Understanding the necessary conditions for avulsion in a delta channel is important in order to

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2 ABSTRACT Understanding the necessary conditions for avulsion in a delta channel is important in order to better predict an avulsion s timing and location. However, the specific conditions required for avulsions are poorly understood. Here, I analyze a theoretical delta simulation using the Delft3D model in an attempt to understand the necessary conditions for the set-up, and trigger of avulsion. I analyze the slope ratio as a predictor of avulsion, the effect of river mouth bar formation in triggering an avulsion, and whether the location of an avulsion can be predicted by the bed-shear stress of flow over a levee. For the conditions I specified, an avulsion is inevitable above a slope ratio of ~ 10 at locations of stable levees. However, I find that the slope ratio necessary for avulsion is highly dependent on geomorphological conditions of the levee and is much lower at locations with unstable levees. I determine that river mouth bar formation can have an impact on the triggering of an avulsion and that avulsions occur at the location of maximized bed shear stress. INTRODUCTION Avulsion is the abandonment of a river channel or delta lobe for a new course. On August 18, 2008, the Kosi River in India broke through its levees and relocated the river 120 kilometers to the east while flooding hundreds of thousands of acres and affecting more than 30 million people (Sinha 2009). The loss of life and property is still unknown, but is assumed to be higher than the more usual flood events because the affected areas were not within the flood plain of the Kosi River and because the people were unprepared for such a disaster (Sinha 2009). Thus, avulsions can have catastrophic effects on people, causing loss of life and property and effecting economics and transportation in the abandoned channel downstream. The problem is not rare

3 either. The Kosi River drains the Himalaya Mountains and has a very high sediment discharge, which causes the system to avulse with an average recurrence interval of only 24 years. More commonly, rivers have an avulsion interval on the magnitude to 1,000 years. Another example is the Mississippi River, where river avulsions lead to the development of new delta lobes. In the last 7,000-8,000 years, there have been 7 major avulsions, each creating a new delta lobe (Figure 1). Figure 1: Four of the Holocene delta lobes of the Mississippi River occurred around the site of the current delta lobe. The avulsion locations are also shown. From Aslan et. al. (2005). Over the past century, the Atchafalaya River, a distributary of the Mississippi River, started taking an increasing portion of the discharge of the Mississippi. The avulsion of the Mississippi down the Atchafalaya bay at point 4 in Figure 1 would shorten the distance to the coast (sea level) by about 390 kilometers (Wellner et. al. 2005). To stop this, the Army Corps of Engineers built a flow control structure in 1963 and the discharge of the Atchafalaya River is now 2

4 controlled at 30% of the water and sediment of the Mississippi in order to save the current Mississippi River Delta (McManus 2002). Without the flow of water and sediment to the delta, wetlands and land would erode below sea-level displacing millions of people and making shipping lanes along the well-developed channel useless. In deltaic systems, avulsions are crucial events in the evolution of the delta. Partial avulsions distribute sediment away from the main channel to wetlands. Full avulsions create new delta lobes through a process of delta lobe extension, avulsion, and abandonment of the old delta lobe and the progradation of a new lobe. Engineered avulsions may even be used to create new wetlands by diverting water and sediment away from the main channel (Paola et al. 2010). Because of these significant impacts, there is need to understand the mechanics of channel avulsion. This would allow us to better predict their timing and location in order to mitigate disaster, but also to control them. The mechanics of channel avulsion are not well understood, in part because they occur infrequently so field data are not readily available. Avulsion initiation is thought to occur in two stages, a set-up in which a channel aggrades and becomes increasingly susceptible to avulsion, and a trigger where a short-term event causes a crevassing in the levee leading to avulsion (Slingerland and Smith 1998). One theory for channel avulsion set-up is that avulsion arises from a differential gradient advantage when the leveeslope becomes some multiple of the down-valley slope (Mackey and Bridge 1995). This occurs as the channel elongates and aggrades and is known as the slope ratio (Figure 2). The elongation of the channel lowers the down-channel water surface slope, and the aggradation of the channel/levee complex increases the slope between the channel levee and floodplain or delta plain. Avulsions are thought to occur at or above a critical slope ratio. 3

