Principles of

PHYSICAL SEDIMENTOLOGY

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Principles of

PHYSICAL SEDIMF,NTOLOGY

J .R.L. ALLEN Department of Geology, University of Reading

CHAPMAN & HALL London· Glasgow· New York· Tokyo· Melbourne· Madras

Published by Chapman & Hall, 2-6 Boundary Row, London SE1 8HN

Chapman & Hall, 2-6 Boundary Row, London SE1 8HN, UK

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Chapman & Hall Australia, Thomas Nelson Australia, 102 Dodds Street, South Melbourne, Victoria 3205, Australia

Chapman & Hall India, R. Seshadri, 32 Second Main Road, CIT East, Madras 600 035, India

First edition 1985 Reprinted 1992

© 1985 J.R.L. Allen

Typeset 9 on 11 point Times by Mathematical Composition Setters Ltd, Salisbury, Wiltshire

ISBN-13: 978-0-412-53090-6 DOl: 10.1007/978-1-46 13-2545-1

e-ISBN-13: 978-1-461 3-2545-1

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the UK Copyright Designs and Patents Act, 1988, this publication may not be reproduced, stored, or transmitted, in any form or by any means, without the prior permission in writing of the publishers, or in the case of reprographic reproduction only in accordance with the terms of the licences issued by the Copyright Licensing Agency in the UK, or in accordance with the terms of licences issued by the appropriate Reproduction Rights Organization outside the UK. Enquiries concerning reproduction outside the terms stated here should be sent to the publishers at the London address printed on this page.

The publisher makes no representation , express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made.

A catalogue record for this book is available from the British Library

Library of Congress Cataloguing in Publication Data

Allen, John R. L. Principles of physical sedimentology.

Includes bibliographies and indexes. 1. Sedimentation and deposition. 2. Hydraulic engineering. I. Title. QE571.A44 1985 551.3 85- 6006

In memoriam Peter Allen

Cover illustration

Front (Upper) Pattern of streamlines round an equatorial section through a sphere in a Hele - Shaw cell.

Front (lower) Current sorted and rounded debris formed from the coralline alga Lithothamnium, Connemara, Republic of Ireland.

Back (upper) Large wave-related ripples in pebbly, shelly very coarse sand, Rocquaine Bay, Guernsey.

Back (lower) Steeply climbing current ripple cross-lamination in vertical streamwise profile, Uppsala Esker, Sweden.

Preface

My aim in this book is simple. It is to set out in a logical way what I believe is the minimum that the senior undergraduate and beginning postgraduate student in the Earth sciences should nowadays know of general physics, in order to be able to understand (rather than form merely a descriptive knowledge of) the smaller­scale mechanically formed features of detrital sedi­ments . In a sense, this new book is a second edition of my earlier Physical processes of sedimentation (1970), which continues to attract readers and purchasers, inas­much as time has not caused me to change significantly the essence of my philosophy about the subject. Time has, however, brought many welcome new practitioners to the discipline of sedimentology, thrown up a multitude of novel and exciting results and problems and, on the personal side, materially altered and (hopefully) sharpened my appreciation of this field. I could not therefore have prepared a second edition in the traditional sense but have instead written Principles of physical sedimentology as an entirely new work. It is similar in scope to Physical processes of sedimentation but, as my overriding aim is to give a well founded account of general physical principles, the book in no way attempts to be exhaustive as regards subject matter. Thus there is no separate chapter on wind-related features and I have omitted altogether any discussion of glacial phenomena. There is instead a new chapter on mass movements and their analysis, and I have placed considerable emphasis on, amongst other things, turbu­lence and vortex phenomena, and on the mechanisms and processes relating to muddy sediments.

