Title Page
 Table of Contents
 II. Brief review of cohesive sediment...
 III. Factors and parameters for...
 IV. Shear strength and bed...
 V. Brief overview comments
 A. Evaluation of characterization...
 B. Comparative characterization...
 C. Determination of shear strength...

Group Title: Miscellaneous Publication - University of Florida. Coastal and Oceanographic Engineering Program ; 91/4
Title: Characterization of cohesive soil bed surface erosion, with special reference to the relationship between erosion shear strength and bed density
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 Material Information
Title: Characterization of cohesive soil bed surface erosion, with special reference to the relationship between erosion shear strength and bed density
Series Title: Miscellaneous Publication - University of Florida. Coastal and Oceanographic Engineering Program ; 91/4
Physical Description: Book
Creator: Mehta, Ashish
Affiliation: University of Florida -- Gainesville -- College of Engineering -- Department of Civil and Coastal Engineering -- Coastal and Oceanographic Program
Publisher: Dept. of Coastal and Oceanographic Engineering, University of Florida
Publication Date: 1991
Subject: Coastal Engineering
Sediments (Geology)   ( lcsh )
Erosion   ( lcsh )
University of Florida.   ( lcsh )
Spatial Coverage: North America -- United States of America -- Florida
Funding: This publication is being made available as part of the report series written by the faculty, staff, and students of the Coastal and Oceanographic Program of the Department of Civil and Coastal Engineering.
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Table of Contents
    Title Page
        Page 1
    Table of Contents
        Page 2
        Page 3
        Page 4
        Page 5
        Page 6
        Page 7
    II. Brief review of cohesive sediment erosion
        Page 8
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        Page 24
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    III. Factors and parameters for characterizing surface erosion rate
        Page 26
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    IV. Shear strength and bed density
        Page 42
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        Page 48
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    V. Brief overview comments
        Page 52
    A. Evaluation of characterization factors in surface erosion
        Page 53
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    B. Comparative characterization of three erosion studies
        Page 66
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        Page 68
    C. Determination of shear strength from time-concentration data obtained in erosion experiments
        Page 69
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Full Text



Ashish J. Mehta
Coastal and Oceanographic Engineering Department
University of Florida, Gainesville, FL 32611

October, 1991


ABSTRACT ........................................................... 4

I. INTRODUCTION .................. ................................... 6

2.1 INTRODUCTION .......................
2.2 MODES OF EROSION ...................
2.3 SURFACE EROSION ....................
2.3.1 Rate of Erosion ...... ..............
2.3.2 A Theoretical Basis ..................
2.3.3 Stirred Flocculent Layer ...............
2.3.4 Stress History and Incipient Entrainment .....
2.4 MASS EROSION .......................
2.5 MUD FLUIDIZATION ...................
2.7 CONCLUDING COMMENTS ...............

. . . . . . . 8
...... .... ..... ..... .... ...8
.................... .......9
. . . . . . . 11
. . . . . . . 11
. .. .. .. .. . .. 12
. .. .. .. .. . .. 14
. .. . . .. .. . .. 17
. .. . . . .. . .. 19
. .. . . . . .. 20
............. ............. 22
. . .. . . . . .. 25

3.1 INTRODUCTION .................... ............................. 26
3.2 CHARACTERIZATION OF EROSION RESISTANCE .......................... 27
3.2.1 Factors/parameters .................................... ........ 27
3.2.2 Sediment Composition ......................................... 28
3.2.3 Fluid Composition .................................... ........ 34
3.2.4 Bed Characteristics .................... ........................ 38
3.3 CONCLUDING COMMENTS ......................................... 40

IV. SHEAR STRENGTH AND BED DENSITY .................................... 42
4.1 INTRODUCTION ....................................... ......... 42
4.2 DEFINITIONS ................................................... 42
4.2.1 Vane Shear Strength ............................................ 43
4.2.2 Bingham Shear Strength ................... ...................... 45
4.2.3 Erosion Shear Strength ................... ...................... 45
4.2.4 Some Experimental Relationships between Shear Strength and Density ............ 48
4.2.5 Mass Erosion .................................... ........... 51
4.3 CONCLUDING COMMENTS .......................................... 51

V. BRIEF OVERVIEW COMMENTS .......................................... 52


A.1 INTRODUCTION ........................................




VI BIBLIOGRAPHY ................... ..................................74
6.1 REFERENCES TO CHAPTER I ........................................ 74
6.2 REFERENCES TO CHAPTER II ........................................ 74
6.3 REFERENCES TO CHAPTER III........................................ 76
6.4 REFERENCES TO CHAPTER IV ...................................... 77
6.5 REFERENCES TO CHAPTER V ........................................ 78
6.6 REFERENCES TO APPENDIX A ........................................ 79
6.7 REFERENCES TO APPENDIX B ...................................... 82
6.8 REFERENCES TO APPENDIX C ....................................... 82



Ashish J. Mehta
Coastal and Oceanographic Engineering Department
University of Florida, Gainesville, FL 32611


The erosion behavior of beds of fine-grained, primarily cohesive sediments has been revisited with the focus
on the physico-chemical basis for developing predictive relations for the rate of surface erosion. Surface or floc-by-
floc erosion can be categorized as one of the four identifiable modes by which cohesive sediment beds erode in
estuaries, and is an important contributor to estuarine turbidity under non-episodic, micro- and meso-tidal coastal
environments. The other three modes include mass erosion, bed fluidization and entrainment of fluid mud. These
modes can become dominant in high energy environments.
The bed shear strength, Ts, that is directly related to surface erosion of flocs, is the primary parameter that
characterizes bed resistance to surface erosion. Other seemingly related quantities, such as the upper Bingham yield
strength and the vane shear strength, have evident uses in cohesive sediment transport process description; yet they
are unsuitable as descriptors of the surface erosion rate. The precise relationships, between 7, and the various
physico-chemical factors and parameters that govern the resistance to the entrainment of flocs (by inter-particle bond
breakup at the bed surface due to an applied flow stress), have not been fully elucidated. Bond strength is
determined by electro-chemical forces, which can be measurably modulated by biochemical effects. In order to
facilitate at least a cursory inter-comparison between erosion rates of different sediment-water systems tested in
different types of apparatuses, it is recommended that a suite of simple physico-chemical factors and parameters be
reported in laboratory and field experiments. These factors and parameters relate to sediment composition, fluid
composition, and bed characteristics.
As an illustration of the predictive relationship for the rate of surface erosion and easily measurable
experimental parameters, the dependence of bed shear strength on a measure of bed density is considered. Given
sediment and fluid compositions, the test procedure for determining the erosion rate, and the method for bed
preparation, an approximate but useful relationship between 7, and the solids volume fraction 4 (= 1-n, where n
is the porosity) can be established experimentally. Based on an examination of previous experimental results and
the desired description, we anticipate the "ideal" relationship to be of the form: 7, = a(O c) where a and p
depend primarily on sediment and fluid compositions, and 0c is the minimum value of 4 at which a space-filling
particulate matrix occurs in the bed. Thus T7 is postulated to be dependent on the excess solids volume fraction, 0 -

With the exception of one study, all the studies reviewed have inadvertently ignored 0, which is tantamount
to setting its value equal to zero. However, shearometric measurements to determine the relationship between the
modulus of elasticity of muds and 0 have yielded non-trivial values of 0. While Coulomb's equation tends to
suggest (indirectly, via the effective stress behavior) that cohesion may exist for 0 < (y as well, is indeed a
measure of the limiting solids volume fraction up to which a cohesive bed occurs. This parameter, and the behavior
of r7 with 0 in the proximity of 0c, require careful further investigation.
Support for this study by the U.S. Army Engineer Waterways Experiment Station, Vicksburg, MS through
contract DACW39-91-M-5490 is acknowledged.


The "classical" description of vertical sediment mass transport of cohesive matter in estuaries, including
erosion, deposition and consolidation (Fig. 1.1), is largely based upon prior scientific conceptualization relying on
the mechanics and description of sand transport. As we shall note in the Chapter II, this description is overly
simplistic, since it wholly ignores the ubiquitous high concentration, fluid-like slurry that occurs between the
cohesive soil bed and the mobile suspension. The bed surface is not a well defined plane, and it is more appropriate
to refer to it as the soil-water or mud-water interface. Characteristically, the sediment concentration (C) profile does
not exhibit a sharp gradient as suggested in Fig. 1.1, neither does the flow velocity (u) become nil precisely at the
interface, which can in fact drag along with the flow.
Given these arguments, the description of Fig. 1.2, even though somewhat idealized, better represents the
vertical mass transport processes than that in Fig. 1.1. Note that erosion can be the entrainment of the sediment-
induced pycnocline (lutocline), or fluidization of the cohesive bed. Deposition can be particulate settling over the
mobile fluid mud layer, or the formation of bed from the fluid mud (which can be mobile or stationary depending
upon the elevation of the zero velocity plane). Under wave action, the description, as shown in Fig. 1.3, is similar
except that wave orbital motion (of amplitude u) can cause the bed to deform viscoelastically and lead to its eventual
fluidization. These descriptions are further explored in Chapter II.


Fig. 1.1: "Classical" definition of sediment bed and
suspension-related processes including erosion,
deposition and consolidation (after Mehta, 1989).

Fig. 1.2: Idealized profiles of instantaneous vertical
concentration and velocity, and mass fluxes relevant to
water column with fine-grained sediment (after Mehta,


I- I

S Lutocline
Fluid Mud
f-------------- ,-----
Stationary Bed

Fig. 1.3: Schematic of cohesive soil bed response to
waves (after Mehta, 1989).

As evident, erosion of the particulate matter leading to an increase in the concentration of suspended matter
in the water column is complicated by the presence of the near-bed, high concentration slurry. Nevertheless, the
typically used process model for bed erosion rate in wide ranging applications involving numerical modeling is a
very simple, expression which relates the rate of erosion to the applied fluid stress at the bed and has coefficients
that must be determined from empirical evidence. One of the earliest expression of this form is due to Partheniades
(1962), and is based on stochastic and phenomenological arguments applied to experimental data on the erosion of
San Francisco Bay mud in a flume. Some early expressions have been summarized by Mehta et al. (1982). The one
most commonly used, noted in Chapter II, is due to Kandiah (1974).
This type of a rate expression appears to yield erosion rates of acceptable accuracy in the microtidal
environment characteristic of many U.S. estuaries, although it does not simulate erosion in situations where fluid
mud plays an important role in fine sediment transport. Given the general applicability of this rate expression
however, these is an engineering interest in developing a better understanding of the relationship between the rate
characterizing empirical parameters and the physical and physico-chemical properties of the sediment-water system.
In this study therefore, and effort is first made in Chapter II to provide a brief physical perspective of cohesive
sediment erosion. This is then followed in Chapter III by considerations on parameters that seem to be influential
in controlling bed resistance to erosion. Finally, in Chapter IV we have briefly reviewed past efforts to relate an
important bed resistance characterizing parameter, the shear strength, to bed density, also an important and relatively
easily measurable property of the cohesive bed.


As a preamble to a review of various modes of erosion of cohesive sediments, it is instructive to consider
a brief description of the vertical structure of the sediment concentration (or density) profile in the estuarine water
column. Accordingly, a definition related sketch for the same is presented in Fig. 2.1. Beginning from the water
surface, the top, mixed layer of mobile suspension is defined as one which is low in concentration, not exceeding
about 0.3 gl-'. This suspension is practically Newtonian, and within it the sediment flocs settle more or less freely,
without significant inter-particle interference. Upward mass diffusion in this zone is neutral, i.e. practically
uninfluenced by sediment.

SMixed Layer Newtonian

Secondary Lutocline Increesingly
Stratified Mobile Suspension with Increasing
Suspension (No Effective concentration
Primary Lutocline Stress) (Focculation Settling)
Primary Lutocline
SLutocline Shear Layer
SMobile Hyperpycnal Highly Non-Newtonlan
SLayer (Fluid Mud) (Hindered Settling)
Stationary Mud
Deforming Cohesive Bed Two-Phased
Stationary Cohesive Bed Bed Skeletal Framework
(Measurable (Consolidation)
Effective Stress)

Fig. 2.1: Horizontal layering of the vertical concentration profile of cohesive sediment in water,
and associated definitions (after Mehta, 1989).

Below this mixed layer settling as well as diffusion are conditioned by sediment concentration effects, and

stratification begins to become apparent. The settling velocity increases with concentration due to flocculation
resulting from inter-particle collisions, and the vertical momentum and mass diffusivities are damped due
comparatively large concentration gradients. A step-like microstructure defined by these gradients, or lutoclines,
is characteristic of this regime in which the suspension becomes increasingly non-Newtonian, typically pseudoplastic
at low shearing rates, with increasing concentration. The step-structures are kinematic waves that propagate upward
or downward depending upon the erosional or depositional state of flow (Smith and Kirby, 1988).
The lutocline shear layer is perhaps the most significant feature of the concentration profile, formed as a
result of buoyancy stabilization of the high concentration suspension. Below this layer the sediment settling flux is
hindered, at concentrations exceeding anywhere between about 4 and 20 g 1-1. This concentration gradient, whose
elevation is determined mainly by hindered settling, may be called the primary lutocline, as opposed to the

secondary lutoclines above whose structure is governed by settling combined with upward mass diffusion (Ross and
Mehta, 1989; Scarlatos and Mehta, 1990). Turbulent boundary layer effects result in shear production and sediment
mixing at the lutocline; however, from the point of view of the vertical distribution of sediment mass the gradient
may remain largely intact even in high energy situations, although its elevation does change with time (Ross and
Mehta, 1989).
The mobile, hyperpycnal layer, commonly called fluid mud, can occur up to concentrations on the order
of 200 g '1. It is essentially a fluid-supported slurry which in some instances, e.g. when the sediment is a bentonite,
approaches Bingham plastic behavior, and plays a significant role in absorbing and dissipating turbulent kinetic
energy. In addition to upward entrainment or downward mobility via dewatering, fluid mud can move horizontally
by an applied stress at the lutocline, or down gentle natural slopes, thus contributing measurably to sediment mass
transport. The stationary mud layer below the fluid mud may or may not be wholly fluid-supported depending upon
its recent stress history. If a measurable effective stress develops due to consolidation, then this layer is defined as
a cohesive bed. Stationarity is here implied in reference to zero net horizontal motion; oscillatory motion is not
precluded and in fact may be quite significant under wave action (Jiang and Mehta, 1991). Waves, via transmission
of normal and shear forces, build up excess pore pressures which essentially inhibit the structural integrity of the
porous bed matrix. Wave particle orbits can as well penetrate the cohesive bed causing it to undergo viscoelastic
deformation, which can eventually lead to its fluidization.
Erosion essentially involves upward entrainment of the bottom sediment mass, which also increases the
potential energy of the system under the influence of an external agency such a unidirectional current or waves. In
fact, a unidirectional flow can be construed as a special case of wave flow of zero frequency. In any event, once
the external agency is removed, the system reverts to the initial potential energy state via particulate settlement. The
nature and the mechanics of erosion that leads to changes in the vertical concentration profile are examined in what

Erosion of cohesive particulate aggregates or floes, dependent as it is on the composition and the structure
of the bottom material that characterizes bottom resistance, and on the character of the eroding force, can occur in
several ways which are not wholly distinct and independent of each other, but may be conveniently treated as such.
We may identify four basic modes, all of which may occur in a given estuarine environment, and thus generate a
complex overall erosion regime of the estuary.
As an illustration of the four modes, consider the depictions in Fig. 2.2a,b,c and d. The first mode is floc-
by-floc surface erosion in which the flocs at the bed-water surface, initially attached to their neighbors by inter-
particle electro-chemical bonds, break up and are entrained as a result of hydrodynamic lift and drag. The second
mode is referred to as mass erosion, wherein the bed fails at a deeply embedded plane such that all the material
above that plane is rapidly brought into suspension. In the third mode the bed is fluidized, i.e. the mud changes



-Bed-Water Interface

(b) Plane of Failure

Fluid Mud

(c) Bed
Destabilized Fluid
SMud-Water Interface


Fig. 2.2: Four modes of cohesive sediment erosion: a)
surface erosion of bed aggregates or flocs; b) mass
erosion of the bed; c) bed fluidization; and d) entrainment
of fluidized mud.

from a particle-supported matrix to a fluid-supported slurry. Finally, in the fourth mode, flow-induced
destabilization of the fluid mud-water interface causes interfacial mixing and entrainment.
Surface erosion under current- and wave-induced bottom stresses has been treated previously (Parchure and
Mehta, 1985; Maa and Mehta, 1987), while mass erosion has been examined on a preliminary basis (Mehta, 1991).
Here, some of the issues related to surface erosion are further explored, and preliminary evidence recapped for the
mass erosion phenomenon. Some evidence for bed fluidization and associated implications for erosion have been
given previously (Ross and Mehta, 1990), and are briefly reviewed here. The phenomena of subsequent
destabilization of the interface and its entrainment have been examined by Scarlatos and Mehta (1992) and Mehta
and Srinivas (1992), and are also briefly reviewed here.

