PDF Evaluation of Sand Transport Models by in Situ Observations ... - Univali

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Journal of Coastal Research SI 39 578 - 581 ICS 2004 (Proceedings) Brazil ISSN 0749-0208

GOMEZ, E. A; AMOS, C. L. and LI, M. Z., 2006. Evaluation of sand transport models by in situ observations under unidirectional flow. Journal of Coastal Research, SI 39 (Proceedings of the 8th International Coastal Symposium), 578 - 581. Itajaí, SC, Brazil, ISSN 0749-0208.

Sand transport rates measured from nine deployments of an annular benthic flume off the western Newfoundland coast and Sable Island Bank (Canada), are compared with predictions using: (1) Engelund and Hansen's total load equation; (2) Einstein-Brown's bedload equation; (3) Bagnold's total load equation, modified by Gadd et al.; and (4) Yalin's bedload equation. The D grain diameters examined were: 0.19 mm (15 trials); 0.33 mm (37 trials); and 0.50 mm (7 trials). Results showed that equation (1) under-predicted in about a 40% for all the grain sizes. Equations (2) and (4) showed almost the same range of under-prediction: approximately 30% for D = 0.19 mm, 40% for D = 0.33 mm and 50% for D = 0.5 mm. The maximum variations on the observed-predicted ratios were obtained by equation (3), over-predicting by a factor of 2.45 and 1.9 for D = 0.19 mm and D = 0.33 mm, respectively, and under-predicting by a factor of 0.42 for D = 0.5 mm, but showing the highest correlations among all the tested models (R = 0.96 and 0.8 for D = 0.19 mm and 0.33 mm, respectively). These variations are related to the inclusion of outliers in the original computation of the grain size dependent -parameter employed by equation (3). Based on the obtained results and through the analysis of published data, a significant improvement on the formulation (3) is suggested.

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ADDITIONAL INDEX WORDS: Sediment transport equations, transport measurements and predictions, annular flume.

ABSTRACT

Evaluation of Sand Transport Models by in Situ Observations Under Unidirectional Flow

E. A. Gómez† ; C. L. Amos‡ and M. Z. Li § ¥

INTRODUCTION

Oceanographers, sedimentologists and coastal engineers frequently need to predict sediment transport rates in the marine environment, coastal areas and rivers. However, the choice of suitable sediment transport equation is by no means clear.

In an field sediment dynamics study on eastern Canadian continental shelf, deployments of instrumented tripods and Sea Carousel (an annular benthic flume; A , 1992) were conducted to monitor sand transport under the combined influences of waves and currents in order to evaluate an hypothetical sand transport pattern on the eastern margin of Canada by means of a sediment transport numerical model - SANDTRANS96 (L and A , 2001). The purpose of this paper is to discuss the first step in the calibration process; an examination of predictions under pure unidirectional flow.

Sand transport rates measured from nine deployments of the Sea Carousel off the western Newfoundland coast and Sable Island Bank (Canada) are compared with rates predicted by various sediment transport equations. Based on the obtained results and through the analysis of published data, a significant improvement on one of the formulations is suggested.

The Sea Carousel is a benthic flume capable of generating near-bed flows up to circa 1 m/s within an annulus 1.0 m in radius, 0.15 m in channel width and 0.30 m in heigth. These flows are induced by driving a moving lid with 8 paddles mounted beneath. The Carousel houses 2 Optical Backscatter Sensors that detect suspended sand mass at heights of 0.03 and 0.18 m above the flume skirt (the skirt usually sits on the seabed); the sensors are calibrated on-line thought filtered pumped samples taken from a sample port in the side of the annulus at a height of 0.20 m above the skirt. The Carousel is also equiped with an electromagnetic current meter that

monitors azimuthal and vertical components of flow at a height of 0.16 m, a shaft end-coder that detects lid rotational speed and a high-resolution Hi8 video camara that monitors close-up bed motion at a shutter speed of 100 frames per second. All data are logged at a rate of 1 Hz. Experiments were run for periods up to 90 minutes. Current speed was increased step-wise up to azimuthal current speed of 1 m/s. Measurements were made under up to 13 levels of controlled constant flow. Bed shear stress was determined using the quadratic stress law based on laboratory calibrations. All flows were normalized to a standard height of 1 m ( ) for comparability with field observations by using the Law of the Wall where the roughness length, , as , and where the bottom roughness ( is the mean grain diameter and is the ripple height; after Jonsson, 1966). Despite the variety in sample sorting, D (1980) indicated that the threshold of the size of a mixture is similar to the threshold for a uniform sediment of the same size; so the samples sizes were used to obtain the critical shear velocities for the initiation of bedload transport u by means of the Y (1977) method.

