Why Do Waterfalls Persist In Fractured Rock?

Knickpoint propagation is one of the fundamental drivers of erosion and channel-head advance in river networks. Where knickpoints are near vertical, waterfalls form and in some cases can maintain their form while propagating upstream. Waterfalls are typically thought to persist because of undercutting of resistant strata, collapse, and headwall retreat (e.g., Niagara Falls). Many waterfalls translate upstream, however, that are able to maintain a vertical face in the absence of undercutting. We explore the conditions under which near vertical knickpoints persist during retreat due to toppling in rock with horizontal and vertical sets of joints (e.g., columnar basalt). At a waterfall, rock columns are affected by shear and drag from the overflowing water, buoyancy from the plunge pool at the foot of the waterfall, and gravity. A torque balance is used to determine the stability of a rock column and any individual blocks that compose the column. Model results suggest that rotational toppling failure should occur about the base of a headwall (and therefore preserve its form during upstream propagation) where columns are tilted in the downstream direction, or slightly tilted in the upstream direction depending on the plunge pool height. Flume experiments were performed to test the model, and the model predicts well the flow necessary to induce failure and the morphology of the headwall. Our model successfully explains the morphology of canyon headwalls in the volcanic terrain of northwestern U.S.A, where catastrophic paleofloods (e.g, Missoula Floods and Bonneville Flood) have carved steep amphitheater-headed canyons in columnar basalt. This model may also explain similar landforms on Mars.