Table Of ContentAronne Armanini
Principles
of River
Hydraulics
Principles of River Hydraulics
Aronne Armanini
Principles of River
Hydraulics
123
Aronne Armanini
Department ofCivil, Mechanicaland
Environmental Engineering
University of Trento
Trento
Italy
Translated byGiusi Zummo
ISBN978-3-319-68099-6 ISBN978-3-319-68101-6 (eBook)
https://doi.org/10.1007/978-3-319-68101-6
LibraryofCongressControlNumber:2017953816
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To my family
Preface
The intention is to collect my lecture notes for the introduction to River
Engineering, a subject I have been teaching to master’s students in Environmental
andLandEngineeringattheUniversityofTrentosince1987.Thiscourseisdivided
intotwoparts:theformerisdevotedtothefundamentalsofriverhydraulics,andthe
latterdealswithcalculationanddesigntoolsusedforriverrestoration.Infullregard
to the location, the course especially focuses on mountain and piedmont streams
which are subject to intense sediment transport and continuous morphological
variations. This first volume contains the key topics of natural watercourse
hydraulics. I deliberately left out, and took for granted, the topics conventionally
dealt with in manuals of hydraulics, hydrodynamics and hydrology, as well as the
problemof unsteadyriver flows addressedwiththe traditional fixed-bed approach.
On the other hand, some hydraulics topics usually neglected in traditional text-
books, for example, vegetation and macro-roughness effects on flows, are consid-
ered in the first chapter, in that they are typical of several gravel bed rivers. The
other chapters are entirely devoted to mobile-bed river hydraulics. I also tried to
emphasize a few aspects which in the past may have been neglected for a limited
knowledge of phenomena but currently required to identify and solve some prob-
lems,forexample,theeffectofnonuniformsedimentsandmathematicalmodeling.
Thestructureofthebookisthesameasmanyriverhydraulicsorsedimenttransport
manuals, both classical like those by H. Walter Graf, M. Yalin, and Pieter Ph.
Jansen et al., and most recent like Pierre Julien’s; it also takes some important
internet contributions by Gary Parker into account. Sometimes, the formulation
of the problems may appear too analytical, which is undoubtedly helpful for
engineering students but rather complex for those who will use it as a reference
bookforapplications.Inmyopinion,however,thestudyofsedimenttransportand
fluvial morphology has always been too empirical, without any attempt to take a
theoreticallookatthesubject.Nowadays,suchamethodisoutdated:asamatterof
fact, design choices demonstrated a reckless disregard of long-term consequences
on watercourse dynamics and, last but not least, hydraulic engineers were highly
competent in the fixed-bed hydraulics, but somewhat reluctant to replace their
conceptualframeworksinadequateforthestudyofnaturalwaterstreamswhichare
vii
viii Preface
simplymobile-boundaryflows.ThisbookfirstappearedinItalianin1999underthe
title Principi di idraulica fluviale (Principles of River Hydraulics); this is the
English version, revised and expanded. Special thanks are due to Giuseppina
Zummo for her professional competence and accuracy in the English translation.
IwouldliketothankPaoloScarfielloforhisvaluablehelpwithseveralgraphsand
chartsofthebook.IamdeeplygratefultomycolleaguesoftheDepartmentofCivil
and Environmental Engineering at the University of Trento for the precious
moments of discussion on nearly all the topics covered in the book, especially to
Michele Larcher, Giorgio Rosatti, and Luigi Fraccarollo. Finally, thank to Giulia
Rossi for her precious help in reviewing the page proofs of the book.