5 Figure 2: A plan view of the locations of the cross-valley slope measurement and the down-valley slope measurement. Modified from Slingerland and Smith Slingerland and Smith (1998) estimated this critical slope ratio for fine-to medium-grained systems to be five or greater regardless of the initial size of the crevasse. This theoretical prediction is based on considering if a crevasse channel will avulse by runaway erosion and enlargement or heal by runaway aggradation and fill with sediment. Törnqvist and Bridge (2002), simulating Holocene Rhine River avulsions using a revised three dimensional fluvial architecture model of Mackey and Bridge (1995), determined that the probability of avulsion occurrence is high when the slope ratio is between three and five for the conditions in their experiment. Although there have been advances in the understanding of the effect of slope ratio on avulsion timing and location, a critical value or range has not been defined. It is possible that the critical slope ratio is substantially different in low-gradient settings like deltas than high gradient settings such as alluvial fans, and in systems of different cohesiveness and sediment flux (Törnqvist and Bridge 2002). 4

6 The trigger of an avulsion is associated with flooding and subsequent breaking of channel levees. This overbank flow may be caused by increased discharge, ice/log jams, or as a result of channel mouth bar stagnation and the subsequent backwater effect (Edmonds et al. 2009). When a river mouth bar stagnates, it acts as an obstruction to flow. This sends a wave of aggradation of the bed upstream, forcing the rise of the water surface, thereby flooding the levees. Edmonds et al. (2009) also propose that the levees break at a location that maximizes the magnitude and duration of the cross-levee bed shear stress as the levees flood. Although there has been significant advancement in the understanding of avulsion mechanics, it is still not clear what the necessary conditions for channel avulsions are. The specific questions addressed in this research are: 1) what is the critical slope ratio above which an avulsion is inevitable? 2) Does the stagnation of a river mouth bar lead to flooding of levees and the triggering of an avulsion? 3) Do levees fail at the location where cross-levee bed shear stress is maximized for the longest duration? I attempt to answer these questions by analyzing avulsions on a river-dominated delta created using the Delft3D hydrologic and morphodynamic model. METHODS Model consideration To test the above theories of channel avulsion, I do a detailed analysis of the time-evolution of a moderately cohesive river-dominated delta created using the fully coupled hydrologic and morphodynamic modeling Delft3D (Lesser et. al. 2004). Delft3D was created and implemented by scientists and engineers at the Delft University of Technology in the Netherlands to numerically simulate the hydrologic and morphodynamic evolution of coastal, river and estuarine areas. Fluid flow and bed morphology are fully coupled, which means changes in the 5

7 bed bathymetry are immediately fed back into flow field calculations (Lesser et. al. 2004). Thus, Delft3D does not set a condition for channel avulsion; rather the location and time of avulsion is determined based on fluid flow and sediment transport equations. Delft3D solves the unsteady shallow water equations over a loose bed of sediment in two dimensions (Lesser et al. 2004). These equations are derived from the three-dimensional Reynolds-averaged Navier-Stokes equations describing incompressible, turbulent, free surface flow. The equations consist of conservation of momentum of unsteady, incompressible, turbulent flow, a turbulence closure model, and conservation of fluid mass. Bed load sediment transport is solved by using a formulation from van Rijn (1984) in which bed load is estimated by the median diameter of grains. Suspended sediment transport is solved by the threedimensional diffusion-advection equation (Edmonds and Slingerland 2007). Experimental Design The delta simulation used in this study is run for 8.31 years in a basin of 600x450 grid cells each 100 m 2. The total computational area is 2,700,000 m 2. The basin slopes to the north, creating depths ranging from 1 to 3.5 meters, which is analogous to Atchafalaya Bay, Louisiana. A 500 meter wide sub-aerial sandy shoreline extends across the southern edge of the basin with an elevation of 1 meter. A rectangular river channel, 250 meters across and 2.5 meters deep, is cut into the sandy shoreline and extends 1000 meters into the basin to the north (Figure 3). A constant discharge of 1000 m 3 /s enters the basin through this channel with an equilibrium sediment flux with total concentration of 0.1 kg/m 3 consisting of seven-grain sizes (Table 1). The western, northern, and eastern boundaries are open water boundaries through which water and 6

