"Applied Science, Faculty of"@en . "Civil Engineering, Department of"@en . "DSpace"@en . "UBCV"@en . "Marti\u00CC\u0081n, Violeta"@en . "2009-11-12T00:00:00"@en . "2003"@en . "Doctor of Philosophy - PhD"@en . "University of British Columbia"@en . "A new theoretical analysis was developed that accounts for variable grain protrusion within\r\nself-formed, stable gravel armour layers. A key feature of the analysis is accounting for the\r\nvariation in drag coefficient, drag force and critical dimensionless shear stress with grain\r\nprotrusion above the virtual bed, which is defined here as the elevation at which the\r\nextrapolated logarithmic velocity profile becomes equal to zero. The central hypothesis is that\r\nself-formed stable armour layers develop through adjustment of grain protrusion such that all\r\ngrains are at the threshold of motion, at least in a statistical sense. This represents the limiting\r\ncase of equal mobility. Testing of the analysis using published flume data shows good\r\nagreement between observed and predicted roughness height, mean velocity and flow depth.\r\nExperimental work on simulating gravel-bed armouring was carried out to obtain more data\r\nand test the assumptions underlying the numerical model. Velocity profiles across and along\r\nthe flume were measured with an acoustic Doppler velocimeter (ADV). To determine the\r\nreliability of ADV measurements in turbulent flows over rough boundaries, a thorough data\r\nanalysis was undertaken. Shear stresses obtained from the force balance (pgYSj), from the\r\nvelocity profiles, or from the Reynolds stress measurements were compared and showed a\r\nreasonable agreement. A unique study on individual grain protrusion was carried out, in\r\nwhich the armoured beds were scanned, digital elevation models (DEM) were developed, and\r\nthen combined with photographs to obtain the information on protrusions. These measured\r\nprotrusions are in good agreement with those calculated in the numerical mod"@en . "https://circle.library.ubc.ca/rest/handle/2429/14800?expand=metadata"@en . "25902784 bytes"@en . "application/pdf"@en . "Hydraulic Roughness of Armoured Gravel Beds: the Role of Grain Protrusion by VIOLETA M A R T I N B.Sc , Civi l Engineering, University of No vi Sad, Yugoslavia, 1989 M.A.Sc., Civi l Engineering, University of British Columbia, 1996 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN THE F A C U L T Y OF G R A D U A T E STUDIES (DEPARTMENT OF CIVIL ENGINEERING) We accept this thesis as conforming to the required standard UNIVERSITY OF BRITISH C O L U M B I A January, 2003 \u00C2\u00A9 Violeta Martin, 2003 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 ClV\j &tT)QMC&t\VQ The University of British Columbia Vancouver, Canada Date f B b . 2 7 Z O Q ^ DE-6 (2/88) ABSTRACT A new theoretical analysis was developed that accounts for variable grain protrusion within self-formed, stable gravel armour layers. A key feature of the analysis is accounting for the variation in drag coefficient, drag force and critical dimensionless shear stress with grain protrusion above the virtual bed, which is defined here as the elevation at which the extrapolated logarithmic velocity profile becomes equal to zero. The central hypothesis is that self-formed stable armour layers develop through adjustment of grain protrusion such that all grains are at the threshold of motion, at least in a statistical sense. This represents the limiting case of equal mobility. Testing of the analysis using published flume data shows good agreement between observed and predicted roughness height, mean velocity and flow depth. Experimental work on simulating gravel-bed armouring was carried out to obtain more data and test the assumptions underlying the numerical model. Velocity profiles across and along the flume were measured with an acoustic Doppler velocimeter (ADV). To determine the reliability of ADV measurements in turbulent flows over rough boundaries, a thorough data analysis was undertaken. Shear stresses obtained from the force balance (pgYSj), from the velocity profiles, or from the Reynolds stress measurements were compared and showed a reasonable agreement. A unique