Bedload Transport in Gravel Streams - Surface
Versus Subsurface Based Transport Analysis
انتقال الأتربة في قيعان الأنهار
التحليل وفق التدرج الحبيبي للطبقات السطحية
بدلاً من الطبقات تحت السطحية
مجلة جامعة النجاح للأبحاث - العلوم الطبيعية - المجلد 19, الإصدار 1, 2005 - 99 - 116
An-Najah Univ. J. Res. (N. Sc.), Vol. 19, 2005, p p 99 - 116 :
Hafez Shaheen
Department of Civil Engineering. Faculty of Engineering. An-Najah National University. Nablus. Palestine.
Panayiotis Diplas
Department of Civil and Environmental Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA. E-mail: shaheen@najah.edu.
Abstract:
Fluid forces and the quantity and ranges of grain sizes present on a streambed are the important factors affecting the transport of sediments. Most bedload transport models are based on single grain size parameter that represents either the surface or the subsurface bed material. Fractional bedload transport analysis is used to account for the different grain sizes. Surface versus subsurface-based fractional analysis of available bedload transport data are compared and the effect of the selection of the dimensionless reference bedload transport parameter is investigated. Fractional analysis has indicated that it is referenced to the size distribution of the bed surface rather than the subsurface and that its necessity increases for bedload data sets that fall closer to the lower end near threshold conditions. The reference value for the dimensionless bedload parameter used in this paper falls within the lower range of the analyzed bedload data set.
الملخص:
القوى الهيدروليكية إضافة إلى الكميات والتدرج الحبيبي للأتربة الموجودة في قيعان الأنهار هي أهم العوامل التي تؤثر على انتقال هذه الأتربة. معظم النماذج التي تتعامل مع انتقال الأتربة تعتمد على تدرج حبيبي ممثلاً للأتربة والمواد في الطبقات السطحية أو الطبقات تحت السطحية لقيعان الأنهار. ولكي يتم أخذ التدرج الحبيبي بعين الاعتبار يجب تحليل انتقال الأتربة في قيعان الأنهار وحساب حمل القاع (Bed load) بوساطة نماذج تعتمد على التحليل الجزئي للتدرج الحبيبي. في هذه الورقة تم مقارنة النماذج التي تعتمد التدرج الحبيبي للطبقات السطحية مع تلك التي تعتمد التدرج الحبيبي للطبقات تحت السطحية وذلك لحساب انتقال الأتربة وحمل القاع (Bed load) وكذلك دراسة تأثير اختلاف القيمة المرجعية (W*r) لانتقال الأتربة في قيعان الأنهار. تبين من الدراسة أن التحليل الجزئي (Fractional Analysis) يجب أن يستند إلى التدرج الحبيبي للطبقات السطحية بدلاً من الطبقات تحت السطحية وأن أهمية هذا التحليل وضرورته تزداد كلما كانت النتائج قريبة من القيم التي تبدأ عندها الحركة من حيث التدرج والقوى الهيدروليكية، فقد أثبتت الورقة أن القيمة المرجعية لحساب انتقال الأتربة في قيعان الأنهار (W*r) يجب أن تكون في حدود القيم الدنيا لمعطيات انتقال الأتربة والمواد المُراد تحليلها.
INTRODUCTION
The transport of sediments from a streambed of mixed sizes depends on the availability of each grain size present on the bed surface and the fluid forces on the exposed grains. In a gravel-bed stream, the bed material is often sorted such that the surface composition is coarser than the subsurface. Many mixed size transport formulas have been developed relative to the grain size of the subsurface material rather than the bed surface. For low Shields stresses the surface layer (pavement) is the main contributor to bedload transport. For higher stresses the subsurface layer is exposed and also contributing to the bedload and, eventually, equal mobility conditions govern. As to Parker (1) , substrate particles can participate in the bedload only to the extent that the local or global scour results in their exposure on the surface.
To accurately estimate sediment transport loads and the participation of the surface versus subsurface particles in the bedload, it may be necessary to know the continuous change of the grain size composition of the surface layer with flow conditions. This is typically unknown, especially during flood conditions, when most of the material is transported. During floods and high shear stress, most bed material is exposed to transport and conditions of equal mobility prevail.
Almedeij & Diplas (2) have used a two-parameter approach, surface and subsurface combination, for predicting bedload transport rates in gravel bed streams. Their formula uses two particle size diameters, one to represent the surface and the other the subsurface materials. The formula implicitly accounts for the variation in the make-up of the surface bed material over a wide range of Shields stresses. This approach is believed to reflect the resulting changes in the contributions made by the pavement (surface) and sub-pavement layers to the bedload transport.
Fractional bedload transport analysis consists of dividing the bed material distribution into several size ranges, each represented by a particle diameter, Di . Fractional analysis requires that the bed size distribution be specified for scaling purposes, however, either the surface or the subsurface size distribution may be used. Traditionally, the subsurface size distribution has been used since it is a known stable distribution that does not vary significantly with flow conditions. Researchers such as Parker (1) , Wilcock & McArdell (3) and Wilcock & Crowe (4) have proposed surface based fractional bedload transport approaches. Parker et al. (5) and Diplas (6) have implemented subsurface-based fractional bedload transport rate calculations for poorly sorted sediments.
