Formulae of Sediment Transport in Steady Flows (Part 1)

This paper makes an attempt to answer why the observed critical shear stress for incipient sediment motion sometimes deviates from the Shields curve largely, and the influence of vertical velocity is analyzed as one of the reasons. The data with d50 = 0.016 ∼ 29.1 mm from natural streams and laboratory channels were analyzed. These measured data do not always agree with the Shields diagram’s prediction. The reasons responsible for the deviation have been re-examined and it is found that, among many factors, the vertical motion of sediment particles plays a leading role for the invalidity of Shield’s prediction. The positive/negative deviations are associated with the up/downward vertical velocity in decelerating/accelerating flows, and the Shields diagram is valid only when flow is uniform. A new theory for critical shear stress has been developed, a unified critical Shields stress for sediment transport has been established, which is valid to predict the critical shear stress of sediment with/without vertical motion.

Have we misunderstood the Shields curve?

<p>The Shields curve, which compiles measurements of fluvial sediment transport thresholds in terms of the nondimensionalized threshold fluid shear stress and shear Reynolds number, is a standard reference in geophysics and hydraulic and coastal engineering and commonly thought to describe the critical flow conditions that are required for flow-driven entrainment of bed sediment. However, recent findings from several independent research groups have challenged this belief on various grounds: (i) particle-bed impacts predominately trigger sediment entrainment [1]; (ii) such impact-triggered entrainment can sustain continuous transport even when flow-driven entrainment events are (almost) completely absent [2, 3, (4)]; and (iii) extrapolating measurements of the transport rate of such impact-sustained continuous transport to zero yields transport thresholds that still fall on the Shields curve [5]. The question that thus emerges from these findings is, if not flow-driven entrainment, then what is the physics behind the thresholds shown in the Shields curve? We will try to give an answer to this question based on our latest research.</p><p> </p><p>[1] Vowinckel et al., Journal of Hydraulic Research, 2016, doi: 10.1080/00221686.2016.1140683</p><p>[2] Pähtz & Duran, Physical Review Fluids, 2017, doi: 10.1103/PhysRevFluids.2.074303</p><p>[3] Lee & Jerolmack, Earth Surface Dynamics, doi: 10.5194/esurf-6-1089-2018</p><p>[4] Heyman et al., Journal of Geophysical Research: Earth Surface, 2016, doi: 10.1002/2015JF003672</p>

Estimating the Rate of Scour Propagation Along a Submarine Pipeline in Time-Varying Currents and in Fine Grained Sediment

Estimating the horizontal rate of scour propagation along a submarine pipeline is a key step in estimating changes in the pipelines burial state and on-bottom stability due to sediment transport. However, whilst recent work has been undertaken to estimate the horizontal rate for non-cohesive uniform sands in steady current, in field conditions currents can vary in time and the sediment can be fine grained and exhibit very different erosion properties to sand. As a first attempt to account for these complications, in this paper we present results from a series of experiments designed to measure the rate of scour along a model pipeline in time varying currents and in a fine grained sediment. The scour experiments are also supplemented by erosion testing, which indicate that the erosion resistance of the fine grained sediment is larger than that predicted by the well-known Shields curve. Based on the scour experiments, it is found that in time-varying currents the scour rate can be predicted using an amalgamation of the results obtained for steady current conditions; this is a convenient result because theoretical predictions already exist for the scour rate in steady current conditions. In the fine grained sediment experiments, it is found that the horizontal rate of scour is much lower than that predicted by existing theoretical models that assume a non-cohesive sandy seabed. To provide an improved estimate of the horizontal rate of scour, a new theoretical model is introduced that relates the horizontal rate of scour to the measured erosion properties of the sediment. This new model is found to agree well with the experimental measurements. Although further experimental testing is recommended, in combination, it appears that these results may be used to better estimate the horizontal rate of scour in both time-varying and fine grained sediment.

