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A visual model for predicting stream response of alluvial gravel-bed rivers Moscote, Nerissa Yarmilla 2002

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A VISUAL MODEL FOR PREDICTING STREAM RESPONSE OF ALLUVIAL GRAVEL-BED RIVERS by Nerissa Yarmila Moscote B.Sc.E., Queen's University, Kingston, 1997 A thesis submitted in partial fulfillment of the requirement for the degree of Master of Applied Science in The Faculty of Graduate Studies Department of Civil Engineering We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH C O L U M B I A December, 2002 © Nerissa Y l Moscote, 2002 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of CAV) I £ i / n g IhejPJKl^^ The University of British Columbia Vancouver, Canada Date JCASIA .Xll ; 3003 DE-6 (2/88) ABSTRACT In this thesis, a visual optimization model, RiverMod, has been developed to predict the channel geometry of alluvial gravel-bed rivers. The model is an extension of a previous model developed by Millar and Quick (1993b). The model is based on equilibrium theory, and also includes a bank stability analysis. The adjustment of the dependent variables of a river reach is quantified according to changes incurred by the independent variables. The primary dependent variables are channel width, depth and slope, and the primary independent variables are the discharge, flow resistance parameters, sediment size distribution and bank stability parameters. RiverMod, written in Visual Basic, provides a user interface that promotes clear and simple model usage for multiple runs with different sediment transport and flow resistance equations. The theory behind the Millar and Quick (1993b) model is discussed, as well as Millar's (2000) meandering-braiding transition and its incorporation into RiverMod. Four sediment transport equations and four flow resistance equations are included as part of the model. The model consists of fixed-channel-slope and variable-channel slope versions. The fixed slope version is equivalent to an experiment where the slope is fixed, and the channel width, depth and sediment transport rate adjust to the discharge. The variable slope version more closely approximates natural stream conditions. Each of these models can be applied to streams with cohesive or non-cohesive bank sediment. The model is applied to two gravel-bed rivers, located in British Columbia. The bank stability of both rivers has been decreased due to logging along the banks. RiverMod is used to quantify the impact of such a disturbance by analyzing past and present channel conditions. Restoration methods are suggested based on model output. This thesis provides a full description of theory underlying the model development and a description of model usage; therefore, this thesis is a complete user manual for the RiverMod optimization model. iii Table of Contents Abstract ii Table of Contents iv List of Tables viii List of Figures ix List of Symbols xii Acknowledgments xiii 1 INTRODUCTION 1.1 INTRODUCTION 1 1.2 USES OF THE MODEL 2 1.3 EQUILIBRIUM 3 1.4 TEMPORAL AND SPATIAL SCALES 3 1.5 INDEPENDENT AND DEPENDENT VARIABLES 4 1.5.1 Adjustment of the Dependent Variables 6 1.6 STREAM IMPACTS AND CHANNEL RESPONSES 7 1.6.1 Urbanization 8 1.6.2 Logging and Agriculture 10 1.6.3 Dams and Reservoirs 11 1.6.4 Mineral Extraction 12 iv 2 MODEL FORMULATION 2.1 THEORETICAL BASIS 21 2.1.1 Extremal Hypothesis 22 2.1.2 Constraints 22 2.2 SEDIMENT TRANSPORT 23 2.2.1 Einstein (1942), Einstein-Brown (1950) 25 2.2.2 Meyer-Peter and Miiller (1948) 27 2.2.3 Ackers and White (1973) 29 2.2.4 Parker, Klingeman and McLean (1982) 32 2.2.5 Discussion of Sediment Transport Equations 34 2.3 FLOW RESISTANCE 35 2.3.1 Manning (1891) 36 2.3.2 Composite Manning (Horton, 1933) 38 2.3.3 Keulegan (1938) 38 2.3.4 Jarrett (1984) 40 2.4 BANK STABILITY 41 2.4.1 Non-Cohesive Bank Sediment 42 2.4.2 Cohesive Bank Sediment 44 2.4.3 Effect of Vegetation on Bank Stability 46 2.5 PLANFORM GEOMETRY 47 v 3 TYPE OF ANALYSIS 3.1 I N T R O D U C T I O N 58 3.2 F I X E D - C H A N N E L - S L O P E MODEL 58 3.3 V A R I A B L E - C H A N N E L - S L O P E MODEL 59 4 USING RIVERMOD 4.1 I N S T A L L A T I O N 64 4.2 F I L E SETUP SCREEN 64 4.2.1 Open an Existing File 64 4.2.2 Creating a New File 65 4.3 MODEL SCREEN 65 4.4 E Q U A T I O N SCREEN 66 4.5 C O M P U T A T I O N SCREEN 66 4.5.1 Model Input 66 4.5.2 Model Output 68 4.5.3 Drop-Down Menu 70 4.5.3.1 File 70 4.5.3.2 Edit 71 4.5.3.3 Output 72 4.5.3.4 Microsoft Excel 74 vi 4.6 PLANFORM SCREEN 76 5 SAMPLE APPLICATIONS 5.1 INTRODUCTION 88 5.2 SLESSE CREEK 88 5.2.1 Investigation 89 5.2.2 Analysis 91 5.2.3 Results 92 5.3 NARROWLAKE CREEK 94 5.3.1 Investigation 95 5.3.2 Analysis 97 5.3.3 Results 98 References 111 vii List of Tables Table 2.1 Bedload transport formulae available in RIVERMOD (adapted from 34 Gomez and Church, 1989) Table 2.2 Values of Manning's roughness coefficient n for natural streams (Chow, 36 1959) Table 2.3 Summary of "best-fit" ks values derived from reach-averaged hydraulic 40 geometry (Millar, 1999) Table 3.1 Results of Millar (1994) active bank stability constraint investigation 61 Table 4.1 Minimum and maximum values for input variables 69 Table 5.1 Slesse Creek channel geometry (MacVicar, 1999) 89 Table 5.2 Input variables for Slesse Creek (adapted from MacVicar, 1999) 91 Table 5.3 Narrowlake Creek channel geometry 95 Table 5.4 Input variables for Narrowlake Creek (adapted from Wilson, 2001) 96 viii List of Figures Figure 1.1 Schematic representation of the graded condition in two time scales 13 Figure 1.2 Statistical model of a river system illustrating the influence of the 14 independent variables on the dependent variables (Hey, 1976 as cited by Hey, 1982) Figure 1.3 A schematic representation of two solution curves showing the optimal 15 geometry (Millar, 1994) Figure 1.4 Illustration of a dependent variable vs. time. 16 Figure 1.5 Idealized watershed showing three zones of erosion, transport and 17 deposition (Kondolf, 1997) Figure 1.6 Drainage net of Rock Creek in 1913, before modern urbanization and in 18 1964 after modern urbanization (Dunne and Leopold, 1978) Figure 1.7 Channel cross-sectional area at bankf ull vs. drainage area of both rural 19 and urban streams in Pennsylvania (Dunne and Leopold, 1978) Figure 1.8 Reduction in sediment supply from the catchment of the San Luis Rey 20 River due to the construction of the Henshaw Dam (Kondolf, 1997) Figure 2.1 Definition Sketch of a simplified trapezoidal channel for Millar and 50 Quick (1993) model (MacVicar 1999) Figure 2.2 A schematic representation of the armour layer in a gravel-bed 51 channel Figure 2.3 Comparison between observed and calculated data for Meyer-Peter 52 and Muller, Ackers and White, Einstein, and Parker, Klingeman and McLean formulae and Elbow River data (Gomez and Church, 1989) Figure 2.4 Relation between grain-size diameter and Manning's roughness 53 coefficient for channels in which the bottom and sides have different roughness characteristics (Horton, 1933) Figure 2.5 Relation of Manning's Roughness Coefficient to Hydraulic Radius 54 (Jarrett, 1984) IX Figure 2.6 Rivers of increasing sinuosity from straight to meandering (Thorne, 55 1997) Figure 2.7 Flowchart for the Planform Model 56 Figure 2.8 Definition sketch of one meander arc length (Millar, 1997; Sediment 57 Transport (CIVL 546) lecture notes - University of British Columbia) Figure 3.1 Flowchart for Millar and Quick (1993b) Fixed-Slope Model (MacVicar, 62 1999) Figure 3.2 Flowchart for Millar and Quick (1993b) Variable-Slope Model 63 (MacVicar, 1999) Figure 4.1 File Setup Screen 78 Figure 4.2 File Setup Screen with selected file name 79 Figure 4.3 Model Screen 80 Figure 4.4 Equation Screen 81 Figure 4.5 Computation Screen for Non-Cohesive Sediment with Einstein-Brown 82 and Keulegan equations in SI Units, using the Fixed Slope Model Figure 4.6 Computation Screen for Cohesive Sediment with Ackers and White 83 and Composite Manning equations in SI Units using the Fixed Slope Model Figure 4.7 Supplementary Output Screen for (a) Non-Cohesive Sediment Model; 84 (b) Cohesive Sediment Model Figure 4.8 Search Screen showing Cohesive Sediment Model Options 85 Figure 4.9 Planform Screen 86 Figure 4.10 Microsoft Excel Spreadsheet with values appended from RIVERMOD 87 Figure 5.1 Location of Slesse Creek Watershed (MacVicar, 1999) 100 Figure 5.2 Airphoto of Slesse Creek (MacVicar, 1999) 101 x Figure 5.3 Slesse Creek lower watershed, showing study reach D in 1936 102 (MacVicar, 1999) Figure 5.4 Slesse Creek calibration, width (W) vs. modified friction angle (<()') 103 Figure 5.5 Restoration of Slesse Creek, altering <t>' (Dsobank = 0.133 m) 104 Figure 5.6 Restoration of Slesse Creek, altering Dsobank 0t>' = 40°) 105 Figure 5.7 Location of Narrowlake Creek Watershed 106 Figure 5.8 Airphoto of Narrowlake Creek (Wilson, 2001) 107 Figure 5.9 Narrowlake Creek calibration, width (W) vs. modified friction 108 angle (<(>') Figure 5.10 Restoration of Narrowlake Creek, altering (j)' (Dsobank = 0.047 m) 109 Figure 5.11 Restoration of Narrowlake Creek, altering Dsobank ( f = 40°) 110 xi List of Symbols A - cross-sectional area A = function of grain diameter (Ackers and White) a = empirical coefficient C - function of grain diameter (Ackers and White) c = soil cohesion Cx = constant (Keulegan) d = depth D = sediment grain size D35 = thirty-fifth percentile bed surface grain diameter O50 = median bed surface grain diameter dso = median sub-surface grain diameter C>50bank = median bank grain diameter of non-cohesive sediment D90 = ninetieth percentile bed surface grain diameter Da = average bed surface grain diameter D g r = grain diameter (Ackers and White) Dx = characteristic grain diameter, where x is % of sediment finer F = fall parameter (Einstein-Brown) f = Darcy-Weisbach friction factor F g r = sediment mobility number (Ackers and White) xii F> = Froude number F S H = factor of safety for mass failure F S T = factor of safety for fluvial erosion g = gravitational acceleration (assumed = 9.81 m/s2) <5b = sediment transport capacity gb* = dimensionless transport rate &bca\c - sediment transport capacity Gbf = bankfull sediment transport capacity G g r = sediment transport (Ackers and White) H = vertical bank height H = Hammer number Hcrit = maximum stable value of H, I = input of sediment at upstream end of channel i'b = specific bed load transport rate (dry weight) (Gomez and Church, 1989) KB = component of the reducing multiplier (Meyer-Peter and Muller) KG = component of the reducing multiplier (Meyer-Peter and Muller) ks = equivalent roughness ' = distance along valley axis L = distance along meander arc length m = function of grain diameter (Ackers and White) n = function of grain diameter (Ackers and White) xiii n = Manning's roughness coefficient tibank = Manning's roughness coefficient for the bank sediment nbed = Manning's roughness coefficient for the bed sediment N s = dimensionless stability number O = output of sediment at downstream end of channel Pbank = bank perimeter Pbed = wetted perimeter of bed Q = discharge Qbf = bankfull discharge qs = sediment discharge rc = radius of curvature Rh = hydraulic radius S = sediment storage S = channel slope S* = transition slope SF = shear force s s = specific gravity of sediment (assumed = 2.65) S v = valley slope U* = shear velocity U,u = mean velocity W = width of channel xiv X = sediment f lux (Ackers and White) Y = depth of channel A = change O = maximum deviation angle along channel G>* = transport parameter (Einstein-Brown) <j>' = modified f r ic t ion angle <(>5o = shear s t ress ratio (Parker, Klingeman and McLean) y = unit weight of water y s = unit weight of sediment Yt = saturated unit weight of soil A, = meander wavelength u = dynamic viscosity v = kinematic viscosity 6 = bank angle Pf = f luid density p s = sediment density x = shear stress x* = dimensionless bed shear s t ress tbank = mean bank shear s t ress Tbed = mean bed shear s t ress tent = cr i t ical shear s t ress fo r fluvial erosion of bank sediment xv T d s o = bed shear stress for the median sub-surface grain size (Parker, Klingeman and McLean) co* = dimensionless bedload transport rate (Parker, Klingeman and McLean) £ = sinuosity ^c = sinuosity calculated using the sine-generated curve v|/ = ratio of forces acting on a particle xvi ACKNOWLEDGEMENTS I would like to thank my supervisor Dr. Robert Millar for his contribution to this thesis. Many other people at the University of British Columbia provided valuable assistance. Edmond Yu answered all my questions about Visual Basic, Andrew Wilson provided all sorts of data concerning Narrowlake Creek and Aleteia Greenwood helped me find all the references used in this thesis. I am grateful to Rafael Ayax Moscote, Norma Moscote and Diana Lavery for their constant support. I am grateful to Mary Ellen Mulligan for her support and excellent editing. Thank you Waverley Mei for working on your thesis while I worked on mine. Thank you Reimy for being born at just the right time. Thank you Ryan for the juice, for believing and so much more. —xiii--Chapter 1 INTRODUCTION 1.1 INTRODUCTION This project is an extension of a hydraulic geometry model developed by Millar and Quick in 1991, 1993 and 1998. Millar developed "a static analytical model based on previous optimization formulations (Millar (1991), Chang (1980), White et al. (1982))". The model is an optimization model which incorporates the effects of bank-stability on the hydraulic geometry of alluvial gravel-bed rivers. The original model, written using Basic, is not very flexible, is difficult to use and is therefore used primarily as a research tool. The computer program described in this thesis, named RiverMod, was written using Microsoft Visual Basic. It combines four separate, related models and includes several new features. It is visual, user-friendly and includes: (i) Four sediment transport relations (ii) Four flow resistance equations (iii) A planform model (iv) A user-interface for input and output of data (v) Compatibility with Microsoft Excel (vi) The ability to save, rewrite and group files 1 RiverMod applies to Single-thread alluvial gravel-bed rivers with mobile beds that have the capacity to modify their channel dimensions (Millar, 1994). The assumption that the model treats the river as an equilibrium system forms the basis for the optimization model. 