The objective of this experiment was to identify the

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1 DETACHMENT IN A SIMULATED RILL T. A. Cochrane, D. C. Flanagan ABSTRACT. The effects of water and sediment inflow to the top of a 25 cm wide rill with a fine sand bed at 5% slope with no rainfall and no infiltration were determined by using a new laboratory apparatus called a rill simulator. A significant sediment feedback effect on the detachment by flow at the top of the flume was determined with data obtained from laser elevation scans. Observations of the detachment that occurred in the rill were thus comparable with those predicted by the detachment equation in the WEPP model (Foster et al., 1995). For low sediment inflow rates, the detachment equation could be adjusted to predict reasonable results of detachment in the rill, but parameter estimation (rill erodibility, critical shear stress, transport capacity) was difficult. Keywords. Rill erosion, Sediment transport. The objective of this experiment was to identify the detachment of sediment in a rill by shallow water flows as influenced by the water flow rate and incoming sediment concentration. The experimental data were compared to predicted values calculated using an excess flow shear stress equation, similar to the one used in the WEPP detachment equation (Foster et al., 1995). Foster et al. (1977) derived a set of equations that are used in modern erosion prediction technology. These equations are derived from the continuity equation for sediment transport, and quasi-steady state flow is assumed: dg dx =D r +q s (1) G = sediment load per unit width (ML 1 T 1 ) x = distance along the channel (L) D r = net detachment rate or net deposition rate by channel flow (ML 2 T 1 ) q s = lateral sediment inflow from adjacent contributing broad shallow flow areas (ML 2 T 1 ) The D r term can either be a net detachment or a net deposition rate. It is believed that both detachment and deposition are always occurring simultaneously, but that Article was submitted for publication in May 1996; reviewed and approved for publication by the Soil & Water Div. of ASAE in November The use of trade names does not imply endorsement by Purdue University or USDA-ARS. The authors are Thomas A. Cochrane, Graduate Research Assistant, Department of Agricultural and Biological Engineering, Purdue University, West Lafayette, Ind., Dennis C. Flanagan, ASAE Member Engineer, Agricultural Engineer, USDA-Agricultural Research Service, National Soil Erosion Research Laboratory, and Assistant Professor, Department of Agricultural and Biological Engineering, Purdue University, West Lafayette, Ind. Corresponding author: Dennis. C. Flanagan, USDA-ARS, NSERL, Purdue University, 1196 Building SOIL, West Lafayette, IN ; tel.: (317) ; fax: (317) ; <flanagan@ecn.purdue.edu>. net detachment or deposition are influenced by the channel flow conditions. Rill detachment is represented by the following equation: D r =D c 1 G T c (2) T c = transport capacity of the flow (ML 1 T 1 ) D c = detachment capacity of the flow (ML 2 T 1 ) The transport capacity of flow (T c ) is the maximum sediment the flow can carry for the given hydraulic conditions. Transport capacity can be computed using several equations and a common way of doing it will be presented later in this section. Detachment capacity is computed by (Foster et al., 1995): D c = K ch (τ τ c ) (3) where K ch = channel erodibility parameter (TL 1 ) τ = average shear stress acting on the soil (FL 2 ) τ c = critical shear stress required for detachment to occur (FL 2 ) The detachment capacity is dependent on soil erodibility properties and the shear stress acting on the sediment by the flow. This shear stress can be calculated in the following way (Foster et al., 1984): γ = specific weight of water (FL 3 ) R = hydraulic radius (L) S f = friction slope (L/L) τ = γ RS f (4) When the transport capacity has been reached for a given flow condition, the system is said to be in equilibrium with net detachment being equal to net Transactions of the ASAE VOL. 40(1): American Society of Agricultural Engineers 111

