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Table 1

Three semi-empirical formulae using different dimensionless numbers

ModelFormulaNotes
USDOT (2001)  S/Y = K Kw (Y/D)−0.65(Fr)0.43 Smax = 3.0 D for Fr > 0.8 
  Smax = 2.4 D for Fr < 0.8 
  K = f (nose shape, current angle of attack, mode of sediment transport, armoring by bed material) 
  Kw = correction factor when (Y/D) < 0.8; (D/d50) > 50 & Fr < 1 
  Kw = 2.58 (Y/D)0.34(Fr)0.65 for U/Uc < Kw = (Y/D)0.13(Fr)0.25 for U/Uc > 1 
Breusers et al. (1977)  S/D = 2KVtanh (Y/DKV = 1 for U/Uc > 1 
  KV = (1 − 2U/Uc) for 0.5 > U/Uc > 1 
  KV = 0 for 0.5 < U/Uc 
Melville (1997)  S/D = K K = f (nose shape, relative water depth, current angle of attack, relative velocity, relative sediment size) 
Conventional nonlinear regression S/Y = 1.46 (Y/D)−0.36(Fr)0.37(U/Uc)0.12  
ModelFormulaNotes
USDOT (2001)  S/Y = K Kw (Y/D)−0.65(Fr)0.43 Smax = 3.0 D for Fr > 0.8 
  Smax = 2.4 D for Fr < 0.8 
  K = f (nose shape, current angle of attack, mode of sediment transport, armoring by bed material) 
  Kw = correction factor when (Y/D) < 0.8; (D/d50) > 50 & Fr < 1 
  Kw = 2.58 (Y/D)0.34(Fr)0.65 for U/Uc < Kw = (Y/D)0.13(Fr)0.25 for U/Uc > 1 
Breusers et al. (1977)  S/D = 2KVtanh (Y/DKV = 1 for U/Uc > 1 
  KV = (1 − 2U/Uc) for 0.5 > U/Uc > 1 
  KV = 0 for 0.5 < U/Uc 
Melville (1997)  S/D = K K = f (nose shape, relative water depth, current angle of attack, relative velocity, relative sediment size) 
Conventional nonlinear regression S/Y = 1.46 (Y/D)−0.36(Fr)0.37(U/Uc)0.12  
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