2.3.1 Rate of Erosion
The time-rate of increase of suspended sediment mass per unit bed area, m, is given in the functional form
by dm
dm= f (Tb-r,,v1,v2V. ) (2.1)

where Tb is the bed shear stress, Tb , is the shear stress in excess of the bed shear strength with respect to
erosion, Tr, and v1...vn are erosion resistance defining parameters. In its most common, general form Eq. 2.1 is
stated as

e ='b-r (2.2)

where EM is a rate coefficient which, when Tr is constant, is equal to the value of e when -T = 0.5 Tb. In general
the magnitudes of EM and 7" can vary widely depending upon the properties of the sediment-fluid mixture and the
bed structure. For example, the range of EM can be from 104 to 10-2 g cm2min1, while T8 can vary from nil for
organic floc layers to as much as 10 Pa for very hard soils (Lavelle and Mofjeld, 1985; Sargunam et al., 1973).
If the bed properties are uniform, T7 remains independent of depth; hence for a fixed rb, the rate of erosion is
constant. More generally, bed properties exhibit stratification with depth, and Tg typically increases with depth so
that as bed scour proceeds e decreases with time.
Examples of T profiles are shown in Fig. 2.3, which gives results from two laboratory flume experiments
using beds of kaolinite. The beds were prepared by deposition of sediment from suspension, and then eroded by


011 0.2 0.3 0.4 0.5 0.6

0.005 \

E 8 Days
0.010 -Day-
w. I

0.015 -. -o
I -

0.020 I II
Fig. 2.3: Kaolinite bed shear strength profiles obtained in flume experiments
(after Parchure and Mehta, 1985).

unidirectional flow after 1 and 8 days of consolidation, respectively. The Ts profiles, derived from the experimental
results (Parchure and Mehta, 1985), show the 8 day profile to be considerably more uniform than the 1 day profile,
which also suggests a discrete change in the structure of the deposit at about 1.5 cm depth.
Some examples of erosion rate expressions obtained by different investigators are given in Table 2.1 (Mehta
et al., 1982; Parchure and Mehta, 1985; Mehta and Maa, 1987). In Eqs. 2.3 and 2.4, w is a dummy variable. The
coefficients an (n = 1, ...8) and pn (n = 1, ...5) are empirical, and (z) implies depth-dependence. In Eq. 2.10,
for erosion by waves, TR is a measure of bed resistance; its value changing with time as wave action continues.

Table 2.1: Expressions for the rate of erosion of cohesive soil beds
Investigators) Expression Number

Partheniades (1962) e = al 1- 1- (11r0-D2 exp(-c2/2)d] (2.3)

Christensen (1965) e = a2 0.5 1 (.1 exp(- /d (2.4)

Kandiah (1974); Arulanandan (1975) e =3 ba (2.5)

Christensen and Das (1973);
Raudkivi and Hutchison (1974);
Gularte (1978) e = P4exp[a4(r,-r)] (2.6)

Lambermont and Lebon (1977) e = as(r P-rs)X (2.7)

Thorn and Parsons (1980) e = a6(z)[r--r,(z)] (2.8)

Parchure and Mehta (1985) e = a7[r-rS(zY)]2 (2.9)

Maa and Mehta (1987)a e= ( b8'R (2.10)

aErosion by waves.

2.3.2 A Theoretical Basis
Surface erosion essentially involves micro-level interactions between hydrodynamic and physico-chemical
forces. Hence the development of any useful theoretical basis to explain the erosion phenomenon amounts to relating
a micro-theory to observations via integration of the micro-level processes over significantly large temporal and

spatial scales. A heuristic interpretation of the chemical reaction rate process theory (Eyring, 1936) is one approach
which, although limited by the nature of the interpretation itself, provides a qualitative basis for the form of Eq. 2.1,
and the effect of temperature on the erosion rate in a quantitative way. The reaction rate process can be briefly
described as follows.
Two molecules A and BC will react to form products AB and C through a weakly bonded and unstable
activated complex, A.B.C, according to

A + BC A.B.C AB + C (2.11)

The arrows imply that the reaction process is reversible such that AB can likewise react with C to produce A and
BC. However, as depicted in Fig. 2.4, conditions for the forward reaction are more favorable than the backward
one, when the total energy of AB + C is less than that for A + BC by an amount AE. The total energy of the
activated complex A.B.C is the highest of the three states such that the energy of activation, E, represents the
energy which must be exceeded for the forward reaction to occur. Likewise E' is the energy of activation for the
backward reaction. "Successful" intermolecular collisions are required for the reaction to proceed either way, and
it can be shown that the fraction of molecules having energy in excess of E is equal to exp[-E/RT] for the forward
reaction, where R is the molar gas constant and T is the absolute temperature. This exponential factor controls the
rate of the forward reaction. Likewise, exp[-E'/RT] determines the rate of the backward reaction; hence the net
reaction rate of the molecular flow units is proportional to the difference, exp[-AE/RT]. This is the basic premise
of the rate process theory.


ZU'T -- -'^ *g'^! ---------------*
.3 T A \ ^ Energy



Fig. 2.4: Relationship between energy required to change the chemical state of matter
(or cause displacement of particulate flow units), and the chemical state (or

Mitchell et al. (1968) applied the rate process theory to soil creep and noted that a force (or stress, 7b) is
required to cause the "forward reaction" to proceed, since otherwise the threshold energy curve will remain
symmetrical (Fig. 2.4 curve with Tb = 0), and no net displacement of the particulate flow units will occur. They
obtained an expression for the strain rate, Es, associated with creep:

e =K ( exp ] (2.12)

where K is a time and structure dependent dimensionless coefficient, k is the Boltzmann constant, hp is the Planck's
constant, and E" is the experimental activation energy, which is proportional to r, the shear stress on the particulate
flow units in the creeping soil. Interpreting Eq. 2.12 for surface floc erosion would mean that %s would represent
the erosion rate e, and 7 would be replaced by the excess shear stress, ,r rs (Gularte, 1978). In summary we
therefore note the following:

1. Surface erosion can be thought of as a rate process in which particle or floc entrainment occurs when there is
a "successful" application of flow-induced turbulent shear causing the inter-particle cohesive bonds to break. This
probabilistic behavior highlights the essentially stochastic nature of the erosion phenomenon, as originally highlighted
by Partheniades (1962; 1965).

2. By virtue of Eq. 2.4, the log of e/T must be proportional to 1/T in analogy with the Arrhenius relationship for
chemical reaction rates.

The second point is essentially a test of the applicability of the rate process theory to surface erosion. Kelly
and Gularte (1981) conducted erosion tests using a remolded grundite (with 50 % water content) in a recirculating
water tunnel in which the water temperature could be carefully controlled and altered. The erosion rate data in
Fig. 2.5 obtained at a constant applied fluid stress and different temperatures indeed confirm the Arrhenius trend,
and demonstrate the sensitivity of the erosion rate to water temperature.

2.3.3 Stirred Flocculent Layer
Since bed scour is reflected in the corresponding variation of the sediment mass in suspension, it is worth
examining the behavior of the suspension in terms of time-variation of the water column depth-averaged
concentration, C (as a representative of the suspension sediment mass), resulting from surface erosion of flocs. In
Fig. 2.6, typically observed variation of C with time is sketched qualitatively, together with what is believed to
occur at and near a stratified bed surface. Considering the situation in which the applied bed shear stress, Tb, is
initially greater than the bed shear strength 7,, C will increase relatively rapidly at first but, as the excess sheath
stress, Tb 7,, decreases with increasing scour, the rate of rise of C will decrease. Eventually Tb will equal 7, at
some final depth of scour at which C will attain a practically constant value, with a very small rate of further

o 5x10-4

5 _

S 5x10-s6
0 -

U Grundite
0 S
S10-6 I I I
3.2 3.3 3.4 3.5 3.6
1/T (K x 10-3)
Fig. 2.5: Arrehenius relationship between the rate of
erosion and absolute temperature (after Kelly and
Gularte, 1981).


:.:... .. .....
z .... .i.i..i.ii .i.ii .i ..i ........................

c~Ci 4E>

..... ............................................................. ........... ......................- ................ ........ ...

M c } Near-Bed
........................................ ............ tirred
... ............. r- ................................ ..... .......... ....... Layer

__ Initial
Scus Bed Level
Scour Final

Fig. 2.6: Schematic of entrainment and settling during erosion of a stratified bed at a constant applied stress.


increase due to the fact that the instantaneous bed shear stress will in general fluctuate about the turbulence-mean
value (represented by T'b), and, likewise, the bed shear strength at any horizontal plane can exhibit a variability about
the mean value, r,. Viewing the bed (initially at z = 0) in conjunction with the variation of C, the erosion flux
(arrow upward from the bed) will eventually will become practically zero as well.
The vertical mass fluxes can also be viewed from another, compatible, perspective. This perspective is
based on what occurs at z = 6, a small height above the bed. We may conceive of a comparatively thin near-bed
"stirred" flocculent layer whose upper and lower boundaries straddle the z = 6 level. This layer can be construed
to serve as a storage volume for the eroding bed sediment. Starting with a clear water column, initially there would
be no sediment in this layer, so that the mean concentration in the layer, Cb, would be zero. With the
commencement of erosion however, Cb will rise and, per unit time, more sediment will go into the layer from the
bottom by erosion than will leave through the upper level of the layer due to upward entrainment by turbulent
diffusion. Once, however, there is sediment in suspension, settling will occur and a convective circulation cell set
up, with sediment moving upward as well as downward across the z = 6 level. Finally, as bed erosion stops, the
upward and downward fluxes (arrows) will become equal in magnitude, implying an equilibrium condition. Thus,
the process of erosion can be explored either as one of bed scour at z = 0 involving upward mass flux only
(Parchure and Mehta, 1985), or as one involving simultaneous exchange due to upward entrainment and settling at
z = 6 (Lick, 1982). While in both cases Eq. 2.2 can represent the upward mass flux, in the second case, i.e. at
z = 8, a rate expression for settling must be included as well (Ross and Mehta, 1989).
Evidence of exchange of sediment between that in a dilute suspension and in the stirred flocculent layer,
and hence by inference the occurrence of such a layer, was demonstrated by Krone (1962) in a flow recirculating
flume using sediment from the San Francisco Bay. The sediment was initially fully suspended in saline water by
mixing it with this water at a high flow velocity such that the mean suspension concentration, Co, was 1.35 gl-1.
The velocity was then lowered to 8.5 cm s- and the subsequent rate of dilution of the suspension was determined
by measuring the depth-mean suspension concentration, C, at different times t. A very small fraction of the initially
suspended sediment (having a very small initial concentration, Co) was labelled with gold-198 radioisotope, and the
dilution rate of the total sediment was compared with that of the labelled one. Both labelled and unlabelled sediments
exhibited a first order rate of dilution, i.e. dC/dt was found to be equal to -aC(t), where a is the settling rate
constant. However, the labelled material was diluted at a faster rate than the total; the respective a values being
0.175 s1 and 0.109 s-1 (Fig. 2.7a). Assuming that labelling did not materially change the settling property of the
sediment, it can be inferred that as the sediment was settling, some of it was also re-entrained from the formed
stirred layer. Thus the effective rate with which the total sediment settled was lower than the actual rate at which
it settled; the latter being given by the rate of settlement of the labelled sediment.
To illustrate the above point consider the simple case depicted is Fig. 2.7b, in which at time t the number
of unlabelled and labelled particles in suspension is 9 and 6, respectively. At time t + at the corresponding numbers
are 8 and 3, so that effectively the rate of settlement of the labelled particles would be three times that of the
unlabelled ones. This difference arises because, due to the presence of a much larger number of unlabelled particles

0 1
~San Francisco
SBay Mud



O Co (Total Sediment) = 1.35 gl-1 o


Labelled 0 Unlabelled O *

So0 O
.0 so, 1%

OO Bed 0O

@ t @ t+At
Fig. 2.7: a) Time-concentration relationship during the deposition of
total and labelled suspended sediments in a flume (after Krone, 1962); b)
schematization of the settling and exchange behaviors of unlabelled and
labelled sediments (after Mehta, 1991).

in the bed than labelled ones, more of the former are re-entrained from the bed than the latter during the interval

2.3.4 Stress History and Incipient Entrainment
If the flow were stopped, the fluid-like stirred flocculent layer would rapidly form a particle-supported
matrix, or a cohesive bed, and the bed shear strength against erosion, Tg, would increase quite rapidly in the first
day or two due to dewatering, and also due to gelling in clays. Gelling involves the development of a structural
arrangement of the water molecules in the pore water close to the clay particles via hydrogen bonding. This
adsorbed, non-liquid water is 10 to 20 molecular layers thick (Grim, 1968), with density well in excess of 1 g cm3,
e.g. up to 1.4 g cm-3 (Martin, 1962). This arrangement causes a slight expansion of the soil matrix due to the
additional structural stresses that develop, hence some additional water is taken up by the soil. Shearing the matrix
will break up the structure and release the water. Thus, if a slurry of clay and water that has remained undisturbed
for several days were sheared, a tensiometer placed within the slurry would show a significant drop in suction, as

illustrated for a K-montmorillonite slurry (less than 2 /um median size, water content, w = 44% on oven-dry basis)
in Fig. 2.8 (Day and Ripple, 1966). After shearing is over the suction will rise slowly to the previous undisturbed
value. A much more dilute suspension (less than 1 lzm, w = 850%) did not exhibit any recovery.

28 I I I

San Joquin (< 2 pm, w= 44%)


Z 16-

o 12

8 K Montmorillonite (


0 I I I- 1 -I I I I --
0 2 4 6 8 10 12 14 16 18
TIME (days)

Fig. 2.8: Effect of shear on tensiometer suction in K-montmorillonite (San Joaquin)
(after Day and Ripple, 1966).

The thixotropic state of the bed, as reflected in gelling, as well as the packing arrangement of the flocs
influence the erosion process. Thus a bed that is formed by deposition from suspension will in general erode at a
different rate than a bed which has been compacted or remolded in situ (Mehta and Partheniades, 1979).
A final comment on surface erosion concerns laboratory flume observations which reveal that incipient floc
entrainment can occur under conditions in which the ambient fluid in the vicinity of the aggregate is viscous
dominated. Consider for example 0.2 Pa as a typical value of the bed shear stress at incipient erosion (Parchure and
Mehta, 1985). It can be shown that the corresponding friction velocity, u. = 0.014 m s1. Then, given a typical
bed roughness k = 4.6x104 m for cohesive sediment beds in laboratory flumes (Mehta, 1973), the roughness
Reynolds number Rw = u*k/v = 6.4, where v is the kinematic viscosity of water. At this very low value of RI,
the surface floc will be submerged in a viscous sublayer. Thus bond breakup will occur by the torque due to the
viscous stress which itself will be due to the transfer of momentum across the boundary between the sublayer and
the ambient turbulent flow field. In this context at least, studying the growth and breakup of estuarine cohesive
sediment flocs in viscous flow fields (e.g. Krone, 1963) seems justified.


Equation 2.2, although derived from surface erosion studies, has also been used for simulating mass erosion
in an approximate way. Commonly, erosion of this type has been believed to occur at applied shear stresses that
are considerably higher than those at which surface erosion occurs (Ariathurai et al., 1977). Furthermore, when
the soil is hard, pitting of the bed due to dislodgement of large pieces of the soil is often observed. In such a case
the erosion rate coefficient, EM, can be significantly larger than that for surface erosion of the same bed.
The stresses at which mass erosion occurs in fact strongly depend on the bed composition and structure.
When for example a high organic content is present, the bed may fail at fairly low stresses. Fig. 2.9 shows results
from a test in a flume in which a bed of mud from Lake Okeechobee, Florida was eroded by applying a series of
bed shear stresses of increasing magnitude from 0.15 to 0.65 Pa over constant durations of 90 min. This mud was
very high in organic content; loss on ignition was found to be 40% (by weight). The bed, having a mean density
of 1.07 g cm-3, was pre-prepared in native lake water and placed in the flume. As observed, when the stress was
increased to 0.65 Pa, the suspension concentration increased rapidly, essentially amounting to failure. The
occurrence of failure was in fact confirmed visually by the near-total scour of the bed that occurred. The resulting
very high concentration values are not plotted in the figure. The rate constant, EM, for mass erosion (from the slope
of the concentration-time curve at 'b = 0.65 Pa) was found to be 9x104 g cm'2min-1, and the erosion shear
strength, -; = 0.65 Pa.

S 12 I
0.15 Pa 0.25 Pa 0.35 Pa 0.45 Pa 0.55 Pa 0.65 Pa
o 10

X 8

0 6

z 2
U) 0 100 200 300 400 500
TIME (min)

Fig. 2.9: Erosion response of a bed (density 1.07 g cmn3) of mud from Lake Okeechobee,
Florida, to increasing applied bed shear stress in a flume (after Hwang, 1989).

The stress at which failure occurred was essentially the "bulk" strength of the bed, which was quite uniform
over the depth by virtue of the role of the fibrous organic matter in determining the bed matrix. It should be noted
that at densities less than 1.065 g cm3 the mud occurred as a predominantly fluid-supported slurry, which did not

possess a structured matrix (Hwang, 1989); hence at this density surface erosion and mass erosion practically
represented the same particulate entrainment process.

For convenience of treating the fluidization process, basic soil mechanical definitions are presented here.
Fig. 2.10 is an idealized sketch of stress profiles in a three-layered cohesive sediment concentration profile. In the
mobile suspension layer the total pressure (vertical stress), r, is equal to the hydrostatic pressure, Ph, of the
suspension. In the fluid mud layer the total pressure increases more rapidly with depth due to higher density;
however, the effective stress, o' (= a Pw), is still zero. Finally, in the cohesive bed, structural integrity between
closely packed flocs results in a space-filling framework which partially self-supports the soil medium. The pore
pressure in the bed is equal to the hydrostatic pressure plus the excess pore pressure, Au, which represents the
component of the bed material not supported by the porous solid matrix. Fig. 2.10 represents a partially consolidated
state, which may or may not be in equilibrium with the prevailing hydrodynamic conditions. Consolidation proceeds
as the excess pore pressure approaches zero, resulting in a maximum effective stress.

Water Surface y

Mobile Suspension

.Ph = C
O Fluid Mud Surface v
O'=0 Fluid Mud
> __Bed Surface q7

Pw Bed



Fig. 2.10: Soil mechanical definitions related to stresses in a
water column with a sediment bed and fluid mud.

As noted previously, waves provide one significant bed fluidization mechanism. Alone, waves can result
in an overall loosening of bed deposit, thereby causing fluid mud layer formation. In an effort to understand the
role of wave loading in the fluidization of the bed, i.e. fluid mud layer formation, miniature pore and total pressure
transducers were used to continuously monitor the stress levels in an estuarine mud subjected to progress, non-

breaking waves in a flume (water depth 31 cm, mud depth 12 cm, wave height 6 cm, period 1 s) (Ross and Metha,
1990). An illustrative plot (Fig. 2.11) of wave-averaged stress levels in the mud shows measurements of effective
stress profiles obtained by these gauges. By tracking an arbitrary, but very small, effective stress level, the fluid
mud/bed interface based on this definition could be determined as fluidization proceeded.