2 deposition. As flow conditions change, either detachment or deposition will be favored. One important problem in modern erosion science is the accurate estimation of sediment transport capacity. A wide range of sediment transport equations exist, but only a few can be used for the shallow flows and low flow rates that agricultural erosion prediction requires. Alonso et al. (1981) studied applicability of different transport formulas. Sediment transport predictions of nine formulas were compared to measurements of flume and field data. The formulas used were the total load formulas of Ackers and White (1973), Engelund and Hansen (1967), Yang (1973), Laursen (1958), and the EM-1 and EM-2 formulas proposed by Engelund and Fredsoe (1976); and the bed load formulas of Meyer-Peter and Muller (1948), Bagnold (1956), and Yalin (1963). The study concluded that the formulas that give the best predictions are the Yalin, Yang, and Laursen formulas. The best equation for transport in shallow flows was the Yalin formula. This equation has been analyzed by others including Foster and Meyer (1972), and based on its assumptions, derivation, and experiments is one of the best functions currently available for predicting sediment transport in shallow flows. Meyer et al. (1983) conducted a series of experiments to measure the transport capacity of sands along crop-row furrows. These experiments were conducted on a noninfiltrating parabolic flume 1.8 m long with a w 2 = 3600d, width to depth ratio. The flume was set to the desired furrow grade and flow rate, while sediment was added until the transport capacity was reached. Combinations of four furrow gradients, four flow rates, and four particle diameter groups were tested with rainfall (122 mm/h) and without rainfall. The water inflow was reduced by the same amount as the rainfall addition so that the water outflow would be equal to the runs without rainfall. The study concluded that furrow gradient was a very influential factor on sediment transport. As furrow gradient increased, sediment transport capacity increased rapidly. To a lesser extent, flow rate and particle size also affected the sediment transport capacity. Transport capacity increases as particle size decreases and as flow rate increases. Meyer et al. (1983) reported flow depths between 5 and 15 mm. Results from Meyer et al. (1983) were compared with data presented in this article. A study of the magnitude and range of velocities and shear stresses that occur in rills was studied by Foster et al. (1984) using a full scale fiberglass fixed bed, which replicated a rill on an eroded soil. They found that the flow characteristics along the rill were nonuniform. Flow velocity along the rill varied as a normal distribution. Rill form roughness appeared to have an overall greater influence on shear stress than grain roughness although there was considerable nonuniformity. Results also indicated that for steeper slopes the influence of rill form roughness decreased significantly. MATERIALS AND METHODS The rill simulator designed for this experiment consists of a 3.66 m long flume constructed from steel angles and galvanized sheet metal (fig. 1). The flume bed slope could be adjusted from 0 to 20%. The cross-sectional shape of the rill simulator (fig. 2) permits change in rill width as well as 74% Figure 1 Rill simulator. 59% Figure 2 Rill simulator cross-section and data acquisition system. the possibility to run experiments with either rectangular channel rills or with trapezoidal shaped rills. The rill width for the rectangular channel can range from 10 to 28 cm (fig. 2). The rill simulator also features the ability to simulate water infiltration through the sediment by changing the water tension with drains located at the bottom of the flume. A sediment feeder used in previous experiments (Davis, 1978) was modified and adapted for use as the main source of sediment input to the top of the rill simulator. The dry sediment was mixed with inflowing water and was directed to a water shoot which guides the water into a box which then routes the water and sediment mixture to the top of the 112 TRANSACTIONS OF THE ASAE

3 rill. The rate of sediment feeding could be set to two distinct feed rates, one delivering 5.3 g/s and the other delivering 10.8 g/s of sediment. The sediment chosen for all the experimental runs was a fine sand (326 μm average diameter). Bulk density measurements were made by laser scanning a 15 cm 2 surface of flat sand, excavating a volume of soil, and then rescanning the same area. The sand was weighed and the volume was computed by subtracting the initial laser scan from the final laser scan. Saturated bulk density was calculated to be 1.61 g/cm 3 and dry bulk density was 1.58 g/cm 3. A data acquisition system was designed and built to gather and collect data from the sensors and controllers on the rill simulator. The major component in the system is the data acquisition