1.2 USES OF THE MODEL The model has two primary applications: I t has proven to be both an effective teaching and research tool. The following is a list of possible uses: (a) River adjustments: RiverMod can help interpret river adjustments by helping researchers and students gain a further understanding into the behaviour of rivers and also predict future changes. (b) Activities that impact rivers: The model can aid in monitoring the effects of disturbances such as urbanization, agricultural development, the construction of dams and reservoirs and logging on river channel geometry. The effects of natural processes such as wild f ire or climate change can also be studied. (c) Sensitivity Analysis: The model can be used to run a sensitivity analysis in order to determine how sensitive a variable is to a particular activity. (d) Calibration: The program can also be calibrated to the observed geometry. This can assist in the determination of a variable which is hard to measure with field evaluations. 2 1.3 EQUILIBRIUM RiverMod analysis can be applied to a reach of a river considered to be in equilibrium. For the purposes of this study, a channel will be considered to be in equilibrium when the following conditions are met (Millar, 1994): (i) "The mean hydraulic geometry of the channel reach remains unchanged over an appropriate time scale for which a steady-state equilibrium can be assumed. (ii) There is no net erosion or deposition along the reach. (iii) Any perturbations from equilibrium geometry will be offset and the equilibrium geometry restored." 1.4 TEMPORAL AND SPATIAL SCALES A reach of a river can be said to be in equilibrium when continuity is conserved during specific temporal and spatial scales. Three principal time scales should be considered: Engineering time, which usually spans between 100 and 200 years; geomorphic, or graded time, which is usually less than 10,000 years and; geologic time, which is usually greaier than 10,000 years. For example, over a geologic time frame, the slope may appear to be constantly changing i.e. adjusting toward equilibrium. But in the short-term, the slope will appear to have reached a state of approximate equilibrium (see Figure 1.1). 3 Adjustments needed to achieve grade usually occur over several decades or over hundreds of years. RiverMod analysis applies to engineering time scales over which a reach or a river can be considered to be in an approximate equilibrium. Equilibrium of a specific system depends on the spatial scale. Generally, an entire river will not be in equilibrium, but certain reaches of the river may be. The term "reach of a river" is usually used because different reaches of the same river may exhibit different channel patterns and therefore different ultimate graded conditions at the same point in time. 1.5 INDEPENDENT AND DEPENDENT VARIABLES In order to study the way in which rivers adjust their form and dimensions, the variables defining the hydraulic geometry of the channel must be identified and the independent and dependent variables must be specified (Hey, 1982). An independent variable is imposed externally on the system; a dependent variable is determined by the value of the independent variables (Vanoni, 1975). I^ac\/\car (1999) defines the independent variables as those imposed on the reach, namely: climate, geology, runoff, vegetation type, vegetation density, and relief. Climate, geology and runoff determine the discharge, sediment size and sediment yield. Bank stability is controlled by the vegetation type and density and relief determines the valley slope. At the decade time scale, the independent variables become: discharge of water, 4 sediment discharge, sediment size, bank stability (bank vegetation and soil properties) and valley slope. The dependent variables are hydraulic geometry variables which respond to changes in the imposed independent variables. The primary dependent variables can be considered to be width, depth and bed slope. Other secondary dependent variables, which can be determined from the primary ones are velocity, sinuosity, meander arc length, maximum depth and height of bedforms (MacVicar, 1999). Figure 1.2 is a statistical model of a river system which illustrates the relationship between the dependent and independent variables (Hey, 1976 as cited by Hey, 1982). Any significant change in the independent variables will produce a new regime channel geometry which corresponds to the modified values of the controlling variables. When the channel is again stable, it will be defined by the new independent variables (Hey and Thorne, 1986). When using RiverMod to analyze a river reach, the water and the sediment discharges constitute primary independent variables. The channel slope, width and depth constitute primary dependent variables (Vanoni, 1975). RiverMod attempts to quantify channel changes. The independent variables are input into the model and the corresponding dependent variables are estimated. In this way changes in both the dependent and independent variables of the river system can be simulated. 5 1.5.1 Adjustment of the Dependent Variables The dependent variables are mutually dependent and a river may adjust its width, depth and slope simultaneously (Henderson, 1966). There are three main governing equations for a river system associated with the independent variables. They are the flow resistance equation, the sediment transport equations and a bank stability relation (Henderson, 1966). Although there are an infinite number of combinations of width, depth and slope values for the given independent variables, Gilbert (1914) has shown through flume experiments that these may still be tending toward an optimum determined by the independent variables. The optimum is assumed here to represent an equilibrium condition. Figure 1.3 is a schematic representation of two solution curves illustrating the theory behind Gilbert's (1914) flume experiments. In Figure 1.3(a) discharge and slope are held constant and an optimum width develops which corresponds to the maximum sediment transporting capacity, similar to Gilbert's flume experiments, described above (Gilbert, 1914). In Figure 1.3(b) discharge and sediment transport are held constant and the optimum is now at the minimum slope. This second case mimics the behaviour of most natural rivers over engineering time scales (Millar, 1994). When a channel responds to a disturbance or a change in the independent variables, generally, the fastest changing dependent variables are the depth and the width. The slope is the slowest of these three variables to change (Booth, 1990). Figure 1.4 illustrates the dependent variables of the river initially fluctuating about the 6 equilibrium condition, until a large change is imposed. During adjustment to a new, post-disturbance equilibrium, the channel passes through a transient adjustment phase. The non-equilibrium transient phase could persist for years, or decades. Figure 1.4 also shows that at any point during the pre-disturbance stage, the dependent variables may not be in constant equilibrium, but may be in equilibrium in a statistical or average sense. 1.6 STREAM IMPACTS AND CHANNEL RESPONSES The river system, viewed as an ideal watershed, can be divided into three zones of erosion, transport and deposition (see Figure 1.5). The transport of sediment is continuous and any changes , or disturbances, which affect any reach within the catchment may affect the river downstream (Kondolf, 1997). Occasionally, cessation of the disturbance will return the stream back to its natural conditions. However, more often, "although riparian pressures have been removed, continued disturbance on a watershed scale may limit the ecological conditions and override the influence of channel adjustments" (Magilligan and MacDowell, 1997). The following sections discuss the independent variables, stream impacts and subsequent channel responses . (a) Peak flow discharge: Channels adjust to the dominant discharge, which is at or near bankfull discharge (about the 2-year flood), when most sediment transport occurs (Werritty, 1997). 7 (b) The sediment load and calibre: The sediment supply and the size of the bed material will likely be a f f e c t e d by any change that produces an instabil ity in the flow regime (Hey and Thorne, 1986). (c) Bank stabi l i ty : The bank type (cohesive or non-cohesive) determines whether the channel is more susceptible to fluvial erosion or mass fai lure. Both fluvial erosion and mass fai lure may be functions of parameters such as vegetation (Mil lar, 1994; MacVicar , 1999). (d) The valley slope: The valley slope is considered relatively constant in engineering t ime scales; the re fo re , channel changes and impacts will only be discussed as they pertain to bank-ful l discharge, the sediment load and calibre, and the bank stabil i ty. 1.6.1 Urbanization Urbanization near a stream of ten signifies more impervious areas in the vicinity of the stream. Typical examples of urban development include the construction of paved s t ree ts and sidewalks, sewers, houses and other buildings, and parking lots. Sur face cover might initially increase the sediment load during construction (Dunne and Leopold, 1978) and later decrease the availability of sediment and increase the amount of water reaching the stream, causing increased channel erosion or stream incision (Macklin and Lewin, 1997). 8 Although there may be an mcrease in the volume of runoff reaching the stream, many tributaries intended to carry runoff toward a channel, may get buried or eliminated. This might result in the disappearance of many smaller channels that under natural conditions assisted in keeping both sediment and runoff distributed. Rock Creek located in the Washington, D.C. Area, provides an example of such an event. Figure 1.6 shows the drainage net for this creek in 1913 and 1964, both before and after modern urbanization (Dunne, and Leopold, 1978). Figure 1.7 shows a graph of channel cross-section vs. drainage area for both rural and urban streams in Pennsylvania. I t shows that rural streams have, on average, smaller cross-sections than their urban counterparts of similar size (Dunne and Leopold, 1978). Another recent study comparing rural and urban catchments in southeastern Pennsylvania found that, overall, urban streams were wider and straighter than their rural counterparts (Pizzuto, et al., 2000). The bankfull sediment load may Increase or decrease depending on the type of development. During the development stages, effects such as land clearing may temporarily increase the sediment load, but once development is completed, if the area is well paved, the sediment load may decrease. The median grain-size (D50) is usually utilized as an indicator of the distribution. I t is a very difficult parameter to predict because the nature in which it is affected depends very highly on the type of development and the D50 of any new materials introduced to the system, or any materials removed from the system. Therefore in most cases it is assumed to remain constant (Personal 9 Communication, Millar, 1998; Human Impacts on River Systems (CIVL 598) lecture notes -University of British Columbia). The effect of urbanization on bank stability is also difficult to predict. Post-development stabilization of the banks would increase the bank stability. Without it, with the removal of riparian vegetation it would decrease. 1.6.2 Logging and Agripulture In forested drainage basins, trees are normally cut down in order to use the wood or for farming or grazing to take place (Macklin and Lewin, 1997). (a) Logging: The most obvious effect of logging activity is the increase in sediment load conveyed into the channel. Large amounts of disturbed soil from increased activity, coupled with the upheaval of tree-root systems, cause channel instability by increasing the occurrence of mass soil movements and landslides, which can then increase the sediment load (Dunne and Leopold, 1978). The sediment size would probably remain unchanged, since any incoming sediment would consist of a larger quantity of the same source. In most areas affected by logging, bank stability is decreased. Buffer strips of adequate size, left adjacent to the streambanks, might reduce the impact of deforestation. Logging usually reduces the amount of large woody debris (LWD) in a 10 channel, further reducing the bank stability, since LWD can partially armour banks, add to channel roughness and act as a sediment trap. (b) Agriculture: Land is often cleared of trees to facilitate cultivation or grazing; therefore, the initial stages of agricultural development may have similar effects on a channel as logging. If land clearance spreads to steeper slopes, gullying and mass wasting can increase the proportion of coarse material entering the channel (Clark and Wilcock, 2000), and therefore change the grain-size distribution of the stream. This can adversely affect those species of wildlife dependent on the stream. Magilligan and McDowell (1997) conducted a study which investigated the geomorphic adjustment following the removal of cattle grazing. They observed that in those catchments where cattle grazing had been removed for at least 10 years the bankfull and low flow widths had narrowed and the bed had been remobilized into more pool area. 1.6.3 Dams and Reservoirs The primary effect the construction of a dam would have on a channel is the interruption of the sediment transport of the river. The bedload and all or some of the sediment load is trapped upstream of the dam in the reservoir. The water released by the dam may then erode the bed and banks downstream of the dam, decreasing the bank stability and reducing the total sediment load of the system. Figure 1.8 shows the 11 predicted natural yield of a river and the actual yield after dam construction. The actual yield is markedly less than the predicted natural value (Kondolf, 1997). Increased erosion could possibly change the particle size of the bed. In a gravel-bed river this could signify larger grains downstream of the dam. This can threaten salmonid spawning sites if the bed becomes so coarse that the fish can no longer move the gravel (Kondolf, 1997). 