S\ -- 0 min
m O 15 min -
A 30 min
S% E 60 min
l 3 120 min -

6 %

an estuarine mud (after Ross and Mehta, 1989).

Fig. 2.12 shows the variation of the bed level defined by the 1 Pa effective stress (a very small value)
elevation with time compared to the visual (as seen through the side wall of the wave flume) upper fluid mud
interface, a lutocline, recorded for one such test. The upper fluid mud interface is shown to have been
approximately constant with time, while the fluid mud/bed interface continued to decline due to fluidization. This
process occurred while no consistent or drastic change in bottom mud concentration (density) was observed, even
as near the bed surface the density varied between 154 to 183 g-1.
An important conclusion that can be reached from these experiments is that structural breakdown of bed
deposit and consequent fluid mud formation can occur from waves with no measurable change in the density profile
with depth. Calculations using the concept of momentum diffusion into fluid mud in an estuary show (Ross and
Mehta, 1989), that a very mild imposed shear stress (- 0.01 Pa) at the mud-water interface, resulting in weak
unidirectional flows (- 10 cms-1), can cause high horizontal transport rates (~ 1 kg mnIs-1 per unit width) of this
newly fluidized bed material. Following fluidization, transport can also occur as slump flow down mildly sloping
beds (Kendrick and Derbyshire, 1985).
beds (Kendrick and Derbyshire, 1985).

S14 Mobile Suspension

O 13 Lutocline
r_12 - "- --------
o 12 -

1 Fluidized Mud
154 gl-1
I (16 gl-1) Cohesive Bed Boundary
> 1 (16i .( (1 Pa Elevation)
o(183 -1)
S 8- 8
S Cohesive Bed
LU 7 168 gl-1)
u. 61
0 30 60 90 120
TIME (min)

Fig. 2.12: Time-variation of cohesive bed and fluid mud levels in a wave flume
test (after Ross and Mehta, 1989).

Once the bed is fluidized, e.g. by wave action over a settled bed, interfacial entrainment of the fluid mud
by the overlying shear flow can be treated as a stratified flow problem involving two fluid layers, namely water
above mud, with an interfacial zone of finite thickness between the two layers. Entrainment occurs by turbulent
mixing at the interface which is destabilized by shear, with the disturbance of the interface governed by the locally
steep velocity and density gradients. Starting with an initially horizontal interface, a slight disturbance generates a
wave-like vortex sheet typical of the Kelvin-Helmholtz instability, which eventually stretches and folds, leading to
thickening and vigorous mixing of the interface. This sequence of events has been theoretically simulated in
Fig. 2.13 (Scarlatos and Mehta, 1992), in which the non-dimensional time t* = (r/L2)t, where r is the circulation
and L is a characteristic interfacial wave length.
The entrainment flux can be shown to dependent on the Richardson number, Ri, as shown in Fig. 2.14,
which is based on experimental studies carried out in a "race-track" flume using fluid muds composed of a
commercial kaolinite, volclay bentonite, and a natural mud (Mehta and Srinivas, 1992). The data points are for the
kaolinite. The Richardson number Ri = hAb/U2, where h is the depth of the upper mixed layer, U is the mean
velocity of this layer and Ab is the interfacial buoyancy step; buoyancy being defined as b = g(pf Pw), with g =
acceleration due to gravity, pf = fluid (sediment-laden) density and p, = water density. The non-dimensional
entrainment rate, E = (g/pAbU).dm/dt, where m is defined below Eq. 2.1.
Based on the quasi-stationary energy budget for the mixed layer in the presence of entraining sediment,
the following expression relating E with Ri can be obtained:

- t* =

ran. aogo8800 8aei l

-.88g8l I-.O I
1.0 2.0
L :>< L,)

t* = 0.4














-> XIL
0 po08q0t? o,2.0
F---^.&;: --
- o oooo o
0 0 00 0 0

So o (e)
0O 0

Fig. 2.13: Simulated time-evolution of the vortex sheet at the water-fluid mud boundary (after
Scarlatos and Mehta, 1992).




t* = 2.0
0 0
0 0 00 0
0 000 0

- ... .... -- ... .. ... .. -- i


f Xl

I 10 *

O -
Z 10-3
5g *- *^ Eq.2.14 2.1

S-4 *

number (after Mehta and Srinivas, 1992).

E = A^i-' DRi (2.13)
Z 10

0 .

1 10 102

Fig. 2.14: Non-dimensional fluid mud entrainment flux versus Richardson
number (after Mehta and Srinivas, 1992).

E = ARi1 DRi (2.13)

where the first term on the right hand side is commonly given in thermohaline entrainment expressions at low values
of Ri, while the second term arises from the effects characteristic of cohesive muds including particulate settling
and cohesion, and possibly the ratio of mud viscosity to water viscosity. The coefficients A and D must in general
be determined experimentally. The effects of mud properties in retarding entrainment seem to become important
with increasing Ri, with the result that for Ri greater than about 10, the entrainment flux of mud drops off much
more rapidly with increasing Ri than, say, the corresponding flux of salt. Furthermore, turbulence is drastically
damped across the sediment-water interface (Wolanski et al., 1989).
For values of Ri less than about 10, at comparatively high entrainment rates, the first term on the right
hand side indicates dm/dt to be proportional to U3, which is equivalent to rb.U, and is analogous to what occurs
in salt-stratified flows (Narimousa and Fernando, 1987). Thus entrainment in this situation depends on fluid power
(which is proportional to U3) rather than stress (which is proportional to U2), hence Eq. 2.2 is not applicable to
fluid mud entrainment.

Cohesive sediment erosion requires an understanding of the physico-chemical properties of the eroding
material which in turn characterize erosion resistance. Surface erosion is complicated by the deformation of the bed
matrix, and the occurrence of a "stirred" flocculent layer whose behavior, not well understood at present, is critical
in controlling near-bed aggregate dynamics (Newman, 1990). Like strong beds, weak ones can as well undergo
surface or mass erosion; the latter being the case when the bed bulk strength is exceeded. Since mud fluidization
and fluid mud entrainment are distinctly different from bed erosion, and since they are naturally ubiquitous,
understanding their underlying physics in tandem with the mechanics of bed erosion poses challenging issues for
future research.
In Chapter III, we shall revert to the issue of surface erosion, specifically focussing on the development
and application of a framework for characterization of the sediment-water system that would facilitate the estimation
of the rate coefficient, EM, and the shear strength, T,, in Eq. 2.2.


The dependence of the rate of surface erosion on the physico-chemical properties of the sediment-water
mixture causes a considerable difficulty in identifying all the parameters that govern erosion resistance. Earlier
attempts to characterize the erosion rate were based on the selection of governing parameters prevalent in soil
science. A summary of some of the early studies on cohesive sediment erosion is found in Partheniades (1971).
Kandiah (1974, p. 53) has listed eight empirical relationships between erosion shear strength and soil indices
including plasticity index, dispersion ratio, percent organic matter, vane shear strength, cation exchange capacity,
mean particle size, calcium-sodium ratio, and percent clay. A limitation of several of these studies and the derived
relationships arises from that fact that it is inappropriate to relate floc erosion, a surface phenomenon, to soil
parameters such as the Atterberg indices (e.g. plasticity index), which relate more to the soil bulk strength than to
surface floc strength. The inadequacy of this approach was first pointed out by Partheniades (1962), who tested
(eroded) two beds of mud from the San Francisco Bay. The first was remolded at field moisture content of about
110%. The remolded shear strength at yield point was about 0.53 kPa. The second bed was flocculated and
deposited in the flume directly from suspension at a very low flow velocity. The ratio of the strengths of the dense
bed to the flocculated bed, measured by a specially designed penetrometer, was 100:1. However, the minimum shear
stress at which erosion was first observed was found to be of the same order of magnitude for the two beds.
Partheniades therefore concluded that since surface erosion was due to the breakup of inter-particle electro-chemical
bonds, erosion must be characterized by parameters that represent the cohesive bond strength of the surface flocs.
Relying upon several relevant studies, Kandiah (1974) used the above observation of Partheniades as the
basis for developing a new framework for identifying factors/parameters that are known to relate to surface erosion.
This framework consists of grouping the factors/parameters characterizing the rate of erosion into tow main
categories: 1) factors/parameters defining the erosive force, and 2) factors/parameters defining erosion resistance.
In order to make a comprehensive evaluation of erosion-related literature along the lines of this type of a
framework, Parchure (see Hayter and Mehta, 1982) examined methods employed for the application of the bed shear
stress as the erosive agent, and considered the following three factors for characterizing erosion resistance:
1) sediment composition, 2) pore and eroding fluid compositions, and 3) bed structure. In addition, Parchure
examined aspects related to coagulation and settling, the choice of erodibility index and measure of erosion, adopted
by different investigators. This evaluation resulted in a generic framework for the experimental methodology for
erosion studies, as shown in Fig. A. 1 in Appendix A. In that appendix, the various items related to erosion have
been qualified by illustrative references (experimental studies) in Tables A. 1 through A.7.
An evident conclusion from the study given in Appendix A was that the number of factors/parameters
considered in the literature was excessive, and that fewer, significant factors/parameters must be selected for a
realistic characterization of surface erosion. Following the evaluation procedure of Parchure, Mehta (1981) selected
three studies on cohesive sediment erosion (Partheniades, 1962; Christensen and Das, 1973, and Ariathurai and

Arulanandan, 1978), and examined them within a more narrowly defined set of factors/parameters, recognizing
however that for characterizing the erosive agent, the type of apparatus used and bed size are additional factors that
must be considered in conjunction with the method of application of the bed shear stress. Tables B.1 through B.4
in Appendix B provide the comparison, from which the following main observations can be made:

1. Significant diversity of apparatuses, sampling methods and bed size employed exist,
2. There is inadequate characterization of the fluids,
3. There is a lack of reference, where relevant, to influential organic and biological factors/parameters.

Unlike conditions relevant to soil erosion, for submerged estuarine mud erosion it is typically acceptable
to consider the pore and eroding fluid compositions to be the same, assuming equilibration. This was for instance
the case in the studies of Partheniades (1962) and Christensen and Das (1973). In the study of Ariathurai and
Arulanandan (1978), the pore fluid was specifically altered relative to the eroding fluid. This approach revealed
some very important physico-chemical influences; however at the same time considerably increased the need to
define a number of parameters in addition to those that would have to be defined if the fluid composition were the
same in the pores and in the ambient eroding fluid medium.
In the next section we will consider a list of factors/parameters that can be reported/measured relatively
easily, and construed as being minimally necessary to characterize the resistance to erosion.

3.2.1 Factors/parameters
From an engineering perspective typically involving equilibrated sediments, the following suite of
factors/parameters is recommended to characterize erosion resistance:
1. Sediment Composition
Particle size distribution
Minerals (clay and non-clay)
Organic matter
Cation exchange capacity
Biochemical parameters
2. Fluid Composition
Cation concentration
Total salt concentration

3. Bed Characteristics
Bed density
Bed preparation method (in laboratory studies)
This list is by no means complete in terms of possible influences of other factors/parameters; here we are concerned
with the reportage of only what are believed to be the most important factors/parameters that should facilitate an
inter-comparison between different studies, at least on a cursory basis. Furthermore, as noted, pore and eroding
fluids are considered to have the same composition. When such is not the case, i.e. the pore fluid composition
differs from that of the eroding fluid, the sodium adsorption ratio (SAR) can be an important parameter governing
soil hardness. This ratio is define as

SAR = a(31)
1 {[Ca"] + [Mg"] }2

where the square brackets indicate concentration in milliequivalents per liter (Arulanandan et al., 1975). This ratio
inherently recognizes the prevalence and importance of Na+ +, Ca+ + and Mg+ + ions commonly found in soils.
We shall briefly examine the significance of influential parameters and factors in the sequel, without
explicitly considering SAR as a necessary characterization parameter, even though SAR measurements are quoted
in several cases.

3.2.2 Sediment Composition
Particle Size Distribution: The central tendency, e.g. the median size, and the spread, e.g. the uniformity
coefficient, can be equally important. Furthermore, the dispersed as well as flocculated particulate states are
important; however, for simplicity we recommend that only the dispersed particles be considered when
characterizing size.
Cohesion becomes quite important when the particles are smaller than about 16 /m, and the effect is such
that when conditions favoring coagulation of the dispersed particles are present, the floc size and settling velocity
differ markedly from those of the constituent dispersed particles. An indication of the degree of enhancement of the
settling velocity due to flocculation is obtained from the illustrative results of Table 3.1 (Mehta et al., 1989), which
are derived from the studies of Migniot (1968) and Chase (1979) in settling columns. For dispersed particle
diameters of 20, 2, and 0.2 pm, the corresponding Stokes settling velocity of the dispersed particles, floc settling
velocity, and the floc diameter are given. The ratio of floc to Stokes velocity given in the last column ranges from
1.1 at a dispersed particle diameter of 20 jm to 4,600 at 0.2 /m. Furthermore, while Stokes velocity is observed
to decrease rapidly with dispersed particle size, the floc settling velocity and diameter retain the same orders of
magnitude due to increasing cohesion with decreasing dispersed particle size.
Since particles greater than 16 /m will typically be present, sedimentary heterogeneity tends to lead to
sorting effects that ultimately influence both the vertical and the horizontal distributions of the bottom material in

Table 3.1: Primary particle and floe diameters and settling velocities.

Primary particle Stokes settling Floe settling Floe velocity
diameter, velocity, velocity Floe diameter, divided by
(/tm) (mm s-1) (mm s'1) (Om) Stokes velocity

2 x 101 2.4 x 10-1 2.7 x 10-1 8.8 x 101 1.1 x 100

2 x 100 2.4 x 10-3 1.7 x 10-' 5.6 x 101 7.1 x 101

2 x 10-1 2.4 x 10-5 1.1 x 10-1 3.4 x 101 4.6 x 10

the estuary. For instance, sorting due to differential settling has been studied during deposition that leads to bed
formation. A consequence of differential settling is that once rapidly falling particles settle out of suspension, the
remaining material settles at a rapidly and continuously decreasing rate; hence ignoring differential settling will lead
to an over-prediction of the rate of particulate deposition.
It is customary to assume that the rate of deposition from an initial suspension (of concentration Co) is a
first order dilution process, i.e. the rate of decrease of the instantaneous concentration, dC/dt, is proportional to
the instantaneous concentration, C(t). This law of dilution can be assumed to be valid for initial concentrations up
to 0.3 g 1-', but its applicability can be extended up to about 1 g 1-1. The proportionality coefficient includes the
settling velocity. If the settling velocity is assumed to be constant, then log(C/Co) will be linearly proportional to
time (Krone, 1962), i.e. the decay will be exponential. However, as shown in Fig. 3.1, this law will over-predict
the rate of deposition, which can be modeled more realistically if the size, and hence the settling velocity distribution
of the sediment is taken into account. This modified deposition relationship is contingent upon sediment and fluid
compositions, and it is particularly relevant to the settling behavior of weakly cohesive clays such as kaolinite
(Mehta and Lott, 1987). The data points were obtained from a deposition experiment in a flume using a commercial
kaolinite in distilled water. The bed shear stress during deposition was 0.13 Pa.
A relevant consequence of sorting of this type during deposition is the development of a bed that is
stratified in terms of dispersed particle size. Bed erosion behavior will therefore be contingent upon the nature of
stratification produced. Identification of dispersed particle profiles requires very sensitive measurements; Parchure
(1984) could not resolve any particulate stratification in his experimental beds using a fairly sensitive method, which
possibly did not have the resolution required for this purpose. Nevertheless, it must be emphasized that the effect
of particle size on the rate of erosion is evident in experimental studies (Kandiah, 1974; Davis, 1991).


o Decay Law

o) -2.0 -

-30 Exponential
-3 Decay

0 2 4 6 8 10
TIME (hr)

Fig. 3.1: Time-concentration relationship in a flume
deposition experiment with kaolinite suspended in distilled
water (after Mehta and Lott, 1987).

Minerals: The importance of the influence of clay- and non-clay minerals is self-explanatory; here a single example
should suffice. Fig. 3.2 illustrates the influence of changing mineral composition on the relationship between the
erosion rate and the bed shear stress (in accordance with Eq. 2.2) in tests conducted by Kandiah (1974) using
remolded soils in a concentric cylindrical apparatus. The soil matrix material was Yolo loam silt, to which
montmorillonite (volclay bentonite) was added in different proportions from 10 to 30%. The eroding fluid was
distilled water, while the pore fluid SAR was 2.5, and the average salt concentration in the pore fluid was 20 meq
11. The pore fluid pH was 7. Notice the measurable decrease in the rate of erosion with increasing percent (by
weight) of montmorillonite. As also seen from Table 3.2, the erosion rate constant, EM, and the bed shear strength,
7r, change monotonically with increasing clay fraction.

Organic Matter: The presence of organic matter, especially if greater than about 5% by weight, can complicate the
characterization process. A dispersing agent will not have the desired effect on the natural, flocculated sample, and
the size distribution of the material obtained after addition of dispersing agent will not be wholly meaningful. In fact,
when the organic fraction is very high, e.g. over 25%, there may be no unique correlation between the dispersed
particle size- and the floc size-distribution. Likewise, cation exchange capacity values (to be discussed later) will
be spurious in terms of their relation to clay cohesion.

T" Matrix Material Yolo Loam Silt 10%
E Salt Conc. 20 meq I-1
E SAR 2.5 20%

0.01 -

0 2 4 6 8

Fig. 3.2: Erosion rate versus shear stress for mixtures of montmorillonite and Yolo
loam (after Kandiah, 1974). Percent indicate montmorillonite.

Table 3.2: Erosion rate coefficients, EM and rs, for soils with varying clay content and organic matter based on
data of Kandiah (1974).