board, which was a CIO-AD16 manufactured by Computer Boards, Inc., on which we used eight differential input channels. The board was mounted in a Mhz PC and 37 pin extension cables were extended out to analog and digital connector boards. This board has the capabilities of controlling different electronic components that can be used with the rill simulator such as a variety of flow sensors, endplate movement motors, and other measurement sensors. The data acquisition board is controlled by a program that can convert the readings from all the sensors to digital values, keep track of time, control the movement of the end plate if needed, and handle all the required analog to digital conversions. A diagram of the data acquisition system is also shown in figure 2. An Omega FP7001 flow sensor was used to measure the water inflow to the top of the flume. This paddle wheel flow sensor was chosen due to its ability to measure large quantities of water flow (18 to 326 L/min). The sensor was installed underneath the water trough of the sediment feeder and measured all clear water that entered the flume before sediment was added. A one by three meter laser scanner (Flanagan et al., 1995) was used to take elevation measurements of the bed surface before and after each run. The scanner uses a camera with open lenses, and an optical sensor is mounted in the place of film. The optical sensor detects the intense light spot that a helium-neon laser projects on the surface of the sediment and transforms it to bit readings. These readings are then stored in a file in the computer for future use in imaging and mapping. The laser scanner has an estimated resolution of approximately 0.2 mm. For this experiment, the scanner was kept in a constant, fixed position over the simulated rill. EXPERIMENTAL STUDIES: SET-UP AND PROCEDURE The bed was set to a slope of 5%, a width of 25.4 cm, and a rectangular cross-section (the side walls of the flume were used to form a rectangular channel). Each experimental run had a duration of 10 min in which rain and infiltration were not present. The six treatments which were repeated twice are listed in table 1. The sand on the bed (8500 cm 2 ) was smoothed and leveled to a height of 3.2 cm below the edge of the walls of the bed. The end plate was set to the same level as the sand. Finally, the surface of the sand was scanned using the laser scanner. The area of the scan was 4860 cm 2, which is 57% of the total area of the bed as shown in figure 3. The length of the scan was restricted by the laser scanner length and the width was limited by the rill simulator side walls. The sediment feed rate was adjusted before each experimental run and assumed to be constant throughout the experiment. For each experiment the desired water inflow was initially selected and was measured continuously during the experiment by the flow sensors. The average velocity of the flow and the sediment concentration were measured at one minute intervals during each run (9 readings per 10 min). Velocity was measured by spraying a fluorescent dye at the top of the rill and timing how long it took for the greatest concentration of dye to travel 2.5 m on the bed. Sediment concentration was determined gravimetrically. Average flow depth was estimated using the flow rate and velocity measurements in the following way: h = Q V w where h is the average flow depth (m), Q is the water flow rate through the rill (m 3 /s), V is the average velocity of flow (m/s), and w is the width of the rill (0.254 m). This calculation was also cross-checked by measurements of flow depth taken by hand during each run. Hand measurements were taken every minute at two different cross-sections of the rectangular rill using a marked ruler. The changes on the surface of the rill bed were visually observed and instrumentally measured using a laser scanner. Elevation of the bed surface was measured with the laser scanner before and after each run. Elevations at each point were then subtracted from each other to obtain a difference in elevations for the entire scan area. To facilitate data processing and presentation of results, the scan area was divided into 10 sections and the height change and volume change for each of these sections were calculated. The geographic information systems GRASS (CERL, 1991) and ARC/INFO (ESRI, 1995) were used for elevation map construction and image analysis. RESULTS OF LABORATORY TESTS The laser scan data are the most important results of this study, as they offer a qualitative and quantitative representation of the erosion processes that occurred in the rill bed. Changes in volume of ten areas as well as maps based on laser scans are shown in figure 4 through figure 9. Sediment Inflow (g/s) Table 1. Detachment treatments Water Inflow (L/min) Figure 3 Laser scan area (not to scale). VOL. 40(1):