Physical sedimentology is essentially an observational science. It is important not only to look hard at and think about sedimentary rocks and modern sediments and processes in the field, but also to strengthen one's intuitions and resolve one's uncertainties by frequently making experiments in the laboratory. In the firm belief that the user of this book will find them helpful, instruc­tive and worth the time to be spent on them, I have therefore described and in many cases illustrated a large number of simple laboratory experiments. These are further elaborated in a companion laboratory hand­book, Experiments in physical sedimentology, in which many additional experiments will also be found. It can­not be too strongly emphasized, and especially to those readers beginning in sedimentology, that elaborate

ix

apparatus is generally not required for the making of useful sedimentological experiments. Most of the equip­ment needed for those I describe can be found in the kit­chen, bathroom or general laboratory , and the materials most often required - sand, clay and flow-marking substances - are cheaply and widely available. As described, the experiments are for the most part purely qualitative, but many can with only little modification be made the subject of a rewarding quantitative exer­cise. The reader is urged to tryout these experiments and to think up additional ones. Experimentation should be as natural an activity and mode of enquiry for a physical sedimentologist as the wielding of spade and hammer.

Although a quantitative treatment played an import­ant role in Physical processes of sedimentation, I very largely ducked in that book the issue of the derivation of equations, preferring to shelter behind such evasions as 'it can be shown that ... ' . This I now believe was wrong and, while it might have painlessly provided him or her with useful formulae, gave the reader no key to understanding or basis for attacking new situations from first principles. This nettle has been firmly grasped in Principles of physical sedimentology, in which I have included an introductory chapter setting out the essence of mechanics and fluid mechanics, and in which I de­rived as many relationships as possible from first prin­ciples, writing out all but the most glaringly obvious steps; only in the case of certain essential aspects of water waves are the mathematical requirements beyond the level of this book. The user with a knowledge of elementary algebra and calculus should therefore have no difficulty in following my developments and, by example, should emerge confident that he or she can tackle new situations. The mathematics introduced is in­tended to do no more than to serve the requirements of the particular physical problem; the reader should not allow himself or herself to be overawed by the symbols and equations, but should in turn make them his or her servants. A word of caution is nonetheless due. The price of a mathematically simple analysis is with some problems a degree of simplification that might horrify a specialist researcher. I make no apology for this, so long as the point is noted, as I believe it is better to see the truth indistinctly than not at all! It is best, of course, to see the truth clearly and vividly.

No book of this kind can be prepared without help of many kinds from many people. I am deeply indebted to Mr Roger Jones of George Allen & Unwin Ltd, who encouraged me to bring out a revision of my earlier work, and who contributed materially, along with Mr G. D. Palmer, to whom I am also grateful, to the character of the present book. Dr Iaakov Karcz, Dr Michael Leeder and Dr John Southard made many help­ful and important suggestions for the structure of the book in its early stages, and to them I express my gratitude. I am also greatly indebted to many friends and colleagues who made suggestions for the improve­ment of particular chapters or sections and who generously made available illustrative material, in some

x

cases previously unpublished. My final scientific in­debtedness is to the many sedimentologists and re­searchers in other disciplines whose work I cannot directly acknowledge, on account of the need to keep the 'Readings' to a reasonable length. Mrs Audrey Conner, Mrs Gillian Coward, Mrs Mary Downing and Mrs Dorothy West are warmly thanked for their endur­ing patience and skilful typing. It is a pleasure to thank Mr J. L. Watkins for his help with the photographic work and for his general advice on photographic matters.

John R. L. Allen Reading

Contents

Preface ix 4 Sliding, rolling, leaping and making Tables xiii sand waves 55 Notation xiv 4.1 Some field observations 55

4.2 Setting particles in motion 56 4.3 Defining the rate of sediment

1 Concepts and rules of the game 1 transport 58

1.1 Matter and influences 1 4.4 Physical implications of sediment

1.2 Flow rate 3 transport 59 4.5 Sediment transport modes 62 1.3 Law of continuity (conservation 4.6 Appearance and internal structure of mass) 5

of bedforms 63 1.4 Law of conservation of momentum 6 4.7 How do bedforms move? 67

Bedforms and flow conditions 71 7 4.8 1.5 Law of conservation of energy Making wavy beds 74 Energy losses during fluid flow 10 4.9 1.6