Soil Characteristics M 7s
(g cm- min-1) (Pa)

Yolo loam +10% 1.25x10-2 2
montmorillonite (Fig. 3.2)

Yolo loam +20% 1.20x10-2 2.4
montmorillonite (Fig. 3.2)

Yolo loam +30% 8.20x10-3 2.7
montmorillonite (Fig. 3.2)

Illitic soil +0% OM (Fig. 3.3) 1.40x10-2 1.8

Illitic soil +0.85% OM (Fig. 3.3) 1.25x10-2 2.4

Illitic soil +2.7% OM (Fig. 3.3) 1.20x10-2 4.3

Illitic soil +5.6% OM (Fig. 3.3) 2.55x10-2 3.6

The issue of organic matter characterization has not been fully resolved; nevertheless, the effect of organic
fraction on erodibility has been clearly demonstrated, e.g. as observed in Fig. 3.3, taken from Kandiah (1974).
Organic matter (OM, composed of air dried, crushed and sieved steer manure), was deliberately added in varying
proportions to the soil matrix composed of 30% illite and 70% silica flour (SAR = 3 and total salt concentration
in the pore fluid = 20 meq 171). Table 3.1 lists the values of EM and r. for samples with OM ranging from 0 to
5.6% (by weight). Note that increasing OM up to 2.7% changed the erosion rate constants in a consistent way,
causing an increase in erosion resistance, but when OM was further increased to 5.6%, the ;r value dropped and
EM increased, i.e. the trend was reversed and the bed became more erodible than at OM = 2.7%. This increase
in erodibility may be due to the open structure of the soil matrix in the presence of comparatively high amount of
OM, a trend that has been corroborated in flume erosion experiments involving a lake mud with high fraction of
organic material (Hwang, 1989).

30 % Illite 0%OM
E 0.02 70 % Silica Flour
M 2 Salt Cone. 20 meq-1
SAR 3.0
E 0.85% OM

Z 3
S0.01 6/ 6%OM--

0 2.7 %%OM

0 2 4 6

Fig. 3.3: Erosion rate versus shear stress for an illitic soil with varying organic
matter (after Kandiah, 1974).

Cation Exchange Capacity: The CEC is an obvious candidate for reportage as far as surface erosion characterization
is concerned, since it is a direct measure of cohesion arising from inter-particle, electro-chemical bonds between
clay particles. Increasing CEC generally implies increasing cohesion. Table 3.3 lists CEC values of major clay-types
(Grim, 1968). As can be judged from the magnitude of CEC observed, montmorillonite is a very active and
cohesive clay, while kaolinite is in only weakly cohesive. Illite is intermediate.

As an illustration of the effect of CEC on erosion, experimentally obtained relationship between CEC and
EM is shown in Fig. 3.4 for a wide range of remolded soil samples (Ariathurai and Arulanandan, 1978). The SAR
was >30, a high value, and the total salt concentration in the pore fluid was 20 meq 1-1, while the eroding fluid

Table 3.3: Cation exchange capacity of clay minerals, in milliequivalents per 100
g (after Grim, 1968).

(meq per 100 g)

3 15
5- 10

Halloysite 2H20
Halloysite 4H20




40 50
80- 150
10 40
100- 150
10 40

3- 15

Salt Cone. 20 meq I-1
SAR > 30




CEC (meq per 100 g)

Fig. 3.4: Variation of erosion rate constant, EM, with cation
exchange capacity (after Ariathurai and Arulanandan, 1978).


0.030 I-

c 0.020



was distilled water. Note the rapid decrease in EM, as the soil changed from dispersed to flocculated with increasing
CEC. The influence of CEC in this series of tests was evidently negligible for CEC > 10.

Biochemical Parameters: The diversity of biochemical effects makes erosion resistance characterization an
exceptionally difficult task. Davis (1991) refers to influences from armoring, biodeposition and microfloral adhesives
on bed resistance to erosion. From an engineering perspective we must leave this issue open until commonly agreed
upon parameters and their influences on surface erosion are established in quantitative terms. Among the potential
candidates are total chlorophyll a and total adenosine triphosphate (ATP). These two measures are widely accepted
as efficient indicators of the development of bed resistance influencing microalgal communities (chlorophyll a) and
the total microbial community (ATP) in sediments.

As an illustration of the influence of chlorophyll a, consider a study by Montague et al. (1992) in which
replicate microcosms, shaded to various degrees, and containing wet-sieved natural estuarine sediments and water,
were incubated outdoors for 10 days. At the end of this period, relative erodibility was measured by stirring. An
erodibility coefficient, which is essentially related to EM, was defined as grams of sediment eroded per rpm of
stirring. As observed in Fig. 3.5, the erodibility coefficient fell with increasing chlorophyll a. At the same time the
critical stirring speed, which is related to Ts, increased with increasing chlorophyll a. In other words the resistance
to erosion increased with increasing chlorophyll a. This impact was the result of a thin surficial microbial film
formation under sunlight. In a separate set of analogous experiments in a flume in which erosion was induced by
steady, turbulent shear flow as opposed to a stirrer, Parchure (1984) estimated the thickness of the film to be on
the order of 4 mm.

3.2.3 Fluid Composition
Cation Concentration
The effect of cationic valence and concentration on cohesion can be examined in a simple way through the
effects different cations have on the diffuse electric double layer of the clay micelle. The simple Gouy-Chapman
model can, for instance, be used to calculate the equilibrium double layer thickness (DLT) under the action of two
opposing forces, the double layer repulsive force and the London-van der Waals attractive force (van Olphen, 1963).
In Fig. 3.6 calculation of this nature are presented in terms of the relationship between DLT and cationic
concentration for mono-, di- and tri-valent cations (Kandiah, 1974). Since with increasing valence the ions are
increasingly attracted to the clay particle surface assuming the same diffusive tendency away from the surface, DLT
decreases from mono- to tri-valent ion. For the same valence, increasing the ionic concentration decreases the
diffusive tendency and hence decreases DLT by bringing the ions closer to the particle surface.
By conducting erosion experiments on a homoionic, 30% illitic clay soil, Kandiah (1974) plotted 7, against
DLT in Fig. 3.7, which clearly demonstrates a strong dependence of ;s on DLT and hence, by inference, on
cationic valence and concentration. For DLT > 20 A there was practically no erosion resistance. Typically, the

4.5 5.5 6.5

Fig. 3.5: Erodibility coefficient (open squares) and critical stirring speed (filled
squares) versus chlorophyll a in microbe incubated sediment beds shaded to various
degrees (after Montague et al., 1992).

1-40 -


u 30

I- 20 -60 80 10

Fig. 3.6: Calculated relationship between double layer thickness and
electrolyte concentration for mono-, di-, and tri-valent nations (after

Kandia Trivalent, 1974).
0 20 40 60 80 100

Fig. 3.6: Calculated relationship between double layer thickness and
electrolyte concentration for mono-, di-, and tri-valent cations (after
Kandiah, 1974).



Pe 4--



0 5 10 15 20 25

Fig. 3.7: Relationship between bed shear strength, Ts, and double
layer thickness, DLT, for a homoionic, 30% illitic clay soil (after
Kandiah, 1974).

important cations will be Na+, Ca++ and Mg++, and also K+, Fe++ and Al1++ to a lesser extent (Parchure,
1984). Reporting the first three ionic concentrations makes it feasible to calculate SAR, if necessary.

Total Salt Concentration: Salinity, e.g. as measured by NaCl concentration, is the most obvious characterization
parameter of interest in estuaries. As noted in Table 3.4 (Ariathurai, 1974), major clay types are coagulated at fairly
low salinities, although the effect of salinity on the floc structure continues to be important up to at least 10 g r1
(Krone, 1962). In the laboratory, processed sodium chloride is often used to simulate sea salt effect. This may be
an acceptable engineering practice, but as shown in Table 3.5 (Bolz and Tuve, 1976), the two are not quite the
The effect of salinity on floc structure translates into the corresponding influence on the bed shear strength,
hence erosion. In Fig. 3.8 (Parchure and Mehta, 1985), the shear strengths of the top, thin layer of beds composed
of a lake sediment with water at different salinities and consolidated for 1.7 days are plotted against the
corresponding salinities. The bar over T7 indicates that the shear strength is a mean value for the eroded layer.

Table 3.4: Critical cation concentrations and corresponding salinity for potential
coagulation in seawater (after Ariathurai, 1974).

Clay Total Cation
Type Concentration Salinity
(meq 1-1) (gl1)

Kaolinite 1.0 0.6
Illite 2.0 1.1
Montmorillonite 4.3 2.4

Table 3.5: Cation concentrations in processed sodium chloride and standard sea salt
(after Bolz and Tuve, 1976).

Cation NaCI Sea Salt
(ppm) (ppm)

Sodium 357,460 301,720
Calcium, Magnesium 50 47,770
Potassium 10 10,860
Phosphate 1 -
Iron 0.5

4 6 8

10 12

Fig. 3.8: Variation of mean shear strength of the top bed layer composed of a
lake mud with salinity (after Parchure and Mehta, 1985).





I I I .,-
--~e M.--


_ / Lake Mud -


0 2

Notice the significant effect of salinity on the shear strength up to about 10 ppt (10,000 ppm), in agreement with
prior observations of Krone (1962).

pH: For given cation concentrations, whether a clay is dispersed or coagulated depends on pH. Hence pH is an
independent parameter that must be measured (and controlled in laboratory experiments). Fig. 3.9 shows this type
of a relationship for a montmorilonite (Kandiah, 1974). SAR and total cation concentration refer to the pore fluid;
the eroding fluid was distilled water.

0 10 20 30 40 50

Fig. 3.9: Coagulation-dispersion boundary curves for a
montmorillonite at three pH ranges (after Kandiah, 1974).

Temperature: The influence of temperature (absolute scale) on the rate of erosion was mentioned in Section 2.3.2
in connection with the rate process theory. See for example Fig. 2.5 (Gularte, 1981), in which the erosion rate-
temperature plot closely follows the Arrhenius relationship. In Fig. 3.10, an additional illustration of experimentally
determined relationship between the erosion rate constant, eM, and temperature is shown (Ariathurai and
Arulanandan, 1978). The pore fluid SAR was "low", and total salt concentration 20 meq 11.

3.2.4 Bed Characteristics
Bed Density: Given sediment and fluid characteristics, bed density is the most important parameter governing
surface erosion. Here we will illustrate the effect with the single example of Fig. 3.11, in which the rate of erosion
is plotted against current speed, U, for mud from the San Francisco Bay tested in a flume (Villaret and Paulic,

0.020 Salt Conc. 20 meq I
: Low SAR
E 0.015 -
E y

S0.010 -

0.005 I I I I
0 10 20 30 40 50

Fig. 3.10: Variation of erosion rate constant, eM, with temperature
(after Ariathurai and Arulanandan, 1978).

p = 1.2 gcm"3

15 x 10-2

C 1.4 g



C ~1.6 gcm-
S1 x 10-3

0 0.4 0.8 1.2

Fig. 3.11: Variation of erosion rate with current speed at
different bed densities for San Francisco Bay mud (after
Villaret and Paulic, 1986).

1986). In these experiments, beds of three different densities were placed in the flume from pre-prepared slurries.
The bed density in each case was vertically quite uniform. This mud, which was montmorillonitic, is observed to
be considerably more resistant to erosion at a density of 1.6 g cm3 than at 1.2 g cm-3.

Bed Preparation Method: The manner in which a sediment bed of a given mean density and fluid composition will
erode in a given flow field is significantly determined by the vertical structure of the bed, as reflected primarily in
the vertical density profile. Note however that density is by no means an exclusive determinant of erosion
characteristics in this case, since vertical variations in the particulate composition of the flocs, floc structure and
strength, and the recent stress history (e.g. degree of gelling) can exercise influences that are not wholly embodied
in density. Nevertheless, for engineering purposes, the density profile as indeed of paramount importance in
characterizing erosion resistance.

As noted in Section 2.3.1, the degree of density stratification of the bed has a significant influence on the
rate of erosion. Considering Eq. 2.2 for example, a bed whose properties are invariant with depth, i.e. having a
constant rs, will erode at a constant rate under a constant applied stress, Tb. If on the other hand 7, increases with
depth for example, then the rate of erosion will decrease with time. To demonstrate this point, two beds of kaolinite
were eroded in a flume (Mehta and Partheniades, 1979). This first was deposited gradually from suspension under
a low velocity, while the second was prepared outside the flume at a density close to that of the mean density of
the first bed. Fig. 3.12 shows the time-variation of the depth-mean suspended sediment concentration of the first
bed as it was eroded at 'b = 0.21 Pa. Note the rapid initial increase in concentration followed by approach to a
constant value as the erosion rate decreased with time for this stratified bed. As shown in Fig. 3.13, the second bed
(eroded at rb = 0.41 Pa) eroded at a more or less constant rate, since it was practically uniform. These examples
essentially demonstrate the need to obtain accurate vertical profile of bed density as a measure of the degree of

Two issues, relevant to what follows in Chapter IV, that have been inherently or otherwise alluded to
above, include 1) the importance of knowing the bed shear strength (rs), and 2) the possibility of correlating T with
bed density for estimating 7, for predicting the surface erosion rate. Prediction of T7 of course also requires prior
knowledge of the erosion rate constant (EM) in addition to rs. However, in Chapter IV we will restrict ourselves
to the matter of 7, versus density correlation as an illustration of the usefulness of density, which is one of the
several parameters we have recommended for reportage (in Section 3 above), for characterizing the rate of surface
erosion. As noted elsewhere (Mehta, 1988), it is in fact feasible to relate cM to 7,, thus demonstrating that 7, is the
primary surface erosion-determining parameter.

1 0.12
n z 0.10
w -
9 u 0.08
cnu 0.06

. 0.02

< n

2 4 6 8 10 12 14 16 18 20 .22


TIME (Hours)

Fig. 3.12: Time-variation of relative suspended sediment concentration for a stratified
kaolinite bed (after Mehta and Partheniades, 1979).


0 0

4 8 12 16 20 24 28 32 36 40 44 48
TIME (Hours)

Fig. 3.13: Time-variation of suspended sediment concentration for a uniform kaolinite bed (after
Mehta and Partheniades, 1979).

- o

-b 0.21 Pa


l l l l l l l l i l . . . *

_ I I I I I I I I I I I I I II I I I i I
S0 o
6 -

b T=0.41 Pa
"cb 0.41 P



As we noted in Chapter III, the need to estimate values of the bed shear strength as the primary measure
of erosion, and the relative facility with which bed density, or its measure can be determined, and furthermore, the
observation that increase in the shear strength appears to occur in tandem with a corresponding increase in bed
density, present an opportunity to examine the potential relationship between the shear strength and density as a
predictor of shear strength from measured bed density.
We are supported in this assertion by the early observations, among others, of Seed and Chan (1959) who
investigated the structure and strength characteristics of compacted clays. One of their conclusions was that since
"the strength of compacted clay seems to depend primarily on the dry density, water content and soil structure,
together with the associated pore-water pressures, at a constant value of the water content, the strength is likely to
increase progressively with increase in dry density". Unfortunately, difficulties from the standpoint of chemical
physics immediately arise when a justification is sought in considering a relationship between shear strength and
density from first principles. In that connection we shall first state relevant definitions.

Mass density, here selected as the bulk (total) value for a saturated soil, is expressed as

M 1+w (4.1)
p s Pw
V 1+e

where M = total weight of sample, V = total volume of sample, w = water content (weight of water divided by
weight of solids), e = void ratio (volume of water divided by volume of solids), s = specific gravity of solids
(density of solids; also called granular or particulate density, ps, divided by the density of water at 40C) and p, =
density of water. Investigators have also used the dry mass density, defined for a saturated soil as

M, p (P-P p (4.2)
S V 1+w (p,-p.)

where M. = mass of solids. In cohesive sediment transport studies, Pd is more commonly referred to as dry mass
concentration, C. Since mass density (bulk or dry) is a physical quantity, it bear no direct relation to any physico-
chemical quantity, including shear strength for example. The solids volume fraction, 0, equal to the volume of
solids divided by the total volume, is, on the other hand, recognized to be the more appropriate parameter in
sediment settling and consolidation descriptions, and especially in mud rheology, which does relate to soil physico-
chemical properties. The solids volume fraction is also given by

4 = 1-n Pd C (4.3)
P, P,

where n = porosity (volume of water divided by volume of solids). 4 is thus easily obtained from C, knowing p,.
In surface erosion work a multitude of definitions have been used to characterize bed strength. Krone
(1962) used a penetrometer consisting of a screen of 0.76 mm wire mesh spaced 6.4 mm apart. Weights required
to push the screen into the bed to different depths were recorded. This method, which tends to measure, at least
in part the compressive strength of the bed matrix, showed no consistent correlation with bed density. Most
subsequent studies have therefore attempted to use some measure of shear strength to characterize strength. Three
prominent ones include: vane shear strength, r,, Bingham yield strength, ry, and the bed shear strength with respect
to erosion, 7. Let us consider experimentally determined relationships between these measures of bed shear and
bed density.

4.2.1 Vane Shear Strength
In Fig. 4.1 the vane shear strength, Tr, is plotted against bed density, p for mud from Lake Okeechobee,
Florida. Mud samples as bottom cores were obtained from several locations within the area of the lake where the
material consists of allothigenous mud, in which kaolinite was the main clay constituent, with 40% (by weight)
organic matter (Hwang, 1989). The cores were analyzed in the laboratory for layer-by-layer determination of Tr
and p. Data scatter is significant, mainly due to the variability in sample composition and texture. The linear
relationship shown between Tv and p is obviously rather speculative; nevertheless a point of interest is the likelihood
of the existence of a minimum density, in this case 1.065 g cm-3, below which the mud apparently had no
measurable vane shear strength.
While in many instances ,v correlates with Ts, as a general rule such a correlation is moot at best. Consider
for example the plots of Tv against 7, in Fig. 4.2. Note that while for seven soil samples ,r increased with Ts, for
the San Suba sample to correlation was inverse of the rest.
Since the erosion shear strength, Ts, is related to the inter-particle bond strength, especially for soft
deposits, it tends to be of the same order of magnitude as the strength of the flocs themselves, e.g. in the range of
0.02 to 0.5 Pa (Krone, 1963). On the other hand the vane shear strength ,r, which is shown to be as much as three
decades greater in magnitude than rs, is a decidedly unsuitable measure of surface erosion resistance (Partheniades,
1965). This point can be stressed with the help of a somewhat crude but plausible argument involving length scales
(Mehta, 1991).
Consider a resistance defining length scale, Lr = characteristic floc size, and two disruption defining length
scales; L, = vane shear length scale and Lt = near-bed turbulent eddy length scale. We will select Lr = 0.1 mm
= 10-4 m as a typical value, and L, = 1 cm = 10-2 m (vane dimension). We note that the ratio Lr/L = 102,
which we heuristically interpret to imply that the scale of the device that disrupts the flocs in the vane shear test

Tv = 19.8 (p 1.065)

Z3- *

.* /* *
2 o
a .. *f
g 10
z *
> 0 *

1 4 1.1 1.2 1.3 1.4

1.065 g cm-3 DENSITY, p (g cm-3)
Fig. 4.1: Plot of vane shear strength versus bed density for mud
from Lake Okeechobee, Florida (after Hwang, 1989).