4 64% 100% Figure 7 Repetition 1 (top) and repetition 2 (bottom) L/min water inflow, 0 g/s sediment feed rate. 65% Key for figures 4-9 Shading gradations which depict detachment/deposition depths on sand bed after an experimental run (measured by laser scans). Figure 8 Repetition 1 (top) and repetition 2 (bottom) L/min water inflow, 5.3 g/s sediment feed rate. 64% 64% Figure 4 Repetition 1 (top) and repetition 2 (bottom) L/min water inflow, 0 g/s sediment feed rate. 65% Figure 5 Repetition 1 (top) and repetition 2 (bottom) L/min water inflow, 5.3 g/s sediment feed rate. 64% Figure 6 Repetition 1 (top) and repetition 2 (bottom) L/min water inflow, 10.8 g/s sediment feed rate. Figure 9 Repetition 1 (top) and repetition 2 (bottom) L/min water inflow, 10.8 g/s sediment feed rate. Lighter areas are regions of significant detachment and the darker areas are regions of sediment deposition as shown in the key for figures 4 to 9. Detachment rates (volume changes) at the top of the rill simulator were similar between replications, but they varied considerably close to the outlet of the rill. Channelization caused variations in measured detachment volumes. This kind of meandering of the flow was also observed by scientists who studied shallow flow of water over uniform sediment without rainfall. In a study by Meyer and Monke (1965), these channels were observed at different slopes, but were most common in the range of 4 to 13%. A formation of a sediment island near the top of the rill is clearly visible in figure 4. The formation of this island was probably a consequence of the side wall effects on the water inflow and the fact that there was no rainfall present. Rainfall would have induced turbidity in the shallow flow of water making formation of islands more difficult. Side wall effects cause changes in flow velocity near the edges of flumes due to different hydraulic roughness as compared to the bed surface. Similar effects were also observed by Vanoni and Brooks (1957). After the island, the flow formed areas of preferential flow, more specifically on the left side, when facing down slope, of the rill simulator wall. A sediment feed rate of 5.3 g/s, as shown in figure 5, reduced the detachment rate at the top of the rill. Towards 114 TRANSACTIONS OF THE ASAE

5 the end of the rill, areas of preferential flow were again present and values of volume change differed from one repetition to the other. Deposition was measured at the end of the rill in replication 2. As mentioned before, the laser scans could not cover the entire width of the rill, which, together with the visual observation of flow meandering on the sediment bed contributed to the variability in volume changes between replications. As the sediment feed rate was increased to 10.8 g/s, the detachment rate at the top of the rill diminished further and sediment islands formed closer to the top as shown in figure 6. At this higher sediment feed rate, the bed alternated between detachment and deposition regions. When the water flow rate was increased to 30.3 L/min, the difference in volume changes between repetitions decreased. The larger flow created a more uniform detachment rate as seen in figure 7 through figure 9, probably as a consequence of increased turbulence. Island formation was also reduced when compared to the treatments at the lower flow rate. As flow rate increases, side effects become less influential (Chang, 1992), which could add to the explanation of why the bed was more uniform. The same trends of detachment observed with the 22.7 L/min flow rate were observed with larger flow. In figure 7, greater detachment was measured at the top of the bed where clear water was introduced to the bed, than in the same area in figure 8 with the moderate level of sediment inflow. Initial detachment was further reduced when the sediment inflow was greater (fig. 9). These relationships are shown in figure 10 and 11. These graphs show the average detachment that occurred in the first and second intervals of the laser scans for water inflows of 22.7 and 30.3 L/min and inflow sediment feed rates of 0, 5.3, and 10.8 g/s. These results indicate that water containing no sediment caused more erosion than flow carrying sediment