Measured sand transport rates ( ) obtained with the Sea Carousel deployments were compared with predictions ( ) using: E and H (1967) total load equation;

Einstein-Brown bedload equation (B , 1950); B (1963) total load equation, modified by G . (1978); and Y (1963) bedload equation. All these methods are coded within the numerical model SEDTRANS96 (L and A , 2001). The bedform transport rates of sand (or mean submerged mass discharges) were obtained though measured ripple height (in video) and the rates of ripple migration, using a static bottom-sediment volume concentration of 0.65 and a sediment and water density of 2650 kg/m and 1026 kg/m respectively.

The suspended sediment transport rates (through bedform bypassing, saltation and suspension) were calculated by multiplying the suspended sediment concentration by the current speed and the flume cross section.

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INSTRUMENTATION AND METHODS

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†Instituto Argentino de Oceanografía

CC 804, Florida 8000 8000 Bahía Blanca Argentina

gmgomez@criba.edu.ar

‡ School of Ocean and Earth Science Southampton Oceanography Centre Southampton, Hampshire SO14 3ZH, United Kingdom cla8@soc.soton.sc.uk

¥Bedford Institute of Oceanography Geological Survey of Canada P.O. Box 1006 Dartmouth, Nova Scotia B2Y 4A2, Canada mli@nrcan.gc.ca

Journal of Coastal Research Special Issue 39, 2006,

§ Universidad Tecnológica Nacional FR Bahía Blanca 11 de Abril 461

8000 Bahía Blanca, Argentina

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RESULTS

ANALYSIS AND DISCUSSION

Three median grain sizes were examined in this study:

0.19 mm (fine sand); 0.33 mm (medium sand); and 0.50 mm (medium-coarse sand). Results were obtained at seven sites in eastern Canada; six from the shoreface of western Newfoundland and one from Sable Island Bank. The sediments from the first six sites were composed of moderate to poorly sorted sand and were obtained in depth less than 20 m. The Sable Island Bank sample was located in 40 m of water and was well sorted medium sand ( = 0.33 mm). Ripple morphology and migration was observed in all cases, as was observations on sand bypassing and saltation layer thickness. Ripple heights ranged from 0.5 cm to 12.7 cm.

Observed-predicted ratios for each tested equation are shown in Figure 1 as well as the respective regressions for each . The relative high correlation observed in all equations for

= 0.5 mm (greater than 0.9) are related to the scarcity of data for this grain size (7 trials). For all the grain sizes the Engelund and Hansen equation under-predicted in about a 60%. The Einstein-Brown and Yalin equations showed almost the same range of under-prediction: approximately 70% for = 0.19 mm, 60% for = 0.33 mm and 50% for = 0.5 mm. The Bagnold equation modified by G . showed the maximum variations on the observed-predicted ratios. This

equation over-predicted by a factor of 2.45 and 1.9 for = 0.19 mm and = 0.33 mm, respectively, and under-predicted by a factor of 0.42 for = 0.5 mm. However, this equation showed the highest correlations: = 0.96 and 0.8 for = 0.19 mm and 0.33 mm, respectively.

The transport rates predicted by the four transport theories tested here are about in the range of 0.5 - 2 times the measured values, which are good results for sediment transport theories (W , 1975). However, attention should be drawn to the dissimilar behavior of G (1978) equation as it is the only tested equation which over-predicts the transport rate for

= 0.19 mm and 0.33 mm, but under-predicts the transport rate for = 0.5 mm. Yet it gives the highest correlations among all the tested equations Contrary, in a comparative study of measured and predicted bed-load transport rates using five sediment transport theories, H (1981) found that G predictor gave the best agreement with observed sediment transport rates, indicating simultaneously that this equation appears to be least sensitive to changes in roughness length and particle size than others. For such reasons, G

(1978) formulation is particularly analyzed below.

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Figure 1. Observed-predicted ratios for each tested equation. Notice the dissimilar behavior of G 's (1978) restructured version of B s (1963) equation, despite it shows the highest correlations among all the tested models.

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Since some parameters of the transport concept outlined by B (1963) were hard to be measured, S (1972) proposed some modifications on the original equation obtaining:

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where and are the sediment and fluid density, respectively;

is the bed-shear velocity, the acceleration of gravity and a proportionality coefficient.