1.6.4 Mineral Extraction (a) Instream Gravel Mining: Instream gravel mining - the extraction of gravel directly from the stream bed - may cause channel incision upstream and downstream of the mining site, due to sediment shortage, coarsening of the bed, and lateral channel instability. (b) Metal Mining: Before mining legislation, waste from mine sites was discharged directly into the nearest channel, altering the entire fluvial system. Changes include: hindering vegetation growth along the banks, negatively affecting the bank stability; changes in channel pattern over short periods of time (Macklin and Lewin, 1997); and the presence of toxic materials in the fluvial system due to the extraction and processing of metal ores for up to thousands of years (Macklin, 1996). 12 e q u i l i b r i u m 10,000 time (years) a s s u m e d e q u i l i b r i u m 200 time (years) Figure 1.1. Schematic representation of the graded condition in two time scales, (a) The dotted line represents the graded condition the river is trying to adjust to through changes in its slope, (b) This is a close-up of the box shown in (a). The scale is much and over 200 years the river may be said to be in equilibrium (represented by the dotted line). 13 V A L L E Y S L O P E S I N U O S I T Y V E L O C I T Y + + + + T + B E D A N D B A N K S E D I M E N T C H A N N E L S L O P E D I S C H A R G E H Y D R A U L I C R A D I U S S E D I M E N T O U T P U T It W E T T E n P F R I M E T E R O U T P U T / I N P U T S E D I M E N T I N P U T Figure 1.2. Statistical model of a river system illustrating how the dependent variables are influenced by the independent variables. Valley Slope, Bed and Bank Sediment, Discharge and Sediment Input are the independent variables (located in the four corner boxes). A "+" indicates the two variables are directly related. A "-" indicates the two variables are inversely related (Hey, 1976 as cited by Hey, 1982). 14 (a) (b) Width Figure 1.3. A schematic representation of two solution curves showing optimal geometry, (a) Discharge and slope are held constant and an optimum width develops which corresponds to the maximum sediment transporting capacity, (b) Discharge and sediment load are held constant and the optimum occurs at the minimum slope (Millar, 1994). 15 dependent variable p r e - d i s t u r b a n c e t r a n s i e n t p o s t - d i s t u r b a n c e phase time Figure 1.4. Illustration of a dependent variable vs. time. The equilibrium pre-disturbance stage, transient phase and post-disturbance stage are visible. The fluctuations about the equilibrium condition can be seen in both the pre- and post-disturbance stages. It is difficult to predict the precise path of the transient phase. 16 Figure 1.5. Idealized watershed showing three zones of erosion, transport and deposition (Kondolf, 1997). 17 Figure 1.6. Drainage net of Rock Creek in 1913, before modern urbanization and in 1964 after modern urbanization (Dunne and Leopold, 1978). 18 Figure 1.7. Channel cross-sectional area at bankfull vs. drainage area of both rural and urban streams in Pennsylvania (Dunne and Leopold, 1978). 19 •J} t o o 2 c E <D CO 01 . 3 o e S> 6 h NATURAL YIELD \ 1940 A C T U A L YIELD (WITH D A M EFFECT) i 1950 I960 1970 Figure 1.8. Reduction in sediment supply from the catchment of the San Luis Rey River due to the contruction of the Henshaw Dam (Kondolf, 1997). 20 Chapter 2 MODEL F O RMU L A T ION In this chapter the analytical basis for RiverMod is discussed, and the algorithms used to determine sediment transport, flow resistance, bank stability and planform geometry are formulated. 2.1 THEORETICAL BASIS The model presented in this thesis is an extension of a previous model developed by Millar and Quick (1993, 1998) and Millar (2000). I t models the hydraulic geometry of an alluvial gravel-bed channel. The main contribution of this model, as compared with previous ones, is the fact that it assesses the bank stability of the channel. The model operates under the assumption that a river will tend toward an equilibrium geometry. The dependent variables adjust according to the independent variables in order to reach an optimum geometry which Satisfy the discharge, the bank stability and the bedload constraint. The channel is assumed to have a trapezoidal cross-section (see Figure 2.1). 21 2.1.1 Extremal Hypothesis There are seven channel geometry equations mentioned in Mi l lar and Quick (1993b) and eight principal dependent variables. The equations are fo r flow resistance, continuity, velocity, mean bank shear stress, mean bed shear s t ress , bank stabi l i ty and sediment transport . The variables are bed width (W) or perimeter (P), channel depth (Y), channel slope (5), f r ic t ion factor (f), mean velocity (u), mean bed shear stress (ibed), mean bank shear st ress (thank), and bank angle (6) As there are more variables than there are equations to solve fo r the variables, an additional relation is necessary. An "extremal hypothesis" is introduced which states that "the channel geometry will adjust until the sediment transport capacity of the channel is equal to the value supplied f rom upstream" (Millar and Quick, 1993b). The extremal hypothesis allows an optimum solution to be obtained. The main function of the model is to solve the seven equations with the extremal hypothesis in order to obtain an optimum channel geometry, performed by a computer routine. 2.1.2 Constraints There are th ree constraints that must be sat is f ied in order to f ind an optimum hydraulic geometry fo r a given channel. These are bedload, discharge and bank stabi l i ty constraints. The bedload constraint ensures that the channel is in equilibrium, and the 22 sediment load is transported through the reach without net deposition or erosion (Millar, 1994). The discharge constraint ensures the discharge capacity of the channel is equivalent to the bankfull discharge (Qbf), given by: UA = Qbf (2.1) where U is average velocity, A is cross-sectional area and Qbf is bankfull discharge. The bank stability constraint ensures that the banks are stable with respect to both mass failure and fluvial erosion. 2.2 SEDIMENT TRANSPORT Hans Albert Einstein defined a bedload formula as "an equation linking the rate of bedload transportation with the properties of the grain and of the flow causing the movement" (Einstein, 1942). Bedload is fluvial sediment transported along the bed of a channel by rolling, sliding or saltation. I t is very difficult to accurately measure the bedload transport rate of gravel-bed rivers, and we are generally forced to rely on predictive relationships. At present, no universal bedload transport equation exists (Reid eta/., 1997). Einstein (1950) sums up one main reason: "sediment movement and river behaviour are inherently complex natural phenomena involving a great many variables". So far, the development of bedload transport equations has relied on empirical and experimental work, mostly carried out in flume studies employing uniform bed materials (Reid et al., 23 1997) even though most natural gravel-bed rivers tend to have non-uniform bed material size distributions. Another obstacle in the quest for a universal bedload transport formula is the fact that the existing formulae can only be tested with field data (Reid et al, 1997). RiverMod contains four established, well-known sediment transport equations. Einstein-Brown (1950), Meyer-Peter and Muller (1948), Ackers and White (1973) and Parker, Klingeman and McLean (1982). These particular equations were included in RiverMod because: 1. The parameters required as input variables are usually readily available, or easy to measure; 2. The parameters they require are similar to each other, and therefore it is easy for the user to use more than one equation with available data; 3. The equations are all well-established and well known and have each been included in several comprehensive reviews of bedload transport equations; 4. The user can compare the different answers obtained by using the different sediment transport relationships; 5. The conditions under which a particular equation was derived might be similar to the conditions of the river reach in question. In the fixed slope model within RiverMod, the bedload transport equation is used to determine the sediment transport capacity (in kg/s or Ibs./s) of the stream. In the variable slope model, the sediment transport capacity becomes an input variable and it is 24 used in conjunction with the selected transport equation to determine the slope of the stream. Gomez and Church (1989) expertly summarize the general assumptions, which are usually followed when applying bedload transport formulae; (i) that the flow, sediment properties and bedload transport rate are constant for the period in question; (ii) that the bedload transport rate is a unique function flow and sediment parameters; (iii) that the maximum amount of bedload is being transported. 2.2.1 Einstein (1942). Einstein-Brown (1950) Einstein originally developed an empirical bedload equation in 1942, which he replaced in 1950 with an analytical version (Gomez and Church, 1989). Also in 1950, Rouse, Boyer and Laursen modified Einstein's 1950 function and named it after Brown, author of Chapter XII of the book Engineering Hydraulics(Rouse (ed), 1950, as cited in ASCE Task Committee, 1971). Most bedload transport equations are based on the theory that transport is a function of the excess of a flow quantity above the threshold value for initiation of motion of the sediment particles in a channel bed. The Einstein formula is an important exception to this trend. Based on numerous experiments on bedload, Einstein concluded that "a distinct condition for the beginning of transportation does not seem to exist" 25 (Einstein, 1942). There is a continuous relationship between bedload transport intensity and flow intensity (Reid et al, 1997). The original equation was developed as an empirical relation based on the probability of particle movement (Gomez and Church, 1989). F= - + 3 6 1 / 2 - 3 6 1 / 2 (2 2) * 1 qs Pf F(p,~ Pf)9t*\P.- Pf 9A& (2.3) y = P , - l , _ g _ ( 2 4 ) Pf 5 R H Where F is a parameter for settling velocity, gb* is the dimensionless transport rate, u/ is the ratio of the forces acting on a particle, v is kinematic viscosity, g is gravitational acceleration, pf is fluid density, p s is sediment density, D is the sediment grain size, q s is sediment discharge, S is channel slope and Rh is hydraulic radius. Note that the dimensionless bed shear stress (T*) and u/ are inversely proportional to each other. The dimensionless transport rate (gb*) is calculated using: 26 / / r* < 0 g* = 0 (2.5) / / 0 < r* < 0.093 g* = 2.15e~°'39^ (2.6) ifr*> 0.093 #,* = 40(r*) 3 (2.7) The sediment transport capacity (in kg/s) is determined using: * L = * - ^Ao (2-8) 2.2.2 Meyer-Peter and Muller (1948) The Meyer-Peter and Muller formula is an extension of the Meyer-Peter formula derived in 1934 (Gomez and Church, 1989). It is an empirical law of bedload transport based on experimental data. This formula is exclusively for the movement of bedload and suspended load is not considered (Meyer-Peter and Muller, 1948). /Q YS - 0.047 (ys - r) . r J r s - r (2.9) 27 26 1 (2 .10 ) n u 1 (2.11) y*AS X n where ib is specific bedload transport rate, y is the unit weight of water, y s is the unit weight of the sediment, Q B / Q is a reducing multiplier which accounts for the amount of discharge acting on the bedload, KB / K S is a reducing multiplier which accounts for form resistance, V is the depth of the channel, D90 is the ninetieth percentile bed surface grain diameter, u is mean velocity, n is Manning's roughness coefficient and n' is Manning's grain roughness coeffcient. Meyer-Peter and Muller concluded that the initiation of motion is dependent on a certain magnitude of the shear stress. They also utilize two different grain diameters in their calculations, D90 and Da. This is to account for the difference in composition between the grain composition of the stationary bed and that of the mobile bed. The description of the procedure used by RiverMod to calculate the sediment transport capacity follows. First, the grain fAonnmq's n (n'), is calculated using: (2.12) 26 28 Next the dimensionless bed shear is determined, applying: f/0 r \ T {rOa(ss-l)j (2.13) Then, the value of t* is evaluated, in order to determine the dimensionless bedload (gb*) using: //*-*'< 0.047 gb* = 0 (2.14) //*-*'> 0.047 _>6* = 8(r*'-0.047)3^ (2.15) Equation 2.9 can be reduced to Equation 2.15 by assuming KB/KG = 1 for planar beds and Q B / Q = 1 for wide channels and by substituting values of ys - 26000 N/m3, y = 9800 N/m3 and g = 9.8 m/s2 (Gomez and Church, 1989). And finally, the sediment transport capacity (in kg/s) can be determined using: * L = * V ^ V ^ W (2-16) 2.2.3 Ackers and White (1973) Ackers and White developed a new framework for the analysis of transport data (Ackers and White, 1973). It is based on both dimensional analysis and physical arguments. They derived three key dimensionless parameters F g r (sediment mobility number), D g r (grain diameter) and G g r (sediment transport) (Ackers and White, 1973). Their formulae can be seen below. 