Comparison of Linear and Nonlinear Models for Cohesive Sediment Detachment: Rill Erosion, Hole Erosion Test, and Streambank Erosion Studies

Abstract

Cohesive sediment detachment is typically modeled for channels, levees, spillways, earthen dams, and internal erosion by using a linear excess shear stress approach. However, mechanistic nonlinear detachment models, such as the Wilson model, have recently been proposed in the literature. Questions exist as to the appropriateness of nonlinear relationships between applied shear stress and the erosion rate. Therefore, the objective of this research was to test the appropriateness of linear and nonlinear detachment models for cohesive sediment detachment using three data sets: (1) rill erodibility studies across a limited range of applied shear stress (0.9–21.4 Pa), (2) hole erosion tests (HETs) across a wide range of applied shear stress (12.6–62.0 Pa), and (3) streambank erodibility as quantified by jet erosion tests (JETs) for the linear excess shear stress equation and the nonlinear Wilson model across a small range of shear stress (1–4 Pa). The Wilson model was also incorporated into the bank stability and toe erosion model (BSTEM) as an option for simulating fluvial erosion and used to simulate bank retreat in the streambank erodibility study. The Wilson model was shown to be an appropriate particle detachment rate model from previously published data on rill erodibility, HETs, and JETs. Using a nonlinear detachment model also alleviated questions about the most appropriate solution technique for deriving erodibility parameters from JETs. In situ and laboratory tests sometimes use a limited range of applied shear stress, and therefore users of these measurement techniques should be aware of the potential nonlinear behavior of cohesive sediment detachment especially at higher shear stress. The results suggest advantages for the nonlinear Wilson detachment model and also identify the need for additional research to evaluate the various detachment models for laboratory HETs and in situ JETs across a wider range of soil types and additional reach-scale streambank erosion studies.