30 11


> 20

w 15
QT K177A
2 10 -
I K177 K319
1J 0,Kl16 -

5 -J5


Fig. 4.2: Vane shear strength versus erosion shear strength
for cohesive soils (after Task Committee, 1968).

is incompatible with the floc scale; the vane actually measures bulk resistance which is the integral of the resistance
of a very large number of flocs. This difference can in turn be considered to be the explanation for the ratio r.7s/
< <1. Next we will assume L, = (v3/en)14, the Kolmogoroff turbulent eddy length scale, where v is the kinematic
viscosity of water and en is the rate of kinetic energy dissipation. We have v = 10-6 m2 s"1 for water, and en = 10-2
m2 s"3 as a reasonable value of the dissipation rate corresponding to typical rms velocity fluctuations on the order
of 10-2 m s-1 near the bed (Hinze, 1959). Thus L = 10-4 m, which yields L/Lt = 1. This result is of course
expected since eddy induced stresses are responsible for floc breakup.

4.2.2 Bingham Shear Strength
The constitutive equation for a Bingham plastic is

r = Ty + p (4.4)

which relates the applied stress, r, to the strain rate, j, with y = dynamic viscosity of mud and 7y = Bingham yield
strength. For most muds Eq. 4.4, which implies that for all 7 7y the mud will not yield to the applied stress,
represents an approximation. This is so because muds tend to creep even at very low stresses. Fig. 4.3a shows the
T versus 7 flow curve for a mud from the Rotterdam harbor (Parker and Kirby, 1982), which indicates the mud to
be a pseodoplastic rather than a Bingham plastic. The upper Bingham yield strength, TB, obtained by extrapolation
as indicated, is most commonly considered to be a representative measure, or an approximation, of Ty. Note the
effect of changing mud dry density, Pd, on TB. In Fig. 4.3b a portion of the same data as those for pd = 0.126 g
cm-3 in Fig. 4.3a is replotted for very low strain rates. Note that by a mere replotting of the same data, the
estimated value of TB drops from about 15 Pa to 4.6 Pa. It is evident from this simple illustration that TB is an
imprecise indicator of yield strength. It is consequently concluded that while values of rB obtained using a consistent
procedure in a single set of experiments may be internally and, therefore, relatively consistent, it would be difficult
to compare the magnitudes of rB obtained in different experiments using different apparatuses and data analysis
procedures. Furthermore, the physical basis upon which the definition of 7B, or rather ry, rests is not wholly
commensurate with the definition of 7,. Thus whether Ty can be an appropriate measure of rs remains unclear even
though, since both seemingly correlate with density, an empirical relationship between Ty and rs can be established.
The problem of characterizing TB poses additional difficulties in using it to represent erosion resistance.
Fig. 4.4 shows the variation of TB with dry density, pd, for mud from the harbor in Avonmouth, UK
(Owen, 1970). Note that for the same initial sample, the fluid salinity was varied from 0.8 to 33.3 ppt for ten sub-
samples tested, and this variation in fluid composition partly explains the cause of some of the observed data scatter.

4.2.3 Erosion Shear Strength
In Appendix C, the procedure by which Parchure and Mehta (1985) calculated depth-profiles of T. in flume
experiments involving layer-by-layer erosion of the bed is given. When the -T profiles are compared with the

O. 16

06 12 pH = 7.1
Cu) Salinity 30 ppt

4 Pd = 0.071g cm3

% I I I 1
50 100 150 200 250
(a) STRESS RATE, j(s-')


pd = 0.126 g cm-3
6 -

S4- -

S 2

0 0.2 0.4 0.6 0.8 1.0 1.5 2.0 2.5

Fig. 4.3: Stress versus strain rate flow curves for Rotterdam mud (after Parker
and Kirby, 1982).

10.0 I I I I I

g 6.0- o0 -



Z- o0
L- o00
<' o o o -

U 0 0
S2.0- O

S .0 0-
8 00
0 I I
M 2TBl115 Pd
W 1.0
C. 0
0.8- 0

0.6 0

0.08 0.1 0.15 0.2 0.3 0.4
DENSITY, pd (g cm-3)

Fig. 4.4: Plot of upper Bingham yield strength versus
mud density for Avonmouth (UK) mud (after Owen,

corresponding bed density profiles from experiments such as those, e.g. as shown in Figs. C.2 and C.3, the
dependence of T. on bed density, even though rather obviously very approximate, becomes evident.
Fig. 4.5 shows the flume-determined relationship between Ts and the solids volume fraction, 4, for a mud
from Chikugo estuary, Japan (Kusuda et al., 1984). Also indicated is the corresponding water content, w. This
relationship is an early example of the recognition of f as a correlator of rs. As noted next, other investigators have
also obtained similar relationships, although with density rather than 0. Densities have been converted to 0 for inter-


)3 0.05 0.1 0.2

Fig. 4.5: Erosion shear strength versus solids fraction
(and water content) for Chikugo estuary (Japan) mud
(after Kusuda et al., 1984).

4.2.4 Some Experimental Relationships between Shear Strength and Density
A few illustrative relationships, including those mentioned above, of the general form


are noted chronologically in Table 4.1. In Eq. 4.5 rn can be Tr, or Ts, and f has been chosen as the appropriate
measure of density. The constants a and f are experimental. Note that of those expressions listed we recognize only
the ones obtained from erosion experiments in flumes as being genuine representatives of shear strength predictors
for Eq. 2.2. These include the expressions of Thorn and Parsons, Kusuda et al., Villaret and Paulic and Hwang
(second). The relationship attributed to Krone (1963) was actually obtained by Ross (1988) using experimental data
of Krone, whose purpose in obtaining yield strength values was for calculating the shear strength of flocs, rather
than the strength of the cohesive bed with respect to its erosion.
It is interesting to observe from Table 4.1 that, while the value of a varies widely, over three orders of
magnitude, f varies over a much narrower range, irrespective of the parameter used to measure shear strength. It
is possible that as far as the role of density in governing the shear strength is concerned, # has a more intrinsic
physico-chemical meaning than a, which seems to represent a scaling factor dependent upon the measure of shear
involved. In fact the high degree of variability of a is one indication that the different measures of shear strength
are not mutually compatible.

T, = avP

Table 4.1: Some expressions relating shear strength with solids volume fraction

Investigators) Expression a 0 0 Range

Krone (1963)a rB = a0a 466 2.55 0.008 to 0.57
Migniot (1968) 7B = aCtO variable 4.00 0.094 to 0.19
Owen (1970) r7 = a< 1,110 2.33 0.042 to 0.11
Thorn and Parsons (1980) Ts = a4t 37.5 2.28 0.014 to 0.12
Kusuda et al. (1984) r7 = a<4 6.5 1.60 0.032 to 0.11
Villaret and Paulic (1986) Ts = c4IP 1.65 1.00 0.10 to 0.38
Hwang (1989)b T, = a(<-4)0 22.6 1.00 0.06(=4t) to 0.26
Hwang (1989)b r.-Tt = a(0-0) 1.00 0.20 0.06 (=4,)C to 0.17

aSee Ross (1988), p. 25.
bps = 2.14 g cm-3 for calculating 4 from density. Where applicable, for all other studies cited above, ps = 2.65
g cm3 has been assumed.
C7sp = 0.05 Pa at 4 = Ot.

In connection with the relationship between shear strength and density, we must note a problematic issue
concerning the definition of the cohesive bed. In Fig. 2.1 we defined the cohesive bed as one having a measurable
effective normal stress, a'. Now let us consider the following version of the well-known Coulomb's equation for
shear strength, T:

S= C, + o'tanO, (4.6)

where Ce = cohesion, and Oe = angle of internal friction. Considering Eq. 4.6 in conjunction with the bed
definition in Fig. 2.1 we observe that cohesive shear strength, equal to Ce, can be measurable above the bed as well
(where a' = 0), particularly within the high concentration slurry that may occur over the bed. Thus the lowest value
of 4 (or p) up to which relationships of the form of Eq. 4.5 would be valid in neither known, nor understood in
physico-chemical terms. Studies on the elastic characteristics of muds indicate that, starting with a comparatively
dilute suspension, as the density is increased a space-filling solids volume fraction, 0, is reached, and that as 4
increases above 0., the shear modulus, G, increases rapidly with 4, and that for values of 4 < 4 G is very small
(James et al., 1988). See for example Fig. 4.6, in which G is observed to be a strong function of the excess volume
fraction, 4 ,c. Heuristically recognizing the similarity between the behaviors of G and rs, we postulate the
following functional expression for r,:

', = a(4-^" (4.7)


1000 -

O -
500 -


0 0.05 0.10 0.15

Fig. 4.6: Shear rigidity modulus as a function of solids volume fraction
for sediment S1 (after James et al., 1988).

where a and 3 have the same physical meaning as in Eq. 4.5. Experiments with selected clayey sediments to
determine the dependence of G on 4 have shown <0 to be on the order of 0.03 to 0.05 (James et al., 1988),
although the actual range of ,c for naturally occurring materials is undoubtedly wider. Note that the lower limit
values of 4 for the applicability of expressions of the form of Eq. 4.7 in Table 4.1 do not in general correspond
to 0,; those limits only indicate the lowest 4 values chosen in the experiments in developing the respective
expressions given. By not specifying the lower bound of 4 over which their derived relationships of the form of
Eq. 4.7 are valid, the investigators, with the exception of Hwang (1989), inadvertently ignored the existence of 0.
Without the benefit of their experimental data from which the lowest value of 4 used in the experiments can be
obtained, one may be led to set 40 equal to zero, which would be incorrect in the physical sense.
Hwang (1989) obtained a lower bound, 4t from the plot of Fig. 4.1 as that value of 4 (obtained from
p = 1.065 g cm-3), at and below which ,v = 0. It was considered that for all 4 < 4,t, the mud occurred as a fluid
slurry without a structure-supporting matrix. This selection procedure for 4,, very approximate at best, was an
attempt to evaluate fc, although the latter must be determined more rigorously (James et al. 1988). Note also that
to-date any relationship or a correspondence between oc and the density at which a measurable effective stress, a',
occurs has not been established.

4.2.5 Mass Erosion
Preliminary experiments by Hwang (1989) suggested that, assuming the applicability of Eq. 2.2 in
characterizing the rate of mass erosion, the parameters EM and -s possibly depend on density. These experiments,
one set of results from which were noted in Section 2.4, yielded values of r, for mud from Lake Okeechobee given
in Table 4.2. Note that for each of the three bed densities, mass erosion, marked by a total failure of the bed, was
initiated at higher shear stresses (equal to the corresponding shear strengths indicated) than those at which incipient
surface floc entrainment occurred. As Cervantes (1987) has noted however, it is not certain if additional governing
parameters are involved, e.g. the rate of application of the bed shear stress.

Table 4.2: Tr values for surface erosion and mass erosion at selected bed densities
for mud from Lake Okeechobee, Florida (after Hwang, 1989)

Density, p Shear Strength, T. (Pa)
(g cm3) Surface Erosion Mass Erosion

1.07 0.34 0.55
1.09 0.55 0.75
1.12 0.43 0.75

For reasons cited, Eq. 4.7 is inherently approximate; nevertheless its use in cohesive sediment transport
application is evident. It essentially enables the determination of bed shear strength profiles, vital in erosion
calculations, from relatively easily and routinely measured bed density profiles. Note however, that since the
coefficients a and (3 (ignoring c for the moment) are laboratory-determined, their applicability to field situations
can be questioned. Given that scaling is likely to be embodied in a while P has a more intrinsic physico-chemical
meaning, it is recommended that, if necessary, a be adjusted by calibration based on field transport conditions,
while retaining the value of 3 determined in the laboratory.
In those calculations in which the shear strengths of top, very thin layers of comparatively soft muds are
important, fc may play a recognizable role in determining the accuracy of computational results. Shearometric
measurements are required in determining its value (James et al., 1988). On the other hand, in many prototype
situations the magnitude of T; can be one or as much as two orders of magnitude smaller than the bed shear stress,
Tb. In this case the accuracy of ;r will not be an overly limiting factor in governing the accuracy of erosion
computations; hence c, can be assumed to be zero.


As a summary of the findings of Chapter IV, let us first restate Eq. 2.2 in a slightly more general form:

'r(Z) (5.1)
eM(z) T3(z)

where we recognize the depth-variability of the shear strength (and EM) in a cohesive bed. In the same vein, Eq.
4.7 can be stated as

',(Z) = aOL(Z)-J1P (5.2)

Since a, #f and oc are sediment/fluid-specific, and 0(z) depends on the stress history of the bed (and must therefore
be obtained from density measurement), the possibility of making Eq. 5.1 a practical predictive expression depends
on our ability to estimate EM(Z) from O(z), if such an estimation were feasible. Experimental evidence based on
comparative studies, e.g. Arulanandan et al. (1980) and Hunt (1981), and others, e.g. Villaret and Paulic (1986),
suggest that a relationship between cE and ;, and therefore between EM and 0 may exist. While an elucidation of
such a relationship is beyond the present scope, it is clearly the required next step for a comprehensive treatment
of the applicability of Eq. 5.1.
We have also seen in Chapters II and III the effect of temperature on eM, from previous studies. If eM and
r, are indeed related, then -r must also be temperature dependent, and in fact, given that Tr is the primary
representative of surface erosion resistance, the effect of temperature on EM must in reality reflect the effect of
temperature on the internal energy and the bond strength of the cohesive soil bed matrix, via the dependence of 7,
on temperature. In summary we therefore recognize the need to examine the relationship between em and 7,, and
the variation of 7, with (absolute) temperature as deserving future consideration.


Researchers have historically attempted to understand cohesive sediment erosion characteristics through
laboratory experiments using a variety of apparatuses, techniques and measurements. However, due to inadequate
knowledge on this subject during the early stages of the research efforts, some of the parameters found to be
important by one researcher were not measured by other researchers and vice versa. This matter posed the following
difficulties in comparing and evaluating the results of different researchers:
1) There was a lack of consistency in the selection of parameters or indices used to characterize the sediment,
the fluid, the bed structure, and the erosion process.
2) Contradicting conclusions were offered, e.g. on the correlation of bed shear strength with bed density.
3) Different notions prevailed in defining the "critical" shear stress for erosion.
4) Size of the experimental apparatus, duration of tests and the range of magnitudes of parameters showed
wide variations.
5) Different views existed on the interpretation of data, e.g. on the definition of a "steady state" concentration
and the degree of exchange of material between the bed and the water column.
The purpose of this appendix, adapted from Hayter and Mehta (1982), is to reveal the diversity of physico-
chemical parameters measured and experimental methods employed by researchers in investigating the erosion
behavior of cohesive sediments. This diversity greatly enhances the complexity of this subject matter and makes the
task of comparing the results of different studies a difficult one. Nevertheless, the following review also assists in
developing an analysis framework considered in Chapter III.

The following procedure is generally adopted in laboratory studies:
1) A sediment of interest is selected; it may be a pure clay mineral, a mixture of clay minerals, or a mixture
of clay and non-clay minerals. It may also contain organic matter. The sediment is described with the use
of certain characterizing indices.
2) Pore and eroding fluids of interest are selected and characterized.
3) A sediment bed is formed in the selected laboratory apparatus and is characterized by suitable parameters.
Several parameters/indices are used to determine the effect of the pore and eroding fluids on the structure
of the bed.
4) Erosion of bed is not measured directly, since bed scour is not easily visualized in the turbid water column.
Erosion is usually estimated from an analysis of relevant data, such as the change in suspension
concentration as a function of time during the course of the experiment. This approach is schematized in
Fig. A.1.


Fig. A.1: Diagramatic representation of the steps in the determination of the rate of erosion of fine

Since there are very few well-established parameters or indices to characterize cohesive sediments, the
fluid, bed structure or the rate of erosion, a high degree of diversity exists in laboratory studies with respect to each
of these factors. However, these studies can, in general, be classified into one of the following seven categories:
1) Bed shear stress application
2) Characterization of sediment
3) Characterization of (pore and eroding) fluid
4) Characterization of coagulation and settling

5) Characterization of bed structure
6) Characterization of erodibility index
7) Measure of erosion
A list of parameters identified in each of these seven areas is given under Tables A. 1 through A.7. Each
table is followed by references to typical studies related to each parameters given in the table. These references are
listed in the same order and denoted by the same serial number as the parameters, and are prefixed by the
alphabetical letter corresponding to the table. This tabulation has been carried out in order to organize the large
number of research topics on the erosive behavior of cohesive sediments into a few relatively well-defined
categories, and to provide a list of several early studies relevant to the subject matter.

