Streams incise bed rock by cutting and quarrying rock exposed in the stream beds. The bed-rock-cutting mechanism is conceptually simple; except where solution or flow cavitation is acting, it must be abrasion by entrained sediment (Shepherd and Schumm, 1974). When a sediment particle strikes the bed, some of its kinetic energy may be expended in fracturing the bed material. Fractures from a severe enough impact, or coalescing fractures from a series of impacts, allow separation of a particle of bed material which is then carried away by the flow. The abrasion rate at a point will thus be proportional to the local sediment transport rate and will depend upon the details of the fluid flow.
This paper describes a bed-load-abrasion, stream-incision model developed from engineering sandblast-abrasion theory. This model is not generally applicable to bed-rock incision because extensive bed-rock reaches in stream channels often develop complex morphologies which prevent hydraulic analysis at an appropriate scale. However, predominantly alluvial streams with short (compared to channel width) bed-rock reaches have relatively simple hydraulic geometry. The bed-rock reaches are local base levels, and they control incision; the alluvial reaches control channel geometry and sediment-transport rate. Model parameters can be evaluated in this case, which is common in streams incised into tilted, layered rocks of variable resistance to abrasion. Analysis of incision by a glacially diverted gravel-bed stream (Foley, 1980a, 1980b) is used to illustrate application of the model and to test the validity of the model.