Adjusting The Excessive Shear Stress Equation To Improve Stream Bank Erosion Rates Among Different Channel Bank Characteristics

Stream bank erosion rates are commonly modeled using the excess shear stress equation εr = kd(τ-τc)^a, where the exponent a is assumed to be unity. The coefficient of erodibility kd, and the critical shear stress τc [Tau c] are properties of the bank soil and the applied shear stress τ [Tau] is a function of the channel geometry, boundary roughness, and discharge. This equation appears to overestimate bank erosion likely due to τ influenced by channel morphology and bank vegetation, among other factors. The objective of this study was to determine whether the excess shear stress equation could be parameterized with an α [alpha] coefficient to more accurately estimate stream bank erosion rates accounting for the effects of channel curvature and bank vegetation. The study included seven stream bank sites at Beaver, Bullrun, and Stock creeks located in Knox County, Tennessee with USGS gaging stations located downstream. Streambanks were composted of cohensive soils. Bank erosion pins were placed at four channel morphology/vegetation categories to measure retreat or soil deposition; they were straight and curved channels with and without woody bank vegetation. At each channel cross-section, 45-cm steel pins were installed vertically along the lower, middle, and upper portion of the banks. A mini-jet test device was used to approximate kd and the τc applying a single pressure at approximately 45 kPa and the Blaisdell solution method. Flows and stage heights were modeled with HEC-RAS to determine the τ at each pin. Pin erosion averages varied by category and bank retreat ranged from 0.9 to 23.8 cm during the one-year study period. Retreat measurements were used as estimates of site erosion rates εr [Epsilon r]. With all the parameters being known, α parameters in the modified excess shear stress equation were solved for each of the erosion pins for the different channel categories. The α values typically varied between about 0.001 and 0.73 showing that excess shear stress equation over predicts erosion. Due to the wide range of alpha values computed, further research is needed to better assess the factors that influence bank erosion and improve the predictability of bank retreat rates.