Deriving Erodibility Parameters of a Mechanistic Detachment Model for Gravels

Abstract

<abstract> <b><sc>Abstract.</sc></b> Recent research has proposed the use of a mechanistic detachment model, called the Wilson model, in place of the excess shear stress equation for predicting the detachment of cohesive soils during erosion. However, this mechanistic detachment model was also proposed as being valid for noncohesive soils but with limited evaluation. Such erodibility parameters are often needed in erosion models developed using a single detachment rate approach for both cohesive and noncohesive soils. Therefore, the objectives of this research were to evaluate the applicability of the Wilson model for noncohesive soils and to evaluate a procedure for deriving the erodibility parameters (b₀ and b₁) from flume experiments. Gravel samples were extracted from composite streambanks on the Barren Fork Creek in eastern Oklahoma. The samples were sieved into particle size classes, and then at least triplicate flume experiments were performed (gravel sizes of 0.45, 0.60, 1.30, and 1.90 cm). Flow rate, water surface elevation, and scour depth were measured to estimate the energy slope, scour rate, and effective shear stress. The Wilson model was fit to the scour depth data to derive b₀ and b₁ using the generalized reduced gradient method to minimize the error between the predicted and measured scour. Constraints were required within the solver routine to limit potential solutions of b₁. Similar to cohesive soils, b₀ and b₁ had similar relationships to but different magnitudes than the erodibility coefficient (k_d) and critical shear stress (τ_c) for these gravels. Equivalent b₁-τ_c relationships were derived from the flume tests as compared to the theoretical b₁-τ_c relationship in the Wilson model. The b₀-b₁ and k_d-τ_c relationships followed power law relationships. This research supports the applicability of the nonlinear mechanistic detachment model for noncohesive gravels.