Middleton G.V. (Ed.) Encyclopedia of Sediments and Sedimentary Rocks
Подождите немного. Документ загружается.
GRAIN THRESHOLD 345
Mosley, M.P., and Tindale, D.S., 1985. Sediment variability and bed
material sampling in gravel-bed rivers. Earth Surface
Processes
and
Landforms, 10: 465-482.
Nicholson, W.L., 1970. Estimation of linear properties of particle size
distributions. Biomelrika, 57: 273-297.
Pye,
K., 1994. Properties of sediment particles. Chapter 1 In Pye, K.
(ed.),
Sediment Transport and Depositional
Processes.
Oxford:
Blackwell Scientific, pp. 1-24.
Rice,
S.P., and Church, M., 1996. Sampling surficial fiuvial gravels: the
precision of size distribution percentile estimates. Journal of Sedi-
mentary Research, 66: 654-665.
Sneed, E.D., and Folk, R.L., 1958. Pebbles in the lower Colorado
River, Texas: a study in particle morphogenesis. Journal of Geology,
66:
114-150.
Truesdell, P.E., and Varnes, D.J., 1950. Chart Correlating Various
Grain-size Definitions of Sedimentary Material. Washington: United
States Geological Survey.
Turcotte, D.L., 1992. Fractals and Chaos in Geology and Geophysics.
Cambridge University Press.
USFIASP (United States Federal Interagency Sedimentation Project.),
1957.
The Development and Calibration of the Visual-Accumulation
Tube. Minneapolis: St.Anthony Falls Hydraulic Laboratory.
Wadell, H., 1933. Sphericity and roundness of rock particles. Journal
of Geology, A\\
310-331.
Wentworth, C.K., 1922. A scale of grade and class terms for clastic
sediments. Journal of Geology, 30: i71-i92.
Wolcott, J., and Church, M., 1991. Strategies for sampling spatially
heterogeneous phenomena: the example of river gravels. Journatof
Sedimentary
Petrology,
61: 534-543.
Wolman, M.G., 1954. A method of sampling coarse river bed material.
American Geophysical
Union,
Transactions, 35: 951-956.
Zingg, T., 1935. Beitrag zur Schotteranalyse. SchweizeriseheMineralo-
gisehe UndPetrologische Mitteilungen, 15: 39-140.
Cross-references
Angle of Repose
Armor
Fabric, Porosity and Permeability
Flocculation
Grading, Graded Bedding
Grain Settling
Imbrication and Flow-oriented Clasts
Sedimentologists
Statistics Applied to Sediments
GRAIN THRESHOLD
As the velocity of flowing water progressively increases over a
bed of sediments, a condition is eventually reached when
individual grains are dislodged and begin to be transported.
This condition of first grain movement is called the thresiioldof
sediment motion, or more concisely, grain threshold. It is the
first stage in producing a transport of sediment, and in that
context equations have been developed to correlate the
quantity of sediment being transported to the difference
between the measured flow strength (velocity, discharge, or
mean stress) and that required to initiate sediment motion,
thereby predicting zero transport prior to the threshold
condition. In another application geologists have employed
evaluations of grain threshold in interpretations of modern
and ancient sedimentary deposits, for example to assess
discharges of extreme floods from the maximum sizes of
cobbles or boulders that were moved.
It might appear that the analysis of sediment threshold is a
simple problem that can be solved through a series of
10"'
I 10 10^
GRAIN DIAMETER, D (mm)
Figure G26 The threshold curve developed by Hjulstr0m (1939), but
with the data he used included.
laboratory flume experiments, each using a different grain
size.
A number of such experiments have been performed,
usually with sediments having nearly uniform grain sizes, each
experiment being conducted with a single sieve fraction.
However, natural deposits of sediments contain ranges of
particle sizes, and often include minerals that have different
densities. Selective grain entrainment can then be important,
for example involving the movement of various sizes of cobbles
in a stream by floods having different discharges, or the
formation of heavy-mineral placers in sands when the light
minerals are selectively entrained and transported away,
leaving behind the heavy minerals.
The earliest and still best known attempt to quantify the
grain-threshold condition was that of Hjulstrem (1939),
yielding the graph in Figure G26. Hjulstram compiled the
threshold measurements in the sand-size range, obtained by
previous investigators in flume experiments, and data on flow
velocities required to erode cohesive clays and silty soils. An
interesting result seen in his grain-threshold curve is the
presence of a minimum at a grain diameter of about 0.5 mm to
1mm, a minimum threshold velocity of about 20 cm per
second. Accordingly, it would be easiest to erode fine sand,
whereas silt and clay, as well as coarser sand and gravel,
require greater velocities for grain movement. The increased
velocity needed to transport coarser grains is what one would
expect. That it takes higher velocities to erode the fine-grained
clays and silts results from cohesion binding the particles.
Although the Hjulstrom curve is reproduced in many
textbooks, generally it should not be used in applications.
This is because the evaluated threshold velocity is the average
velocity as might be measured in a river, related to the river's
discharge. It has no reasonable counterpart to a current in the
ocean, which is characterized by a bottom boundary layer of
increasing velocities with distance above the seafloor. In such a
case it is necessary to relate the grain threshold to the velocity
measured at some specified level above the bottom. In their
review of the available threshold data. Miller et al. (1977)
present such a threshold graph where the mean-flow threshold
velocity is measured at
1
m above the bottom.
Rather than using a measure of the current's velocity,
generally it is preferable to express the grain-threshold
condition in terms of the mean stress exerted by the current
on the sediment, the force per unit area. This stress is related to
the gradient of increasing flow velocities above the bottom.
346
GRAIN THRESHOLD
and thus
to the
frictional drag coupling
the
water flow
and
seafloor, representing
in
part the forces that are exerted
on the
individual sediment grains. The curve derived
by
Miller etal.
(1977)
for
the threshold flow stress,
T,,
is
shown
in
Figure G27.
