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Simons Et Al. 2004 Geomorphic, Hydrologic, Hydraulic and Sediment Concepts Applied To Alluvial Rivers By Daryl B. Simons, Ph.D., P.E., D.B. Simons & Associates, Inc.; Everett V. Richardson, Ph.D., P.E., Ayres Associates, Inc.; Maurice L. Albertson, Ph.D., P.E., Colorado State University; Robert J. Kodoatie, Ph.D., Diponegoro University, Indonesia. 2004 Daryl B. Simons Published by Colorado State University OPEN FILE INTERNET – FREE DOWNLOAD Dedicated to Major Contributors to the Concepts of Flow of Water and Sediment in Alluvial Channels: Paul C. Benedict, U.S. Geological Survey; Donald C. Bondurant, U.S. Corps of Engineers; Whitney M. Borland, U.S. Bureau of Reclamation; Bruce R. Colby, U.S. Geological Survey; Brynon C. Colby, U.S. Geological Survey; Hans A. Einstein, University of California, Berkeley; Dave W. Hubbell, U.S. Geological Survey; E.W. Lane, U.S. Bureau of Reclamation; Emmett M. Laursen, University of Arizona; Luna B. Leopold, U.S. Geological Survey; Carl F. Nordin, U.S. Geological Survey; Hunter Rouse, University of Iowa; Stanley E. Schumm, Colorado State University; Lorenzo G. Straub, University of Minnesota; and Vito A. Vanoni, California Institute of Technology. iii Table of Contents LIST OF SYMBOL ....................................................................................... V ABSTRACT ................................................................................................. IX 1. INTRODUCTION ................................................................................... 1 2. FUNDAMENTALS THAT MUST BE INTEGRATED INTO THE TRANSPORT ANALYSIS OF AN ALLUVIAL CHANNEL ................ 2 2.1 ALLUVIAL GEOMORPHOLOGY ............................................................... 2 2.2 REGIMES OF FLOW AND BEDFORMS IN ALLUVIAL CHANNELS ................. 2 2.2.1 Bed Configuration ....................................................................... 5 2.2.2 Plane Bed Without Sediment Movement ....................................... 7 2.2.3 Ripples ........................................................................................ 8 2.2.4 Dunes .......................................................................................... 8 2.2.5 Plane Bed With Movement ........................................................... 9 2.2.6 Antidunes .................................................................................. 10 2.2.7 Chutes and Pools ....................................................................... 10 2.2.8 Regime of Flow, Configuration, and Froude Number ................. 10 2.2.9 Bars .......................................................................................... 12 2.3 GEOMORPHIC RELATIONS THAT ASSIST PRELIMINARY ANALYSIS OF ALLUVIAL CHANNELS ......................................................................... 14 2.4 APPLICATIONS OF GEOMORPHIC AND HYDROLOGIC ANALYSIS ............. 14 2.5 DATABASE ......................................................................................... 18 2.6 THE THREE-LEVEL ANALYSIS OF ALLUVIAL RIVERS ............................ 21 3. RESISTANCE TO FLOW IN ALLUVIAL RIVERS ........................... 25 3.1 CLASSIFICATION OF OPEN CHANNELS .................................................. 26 3.2 VARIATION OF MANNING’S RESISTANCE COEFFICIENT FOR ALLUVIAL CHANNELS ......................................................................................... 27 3.3 FORM ROUGHNESS.............................................................................. 31 3.4 SELECTING ROUGHNESS COEFFICIENTS FOR A PRACTICAL CASE ........... 32 3.5 DATA REQUIRED TO ESTIMATE MANNING'S N, VELOCITY, STAGE, AND SEDIMENT TRANSPORT ....................................................................... 33 3.5.1 Data Required for Alluvial Channels ......................................... 33 3.5.2 Data Required for the Floodplain .............................................. 34 3.6 CONCEPTS TO REMEMBER ................................................................... 34 4. BEGINNING OF MOTION .................................................................. 36 4.1 INTRODUCTION ................................................................................... 36 4.2 REPRESENTATIVE DIAMETER OF A BED-MATERIAL MIXTURE ............... 37 4.3 THEORETICAL CONSIDERATIONS ......................................................... 40 4.4 THEORY OF BEGINNING OF MOTION .................................................... 40 4.5 EXPERIMENTAL APPROACHES ............................................................. 42 4.6 SHIELDS DIAGRAM ............................................................................. 44 4.7 OTHER FORMULAE DEFINING THE BEGINNING OF MOTION ................... 46 4.8 APPLICATION OF BEGINNING OF MOTION TO PRACTICAL PROBLEMS ..... 