Constructing the Shields Curve: Part C — Cohesion by Silt, Hjulstrom, Sundborg

The ‘standard’ Shields curve is intended for determining an erosion criterion for non-cohesive particles. Non-cohesive in this respect means that the particles are subject to drag and lift forces and subject to turbulent instantaneous velocities. The particles are not subject to inter-particle attraction or repulsion forces such as van der Waals forces and electro-chemical forces. The bed also is not subject to shear strength or yield stress. A cohesive sediment however is subject to these phenomena, resulting in higher critical shear stresses and higher Shields values. The cohesive effect can result from the presence of a silt (quartz) fraction or the presence of a clay fraction in the sediment. Here only the presence of a silt fraction will be considered. The silt particles in general are small enough to be subject to van der Waals forces. These attraction forces are strong enough to act like glue between the larger sand particles. In order to determine these attraction forces a Virtual Attraction Particle Diameter (VAPD) is introduced. The VAPD is the diameter of a virtual silt particle that can explain for the attraction forces in combination with the d50 of the sand. The VAPD will be in the range of the d1-d5. The van der Waals forces (if strong enough) increase the critical shear stress and thus the Shields parameter with a factor, which is inversely proportional with the d50 and inversely proportional with the VAPD (the diameter of the smallest fraction of the silt particles) to the third power. The relation often found in literature for this factor, inversely proportional with the d50 to the second power, can be explained by the fact that there is often a relation between the d50 and the VAPD. The smaller the d50, the smaller the VAPD. This however can lead to inverse proportionalities with different powers between the first power and the third power, depending on the coincidental choice of the diameter of the silt fraction. The model developed also shows that there does not exist a single Shields curve for sands with a cohesive silt fraction, but for a given set of the sediment density, the maximum sediment density (minimum porosity) and the VAPD, a Shields curve can be constructed. Using a density of 1.95 ton/m3, a minimum porosity of 0.32 (a rather uniform PSD) and a VAPD of 3 μm, the Brownlie equation can be approximated very closely. If the silt does not contain particles with a diameter smaller than 10 μm, there is hardly any cohesive effect. If the silt however contains a fraction of particles with a diameter around 1 μm, the cohesive effect is huge and already influences sand particles with a diameter of 1 mm. The model developed has been verified and validated with experiments from literature and gives a very good match, both quantitatively and qualitatively. The model developed also gives a good explanation of the famous Hjulström and Sundborg diagrams and gives these diagrams a more fundamental basis.

Innovative Structure Improvement of a Glare Shield

A glare shield is usually installed on the cement crash barrier to block strong light from the vehicles in contrary direction. It is useful to prevent car accidents and increase the safety of driving. This study uses the contradiction matrix in the TRIZ method, 39 engineering parameters, and 40 inventive and innovative principles to identify the areas of improvement to address the above problems. There are two features of our study. (1) We install a spring structure for the sake of reducing the damage rate of glare shields. When glare shields suffer from strong wind, a flexible structure located at base can let glare shields curve and spring back to original position, and therefore endures more powerful wind hit. In addition, the spring back function lets the guide post automatically return to original position to block strong light and protect drivers. This structure will have more durable service life, so, it can be used to reduce the maintenance times, and cost for the users.(2) We add solar LED light on the body of a glare shield, that can enhance the alert function when attacked by strong wind on the night time or insufficient light and then reduce the accident rate.

Constructing the Shields Curve

Prediction of the entrainment of particles is an essential issue for the study of erosion phenomena in many applications. The original Shields curve describes the entrainment of many particles at many locations and is thought critical to general transport. The mechanisms involved in general are sliding, rolling and lifting, new models of which have been developed. I will introduce concepts for the determination of the effective velocity and the acting point of the drag force, based on integration of the drag force over the cross section of the exposed particle (where most earlier models were based on integration of the velocity), the behavior of turbulence intensity very close to the virtual bed level and the factor of simultaneous occurrence of the small turbulent eddies. The resulting values of the Shields parameter, based on practical and reasonable properties, are compared with data, resulting in the best correlation for the sliding mechanism with the data of many researchers. The Shields parameter found for rolling and lifting overestimates the measurements from literature. Sliding seems to be the mechanism moving the top layer of the particles, while rolling and lifting are much more mechanisms of individual particles. In the new model it is considered that in the laminar region entrainment is dominated by drag and the influence of small turbulent eddies reducing the thickness of the viscous sub-layer, while in the turbulent region this is dominated by drag and lift. The transition region is modeled based on sophisticated interpolation. The model also describes the influence of exposure and protrusion levels and is compared with data of laminar main flow. The model correlates very well with the original data of Shields and data of others and also matches empirical relations from literature. The model is suitable for incorporating exposure and protrusion levels and laminar main flow.

A method for the formulation of Reynolds number functions

A general method for the formulation of flow characteristics which are functions of the Reynolds number of the system is presented. It is assumed that the flow characteristics exhibit a strong variation with the Reynolds number when the Reynolds number is "small," and that they become independent of it when the Reynolds number is "large." The method is illustrated by finding mathematical expressions for the experimentally determined "roughness" function curve and for the sediment transport initiation curve (Shields' curve), which are relevant for the analysis of flow and sediment transport in pipes and open channels. The two expressions thus obtained can be used in practice for computational purposes.Key words: Reynolds number functions, mathematical expression, roughness function, Shields' curve.

INITIAL MOTION IN COMBINED WAVE AND CURRENT FLOWS

Measurements are presented of the conditions for the initial motion of sediment under combined steady and oscillatory flow. The measurements were made in a steady flow flume with an oscillating tray set into its bed. The direction of oscillation of the tray was at right angles to the axis of the steady flow flume. Four different grades of sand were tested. It is found that the critical condition for the initiation of motion is reasonably represented by a critical value of the vector sum of the component shear stresses assuming no nonlinear interaction between the steady and oscillatory flows. The resultant bed shear stress was also calculated with the aid of several combined wave-current models. The results of these various approaches are compared with Shields curve.