Modeling pebble abrasion during bed load transport is of fundamental importance in fluvial geomorphology, as it may help to understand downstream fining patterns along gravel bed rivers. Here we review a recently published analytical abrasion model called box equations, which can simultaneously track the shape and size evolution of large pebble populations as the cumulative effect of binary collisions between particles. The model predicts that pebble shapes move away from the sphere and develop sharp edges due to collisional abrasion by sand. We present a field study on the downstream evolution of basalt particle shape and size along the Williams River in the Hunter Valley, Australia. Pebbles get flatter and thinner, and several aquafacts (i.e., abraded pebbles with sharp edges) emerge in the downstream reaches, both suggesting the importance of abrasion by sand. Applying box equations with a few fitted parameters, we present a numerical simulation which reproduces both the shape and size evolution of pebbles along the Williams River. The simulation allows tracking of the shape and size evolution of individual particles as well, revealing an interesting phenomenon that particle size controls shape evolution. Box equations, in combination with existing transport concepts, provide a framework for future shape and size evolution studies in sedimentary environments. In particular, they may help to assess the relative importance of size selective transport versus abrasion in causing downstream fining in gravel bed rivers.
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