasing β. This pattern is also observed in Wint, the energy expended in deforming the host rock. The opposite is true for gravitational work, or work done against gravity in uplifting host rock, as well as with frictional work, or energy dissipated with frictional slip on the fault, and Wseis, or seismic energy released during slip events. Effects of variation in H are not as large as for β, but Wgrav, Wfric, and Wseis increase with increasing H, with Wint and Wext decreasing across the same range. Remarkably, however, for a narrow range of roughness amplitudes which are commonly observed along natural faults, the total work of the system remains approximately constant, while slightly larger than the total work of a planar fault. Faults evolve toward the most mechanically efficient configuration; therefore we argue that this range of roughness amplitudes may represent an energy barrier, preventing faults from removing asperities and evolving to smooth, planar discontinuities. A similar conclusion is drawn from simulations at relatively shallow depths, with results showing that shallower faults have larger energy barriers, and can be mechanically efficient at higher roughness amplitudes.