Interactions among topographically induced elastic stress, static fatigue, and valley incision

[1] Gravity acting on topography creates differential stress, which, for sufficiently high, steep topography, can fracture intact bedrock. If static fatigue governed the time dependence of that fracturing, a feedback should exist between incision of the landscape and fracturing. The timescale for static fatigue decreases exponentially with differential stress. By creating deeper, steeper valleys, incision should increase the differential stress and, as a result, accelerate fracturing of intact rock. Because both fluvial systems and hillslopes can transport fractured rock much more easily than they can both erode intact rock and then transport its products, topographically induced fracturing could play a crucial role in landscape evolution, especially of steep terrain. Predicting differential stress useful for general rules in geomorphology, however, appears to be difficult, in part because the stress distribution depends sensitively on the precise form of the topography and, perhaps more importantly, because the differential stress for specific topography can differ not only in magnitude but also in sign for small differences in Poisson’s ratio. Nevertheless, it appears possible that in steep terrain where rivers are capable of moving bed load sufficiently rapidly, the rate-limiting process for incision might be static fatigue of the rock under stress due to gravity acting on the adjacent topography.