Of interest
is the
absence
of a
pronounced minimum like that
seen
in the
Hjulstrom curve. This
is
because Miller etal. (1977)
utilized only laboratory flume data extending down through
silt grain sizes, where
the
cohesive effects
of
clay
and
organic
matter were excluded. Even without
the
presence
of
cohesion
to produce
a
distinct minimum
in the
curve, there still
is an
inflection with different slopes
to
either side. This
is
attributed
to the changing character
of
the water flow immediately above
the
bed of
sediments. With small grain sizes
and
generally
reduced flow strengths required
for
their movement, there may
be
a
viscous sublayer
at the bed
which
has a
reduced level
of
turbulence that acts
to
move the grains.
In
contrast, with larger
grains
and the
absence
of a
viscous sublayer, individual
particles shed eddies
and
absorb more
of the
drag. Such
relationships between
the
nature
of
the flowing fluid
in
close
proximity
to the
sediment
bed and its
importance
to the
initiation
of
grain movement were initially investigated
by the
German engineer Albert Shields
in
1936, and more recently
by
Yalin and Karahan (1979). Of importance, such considerations
led
to the
development
of
dimensionless graphs
for the
presentation
of
grain-threshold data, where
the
sediment
grains might be composed
of
magnetite
or
some other mineral,
and
the
experiments included viscous fluids such
as
glycerin
and oils, as well as water. The result is
a
"universal curve" that
is applicable
to
various combinations
of
grain densities
and
fluids, contrasting with the curves
of
Figures G26 and G27 that
are limited
in
applications
to the
threshold
of
quartz-density
grains
in
water.
Figure
G27
reveals
a
considerable degree
of
data scatter
above
and
below
the
threshold curve, perhaps surprisingly
so
in that
the
measurements were obtained
in the
controlled
conditions
of
laboratory flumes. Furthermore, systematic
differences
are
found between
the
data derived from different
studies, evident
in
Figure G27
by the
plotting position
of
the
gravel threshold measurements obtained
by
Neill (1968). This
scatter
is due
largely
to the
rather subjective nature
of
sedi-
ment threshold determinations,
it
being
the
experimenter's
500
I
s
tn
tn
UJ
<r
10 k-
10-'
;
1
I—TT-rrrn
p—i i i i iii| i—i
'
THRESHOLD OF UNIFORM
SIZE QUARTZ GRAINS
-
IN WATER
:
(after Miller et ol..l977)
II
11
1
1
:
. ^ r, = 15.4
0""
<<-
' 1
'"I
'—i—r^
/
•
/
OO ;
°\ '
Neill (1967)
gravel dote
1
-
:
10'
10
GRAIN DIAMETER,0 (cm)
judgement
as to
just
how
much grain movement constitutes
"threshold". The condition has been variously taken
as
"weak
movement", "general
bed
movement",
and f^or a
single stone
to
be
"flrst displaced"
or to
experience "scattered movement".
This subjectivity
in the
determination
of the
grain-threshold
condition needs
to be
recognized
in
applications where
Figure G27,
or
any other threshold curve,
is
used.
In
addition,
the idealized conditions
of the
flume experiments must
be
recognized, which excluded grain cohesion, represented
experiments with only
a
narrow range
of
grain sizes
(a
sieve
fraction),
and
where
the bed of
sediments
was
carefully
smoothed
in
order
to
avoid irregularities that might affect
the results. Smoothing
the
sediment
of
course eliminated
the
effects
of
bedforms such
as
previously formed ripple marks,
which
can
affect
the
grain-threshold condition
in
natural
environments.
The use
of a
narrow range
of
grain sizes
in
the experiments
also departs from most natural sediments where there
can be
large ranges
of
sizes available
for
transport,
and
also different
grain densities. This leads
to the
occurrence
of
selective
grain
entrainment, where with increasing flow velocities and stresses,
progressively larger
and
more dense grains
can be
moved.
Laboratory
and
field measurements have been undertaken
to
document this process,
and
example results
are
given
in
Figure G28, compiled
by
Komar (1987). Shown
is a
series
of
selective-entrainment curves that obliquely cross
the
threshold
curve (dashed)
for
uniform grain sizes, the same curve given
in
Figure G27.
The
data
of
Milhous
and
Carling
are for
gravel
entrainment
in
streams, while that
of
Hammond
is
from
the
observed movement
of
gravel
on the
continental
shelf.
The
experiments
of Day
were undertaken
in
laboratory flumes,
using various gravel-size mixtures. Each curve represents
the
largest gravel particle that
is
moved
at a
particular flow stress.
Such
an
assessment
is
referred
to
as flow competence, with
one
important application being
to
evaluate
the
magnitudes
(stresses, velocities
and
discharges)
of
extreme floods from
the maximum sizes
of the
cobbles
and
boulders that were
S
10
1
SELECTIVE ENTRAINMENT
FLOW COMPETENCE
alter Komor (1987)
unitorm groins
Milhous (1973)
10
I 10
MAX. GRAIN DIAMETER.D,(cm)
Figure G27 The flow stress
T,
required
for
the threshold
of
quartz-
density grains of diameter D in water, based on the data compilation
of
Miller
etal.
(1977).
Figure G28
A
series
of
selective entrainment
or
flow-competence
threshold curves
for
the flow stress that moves the maximum grain
diameter Dm within a deposit of mixed grain sizes. The dashed curve
is
for the threshold
of
uniform sediments, the same
as
given
in
Figure C27
[after Komar (1987)].
GRAVITY-DRIVEN MASS FLOWS
347
transported. The curves shown in Figure G28 all demonstrate
that with a mixture of grain sizes available for transport, the
stronger the flow (the higher the value of the flow stress), the
larger the maximum sizes of gravel particles moved. Each
selective entrainment curve crosses the curve based on uniform
grain sizes at approximately its median grain size, so in general
the use of the curve in Figure G27 represents the threshold of
that median size within the deposit of mixed sizes. A more
detailed review of selective grain entrainment is provided by
Komar (1996), including the presentation of curves and
equations for flow competence evaluations, together with a
review of grain sorting by particle density in the sand-size
range, important to the formation of placers.
Paul D. Komar
Bibliography
Hjulstrem, F., 1939. Transport of detritus by moving water. In
Trask, P.O. (ed.). Recent Marine Sediments. American Association
of Petroleum Geologists, pp. 5-31.
