Predictions of the equilibrium depth and time scale of local scour below a partially buried pipeline under oblique currents and waves

Abstract

This paper presents experimental results on temporal developments of local scour below a partially buried pipeline under oblique currents/waves. The effects of the flow incident angle (α ≤ 45°, α = 0° denotes that the currents/waves are perpendicular to the pipeline) and the embedment-to-diameter ratio (e/D ≤ 0.5, e/D = 0 denotes no embedment) on the equilibrium depth and time scale of scour were quantitatively investigated. The experimental results indicate that with the increase of the embedment-to-diameter ratio from 0 to 0.5, the equilibrium depth of scour decreases by up to 30 and the time scale increases by approximately 5 times. With the increase of the flow incident angle from 0° to 45°, the equilibrium depth decreases by approximately 25% and the time scale increases by approximately 0.7 times. A uniform empirical relationship between the equilibrium depth for arbitrary conditions (S, i.e., for α > 0° or e/D > 0) and that for a conventional case (S0, for α = 0° and e/D = 0) is newly proposed for both current and wave conditions based on theoretical derivation and curve fitting to the experimental data, where S0 can be easily predicted from existing empirical formulae. The correlation analysis indicates that the experimental results of the equilibrium depth can be well represented by the newly proposed formula. For predicting the time scale of scour process, a theoretical approach based on the erosion rate of sediment, which was originally proposed for a conventional case, is expanded to arbitrary conditions. It is indicated that the time scales of scour obtained from the theoretical approach are well coincident with the experimental values. Finally, an empirical relationship between the time scale for arbitrary conditions (T) and that for a conventional case (T0) was established based on the theoretical derivation. The newly proposed empirical formula is found to provide satisfactory predictions of the time scale compared with the present experimental results and those published.