29 4 = GgrYs u gr (2.17) gr gr / v / A - J -1 (2.18) 0 =D 9<-(2.19) u: ,1-n u 32log(10% (2.20) (Gomez and Church, 1989). Where u* is shear velocity, and A, C, m and n are all dimensionless functions of the grain diameter. For coarse sediments (Dgr > 60), where only bedload is being transported, the four parameters are all constant: n = 0; A = 0.170; m = 1.50; C = 0.025 For mixed transport (1 < Dg r < 60), parameters are calculated using: n = 1 - 0.56logO, gr (2.21) A = 0.23/ V / 9r J 0.14 (2.22) m = 9.66/ + 1.34 (2.23) £ _ jQ(2.86logO^.-( log^) 2 -3.53) (2.24) 30 During field analysis, Ackers and White concluded that the D35 bedload value was the "most appropriate when making predictions of total sediment load" (Ackers and White, 1973). The Ackers and White method for predicting bedload transport is useful for grain sizes larger than 0.04 mm. It seems to be fairly accurate when predicting initiation of motion, although the authors caution against its use in unsteady flow conditions. The description of the procedure used by RiverMod to calculate the sediment transport capacity follows. The dimensionless grain diameter (Dgr) is first calculated, using Equation 2.19. Then the sediment mobility number (Fg r) A, C, m and n are calculated using Equations 2.20-2.24. Next the sediment flux (X) is calculated using: X = 5 A ^ r (2.25) v U , Ggr is determined using Equation 2.18 and U*, the shear velocity and calculated using: U* = V_^5 (2.26) And finally, the sediment transport capacity (in kg/s) can be determined using: e b , =XQ (2.27) 31 2.2.4 Parker, Klingeman and McLean (1982) The Parker, Klingeman and McLean formula takes the form: 4 = 14001 Ys (2.28) // </>5Q < 0.95 a* = 0 (2.29) // 0.95 < ^ 5 0 < 1.65 co* = 0.0025exp[l4.2(<z)50 -1) - 9.28(^50 -1) 2] (2.30) if K > I - 6 5 co' 11.2 f 0 .822^ V 5^0 J (2.31) "50 0.0876 (2.32) (2.33) (Gomez and Church, 1989). Where <b50 is a shear stress ratio, co* is the dimensionless bedload transport rate, Td5o is the bed shear stress for the median sub-surface grain size, i is shear stress, dso is the median sub-Surface grain diameter and Ss is the Specific gravity of the sediment. This formula was the first to account for an armour layer and its effect on bedload transport rates, which is present in almost all gravel rivers (see Figure 2.2). 32 Bakke et al. (1999) define the layer termed "armour" or "pavement" as the layer extending to "the bottom of the largest surface particle". The "subarmour" or "subpavement" was identified as the layer just below the pavement of equal thickness. Based solely on field work, the empirical relations for the dimensionless bedload transport (co*) were derived from bedload measurements from Oak Creek (Parker et al., 1982), a small, steep gravel-bed stream in Oregon. Parker et al. (1982) theorized that the armour layer varies with shear stress and sediment load and that for conditions exceeding the critical stress of the pavement, the bedload grain size distribution of the pavement is approximately the same as that of the subpavement, so that: D50 ~ dso They developed the "equal mobility hypothesis", which states that surface coarsening develops to render all size fractions equally mobile (Parker et al, 1982) once the critical condition for movement was exceeded (Gomez and Church, 1989). If an equilibrium condition develops, a balance has been achieved between the bed material supply and the transporting capacity of the reach (Bakke et al, 1999). The description of the procedure used by RiverMod to calculate the sediment transport capacity follows. First, the shield's stress for median diameter of the subpavement (Td5o) is calculated using Equation 2.32. Next the shear stress ratio (q>50) is determined, using Equation 2.33. Then, Equations 2.29 - 2.31 are used to compute the dimensionless bedload transport (co*). And finally, the sediment transport capacity (in kg/s) can be determined using: 33 * L = M * ^ Aed^g{ss-\)d^ (2.34) 2.2.5 Discussion of Sediment Transport Equations Table 2.1 summarizes the sediment transport equations discussed in the preceding sections. Table 2.1. Bedload transport formulae used by RiverMod (adapted from Gomez and Church, 1989) Formula Particle Size Range (mm) employed in derivation Comments Meyer-Peter and Muller (1948) 0.40 - 28.65: uniform sediments, mixtures and light-weight materials "should be used for pure bedload transport. Solid material rolling or jumping along the bed of a river" (Meyer-Peter and Muller, 1948) Parker, Klingeman and McLean (1982) 0.60 - 102.0: natural mixture (field data) "restricted to small-to-medium-sized paved gravel bed streams with steep or moderate slopes, which are not dominated by sand load" (Parker et al., 1982) Ackers and White (1973) 0.04 - 4.94: uniform sediments and light-weight materials. dimensional analysis and physical arguments were used to develop this general function (Ackers and White, 1973) Einstein (1942,1950) 0.785-28.65: uniform sediments and light materials restricted to steady, uniform flow, plane bed conditions (Gomez and Church, 1989) In 1989 Gomez and Church conducted an extensive review of 12 well-known sediment transport formulae for gravel-bed rivers. The review tested each equation with four sets of river data and three sets of flume data with maximum consistency in all tests conducted. The survey illustrated the fact that very different results can be obtained, depending on which sediment transport equation is used. 34 Figure 2.3 shows a comparison between observed and calculated data using the data from the Elbow River, a gravel-bed channel. It also demonstrates that any sediment transport equation used will perform better if the conditions of the reach in question are similar to the conditions under which the particular formula was derived. These predictive relationships should be used in conjunction with another form of analysis, including, but not limited to, laboratory experiments, the use of air photos and field work. 2.3 FLOW RESISTANCE Many equations have been proposed to relate average velocity in open channels to flow resistance (Hey, 1979). RiverMod uses four flow resistance relationships to establish the average velocity of the flow through and iterative process, ultimately determining the width and slope of the channel. The four relationships are Manning (1891), Composite Manning (Horton, 1933), Keulegan (1938), and Jarrett (1984). Because each channel has its own characteristic bedforms, profiles, flow resistance and sediment transport, it is important to use a resistance equation which has been designed for use with a similar channel to the study channel (Bathurst, 1978). In order to obtain the velocity and ultimately the channel dimensions, the bankfull discharge, channel slope, grain size distribution and roughness coefficient (except for Jarrett (1984) Equations) are needed (Bathurst, 1997). 35 2.3.1 Manning (1891) The Manning formula, which was presented in 1891, is the most widely used of all uniform-flow formulae for open-channel flow computations (Chow, 1959). It is known in many countries under several combinations of the names Sauckler, Hagen, Manning and Strickler (Williams, 1970). It can be written as: U = -R?S* (2.35) n where n is Manning's roughness coefficient. In order to use the Manning formula, one must determine an adequate value for Manning's roughness coefficient, n, because its value cannot be directly measured. This value is normally estimated either from experience, by using an empirical relationship or from documented cases (Bathurst, 1982). Table 2.2 supplies average values of Manning's n for numerous types of natural streams. Table 2.2. Values of Manning's roughness coefficient nior natural streams (adapted from Chow, 1959) Type of Channel and Description n I Top width < 30 m (a) Streams on a plain (i) clean, straight, full stage, no riffles or pools 0.020 (ii) same as above, but more stones and weeds 0.024 (iii) clean, winding, some pools and shoals 0.027 (iv) same as above, but some weeds and stones 0.030 (v) same as above, lower stages, more ineffective slopes and sections 0.032 (vi) same as (iv) but more stones 0.034 (vii) sluggish reaches, weedy, deep pools 0.047 36 (viii) very weedy reaches, deep pools, or f loodways with heavy stand of timber and underbrush 0.067 (b) Mountain streams, no vegetation on banks, usually steep (i) bottom: gravel, cobbles, and a few boulders 0.027 (ii) bottom: cobbles with large boulders 0.034 II Flood plains (a) Pasture, no brush (i) short grass 0.020 (ii) high grass 0.024 (b) Cultivated areas (i) no crop 0.020 (ii) mature row crop 0.024 (iii) mature field crop 0.027 (c) Brush (i) scattered brush, heavy weeds 0.034 (ii) light brush and trees, in winter 0.034 (iii) light brush and trees, in summer 0.040 (iv) medium to dense brush, in winter 0.047 (v) medium to dense brush, in summer 0.067 (d) Trees (i) dense willows, summer, straight 0.101 (ii) cleared land with tree stumps, no sprouts 0.027 (iii) same as above, but with heavy growth of sprouts 0.040 (iv) heavy stand of timber, a few down trees, little undergrowth, flood stage below branches 0.067 (v) same as above, but with flood stage reaching branches 0.081 III Top width > 30 m (a) Regular section with no boulders or brush (b) Irregular rough section In order to use documented cases as reliable sources of values for Manning's n, one must first consider the factors affecting it, such as channel surface roughness, vegetation, irregularities, alignment, silting and scouring, and obstructions (Chow, 1959). The user inputs a value for Manning's roughness coefficient (n) and the model calculates the velocity using Equation 2.35 37 2.3.2 Composite Manning (Horton, 1933) Originally developed by Horton (1933), this equation is useful when determining the dimensions or velocity of a channel whose bed and banks display differing degrees of roughness (Horton, 1933). An equivalent roughness is derived using: where nbank and nbed are Manning's roughness coefficients for the bank and bed respectively, Pbank is the wetted perimeter of the bank and Pbed is the bed perimeter. Horton (1933) assumed the velocity was constant over the area and found that the values of both nbed and nbank vary with depth. Figure 2.4 shows the variation in equivalent n with depth for rectangular and trapezoidal channels. The user inputs a value of n for the banks and one for the bed and the model calculates a composite value for n using Equation 2.36 and velocity using Equation 2.35. 2.3.3 Keulegan (1938) Keulegan (1938) applied principles already established for use in circular pipes to turbulent flow in open channels and derived a formula for velocity distribution and hydraulic resistance. (2.36) 38 The Keulegan flow resistance equation, together with the Darcy-Weisbach equation, is one of the most well-known and widely-used equations for open channels. The two equations are given below: 1 2 ^ f = 2.03log (2.37) (2.38) where f is the friction factor and ks is the equivalent roughness height. Although ks is actually a measure of the effect of any roughness element on the flow (Bathurst, 1982). Originally, the value of ks was determined experimentally for each channel type. Others have since set it equal to a certain grain-size diameter, commonly D50, D65 and D90 (Bray, 1982). Most studies of ks find that it is dependent on the grain-size distribution of the sediment. For non-uniform conditions, ks is usually expressed as: where Cx is a constant, Dx is the characteristic grain diameter of which x percentage of sediment is finer (Millar, 1999). As shown in Table 2.3, below, values of ks can vary greatly. (2.39) 39 Table 2.3. Summary of "best-fit" ks values derived from reach-averaged hydraulic geometry (Millar, 1999) Source k s Bray (1980,1982) 6.8D 5 0 3.5D 84 Charlton et al.. (1978) 3.5D90 Gr iff iths (1981) 5.0D50 Hey (1979) 3.5D 8 4 Leopold et al. (1964) 3.9D 84 Limerinos (1970) 3.2D84 Millar (1999) 2.9D 8 4 In spite of the great uncertainty associated with these values, according to Millar (1999) they "still represent the best approach to estimating velocity in ungauged gravel-bed rivers." The user inputs the value of ks, which is the equivalent roughness height for the reach. The model, then calculates f using Equation 2.37 and uses this value to determine the velocity using Equation 2.38. 2.3.4 J a r r e t t (1984) The Jar re t t equation was developed to predict Manning's roughness coefficient, n, for high-gradient streams, with a slope greater than 0.002 (Jarrett, 1984). I t is as follows: n = 0.39/?,0165038 (2.40) 40 Jorrett (1984) found that for uniform flow, Equation 2.40 could be substituted directly into Manning's velocity equation (Equations 2.35). Jarrett (1984) found that most guidelines available for high-gradient streams do not take into account how the roughness elements change, with a change in gradient and therefore depth. As part of Jarrett's study, 21 natural streams were used, which represented a wide range of channel type, width, depth, slope, roughness and bed-material size. Figure 2.5 shows the relationship between Manning's roughness coefficient and hydraulic radius, from which Jarrett deduced that the roughness decreases with flow depth (Jarrett, 1984). Equation 2.40 should be used for natural streams with: 1. stable bed and banks; 2. slopes from 0.002 - 0.04; 3. hydraulic radii which do not include wetted perimeter of bed particles, and; 4. little or no suspended sediment (Jarrett, 1984). The model calculates a value of n using Equation 2.40 and then input into Equation 2.35. 