Komar, P.D., 1987. Selective grain entrainment by a current from a
bed of mixed sizes: a reanalysis. Journal of Sedimentary Petrology,
57:203-211.
Komar, P.D., 1996. Entrainment of sediments from deposits of mixed
grain sizes and densities. In Carling, P.A., and Dawson, M.R.
(eds.).
Advances in
Fluvial
DynamicsandStratigraphy.
John Wiley &
Sons Ltd., pp.
127-181.
Miller, M.G., McGave, I.N., and Komar, P.D., 1977. Threshold of
sediment motion under unidirectional currents. Sedimentologyl 24:
507-527.
Neill, G.R., 1968. Note on initial movement of coarse, uniform hed-
mate&d\. Journal of Hydraulic Research, 6: 173-176.
Yalin, M.S., and Karahan, E., 1979. Inception of sediment transport.
American Society of Civil Engineers,' Journal of the Hydraulics
«, 105( HYll) 1433-1443! ' '
Cross-references
Armor
Eolian Transport and Deposition
Flow Resistance
Flume
Grain Size and Shape
Placers
Sediment Transport by Unidirectional Water Flows
Surface Forms
GRAVITY-DRIVEN MASS FLOWS
Introduction
Gravity-driven mass flows, also known as sediment gravity
flows, include a spectrum of phenomena in which more-or-less
coherent mixtures of grains and intergranular fluid flow down
slopes. At one end of this spectrum are dilute flows in which
momentum is transferred mostly by fluid forces and sediment
is largely a passive cargo that increases the effective fluid
density. These dilute mass flows are part of a larger class of
fluid dynamical phenomena known as gravity currents
(Simpson, 1987; Bonnecaze et aL, 1993). At the other end of
the spectrum are concentrated mass flows such as granular
avalanches and debris flows. Forces exerted by interacting
solid grains dominate momentum transfer in such flows,
although fluid forces can mediate grain interactions (Savage
and Hutter, 1989; Iverson, 1997).
A complete gradation of mass flows probably exists between
the dilute (fluid-dominated) and concentrated (grain-
dominated) end members of the spectrum. Most research
emphasizes one end member or the other, but this article
considers the full spectrum of mass flows and emphasizes
unifying physical principles that help explain similarities and
differences among flows with diverse origins, compositions,
and modes of deposition. A fully unified physical theory
applicable to all gravity-driven mass flows does not yet exist,
however.
A variety of nomenclature is commonly used to describe and
categorize gravity-driven mass flows that occur in subaerial,
subaqueous, and volcanic environments (Table G16). This
article does not emphasize nomenclature, because nomencla-
ture is less important than is understanding the phenomena
that govern flow behavior and sedimentation.
Macroscopic dynamics: unsteady flow
witb a free surface
All gravity-driven mass flows share some macroscopic traits
that are largely independent of sediment concentration and the
detailed behavior of solid and fluid constituents. One universal
trait is unsteady, nonuniform motion—that is, motion that
changes with time and position. Unlike ocean currents and
river floods, gravity-driven mass flows typically have distinct
starting and ending points in space and time. Most flows
originate from static rock or sediment masses in steeply sloping
source areas, accelerate and elongate as they move downslope,
and then decelerate on flatter slopes, where they eventually
form deposits. The character and composition of mass flows
can evolve as changes in mass and momentum distributions
occur during various stages of motion.
Another universal feature of gravity-driven mass flows is an
unbounded upper surface that is free to change its shape. The
presence of this deformable free surface fundamentally
distinguishes gravity-driven mass flows from flows in pipes
or other containers and also from rigid landslides that
translate down slopes. The free upper surfaces of mass flows
evolve rapidly after motion commences; most flows quickly
develop blunt heads or snouts and tabular bodies with
horizontal dimensions much greater than their thicknesses
(Figure G29).
The tabular geometry of gravity-driven mass flows allows
their macroscopic rriotion to be analyzed using shallow-flow
theory. This well-known theory results from applying the
principles of mass conservation and momentum conservation
(Newton's laws of motion) to a deformable body flowing
down a slope, and from using approximations that are
generally suitable if the thickness of the body is much less
than its areal extent. Vreugdenhil (1994) and Gray el aL
(1999) provide detailed derivations of shallow-flow theory for
water floods and granular avalanches, respectively, and Parker
et al. (1986) and Iverson and Denlinger (2001) provide
derivations for dilute and concentrated grain-fluid mixtures,
respectively.
The equations of shallow-flow theory express the effects of
macroscopic mass and momentum conservation on mass-flow
behavior. A simple but instructive form of the equations that
348
GRAVITY-DRIVEN MASS
FLOWS
Table
C16
Names
and
tittriiiutes
of
some
common
f^ravity-driven
m^iss
flows.
"Ambient
fluid" is the
fluid
surrounding
the flow.
"Intergr.inular
fluid" is the
fluid wilhin
the flow.
"Sediment
contcnlration" is
high
or low
depending
on
whether
grains
or
fluid
dominate
momentum transfer
Name
of
flow
Rock
avalanche
Debris
flow
Mud
flow
Lah;ir
Pyroclastic
flow
Ash
flow
Turbidity
current
.Ambient
fluid
Air
Air or
water
Air or
water
Air (at
volcano)
Air (at
volcano)
Air (at
volcano)
Water
Inlergranular
Air
Waier
Water
Water
Air
Air
Water
Attributes
of
flow
Sediment
fluid
concentration
High
High
High
High
High
Low
Low
Predominant
grain
size
Sand
and
larger
Sand
and
larger
Sand
and
smaller
IJndilTerentialed
Sand
and
larger
Sand
and
smaller
Sand
and
smaller
Dilute
tail
Body Concentrated
snout
Figure
C29
Schematic
vertical
cross
section
of a
generic
gravity-
driven
mass
flow,
with
identification
of
morphological
features
and
variables defined
in the lext.
Vertical
exaggeration
is
about
10-lOOx
describe flow in one direction is
= 0
n^-
d{hv)
di
— (/' ~
/'(j).?