8 sediment can pass and have been set at a temporally constant water level of 0 meters throughout the simulation. Bed roughness is set at constant Chezy value of 45 m 1/2 /s. Figure 3: The initial basin bed-elevations. Yellow to green is above sea-level. Blue to purple is below sea-level. The bed is composed of ten meters of evenly mixed cohesive and non-cohesive sediment consisting of seven grain sizes: four non-cohesive sediment fractions and three cohesive sediment fractions (Table 1). Cohesive sediment can only be transported in suspension and is defined as silt-sized and finer (<64 µm). In this simulation there are three cohesive sediment fractions of medium-grained silt (30 µm). Non-cohesive sediment can be transported as bed or suspended load and is greater than silt-size (> 64 µm). All grains are assumed to have a density of 2,650 kg m -3. The input sediment discharge is based on a normal grain size distribution with D50 of µm. 7

9 Table 1: Sediment grain sizes and their properties Sediment Sediment type Sediment concentration (kg/m 3 ) Grain size (µm) Thickness at bed (m) Settling velocity (m/s) 1 Non-cohesive N.A. 2 Non-cohesive N.A. 3 Non-cohesive N.A. 4 Non-cohesive N.A. 5 Cohesive Cohesive Cohesive The simulation is run for a period of 8.31 years. A time step of three seconds is used to obey stability criteria set by grid cell size and water depth. A spin-up interval of 720 minutes at the beginning of the simulation is used to allow the flow field to equilibrate before the sediment flux and bed is released to allow morphological changes to occur. Delft3D uses a morphological scale factor to speed up bed adjustments, which was set to 175. Output is sampled every days throughout the simulation for a total of 52 data outputs. Analysis The delta simulation results are viewed using Delft-3D Quickplot and analyzed in Matlab. Bed elevation, water level, depth, velocity, and bed shear stress are exported to Matlab for analysis. The time-evolution of the delta is first assessed qualitatively by viewing a bed elevation contour plot at each time step. Avulsions are noted as events where a new channel breaks through the channel levee of a channel and captures some or all of the flow. Each avulsion is assessed qualitatively by using a bed-elevation contour plot overlain with fluid flow depth-averaged velocity vectors. The time of avulsion is recorded and defined as the first channelization of the levee. The condition of the levees prior to avulsion is recorded; it is noted whether or not the 8

10 levee was flooded for an extended period before avulsion, an old crevasse channel is present in the levee, or if a topographic low is cutting into the levee. Slope Ratio The slope ratio at the time of avulsion is calculated at the time step before avulsion. The crosslevee water surface slope is calculated by extracting the water surface elevation at points along a transect 50 meters long from the channel levee into the delta-plain along the path of the future avulsion. The water surface elevation is plotted against the distance from the levee to each water level point, and a best fit line is calculated. The slope of this line is the water surface slope. The down-channel water surface slope is measured along the middle of the channel from the point of avulsion meters downstream. The slope ratio is calculated by dividing the cross-levee slope by the down-channel slope. Channel Mouth Bar Effects The effect of the stagnation of a channel mouth bar on avulsion is analyzed by noting at which time step a channel mouth bar stagnates compared to when the channel avulses. The water surface profile from the site of avulsion to the channel mouth bar was plotted through time to see if a wave of aggradation goes upstream and floods the levees. Shear Stress on the Levees The location of the avulsion on the levee is analyzed to test the theory that avulsions occur at the point along the levee where the bed shear stress is maximized for the longest duration. Bed shear stress is extracted at points along the channel levee on either side of the avulsion location. The 9

11 bed shear stress transect is plotted through time to determine where the levee experiences the highest bed shear stress for the longest duration. RESULTS Due to the high sediment flux, the delta evolves rapidly in the shallow basin. Eight avulsions occur during the evolution of the delta (Figure 4). Two avulsions, numbers one and two, are full avulsions and capture all of the flow. Six avulsions, numbers three through eight, are partial avulsions and either close, or are still diverting some of the flow by the last time step. Figure 4: Time step 49 termination of the simulation. The locations of eight identified avulsions are shown. Avulsions are numbered in the order in which they occurred. Avulsion One Avulsion one occurs at time step 16 (Figure 5). The parent channel is elongating to the east and the channel avulses to the north. The new channel becomes the main channel and the parent channel takes a small percentage of the flow and the delta lobe atrophies. The slope ratio at the 10