47 5. SEDIMENT TRANSPORT................................................................... 54 5.1 HISTORIC NOTE .................................................................................. 54 5.2 FUNDAMENTALS OF SEDIMENT TRANSPORT ......................................... 59 5.3 SUSPENDED BED SEDIMENT DISCHARGE .............................................. 61 5.4 PROCEDURE TO DEVELOP NEW SEDIMENT TRANSPORT RELATIONS ...... 65 5.4.1 Scope of Study ........................................................................... 65 5.4.2 Correlation Coefficient Analysis of 10 Selected Equations .......... 69 5.4.3 Total Load Equations Based on Advection-Diffusion, Energy Balance and Stream Power Concepts ......................................... 71 5.4.4 Einstein’s Method ...................................................................... 71 5.4.5 Statistical Approach .................................................................. 72 5.5 FUTURE MODIFICATIONS OF TRANSPORT RELATIONSHIPS .................. 105 6. SUMMARY AND CONCLUSIONS ................................................... 106 7. BIBLIOGRAPHY ............................................................................... 110 v LIST OF SYMBOL b, c coefficients in modified Simons equation C sediment concentration percent by weight Cc correlation coefficient Cui ,Cmi ,Cli concentration distribution of the upper, middle and lower zones Cw concentration of wash load CS coefficient of shear d or y flow depth da critical size for armoring d* the dimensionless grain diameter is expressed as d* 1/3 ( s / w 1)g 2 ds v d50 0mean diameter of sediment d average diameter of sediment d50 / ratio of the median grain size to the laminar sublayer and defined as d50 ud50 11.6v d84 particle size of which 85% of the bed is finer th di geometric mean diameter of particle of the i size ds particle diameter of bed material ' u ' f functional relation of u / i i functional relation of u /i Fd the form drag component Fu the viscous drag component FB the buoyant force component Fr Froude number, u gd g gravitational acceleration G the slope of the size distribution for sediment curve i data set or point number I1I2 integrals of Einstein’s form of suspended sediment equation ks coefficient of roughness for the bed or roughness coefficient according to Strickler Lb bed load which is defined as the transport of sediment particles that are in vi close contact with the bed Lbm the capacity limited bed-material load Lm measured sediment Ls suspended load defined as the suspended sediment passing through a stream cross section above the bed layer LT the total sediment load Lu unmeasured sediment that is the sum of bed load and fraction of suspended load below the lowest sampling elevation Lw wash load which is the range of fine particle not found in the bed d5 > d10. and is determined by available bank and upslope supply n Manning’s roughness coefficient n number sediment size fractions N Newtons N total number of data sets P wetted parameter Pc is the percent of sediment coarser than the critical size for armoring Pi fraction of bed material for diameter particle size di Psi,Pbi the fraction of suspended material and fraction of bed material of di 30.2d PE transport parameter due to Einstein and defined as PE 2.303log q q dimensionless unit discharge * 3 gd50 qb the unit discharge of bed sediment load qs the unit discharge of suspended sediment load qsi the unit suspended load discharge in Einstein’s approach qT the total unit discharge expressed in dry weight per unit time and width for any system of unit qt the unit sand discharge (mg/m/day) or (ft 3 /ft of width/s) qti the total unit bed-material load discharge in Toffaletti’s method for the sediment of size di Qs the total sediment discharge r’ hydraulic radius of bed grain roughness RD the mean discrepancy ratio R the mean discrepancy ratio ' Rb the bed hydraulic radius associated with the grain roughness 3 gd50 Rg the bed hydraulic radius associated with the grain roughness Rg v s scattering of the discrepancy ratio s S channel slope Spw specific stream power which is defined as SpQS / w vii u the mean velocity / u* shear velocity o uc the average velocity at incipient motion uS the unit stream power uS / the dimensionless unit stream power x correction factor in the logarithmic velocity distribution related to the apparent roughness of the bed surface as determined for values ' ks / 11.6v / u X the characteristic grain size of the mixture in Einstein’s method X1 computed sedimentation X average of computed sedimentation YL equal to Log f (u /i s Y parameter in the relationship Y Rg Y1 measured sedimentation Y average of measured sedimentation iu Zi the exponent defined as Zi C2ds GREEK SYMBOLS
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