study on individual grain protrusion was carried out, in which the armoured beds were scanned, digital elevation models (DEM) were developed, and then combined with photographs to obtain the information on protrusions. These measured protrusions are in good agreement with those calculated in the numerical model. TABLE OF CONTENTS Abstract ii Table of Contents iii List of Tables vi List of Figures vii List of Symbols xii Acknowledgements xiv 1. Introduction 1 1.1. Purpose of Present Work 1 1.2. Approach to Analysis and Scope of the Present Work 4 2. Literature Review 6 2.1. Armouring Processes 6 2.2. Velocity Profile, Virtual Bed Position and Representative Roughness Height 10 2.3. Relationships Amongst Different Roughness Parameters 17 2.4. Critical Shear Stress 19 3. Numerical Model 23 3.1. Introduction 23 3.2. Hypothesis 23 3.3. Model Development 24 3.3.1. Velocity profile and the location of the virtual bed 25 3.3.2. Drag force and drag coefficient 27 3.3.3. Variation of critical shear stress with grain protrusion 31 3.4. Computational Scheme 34 3.5. Model Behaviour 38 4. Experimental Work and Data Analysis 40 4.1. Introduction 40 4.2. Hydraulic Parameters - Depth, Slope, Discharge and Temperature Measurements 44 4.2.1. Bed and water surface elevation measurements 44 4.2.2. Discharge measurements 56 4.2.3. Temperature measurements 57 4.3. Flow Velocities 59 iii 4.3.1. Measurements 60 4.3.2. Data analysis 61 4.3.3. Velocity profiles 67 4.4. Reynolds Stresses from A D V Measurements 75 4.4.1. Boundary interference 77 4.4.2. Inclusion of data edited with the 40% correlation filter 77 4.4.3. Inclusion of the zero shear stress value at the water surface 81 4.5. Sediment Sampling and Analysis 85 4.5.1. Original material 85 4.5.2. Bed surface material 88 4.5.3. Bed surface appearance 92 4.5.4. Eroded material 97 4.6. Grain Protrusion Measurements 100 4.6.1. Measurements 100 4.6.2. Data analysis 103 4.7. Experimental Conclusions 112 5. Results 113 5.1. Experimental Results 113 5.1.1. Shear velocities, u 113 5.1.2. Roughness parameter, ks 123 5.1.3. Hydraulic conditions - variation with time 126 5.1.4. Grain protrusion calculations '. 128 5.2. Numerical Model Results 135 5.2.1. Selection of experimental data for testing 135 5.2.2. Comparison with previous studies 140 5.2.3. Grain Protrusion Model predictions for ks, U and Y 144 5.2.4. Grain Protrusion Model predictions for H 148 6. Discussion and Conclusions 151 6.1. Analytical Considerations 152 6.1.1. Protrusion prediction 155 6.2. Experimental Considerations 158 iv 6.2.1. Bed formation processes 160 6.2.2. Slopes 161 6.2.3. Velocities 162 6.2.4. Protrusions 163 6.2.5. Microbedform development 163 6.3. Discussion on Bed Armouring Processes 165 6.4. Recommendations and Possible Future Development 169 6.5. Conclusions 170 7. References 172 Appendix A: Velocity Measurements 182 Appendix B: Velocity Profiles 193 Appendix C: Sediment Sampling Considerations 206 Appendix D: Sample Spreadsheets from the Grain Protrusion Model 214 v LIST OF TABLES 4.1. Initial and final hydraulic parameters for Runs 1 through 5 54 4.2. Average degradations at the end of Runs 1 through 5 56 4.3. Physical properties of water and Reynolds numbers for Run 1 59 4.4. Grain size distributions for the for the armour layers 91 4.5. Grain size distributions for the original and eroded materials 99 5.1. Measured depths and friction slopes, and calculated shear velocities for all five runs for various segments of the test section 117 5.2. Shear velocities obtained from velocity profiles for all five runs 119 5.3. Shear velocities obtained from Reynolds stresses for all five runs 121 5.4. Values of the roughness coefficient, k s, calculated from velocity profiles, and from depths, slopes, and mean velocities for all five experiments 124 5.5. Statistical properties for the whole bed and for different grain size elevations in Run 4 132 5.6. Statistical properties for the whole bed and for different grain size elevations in Run 5 132 5.7. The protrusions measured with the laser and the protrusions predicted in the Grain Protrusion Model for Run 4 and Run 5 148 6.1. Comparison of protrusion heights calculated in the model 157 B - l . Results of sieving for the original material for four sub-samples 209 B-2: Results of sieving for two samples of the transported material in Run 5 210 B-3. Characteristic grain sizes for three samples of Run 5 211 VI LIST OF FIGURES 2.1. Type of armour layer development depending on bed material supply 9 2.2 Observed and predicted values of: (a) roughness height, k s; and (b)mean velocity, U , for experiments of Proffitt (1980) and Saad (1986) 16 3.1. Definition sketch for non-uniform sediment 26 3.2. Drag force position on a protruding grain 28 3.3. Results of the numerical integration for the drag force position 29 * 3.4. Variation of drag coefficient (Co ) with relative protrusion (H/D) 31 3.5. Variation of non-dimensional critical shear stress (xc*) with relative protrusion (H/D) (after Chin, 1985, and Fenton and Abbott, 1977) 33 3.6. Grain Protrusion Model flow chart 37 3.7. Simulated results for Run 3-1 from Proffitt (1980): (a) Variation in relative protrusion, H/D; (b) Cumulative grain shear stress 38 4.1. Schema of the experimental apparatus (from Martin, 1996) 42 4.2. The adjustable sediment sill at the end of the test section 47 4.3. Bed, water surface and energy slopes for Runs 1 through 3 (Figures a to c) 51 4.4. Bed, water surface and energy slopes for Runs 4 and 5 (Figures a, b) 52 4.5. Friction slopes determined for each run and for different parts of test section 53 4.6. Degradation through time for Runs 1 through 5 for a point on a flume centreline 2 m downstream from the beginning of the test section 55 4.28. Bed development through time for Run 3 along the flume centreline and for the whole test section 55 4.29. VersaFLO flow meter: (a) The multiprocessor transmitter and a pair of transducers; and (b)The transducers mounted on the inlet pipe (ID 10\") 57 4.30. The SonTek Micro A D V: (a) The sensor mounted on a flexible cable; and (b) The sampling volume (from SonTek's web site) 60 4.10. Locations for velocity profile measurements 61 4.11. Velocity profiles for Run 5 - across: (a) cross section A; (b) cross section B; (c) cross section C 72 4.12. Velocity profiles for Run 5 without data for bottom 2 cm - across: (a) cross vii section A ; (b) cross section B; (c) cross section C 73 4.13. Velocity profiles for Run 5 without data for bottom 2 cm - along: (a) Right profiles; (b) Centreline profiles; (c) Left profiles 74 4.14. Determination of the total shear stress at the bed form Reynolds stresses for Run 4, cross-section A, centreline profile 76 4.15. A D V measurements for the centreline profile of cross-section B, Run 5: (a) Reynolds stresses; and (b) Percent of data retained for analysis 78 4.16. Shear stress values on the bed for all runs determined from Reynolds stress profiles derived from data edited with 40% vs. 70% correlation filter 80 4.17. Determination of the bed shear stress based on the Reynolds stress: trendline forced to zero at water surface; zero value at water surface included in trendline; and with trendline fitted only to the linear part of the measured profile 82 4.18. Total bed shear stress values determined with the zero value at surface included in the trendline vs. the total bed shear stress values determined from the linear part of the Reynolds stress only 83 4.19. Grain size distributions for three different samples of the original material 87 4.20. Results of a conversion from an areal to a volumetric sample 88 4.21. Imprint after an areal sample was taken 89 4.22. Grain size distributions for the armour layers in Runs 1 through 5 90 4.23. Bed coarsening due to increased shear stress: (a) Initial bed conditions; and (b) through (f) Final bed conditions for Runs 1 to 5 93 4.24. Run 4 - Bed surface comparison: (a) After 45 hours; and (b) After 62 hours 96 4.25. Grain size distributions for the eroded materials 98 4.26. (a) The DynaVision SPR-04 laser displacement meter (from L M I Technologies Inc. web site); (b) Instrument mounting; and (c) The control frame with the white wires as reference points lowered into the flume 101 4.27. DEMs for Run 5 with a 2 mm contour spacing for Z: (a) Initial measurements; and (b) Measurements after the bed was coated with a very fine layer of baking powder 103 