(Eq. 1)
- r
(Eq. 2)
in which the independent variables are time. I. and downslope
distance, .v. and the dependent variables are the flow thickness
h(.\-j) and velocity v'{.v,/) (Figure G29). I'aramcters in the
equations include the mass density o'i the llowing mixture. />.
the mass density oi the ambient fluid through which the
mixture flows,
(}„.
the tnagnitude of gravitational acceleration,
g. the slope angle. ('. and a lateral stress coefficient, k (equal to
I if the mass flow behaves as a fluid but varying from about 1/5
to 5 if grain-contact stresses arc important (Iverson. 1997)). All
of these parameters can be measured or estimated with fair
accuracy, and all are assumed to be constants in equations 1
and 2. A more enigmatic quantity in equation 2 is the resisting
shear stress, r, which can vary greatly depending on whether
solid or fluid forces are dominant. Before considering the
differing effects of solid and fluid forces, however, it is
important to assess the terms in equations I and 2 that arc
universal and responsible for strong similarities among
gravity-driven mass flows.
Each term in the mass-conservation equation
1
involves the
product of /) (mass per unil volume) and a velocity that
describes the rate at which mass is redistributed within a
deforming flow. The velocity 9/f/?f expresses the change in
the free-surface height due to movement of mass normal to
the bed. and the velocity
c(hv)/?>.\
expresses mass redistribution
parallel to the bed. A term can be added to equation 1 to
express the velocity at which erosion or deposition normal
to the bed adds or subtracts mass from the moving flow.
but this term is omitted for the present because it
significantly complicates the accompanying momentum
equation 2.
The moinentum-conservation equation 2 includes terms in
brackets that are like the terms in brackets in the mass-
conservation equation I. except the terms in equation 2
contain an additional v. This relationship between mass-
conservation and momentum-conservation terms is no acci-
dent, as the additional v's in equation 2 reflect the definition of
momentum: mass times velocity. Overall, the terms in brackets
on the left side of equation 2 express the rate at which a
segment of the deforming flow accelerates in response to the
evolving balance between driving and resisting stresses. These
inertial terms represent the "ma" term in Newton's famous
equation. •'F = ma." Inertial terms play a crucial role in mass-
flow dynamics, and they cannot be neglected in efforts to
understand mass-flow deposition.
The terms on the right side of equation 2 represent the "F"
term in "F = ma," and they express the balance of stresses that
drive and resist mass-flow motion. The first term. (p-pu)^h
sin(),
is the driving stress due to the component of gravity
that pulls the mass downslope. The gravitational pull is
effectively reduced by the presence of ambient fluid with
density p,,. because the ambient fluid exerts an upward
buoyancy force on the flowing mass. However, this buoyancy
force is negligible in concentrated subaerial flows, which
typically have plp,i>
1,000.
The second term on the right side
of equation 2 is the longitudinal stress due to the buoyant
weight of flowing material that pushes against adjacent
material upslope and downslope,
—
(p
—
f),,)glikcos.O(dh/c.\).
This longitudinal stress resists motion if the flowing mass
thickens in the downslope direction (DA/c.v < 0), but it helps
drive motion if the mass tapers downslope
(6/J/C1A
> 0). The
third term on the right side of equation 2 is the resisting stress
due to internal and basal shearing, —r. If the terms on the right
sidcofequation2sum to zero, the mass is static or has constant
velocity; otherwise the mass accelerates or decelerates.
Equation 2 reveals that evolution of gravity-driven tnass
flows into tabular fonns is attributable to gravity
itself.
When
a mass flow commences, the leading edge of the flow
experiences more driving force than resistance as gravity pulls
it downslope. (Otherwise it would not move!) Moreover, the
leading edge is pushed forward by the weight of the mass
behind it. because dh/v.\<{) necessarily applies in the tapered
leading edge. Behind the tapered leading edge there necessarily
GRAVITY-DRIVEN MASS FLOWS
349
exists a region in which 0/)/0.v > 0, and in this region the
distribution of weight exerts a backward (upslope) force on the
trailing mass, which causes it to lag behind. The flowing mass
thereby flattens into a tabular body, and continued tapering of
the leading edge persists until the mass begins to decelerate or
additional forces locally increase resistance and produce a
blunt front or snout.
Two distinct mechanisms produce blunt fronts or snouts at
the heads of gravity-driven mass flows. In dilute Hows the
mechanism involves the ambient fluid {water or air) that is
displaced by an advancing flow front (Simpson, 1987).
Acceleration of the atnbicnt lluid produces an inertial reaction
stress approximately equal to
^p,,yj,,.,,j.
where iv,,,,,,/ is the
velocity of the advancing flow front. The reaction stress pushes
against the flow front and produces resistance in addition to
that included in the momentum equation 2. However, this
additional resistance plays an important role only if 5Pi,i7,,,,«/
has a tnagnitude comparable to that of the internal stresses
affecting the flow. As indicated on the right side of equation 2.
internal stresses have magnitudes proportional to (p-p^,)gh. A
useful criterion for evaluating the importance of (he flow-front
reaction stress compares the values ^^kpa^eaii ^""^ (p~P«),?/'
by
employitig
their
ratio
Fr\.,,i
=
[pJiP
-
PM^^HI
l^'^)-
where
Fr is
known as
a
densiomciric
Fwiuk'
number.
Experiments have shown that Fr^,,,,j ^ 0.5 is typical of
advancing fronts of dilute mass flows (Middleton. 1993). Eor
example, for a dilute subaqtieous flow with a thickness of
1
m
and a density 10 percent greater than that of the ambient water
through which it flows,
Frj,,,_,^,
^0,5 occurs when flow speeds
reach about U.7m per second. Such speeds are readily
attainable, and dilute flows can therefore develop bkmt snouts
solely as a consequence of the inertia of the ambient
fluid.
