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Constructing the Shields Curve

[+] Author Affiliations
Sape A. Miedema

Delft University of Technology, Delft, The Netherlands

Paper No. OMAE2011-49232, pp. 825-840; 16 pages
  • ASME 2011 30th International Conference on Ocean, Offshore and Arctic Engineering
  • Volume 7: CFD and VIV; Offshore Geotechnics
  • Rotterdam, The Netherlands, June 19–24, 2011
  • ISBN: 978-0-7918-4439-7
  • Copyright © 2011 by ASME


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.

Copyright © 2011 by ASME



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