Table A.1: Bed shear stress application

1. Method
a. Unidirectional flow in a laboratory flume or in a rotating cylinder apparatus
b. Jet impinging on cohesive sediment bed
c. Wave induced bed shear stress

2. Measure
a. Velocity of flow
b. Velocity of jet
c. Bed Shear Stress (Tb)
d. Series of Bed Shear Stresses (rb. b 'Tb
1 2 n

b T7b
n n-1
e. Shear Stress Ratio: 7r =

f. Excess Shear: Tb Ts
g. Normalized Excess Bed Shear Stress (Ar)x

h. Equilibrium Bed Shear Stress, T7q

Illustrative references for Table A. 1

Unidirectional flow in straight flume
Unidirectional flow in rotating annular channel
Unidirectional flow in rotating cylinder
Submerged vertical jet
Wave induced shear

Velocity of flow
Velocity of jet
Shear Stress Ratio
Excess Shear
Equilibrium Bed Shear
Series of Bed Shear Stresses

Normalized Excess Bed Shear Stress
Bed Shear Stress

Krone (1962)
Yeh (1979)
Espey (1963)
Moore and Masch (1962)
Tubman and Suhayda (1977)

Krone (1962)
Dunn (1959)
Parchure (1980)
Thorn and Parsons (1977)
Thor and Parsons (1977)
Parchure (1980)
Thorn and Parsons (1980)
Parchure (1980)
Krone (1962)
Partheniades (1962)
Yeh (1979)




Table A.2: Characterization of sediment

1. Type of Material

a. Minerals
1) Clay mineral alone
2) Mixture of clay minerals in varying proportions
3) Mixture of clay mineral and non-clay mineral, both in the fine sediment range
b. Soils, Muds and Clay
1) Mixture of cohesive and non-cohesive (such as sand) sediments
2) Mixture of clay material and organic matter or organic compounds
3) Sediments from natural environment (classified according to the Soil Classification
c. Non-soil Fine Materials

2. Clay Structure

a. Electrical forces acting between particles
1) Net Energy of Attraction
2) Double Layer Thickness
b. Particle arrangement or fabric consisting of texture and particle orientation

3. Particle Size Distribution

a. Median Diameter
b. Effective Size
c. Uniformity Coefficient
d. Curvature Coefficient

4. Cation Exchange Capacity

5. Exchangeable Sodium Percentage

6. Sodium Adsorption Ratio

7. Dielectric Constant

8. Silica-sesquioxide Ratio

9. Chemical Composition

10. Specific Gravity

11. Hydration or Adsorbed Water

12. Antecedent Water

13. Aging


Illustrative references for Table A.2

B.1. Type of Material
B. 1. Clay Minerals and Mixtures
1. Kaolinite

2. 40% Montmorillonite
+60% Silica flour
3. 40% Illite
+60% Silica flour
4. 40% Kaolinite
+60% Silica flour
5. Grundite: 50% llite + 50% Silt
6. English Kaolinite (finer than 1 im)
Georgia Kaolinite (between 21m and 84m)
7 Sand-clay lamination
B.1. Soils, Muds and Clay
1. Iredell Sandy Clay Loam
Davidson Clay
Putnam Soils
2. San Francisco Bay Mud
(Predominantly Montmorillonite and Illite)
3. Ferandina Beach Mud
4. Boston Blue Clay
5. Lake Francis Sediment
6. Lake Erie Sediment

7. Grangemouth Mud
8. Avonmouth Mud
9. Norwegian Marine Clays
10. Soils within the Australian Environment
11. Taylor Marl
12. Yolo Loam (Montmorillonite, Kaolinite, Mica and
13. Mare Island Strait Sediment
14. Belawan Mud
15. Taunton River Spoil
Thames River Spoil

Christensen and Das (1973)
Mehta (1973)
Yeh (1979)
Parchure (1980)
Alizadeh (1974)

Alizadeh (1974)

Alizadeh (1974)

Christensen and Das (1973)
Raudkivi and Hutchison (1974)

Terwindt et al. (1968)

Lutz (1934)

Partheniades (1962)
Krone (1962)
Yeh (1979)
Lambe (1958)
Parchure et al. (1981)
Fukuda (1978)
Lee (1979)
Thorn and Parsons (1977)
Owen (1975)
Bjerrum (1954)
Aitchison (1956)
Espey (1963)
Arulanandan (1975)

Krone (1962)
Thorn and Parsons (1980)
Gularte et al. (1977)


Illustrative references for Table A.2 (continued)

B.1. Non-Soil Fine Minerals
1. Polyvinyl chloride
2. Silver iodide

B.2. Nature of Clay Structure
B.2. Electrical Forces
1. Bed shear strength as a function of net energy of

B.2. Particle Arrangement
1. Fabric of consolidated kaolinite
2. Particle orientation in clays
3. Fabric changes in kaolin
4. Structure of compacted clay
5. Importance of structure to clay behavior
6. Structure of compacted soils
7. Structure of clay
B.3. Particle Size Distribution
B.4. Cation Exchange Capacity
B.5. Exchangeable Sodium Percentage

B.6. Sodium Adsorption Ratio
B.7. Dielectric Constant

B.8. Silica-sesquioxide Ratio



Mineral Composition
Specific Gravity
Absorbed Water

Antecedent Water

Bibeau and Matijevic (1973)
Vincent et al. (1971)

Kandiah (1974)

Martin (1965)
Morgenstem and Tchalenko (1967)
McConnachi (1974)
Lambe (1958)
Mitchell (1956)
Pacey (1956)
Casagrande (1932)
Kranck (1981)
Kandiah (1974)
Kandiah (1974)
Gardner et al. (1959)
Kandiah (1974)
Kandiah (1974)
Alizadeh (1974)
Middleton (1930)
Bennett (1926)
Gibbs (1977)
Kranck (1981)
Lambe (1958)
Martin (1962)
Grissinger (1966)
Grissinger (1966)

Table A.3: Characterization of fluid

1. Type of Fluid

a. Distilled Water
b. Double Distilled/Redistilled Water
c. Deionized Water
d. Distilled Deionized Water
e. Reconstituted Water
f. Fresh Water
g. Salt Water
h. Fluid other than Water

2. Cations and/or Anions Constituting Electrolyte, as Represented by:

a. Salinity of Fluid
b. Chlorinity of Fluid
c. Electrical Conductivity
d. Sodium Adsorption Ratio of the Fluid
e. Concentration of Electrolyte
f. Activity of Solute
g. Ion Valence
h. Anion Adsorption
i. Hydration Radius

3. pH

4. Temperature

5. Other Chemicals

Illustrative references for Table A.3

C.1. Type of Fluid
1. Salt Water
2. Distilled Water
3. Fresh Water

Partheniades (1962)
Mehta (1973)
Fukuda (1978)
Sheng and Lick (1979)
Parchure et al. (1981)
Raudkivi and Hutchison (1974)
Raudkivi and Hutchison (1974)
Liou (1970)

4. Reconstituted Water
5. Distilled Deionized Water
6. 0.1 M Solution of NaNO3
7. Carbon Tetrachloride

Illustrative references for Table A.3 (continued)

C.2. Electrolyte Ions
1. Electrolyte Concentration

Ion Valence
Dielectric Constant

Sodium Adsorption Ratio
Hydration Radius


Lambe (1958)
Gardner et al. (1959)
Lambe (1958)
Lambe (1958)
Alizadeh (1974)
Kandiah (1974)

Migniot (1968)
Kandiah (1974)
Lambe (1958)
Whitehouse et al. (1960)
Gularte (1978)
Kandiah (1974)
Lambe (1958)
Gularte (1978)
Christensen and Das (1973)

C.5. Other Chemicals
Sugar Solution

Gade (1958)

Table A.4: Characterization of coagulation and settling

Settling Rate of Sediment-water Interface
Settling Velocity
Microscopic Observation
Change in the order of Aggregation
Change in Permeability of Suspension
Degree of Coagulation



Illustrative reference for Table A.4

D. 1. Settling Rate of Interface Thorn and Parsons (1977)
D.2. Settling Velocity Whitehouse et al. (1960)
D.3. Microscopic Observations Bowles (1969)
D.4. Order of Aggregation Krone (1978)
D.5. Permeability of Suspension Lutz (1934)
D.6. Degree of Coagulation Harris et al. (1966)

Table A.5: Characterization of bed structure

Type of Bed: a) Placed (Remolded) Bed
b) Deposited Bed
c) Compacted Bed
Physical Properties Soil Indices
1. Water Content, or 1. Liquid Limit
Moisture Content 2. Plastic Limit
2. Degree of Saturation 3. Shrinkage Limit
3. Swelling 4. Plasticity Index
4. Permeability, or 5. Liquidity Index
Hydraulic Conductivity 6. Unconfmed Compression Strength
5. Porosity 7. Consistency
6. Void Ratio 8. Relative Consistency
7. Dry Density 9. Sensitivity
8. Relative Density 10. Thixotropy
9. Unit Weight, or 11. Activity of Clay
Bulk Unit Weight 12. Compressibility Coefficient
10. Dry Unit Weight or 13. Compression Index
Dry Density 14. Group Index
11. Saturated Unit Weight 15. Diffusivity
12. Submerged Unit Weight 16. Rate of Wetting Front Advance
13. Volumetric Soil Solution Content 17. Dilatancy
14. Solids Volume Fraction 18. Dry Strength
15. Water Volume Fraction 19. Toughness
16. Equilibration Time/Aging

Illustrative references for Table A.5

Physical Properties
1. Water Content
2. Solids Volume Fraction
3. Water Volume Fraction
4. Hydraulic Conductivity
5. Volumetric Soil Solution Ratio
6. Bed Density
7. Swelling
8. Aging
Soil Indices
1. Density, Liquid Limit
2. Vane Shear Strength, Plasticity Index
3. Plasticity Index
4. Shear Strength, Angle of Repose, Specific Weights of
Fluid and Sediment, Particle Size
5. Unconfined Compression Strength
6. Diffusivity of Water in Soil
7. Rate of Wetting Front Advance

Lee (1979)
Kandiah (1974)
Kandiah (1974)
Dane and Klute (1977)
Dane and Klute (1977)
Thorn and Parsons (1980)
Kandiah (1974)
Grissinger (1966)

Carlson and Enger (1962)
Dunn (1959)
Smerdon and Beasley (1959)
Sundborg (1956)

Flaxman (1963)
Gardner et al. (1959)
Christenson and Ferguson (1966)

Table A.6: Erodibility index

1. For Sediment Bed
a. Critical Shear Stress for surface erosion
b. Bulk Shear Strength/Vane Shear Strength
c. Floc Shear Strength at bed surface
d. Critical Shear Stress at which the rate of erosion changes from "low" to "high"
e. Characteristic Shear Stress
f. Change in Concentration of Suspension as a Function of Time
g. Dispersion Ratio
h. Erosion Ratio
i. Steady State Concentration
j. Limiting Flow Velocity
k. Erosion Factor
1. Erosion Index
2. For Sediment Suspension: Rheologic Properties
a. Bingham Shear Stress
b. Dynamic Viscosity of Fluid
c. Kinematic Viscosity of Fluid
d. Viscosity of Sediment Suspension
e. Zeta Potential

Illustrative references for Table A.6

Erodibility Index for Sediment Beds
Critical Shear Stress
Bulk Shear Strength

Floc Shear Strength
Critical Shear Stress for Erosion Rate
Characteristic Shear Strength
Dispersion Ratio
Erosion Ratio
Limiting Flow Velocity
Erosion Index/Erosion Factor

Rheological Properties
Rheological Properties of Estuarial Muds
Suspensions of Rigid Particles
Bingham Shear Strength of a Deep Marine Sediment
Zeta Potential
Particle Growth Rate
Colloidal Dispersion

Kandiah (1974)
Krone (1962)
Partheniades (1962)
Krone (1963)
Espey (1963)
Parchure (1980)
Middleton (1930)
Middleton (1930)
Miller (1960)
Dash (1968)

Krone (1963)
Jeffrey and Acrivos (1976)
Das (1970)
Krone (1962)
Kandiah (1974)
Sugimoto (1978)
Zeichner and Schowalter (1977)

Table A.7: Measure of erosion

1. Type of Erosion
a. Surface Erosion
1) Flocculated Particles
2) Deflocculated Particles
b. Mass Erosion
1) Flocculated Particles
2) Deflocculated Particles

2. Method used to Determine Erosion Rate
a. The rate of change of:
1) Suspension concentration (dC/dt)
2) Bed elevation (dz/dt)
3) weight of sediment in bed (dW/dt)
where, C = concentration of sediment in suspension
z = elevation of sediment bed
W = weight of sediment in the bed
t = time
b. Time required to reach Steady State Concentration (Ceq)
c. Equilibrium depth of scour

Illustrative references for Table A.7

G.1. Type of Erosion
Surface Erosion Partheniades (1962)
Mass Erosion Yeh (1979)
G.2. Method used to Determine Erosion Rate
dC/dt Partheniades (1962)
dz/dt Thorn and Parsons (1977)
dW/dt Espey (1963)
Ceq Partheniades (1962)
Equilibrium depth of scour Parchure (1980)



This appendix, adapted from Mehta (1981), is a comparative characterization of three early erosion studies:

Partheniades (1965), Christensen and Das (1973) and Ariathurai and Arulanandan (1978). The basis for selecting

the characterization categories in Tables B.1 through B.4 is mentioned in Chapter III. For further details, Mehta

(1981) must be consulted. This comparison highlights the wide variability in the apparatus used, procedure for

estimating erosion, range of bed shear stresses covered, sediment and fluid properties and the method of bed

preparation. The use of different apparatuses is particularly significant, since it introduces essentially unquantifiable

effects in the results, thus making a genuine examination of the effects of sediment and fluid compositions and bed

structure on the rate of erosion difficult.

Table B.1: Apparatus, sampling method, bed size and stress

Investigators) Apparatus Sampling Method Bed Size Shear Stress
Range (Pa)

1. Partheniades Recirculating steel flume Samples of eroding fluid 55,742 cm2 surface area 0.12 2.87
of rectangular cross- withdrawn at discrete
section, 18.3 m long, time intervals and
0.3 m wide, 0.46 m analyzed gravimetrically

2. Christensen and Circular brass tube 2.54 Weight of tube taken 61 cm2 surface area, 0.29 1.05
Das cm diameter, 10.2 cm before and after the test 0.32 cm initial thickness
long, inner side lined to determine loss of bed
with a layer of material
compacted sediment,
eroding fluid passed
through tube

3. Ariathurai and Rotating annular Weight of eroding fluid 215 cm2 surface area0.3
Arulanandan cylinder 10.2 cm in obtained before and after 9.0
diameter, 1.3 cm wide the test to determine loss
annular space filled with of bed material
eroding fluid, cylindrical
bed specimen prepared
by consolidation
supported by a mandrel
and placed concentrically
in the plastic outer
cylinder, which was

Table B.2: Sediment properties

Clay Type Grain Size Other Properties

1. San Francisco Bay mud principal 60% finer than 2 pm, 40% between 2 pm Iron content: 33 mg g-1
mineral: Montmorillonite and some and 50 pm

2. Kaolinite 53 % finer than 2 pm
Grundite (50% llite + 50% silt) 62% finer than 2 pm

3. Illite 30% + Silica Flour 70% Median diameter 0.5 pm CECa varied from 3 to 28
meq 100 g-1

aCation exchange capacity.

Table B.3: Pore and eroding fluid properties

Comment Salinity Temperature pH Other Ionic

1. Both fluids same 33 gl-1 NRa NR Some iron oxide
introduced due to
corrosion in test
Concentration not

2. Fluid used in soil preparation 0 Tests conducted at NR
same as eroding fluid constant
varying from 130
C to 350 C

3. Eroding fluid: distilled water Concentration of Tests conducted at Eroding fluid pH Sodium
Pore fluid: variable composition Na+, Ca"+ and constant 7.0, initial clay Adsorption Ratio
Mg++ ions in pore temperature, pH varied from varied from 2 to
fluid varied from varying from 9.50 4.2 to 10.2 50
10 to 80 meq 11 C to 420 C

aNot reported.

Table B.4: Bed properties

Bed Type

1. Remolded for series I and II, flow
deposited for series mI

Water Content

Series I: 110
Series II: 120
Series II: NR

Shear Strength

Yield: 525
Failure: 1245
Floc shear strength:

Consolidation and/or
Pre-Erosion Contact

Contact time:
Series I: 40 days
Series II: 15 days
Series HI: NR

2. Compacted under a static device remoldedd) Varied from 25 to 47

3. Consolidated for two weeks with increasing NR
load up to 1 kg cm-2

Mixing: 24 hr.
consolidation: 2 weeks,
contact with eroding
fluid: few hours



The following procedure for determining vertical profiles of the erosion shear strength, r,, is adapted from
Parchure and Mehta (1985). An example of the variation of depth-mean concentration, C, with time, t, during
erosion in a flume test under series KS kaolinitee in salt water) is shown in Fig. C.1. The bed was consolidated for
a period of 1.7 (= Tdc) days prior to its resuspension. The depth of flow, h, was 26 cm. Beginning with 0.10 Pa,
,b was increased in time-steps in a manner such that the ratio (T'bi+l 7bi)/rbi, where rbi is the value of Tb
corresponding to the ith time-step and i = 1, 2, ..., was maintained constant at 0.2. The step duration, T, for each
Tbi was selected, after some trials, to be 1 hr. During the first seven steps, C is observed to have approached a
constant value at the end of each step, while in the last step, C continued to increase at the end. This information,
together with the bed density profile, was used to estimate the shear strength profile as well as determine an erosion
rate expression as noted next.
With reference to Fig. C. 1, at the end of each of the first seven steps, bed erosion was practically arrested,
the rate, dC/dt, at the end of a step being less than 5% of the corresponding value at the beginning (Parchure,
1984). Knowing the depth-varying density p(z) and the increment AC over duration T, the corresponding scour
depth, Az, was computed through the expression

TIME, t (hrs)
5 6 7 8 9 10

1 -

S1= 8
Z 4
0 1=7
Fn 5 1 6
S1 =5
Ct 6 b=-0l Pa I=2 1=3 '="
n 73 4 5III
0 1 2 34
TIME, t (hrs)

Fig. C. 1: Concentration-time profile in erosion test, series KS, Tdc =
1.7 days (after Parchure and Mehta, 1985).

Az = hAC (C.1)

beginning with the initial bed-water interface at z = 0. The measured p(z) profile corresponding to the test of
Fig. C. 1 is shown in Fig. C.2. Thus, for example, considering the first step, AC = 0.4 gl-1. Given p = 173 gl1,
Eq. C. 1 yields Az = 0.06 cm (this value of p is the mean over Az which implies that, since in general p varies with
z, Eq. C.1 must be solved for Az iteratively). At the depth of 0.06 cm, therefore, it can be inferred that Ts = rb
= 0.1 Pa, since erosion was arrested when the applied stress equalled the shear strength at a certain depth of scour.
The computation was repeated for the next step and so on. The resulting rs(z) profile is shown in Fig. C.3, In which
points 2-8 correspond to the first seven steps. Points 1 (corresponding to z = 0) and 9 were obtained using different
procedures as follows.