4.10 A wave theory of bedforms 75 1.7 Newton's laws of motion 11 1.8 Fluid viscosity 12 Readings 78

1.9 Boundary layers 13 5 Winding down to the sea 81 1.10 Flow separation 15

5.1 Introduction 81 1.11 Applying the concepts and rules 16 5.2 Drag force and mean velocity of a

Readings 19 river 83

2 Pressed down and running over 21 5.3 Energy and power of channelized currents 85 2.1 Introduction 21

5.4 Why flow in a channel? 86 2.2 Particle composition and density 21 5.5 Width: depth ratio of river 2.3 How big is a particle? 22

channels 87 2.4 What form has a particle? 24 5.6 Long profiles of rivers 88 2.5 How close is a packing? 27 5.7 An experimental interlude 89 2.6 Kinds of packing 27 5.8 Flow in channel bends 91 2.7 Voids 30 5.9 Sediment particles in channel 2.8 Controls on packing 30

bends 94 2.9 How steep is a heap? 35 5.10 Migration of channel bends 96 2.10 Building houses on sand 36 5.11 A model for river point-bar Readings 37

deposits 99 3 Sink or swim? 39 Readings 100

3.1 Two introductory experiments 39 6 Order in chaos 103 3.2 Settling of spherical particles 6.1 Introduction 103

arrayed in a stagnant fluid 40 6.2 Assessing turbulent flows - how 3.3 Settling and fluidization 44 to see and what to measure 104 3.4 Flow in porous media 44 6.3 Character of an ideal eddy 107 3.5 Controls on permeability 45 6.4 Streaks in the viscous sub layer 108 3.6 Settling of a solitary spherical 6.5 Streak bursting 113

particle in a stagnant fluid 46 6.6 Large eddies (macroturbulence) 115 3.7 Settling of a solitary non-spherical 6.7 Relation of small to large

particle in a stagnant fluid 49 coherent structures 120 Readings 53 Readings 121

xi

7 A matter of turbidity 123 11 Twisting and turning 201 7.1 Introduction 123 11.1 Introduction 201 7.2 A diffusion model for transport in 11.2 Mixing layers 201

suspension 124 11.3 Jets 206 7.3 Transport in suspension across 11.4 Corkscrew vortices 210

river floodplains 129 11.5 Horseshoe vortices due to bluff 7.4 Limitations of diffusion models 133 bodies 215 7.5 A dynamical theory of suspension 133 11.6 Horseshoe vortices at flute marks, 7.6 A criterion for suspension 136 current ripples and dunes 218

Readings 136 Readings 219

8 The banks of the Limpopo River 139 12 Sudden, strong and deep 223 8.1 Introduction 139 12.1 Some experiments 223 8.2 Clay minerals 139 12.2 Kinds of gravity current 224 8.3 Deposition of muddy sediments 142 12.3 Difficulties with gravity currents 225 8.4 Packing of muddy sediments 143 12.4 Drag force and mean velocity of a 8.5 Coming unstuck 144 uniform steady gravity current 226 8.6 Erosion of muddy sediments l'iO 12.5 Shape and speed of a gravity-8.7 Drying out 153 current head 227

Readings 158 12.6 Why does the nose overhang? 229 12.7 Lobes, clefts and sole marks 229 12.8 Billows on the head 231

9 Creeping, sliding and flowing 159 12.9 Gravity-current heads on slopes 233 12.10 Dissipation of sediment-driven 9.1 Introduction 159

gravity currents 233 9.2 Mass movements in general 159 Soil creep 161 12.11 Sloshing gravity currents 236 9.3

12.12 Turbidity-current deposits 237 9.4 Effective stress and losses of strength 163 Readings 240

9.5 Sub-aerial and sub-aquatic slides 165 9.6 Debris flows 172 13 To and fro 243 9.7 Mass-movement associations 177

Readings 178 13.1 Some introductory experiments 243 13.2 Making wind waves 244 13.3 Making the tide 245 13.4 Waves in shallow water 247