Concentrated subaerial mass flows develop blimt snouts
through an entirely different mechanism, which entails local
thickening due to locally enhanced internal friction. Atnbient
fluid has negligible effect on concentrated subaerial flows, in
which p,,<.p and Fr^^,_,^/<0.1 arc typical. However, intense
grain interactions in such flows cause efficient grain-size
segregation that almost invariably leads to a cumulation of
coarse clasts at flow fronts (Iverson. 1997; Vallance and
Savage, 2()0()). Commonly these coarse clasts are more angular
than the smaller clasts in the flow, and they produce more
internal friction (Pouliquen
clal..
1997). Coarse-grained fronts
also dissipate pore-fluid pressures in liquid-saturated mass
flows, thereby enhancing local resistance and growth of blunt
snouts (Major and Iverson, 1999). Feedbacks involving grain-
size segregation, pore-fluid pressure, and flow-front resistance
indicate that micromechanics on the scale of individual grains
can play a key role in macroscopic flow dynamics.
Concentrated subaqueous mass flows (such as submarine
debris flows) constitute a hybrid case in which blunt fronts
may develop through a combination of grain-size segregation
and the inertia of ambient
fluid.
Such flows can begin to
hydroplane on a thin film of water when flow is fast enough
that yvi,,,,j ^ 0.2: in such instances the snout tnay detach from
the mass-llow body and run oul in ad\ance of it (Mohrig
flal..
1998).
Micromechanics: steady uniform shear flows
Momentum transfer on the scale o\' individual grains and
similarly small elements of fluid occurs differently in dilute
and concentrated tnass flows. In dilute flows viscosity and
turbulence of the fluid phase cause most micromechanica!
momentum transfer. In concentrated flows enduring grain
contacts and brief grain collisions are more itnportant,
although fluid may mediate grain interactions. These diverse
modes of micromechanical momentum transfer arc not
represented explicitly in macroscopic models o\' mass flow,
but are instead represented by stresses. Thus, micromechanics
provides a basis for assessing the factors that determine the
resisting shear stress r and the lateral stress coel'ticient k that
appear in equation 2.
Micromechanics can be quantifled most simply by focusing
on ideal, steady, uniform, shear flows (Figure G30). which are
called "rheometric" flows because exact knowledge of the
inacroscopic state of stress aids determination of rheological
relationships between stress and deformation. Many investiga-
tions of mass-flow mechanics have emphasized ideal, rheo-
metric flows
(e.g..
Bagnold. 1954; Lowe. 1976; Chen. 1987).
but it is important to recognize that this idealization balances
the driving stress (p-pjgh sin 0 against just one term (T) in a
general mass-flow momentum equation such as equation 2.
Therefore, the (bllowing characterization of steady, unifortn.
shear flows provides limited insight about unsteady flows in
which all the terms in eqtiation 2 are important.
Sediment concentration and the strength of
the
effective gravi-
tational force per unit volume (/)-/),,),e, arc the most obvious
causes of differing styles of micromechanical momentum trans-
fer in dilute and concentrated mass flows. Effects of volumetric
sediment concentration (uj and gravitational forces can be
quantified in a rudimentary way by evaluating the ratio of the
buoyant unit weight of the flowing mixture to its total unit
weight, which yields the normalized bulk density
p
=
-
Pa
(Eq.
3)
where /(, and f>, are the densities of the solid grains and
intergranular
fluid,
respectively, and p =
psi>.
+ P/(\-<'<;) is the
bulk density of the grain-fluid mixture. The fundamental
importance of p' is evident from the fact that this quantity
appears as a governing parameter on the right-hand side of the
macroscopic momentum equation 2 if the equation is normal-
ized by dividing all terms by pgh.
Unfortunately, no universal criterion exists for distin-
guishing concentrated, grain-dominated flows from dilute.
Figure
G30
Srheniiitit
verticil
tToss
section
of
a
steady,
uniform,
gravitv-driven
shear
t'low
with
a
hypothetical
velocity
profile.
The
mixture
shear
rdte
is
related
to the
velocity
profile
slope
by 7 =
dv/dy
and
is
approximated
by •; =
T'/h,
where
v is the
average
velocity
over
the
interval y-Oto
y—h.
350
GRAVITY-DRIVEN
MASS FLOWS
fiuid-dominated flows solely on the basis of values of p'. For
steady shear flows in which the ambient fluid is water and the
solid phase consists of lithic grains with density -- 2.700
kg/m"*.
flows are probably in the concentrated regime if p' > 0.4. and
arc likely in the dilute regime if// < 0.2. Intermediate values of
p'
indicate a transitional regime that is neither concentrated
nor dilute. If the ambient fluid is air, /)„ ^
0
and // ^ I apply in
most cases, and iKi'Jpii I -"J is a tnore useful parameter than
//
for distinguishing concentrated and dilute flows (Iverson
and Vallance. 2001).
Concentrated
flows
Large values (-^1) of the dimensionless parameters // and
p_^Vs/
/'/(l-i'.J indicate that solid grains are likely to dominate
momentum transfer, but these parameters provide no in-
formation about the effects of flow size, the rate of
deformation, or the vigor of grain interactions. Additional
dimensionless parameters include these effects by including
flow thickness, h, grain diameter. (>. fluid viscosity, fi. and
mixture shear rate, y in their deflnitions. These dimensionless
parameters may be tertned the
Savage,
Sioke.s,
and BugnoUl
minthers. defined here as (cf. Iverson, 1997: Iverson and
Vallance. 2001)
/V.Sav
=
f6-
., fty ,,
p,•}<•)-
.1/2
Pf)gh
{p,-pf)gh fi
(Eq.4a.b.c)
where /. is the "linear concentration" of grains defined by
Bagnold (1954). For spherical grains, the linear concentra-
tion is related to the volumetric concentration by / =
"!•'("+"'
—
"!"')-
where i'* is the maximum concentration that is
geometrically possible. The numbers defined in equation 4a.b.c
take no account of fluid turbulence, which is assumed
negligible owing to the high concentration of solid grains.
(Although concentrated mass flows can be highly agitated
when they move rapidly down rough slopes, agitation of the
granular mass is not the same as fluid turbulence.)