12 time of avulsion is Before avulsion, the levees were flooded and were never sub-aerial. The occurrence of the avulsion to the north makes sense because the channel was elongating in a direction in which the basin is flat, whereas the cross-levee slope to the north is imposed by the initial basin conditions. Figure 5: Time evolution of avulsion one. Bed elevation is overlain with velocity vectors. Avulsion Two Avulsion two occurs at time step 24 (Figure 6). The parent channel is elongating to the north and the channel avulses to a topographic low to the west. This channel captures all of the flow from the parent channel and causes a major delta lobe switch. Figure 7 shows the evolution of lip height of the new channel to the parent channel. The new channel has eroded to the depth of the parent channel by time step 33. By time step 45, this channel has captured about 99% of the 11

13 flow (Figure 8). The slope ratio at the time of avulsion is The levees were sub-aerial before flooding and the subsequent avulsion. The channel breaks through the levees into a topographic low that is not cutting into the levee, but is further into the basin. Figure 6: Time evolution of avulsion two. Bed elevation contours overlain with velocity vectors. The levees first begin to flood at time step 21. The levees begin eroding in time step 22. By time step 23, two crevasses have formed in the levee. These levees deepen at time step 24. At time step 25, the avulsion occurs as the southern channel rapidly erodes. By time step 26, the channel is the main distributary. Note: The channel to the south of the avulsion is open since the parent channel formation. Avulsion occurs north of this channel. A mid-channel bar (To the south, not shown) is migrating towards this distributary channel forcing water around it into the new channel 12

14 Figure 7: Bed elevation of the lip height versus distance from start of transect to end. The left side of the graph is located in the main channel. The right side of the graph is located in the channel created by the avulsion. Cool to warm colors are increasing time. The new channel has eroded down to the level of the old channel by time step 33. Figure 8: Discharge of water flowing through the new channel divided by the discharge in the parent channel one time step prior to avulsion initiation. 13

15 Avulsion Three Avulsion three occurs at time step 28 (Figure 9). The parent channel is elongating to the north and the channel breaks through its levees to the east. The slope ratio at the time of avulsion is The avulsion breaks through sub-aerial levees that were flooded just prior to avulsion. The avulsion goes to a pre-existing channel in a topographic low and quickly bifurcates. This is a partial avulsion that captures some of the flow then heals as avulsion two, which is directly upstream, captures most of the flow. Figure 9: Time evolution of avulsion three. 14

16 Avulsion Four Avulsion four occurs at time step 32 and is located on the new channel formed by avulsion two (Figure 10). The parent channel is flowing to the west and the avulsion occurs to the northwest. The new channel captures most of the flow and becomes the main channel of the delta system. The slope ratio at the time of avulsion is The levees are never sub-aerial prior to avulsion and high flow is going over the levee in all time steps from levee formation until channel avulsion. There is a pre-existing scour in the levee. Figure 10: Time evolution of avulsion four 15

17 Avulsion Five Avulsion five occurs at time step 45 and is located on the channel formed by avulsion 4. The parent channel is flowing to the east and the avulsion occurs to the north. The new channel captures a small portion of the flow and remains open until the end of the simulation. The slope ratio at the time of avulsion is The levees are only sub-aerial one time step before avulsion, and a pre-existing channel compromises the levee stability as it forms. The avulsion occurs where the topographic low cuts into the channel. Figure 11: Time evolution of avulsion five. 16

18 Avulsion Six Avulsion six occurs at time step 46, 250 meters upstream of avulsion five (Figure 12). The channel breaks through its levees to a topographic low to the south. The new channel captures only a small portion of the flow but remains open until the end of the simulation. The slope ratio at the time of avulsion is The levees are sub-aerial for only one time step before avulsion and the avulsion occurs at the location of a scour in the levee. Figure 12: Time evolution of avulsion six. 17

19 Avulsion Seven Avulsion seven occurs at time step 47 (Figure 13). The slope ratio at the time of avulsion is There are sub-aerial levees for multiple time steps before avulsion. A channel is cut into the levee just south of the location of avulsion. This channel is flowing to the southwest while the parent channel is flowing to the north. The channel avulses to the northwest and rapidly erodes and captures some of the flow of the parent channel. The channel is still active at the end of the simulation, but is starting to heal. Figure 13: Time evolution of avulsion seven. 18