0 0.2 0.4
DENSITY, p (gl-1) 4

5 7
00 100 200 300 400 6

N 2 0.5 8

Wj4 0-
5 I I I

1.0 I

Fig. C.2: Bed density profile, series KS, Tde = 1.7 Fig. C.3: Bed shear strength profile, series KS,
days (after Parchure and Mehta, 1985). Tdc = 1.7 days (after Parchure and Mehta, 1985).

The time-concentration profile in Fig. C. 1 corresponding to the last step indicates that either the duration
T was insufficient for the condition Tb = 7T to be attained at some depth, or that Tb exceeded the maximum shear
strength, Tsm, in which case erosion would not be arrested even after several days (Krone, 1962). Given that the
latter condition did not occur in a particular step, the following best-fit rate of erosion expression relating the erosion
rate, e(= hdC/dt) to Tb rs (Parchure and Mehta, 1985):

In e = a(rb-T)12 (C.2)

was used to estimate T,, by assuming that the applicability of the rate expression was valid over the entire bed depth,
since Ts was the only unknown. Point 9 in Fig. C.3 was obtained in this manner. In Eq. C.2, ef is defined as the

floc erosion rate, and a is a factor which can be shown to be inversely proportional to the absolute temperature
following the rate process theory (Parchure, 1984). This equation differs from the expression based on the rate
process theory (see Section 2.3.2) in that 7-b Tg is raised to the 1/2 power in Eq. C.2. In analogy with the rate
process expression, however, it may be permissible to regard a to be proportional to (rb 7s)'1/2, as considered in
greater detail elsewhere (Dixit, 1982; Parchure, 1984). The floc erosion rate, ef, is the value of e when Tb Ts =
0, when no mean flow velocity dependent surface erosion occurs, by definition. As a consequence of the stochastic
nature of Tb and 7,, however, some entrainment of flocs will occur even when the condition Tb = 7, is first attained.
Inasmuch as direct measurement of ef would require tests of unreasonably long durations, ef was evaluated by
plotting In e against (Tb Ts)"1/2 = 0 axis (Parchure, 1984).
Point 1 corresponds to go, the value of 7, at z = 0. Procedures for estimating T,, as well as ,sm are noted
later. It is noteworthy that an analysis of the results of all the tests carried out by Parchure (1984) suggested a three-
zoned description of the r,(z) profile as depicted in Fig. C.4 (Parchure and Mehta, 1985). Zone 1 of thickness ze
can be considered to be bounded by shear strength Tso at z = 0 and Ts at z = ze. Zone 2 of thickness zd terminates
at a depth where Ts = Tsm, below which zone 3 of constant or nearly constant shear strength Tsm occurs. An
important difference between zones 1 and 2 is that the gradient dr,/dz is relatively much larger in zone 1 compared
with that in zone 2.

--> Tso <-STRENGTH, Ts



S <-Tsm -

Fig. C.4: Schematic representation of three-zoned
description of bed shear strength profile (after Parchure
and Mehta, 1985).

Both 7ro and Tg as well as z, can be estimated from a plot of C(T), the concentration at the end of a step,
against the corresponding Tb. Such a plot based on the test of Fig. C. 1 (Td = 1.7 days), as well as for two other
tests corresponding to Tde of 1 and 5.6 days is shown in Fig. C.5. It is possible to approximate the curve for each

Tdc ZIsc
S8- Symbol (days) (Pa)
0 1.0 0.21
0 7 n 1.7 0.29
:I* 5.6 0.34

O 6

cc 5
W 4
0 3
z 2
z 1
C 00 0.1 0.2 0.3 0.4 0.5

Fig. C.5: Concentration C(T) at the end of time-step
against corresponding bed shear stress, Tb, series KS,
Tde = 1, 1.7 and 5.6 days (after Parchure and Mehta

test by two linear segments which meet at a point corresponding to Tb = rsc (= 0.29 Pa for Tde = 1.7 days). The
corresponding depth, ze, can be obtained, in general, from Eq. C.1. For all Tb < s,,, the rate of erosion was
relatively low compared to that corresponding to Tb > Trc, by virtue of the nature of the T7(z) profile shown in Fig.
C.4. Based on the adopted procedure for data analysis, it can be readily shown that

dC p(z)
drb h dr, (C.3)

Ignoring, for the sake of illustration, the usually observed increase in p with z as in Fig. C.2, it is noted that in zone
1, a relatively high drs/dz corresponds to a low dC/dTb and vice versa in zone 2. Indeed, the p(z) variation enhances
these trends. Finally, the shear stress, r, at which incipient erosion of the initial bed surface (z = 0) occurs, is
obtained by extrapolating the lower line in Fig. C.5 for each test to intersect the C(T) = 0 axis. This procedure,
which is an indirect way of determining the incipient erosion, yields rso = 0.04 Pa from Fig. C.5 (Parchure, 1980,
1984). Note that unlike incipient motion of sand grain at the bed under clear water, incipient floc entrainment can
not be visually detected easily.

With reference to the maximum shear strength Tsm (Fig. C.4), the following empirical relationship was
found to be applicable in an approximate way:

V= o (C.4)

where p has a unique value for each time-step equal to the slope of a line obtained by plotting In E on the ordinate
against (rb Ts)/7s on the abscissa for a given time-step. When T- = r,, 3 = 3o. Details of the manner in which
Eq. C.4 was selected have been given elsewhere (Parchure, 1984). It suffices to note that, whereas the dimensions
of fl depend on those of E, the ratio P/Po in Eq. C.4 is dimensionless. Tsm occurs at a depth z, + zd which could
be larger than the total bed depth in the flume. In this case, rsm can be estimated from a plot of In rs against P by
extrapolating the line to intersect the P = 0 axis according to Eq. C.4 (Parchure and Mehta, 1985).
In Fig. C.6, 7,(z) profiles obtained under series KS are shown. For each consolidation period, Tde (ranging
from 1 to 10 days), rs is observed to increase with depth. Two factors causing such an increase can be: (1) gelling
and consolidation and associated physico-chemical changes and overburden; and (2) variation of primary particle
size with depth. The network-like flocculated structures formed while the sediment is in suspension are crushed due
to overburden after they deposit. Crushing increases the bed shear strength because flocs of a given density and
shear strength break up into constituent units which are more dense and possess a higher shear strength (Krone,
1963). Successive breakdowns of flocs with time results in increasing 7, with depth. Beyond a certain overburden,
however, the flocs are difficult to crush further without applying external compressive force (Ariathurai and
Arulanandan, 1978). T, therefore approaches a maximum, Tsm (Fig. C.4).

0 0.2 0.4 0.6 0.8

SE Tsm = 0.57 Pa

N Tdc
0.5- Symbol (d
0 ,' 1.0
0 1.7
LU A 3.0
Q 0 5.6
A 10.0
1.0 III

Fig. C.6: Bed shear strength profiles, series KS, Tde = 1, 1.7, 3, 5.6 and
10 days (after Parchure and Mehta, 1985).


Kandiah, A., 1974. Fundamental aspects of surface erosion of cohesive soils. Ph.D. Dissertation, Univ. Of Calif.,
Mehta, A.J., 1989. On estuarine cohesive sediment suspension behavior. J. Geophys. Res., 94(C10): 14303-14314.
Mehta, A.J., Parchure, T.M., Dixit, J.G. and Ariathurai, R., 1982. Resuspension potential of deposited cohesive
sediment beds. In: Estuarine Comparisons, V.S. Kennedy ed., Academic Press, New York: 591-609.
Partheniades E., 1962. A study of erosion and deposition of cohesive soils in salt water. Ph.D. Dissertation, Univ.
of Calif., Berkeley.

Ariathurai, R., MacArthur, R.C. and Krone, R.B., 1977. Mathematical model of estuarial sediment transport.
Tech. Rept. D-77-12, U.S. Army Eng. Waterways Expt. Sta., Vicksburg, MS.
Arulanandan, K., 1975. Fundamental aspects of erosion of cohesive soils. J. Hydr. Div., ASCE, 101(HY5): 635-
Christensen, B.A., 1965. Discussion of erosion and deposition of cohesive soils (by E. Parthenaides). J. Hydr.
Div., ASCE, 91(HY5): 301-308.
Christensen, R.W., and Das, B.M., 1973. Hydraulic erosion of remolded cohesive soils. In: soil erosion: causes
and mechanisms, prevention and control, Special Rept. 135, Highway Res. Board, Washington, DC: 52-74.
Day, P.R. and Ripple, C.D., 1966. Effect of shear on suction in saturated clays. Soil Sci. Soc. Amer. Proc., 30:
Eyring, H., 1936. Viscosity, plasticity and diffusion as examples of absolute reaction rates. J. Chem. Phys., 4: 283-
Grim, R.E., 1968. Clay Mineralogy. 2nd ed., McGraw-Hill, New York.
Gularte, R.C., 1978. Erosion of cohesive sediment as a rate process. Ph.D. Dissertation, Univ. of Rhode Island,
Kingston, RI.
Hinze, J.O., 1959. Turbulence, McGraw-Hill, New York.
Hwang, K.-N., 1989. Erodibility of fine sediment in wave-dominated environments. M.S. Thesis, Univ. of Fla.,
Gainesville, FL.
Jiang, F. and Mehta, A.J., 1991. Some observations on fluid mud response to water waves. In: Dynamics and
Exchanges in Estuaries and the Coastal Zone, D. Prandle ed., Springer-Verlag, New York (in press).
Kandiah, A., 1974. Fundamental aspects of surface erosion of cohesive soils. Ph.D. Dissertation, Univ. Of Calif.,
Kelly, W.E. and Gularte, R.C., 1981. Erosion resistance of cohesive soils. J. Hydr. Div., ASCE, 107(HY10):

Kendrick, M.P. and Derbyshire, B.V., 1985. Monitoring of a near-bed turbid layer. Rept. SR44, Hydraulics
Research, Wallingford, UK.
Krone, R.B., 1962. Flume studies of the transport of sediment in estuarial shoaling processes. Final Rept., Hydr.
Engrg. Lab. and San. Engrg. Res. Lab., Univ. of Calif., Berkeley, CA.
Krone, R.B., 1963. A study of theological properties of estuarial sediments. Tech. Bull. No. 7, Committee on Tidal
Hydraulics, U.S. Army Eng. Waterways Expt. Sta., Vicksburg, MS.
Lambermont, J. and Lebon, G., 1978. Erosion of cohesive soils. J. Hydr. Res., 16(1): 27-44.
Lavelle, W.J. and Mofjeld, H.O., 1985. Do critical stresses for incipient motion and erosion really exist?. J. Hydr.
Engrg., 113(3): 370-385.
Lick, W., 1982. Entrainment, deposition and transport of fine-grained sediment in lakes. Hydrobiologia, 91: 31-40.
Maa, P.-Y. and Mehta, A.J., 1987. Mud erosion by waves: A laboratory study. Cont. Shelf Res., 7(11/12): 1269-
Martin, R.T., 1962. Adsorbed water on clay: a review. Proc. Ninth National Conference on Clays and Clay
Minerals, Pergamon Press, New York: 28-70.
Mehta, A.J., 1973. Depositional behavior of cohesive sediments. Ph.D. Dissertation, Univ. of Fla., Gainesville,
Mehta, A.J. and Partheniades, E., 1979. Kaolinite resuspension properties. J. Hydr. Div., ASCE, 105(HY4): 409-
Mehta, A.J., 1989. Fine sediment stratification in coastal waters. Proc. Third National Conference on Dock &
Harbour Engrg. K.R.E.C., Surathkal, India: 487-492.
Mehta, A.J., 1991. Review notes on cohesive sediment erosion. Proc. Coastal Sediments '91, ASCE, New York:
Mehta, A.J. and Srinivas, R., 1992. Observations on the entrainment of fluid mud by shear flow. In: Nearshore
and Estuarine Cohesive Sediment Transport, A.J. Mehta ed., Springer-Verlag, New York (in press).
Mitchell, J., Campanella R.G. and Singh, A., 1968. Soil creep as a rate process. J. Soil Mech. and Found. Div.,
ASCE, 94(SM1): 231-253.
Narimousa, S. and Fernando, H.J.S., 1987. On the sheared interface of an entraining stratified fluid. J. Fluid
Mech., 174: 1-22.
Newman, K.A., 1990. Cycling of fine particles between water and sediments. Ph.D. Dissertation, Mass. Inst.
Technol., Cambridge, MA.
Parchure, T.M. and Mehta, A.J., 1985. Erosion of soft cohesive sediment deposits. J. Hydr. Engrg., 111(10):
Partheniades E., 1962. A study of erosion and deposition of cohesive soils in salt water. Ph.D. Dissertation, Univ.
of Calif., Berkeley.
Partheniades, E., 1965. Erosion and deposition of cohesive soils. J. Hydr. Div., ASCE, 91(1): 105-139.

Raudkivi, A.J. and Hutchison, D.L., 1974. Erosion of kaolinite clay by flowing water. Proc. Royal Soc., London:
Ross, M.A. and Mehta, A.J., 1989. On the mechanics oflutoclines and fluid mud. J. Coast. Res., SI5: 51-61.
Ross, M.A. and Mehta, A.J., 1990. Fluidization of soft estuarine mud by waves. In: The Microstructure of Fine-
grained Sediments: From Mud to Shale, R.H. Bennett ed., Springer-Verlag, New York: 185-191.
Sargunam, A., Riley, P., Arulanandan, K. and Krone, R.B., 1973. Physico-chemical factors in erosion of cohesive
soils. J. Hydr. Div., ASCE, 99(HY3): 555-558.
Scarlatos, P.D. and Mehta, A.J., 1990. Some observations on erosion and entrainment of estuarine fluid muds. In:
Residual Currents and Long-term Transport, R.T. Cheng ed., Springer-Verlag, New York: 321-332.
Scarlatos, P.D. and Mehta, A.J., 1992. Instability and entrainment mechanisms at the fluid mud-water interface.
In: Nearshore and Estuarine Cohesive Sediment Transport, A.J. Mehta ed., Springer-Verlag, New York
(in press).
Smith, T.J. and Kirby, R., 1988. Generation, stabilization and dissipation of layered fine sediment suspensions. J.
Coast. Res., SI5: 63-73.
Wolanski, E., Asaeda, T. and Imberger, J., 1989. Mixing across a lutocline. Limnol. Oceanogr., 34(5): 931-938.

Ariathurai, R., 1974. A finite element model for sediment transport in estuaries. Ph.D. Dissertation, Univ. of
Calif., Davis, CA.
Ariathurai, R. and Arulanandan, K., 1978. Erosion of cohesive soils. J. Hydr. Div., ASCE, 104(HY2): 279-283.
Arulanandan, K., Loganathan, P. and Krone, R.B., 1975. Pore and eroding fluid influences on surface erosion of
soil. J. Geotech. Div., ASCE, 101(1): 51-66.
Bolz, R.E. and Tuve, G.L., 1979. Handbook of tables for applied engineering science. Chemical rubber Co.,
Cleveland, OH.
Chase, R.R.P., 1979. Settling behavior of settling aquatic particles. Limnol. and Oceano., 24(3): 417-426.
Christensen, R.W., and Das, B.M., 1973. Hydraulic erosion of remolded cohesive soils. In: soil erosion: causes
and mechanisms, prevention and control, Special Rept. 135, Highway Res. Board, Washington, DC: 52-74.
Davis, W., 1991. Evaluating sediment variables that may predict seabed response to resuspension energy. In:
Equipment and facilities needs for hydraulic research, a workshop, R.B. Krone and W.H. McAnally eds.,
Hydraulics Lab., U.S. Army Engineer Waterways Expt. Sta., Vicksburg, MS: Ch. 3.
Hayter, E.J. and Mehta, A.J., 1982. Modeling of estuarine fine sediment transport for tracking pollutant movement.
Rept. UFL/COEL-82/009, Coastal and Oceanographic Engineering Dept., Univ. of Fla., Gainesville, FL.
Hwang, K.-N., 1989. Erodibility of fine sediment in wave-dominated environments. M.S. Thesis, Univ. of Fla.,
Gainesville, FL.
Kandiah, A., 1974. Fundamental aspects of surface erosion of cohesive soils. Ph.D. Dissertation, Univ. Of Calif.,

Krone, R.B., 1962. Flume studies of the transport of sediment in estuarial shoaling processes. Final Rept., Hydr.
Engrg. Lab. and San. Engrg. Res. Lab., Univ. of Calif., Berkeley, CA.
Mehta, A.J., 1981. A review of erosion functions for cohesive sediment beds. Proc. First Indian Conf. Ocean
Engrg., Indian Inst. Technol., Madras, India, I: 83-90.
Mehta, A.J., 1988. Laboratory studies on cohesive sediment erosion and deposition. In: Physical Processes in
Estuaries, J. Dronkers and W. van Leussen eds., Springer-Verlag, Berlin: 427-445.
Mehta, A.J. and Partheniades, E., 1979. Kaolinite resuspension properties. J. Hydr. Div., ASCE, 105(HY4), 409-
Mehta, A.J. and Lott, J.W., 1987. Sorting of fine sediment during deposition. Proc. Coastal Sediments'87, ASCE,
New York: 348-362.
Mehta, A.J., Hayter, E.J., Parker, W.R., Krone, R.B. and Teeter, A.M., 1989. Cohesive sediment transport. I:
process description. J. Hydr. Engrg., 115(8): 1076-1093.
Migniot, C., 1968. A study of the physical properties of different very fine sediments and their behavior under
hydrodynamic action. La Houille Blanche, 7, 591-620 (in French with English abstract).
Montague, C.L., Parchure, T.M. and Paulic, M., 1992. The stability of sediments containing microbial
communities: initial experiments with varying light intensity. In: nearshore and estuarine cohesive sediment
transport, A.J. Mehta ed., Springer-Verlag, New York (in press).
Parchure, T.M., 1984. Erosional behavior of deposited cohesive sediments. Ph.D. Dissertation, Univ. of Fla.,
Gainesville, FL.
Parchure, T.M. and Mehta, A.J., 1985. Erosion of soft cohesive sediment deposits. J. Hydr. Engrg., 111(10):
Partheniades E., 1962. A study of erosion and deposition of cohesive soils in salt water. Ph.D. Dissertation, Univ.
of Calif., Berkeley.
Partheniades, E., 1971. Erosion and deposition of cohesive materials. In: River mechanics, H.W. Shen ed., H.W.
Shen Publisher, Fort Collins, CO, Ch. 25.
van Olphen, H., 1963. Clay colloid chemistry, Wiley, New York.
Villaret, C. and Paulic, M., 1986. Experiments on the erosion of deposited and placed cohesive sediments in an
annular flume and a rocking flume. Rept. UFL/COEL-86/007, Coastal and Oceanographic Engrg. Dept.,
Univ. of Florida, Gainesville.