and that the detachment rate was directly related to the sediment load in the flow. This is consistent with equation 2, more specifically with the (1 G/T c ) term. With higher sediment load, G, for a given level of flow, this term is reduced, which in turn reduces the amount of detachment in the rill. For the remaining downstream scan regions, the combination of deposition, flow meandering, Figure 10 Influences of flow and sediment feed rate on first scan interval detachment (64 to 91 cm from top of bed). Figure 11 Influences of flow and sediment feed rate on second scan interval detachment (91 to 118 cm from top of bed). and variability between replications resulted in no significant differences in rill detachment between the different sediment feed rates or flow rates. The detachment rate decreased down the bed, and the gradient at the top of the bed decreased slightly throughout the experimental run. The rate of resuspension or detachment of sediment was greatest when there was no sediment in the inflow water. As flow detaches and transports sediment, the rate of detachment diminishes until an equilibrium is reached where the flow is carrying the maximum amount of sediment. Changes in the flow characteristics due to localized deposition (islands), and channelization (edge effects), destabilize the system. The fixed end plate at the flume exit prevented detachment and acted to decrease the bed slope. This decrease in slope was probably responsible for some of the deposition which occurred near the end of the flume. The slight change in gradient at top of the bed could also influence shear stress in localized areas near the top of the bed. The sediment concentration in the outflow was sampled nine times during each run and was quite variable with no clear trend relative to the time of sampling. An analysis of variance was conducted to estimate the effects of the two factors (water and sediment inflow) on the sediment concentration in the outflow of the rill simulator. From the F-test at the 95% probability level, the water inflow amounts used had no significant influence on the overall sediment discharge concentration. This was also true for the effects of the sediment inflow rates. Although each of the factors by themselves did not influence sediment discharge, the interaction of water and sediment inflow was a significant effect. Most of the treatments had sediment Table 2. Sediment discharge concentration means (g/l) and multiple comparison groupings Sediment Water Inflow Inflow 22.7 L/min 30.3 L/min 0 g/s 49 a* 44 a 5.3 g/s 47 a 45 a 10.8 g/s 45 a 62 b * Means followed by like letters are not significantly different at the α = 0.05 level using the SNK multiple comparison test. VOL. 40(1):

6 concentrations in the range of 43 to 49 g/l except for the last treatment with both the largest amounts of sediment and water inflow, which had a sediment concentration of 61 g/l. The means and multiple comparison groupings of the sediment discharge concentrations are shown in table 2. DETACHMENT MODELING Some simple modeling was performed using the detachment equations presented earlier in this article. Since the laser scan results were divided into 10 control areas, a finite difference approach was used in which the detachment equation was written as follows: G out =G in + X out X in K r τ τ c 1 G T c (5) G out, G in = sediment load going in and out of interval [kg/(m s)] X out, X in = distance down slope (m) K r = rill erodibility (s/m) τ = shear stress of flow (N/m 2 ) τ c = critical hydraulic shear (N/m 2 ) T c = transport capacity [kg/(m s)] The initial sediment load, G in.,was known and the concentration output G out, of one interval was assumed equal to the initial concentration of the next interval. Difficulties arise in determining the correct values for the critical shear stress, the rill erodibility, and the transport capacity. In the initial trial, τ c and K r were set equal to 1.02 N/m 2 and s/m, respectively. These values were the same as those for the Bonifay sandy soil in the WEPP field experiments (Laflen et al., 1991). The Bonifay soil was chosen because it was thought to be the closest published representation of the sand used in this study. Transport capacity was estimated by using Yalin s (1963) formula. The shear stress of flow was calculated from the initial bed slope and the average computed flow depth. It was believed that the change in slope due to detachment at the top of the rill was minimal. In the initial trials using the Bonifay soil erodibility