When are Sediment Particles Suspended?

1. When are Sediment Particles Suspended? Nian-Sheng Cheng School of Civil and Environmental Engineering Nanyang Technological University, Singapore

2. Why this topic? • Fundamentally important • physics of particle-fluid interaction • Practically useful • numerical modeling • physical modeling • Existing results are incomplete

3. Previous studies Bagnold (1966) Assumption: No particles are in suspension unless upward flow velocity v’up > settling velocity w Taking v’up = 1.25u* yields Particles remained in suspension if u* > 0.8 w

4. 0.01 Z = 0.1 0.25 0.5 1 5 • Xie (1981) formulated critical condition using • Rouse concentration distribution. • Suspension initiates • if < 5 • or u* > 0.5w y/h

5. Van Rijn (1984) • argued that suspension started when particles jumped a height of 100d. • u* > 0.4 w (for d* > 10) • u* > (4/d*) w (for d* = 1-10) • Here, d* = dimensionless particle diameter • = d[(s/-1)g/2]1/3

6. Sumer (1986) • * > 17 / R* (R* < 70) • * > 0.27 (R* >70) • Here, • * = dimensionless shear • stress • = u*2/[(s/-1)gd] • R* = shear Reynolds number • = u*d/ • Celik and Rodi (1991) • * > 0.15 / R* (R* < 0.6) • * > 0.25 (R* >0.6)

7. Critical condition for initial suspension

8. Relationships among parameters (Cheng 1997)

9. Probability Analysis (Cheng and Chiew 1999) Assume that suspension of sediment particles occurs when Define suspension probability as If v’ follows Gaussian distribution

10. Suspension Probability approximated as

11. Two flow regimes 1. Rough bed Experimental studies have shown that  u* (Grass 1971, Nezu 1977, Kironoto and Graf 1995)

12. Suspension probability for rough bed

13. Two flow regimes 2. Smooth bed

14. 0.5d 2d 2.75d Bed Level 0.25d Lower boundary of suspended load

15. 20 5 10 Re* = 1 15 Suspension probability for smooth bed

16. Suspension probability for rough bed

17. Critical condition with various probabilities P=0.1 0.01 0.001 0.0001

18. Sensitivity of function * - Re* to lower boundary of suspended load (P=1%)

19. Critical condition expressed in terms of z = wd/ (P=1%)

20. Rouse parameter as criterion • Its constant values, e.g. z = 5, • can be used as an index only for large d* • say, d* > 50 • Otherwise, sediment cannot be suspended • even for small z • Generally, z varies with d* • for initial suspension

21. Index z combined with * Suspended load Bed load / bed material

22. Extension to incipient sediment motion P=0.1 0.01 0.001 0.0001

23. Predicted condition for incipient sediment motion P = 10-7

24. Identification of Bedload and Suspended Load P=10-7 Bed load P=1% Suspended load

25. Identification of Bedload and Suspended Load P=1% Suspended load Bed load P=10-7

26. Identification of Bedload and Suspended Load P=1% Suspended load u*/w Bed load P=10-7

27. Criteria expressed in terms of settling velocity For initial sediment suspension For initial sediment motion

28. Critical condition for initial motion 

29. Critical condition for initial suspension

30. Conclusions Differences in the critical condition for initial suspension may be due to different standards used. They are associated with various suspension probabilities Constant value of Rouse parameter can be used as an index only for large d* The incipient sediment motion may be described with very low suspension probability