EFFECT OF FORM FRICTION ON THE SEDIMENT RATING CURVE

Victor M. Ponce, Member, ASCE
Professor, Department of Civil and Environmental Engineering
San Diego State University, San Diego, California 92182-1324.

David S. Smith, Member, ASCE
Senior Hydraulic Engineer, WEST Consultants, Inc.
San Diego, California 92127-1671.

Martin J. Teal, Member, ASCE
Vice President, WEST Consultants, Inc.
San Diego, California 92127-1671.

ABSTRACT

A comprehensive field data set is used to detect trends in sediment rating curves. Measured sediment rating curves for six alluvial rivers are examined for a wide range of discharges. At high discharges, the sediment rating curve asymptotically approaches a maximum value of sediment concentration. At low discharges, the documented drop in sediment concentration is attributed to form friction. In all cases, Manning's n decreased as sediment transport increased, supporting the cause-effect linkage between channel friction and shape of the sediment rating curve.

INTRODUCTION

The computation of sediment transport has many difficulties, including the role of grain and form friction, armoring, and flow unsteadiness. Despite these difficulties, it is usually possible to develop a sediment rating curve for a given site based on an appropriate sediment transport relation and/or measured field data.

The sediment rating curve is a log-log plot of bed material discharge (kN d-1) versus water discharge (m3 s-1). At high water discharges, the sediment rating curve asymptotically approaches a maximum value of sediment concentration (American Society of Civil Engineers 1975, p. 476). Ponce (1988) examined this feature of the sediment rating curve and referred to the maximum value as the "ultimate sediment concentration."

The nature of the sediment rating curve, where the sediment concentration reaches a maximum value at high discharges, suggests that there is a mechanism acting to reduce the sediment concentration at low discharges. It is surmised here that this mechanism is form friction. Thus, the objective of this paper is to show, using comprehensive field data sets, that form friction is largely responsible for the documented drop in sediment concentration at low discharges and, therefore, for the shape of the sediment rating curve.

Specifically, it is shown that at high discharges, bed shear stresses and sediment transport increase; however, the sediment rating curve asymptotically approaches a maximum sediment concentration (American Society of Civil Engineers 1975). At low discharges, form friction acts to reduce sediment concentration below that which could be attained if it were absent. Thus, the effect of form friction is to produce a drawdown of the sediment concentration below the "ultimate" value (Colby 1964; Ponce 1988). This behavior explains the complexity of sediment transport computations through a wide range of discharges, from low to high.

THE FIELD DATA SET

We used the data assembled by Williams (1995), who produced a database comprising data used by Ackers and White (1973), Brownlie (1981a,b), Engelund and Hansen (1967), and Yang (1973) in the development of their sediment transport relations. In particular, the Brownlie data set included approximately 7000 sets of field and laboratory data.

Williams (1995) filtered the data to include only points with the following features:

  1. Gradation coefficient less than 5, to eliminate bimodal size distributions.
  2. Sand median grain size (0.062 to 2.0 mm).
  3. Aspect ratio (width to depth) greater than 4.
  4. Hydraulic depth to median grain diameter ratio greater than 100.
  5. Measured sediment concentration greater than 10 ppm.
The following six sets of Brownlie's data (Brownlie 1981b) were used for the present analysis:
  1. 63 data points from the Atchafalaya River (Toffaleti 1968).
  2. 40 data points from the Niobrara River (Colby and Hembree 1955).
  3. 38 data points from the Middle Loup River (Hubbell and Matejka 1959).
  4. 51 data points from the Rio Grande River (Nordin and Beverage 1965).
  5. 156 data points from the Mississippi River (Toffaleti 1968).
  6. 29 data points from the Red River (Toffaleti 1968).

Within each data set, each data unit consisted of the following:

  1. Water discharge
  2. Channel width
  3. Hydraulic depth
  4. Bottom slope
  5. Median grain diameter
  6. Gradation coefficient
  7. Sediment specific gravity
  8. Measured sediment concentration
  9. Water temperature

In addition, the Niobrara River data set included bedform type. Although no explicit reference to bankfull discharge was found for the data, examination of depth versus width and depth versus discharge plots indicates that most, if not all, of the data points for the six sets used herein were collected at flows less than bankfull.

METHODOLOGY AND RESULTS

Measured sediment rating curves, including a regression line fit to the data using a power law, are shown in Figs. 1-6. For each data unit, the water discharge, channel width, hydraulic depth, and bottom slope were used to calculate Manning's n (Chow 1959). For simplicity, channel shape was assumed to be rectangular.

For each data set, the calculated values of Manning's n were plotted on a secondary y-axis, so that the trend in sediment rating could be readily compared with the trend in Manning's n. A power law regression was also performed for the roughness values, although they exhibited much more scatter than the sediment transport data. For the Niobrara River data set, the bedform type is indicated by the pattern of the Manning's n data point marker, as described by the legend of Fig. 2.