Cervantes, E.E., 1987. A laboratory study of fine sediment resuspension by waves. M.S. thesis, Univ. of Florida,
Gainesville, FL.
Hinze, J.O., 1959. Turbulence, an introduction to its mechanism and theory. McGraw-Hill, New York.
Hwang, K.-N., 1989. Erodibility of fine sediment in wave-dominated environments. M.S. Thesis, Univ. of Fla.,
Gainesville, FL.

James A.E., Williams, D.J.A. and Williams, P.R., 1988. Small strain, low shear rheometry of cohesive sediments.
In: Physical processes in estuaries, J. Dronkers and W. van Leussen eds., Springer-Verlag, Berlin: 488-
Krone, R.B., 1962. Flume studies of the transport of sediment in estuarial shoaling processes. Final Rept., Hydr.
Engrg. Lab. and San. Engrg. Res. Lab., Univ. of Calif., Berkeley, CA.
Krone, R.B., 1963. A study of theological properties of estuarial sediments. Tech. Bull. No. 7, Committee on Tidal
Hydraulics, U.S. Army Eng. Waterways Expt. Sta., Vicksburg, MS.
Kusuda, T., Umita, T., Koga, K., Futawatari, T., and Awaya, Y., 1984. Erosional process of cohesive sediments.
Wat. Sci. Tech., 17: 891-901.
Mehta, A.J., 1991. Review notes on cohesive sediment erosion. Proc. Coastal Sediments '91, ASCE, New York:
Migniot, C., 1968. A study of the physical properties of different very fine sediments and their behavior under
hydrodynamic action. La Houille Blanche, 7, 591-620 (in French with English abstract).
Owen, M.A., 1970. Properties of a consolidating mud. Rept. INT 83, Hydr. Res. Sta., Wallingford, UK.
Parker, W.R. and Kirby, R., 1982. Time dependent properties of cohesive sediment relevant to sedimentation
management European experience. In: Estuarine Comparisons, V.S. Kennedy ed., Academic Press, New
York: 573-589.
Seed, H.B. and Chan, C.K., 1959. Structure and strength characteristics of compacted clays. J. Soil Mech. and
Found. Div., ASCE, 85(SM5): 87-128.
Task Committee of ASCE, 1968. Erosion of cohesive sediments. J. Hydr. Div., ASCE, 94(HY4): 1017-1049.
Thorn, M.F.C. and Parsons, J.G., 1980. Erosion of cohesive sediments in estuaries: an engineering guide. Proc.
Third Intl. Symp. on Dredging Technol., Paper Fl, BHRA, Bordeaux, France.
Villaret, C. and Paulic, M., 1986. Experiments on the erosion of deposited and placed cohesive sediments in an
annular flume and a rocking flume. Rept. UFL/COEL-86/007, Coastal and Oceanographic Engrg. Dept.,
Univ. of Florida, Gainesville.

Arulanandan, K., Gillogley, E. and Tully, R., 1980. Development of a quantitative method to predict critical shear
stress and rate of erosion of natural undisturbed cohesive soils. Tech. Rept. GL-80-5, U.S.Army Engrg.
Waterways Expt. Sta., Vicksburg, MS.
Hunt, S.R., 1981. A comparative review of laboratory data on erosion of cohesive sediment beds. UFL/COEL/MP-
81/007, Coastal and Oceanographic Engrg. Dept., Univ. of Fla., Gainesville, FL.
Villaret, C. and Paulic, M., 1986. Experiments on the erosion of deposited and placed cohesive sediments in an
annular flume and a rocking flume. Rept. UFL/COEL-86/007, Coastal and Oceanographic Engrg. Dept.,
Univ. of Florida, Gainesville.

Aitchison, M.E., 1956. The nature, extent and engineering significance of the conditions of unsaturation in soils
within the Australian environment. Ph.D. Dissertation, Univ. of Melbourne, Melbourne, Australia.
Alizadeh, A., 1974. Amount and type of clay and pore fluid influences on the critical shear stress and swelling of
cohesive soils. Ph.D. Dissertation, Univ. of Calif., Davis, CA.
Arulanandan, K., 1975. Fundamental aspects of erosion of cohesive soils. J. Hydr. Div., ASCE, 101(HY5): 635-
Bennett, H.H., 1926. Some comparisons of the properties of humid-tropical and humid-temperate American soils:
with special reference to the indicated relations between chemical composition and physical properties. Soil
Sci., 21: 349-375.
Bibeau, A.A. and Matijevic, E., 1973. Stability of polyvinyl chloride latex III-effects of simple electrolytes. J.
Colloid and Interface Sci., 43(2): 330-338.
Bowles, F.A., 1969. Microstructure of unconsolidated and consolidated marine sediments. J. Sedi. Petrol., 39(4):
Bjerrum, L., 1954. Geotechnical properties of Norwegian marine clays. Pub. No. 4, Norwegian Geotech. Inst.,
Oslo, Norway.
Carlson, E.J. and Enger, P.F., 1962. Tractive force studies of cohesive soils for design of earth canals. Rept. No.
HYD 504, Hydraulics Branch, U.S. Dept. of Interior, Bureau of Reclamation, Denver, CO.
Casagrande, A., 1932. The structure of clay and its importance in foundation engineering. J. British Soc. of Civil
Engrs. In: Contributions to Soil Mechanics, BSCE, 1925-1940: 72-112.
Christensen, R.W. and Das, B.M., 1973. Hydraulic erosion of remolded cohesive soils. Spec. Rept. 135, Highway
Research Board, Washington, DC: 8-19.
Christenson, D.R. and Ferguson, H., 1966. The effects of interaction of salts and clays on unsaturated water flow.
J. Soil Sci. Soc. Amer., 30: 549-553.
Dane, J.H. and Klute, A., 1977. Salt effects on the hydraulic properties of a swelling soil. J. Soil Sci. Soc. Amer.,
41: 1043-1049.
Das, M.M., 1970. Study of Bingham shear strength of a deep marine sediment by capillary viscometer. Rept. HEL-
21-6, Hydr. Engrg. Lab., Univ. of Calif., Berkeley, CA.
Dash, U., 1968. Erosive behavior of cohesive soils. Ph.D. Dissertation, Purdue Univ., Lafayette, IN.
Dunn, I.S., 1959. Tractive resistance of cohesive channels. J. Soil Mech. and Found. Div., ASCE, 85(SM3): 1-14.
Espey, W.H., 1963. A new test to measure the scour of cohesive sediment. Tech. Rept. HYD 01-6301, Hydr.
Engrg. Lab., Dept. of Civil Engrg., Univ. of Texas, Austin, TX.
Flaxman, E.M., 1963. Channel stability in undisturbed cohesive soils. J. Hydr. Div., ASCE, 89(HY2): 87-96.
Fukuda, M.K., 1978. The entrainment of cohesive sediments in freshwater. Ph.D. Dissertation, Case Western
Reserve Univ., Cleveland, OH.

Gade, H.G., 1958. Effects of non-rigid, impermeable bottom on plane surface waves in shallow water. J. Marine
Res., 16(2): 61-82.
Gardner, W.H., Mayhugh, M.S., Goertzen, J.O. and Bower, C.A., 1959. Effect of electrolyte concentration and
exchangeable sodium percentage of diffusivity of water in soils. J. Soil Sci. Soc. Amer., 88: 270-274.
Gibbs, R.J., 1977. Clay mineral segregation in the marine environment. J. Sedi. Petrol., 47(1): 237-243.
Grissinger, E.H., 1966. Resistance of clay systems to erosion by water. Water Resources Res., 2(1): 131-138.
Gularte, R.C., 1978. Erosion of cohesive sediment as a rate process. Ph.D. Dissertation, Univ. of Rhode Island,
Kingston, RI.
Gularte, R.C., Kelley, W.E. and Nacci, V.A., 1977. The threshold erosional velocities and rates of erosion for
redeposited estuarine dredge materials. Paper H-3, Proc. Second Intl. Symp. Dredging Technol., BHRA,
Texas A & M Univ. College Station, TX.
Harris, H.S., Kaufman, W.J. and Krone, R.B., 1966. Orthokinetic flocculation in water purification. J. San.
Engrg. Div., ASCE, 92(SA6): 95-111.
Hayter, E.J. and Mehta, A.J., 1982. Modeling of estuarine fine sediment transport for tracking pollutant movement.
Rept. UFL/COEL-82/009, Coastal and Oceanographic Engineering Dept., Univ. of Fla., Gainesville, FL.
Jeffrey, D.J. and Acrivos, A., 1976. The theological properties of suspensions of rigid particles. J. Amer. Inst.
Chem. Engrs., 22(3): 417-432.
Kandiah, A., 1974. Fundamental aspects of surface erosion of cohesive soils. Ph.D. Dissertation, Univ. of Calif.,
Davis, CA.
Kranck, K., 1981. Particulate matter grain-size characteristics and flocculation in a partially mixed estuary.
Sedimentology, 28(1): 107-119.
Krone, R.B., 1962. Flume studies of the transport of sediment in estuarial shoaling processes. Final Rept., Hydr.
Engrg. Lab. and San. Engrg. Res. Lab., Univ. of Calif. Berkeley, CA.
Krone, R.B., 1963. A study of theological properties of estuarial sediments. Tech. Bull. 7, Committee on Tidal
Hydraulics, U.S. Army Eng. Waterways Expt. Sta., Vicksburg, MS.
Krone, R.B., 1978. Aggregation of suspended particles in estuaries. In: Estuarine Transport Processes. P. Kjerfve
ed., Belle W. Baruch Library in Marine Science, No. 7, Univ. of S. Carolina Press, Columbia, SC: 177-
Lambe, T.W., 1958. The structure of compacted clay. J. Soil Mech. and Found. Div., ASCE, 84(SM2): 1-34.
Lee, D.Y., 1979. Resuspension and deposition of Lake Erie sediments. M.S. Thesis, Case Western Reserve Univ.,
Cleveland, OH.
Liou, Y.D., 1970. Hydraulic erodibility of two pure clay systems. Ph.D. Dissertation, Colorado State Univ., Fort
Collins, CO.
Lutz, J.F., 1934. The physico-chemical properties of soils affecting soil erosion. Res. Bull. 212, Agricultural Expt.
Sta., Univ. of Missouri, Columbia, MO.

Martin, R.T., 1962. Absorbed water on clay: a review. Proc. Ninth Natl. Conf. on Clays and Clay Minerals,
Pergamon Press, New York: 28-70.
Martin, R.T., 1965. Quantitative fabric of consolidate kaolinite. Res. Rept. 65-47, Soils Pub. No. 179, Dept. of
Civil Engrg., Mass. Inst. Technol., Cambridge, MA.
McConnachi, I., 1974. Fabric changes in consolidated kaolin. Geotechnique, 24(2): 207-222.
Mehta, A.J., 1973. Depositional behavior of cohesive sediments. Ph.D. Dissertation, Univ. of Fla., Gainesville,
Middleton, H.E., 1930. Properties of soils which influence soil erosion. Tech. Bull. 178, U.S. Dept. of Agriculture.
Migniot, P.C., 1968. A study of the physical properties of different very fine sediments and their behavior under
hydrodynamic action. La Houille Blanche, 7: 591-620 (In French, with English abstract).
Miller, C.R., 1960. A critique on stable channels in cohesive materials and a research proposal. Res. Rept. 333,
Agriculture Research Service, U.S. Dept. of Agriculture.
Mitchell, J.K., 1956. The importance of structure to the engineering behavior of clay. D.Sc. Thesis, Mass. Inst.
Technol., Cambridge, MA.
Moore, W.L. and Masch, F.D., 1962. Experiments on the scour resistance of cohesive sediments. J. Geophys.
Res., 67(4): 1437-1446.
Morgenster, N.R. and Tchalenko, J.S., 1967. The optical determination of preferred orientation in clays and its
application to the study of microstructure in consolidated kaolin. Proc. Royal Soc. of London, Ser. A300:
Owen, M.W., 1975. Erosion of Avonmouth mud. Rept. INT 150, Hydr. Res. Sta., Wallingford, UK.
Pacey, J.G., 1956. The structure of compacted soils. M.S. Thesis, Mass. Inst. Technol., Cambridge, MA.
Parchure, T.M., 1980. Effect of bed shear stress on the erosional characteristics of kaolinite. M.S. Thesis, Univ.
of Fla., Gainesville, FL.
Parchure, T.M., Dixit, J.G. and Mehta, A.J., 1981. Erosive characteristics of Lake Francis sediment. Spec. Rept.,
Dept. of Coastal and Oceano. Engrg., Univ. of Fla., Gainesville, FL.
Partheniades, E., 1962. A study of erosion and deposition of cohesive soils in salt water. Ph.D. Dissertation, Univ.
of Calif., Berkeley, CA.
Raudkivi, A.J. and Hutchison, D.L., 1974. Erosion of kaolinite clay by flowing water. Proc. Royal Soc., London:
Sheng, Y.P. and Lick, W., 1979. The transport and resuspension of sediment in a shallow lake. J. Geophys. Res.,
84(C4): 1809-1826.
Smerdon, E.T. and Beasley, R.P., 1959. The tractive force theory applied to stability of open channels in cohesive
soils. Res. Bull. 715, Agricultural Exp. Sta., Univ. of Missouri, Columbia, MO.
Sugimoto, T., 1978. Effects of convection and Brownian motion on particle growth rate in colloidal dispersion. J.
Amer. Inst. of Chem. Engrg., 24(6): 1125-1127.

Sundborg, A., 1956. The river Klaraven, a study of fluvial processes. Bull. 52, Inst. Hydr., Royal Inst. Technol.,
Stockholm, Sweden.
Terwindt, J.H.J., Breusers, H.N.C. and Svasek, J.N., 1968. Experimental investigation on the erosion-sensitivity
of a sand-clay lamination. Sedimentology, 11: 105-144.
Thorn, M.F.C. and Parsons, J.G., 1977. Properties of grangemouth mud. Rept. EX781, Hydr. Res. Sta.,
Wallingford, UK.
Thorn, M.F.C. and Parsons, J.G., 1980. Erosion of cohesive sediments in estuaries: an engineering guide. Proc.
Third Intl. Symp. on Dredging Technol., Paper Fl, BHRA, Bordeaux, France.
Tubman, M.W. and Suhayda, J.N., 1977. Wave action and bottom movement in fine sediments. Proc. Fifteenth
Coast. Engrg. Conf., ASCE, New York: 1168-1183.
Vincent, B., Bijsterbosch, B.H. and Lyklema, J., 1971. Competitive adsorption of ions and neutral molecules in
the stern layer on silver iodide and its effect on colloid stability. J. Coll. Interf. Sci., 37(1): 171-178.
Whitehouse, U.G., Jeffrey, L.M. and Debbrecht, J.D., 1960. Differential settling tendencies of clay minerals in
saline waters. Proc. 7th Natl. Conf. on Clays and Clay Minerals, Pergamon Press, London: 1-79.
Yeh, H.Y., 1979. Resuspension properties of flow deposited cohesive sediment beds. M.S. Thesis, Univ. of Fla,
Gainesville, FL.
Zeichner, G.R. and Schowalter, W.R., 1977. Use of trajectory analysis to study stability of colloidal dispersion in
flow fields. J. Amer. Inst. of Chem. Engrg., 23(3): 243-254.

Ariathurai, R. and Arulanandan, K., 1978. Erosion of cohesive soils. J. Hydr. Div., ASCE, 104(HY2): 279-283.
Christensen, R.W. and Das, B.M., 1973. Hydraulic erosion of remolded cohesive soils. Spec. Rept. 135, Highway
Research Board, Washington, DC: 8-19.
Mehta, A.J., 1981. A review of erosion functions for cohesive sediment beds. Proc. First Indian Conf. Ocean
Engrg., Indian Inst. Technol., Madras, India, I: 83-90.
Partheniades, E., 1965. Erosion and deposition of cohesive soils. J. Hydr. Div., ASCE, 91(1): 105-139.

Ariathurai, R. and Arulanandan, K., 1978. Erosion of cohesive soils. J. Hydr. Div., ASCE, 104(HY2): 279-283.
Dixit, J.G., 1982. Resuspension potential of deposited kaolinite beds. M.S. Thesis, Univ. of Fla., Gainesville, FL.
Krone, R.B., 1962. Flume studies of the transport of sediment in estuarial shoaling processes. Final Rept., Hydr.
Engrg. Lab. and San. Engrg. Res. Lab., Univ. of Calif. Berkeley, CA.
Krone, R.B., 1963. A study of theological properties of estuarial sediments. Tech. Bull. 7, Committee on Tidal
Hydraulics, U.S. Army Eng. Waterways Expt. Sta., Vicksburg, MS.
Parchure, T.M., 1980. Effect of bed shear stress on the erosional characteristics of kaolinite. M.S. Thesis, Univ.
of Fla., Gainesville, FL.

Parchure, T.M., 1984. Erosional behavior of deposited cohesive sediments. Ph.D. Dissertation, Univ. of Fla.,
Gainesville, FL.
Parchure, T.M. and Mehta, A.J., 1985. Erosion of soft cohesive sediment deposits. J. Hydr. Engrg., ASCE,
111(10): 1308-1326.

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