2.4 BANK STABILITY There are two types of erosion affecting the banks of gravel-bed rivers: mass failure and fluvial erosion. The precise way in which the banks and consequently the river geometry are affected depends on the type of erosion as well as the sediment 41 composition of the banks. This thesis deals with either strictly non-cohesive or cohesive bank sediment. A soil is considered cohesive if its properties are influenced primarily by clay and Silt Size particles, where cohesive forces exist between particles. Sediment whose properties are influenced by sand and gravel size particles are referred to as cohesionless, or non-cohesive (Craig, 1992). 2.4.1 Non-Cohesive Bank Sediment Mass failure of non-cohesive bank sediment occurs when the bank angle (0) exceeds the friction angle (<|)), which is not subject to fluid shear stresses. The factor of safety is given by: FM = ^ (2.41) * tan6? where Tb a n k is the mean bank shear stress, y is the unit weight of water, S s is the specific gravity of the sediment, and Dsobank is median bank grain diameter. Loosening of individual clasts through weathering can reduce the friction angle (Lawler eta/., 1997). Oversteepening of the banks due to erosion of the bank toe can increase the bank angle. Both of these processes may cause mass failure in banks composed of non-cohesive sediment. Assessing the stability of undrained and drained 42 banks is similar with the addition that failure may result from an increase in pore water pressure under submerged conditions (Thorne, 1982). The flow of water and sediment in the main river channel produces shear stresses on the bed and banks. If this stress, which is proportional to the velocity gradient, is increased sufficiently, fluvial entrainment of the sediment will occur (Thorne, 1982). In order for a particular grain to remain stable, its frictional forces must resist gravity and the forces exerted by the fluid. The limiting bank stability is: where Tbankc and tbedc are the critical shear stresses acting on a grain located on the bank and bed respectively (Chow, 1959; Henderson, 1966; as cited by Millar, 1994). In the original relation, can only achieve a maximum of 40°, but if the effects of bank vegetation and consolidation are included, § can be replaced with an in situ value which can reach a maximum of 90° (Millar, 1994). The final relation is: This equation is used in order to determine whether the banks of a stream composed of non-cohesive bank sediment are stable with respect to both mass failure and fluvial erosion which accounts for the effects of bank vegetation and consolidation of the bank sediment (Millar, 1994). (2.42) (2.43) 43 2.4.2 Cohesive Bank Sediment In order to assess the stability of a channel bank with respect to mass failure, the motivating and resisting forces acting on the bank must be balanced. The motivating force is due to the weight of the soil and the resisting force is composed of the cohesion (c) and internal friction angle (<(>) of the soil (Millar, 1994). ^Aass failure occurs when the critical bank height is reached (Lawler eta/., 1997). The factor of Safety with respect to mass failure (FSH) must be greater than or equal to one. It is calculated using: FS = ^crif = N*C (2 44) ^ " H Hyt 1 ] where H is the vertical bank height; HCht is the maximum height at which the banks are stable; y t is the saturated unit weight of soil; and N s is a dimensionless stability number, given by: Ns = 3.83 + 0.052 (90 - 0) - 0.0001 (90 - 6f (2.45) where 9 is the bank angle (Millar and Quick, 1998). 44 There are several ways mass wasting can occur. The mode of bank failure depends on the bank angle, material properties such as grain size and soil cohesion and the location of the groundwater table or channel water level. Fluvial erosion of cohesive banks usually signifies parcels of soil, not individual grains are being eroded. This is because of the strong cohesive forces that exist between the grains (Lawler et al., 1997). Erodibility is a function of many factors, including mineralogy, particle size, temperature of the water and moisture content of the soil. For example, hard, dry banks are more resistant than wet banks, which are more easily eroded (Thorne, 1982). In order for the channel banks to be considered stable, the factor of safety with respect to fluvial erosion (FST) must be greater than or equal to one. It is calculated using: f=5x = (2.46) 1bank where T b Q n k is the mean bank shear stress and T c r i t is the critical bank shear stress (Millar and Quick, 1998). T b ank can be calculated using: 45 1 bank rys SFbank 4K (2.47) where SFbank = 1-766 f p \ ^ +1.5 -1.4026 P \rbank (2.48) 2.4.3 Effect of Vegetation on Bank Stability There have been many studies conducted to determine the influence of riparian vegetation on the bank stability of gravel-bed rivers (Hey and Thorne, 1986; Millar and Quick, 1993; Beeson and Doyle, 1995; Millar, 2000). Beeson and Doyle's (1995) study of four streams in southern British Columbia compared bank erosion in vegetated and non-vegetated channel bends and found that riparian vegetation decreases bank erosion. They also concluded that the denser the vegetation, the more effective it was at reducing bank erosion and therefore increasing bank stability. The theory presented by Millar and Quick (1993b) for channels with non-cohesive banks, was tested using published data values as input, and the output was compared to the observed channel geometry. The modified friction angle ((j)') was used to quantify the influence of bank vegetation and 40° is a reasonable value for non-vegetated banks (Millar, 2000). Millar and Quick (1998) tested the theory for channels with cohesive 46 banks and concluded that bank vegetation has an effect on the critical shear stress (tent), which has a large influence on the stable channel width. RiverMod incorporates a measure of bank vegetation by utilizing the internal bank friction angle ((()') as an indicator of bank vegetation strength (Millar and Quick, 1993). It increases with increased density of bank vegetation (Millar, 2000). 2.5 PLANFORM GEOMETRY Rivers are often classified based on their planform geometry. Braided channels are those with relatively stable alluvial islands and therefore two or more separate channels (Leopold and Wolman, 1957). A meandering river has a single winding and sinuous channel. The planform of a river is dependant on the bed slope and discharge. For a given discharge, meanders will occur on smaller slopes than braids (Leopold and Wolman, 1957). River slopes can adjust through the process of meandering. As a river creates meanders and the sinuosity of those meanders increases, the channel slope decreases. Figure 2.6 shows three streams with increasing sinuosity from straight to meandering. The valley slope is built-up over time through aggradation. The channel slope adjusts to a steady-state condition. Figure 2.7 is a flowchart showing the computations in the planform model. RiverMod determines the planform geometry of the river by comparing the bedslope to the valley slope and the transitional slope. If the bedslope is greater than the valley slope, the channel is unstable and is said to be aggrading. If the bedslope is less than the 47 valley slope, the channel is stable and is either braided or meandering. The transition slope is determined using: where W is the river width and F r is the Froude number (Parker, 1976, as cited by Millar, 2000). The transition slope is compared to the bed slope to determine if the river is braided or meandering: If the river is meandering, the sinuosity (£) and meander wavelength (A.) are determined using empirical relations developed by Leopold and Wolman (1960). These empirical relations ordinarily use a meander wavelength multiplier between 10 and 12, the model uses a default value of 11. The model also utilizes Langbein and Leopold's (1966) sine-generated curve to calculate values for the maximum deviation angle along the channel (O) and the radius of curvature (rc). Langbein and Leopold (1966, as cited by Thorne, 1997), found that the sine-generated curve resembled an idealized river, by approximating the path of least resistance in flowing around a bend. The sine-generated curve is defined by: (2.49) 5 > S* = braided (2.50a) S < S* = meandering (2.50b) 0(0 = $ sin (2.51) 48 where 6 is the channel deviation angle, cD is the maximum value of 0,1 is the distance along the valley axis and L is the distance along the meander arc length (see Figure 2.8). An iterative technique is used to solve the sine-generated curve for O , such that the river sinuosity (£jc) determined using 0 and O is equal to the sinuosity (cj) determined from the bedslope and valley slope. Ultimately the maximum deviation angle is calculated and presented as output (See Figure 2.7). Equation 2.51 can be used to graph the idealized planform geometry of the river. The idealized meander parameters are useful for river restoration, or attempting to return a channel to its natural form. The planform geometry analysis may assist the redesign of sections of channel that have been straightened or channelized (Millar and MacVicar, 1997). 49 w Actual Channel Cross Section Simplified Trapezoidal Cross Section Figure 2.1. Definition Sketch of a simplified trapezoidal channel for Millar and Quick (1993) model (MacVicar 1999). 50 flow coarse upper layer fine lower layer • . • ' - > • • • . ' • . . v - • , : ; ? / S « J - subarmour Figure 2.2. A Schematic representation of the armour layer in a gravel-bed channel. 51 OBSERVED UNIT BEDLOAD TRANSPOHT RATE (kfl/m §-') Figure 2.3. Comparison between observed and calculated data for Meyer-Peter and Muller, Ackers and White, Einstein, and Parker, Klingeman and McLean formulae and Elbow River data (Gomez and Church, 1989). 52 Figure 2.4. Relation between grain-size diameter (D) in feet and Manning's roughness coefficient (n) in imperial values for rectangular and trapezoidal channels in which the bottom and sides have different roughness characteristics (Horton, 1933). 53 Figure 2.5. Relation of Manning's Roughness Coefficient to Hydraulic Radius for four of the streams Jarrett used in his study (Jarrett, 1984). 54 Figure 2.6. Rivers of increasing sinuosity from a straight channel (A) to a meandering channel (C) (Thorne, 1997). 55 Bedslope S, from Fixed or Variable Slope Model Calculate Transitional Slope S* Meandering Planform Calculate Sinuosity \ = S v/S % < 1.1 Straight Channel Valley Slope S v , Input by User Aggrading and Unstable 1.1 > 3.1 Meandering £ > 3 . 1 Calculate Wavelength A. and Radius of Curvature Braided Planform Figure 2.7. Flowchart for the Planform Model. 56 4 * X — ^ -= 0 1 - Q = L / 4 I -R=L/2 1 ^ = 3 1 7 4 1 *-i 1=0 1 I 0 = 0 1 i e= i Figure 2.8. Definition sketch of one meander arc. 57 Chapter 3 T Y P E O F A N A L Y S I S 3.1 INTRODUCTION There are two versions of the original (Millar and Quick, 1993b) model and therefore two versions of RiverMod: a fixed-channel-slope model and a variable-channel-slope model. Each has been formulated for channels with either non-cohesive or cohesive banks. 3.2 FIXED-CHANNEL-SLOPE MODEL The fixed-channel-slope version of RiverMod is equivalent to an experiment where the slope is fixed, and the channel width, depth and sediment transport rate adjust to the discharge. It is useful for examining the effect of bank stability on the channel geometry (Millar, 1994). Discharge and bank stability are the only two constraints that need to be satisfied in the fixed-channel-slope version of the model. Since the value of the slope is input by the user, it is treated as an independent variable. The bedload constraint is only used in the variable-slope version (Millar, 1994). Figure 3.1 is a flowchart for the Millar and Quick (1993b) fixed-slope model. The model starts by selecting a trial value of the bed perimeter (Pbed), bank perimeter (Pbank) and the bank angle (6). These are the primary dependent variables. The other dependent 58 variables can be calculated from these three. Only one of the three primary dependent variables is varied at a time. Once the discharge constraint is satisfied, the channel dimensions are calculated and then the bank stability constraint is assessed. Finally the optimal solution is found at the point of maximum sediment transport (Millar, 1994). Details regarding the dependent and independent variables are discussed in Chapter 4. The fixed-channel-slope model has been formulated for channels with non-cohesive bank sediment and channels with cohesive bank sediment. The discharge constraint is the same for both of these channel types; however, each channel type has its own bank stability constraint (see Section 2.4). Millar (1994) noted that in channels with non-cohesive bank sediment, the bank vegetation tended to increase <(>' and therefore bank stability. In channels with cohesive bank sediment, bank vegetation tended to increase T c r i t . 3.3 VARIABLE-CHANNEL-SLOPE MODEL The variable-channel-slope model more correctly approximates the behaviour of d natural gravel-bed river, since the slope is variable. In the variable-channel-slope version of the model, channel slope (S) is treated as a dependent variable. The bankfull sediment discharge capacity (&bf) is considered an independent variable. This version is similar to the fixed-slope version, with an additional bedload constraint, which requires the bedload transporting capacity of the channel to be equal to the sediment load (Gb) (Millar and Quick, 1993b). 