B.M. Sumer

Onset of scour below pipelines and self-burial

Abstract This paper summarizes the results of an experimental study on the onset of scour below and self-burial of pipelines in currents/waves. Pressure was measured on the surface of a slightly buried pipe at two points, one at the upstream side and the other at the downstream side of the pipe, both in the sand bed. The latter enabled the pressure gradient (which drives a seepage flow underneath the pipe) to be calculated. The results indicated that the excessive seepage flow and the resulting piping are the major factor to cause the onset of scour below the pipeline. The onset of scour occurred always locally (but not along the length of the pipeline as a two-dimensional process). The critical condition corresponding to the onset of scour was determined both in the case of currents and in the case of waves. Once the scour breaks out, it will propagate along the length of the pipeline, scour holes being interrupted with stretches of soil (span shoulders) supporting the pipeline. As the span shoulder gets shorter and shorter, more and more weight of the pipeline is exerted on the soil. In this process, a critical point is reached where the bearing capacity of the soil is exceeded (general shear failure). At this point, the pipe begins to sink at the span shoulder (self-burial). It was found that the self-burial depth is governed mainly by the Keulegan–Carpenter number. The time scale of the self-burial process, on the other hand, is governed by the Keulegan–Carpenter number and the Shields parameter. Diagrams are given for the self-burial depth and the time scale of the self-burial process.

Sinking/floatation of pipelines and other objects in liquefied soil under waves

Abstract This paper presents the results of an experimental study where the sinking and floatation of a pipeline and other objects (namely, a sphere and a cube) in a silt bed was investigated. The bed was exposed to progressive waves. Two kinds of experiments were made: The undisturbed-flow experiments, and the experiments with the structure model (a pipeline, a sphere, and a cube). In the former experiments, the pore-water pressure was measured across the soil depth. The pore-water pressure built up, as the waves progressed. The soil was liquefied for wave heights larger than a critical value. Regarding the experiments with the structure model, the displacement of the structure (sinking or floatation) was measured simultaneously with the pore-water pressure. The influence of various parameters (such as the initial position of the object, the specific gravity, the soil layer thickness, and the wave height) was investigated. It was found that while the pipe sank in the soil to a depth of 2–3 times the pipe diameter, the sphere sank to even larger depths. The pipe with a relatively small specific gravity, initially buried, floated to the surface of the soil. The drag coefficients for the objects sinking in the liquefied soil were obtained.

Experimental study of 2D scour and its protection at a rubble-mound breakwater

Abstract This study deals with the 2D scour at the trunk section of a rubble-mound breakwater. Two breakwater models with slopes of 1:1.2 and 1:1.75 are employed for the experimental study of the scour in a wave flume. 2D scour at a vertical-wall breakwater was also included as a reference case. Tests were conducted with both regular waves and irregular waves. It was found that the scour/deposition pattern in front of the rubble-mound breakwater emerges in the form of alternating scour and deposition areas lying parallel to the breakwater, similar to the case of the vertical-wall breakwater. The maximum scour depth, however, was found to be smaller in the present case than that of the vertical-wall breakwater case. In the case of the irregular waves, the scour depth at the breakwater decreases with respect to that experienced in the case of the regular waves. Countermeasures for toe protection were also investigated for the following cases: (1) the protection apron with one layer of stones and (2) that with several layers of stones. The mechanism of slumping down of stones of the protection apron was also considered. The results of the toe protection study are given in the form of diagrams.

Bed shear stress measurements over a smooth bed in three-dimensional wave-current motion

Wave and current experiments have been carried out with the purpose of measuring the instantaneous bed shear stress over a hydraulically smooth bed, in order to evaluate the extent of the interaction. Measurements have been carried out with a dual-component hot-film probe which, with some constraints, enables the magnitude and direction of the instantaneous bed shear stress to be measured. Results are presented as maximum obtained bed shear stress values over one cycle and the corresponding mean value in the direction of the current for various combinations of waves and current.

Numerical prediction of wave boundary layer over a bed with a change in roughness

Abstract The behaviour of the turbulent oscillatory wave boundary layer over a sudden change in the bed roughness has been studied using a one-dimensional two-equation turbulence model. The 1D model is being used to describe the 2D flow by making a Lagrangian use of the 1D model, making a sudden shift in time of the bed roughness when the fluid particle passes from a region with one roughness to a region with another roughness. Attention was concentrated on two quantities: the period-averaged velocity and the bed shear stress. The results indicated that the near-bed period averaged velocities are different from zero and directed towards the bed section with the larger roughness. This near-bed streaming was found to increase with increasing difference between the roughnesses of the two bed sections and with decreasing values of amplitude-to-roughness ratio. Streaming velocities as high as 10% of the maximum orbital velocity were predicted. The bed shear stress, on the other hand, responded with a strong peak near the step change in roughness; this amplification in the bed shear stress was found to increase with increasing difference in roughness and with increasing amplitude to roughness ratio. Amplifications experienced in the bed shear stress as large as 3–3.5 were predicted.