The dimensionless parameters defined in equations 4a.b.c
have the following physical significance: A'^,,, estimates the
ratio of grain-collision stresses to grain-contact stresses
induced by gravity; A'.s,,, estimates the ratio of viscous fluid
stresses to grain-contact stresses induced by gravity; and
N,},,,.
estimates the ratio of grain-eollision stresses to viscous fluid
stresses if gravity-indttced grain-contact stresses are negligible
{'Vs,;,.-• x;
Ns,,,-*'^-)-
iis in the experiments of Bagnold
(1954). Importantly, the paratneters defined in equation 4 are
interrelated by /Vft,y =
(JYV,,,//V.v,,,)/.--
Figure G.11(A) illustrates a scheme for distinguishing modes
of micromechanical momentum transfer in concentrated,
steady shear flows on the basis of values of
jVi,,,..
A^^v,,, and
NBug-
The flgure indicates that flows with sufflciently small
values of A'.'^,,,. and A'.v,,, generate stresses primarily through
enduring, gravitational grain contacts that produce intergra-
nular rubbing
(i.e..
Coulomb friction). The Coulomb friction
regime is typical of relatively thick flows (/i >l m) with shear
rates less than
10
per second, such as most rock avalanches and
debris flows (Iverson and Denlinger. 2001). The Bagnold
tiumber of such flows is largely irrelevant, because gravity
stresses dominate. On the other hand, if either Ns,n or A'.v,,,
has a value that is of order 1 or larger
—as
may be true in
thin,
rapidly shearing flows Coulomb friction is relatively
unimportant, and the Bagnold number distinguishes flow
regimes in which grain collisions and fluid viscosity dominate
momentum transfer. Boundaries between variousconcentratcd-
flow regimes are indistinct, and a combination oi' Coulomb
friction,
grain collisions, and fluid viscosity may be important
in some eireumstances. Moreover, transitions may occur
between concentrated flow regimes and dilute flow regimes,
particularly if the ambient fluid density p,, is sitnilar to the
intergranular fluid density p/.
Dilute
flows
Dilute mass flows occur most commonly where the ambient
fluid and intergranular fluid are the same, a condition that
facilitates lluid entrainment and sediment dispersal. Examples
of such flows include subaqueous turbidity currents and
subaerial volcanic ash flows. Buoyancy forces due to the
ambient fluid are more important in dilute flows than in
concentrated flows, and for dilute flows the parameter p' has
correspondingly smaller values. [Equation 3 defines p' slightly
differently than do some works on dilute, buoyancy-dominated
tnass flows, which use />„ rather than /) in the denominator
(e.g..
Bonnecaze
eral..
1993; Simpson,1987). However, the two
definitions differ negligibly il" the ambient fluid and inter-
granular fluid are the same and the sediment concentration is
small.)
Commonly, p' is multiplied by g to define a "reduced
gravity," g'=p'g, which appears in a densiometric Froude
number applicable to steady, uniform flows.
—
= i^
g'h
g
(Eq. 5)
The last two forms of equation .S employ the relation.
-••
= v/j. which is a suitable approximation for uniform shear
flows (Figure G3). For cases with
/'>/'„,
equation 5 reduces to
the conventional definition of the Froude number for open-
channel flow of dense liquid
(e.g..
water) beneath ambient air.
Furthermore. Fr" defined in equation 5 bears a strong
resemblance to A'v,,,. dcflned in equation 4a. Both definitions
involve a ratio of inertial forces to gravity forces, but in .Vsv/v
the forces are those of discrete solid grains, whereas in Fr" the
forces arc those of continuous
fluid.
Micromechanical momentum transfer in dilute, gravity-
dri\cn mass flows depends not only on fluid inertia but also on
A.
Concentrated Flows
Inertial grain
How
\
Bagnold
\
Regime
\
\
Macroviscous
Coutomb ^.^T"°'^4oi
Regime
. ^^3
"^
B. Dilute Flows
Turbulent fluid flow
(Re>^OQOj
Dynamic
Regime
Regime
\
Viscous
0
"Sto
>1 0
N
Slo
>1
Figure
G31
A si
heme that uses
values
of
dimensionless
parameters
to
distinguish
dominant
modes
of
mitTomechanical
momentum
tr.insfer
in
steady,
uniform,
gravity-driven shear
t'lovvs
of
grain-lluid
mixtures
(See
Figure
G30).
CIRAVITY-DRIVEN MASS FLOWS
the efleetive fluid
viscosity,
which
is
enhanced
by the
presence
of suspended
sediment.
No
generally applicable formula
describes this
enhancetnent,
but for
dilute (i^<0.1) aqueous
mixtures
of
silt
and
clay-sized
sediment.
Einstein's (1906)
equation provides satisfactory
estimates.
The
Einstein
equation.
/'.•/is-.-//v.-
= /'(l +
2.5tJ,).
indicates that effective viscosity
is
increased only modcriitely
by
suspended
sediment.
Reynolds numbers
are
generally used
to
assess
the
relative
itnportance
ol'
fluid inertia
and
viscosity,
whieh together
detertnine
the
propensity
for
fluid
turbulence.
An
applicable
Reynolds number
(Re) for
dilute mass flows
is
defined
by the
ratio
of Fr and
(Vv,,,
(just
as a
Baiznold number
is
defmed
b>
the ratio
of
yVv,,,.
and
;\'s,,,
for
concentrated
Hows).
The
form
of
this Reynolds nuniber
is
sitnplest
if it is
assumed ihat
p,, =
pj.,
so that
/)' =
<iAp.s—pf)lp-
111
^his
ease
Re-
I
/'
(Eq.
6)
If the faetor l/r, is neglected, equation 6 is identical to the
conventional Reynolds number describing steady, uniform
shear flow of pure fluid with -/
—
v/h.
Eigure G.1I(B) illustrates a scheme that employs Fr'. Re.
and A'.v,,, lor distinguishing regitnes of microniechanical
momentum transfer in dilute, steady shear Hows. Two basic
regimes are identified: a quasistatie regime in which small
values of Vv and A',.,,,, indicate that gravity forces dominate,
and il dynamic regime in whieh either viscous or inertial forces
dominate, depending on the value of Re. Most dilute mass
flows have relatively large values of Er'^ and Re. indicating that
inertial forces and turbulent flow are prevalent (Parker tiai.