20 Avulsion Eight Avulsion eight occurs at time step 48 near the discharge boundary of the delta simulation (Figure 14). The slope ratio at the time of avulsion is The channel breaks through its levees to the east towards a topographic low formed by a pre-existing channel flowing perpendicular to the new channel. The new channel rapidly erodes and elongates. The channel is still elongating at the end of the simulation. There are sub-aerial levees many time steps before the avulsion occurred and there are not pre-existing levee scours. The levees began flooding four time steps before avulsion. Three crevasses formed in the levee, but only one of these led to an avulsion. Figure 14: Time evolution of avulsion eight. 19

21 Summary The slope ratios at the time of avulsion range from 1.22 to However, these avulsions broke through levees with different morphological conditions (summarized in Table 2). Table 2: Summary of avulsions. Geomorphologic conditions of levees are included. Avulsion Number Slope ratio Time step Sub-aerial levees Pre-existing levee scour Instability from topographic low Stable Levees no no no No yes no no Yes yes no no Yes no yes no No no no yes No no no yes No yes yes no No yes no no Yes Role of River Mouth Bars Channel mouth bars formed in the time steps before each avulsion. Before avulsion two and three, a channel mouth bar formed at the mouth of the parent channel at time step 17 (Figure 15). This mouth bar stagnates quickly and becomes emergent at time step 19. The water level begins rising at time step 18 and continues to rise through time step 22, when the levees flood and avulsion is initiated. 20

22 Figure 15: A. Plan view of delta simulation three time steps after river mouth bar formation. The red line runs from the location of avulsion 2 in the south to the location of the mouth bar in the north. B. A graph of water surface elevation along this transect from the location of the avulsion to the location of the river mouth bar. Cool colors to warm colors are increasing time. The water level begins increasing at time step 18 until time step 22 when the levees flood in the location of avulsion. Note: The water flows uphill around the meander because velocity decreases here and kinetic energy of the flow velocity is transferred to potential energy of the increased water surface elevation. 21

23 Bed Shear Stress During the flooding of these levees, the bed shear stress increases as the water level rises over the levee upstream and downstream of avulsion two (Figure 16). Two crevasses form in the levee and the bed shear stress is highest at these two locations. The bed shear stress increases in one crevasse just before avulsion while it decreases in the other crevasse. The channel breaks through the levee at the location of increased cross-levee bed shear stress. Figure 16: A: Location of bed shear stress measurements. This is along the levee at the location of avulsion two. B: Bed shear stress profile along the levee through time. Cool colors to warm colors represent increasing time. 22

24 DISCUSSION The data show a wide range of slope ratios at the time of avulsion, but possibly this results from differing morphological conditions at the avulsion locations. The avulsion sites can be classified based on the stability of the levee. A stable levee is defined as being sub-aerial for multiple time steps before avulsion, and has no pre-existing channel scours in the levee to concentrate bed shear stress. An unstable levee is defined as being sub-aqueous for multiple time-steps before avulsion and/or has a pre-existing channel scour or topographic low from non-deposition compromising levee stability as the levee forms. When slope ratio is plotted against a qualitative axis of levee stability (Figure 17), two clusters are identified: a stable cluster and an unstable cluster. Figure 17: Slope ratio plotted against levee stability. There are two clusters: an unstable cluster (blue) and a stable cluster (green). 23

25 Avulsions two, three, and eight are in the stable cluster and have slope ratios between and Avulsions one, four, five, six and seven are in the unstable cluster and have slope ratios between 1.22 and The instability in the levees at the location of avulsions one, four, five, and six arises from the levees being sub-aqueous and in a few cases also having a channel scour. The levee at the location of avulsion seven is an outlier to this unstable cluster. The levees at this location are sub-aerial for many time steps for avulsion, but there is a pre-existing channel in the levee. This channel is flowing towards the southeast, while the flow in the channel is flowing the north. The avulsion occurs just upstream of this pre-existing channel and the new channel flows to the northeast. This occurred due to a concentration of shear stress just upstream of this new channel. The slope ratio at avulsion seven is 6.69, which is higher than the rest of the avulsions in the unstable cluster, but lower than the slope ratios of the stable cluster. The formation of a channel mouth bar downstream of avulsion two correlates to a rise in water level upstream. The water surface profile shows an increase over the whole transect but does show a wave of aggradation going upstream which may be a result of the low temporal resolution. At the location of avulsion two, we also show that the avulsion occurs at the location where the bed shear stress of flow over the levee is maximized for the longest duration. Future work is needed to confirm that river mouth bar stagnation is a trigger and that avulsion breaks through the levee at the location of highest bed shear stress of flow, because, these hypotheses were tested using only one delta simulation. To confirm these findings of slope ratio and viability of river mouth bar stagnation as a trigger, delta simulations with varying grain size distributions and basin slope need to be analyzed. 24

