The variability of critical shear stress, friction angle, and grain protrusion in water‐worked sediments

Abstract

The erodibility of a grain on a rough bed is controlled by, among other factors, its relative projection above the mean bed, its exposure relative to upstream grains, and its friction angle. Here we report direct measurements of friction angles, grain projection and exposure, and small‐scale topographic structure on a variety of water‐worked mixed‐grain sediment surfaces. Using a simple analytical model of the force balance on individual grains, we calculate the distribution of critical shear stress for idealized spherical grains on the measured bed topography. The friction angle, projection, and exposure of single grain sizes vary widely from point to point within a given bed surface; the variability within a single surface often exceeds the difference between the mean values of disparate surfaces. As a result, the critical shear stress for a given grain size on a sediment surface is characterized by a probability distribution, rather than a single value. On a given bed, the crtitical shear stress distributions of different grain sizes have similar lower bounds, but above their lower tails they diverge rapidly, with smaller grains having substantially higher median critical shear stresses. Large numbers of fines, trapp.ed within pockets on the bed or shielded by upstream grains, are effectively lost to the flow. Our calculations suggest that critical shear stress, as conventionally measured, is defined by the most erodible grains, entrained during transient shear stress excursions associated with the turbulent flow; this implies a physical basis for the indeterminacy of initial motion. These observations suggest that transport rate/shear stress relationships may be controlled, in part, by the increasing numbers of grains that become available for entrainment as mean shear stress increases. They also suggest that bed textures and grain size distributions may be controlled, within the constraints of an imposed shear stress and sediment supply regime, by the influence of each size fraction on the erodibility of other grain sizes present on the bed.

Multi-Fraction Bayesian Sediment Transport Model

“…Figure 10 shows an example the fractional rating curves for the J21 sediment. The results in this and related figures [25] [6] indicate that the model is generally able to infer a reference stress distribution that produces predictions consistent with the observations. While the rating curves generally seem to be appropriate, there is one suspect rating curve, that for the 32.0 mm size fraction.…”

“…Kirchner et al [25] observed that for a given sediment mixture, a multiplicity of bed configuration and transport rates are possible. This phenomenon, while understood and widely accepted, has no general solution.…”

Probabilistic Modeling of Bed-Load Composition

“…Good progress has been made in describing these over the last decade (Kirchner et al 1990;Buffington et al, 1992Johnston et al, 1998and McEwan and Heald, 2001. Nevertheless, to date, these descriptions are entirely empirical (or numerical) and their acquisition requires considerable effort in either the laboratory, field or computational resources.…”

“…Recent work by Kirchner et al (1990) and Buffington et al (1992) has addressed the problem of describing the entrainment of mixed-grain-size sediments in probabilistic terms. They measured friction angles of particles placed on the surface of a mixed-grain-size sediment bed by tilting the bed to an angle at which a particle of interest moved from its position.…”

A Laboratory Study of Streambed Stability in Bottomless Culverts

“…Though Brahms suggested in 1753 that the velocity for incipient motion is proportional to the grain weight raised to the sixth power, this condition is more appropriately analyzed from the concept of a balance of forces acting upon a particle. Incipient motion, however, has further complexities due to the fluctuating characteristics (turbulence) of the flow over a bed of sediment, composed of innumerable particles of various shapes, sizes, orientation, specific weight, protrusion, roughness, and location (Kirchner et al, 1990). Also, incipient motion is influenced by material gradation, friction angle, sorting, and armoring of the bed (Forchheimer, 1914;Buffington, Dietrick, and Kirchner, 1992).…”