Here surface versus subsurface-based fractional analysis of available bedload transport data is presented and compared. The effect of the selection of the dimensionless reference bedload transport parameter, * i W , on the similarity collapse and fractional analysis is also investigated
EXPERIMENTAL DATA
The experimental data obtained by Proffitt (7) are suitable for investigating a wide range of transport rates. He conducted experiments in a non feeding, non-recirculating sediment flume to study armouring due to transport of nonuniform sediments. The bed material and bedload size distributions, bedload transport rates, and corresponding hydraulic data were measured and are suitable for fractional transport analysis using a surface-subsurface combination model. The laboratory data of Proffitt (7) is used here in the fractional analysis.
Proffitt performed four series of experiments. Each series consisted of four experiments. The bed material was kept constant for each series, while each experiment was designed with a different shear stress. Three phases could be identified within each experiment. The initial phase, which typically lasted for about one hour, was characterized by intense and relatively constant bedload transport, measured at the downstream end of the flume. In the initial phase, both surface and subsurface particles (bulk size distribution) have been exposed to transport. The final phase was characterized by the coarsest pavement, which was distinct for each of the sixteen experiments, a condition reached after 20 to 95 hours of run time, and a bedload transport rate of 2.5% or lower of that measured during the initial phase of the corresponding experiment. During the intermediate phase, the channel bed and bedload transport rate transitioned from the initial to the final phase conditions.
Proffitt used a trap with a settling basin to collect the transported sediment at the downstream end of the flume. It is likely that some particles moving in suspension could have settled and were subsequently included in the bedload measurements. In addition, it is noted that fine material, comprising between 0.2 and 1.7% of the total sediment transported during a run, was carried over the top of the trap. The weights and grain size distributions were then adjusted in proportion to the total amount collected. Thus it is necessary to determine the size ranges carried in suspension and remove them from the fractional bedload analysis.
Using the Bridge & Bennett (8) suspension criterion, for sediments having a submerged specific gravity of 1.65 mm and an assumed shape factor of 0.7, it is determined that the maximum particle size in suspension for both the initial and final phases of Proffitt’s experiment ranged from 0.3 to 0.5 mm. Therefore, the present analysis excluded particles smaller than 0.5 mm and dealt with the portion of sediment transported as bedload. Sediments with i D < 0.5 mm, constituted a percentage between 0.21 and 5.31 of the material collected in the sediment trap in all the experimental runs.
CONCLUSIONS
Fractional analysis and similarity collapse approach have been applied to both initial and final phases of the bedload data that has been collected experimentally by Proffitt (7) . Both surface and subsurface-based analysis have been considered in the paper. The paper also investigated the effect of the selection of the dimensionless reference bedload transport parameter, * r W , on the similarity collapse and fractional analysis.
The exposure and response of bed material to the applied shear stresses and thus to bedload transport is varying and subject to change with flow conditions. Therefore the reference bedload parameters can vary accordingly for the different bedload data sets. It has been indicated that the value for the reference parameter be within the lower range of the bedload data presenting the stream or the experiment conditions.
The paper has proved that fractional analysis is referenced to the size distribution of the surface rather than the subsurface. The similarity collapse technique has proved to be sensitive to the selection of the * r W parameter, which should be selected to vary as to the Shields stress values and flow conditions. It should not necessarily represent conditions slightly above the threshold of motion and can be higher. The results of the fractional analysis and the selection of the reference bedaload parameter have been used to evaluate the conditions of equal versus non-equal mobility of the bedload in gravel streams. The results have consistency with the actual and physical conditions of the data.
REFERENCES
1) Parker, G. (1990). Surface-based bedload transport relation for gravel rivers. Journal of Hydraulic Research 28(4) : 417-436.
2) Almedeij, H. J. & Diplas, P. (2003). Bedload transport in gravel-bed streams with unimodal sediment. Journal for Hydraulic Engineering , ASCE 129(11) : 896-904.
3) Wilcock, P.R. & McArdell J.B. (1993). Surface-based fractional transport rates: Mobilization thresholds and partial transport of sand-gravel sediment. Water Resources Research , 29(4) : 1297-1312.
4) Wilcock, P.R. and Crowe, J. C. (2003). A surface-based transport model for mixed-size sediment. Journal of the Hydraulics Division , ASCE 129(2) : 120-128.
5) Parker, G., Klingeman, P.C., & McLean, D.G. (1982). Bedload and size distribution in paved gravel-bed streams. Journal of the Hydraulics Division , ASCE 108 (4) : 544-571.
6) Diplas, P. (1987). Bedload transport in gravel-bed streams. Journal of Hydraulic Engineering , ASCE 113(3) : 277-292.
7) Proffitt, G.T. (1980). Selective transport and armouring of non-uniform alluvial sediments. Report no. 80/22 , Department of Civil Engineering, University of Canterbury, New Zealand.
8) Bridge, J.S. and Bennet, S.J. (1992). A model for the entrainment and transport of sediment grains of mixed sizes, shapes and densities. Water Resources Research 28(2) : 337-363.
9) Yang, C.T. (1996). "Sediment Transport Theory and Practice", McGraw Hill book Company, New York, USA.
10) Parker, G. & Toro-Escobar, C.M. (2002). Equal mobility of gravel in streams: The remains of the day. Water Resources Research 38(11) , 1264: 46 (1-8).
11) Diplas, P. (1992). Effects of mixture properties on transport dynamics. In Billi, Hey, Thorne & Tacconi (eds), "Dynamics of gravel bed rivers", 131-135. John Willy and Sons., New York, USA.
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