4.28. Run 5: (a) A section of a D E M with a 2 mm contour spacing, super-positioned over a photograph of the same area; (b) A shaded relief map for the same area 104 4.29. D E M for Run4 super-positioned on the photograph of the same area; the grid size is 2Dg4 = 34 mm 108 4.30. D E M for Run 5 super-positioned on the photograph of the same area; the grid size is 2Dg4 = 37 mm 109 4.31. Run 4 (units in mm): (a) A contour map of the laser scanned area before slope correction; (b) A contour map of the laser scanned area corrected for a slope of 0.003, the mean bed level is at 135 mm 110 4.32. Run 5 (units in mm): (a) A contour map of the laser scanned area before slope correction; (b) A contour map of the laser scanned area corrected for a slope of 0.012, the mean bed level is at 149.5mm I l l 5.1. Shear velocity values obtained for all five runs using the depth-slope method; the shaded diamonds represent the values accepted for further calculations 116 5.2. Average shear velocities calculated from the velocity profiles 119 5.3. Average shear velocities calculated from Reynolds stress profiles 120 5.4. Comparison of shear velocities determined by using different methods: (a) Depth-slope and Reynolds stress; (b) Depth-slope and velocity profile; and (c) Reynolds stress and velocity profile 122 5.5. Roughness coefficient comparison for values calculated form depth, slope and mean velocities vs. values calculated from velocity profiles for the centreline only or for all profiles for Runs 1 - 5: (a) without sidewall correction; and (b) with sidewall correction 125 5.6. Variation of hydraulic parameters with time: (a) Run 1; and (b) Run 5 127 5.7. Frequency distributions of bed surface elevations: (a) Run 4, a z = 5.1 mm; and (b) Run 4, a z = 5.6 mm 129 5.8. Mean bed elevation and mean elevations for different grain sizes: (a) Run 4, mean bed is at 135 mm; and (b) Run 5, mean bed is at 149.5 mm 131 5.9. Mean grain protrusions with error bars of \u00C2\u00B1 one standard error: (a) Run 4, Mean bed is at 135 mm; and (b) Run 5, mean bed is at 149.5 mm 134 5.10. Initial vs. final friction slopes for the experiments of Gomez (1993), and for this study 137 5.11. Increase in (a) median grain size, and (b) roughness coefficient with increasing shear velocity for experiments of Proffitt, Saad and current study 141 5.12. Increase in bed coarsening with increasing bed shear stress : (a) The mean armour grain size; and (b) The relative coarsening 142 5.13. Variation in Shields' number for the armour layer vs. relative depth 143 5.14. Roughness coefficient comparison with predictions from the numerical model 146 5.15. Mean velocity comparison with predictions from the numerical model 147 5.16. Flow depth comparison with predictions from the numerical model 147 5.17. Comparison between the protrusion measurements obtained with the laser and the predicted protrusions in the Grain Protrusion Model for Run 4 and Run 5 150 6.1. Initial vs. final shear velocities for Runs 1 through 5 160 6.2. Microbedforms in Run 4: (a) A photograph of a bed surface; and (b) A coarse D E M for the same bed, with contours 8 mm apart 164 6.3. \"Accounting for microbedform development in the Grain Protrusion Model: (a) The hydraulic roughness; and (b) The mean velocity 166 A - l . Testing the correlation parameter for A D V measurements in: (a) flow over a smooth boundary; (b) flow over a smooth boundary behind a screen; (c) flow over a rough boundary; (d) flow over a rough boundary in the wake of a large element; and (e) original experimental set-up, Run 5 183 A-2. Correlation parameter for A D V measurements in flows over smooth and rough boundaries for: (a) A D V velocity range set to 100 cm/s; and (b) A D V velocity range set to 250 cm/s 185 A-3. A D V Measurements for Profile 3 - flow over a rough boundary: (a) Velocity data; (b) Percent of data retained for analysis after applying the correlation filter 187 A-4. Filtering based on the correlation coefficient (shaded symbols), or on the spike detection filter with the acceleration threshold of 1.5 g's (open symbols): (a), (c) and (e) are the average velocities at a point; (b), (d) and (f) are Reynolds stresses .. 