26 CONCLUSIONS 1) Based on a Delft3D simulation of delta evolution using seven grain sizes, basin slope of the Atchafalaya bay, and 1,000 m 3 /s discharge, avulsion is inevitable above a slope ratio of ~10. 2) Geomorphological differences in the levee play a large role in the critical slope ratio for avulsion. Avulsions that break though levees that are sub-aqueous and/ or have preexisting channel scours may require a much lower slope ratio than avulsions that break through stable levees. 3) River mouth bar stagnation is a plausible trigger for the imitation of channel avulsion. 4) Avulsion will occur along a levee at the location where the cross-levee bed shear stress in maximized for the longest time. ACKNOWLEDGMENTS I would like to thank Professor Douglas Edmonds of Boston College and his graduate student Rebecca Caldwell for help with setting up the delta simulation. I would also like my advisor Dr. Rudy Slingerland for his guidance and expertise in completing this senior thesis. REFERENCES Aslan, A., Austin, W.J., Blum, M, 2005, Causes of river avulsion: insights from the Late Holocene avulsion history of the Mississippi River, U.S.A Journal of Sedimentary Research v. 75 no. 4, p Edmonds, D.A., Hoyal, D.C.J.D, Sheets, B.A., Slingerland, R.L., Predicting delta avulsions: Implications for coastal wetland restoration. Geology. v. 37, p

27 Edmonds, D.A., and R.L Slingerland 2007, Mechanics of river mouth bar formation: Implications for the morphodynamics of delta distributary networks, Journal of Geophysical Research, v Edmonds, D.A, and Slingerland, R.L., Significant effect of sediment cohesion on delta morphology, Nature Geoscience. v. 3, p Gouw, M.J.P., 2007, Alluvial architecture of fluvio-deltaic successions: a review with special reference to Holocene settings, Netherlands Journal of Geosciences v. 86, p Hajek, E.A., Wolinsky, M.A, 2012, Simplified process modeling of river avulsion and alluvial architecture: Connecting models and field data, Sedimentary Geology, v , p. 1. Lesser, G.R., Roelvink, J.A, van Kester, J.A.T.M, Stelling, G.S., 2004 Development and validation of a three-dimensional morphological model, Coastal Engineering, v. 51, p McManus, John, 2002 The History of sediment flux to Atchafalaya Bay, Louisiana, Geological Society, London, Special Publications, v. 191, p Mohrig, D., Heller, P.L., Paola, C. Lyons, W.J., Interpreting avulsion process from ancient fluvial sequences; Guadalope-Matarranya system (northern Spain) and Wasatch Formation (Western Colorado). Geological Society of America Bulletin, v. 112(12), p Paola, C, Twilley, R.R, Edmonds, D.A, Kim, W, Mohrig, D, Parker, G, Viparelli, E, and Voller, V.R, 2011, Natural processes in delta restoration: application to the Mississippi Delta. Annual Review of Marine Science, v. 3, p

28 Sinha, R, 2009, The Great avulsion of Kosi on 18 August 2008, Current Science v. 97, p Slingerland, R.L. and Smith, N.D., Necessary conditions for a meandering-river avulsion. Geology v. 26, p Slingerland, R.L., and Smith, N.D., River avulsions and their deposits. Annual Review of Earth and Planetary Sciences v. 32, p Törnqvist, T.E, Bridge, J.S, 2002, Spatial variation of overbank aggradation rate and its influence on avulsion frequency, Sedimentology, v. 49, p Wellner, R, Beaubouef, R, Van Wagoner, J, Roberts, H, Sun, T, 2005, Jet-plume depositional bodies-the primary building blocks of Wax Lake Delta, Gulf Coast Association of Geological Societies Transactions, v. 55, p van Rijn, L.C. 1984, Sediment transport; part I, Bed load transport, Journal of Hydraulic Engineering, v. 110, p