]9^b:
Bonnecaze .7i(/.. 1993: Middleton. 1993).
The idealized steady flow regimes depicted in P'igure G3I
help identify pariillels between dilute and concentrated shear
flows.
Eor example. Eigure G31(A) and (B) illustt"ate an anal-
ogy between the Eroude number of diltite flows and Savage
nuniber of concentrated flows. They also illustrate an analogy
between the Reynolds number of dilute flows and Bagnold
ntmiber of concentrated flows. Large values of Re and A'y,,^,
indicate agitated flow regimes in whieh inertial forces
dotninate. and small numbers indicate more quiescent flows.
However, owing to strong buoyancy cflects that reduce the
effect of gravity on most dilute flows, the Reynolds regime in
dilute tlows is more prevalent than is the Bagtiold regime in
concentrated flows.
Micromechanics: unsteady flow, changes of state,
and sedimentation
Gravity-driven mass flows seldom resemble ideal, steady,
uniform, rheometric flows. As mass-flow motion ceases, for
example. •/
—f
0 and behavior necessarily shifts toward the
origins of Eigure G31(A) and/or (B). Thus, the apparent rheol-
ogy ol' mass flows can change as flow speeds ditninish and
quasistatie gravitational forces surpass dynamic forces.
It is instructive to view departures from steady, uniform,
rheometrie flow in tenns of changes in "state variables."" which
characterize partitioning of internal mechanical energy as a
function of position and time (Iverson and Vallance, 2001).
The central idea of the state-variable concept is that grain-fluid
[tiixtitres can exist in differing states, somewhat analogous to
conventional solid and fluid states (Jaeger el uL. 1996). Eor
example, a rapidly flowing granular mixture can behave much
like a fluid, whereas a static deposit of the same mixture can
behave much like a rigid solid. Values of state variables depend
on the composition of a mass flow but also evolve as flow
proceeds from initiation to deposition. Therefore, state
variables differ fundamentally from rheologieal constants.
Two readily identifiable state variables are the nonequili-
brium intergranular lluid pressure, p. which is the observed
fluid pressure minus the local hydrostatic equilibrium pressure,
and the granular temperature. T, which is a measure oi" the
intensity of grain velocity fluctuations around a mean value.
Both/5 and Tare zero in static equilibrium states. Both p and T
can increase during a mass flow through conversion of bulk
potential and kinetic energy to internal mechanical energy, and
both can decrease through degradation of internal mechanical
energy to thcrmodynamic heat. Increases in either /; and T
decrease the rigidity of a grain-fluid mixture and enhance its
tendeney to flow.
Large values of p exist when fluid pressures approximately
balance the total stress due to the weight of the solid-fluid
mixture. In dilute flows, large values of p exist continuously
beeatise the solid grains contribute little of the mixtLire weight.
In concentrated flows, large values of/) citn result from subtle
increases in r^ that occur if the sediment tnixturc settles
gravitationally and transfers stresses to the adjaeent fluid a
process known as Ikjuejaeiion. Liquefaction transiently mimics
the effects of enhanced buoyancy because it reduces Coulomb
friction at grain contacts and inhibits further settlement.
Therefore, a liquefied, concentrated mass flow can to some
degree mimic the behavior of a dilute flow and exhibit great
flow efficiency, but this behavior continues only as long as
liquefaction persists (sec Lic/iicjaclionandF/iiiJi:alloii).
Interdependence of changes in
/>.
7. and
Vv
in unsteady mass
tlows has important consequences for sedimentation. A
rudimentary understanding ol" this interdependenee ean be
gained by considering the relative timescales of vertical grain
settling and downslope tnass-flow motion. Because downslope
mass-flow motion is driven by the potential for gravity-driven
f"reefall. the timescale for motion is \/iJg'. where /, is the flow
length, typically similar to the slope length (Savage and
Hutter. 1989). The timescale for gravity-driven settling of
grains is the same as the timescale of dissipation of p in the
absence of energy conversions that provide new inputs of p
and 7 (Gidaspow. 1994. chapter 12). This settling timescale
is Ir/D. where h is the flow thickness and D is the pore-
pressure diffusivity or "consolidation coefficient.'" Values of D
for tnass-flow mixtures depend on seditnent concentrations
and grain-size distributions and can range over many orders of
tnagnitude; typical values range from about 10 ^m'' per
second in concentrated, elay-rich slurries to about 0.1 m" per
second in dilute suspensions of sand in water. The wide
variation in D values produces wide variation in the ratio of
the pressure-diffusion time seale to the mass-flow motion time
scale-
{lrlD)/^/U^.
If
{/}-
ID)/^/L/g':s> 1. settlement of grains from a moving
tnixture occurs much more slowly than does motion of the
mixture
itself.
In such cases little tendency exists for grain-by-
grain sedimentation, and deposition occurs by relatively
abrupt deeeleration and stoppage of the mass flow as a unit
or series of rapidly accreted units. Such deposition generally
produces massive bedding with few sedimentary structures
(Major. 1997). On the other hand. \f {Ir/Dj/^/Ug^ •^\. grains
can readily settle from a mass flow while it is still moving and
352
GRAVITY-DRIVEN MASS FLOWS
thereby produce bedding and structures reminiscent of fluvial
deposits (Middteton. 1993). Erom a sedimcntological perspec-
tive.
dif"l"erences between gradual, grain-by-grain deposition
and abrupt deposition may constitute the central distinction
between dilute and concentrated mass flows. Importantly, this
distinction depends not only on flow composition but also
on flow size (through dependence of (/r ID)I\JL!g onh and L).
Thus,
large-size geological flows may produce deposits that
differ from those produced by small-scale laboratory flows of
the same composition.
Effects of sorting and mass change
The preceding sections emphasize idealized tnass flows with
more-or-less constant compositions, but in natural environ-
ments, mass flows can be highly heterogenous and can alter
their eompositions through gain or loss of sediment and fluid
in transit. This section eonsiders some of these complications.