In all cases, it is clearly seen that the trend of Manning's n is to decrease as water and sediment discharge increase. For the low discharges, the lack of perfect agreement is attributed to the complex nature of sediment transport. For the Atchafalaya data set (Fig. 1), there may be two relationships for the roughness at low flows, which does not appear to be related to a seasonal effect, according to the published data (Toffaleti 1968). The "jump" in roughness values from approximately 0.02 to 0.03 near a discharge of 2,000 m3 s-1 may be due to change in bedform type, although this information was not collected as part of the data set. The grouping of eleven data points corresponding to discharges less than 2,000 m3 s-1 (Fig. 1), were, however, all taken when depths were below 7.6 m (25 ft), the shallowest of the Atchafalaya data points. The Niobrara River data set (Fig. 2) shows that the bedform changes from dunes (lower regime), through transition, to plane bed (upper regime) as water and sediment discharge increase.

SUMMARY AND CONCLUSIONS

Using comprehensive field data sets, it is shown that form friction is largely responsible for the documented shape of typical sediment rating curves observed in alluvial rivers. Specifically, it has been confirmed that at high discharges, sediment rating curves asymptotically approach a maximum value of sediment concentration. At low discharges, form friction acts to reduce the sediment concentration below that which could be attained in its absence.

Measured sediment rating curves were plotted for six comprehensive data sets. In addition, for each data unit, water discharge, channel width, hydraulic depth, and bottom slope were used to calculate Manning's n. Data was plotted in such a way that the trend in sediment rating could be readily compared with the trend of Manning's n. In all cases, Manning's n decreased as the water and sediment discharge increased. In addition, the Niobrara River data set (Fig. 2) shows that the bedform changes from dunes (lower regime), through transition, to plane bed (upper regime) as the water and sediment discharge increase.

It is concluded that at low discharges, form friction has a significant role in reducing sediment transport, effectively decreasing the sediment concentration below the "ultimate" value. Conversely, at high discharges, form friction is reduced to a minimum, total friction tends to a constant value, and sediment concentration asymptotically approaches the "ultimate" value. These findings clarify our current understanding of sediment rating curves in particular, and sediment transport in general.

APPENDIX I. REFERENCES

Ackers, P., and White, W. R. (1973). "Sediment Transport: New Approach and Analysis," Journal of the Hydraulics Division, ASCE, 99(11), 2041-2060.

American Society of Civil Engineers. (1975). Sedimentation Engineering, Manual No. 54, New York.

Brownlie, W. L. (1981a). "Prediction of Flow Depth and Sediment Discharge in Open Channels." Report KH-R-43A, W.M. Keck Laboratory of Hydraulics and Water Resources, California Institute of Technology, Pasadena, California.

Brownlie, W. L. (1981b). "Compilation of Alluvial Channel Data: Laboratory and Field." Report KH-R-43B, W.M. Keck Laboratory of Hydraulics and Water Resources, California Institute of Technology, Pasadena, California.

Chow, V. T. (1959). Open-channel Hydraulics. McGraw-Hill, New York.

Colby, B. R. and Hembree, C. H. (1955). "Computations of Total Sediment Discharge, Niobrara River near Cody, Nebraska." U.S. Geological Survey Water Supply Paper No. 1357, Washington, D.C.

Colby, B. R. (1964). "Discharge of sands and mean-velocity relations in sand-bed streams." U.S. Geological Survey Professional Paper No. 462-A, Washington, D.C.

Engelund, F. and Hansen, E. (1967). "A Monograph on Sediment Transport in Alluvial Streams." Teknisk Vorlag, Copenhagen, Denmark.

Hubbell, D. W. and Matejka, D. Q. (1959). "Investigations of Sediment Transportation, Middle Loup River at Dunning, Nebraska." U. S. Geological Survey Water Supply Paper No. 1476, Washington, D.C.

Nordin, C. F., Jr. and Beverage, J. P. (1965). "Sediment Transport in the Rio Grande, New Mexico." U. S. Geological Survey Professional Paper No. 462-F, Washington, D.C.

Ponce, V. M. (1988). "Ultimate Sediment Concentration." Proceedings, 1988 National Conference of Hydraulic Engineering, sponsored by the Hydraulics Division of the American Society of Civil Engineers, New York, 311-315.

Toffaleti, F. B. (1968). "A Procedure for Computation of the Total River Sand Discharge and Detailed Distribution, Bed to Surface." Technical Report No. 5, Committee on Channel Stabilization, Corps of Engineers, United States Army, Vicksburg, Mississippi.

Williams, D. T. (1995). "Selection and Predictability of Sand Transport Relations Based Upon a Numerical Index." Ph.D. dissertation, Department of Civil Engineering, Colorado State University, Fort Collins, Colorado.

Yang, C. T. (1973). "Incipient Motion and Sediment Transport." Journal of Hydraulic Engineering, ASCE, 99(10), 1679-1704.