10 Changes of state 181 13.5 Waves in deep water 249

181 13.6 Wave equations 249

10.1 Introduction 13.7 Mass transport in progressive and 10.2 An experiment 181

standing waves 252 10.3 What causes changes of states? 182 13.8 Sediment transport due to wind 10.4 What forces cause deformation? 186

waves and tides 254 10.5 For how long can deformation 13.9 Wave ripples and plane beds 257

proceed? 188 13.10 Sand waves in tidal currents 262 10.6 Complex deformations in cross- 13.11 Longshore bars and troughs 263

bedded sandstones 189 13.12 Waves and storm surges - back 10.7 Load casts 191

to the beginning 264 10.8 Convolute lamination 192

Readings 265 10.9 Wrinkle marks 195 10.10 Overturned cross-bedding 196

Readings 198 Index 268

xii

Tables

1.1 Chief quantities encountered in physical sedimentology 2 2.1 Density of common minerals and rocks 22 2.2 Scale of grade 23 2.3 Effect of adding void-filling spheres to a rhombohedral packing of equal spheres 33 2.4 Packing concentrations and slope angles attained by selected granular materials 34 3.1 Fall and travel of spherical quartz-density particles in a representative ocean current 47 3.2 Bivalve shells (single valves) studied experimentally 51 4.1 Effect of lag distance on behaviour of transverse sandy bedforms 75 5.1 Effect of lag distance on behaviour of channel bends 98

13.1 Wave height related to wind conditions 245 13.2 Relative magnitude of tidal forces 246

xiii

Notation

Physical sedimentology draws on so many fields based on general physics, each with its own hallowed conven­tions (in some instances more than one) regarding the representation of physical quantities, that it has been impossible for me in this book to give the available Roman and Greek symbols a unique meaning in every case. Fortunately, the different usages occur for the most part quite separately, and I have therefore been able to follow at least the more important conventions. Changes of meaning have been clearly indicated in the text. Note that the symbols used least frequently are excluded from the following list.

a a coefficient; long axis of an irregular sediment particle (m); long semi-axis of an ellipsoid (m); acceleration (m S-2)

A flow cross-sectional area (m 2)

b a coefficient; intermediate axis of an irregular sediment particle (m); intennediate semi-axis of an ellipsoid (m)

c short axis of an irregular sediment particle (m); phase velocity of water waves (m s -I); cohesion (Nm- 2)

C constant of integration; fractional volume con-centration of granular solids (non-dimensional)

Co drag coefficient for a particle in relative motion with a fluid (non-dimensional)

Co,o drag coefficient for a solitary particle in relative motion with an infinite fluid (non-dimensional)

Cref reference fractional volume concentration of granular solids (non-dimensional)

d a distance (m); lag distance (m, in some cases non-dimensional); horizontal diameter of water particle orbit beneath water waves (m)

D sediment particle diameter (m, /Lm) DA diameter of circle with same area as a sediment

particle in projection (m, /Lm) Drn mean particle diameter of a mixture (m, /Lm)

Dv diameter of sphere of same volume as a sedi-ment particle (m, /Lm)

Dso median particle diameter of a mixture (m, JLm) E energy per unit volume (J m - 3)

I Darcy-Weisbach friction coefficient for flow in a pipe or open channel (non-dimensional); fre-quency (s -I)

xiv

F Fr g h her

H

I

J

k L

m

M n p P q

Qv

Qrn r R

Re

S

Sr t T

Tb u

u'

U

force (N); sediment flux (kg m- 2 s- l )