parameters, the calculated shear stress, and Yalin s transport capacity, the detachment rate in the scan areas was underpredicted by a factor of 50. We then assumed that the erodibility parameters (τ c and K r ) were not adequate in describing the sand that was used. This could have been due to the fact that the Bonifay soil contained clay and silt whereas the sand used in these experiments was pure silica sand. A second attempt at modeling was made using a portion of the study data for calculating the τ c and K r parameters. According to the detachment equation (eq. 3), the τ c and K r parameters can be calculated by a linear regression fit on the data if the detachment rate, shear stress, and initial sediment load are known. If water without sediment is introduced to the bed, G = 0 and the term (1 G/T c ) = 1, simplifying the equation to D r = K r (τ τ c ). A linear regression fit could then be conducted with the form of Det = a + bτ in which K r = b and τ c = a/b. In the case of this study, the laser scan data was used to find the detachment rate for each of the runs in each of the ten intervals of the scan area. However, since the laser scans did not begin at the very top of the bed, the sediment concentration (G) that enters the first interval of the scan area is not known because an unknown amount of sand from the bed has already been incorporated with the initial flow. To solve this problem, it was first assumed that the sediment outflow was very close to the transport capacity. This assumption was based on the fact that in most of the experiments, there was no detachment at the end or the detachment rate was very small. These values were also compared to transport capacity values obtained by Meyer et al. (1983) for sands and flow of similar values and found to be similar. Secondly, we assumed that transport capacity was reached when the laser scans showed that there was very low detachment on the bed or when deposition occurred. The sediment concentration in the outflow was then taken to be the detachment that had occurred in the rill bed until the point where transport capacity was reached. The shear stress was calculated from the slope and flow depth and the (1 G/T c ) term was averaged to 1/2 over the upstream contributing area where it varies from one at the inlet to zero where deposition begins. In order to maximize the use of available data, these calculations were only performed on the second repetition runs of the experiments with 22.7 L/min water inflow and 30.3 L/min water inflow where the initial sediment concentration going into the bed was 0 g/s. The two equations obtained were: = K r 1.35 τ c = K r 1.60 τ c 1 2 resulting in: K r = s/m τ c = N/m 2 These new parameter values seemed reasonable for the type of sand used in these experiments, they were then used in equation 5, and the results are shown in figures 12 and 13. The detachment in the first five laser scan regions was calculated and compared with the predicted detachment rates from equation 5. Only the first five areas were compared due to the transition to depositional conditions on the lower half of the bed. The predicted values for the experimental runs with 0 and 5.3 g/s feed rate match the observed data closely in all of the experimental runs except for repetition 1 of the 30.3 L/min flow rate and 0 g/s sediment inflow level. In figures 12c and 13c, the predicted values in scan areas 1 to 3 are in poor agreement with the observations. The only difference between these experiments and the previous ones is that the initial sediment feed rate was 10.8 g/s. This feed rate is very close to what Yalin s (1963) formula predicts as the transport capacity, which causes equation 5 to predict much lower values for initial detachment than observed. One possibility is that the shear stress of the flow was much greater than predicted, at least in localized regions in these scan areas. Also, the transport capacity of the flow could have been underestimated by the Yalin formula. Overall, the detachment equations used here did an acceptable job of estimating the observed detachment on the simulated rill, particularly for the case where the inflow sediment load was not close to the estimated sediment (6) 116 TRANSACTIONS OF THE ASAE