59 Figure 3.2 is a flowchart showing the steps that make up the variable-channel-slope model. It is similar to Figure 3.1, except that the channel slope is varied for trial values of Pbed-A strong relationship between the dependent variables is noticed when using the variable-slope model. The final output of the model are the dependent variables: width, depth and slope. They would change in response to changes the independent variables caused by alterations in the stream environment. As the independent variables change, the dependent variables will also adjust in accordance to the new conditions. The dependent variables adjust their values at different rates. According to Booth (1990) the depth and width of the channel adjust at a much quicker rate than the slope. Even though they adjust at different rates, the width, depth and slope of a river are all inter-related and it is unlikely one will change without the others also modifying their values. For channels with non-cohesive channel banks, Millar (1994) notes that if the width of the channel changes, the depth changes in order to satisfy continuity and the slope adjusts to satisfy the bedload constraint. For channels with cohesive channel banks, the model can be used to determine whether a stream is bank-height or bank-shear constrained. In general, only one of these bank stability constraints is active at a time. Millar (1994) documented the change in the active bank stability constraint by varying Qbf, keeping t9bf constant and then varying Gbf, 60 and keeping Qbf constant. In both cases, the remaining independent variables were kept constant for both investigations. The results are shown in Table 3.1 Table 3.1. Results of Millar (1994) active bank stability constraint investigation. Bank-full Discharge (Qbf) in m3/s Bankfull Sediment Transport Capacity (Gbf) in kg/s Active Bank Stability Constraint Qbf < 100 Gbf > 5 bank-shear constrained 100 < Qbf < 250 3 < Gbf < 5 both bank-height and bank-shear constrained Qbf > 250 Gbf < 3 bank-height constrained Whichever bank stability constraint is not active, does not seem to affect the channel geometry (Millar, 1994). In summary, the f ixed-charinel-slope and variable-channel-slope models show that the bank stability greatly affects the geometry of the channel. <j>' is useful as a single parameter for assessing the effects of vegetation on the bank stability in streams with non-cohesive banks. In streams with cohesive banks, T c r i t can be used for the same purpose. 61 Select Trial/3, bed Select Trial 0 Select Trial P» Adjust bank Adjust bod Figure 3.1. Flowchart for Millar and Quick (1993b) Fixed-Slope Model (MacVicar, 1999). 62 Input Independent X Variables J Figure 3.2. Flowchart for Millar and Quick (1993b) Variable-Slope Model (MacVicar, 1999). 63 Chapter 4 USING RIVERMOD This chapter functions as a user manual, by guiding the user while running RiverMod. The following sections illustrate a step-by-step process for the successful operation of the model. 4.1 INSTALLATION RiverMod is installed by inserting the CD and selecting "setup.exe". The installation program will guide the user through the setup process. 4.2 FILE SETUP SCREEN RiverMod prompts a choice between two options: the user can either open an existing file or create a new record, (see Figure 4.1). 4.2.1 Open an Existing File The user can choose to open a file saved earlier, or to return to the opening screen by clicking "Cancel". Once the user chooses which file to open, the name of the file will appear on the screen. Clicking "Open" (see Figure 4.2) will open the file and load the Computation Screen. 64 4.2.2 Creating a New File The user will be guided through the RiverMod screens, which enable a new file to be created. This sequence is demonstrated in the following sections. 4.3 MODEL SCREEN Once the user has chosen to create a new file, the Model Screen is loaded (see Figure 4.3). The Model Screen allows the user to select the Model Type, Bank Type and Unit Type. There are two different model types: the fixed slope model and the variable slope model. There are two different bank types to choose from. The model has been formulated for gravel-bed rivers with either non-cohesive or cohesive bank sediment. The model operates using the SI (Systeme Internationale d'Unites) system of units. However, the user may select between two systems of units: the British Gravitational (BG) system, when working with variables in imperial units, and the SI system when dealing with metric units. Once the user has selected the model, bank and unit type, the Equation Screen is loaded. 65 4 . 4 EQUATION SCREEN The Equation Screen presents the user with four sediment transport models and four flow resistance equations (see Figure 4.4). The sediment transport models are Einstein-Brown (1950), Ackers and White (1973), Meyer-Peter and Muller (1948) and Parker, Klingeman and McLean (1982). The flow resistance equations are Keulegan (1938), Manning (1891), Composite Manning's (Horton, 1933) and Jarrett (1984). The combination of equations will affect the model's ability to accurately predict channel changes. 4 . 5 COMPUTATION SCREEN This screen provides an interface to the nucleus of the model. It is divided into an input section and an output section (see Figures 4.5 and 4.6). The options selected on the Model and Equation Screens determine which variables are needed as input and which will appear as output. 4.5.1 Model Input (a) Discharge Bankfull discharge ( Q b f ) is used in either m3/s or ft 3/s. Often Q b f is taken to be the discharge with a two-year return period (Q2). (b) Roughness Coefficient The roughness coefficient depends on which flow resistance equation has been selected. 66 1. Keulegan - equivalent roughness (ks) in metres or feet. 2. Manning's n - Manning's roughness coefficient (n). It is unitless. 3. Composite Manning's n - Manning's roughness coefficient for the bed of the channel (nbed) and for the channel banks (nbank)-4. Jarrett - this relation calculates a value for Manning's roughness coefficient; therefore no specific roughness input is needed. (c) Sediment Transport Each sediment transport relation requires a particular grain diameter to represent the sediment grain-size distribution. The units should be in metres or feet. 1. The Einstein-Brown model requires the median grain diameter of the bedload sediment (Dso). 2. The Ackers and White model requires the thirty-fifth percentile grain diameter of the bedload sediment (D35). 3. The Meyer-Peter and Muller model requires both the ninetieth percentile grain diameter (D90) and the average grain diameter (D a) of the bedload sediment. 4. The Parker, Klingeman and McLean model requires the median sub-surface grain diameter (dso). (d) Bank Stability The bank stability constraint has been formulated for both cohesive and non-cohesive bank sediments (Millar, 1994). For channels with non-cohesive bank sediment, the median grain diameter of the bank material (Dsobank) and the internal friction angle 67 (<|)') are necessary as input data. Dsobank is in metres or feet and <$>' is measured in degrees. For channels with cohesive bank sediment, soil cohesion (c), critical shear stress (t c r it) and the unit weight of bank sediment (y t) are needed as input data. Soil cohesion and critical shear stress are measured in Pascals or lb/in2 (psi), and y t is measured in N/m3 or lb/ft 3. (e) Channel Slope If the fixed-slope model is used, the reach-averaged bedslope (S) appears on the input screen as an independent variable. It is unitless and is the ratio of the vertical elevation change of the channel to the horizontal distance along the bed. In the variable-slope version of the model, the slope appears only as an output and is therefore a dependent variable. (f) Sediment Transport Capacity If the variable-slope model is used, the sediment transport capacity (Gb) appears as input data, measured in kg/s or Ib/s. In the fixed-slope version, it appears as the output data. 4.5.2 Model Output The surface width (W), mean depth (Y) and bed slope (S) are considered the three primary dependent variables. Surface width and mean depth are calculated in either metres or feet, while bed slope is unitless. The three primary dependent variables appear on the main Computation Screen. Bank height (in metres or feet), bank angle, (in degrees), and sediment transport capacity (in kg/s or Ib/s) further describe the 68 geometry of the channel and are considered secondary dependent variables. They may be viewed on the Supplementary Output Screen by clicking "More Details" (see Figure 4.7) For channels with cohesive bank sediment, two additional output variables appear on the Supplementary Output Screen, are H / H a - i t and TbankAcnt- They are both unitless and further indicators of bank stability. Table 4.1 shows the minimum and maximum values for each of the variables in order for RiverMod to run properly for both SI and Imperial Units. Some of the limits may extend beyond the normal range for a certain variable in a small gravel-bed river. Table 4.1. Minimum and maximum values for input variables Input Variable SI Units Imperial Units Bankfull Discharge, Qbf 0 - 25000 m3/s 0 - 883,000 ft 3/s Equivalent Roughness, ks 0.002 - 1 m 0.0066 - 3.28 ft Manning's Roughness Coefficient, n 0.01 - 0.15 0.01 - 0.15 Bank Manning's Roughness Coefficient, nbank 0.01 - 0.15 0.01 - 0.15 Bed Manning's Roughness Coefficient, nbed 0.01-0.15 0.01-0.15 Thirty-fifth Percentile Grain Diameter, D35 0.0001 - 0.5 m 0.00033 - 1.64 ft Median Gram Diameter, D50 0.0001 - 0.5 m 0.00033 -1.64 ft Ninetieth Percentile Grain Diameter, D 9 0 0.0001 - 0.5 m 0.00033 -1.64 ft Average Grain Diameter, Da 0.0001 - 0.5 m 0.00033 -1.64 ft Median Sub-surface Grain Diameter, dso 0.0001 - 0.5 m 0.00033 -1.64 ft Median Bank Grain Diameter, Dsobank 0.0001 - 0.5 m 0.00033 -1.64 ft Modified Friction Angle, <)>' 20 - 90 0 20 - 90 0 Critical Shear Stress, tcriticai 0 - 150 Pa 0 - 0.02175 psi Soil Cohesion, c 0 - 100,000 Pa 0 - 14.5 psi Unit Weight of Bank Sediment, y t 15, 000 - 40,000 N/m3 95.5 - 254.6 lb/ft 3 Reach-Averaged Bed Slope, S 0.0001 - 0.05 0.0001 - 0.05 Sediment Transport Capacity, Gb 0 - 5000 kg/s 0 -11000 Ib/s 69 4.5.3 Drop-down Menu The drop-down menu at the top of the Computation Screen provides options for data manipulation. Each of these options is detailed below. 4.5.3.1 File (a) Entering Data Data is entered into the Computation Screen and is grouped into records. This enables the user to save several series together as one file. Each record contains the same sediment transport and flow resistance equations as well as the same model type, bank type and unit type. The "New", "Next" and "Previous" buttons enable navigation from one record to another. (b) Saving Data As data is entered into the Computation Screen, it is automatically saved into a file called "RIVERFILE.DAT". Once the user chooses to save the file, RIVERFTLE.DAT is renamed with the user-selected name. Input and output data are saved together as a "DAT' file. The save function operates similarly to other windows-based programs. (c) Open Existing File There are two ways to open an existing file. The first is to select this option on the File Setup Screen when the model is loaded. The second is to choose this option from the File menu, on the Computation Screen. 70 RiverMod's capacity to check for compatibility between saved options and new user-determined options is a powerful and innovative feature that extends previous models. For example, perhaps the file was originally saved using the Einstein-Brown sediment transport relation, and the user wishes to open it using the Ackers and White sediment transport relation. The program would open the files and all of the data common to both options would appear on the screen. The data not held in common by the chosen equations - in this case, the grain diameter - would not appear on the screen. 4.5.3.2 Edit (a) Create a New Record Choosing this option from the Edit Menu enables the user to add a new blank record to the file. The data in the new record is related to the data in the previous record because they share the same model options, but is input to a completely separate model run. The data contained in the text boxes of the new record can be entirely different from the data in previous or subsequent records. (b) Delete and Clear Current Record Deleting a record allows the user to delete the current record from the series. The series will then contain one less record. Clearing a record will leave all the text boxes in the current record blank, but the number of records in the series will remain the same. 71 (c) Search for a Record The "Search for a Record" option under the Edit Menu, permits the user to search for a particular record. This can be done by searching for a particular value of any of the variables contained within the series of records. Using a series of user-friendly screen prompts (see Figure 4.8), the model will locate the first record containing that value. This feature is particularly useful for a user working with a series containing a large number of records. 4.5.3.3 Output (a) Run Choosing "Run" from the Output menu executes the optimization model. Before running, the model automatically scans for three potential errors that can occur during data entry: • empty text boxes; • non-numeric characters: • values outside the permissible range. If an error is located, the program pauses, alerts the user, and allows the user to correct the mistake. The user can then choose the "Run" option again, and the program will proceed with the execution of the optimization model. 