Trento, Italy Aronne Armanini
August 2017
Contents
1 Roughness in Fixed-Bed Streams . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Uniform Flow in Circular Pipes. . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Uniform Flow in Compact Cross-Sectional Channels . . . . . . . . . . 2
1.3.1 Secondary Circulations. . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3.2 Low Submergence Flow. . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.4 Resistance Due to Vegetation . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.4.1 Channels with Fully Submerged Flexible Vegetation . . . . . 12
1.4.2 Channels with Emergent Vegetation . . . . . . . . . . . . . . . . . 16
1.5 Compound Channels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.6 Channels with Composite Wall Roughness . . . . . . . . . . . . . . . . . 21
1.6.1 Shear Stress on Each Portion of the Wetted Perimeter . . . . 25
1.6.2 Limits of Einstein-Horton’s Criterion . . . . . . . . . . . . . . . . 26
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2 Introduction to Sediment Transport . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.2 Characterization of Solid Particles . . . . . . . . . . . . . . . . . . . . . . . . 34
2.2.1 Sediment Density. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.2.2 Geometric Classification. . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.2.3 Empirical Formulae for the Fall Velocity
in Still Water. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.3 Sediment Transport Capacity, Solid Discharge, Wash Load,
and Bed Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.4 Sediment Transport Mechanisms: Bed Transport and Suspended
Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.5 Bed Forms: Ripples, Dunes, and Antidunes . . . . . . . . . . . . . . . . . 43
2.5.1 Classification of Bed Forms . . . . . . . . . . . . . . . . . . . . . . . 44
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
ix
x Contents
3 Initiation of Sediment Motion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.2 The Shields Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.3 Limits and Extensions of the Shields Theory . . . . . . . . . . . . . . . . 54
3.3.1 Definition of the Incipient Motion Condition. . . . . . . . . . . 55
3.3.2 Effect of the Streamline Bed Slope. . . . . . . . . . . . . . . . . . 56
3.3.3 Effect of Side Slopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.3.4 Effect of the Relative Submergence . . . . . . . . . . . . . . . . . 60
3.3.5 Effect of Size Heterogeneity of Bed Material. . . . . . . . . . . 61
3.3.6 Effect of Bed Armoring . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.4 Effect of the Section Form on the Incipient Motion
Condition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.5 Incipient Motion Condition in Channel Bends . . . . . . . . . . . . . . . 66
3.5.1 Critical Mobility Reduction in Bends Induced by
Secondary Circular Flows . . . . . . . . . . . . . . . . . . . . . . . . 66
3.5.2 Effects on the Inner Bank Due to the Drop of the Free
Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.6 Other Criteria for Defining the Incipient Motion Condition. . . . . . 71
3.6.1 Critical Slope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.6.2 Critical Discharge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.6.3 Critical Froude Number and Critical Velocity . . . . . . . . . . 73
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4 Resistance to Flow in Mobile-Bed Channels . . . . . . . . . . . . . . . . . . . 77
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.2 Einstein’s Criterion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.3 Engelund’s Criterion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.4 Van Rijn’s Criterion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5 Bedload Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.2 Einstein’s Bedload Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.2.1 Limits of Einstein’s Approach . . . . . . . . . . . . . . . . . . . . . 96
5.2.2 Einstein’s Equation for qb !1. . . . . . . . . . . . . . . . . . . . 96
5.2.3 Einstein’s Equation for q !0. . . . . . . . . . . . . . . . . . . . . 97
b
5.2.4 Effect of Material Non-uniformity. . . . . . . . . . . . . . . . . . . 98
5.3 Ballistic Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5.4 Sediment Transport Formulae Implying a Critical Threshold
for the Incipient Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.4.1 Du Boys Bedload Approach. . . . . . . . . . . . . . . . . . . . . . . 104
5.4.2 Meyer-Peter and Müller Formula . . . . . . . . . . . . . . . . . . . 106
5.4.3 Smart and Jäggi Formula . . . . . . . . . . . . . . . . . . . . . . . . . 107
5.4.4 Van Rijn Bedload Formula. . . . . . . . . . . . . . . . . . . . . . . . 107
Contents xi
5.4.5 Other Formulae Structurally Similar to the Du Boys
Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
5.5 BedloadFormulaeExplicitlyDependingontheLiquidDischarge
or on the Stream Velocity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
5.5.1 Schoklitsch’s Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
5.6 Sediment Transport of Non-uniform Size Mixtures. . . . . . . . . . . . 109
5.6.1 Dynamic Armoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
6 Suspended Transport and Total Transport. . . . . . . . . . . . . . . . . . . . 115
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
6.2 Flow Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
6.3 Distribution of Suspended Concentrations in Equilibrium
Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
6.3.1 The Rouse Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
6.3.2 The Lane Solution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
6.3.3 The Reference Concentration ca . . . . . . . . . . . . . . . . . . . . 122
6.4 Suspended Load. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
6.5 Total Solid Discharge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
6.5.1 Monomial Formulae. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
7 Mathematical Models of Riverbed Evolution . . . . . . . . . . . . . . . . . . 131
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
7.2 Mass Conservation Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
7.2.1 Equation of Conservation of Solid Mass . . . . . . . . . . . . . . 133
7.2.2 Mass Conservation of the Liquid Phase . . . . . . . . . . . . . . 135
7.2.3 Total Mass Conservation . . . . . . . . . . . . . . . . . . . . . . . . . 137
7.3 Momentum Conservation Equations. . . . . . . . . . . . . . . . . . . . . . . 137
7.3.1 Momentum Conservation Equation of the Liquid
Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
7.3.2 Momentum Conservation of the Solid Phase . . . . . . . . . . . 139
7.3.3 Momentum Conservation of the Mixture. . . . . . . . . . . . . . 139
7.4 Water-Sediment Coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
7.4.1 System in Normal Form. . . . . . . . . . . . . . . . . . . . . . . . . . 144
7.4.2 Boundary Conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
7.5 Stationary Solutions: Section Enlargements and Contractions . . . . 148
7.6 Simplified Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
7.6.1 The Simple Wave Model . . . . . . . . . . . . . . . . . . . . . . . . . 154
7.6.2 The Parabolic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
7.6.3 Complete Hyperbolic Model. . . . . . . . . . . . . . . . . . . . . . . 157
7.7 Adaptive Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
7.8 Non-uniform Sediment Models . . . . . . . . . . . . . . . . . . . . . . . . . . 160
7.8.1 Physical Meaning of the Mixing Layer . . . . . . . . . . . . . . . 164
