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.