Universal scaling relations for pebble abrasion

The process of abrasion of gravel in bed load transport results from particle-to-particle collisions, where the energy involved is sufficient to cause chipping and spallation but not fragmentation of parent grains. The removed rock material is not infinitesimal; daughter products as large as coarse sand can be produced. Although previous work has shown that lithology, grain shape, and energy of collision are contributing factors that control abrasion rates of river-bed material, little is known regarding the relationship between these factors and diminution rates. Here we explicitly isolate and investigate how these three factors influence rates of abrasion and the size distribution of daughter products, with laboratory experiments. The apparatus is a double pendulum (Newton's cradle) that produces well-controlled binary collisions. A high-speed camera precisely measures collision energy, while mass of parent rocks. and the size and shape distributions of daughter products, are measured periodically. We examined abrasion of initially square-cut 'rocks' as they underwent successive collisions in the binary collision apparatus. We have examined mass loss rate for varied lithologies, and observe a similar power-law relationship between impact energy and mass abraded. When normalized by sensible material properties, mass loss curves for all materials collapse onto a single curve, suggesting that the underlying mechanics of abrasion for different materials are the same. The relationship does not display the linear trend expected from pure energetics, and we suggest that this is a shape effect as protruding - and hence easily eroded - corners are worn away. Analysis of daughter-product particle size distributions for different lithology fragments - including natural rocks and also bricks - show the same functional form. Surprisingly, it is the power-law relation expected for brittle materials undergoing fragmentation. This suggests that brittle fracture theory also describes the abrasion of river sediments, albeit over a limited length scale that may be associated with skin depth over which collision energy is attenuated. If these results are general, they may be used to search for the signature of abrasion in size distributions of sand and silt particles in natural streams. The apparent universality of both mass loss curves and particle size distributions is in need of theoretical investigation to better understand the underlying mechanics. However, the results are already proving useful for interpreting the role of in-stream abrasion in downstream fining and the production of sand in field studies.