Asymmetric crack propagation near waterfall cliff and its influence on the waterfall lip shape

Institute of High Performance Computing - 1 Fusionopolis Way, #16-16 Connexis, Singapore 138632

^a vastolag@ihpc.a-star.edu.sg

Received: 15 March 2011
Accepted: 27 September 2011

Abstract

By means of Finite Element Method (FEM) calculations and fatigue fracture mechanics analysis, we show that crack propagation in bedrocks close to the waterfall cliff is preferential towards the cliff face rather than upstream the river. Based on this effect, we derive the corresponding expression for the velocity of recession v_r of the waterfall lip, and find that v_r has a quadratic dependence on the hydrostatic pressure. Quantitatively, this erosion mechanism generates recession rates of the order of ∼cm–dm/y, consistent with the recession rates of well-known waterfalls. We enclose our expression for v_r into a growth model to investigate the time evolution of a waterfall lip subject to this erosional mechanism. Because of the dependence on hydrostatic pressure, the shape of the waterfall is influenced by the transverse profile of the river that generates the waterfall. If the river has a transverse concavity, the waterfall evolves a curved shape. Evolution for the case of meanders with asymmetric transverse profile is also given.