Criterion for Cutoff Size of Bed Material Load Versus Wash Load in Sand Bed Streams. Chris Paola and Gary Parker St. Anthony Falls Laboratory, University of Minnesota Mississippi River at 3 rd Ave., Mpls. MN 55414. Motivation
Criterion for Cutoff Size of Bed Material Load Versus Wash Load in Sand Bed Streams
Chris Paola and Gary Parker
St. Anthony Falls Laboratory, University of Minnesota
Mississippi River at 3rd Ave., Mpls. MN 55414
Case in Point
The middle Fly River, Papua New Guinea, was a typical large sand bed river showing negligible mud in the bed before the onset of the disposal of mine waste in 1985. Since that time, the fraction of mud in the bed has risen to values in excess of 10%, as shown in the plot for the Manda gaging station.
Develop a predictive model for bed grain size distribution and bed slope needed to transport an imposed total load and grain size distribution at an imposed flood discharge, and with no arbitrary wash load cutoff size.
D=Dg2 D84R=submerged specific gravity of sediment (~ 1.65)
z=upward normal distance from bed=Shields stress = (HS)/(RDg)
Statement of the Model
where vsi denotes the fall velocity of the ith size, denotes the Karman constant and zr denotes a reference elevation.
The basic relation is
The sediment entrainment formulation of Garcia-Parker (1991) is as follows, where us denotes shear velocity due to skin friction.
The parameters kr and us are evaluated from Engelund-Hansen (1967) as
Flow velocity is evaluated as
Bed gets muddier as C increases!
Note how the fraction of mud in the bed increases and the geometric mean size of the bed material decreases as concentration increases!
What is the effect of the mud on channel morphology?
In the diagram below equilibrium depth H and slope S are computed for a base case C = 4409 mg/l, but with the load truncated below sizes ranging from 1.95 m to 125 m (and the load concentration adjusted accordingly). The model predicts a WEAK but DISCERNIBLE effect of “wash load” on channel morphology!
Is this effect real?
We suspect not completely so. If the material below a given truncation size is present in such small quantities in the bed that it can comfortably fit within the pores of the coarser material, it should no longer have a discernible effect on channel morphology. We thus (somewhat arbitrarily) define a CUTOFF SIZE FOR WASHLOAD AS ONE SUCH THAT THE FINER MATERIAL WOULD OCCUPY 5% OF THE PORE SPACE OF THE COARSER MATERIAL.
Relation for porosity versus arithmetic standard deviation of bed material (adapted from Beard and Weyl, 1973)
We can define a mechanistically consistent, dynamically varying cutoff size for washload that can fall below 62.5 m if, for example, the imposed load is sufficiently high!