However, Sternberg's calibrations indicated that depends on grain size and on excess shear stress. G . (1978) restructured equation (1) by replacing the shear velocity by the current velocity at 1 m above the bed and removing the dependence of on excess shear obtaining:

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where and are the current velocity and the critical value of current speed for the initiation of motion 1 m above the bed, respectively; and a proportionality coefficient now depending only on grain size. These authors calibrated equation (2) against flume data from G (1966) by averaging the ratio

on 15 trials carried out on two tested grain sizes:

= 0.18 mm and 0.45 mm, obtaining = 7.22 kg s m and = 1.73 kg s m , respectively. This equation shows the practical advantage that it is not necessary to have the direct measurements of u , which is hard to achieve in the field.

By doing the regressions of the Qm from the present study against the corresponding , =1.54, 2.12 and 2.86 kg s m for = 0.50, 0.33 and 0.19 mm, respectively, are obtained (Figure 2/a). It is easy to observe that these results almost follow a linear relationship in the form:

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which for the coarser sand ( = 0.45 mm) gives a value close to that one given by Gadd (1978), but about 2.5 times smaller that their value for = 0.18 mm. When the original G

(1978) data are analyzed, it is observed that in the average of corresponding to = 0.18 mm there were few values that were even one order of magnitude greater than the general trend and up to 46.3 kg s m . When the three greatest values from the

= 0.18 mm in this 15 data set are removed, the average of the

remaining 12 data gives = 2.78 kg s m , now follow the general trend proposed by equation (3) as it can be observed in Figure 2b. So, the following relationship is proposed:

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where the G re-computed results and the data set from the present study are combined.

For the three tested grain sizes, the Engelund and Hansen (1967), the Einstein-Brown (B , 1950) and Yalin (1963) equations under-predicted between 50% and 70%, inversely to the grain size. The Bagnold´s equation modified by G

(1978) showed the maximum variations on the observed- predicted ratios (by a factor of 0.42, 1.9 and 2.45 for = 0.50, 0.33 and 0.19 mm, respectively), but exhibit the highest correlations among the four tested equations. The - trend from this study shows a linear relationship with a slope of the order -4, while G exhibited a value greater than -20, which is explained by the inclusion of outliers up to 46 kg s m from the original data set on the averaged -parameter value for

= 0.18 mm. When these outliers are removed, the new - parameter collapsed within the trend described by the relationship (kg s m ) = -4.057 (mm) + 3.547. So in order to obtain more accurate predictions, the use of this - relationship is recommended.

This investigation was founded by the National Research Council of Argentina (CONICET), the World University Service of Canada (WUSC) and the National Agency for the Promotion of Science and Technology of Argentina (ANPCyT) (Grants 14652 and 14653).

., and K., 1992.

Sea Carousel - a benthic, annular flume. Estuarine, Coastal and Shelf Science, 34:557-577.

R.A., 1963. Mechanics of marine sedimentation. In M.N. Hill (ed). The Sea, vol. 3. Publ. Wiley-Interscience,

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CONCLUSIONS

ACKNOWLEDGEMENTS

LITERATURE CITED

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Figure 2. a) Observed -parameter obtained from the regression of each tested grain size. b) When outliers are removed from G . (1978) averaged value for D = 0.18 mm, the re-averaged value follows the general trends exhibited by the data obtained in this paper. The -D relationship obtained from all data presented here is also shown.

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New York: 507-582.

C.B., 1950. Sediment Transportation. In Engineering Hydraulics, H. Rouse, J. Wiley and Sons (ed), Inc., New York, N.Y., 1039p.

T.J., 1980. A study of initial motion characteristics of particles in graded bed material. Estuarine, Coastal and Shelf Science 10, 181-199.

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Governmental Printing Office, 96 p.

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M.Z. and C.L. 2001. SEDTRANS96: the upgraded and better calibrated sediment-transport model for continental shelves. Computers & Geosciences 27: 619- 645.

R.W., 1972. Predicting initial motion and bedload transport of sediment particles in the shallow marine environment. In Shelf Sediment Transport: Process and Pattern, D.J.P. Swift, D.B. Duane and O.H. Pilkey (eds), Dowden, Hutchinson & Ross, Stroudsburg, pp. 61-82.

and A.D., 1975. Sediment transport theories: a review. Proceedings Institute of Civil Engineers, 59:2, 265-292.

M.S., 1963. An expression for bed-load transportation.

Journal of Hydraulic Division, ASCE, 89(HY3): 221-250.

BROWN,

DAY,

ENGELUND, HANSEN,

GADD, P.E.; LAVELLE, J.W., SWIFT,

GUY, H.P.; SIMONS, D.B RICHARDSON,

HEATHERSHAW,

JONSSON,

LI, AMOS,

STERNBERG,

WHITE, W.R.; MILLI, H., CRABBE,

YALIN,

YALIN, M.S., 1977. Mechanics of sediment transport.

Pergamont Press, Oxford, 290 p.

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