72 There are two slightly different paths the routine can follow, one for the fixed-slope model and one for the variable-slope model. Each is explained in more detail in Chapter 3. Figure 3.1 shows the fixed-slope version of the optimization model and Figure 3.2 shows the variable-slope version of the model. The two methods are very similar and follow this general procedure (Millar and Quick, 1998): (i) Input the independent variables. (ii) The minimum and maximum bounds for Pbed, 9 and Pbank are set. (iii) The midpoints of Pbed, 9 and PbQnk are determined. (iv) Flow resistance and velocity are calculated, using the equation chose by the user, at the midpoint. The bounds of Pbank are adjusted until the discharge constraint is satisfied (UA = Qbf) and the flow resistance and velocity values are also adjusted for each new midpoint value of Pbank-(v) Bank stability: a. For non-cohesive banks, Equation 2 .43 must be satisfied for the banks to be stable, b. For cohesive banks, the bank angle is adjusted until F S H = 1 (Equation 2 .44) and FS T = 1 (Equation 2.46). If the banks are not stable, the channel is too narrow, the bounds for Pbed are reset and the procedure returns to step (iv). If the banks are stable, the routine proceeds to step (vi). 7 3 (vi) The bedload transport is calculated using the equation chosen by the user. If the Pbed value corresponds to the maximum bed load transport, then the optimum solution has been reached and the dependent variables width (W), depth (Y) and bank angle (0) are calculated as output. If the Pbed value does not represent the optimum solution, the procedure returns to step (iii). The final solution represents the steady-state equilibrium geometry of the reach (Millar, 1994). (b) Planform Geometry This option takes the user to the Planform Screen (see Figure 4.9 and Section 2.5). RiverMod will determine the planform geometry for the record which is open when this option is chosen. This feature of the model is useful for river restoration or design purposes (see Section 4.6). 4.5.3.4 Microsoft Excel (a) Open Microsoft Excel Choosing this option from the Output menu opens the spreadsheet program Microsoft Excel (provided it is available on the user's computer). In order for it to function properly, Microsoft Excel must be closed before this feature is executed. Integration of RiverMod with Microsoft Excel adds power and flexibility, allowing the user to: • create graphs and charts; 74 • visually compare the relationship of one variable to another; • visually compare the results obtained using different equations or model options. The model will automatically identify the options chosen by the user and transfer them to the Microsoft Excel worksheet. The worksheet will have a column for each variable with headings, which include the name and units of each variable. Figure 4.10 shows an example where the discharge was increased by 25 m3/s for 5 runs, while all other variables were held constant. Once the user has opened Microsoft Excel, all of its functions are independent of those of RiverMod. If the user wishes to create graphs or move and delete data, he/she must do so from within the Microsoft Excel program. In order to save any new worksheets, graphs or files created in Microsoft Excel, the user must also do this from within Microsoft Excel and not by using RiverMod. As soon as RiverMod is closed, Microsoft Excel, opened by RiverMod will also be closed, so any file handling within Microsoft Excel should be done before RiverMod is terminated. (b) Append to Microsoft Excel Spreadsheet There are two separate append features built into the model. In order to use these features, Microsoft Excel must already have been opened through RiverMod. Both "append" commands add to the spreadsheet the input and output data, found on both the Computation Screen and the Supplementary Output Screen. 75 • Append Current Record to Spreadsheet - this feature is useful for importing the data in the current record into the Microsoft Excel Spreadsheet. • Append All Records to Spreadsheet - this feature allows transfer of the data in all the records into the spreadsheet simultaneously. The "append all" feature can only be executed from Record 1, so that the model can run through the records in order. 4.6 PLANFORM SCREEN The user can access the Planform Screen (see Figure 4.9) from the Computation Screen. RiverMod will use the valley slope, entered by the user, in conjunction with a formulation for the transitional slope (S*) to determine the geometry of the river. If the channel slope is greater than the valley slope, the river is aggrading and unstable. Otherwise, a meandering-braiding transition formulation is used to determine the river planform. Equation 2.49, developed by Parker (1976, as cited in Millar 2000), is used to determine the transitional slope. The transition slope is compared to the bed slope to determine if the river is braided or meandering, using Equations 2.50a and 2.50b. If the river is meandering, the sinuosity (£) and meander wavelength (X) are determined using empirical relations developed by Leopold and Wolman (1960). These empirical relations ordinarily use a meander wavelength multiplier between 10 and 12. The model uses 11 as the default value, but the user may enter an alternate value. 76 The model also utilizes Langbein and Leopold's (1966) sine-generated curve (see Section 2.5) to calculate values for the maximum deviation angle along the channel (<D) and the radius of curvature (rc). This information is useful for river restoration, which attempts to return the channel to its "natural" form. This may require the redesign of sections of channel that have been straightened or channelized. 77 78 79 model Type and Units Model Type (* Fixed Slope Model C Variable Slope Model C Calibration Model OK Cancel Bank Type-<* Non-cohesive Bank Sediment C Cohesive Bank Sediment Units SI Units C Imperial Units U l O l x l Figure 4.3. Model Screen 80 Row Resistance and Sediment Transport Options Choose a Sediment Transport Model Einstein-Brown (1950 i Ackers and White (1973) Meyer-Peter and Muller (1948) Parker, Klingeman and McLean (1982) Choose a Flow Resistance Equation Keulegan [1938 Manning's n (1891) Composite Manning's n (Horton, 1933) Jarrett (1984) Back OK Figure 4.4 Equation Screen 81 Record 1/ 3 - C:\s-rreaml.dat Output Microsoft Excel N on-Cohesive M odel I nput: I ndependent Variables SI Units Discharge (Keulegan Equation] Bankfull Discharge, Q. Equivalent Roughness, ks Sediment Transport (Einstein-Brov Median Grain Diameter, D -in 5& Bank Stability Median Bank Grain Diameter, D. M odified Friction Angle, ^ 1 Channel Slope Reach-Averaged Bed Slope, S Jon-Cohesive Model Output: Reach-Averaged Geometry Surface Width, W Mean Depth, Y Bed Slope, S Change Options More Details > Figure 4.5. Computation Screen for Non-Cohesive Sediment with Einstein-Brown and Keulegan equations in SI Units, using the Fixed Slope Model. 82 Record 1/1 Edit Output Microsoft Excel ohesive Model Input: Independent Variables SI Units Discharge (Composite Manning's Equation Bankfull Discharge, & M Bank Manning's n, Bed Manning's n, Sediment Transport (Ackers and White] Thirty-fifth Percentile Grain Diameter, Pss Bank Stability Critical Shear Stress, Soil Cohesion, c Unit Weight of Bank Sediment, Yt Channel Slope Reach-Averaged Bed Slope, S 0.001 Mean Depth, V Bed Slope, S Change Options Cohesive Model Output: Reach-Averaged Geometry Surface Width, W Figure 4.6. Computation Screen for Cohesive Sediment with Ackers and White and Composite Manning equations in SI Units using the Fixed Slope Model. 83 (a) Figure 4.7. Supplementary Output Screen for: (a) Non-Cohesive Sediment Model, with Einstein-Brown and Keulegan equations in SI Units, using the Fixed Slope Model; and (b) Cohesive Sediment Model with Ackers and White and Composite Manning equations in SI units, using the Fixed Slope Model. 84 J-^ TjSelect a Variable: p. jBankfull j ^ Grain jDisdh^gd Diameter E Bank Manning's n Bed Manning's n r- Critical ~ 0 , ( Shear Stress r S l o p e r Soil Cohesion Unit Weight C of Bank Sediment Figure 4.8. Search Screen showing Cohesive Sediment Model Options. 85 Planform Model '"Determine Planform Characteristics Bed Slope Valley Slope I 0 0 0 1 Meander Wavelength Multiplier The river is meandering in planform Sinuosity, t; Maximum deviation angle along the channel $ Wavelength, X Radius of Curvature, rc r F Corinpute'Rivef] Geometru 620 127.6 m m mm Figure 4.9. Planform Screen. This example shows a meandering stream. 86 Figure 4.10. Microsoft Excel Spreadsheet with values appended from RIVERMOD for ai example using Non-Cohesive Sediment with Einstein-Brown and Keulegan equations in SI Units, using the Fixed Slope Model. In this example, the discharge was increased by 25 m /s for 5 runs, while all other variables remained constant. 87 Chapter 5 SAMPLE APPLICATIONS 5.1 INTRODUCTION The following sections present two examples for using RiverMod. The model is applied to two rivers in British Columbia: Slesse Creek and Narrowlake Creek. Both creeks have been affected by logging, resulting in changes to the bank stability, river width and planform geometry. 5.2 SLESSE CREEK Slesse Creek is a mountain stream situated in southwestern British Columbia and northwestern Washington State (see Figure 5.1). The upper catchment of the river, located on the U.S. side, is in a protected, pristine forested area. The lower reaches of the river, on the Canadian side, have been subjected to clear-cut logging along the banks and floodplain. As a result of this disturbance on the banks, the stream's geometry has changed with active widths increasing by over 3 times from pre-logging to post-logging conditions (MacVicar, 1999). The morphology has changed from a single channel meandering planform to a wide unstable braided planform (see Figure 5.2). This river provides an excellent case Study for RiverMod. The nearby forestry activity has not affected water and sediment Supply, but riparian logging has caused a decrease in the bank stability, due to the loss of bank vegetation. Therefore, the only 88 independent variable to suffer significant change is the internal friction angle, <)>', which decreased from 73° to 40° from 1936-1993 (MacVicar, 1999). 5.2.1 Investigation In order to apply RiverMod to Slesse Creek, the input parameters must be defined for past and present values. f^acV\car (1999) concentrated his analysis on Reach D of Slesse Creek (see Figure 5.3) because the reach is alluvial, the morphology is relatively homogeneous, fish habitat has been greatly decreased and recent restoration efforts have been focused on this reach (Babikaiff and Associates, 1997 as cited by MacVicar, 1999). Site surveys and historic aerial photograph analysis have shown that from 1936-1993 the river width has increased from 28 m to 145 m (see Figure 5.2) while the slope has remained constant at around 0.02 (MacVicar, 1999). The constant slope indicates the fixed-channel-slope version of the model should be used. Table 5.1 shows the reach-averaged channel geometry acquired from air photos (MacVicar, 1999). Table 5.1. Slesse Creek channel geometry (MacVicar, 1999) Year 1936 1973 1993 Width (m) 28 21 145 Sinuosity 1.15 1.12 1.06 Slope 0.019 0.020 0.021 Planform Single thread, wandering Single thread, wandering Braided 89 The following list describes the method for determining input data, as discussed by MacVicar (1999). The input parameters used are shown in Table 5.2. • Bankfull discharge (Qbf) - Gauge records for Slesse Creek were used to determine the bankfull discharge. For the years 1993 and 1973, the short-term mean of flows was used and for 1936, the long-term mean was used. • Flow resistance (ks, n) - No roughness information was available for Slesse Creek. Since the Jarrett (1984) Equation calculates a value of Manning's n (see Equation 2.40) based on hydraulic radius and slope, this option was selected while using RiverMod. • Sediment size (D x ) - A pebble count was taken, where D50 = D50 bonk and the sediment size was assumed to remain constant over the years because no historical particle size distribution information was available. • Modified internal friction angle (<)>')- For vegetated banks, <t)i936and ^1973 were determined by calibrating RiverMod. This was done by using the known channel geometry for each year and entering varying values of ty' until the modelled channel geometry matched the observed channel geometry. For unvegetated banks, ^1993 = 40° was used (Millar and Quick, 1993b). • Channel slope (S) - S1993 was determined through field surveys. S1936 and S1973 were calculated using sinuosities determined from air photos and by comparison with S 1 9 9 3 . 90 Table 5.2. Input variables for Slesse Creek (adapted from MacVicar, 1999) Variable 1936 1973 1993 Qbf (m3/s) 92 67 117 D 3 5 (m) 0.11 0.11 0.11 D 5 0 (m) 0.133 0.133 0.133 D Q (m) 0.166 0.166 0.166 D9o (m) 0.33 0.33 0.33 DsObank (m) 0.133 0.133 0.133 <t>' (°) calibrated using RiverMod 70 73 -f (°) estimated - - 40 S 0.019 0.020 0.021 5.2.2 Analysis The fixed-channel-slope model of RiverMod for rivers with non-cohesive bank sediment was used to analyze Slesse Creek. The selected sediment transport relation was the Einstein-Brown Equation (1950) and the selected flow resistance formula was the Jarrett Equation (1984). The input values listed above were used to run several tests. All input values were held constant and was varied between 40 and 90° in order to establish any influence on river width. This was done for 1936, 1973 and 1993 values. The results can be seen in Figure 5.4. For each of the three years, as <)>', and therefore bank stability, decreases, the width of the river increases. For 1993, the value was extrapolated to less than 40° because =40° resulted in a width of 119 m. The observed width for 1993 was 145 m, which according to RiverMod, 91 corresponds to a value of 35°. Figure 5.4 shows the observed geometry for each of the years. For the rest of the analysis, however, <)>' = 40° was used, the generally accepted minimum value that applies to non-vegetated banks In order to make restoration recommendations, <(>' was plotted against width and depth using 1993 values (see Figure 5.5). The Millar (2000) meandering-braiding transition slope equation, was used to determine the value of necessary to change the river morphology back to a meandering pattern from its present-day braided pattern. It is given by: 5* = 0 . 