Development of a vector-based 3D grain entrainment model with application to X-ray computed tomography (XCT) 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 ( urn:x-wiley:mma:media:esp4608-math-0001) 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 urn:x-wiley:mma:media:esp4608-math-0002 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.