189 A-5. (a) Velocity values obtained using the 40% correlation filter vs. the 70% correlation filter, or the spike detection filter with acceleration threshold set to 1.5 g's; (b) Percentage of data retained for different filtering methods vs. distance from the boundary 191 x B - l . Velocity profiles for Run 1- across: (a) cross section O; (b) cross section A ; (c) cross section B; and (d) cross section C 194 B-2. Velocity profiles for Run 2 - across: (a) cross section A; (b) cross section B ; (c) cross section C 195 B-3. Velocity profiles for Run 3 - across: (a) cross section A ; (b) cross section B ; (c) cross section C 196 B-4. Velocity profiles for Run 4 - across: (a) cross section A ; (b) cross section B ; (c) cross section C 197 B-5. Velocity profiles for Run 1 without data for bottom 2 cm - across: (a) cross section O; (b) cross section A ; (c) cross section B; and (d) cross section C 198 B-6. Velocity profiles for Run 2 without data for bottom 2 cm - across: (a) cross section A ; (b) cross section B; (c) cross section C 199 B-7. Velocity profiles for Run 3 without data for bottom 2 cm - across: (a) cross section A ; (b) cross section B ; (c) cross section C 200 B-8. Velocity profiles for Run 4 without data for bottom 2 cm - across: (a) cross section A ; (b) cross section B; (c) cross section C 201 B-9. Velocity profiles for Run 1 without data for bottom 2 cm - along: (a) Right profiles; (b) Centreline profiles; (c) Left profiles 202 B-10. Velocity profiles for Run 2 without data for bottom 2 cm - along: (a) Centreline profiles 203 B - l l . Velocity profiles for Run 3 without data for bottom 2 cm - along: (a) Right profiles; (b) Centreline profiles; (c) Left profiles 204 B-l2. Velocity profiles for Run 4 without data for bottom 2 cm - along: (a) Right profiles; (b) Centreline profiles; (c) Left profiles 205 C - l . Grain size distribution curves for two sieving tests of the same areal sample of Run 5 206 C-2. Grain size distribution curves for four sub-samples of the original material 208 C-3. Grain size distribution curves for the two transported material samples of Run 5 ... 208 C-4. Grain size distribution curves for three areal samples of Run 5 211 C-5: Grain size distributions for two areal samples of Run 4 taken after 45 and 62 hours 213 xi LIST OF SYMBOLS AD projected grain area normal to the flow above the virtual bed [m2] B constant of integration C the Chezy coefficient Co drag coefficient Co grain protrusion drag coefficient D particle diameter [m] Dgi geometric mean of the grain size interval [m] Dq geometric mean for the sediment mixture [m] DN particle size for which n percent of the particles are finer by weight [m] / the Darcy-Weisbach resistance coefficient FD drag force [N] Ft fraction of grains with diameter \u00C2\u00A3>,\u00E2\u0080\u00A2 present on the bed surface Fr the Froude number g gravitational acceleration [m/s2] Hj individual grain protrusion height [m] ks the Nikuradse's equivalent sand roughness, in this thesis referred to as the hydraulic roughness coefficient [m] n the Manning's resistance coefficient Nj random noise in the A D V signal q unit discharge [m2/s] Q total discharge [m3/s] r grain radius (r = 0.573) [m] R hydraulic radius [m] Re the Reynolds number (Re= UY/ v) 50 bed slope Sf friction, or energy slope St the coherent part of the A D V signal 51 the A D V return signal from a single pulse Sw water surface slope Ss specific gravity for sediment (Ss = pjp) xii u' longitudinal velocity fluctuation [m/s] ur reference velocity for calculating the drag force [m/s] uy flow velocity at elevation^ above the bed [m/s] u shear velocity [m/s] U mean flow velocity [m/s] y depth [m] Y total depth of flow [m] yr position of the drag force acting on a grain [m] z, bed elevation above a datum at cross-section i [m] Zo coefficient describing the hydraulic roughness of the boundary, height above the datum at which u = 0 [m] w' vertical velocity fluctuation [m] (f> particle friction angle K the von Karman's constant equal to 0.4 for clear water flow v kinematic viscosity for water [m2/s] 6 is the angle measured from the horizontal plane passing through the grain centre p water density [kg/m3] ps sediment density [kg/m3]