Development of a vector‐based 3D grain entrainment model with application to X‐ray computed tomography scanned riverbed sediment

Abstract

Sediment transport equations typically produce transport rates that are biased by orders of magnitude. A causal component of this inaccuracy is the inability to represent complex grain‐scale interactions controlling entrainment. Grain‐scale incipient motion has long been modelled using geometric relationships based on simplified particle geometry and two‐dimensional (2D) force or moment balances. However, this approach neglects many complexities of real grains, including grain shape, cohesion and the angle of entrainment relative to flow direction. To better represent this complexity, we develop the first vector‐based, fully three‐dimensional (3D) grain rotation entrainment model that can be used to resolve any entrainment formulation in 3D, and which also includes the effect of matrix cohesion. To apply this model we use X‐ray computed tomography to quantify the 3D structure of water‐worked river grains. We compare our 3D model results with those derived from application of a 2D entrainment model. We find that the 2D approach produces estimates of dimensionless critical shear stress ( τcr∗) that are an order of magnitude lower than our 3D model. We demonstrate that it is more appropriate to use the c‐axis when calculating 2D projections, which increases values of τcr∗ to more closely match our 3D estimates. The 3D model reveals that the main controls on critical shear stress in our samples are projection of grains, cohesive effects from a fine‐grained matrix, and bearing angle for the plane of rotation (the lateral angle of departure from downstream flow that, in part, defines the grain's direction of pivot about an axis formed by two contact points in 3D). The structural precision of our 3D model demonstrates sources of geometric error inherent in 2D models. By improving flow properties to better replicate local hydraulics in our 3D model, entrainment modelling of scanned riverbed grains has the potential for benchmarking 2D model enhancements. © 2019 The Authors. Earth Surface Processes and Landforms Published by John Wiley & Sons Ltd.

X-ray computed tomography reveals that grain protrusion controls critical shear stress for entrainment of fluvial gravels

“…In two runs, baskets were also buried in the shallow pool, giving a total of 20 baskets. Data from two pool-tail baskets were analyzed by Voepel et al (2019). The baskets were covered with the bulk GSD, leaving surface grains free to move under flow.…”

“…The entrainment model (Voepel et al, 2019) resolves all moments for entrainment and resistance force vectors onto a grain's axis of rotation, and identifies the point at which τ equals τ c and, hence, the grain is on the threshold of motion ( Fig. 1).…”

“…For F D and F L , we use the actual projected grain areas perpendicular (A ⊥ ) and parallel (A || ) to the flow, rather than a spherical approximation. F D is modified by an exposure factor (EF adj ), which accounts for the sheltering effect of upstream grains and the possibility of flow deviation from the horizontal (Voepel et al, 2019). F C was not included in the Kirchner model, and is a linear function of the grain contact area with the cohesive matrix (F C = ηA T f M , where η is cohesive force per unit area, A T is total grain surface area, and f M is the proportion of grain surface area in contact with matrix; Voepel et al, 2019).…”

“…F D is modified by an exposure factor (EF adj ), which accounts for the sheltering effect of upstream grains and the possibility of flow deviation from the horizontal (Voepel et al, 2019). F C was not included in the Kirchner model, and is a linear function of the grain contact area with the cohesive matrix (F C = ηA T f M , where η is cohesive force per unit area, A T is total grain surface area, and f M is the proportion of grain surface area in contact with matrix; Voepel et al, 2019). The model does not incorporate the resisting weight of any overlying grains, but we analyze only grains that can move without displacing adjacent grains.…”

“…We have applied this approach to grain entrainment by using X-ray computed tomography (XCT) scans of water-worked sediment beds to produce the first complete suite of grain-geometry parameters from 1055 in situ grains. Measuring parameters directly removes the need for the previous model simplifications, and for each grain, we use our measurements to calculate τ c in a vector-based 3-D moment-balance model for grain entrainment (Voepel et al, 2019). We demonstrate how grain geometry varies with grain size and controls τ c , and compare the τ c values to those derived from standard bedload-transport models.…”