Temporal Scour Variations at Permeable and Angled Spur Dikes under Steady and Unsteady Flows

Spur dikes are river protection structures typically used for flow diversion from erodible banks. However, scouring might be a severe problem that compromises their stability and, consequently, their hydraulic function. This paper aims to study the maximum scour depth at permeable and angled spur dikes under hydrographs of different duration. Experiments were carried out in a rectangular channel 10 m long, 0.76 m wide, and 0.6 m deep. The mobile bed was made of nearly uniform sand with a median grain size of 0.8 mm. A total of 36 new experiments were performed with a detailed data collection over the time (i.e., 216 datasets), which could provide a useful contribution to the topic. The impact of the spur dike orientation angle, θ, and the degree of permeability, φ, on the temporal scour evolution were explored. Results were found physically consistent and revealed that the spur dike permeability implies a significant attenuation of the scouring processes in comparison to the impermeable spur dikes and generally its effect is more beneficial than that from a favorable orientation angle. The differences in percentage between the maximum scour depth for impermeable spur dikes and the maximum scour depths for various degrees of spur dike permeability were found ranging from 44% (at φ = 33% and θ = 60°) up to 88% (at φ = 66% and θ = 120°). Other results include the effect of the hydrograph base-time on the scour depth and the comparison between scouring processes under steady and unsteady flow conditions. By quadrupling the hydrograph base-time, keeping constant the peak and base flood discharges, the maximum scour depths increased by about 29%, 42%, and 25% in case of impermeable spur dike, spur dike with 33% degree of permeability, and spur dike with 66% degree of permeability. Furthermore, starting from dimensional analysis a new empirical model (with coefficient of determination R2 equal to 0.94) is introduced to predict the time-dependent scour depth due to the passage of a flood wave. The model suggests that the main independent dimensionless variables which control local scour processes are: the densimetric Froude number, the time t normalized to the hydrograph base-time, the degree of permeability, and the orientation angle. These dimensionless variables would generalize the laboratory results to the real-world scenarios, although caution should always be taken because of possible scale effects