7 Figure 12 Observed and predicted detachment for scan regions 1-5, for a 22.7 L/min water inflow rate. transport capacity. The mean values of predicted and observed detachment were not significantly different when using a student s t test at α = SUMMARY AND CONCLUSIONS New laboratory methods and equipment were designed and constructed to study erosion in rills. A set of experiments was conducted in which combinations of feed rate (0, 5.3, and 10.8 g/s) and water inflow (22.7 and 30.3 L/min) were studied at a slope of 5% without rainfall. Laser scans were used to estimate detachment by precisely measuring changes in the elevation of the fine sand bed. Sediment discharge from the rill was also measured. The results showed that all the experiments were at least qualitatively compatible with the sediment feedback (1 G/T c ) term in the detachment equation in WEPP (Foster et al., 1995) and other process-based erosion models. Detachment increased with larger flows and decreased when sediment was introduced at the top of the bed. Detachment modeling showed satisfactory predictions of detachment rate for all the experiments with 0 and 5.3 g/s sediment feed rates using calibrated erodibility parameters. Predicted detachment for treatments with 10.8 g/s sediment inflow rate was poor. In future detachment studies, laser scans will be made from the very top of the simulated rill, and rainfall will be applied to reduce flow meandering and island formation. A moveable end plate will also be used to minimize slope changes on the bed. VOL. 40(1):

8 Figure 13 Observed and predicted detachment for scan regions 1-5, for a 30.3 L/min water inflow rate. REFERENCES Ackers, P. and W. R. White Sediment transport: New approach and analysis. J. Hydraul. Div. ASCE 99(HY11): Alonso, C. V., W. H. Neibling and G. R. Foster Estimating sediment transport capacity in watershed modeling. Transactions of the ASAE 24(5): , Bagnold, R. A The flow of cohesionless grains in fluids. Philosophical Trans. Royal Soc. London, Series A 249(964): CERL (Construction Engineering Research Laboratory, U.S. Army Corps of Engineers) GRASS (Geographical Resources Analysis Support System), public domain software, Champaign, Ill.: U.S. Army CERL. Chang, H. H Fluvial Processes in River Engineering. Malabar, Fla.: Krieger Publishing Company, John Wiley & Sons, Inc. Davis, S. S Deposition of nonuniform sediment by overland flow on concave slopes. M.S. thesis. West Lafayette, Ind.: Purdue University. Engelund, F. and J. Fredsoe A sediment transport model for straight alluvial channels. Nordic Hydrology 7: Engelund, F. and E. Hansen A monograph on sediment transport in alluvial streams. Copenhagen, Denmark: Teknisk Vorlag. ESRI (Environmental Systems Research Institute) ARC/INFO GIS program. Redlands, Calif.: ESRI. Flanagan, D. C., C. Huang, L. D. Norton and S. C. Parker Laser scanner for erosion plot measurements. Transactions of the ASAE 38(3): Foster, G. R. and L. D. Meyer Transport of soil particles by shallow flow. Transactions of the ASAE 15(1): Foster, G. R., L. D. Meyer and C. A. Onstad An erosion equation derived from basic erosion principles. Transactions of the ASAE 20(4): TRANSACTIONS OF THE ASAE

9 Foster, G. R., L. F. Huggins and L. D. Meyer A laboratory study of rill hydraulics: II. Shear stress relationships. Transactions of the ASAE 27(3): Foster, G. R., D. C. Flanagan, M. A. Nearing, L. J. Lane, L. M. Risse and S. C. Finkner Hillslope erosion component. In USDA-Water Erosion Prediction Project, Hillslope Profile and Watershed Model Documentation, eds. D. C. Flanagan and M. A. Nearing. NSERL Report #10. W. Lafayette, Ind.: USDA- Agricultural Research Service, National Soil Erosion Research Laboratory. Laflen, J. M., W. J. Elliot, J. R. Simanton, C. S. Holzhey and K. D. Kohl WEPP soil erodibility experiments for rangeland and cropland soils. J. Soil and Water Conserv. 46(1): Laursen, E The total sediment load of streams. J. Hydraul. Div. ASCE 54(HY1):Paper Meyer, L. D. and E. J. Monke Mechanics of soil erosion by rainfall and overland flow. Transactions of the ASAE 8(4): Meyer, L. D., B. A. Zuhdi, N. L. Coleman and S. N. Prasad Transport of sand-sized sediment along crop-row furrows. Transactions of the ASAE 26(1): Meyer-Peter, E. and R. Muller Formulas for bed load transport. In Proc. 2nd Congress of the IAHR, Stockholm, International Association of Hydraulic Research. Vanoni, V. A. and N. H. Brooks Laboratory studies of the roughness and suspended load of alluvial streams. Sedimentation Laboratory Report No. E68. Pasadena, Calif.: California Institute of Technology. Yalin, M. S An expression for bed-load transportation. J. Hydraul. Div. ASCE 89(HY3): Yang, C. T Incipient motion and sediment transport. J. Hydraul. Div. ASCE 99(HY10): VOL. 40(1):

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