0 0 0 2 £ ° 0 6 y 1 7 5 Qb°Z5 (5.1) where S* is the transitional slope, D50 is the median grain diameter, ()>' is the modified internal friction angle and Qbf is the bankfull discharge. Millar (2000) improved on the Parker (1976, as cited by Millar 2000) criterion (see Equation 2.49) by including the effects of bank Stability. Dsobank was also plotted against width and depth for the 1993 value (see Figure 5.6). Using the Millar (2000) meandering-braiding transition slope equation, the Dsobank necessary to change the stream back to meandering was determined. 5.2.3 Results The RiverMod results show that the bank stability parameter (((>') has effectively decreased from 70° in 1936 to 40° in 1993. This decrease, caused by logging on the 92 f loodplain and banks, has led to channel widening. Figure 5.4 shows the variation of <|>' with W for the bankfull discharge of each test year. River restoration could consist of increasing <)>' and/or Dsobank to achieve a narrower, deeper, more stable, single-thread, channel. Holding all other variables constant, including Dsobank at 0.133, it was established that increasing <(>' to 57° would decrease the river width to 62.2 m. A similar analysis, which held <)>' constant at 40°, determined that increasing Dsobank to 0.36 m would decrease the width to 47.8. These two width values, calculated using Equation 5.1, were established as the transitional width between a meandering and braided stream according to the above conditions. Either of these two strategies should change the river back to meandering, over time. Riparian planting and re-vegetation of the f loodplain is a way of increasing <$>' and therefore stabilizing the banks (MacVicar, 1999). This analysis shows the influence the bank stability parameter, <)>' and Dsobank have on W, assuming all other variables are held constant. Several errors are associated with this, since several variables including the sediment size distribution and roughness data were not available for past years. These values were assumed to be the same as the 1993 measured values. The model predicts a change in planform from meandering in 1936 to braided in 1993. Since this has been determined from air photo analysis (MacVicar, 1999), RiverMod is a good predictor of planform geometry in the case of Slesse Creek and can successfully be used for restoration recommendations. 93 5.3 NARROWLAKE CREEK Narrowlake Creek is located in the central interior of British Columbia about 80 km southeast of Prince George (see Figure 5.7). It is a tributary to the Willow River and its f loodplain was extensively logged in the 1960's and 1970's (Wilson, 2001). 35% of the watershed was harvested, including 80% of the riparian bank vegetation (Berry, 1996 as cited by Wilson eta/., 2001). Air photos from 1946 and 1997 (see Figure 5.8) clearly show that the morphology of Narrowlake Creek has changed from a meandering channel before logging to an almost braided channel after logging. The change in Narrowlake Creek's planform geometry over time has been forced by logging on the banks. Accompanying the change to a "semi-braided" morphology is a marked change in channel width. Channel width has doubled from 1946 to 1997, increasing from 29 m to 58 m (Wilson, 2001). Narrowlake Creek is similar to Slesse Creek in that both creeks have undergone a change in planform geometry following logging and disruption of the banks. However, according to Wilson (2001), Narrowlake Creek has experienced a much higher level of disturbance, including the cumulative impacts of road development, stream crossings, vegetation removal and channel avulsions. As a result, sediment supply and upstream conditions of Narrowlake Creek have changed. This is unlike Slesse Creek, where the upper watershed conditions are still pristine. 94 5.3.1 Investigation In order to apply RiverMod to Narrowlake Creek, the input parameters must be defined for past and present values. The following analysis was conducted on treatment Reach 3 as described by Wilson (2001). Historic aerial photographs have shown that from 1946-1997 the river width has increased from 29 m to 58 m while the slope has remained constant at around 0.007 (Wilson, 2001). The constant slope indicates the fixed-channel-slope version of the model should be used. Table 5.3 shows the reach-averaged channel geometry acquired from air photos. Table 5.3. Narrowlake Creek channel geometry. Year 1946 1997 Width (m) 29 58 Slope 0.007 0.007 Planform Single thread, wandering Braided The following list describes the method for determining input data, derived from Wilson (2001). The input parameters used are shown in Table 5.4. • Bankfull discharge (Qbf) - Gauge records do not exist for Narrowlake Creek. Using gauge information from the Willow River, which Narrowlake Creek flows into, an interpolation was performed in order to determine the bankfull discharge (Personal Communication, Andrew Wilson, 2002). 95 • Flow resistance (ks, n) - No roughness information was available for Narrowlake Creek. Since the Jarrett (1984) Equation calculates a value of Manning's n (see Equation 2.40) based on hydraulic radius and slope, this option was selected while using RiverMod. • Sediment size ( D x ) - Sediment size information was only available for 1997. With no historical sediment size data, it was assumed that D 1 9 4 6 = D 1 9 9 7 . Values for both D 5 0 and D s o b a n k , were obtained. • Modified internal friction angle (<)>') - For vegetated banks, cj>i946 was determined by calibrating RiverMod. This was done by using the model inputs along with the known channel geometry for 1946 and entering varying values of ((>' until the modelled channel geometry matched the observed channel geometry. For unvegetated banks, 4)1997 = 40° was used (Millar and Quick, 1993b). • Channel slope (S) - S 1 9 9 7 was measured through field surveys. S 1 9 4 6 was determined using air photos and by comparison with 5 1 9 9 7 . Table 5.4. Input variables for Narrowlake Creek (adapted from Wilson, 2001) Variable 1946 1997 Q b f (m3/s) 31.1 31.1 D 3 5 (m) 0.055 0.055 D 5 o (m) 0.058 0.058 D a (m) 0.093 0.093 D 9 0 (m) 0.088 0.088 D s o b a n k (m) 0.047 0.047 <|>' (°) calibrated using RiverMod 55 96 f (°) estimated 40 S 0.007 0.007 5.3.2 Analysis The fixed-channel-slope model for rivers with non-cohesive bank sediment of RiverMod was used to analyze Narrowlake Creek. The selected sediment transport equation was the Einstein-Brown (1950) and the selected flow resistance equation was Jarrett (1984). The values listed in Table 5.4 were input to RiverMod. ()>' was varied between 40° and 90° to determine its influence on river width, for 1946 and 1997 data. The results can be seen in Figure 5.8. As , and therefore bank stability decreases, the width of the river increases. For 1997, the <)>' value was extrapolated beyond 40° because 40° resulted in a width of 50.8 m. This is a reasonable approximation of the observed W 1 9 9 7 of 58 m. Figure 5.9 shows markers for the observed geometry for each of the curves. In order to make restoration recommendations, <)>' was plotted against width and depth for the 1997 values (see Figure 5.10). The Millar (2000) meandering-braiding transition formulation was used to determine the value of ^' necessary to change the river morphology back to a meandering pattern from its present-day braided pattern. Dsobank w a s plotted against width and depth for the 1993 value (see Figure 5.11). Using the Millar (2000) meandering-braiding transition formulation, the Dsobank necessary to restore the creek's meandering planform was determined. 97 5.3.3 Results RiverMod predicts a meandering channel for 1997. Although the present channel is no longer meandering, it is not quite braided either. Since 1946, the transition slope has been approaching the limit between meandering and braided rivers. The transition slope may approximate conditions necessary for the gradual change from one planform to another. In Wilson (2001) it is assumed that <)>' = 70° for 1946 and f = 40° for 1997, but RiverMod calibration finds <\>' = 55° for 1946. These refined values give the same results as those obtained by Wilson (2001) which show the creek to be meandering in both years, when actually it is close to braided in 1997. Once calibrated, the model still shows a trend towards a braided river. According to what can be seen from air photos and field surveys, the river has begun to change from meandering to braided over the 30 year period between 1946 and 1997, primarily due to logging activity. Although RiverMod does not show this same result, the trend towards a braided river is evident. Since the modified friction angle (<)>') has decreased due to logging and has led to channel widening, any river restoration program should consist of increasing <|>' and/or Dsobank in order to stabilize the banks. These two methods would aid in the development of a narrower, deeper, more stable, single-thread, channel. ()>' could be increased by 98 riparian planting and re-vegetation of the f loodplain. Dsobank could be increased by the addition of larger, stabilizing gravel along the banks of the river. Since RiverMod did not accurately predict the change in planform for Narrowlake Creek, credible values of <t/ and Dsobank were not obtained. According to results obtained by using RiverMod, the bank stability values at the meandering-braiding transition are <)>' = 34° and Dsobank = 0.035 m. These values are lower than the 1997 values, and would most likely decrease the bank stability further, if used in restoration planning. Errors contributing to this could be the lack of historical sediment Size data and roughness values. Since no gauge exists on Narrowlake Creek, the bankfull discharge was extrapolated, and therefore may not be the true bankfull discharge. The level of disturbance on Narrowlake Creek is much higher than that of Slesse Creek (Wilson, 2001). This could account for the higher degree of success in the application of RiverMod to Slesse Creek over Narrowlake Creek. The higher level of disturbance on Narrowlake Creek could also signify a larger level of uncertainty associated with input data. It could also mean that there are more factors influencing the decrease in bank stability than RiverMod can account for. The model should predict a change in planform from meandering in 1946 to braided in 1997, since this has been determined from air photo analysis (Wilson, 2001), RiverMod is a good predictor of planform geometry in the case of Slesse Creek and has provided useful information in the case of Narrowlake Creek. 99 Figure 5.1. (a) Location of Slesse Creek Watershed; (b) Slesse Creek Watershed (MacVicar, 1999) 100 (a) Figure 5.2. Airphoto* of Slesse Creek: (a) 1936,1:22000 scale; (b) 1973,1:19050 scale; (c) 1993,1:17650 scale (MacVicar, 1999). 101 Chilliwack River Scale 1:22,200 Figure 5.3. Slesse Creek lower watershed, showing study reach D in 1936 (MacVicar, 1999). 102 o ON o oo o O Ol •o o ID O o (ui) M+p.iM 103 a >-_n o a c_ o 4 ->-£ . +-W £ o cn -t-o £_ "a <j "a -t-O a s o V) _v> o £ in cn c a C O o H— "O W O £ > vO C O ON * — i II 0) £_ a cr c o '•»-a t_ .a "a < J CD £_ <o CD V) J — V) ro . ON ro ON cn c a in" cn ON —^t n o L. (ui) qjdaa 00 CM 1^ CO CM T-ii O O I 1 1 1 1 u P 104 (ui) u,4.daq o o o o o o E o o o w vO Cd O 0 0 O „ f 0 0 l _ -w—t y—t f~i ^ (UJ) H+pjM * LL 105 Figure 5.7. Location of Narrowlake Creek Watershed 106 Figure 5.8. Airphotos of Narrowlake Creek: (a) 1946; (b) 1997 (Wilson, 2001). 107 o o 0 0 o W o cn •o o in o o CO ("0 H+P.'M I I o >-4-£ o cn T3 +-a £_ £ "a o "a 3 -t-<J a 5 o o £ >-lO _o cn c a o c M — " O O £ 2 's c o •4-a i_ .D "a o i_ VJ o s_ s_ a Z O N in O N T—I I I I_ a 3 CT 3 ^ 108 (UJ) u,j,daq REFERENCES Ackers, P., and White, W.R., 1973: "Sediment transport: New approach and analysis." 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Rouse, H., 1965: "critical analysis of open channel res\s-far\ce." Journal of the Hydraulics Division, ASCE, 9 (HY4), 1-25. Streeter, V.L., and Wylie, E.B., 1981: Fluid Mechanics. McGraw-Hill Ryerson Limited, 562p. Thorne, C.R., 1982: "Processes and menchanisms of bank erosion." In Gravel-Bed Rivers, R.D. Hey, J.C. Bathurst, and CR. Thorne (Eds.), John Wiley A Sons, Chichester, 227-271. Thorne, C.R., 1997: "Channel types and morphological classification." In Applied Fluvial Geomorphology for River Engineering and Management, Thorne, C.R., Hey, R.D., and Newson, M.D., (Eds.). John Wiley and Sons, 175-222. Vanoni, V.A., 1975: Sedimentation engineering. ASCE Manuals and Reports on Engineering Practice, 745p. Werritty, A., 1997: "Short-term changes in channel stability." In Applied Fluvial Geomorphology for River Engineering and Management, Thorne, C.R., Hey, R.D., and Newson, M.D., (Eds.). John Wiley and Sons, 47-65. Wilcock, P.R., 2001: "Toward a practical method for estimating sediment-transport rates in gravel-bed rivers." Earth Surface Processes and Land forms, 26, 1395-1408. White, W.R., Bettress, R., and Paris, E., 1982: "An analytical approach to river regime." Journal of Hydraulic Engineering, 108 (10), 1179-1193. 115 Williams, &.?., 1970: "Manning formula - a misnomer?" Journal of the Hydraulics Division, ASCE, 96 (HY1), 193-200. Wilson, A., 2001: "Predicting channel change in Narrowlake Creek in the Central Interior: A tool for watershed protection and restoration." Watershed Restoration Technical Bulletin: Streamline, 5 (4), 8-12. Wilson, A., Nesbit, B. and Pillipow, R., 2001: "Riparian restoration at the Narrowlake Creek Demonstration Watershed." Watershed Restoration Technical Bulletin: Streamline, 6 (3), 24-29. 116 

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