Froude number = U/(gh )112 (non-dimensional) acceleration due to gravity (m S-2)

flow thickness (m) critical flow thickness, e.g. in Froude number or wave equations (m) hydraulic head (m); height of bedform (m); height of water wave (m) unit sediment transport rate on basis of im­mersed weight (J m- 2 s- I ); sediment particle stability number (various definitions) (non­dimensional) unit sediment transport rate on dry-mass basis (kgm-1s- l )

a coefficient; specific permeability (/Lm 2) a length (m); wavelength of bedform, water wave, or channel sinuosity (m) an exponent; mass (kg); sediment load (nor­mally immersed-weight basis) (N m- 2)

mass (Kg); momentum flux (N m- 2)

a number or exponent fluid pressure (N m- 2)

sediment fractional porosity (non-dimensional) volumetric fluid discharge per unit width of flow (m 2 S-I)

total volumetric discharge (m 3 s -I) (the subscript v is commonly dropped) total mass discharge (kg s -I) radical distance or radius (m) radius (m); sediment dry-mass deposition or erosion rate (rate of transfer) (kg m -2 s -I) Reynolds number = (length x velocity x density)/viscosity (non­dimensional) slope of water surface and/or bed in open chan­nel (non-dimensional) Strouhal non-dimensional frequency = ID/ VO time (s) time for settlement of liquidized bed (s); surface tension of a liquid (N m -I) non-dimensional burst period instantaneous flow velocity measured in x-direc­tion (m S-I)

fluctuating component of velocity measured in x-direction (m s -I) local flow velocity (laminar case) or local time-

averaged velocity (turbulent case) measured in x-direction (m s -I)

Ubrn celerity of bedform (m S-I) x Uer critical value of flow velocity or sediment

erosion threshold (m s -I) Y Urn local depth-averaged flow velocity in x-direction

(m S-I) y Urnax maximum x-directed velocity shown in a velocity

profile, or maximum horizontal velocity ob- z served on a near-bed water particle orbit beneath water waves (m s -I) Z

Uo velocity of undisturbed x-directed stream out-side boundary layer (m s -I) ex

Uorn overall mean x-directed velocity (m s - I) {3 Us mean sediment particle transport velocity

(m S-I) 'Y

UT shear velocity = (T1e)112 (ms- I ) li v instantaneous flow velocity measured in y-direc-

tion (m s -I) .l v I fluctuating component of velocity measured in

y-direction (m s -I) E

V volume (m3); local time-averaged flow velocity r measured in y-direction (m s -I); terminal fall 1/

velocity of particle in a fluid, measured relative to ground (m S-I) 1/a

Vo terminal fall velocity of a solitary particle in an 0 infinite fluid, measured relative to ground (m S-I) Ocr

Vrel relative velocity between a particle and a fluid e (m S-I) (J

Vs superficial velocity (m s -I) Vs•er superficial velocity necessary for fluidization of

a granular aggregate (m s -1) T

W flow width (m); instantaneous flow velocity Ter

measured in z-direction (m s -I) Ts

w' fluctuating component of velocity measured in <Pi z-direction (m s -1) <Pr

W local time-averaged flow velocity measured in z-direction (m s -1); vertical velocity of interface w

xv

associated with settling of a particle dispersion (m S-I)

distance measured in general direction of flow (m) distance measured normal to flow boundary or free surface (m) non-dimensional distance normal to flow boundary = eyUT/1/ distance measured parallel to flow boundary or free surface but perpendicular to x-direction (m) non-dimensional transverse distance = ezUT/1/

(alpha) an angle (beta) an angle (generally bed or water-surface slope) (gamma) sediment bulk density (kg m- 3 )

(delta) a small increment; boundary-layer thickness (m) (delta) the difference between two values of a quantity (epsilon) eddy diffusion coefficient (m 2 s -I)

(zeta) angle of bedform climb (eta) dynamic (molecular) viscosity of a fluid (N sm- 2, Pa s) apparent viscosity (N s m - 2) (theta) an angle; non-dimensional shear stress (various definitions) critical value of non-dimensional stress (rho) fluid density (kg m - 3)

(sigma) standard deviation of particle size distribution (m, /Lm); solids density (kg m- 3);

normal stress (N m - 2)

(tau) shear stress (N m -2) critical value of shear stress (N m -2) shear strength (N m - 2 )

(phi) angle of initial yield of cohesionless grains residual angle after shearing of cohesionless grains (omega) power of a fluid stream (W m- 2 )