Grain-size sorting alTects both the dynamics and deposits of
mass flows. Generally, concentrated tnass flows selectively sort
large grains upward and toward flow tiiargins. and thereby
produce inversely graded deposits with coarse-grained
peri-
meters. The sorting mechanists may be multifaceted (Vallance
and Savage. 2000). but the dominant mechanism appears to be
kinetic
sieving
(Middleton. 1970). Kinetic sieving occurs only
when u,- is sufficiently large that spaces between grains are
typically smaller than the grains themselves. Then agitation of
the mixture allows unusually small grains but not unusually
large grains to fall downward though intergranular voids,
leaving a residue of large grains at the flow surface. Once this
surface residue f"orms, a cumulation of coarse clasts tends to
form at mass-flou margins because surflcial sediment generally
moves downslope more rapidly than does sediment nearer the
bed.
Coarse clasts that accumulate at flow margins produce
blunt snouts as noted above, and can control the geometry of
lobate deposits (Pouliquen ei a!.. 1997; Major and Iverson.
1999).
Sorting in dilute mass flows is influenced more by fluid
forees than grain-to-grain interactions. In dilute flows sorting
has much in cotnmon with that in typical fluvial systems, and it
generally produces nortnally graded beds and a variety of
sedimentary structures that tnay occur in characteristic
sequences (Middletoti. 1993). Dilute flows are unlikely to
produce inversely graded beds or concentrations of coarse
clasts at the perimeters of deposits.
Mass flows can not only sort sediment but can also gain or
lose sediment (and fluid) in transit, with fundatnental
implications for Row dynamics and deposits
(e.g..
Imran
cial..,
1998). Mass acquisition or loss is easily represented in the
mass-conservation equation I by adding a term
pE(.x.
I) to the
right-hand side, where E is the rate of erosion (or
—E
is the
rate of deposition). A corresponding term —pvEtw I) must
then be added to the right-hand side of the momentum-
conservation equation 2 to account for the f"orce {expressed as
a stress) required to accelerate the eroded scditiient from zero
velocity to velocity r. However, this added momentum-
expenditure term provides no information about the forces
that determine the magnitude of
E.
The term does not account
of the additional force required to detach sediment eroded
from a bed at rest, nor for the additional f"oree exerted by the
bed to decelerate sediment that is deposited.
The difficulty of accounting completely for the forces
associated with nonzero E has hindered rigorous Inclusion of
mass-ehange terms in models of concentrated mass flows. Eor
dilute mass flows this difficulty has been circumvented by
omitting fcnns such as -pvE(x.t) (Imran el al., 1998). The
omission is justifiable only if sediment entrainment (or
deposition) has negligible effect on momentum conservation
in the mass flow as a whole.
Conclusion
Gravity-driven mass flows occur in a variety of subaerial and
subaqueous environments. The principles of mass and
momentum conservation provide a framework f"or under-
standing the behavior of all gravity-driven mass flows, but
dilute and concentrated flows have some distinct differences.
Dilute flows generally occur where the ambient fluid and
intergranular fluid are very similar and the sediment is
sufficiently fine that it is readily dispersed b\ fluid turbulence.
The ambient fluid affects the dynamics of dilute flows by
exerting quasi-static buoyancy forces that reduce the effect of
gravity and by exerting inertial reaction forees that retard
motion of advancing flow fronts. Deposition by dilute flows
can occur by settling of individual grains, and can produce
sedimentary structures reminiscent of fluvial deposits.
Concentrated mass flows involve significant tnomentum
exchange by solid grains, which is absent in dilute flows. The
density of concentrated flows substantially exceeds that of the
surrounding ambient
fluid,
particularly in subaerial environ-
ments. Therefore, effects of buoyancy are relatively small in
concentrated flows, and effects of grain-size sorting are
amplified by strong interactions between sediment clasts.
Sorting commonly produces inversely graded vertical profiles
and coarse-grained perimeters that enhance friction and
growth of blunt snouts at flow f>onts. The timescale of grain
settling in concentrated flows commonly exceeds the timescale
of downslope mass-flow motion. Thus, concentrated flows can
produce massive beds with few features reminiscent of fluvial
deposits.
Richard M. Iverson
Bibliography
Biignold.
R.A., 1954. Experiments on a gravity-free dispersion of large
solid spheres in a Newtoniim lluid under shear. Pioci-filinirsoftlu'
RovtilSociclyi/ Loiitioii.
Ser.
A, 225: 49 63.
Bonnecaze. R,t.. Hiippert,
II.E.,
iind Lister. J.R.. 1993. Partiele-
driven gravity currents. Joiiriuil of Fluid Akrlumics. 230: 339-369.
Chen.
C.L.. 1987. Comprehensive review of debris-ilow modeling
concepts in Japan. In Costa. J.E., and Wieczorek. G.F. (eds.),
Dchri.s Fkiws/Avalamiu's: Pnni'ss. Rccogniiion. tiinl Miiigaiidii.
Geological Society of America Reviews in Engineering Geoioijy,
7. pp. 13 29.
Einstein.
A.. 1906. A new determination of moleculiir dimensions.
.AmuilciiderPlivsik. 19: 2H9 306.
Gidaspow. D.. 1994. Mulliplmsi- Flow mid Fliiidiziilion. Academie
Press.
Gray, .I.M.N.T,. Wieland. M.. and Hutter. K.. 1999. Gravity driven
tree surlacc How of granular avalanches over complex basal
topography.
Pyocccdim^sofdic
RoviilSucieivof
Landon.
Ser. A, 455:
IS4I 1K74.
Imniii.
J.. Parker.
CJ..
and Katupodes. N., 1998. A numerical model o(
channel inception on submarine fans. Joiinitd of
Geoplivsiccil
Resc'cmii.
C103: i2i9-l238.
Iverson.
R.M., 1997. The physics of debris flows.
Ri'vU-ws
of
Cvoplnsiis. 35: 245-296.
Iverson.
R.M.. and Denlinger. R,P.. 2001. Flow of variably fluidized
granular masses across three-dimensional terrain: I. Coulomb
mixture theory. JininuilofGeophysiciilRvscairh. B106: 537- 552.
GUTTERS AND CUTTER CASTS
353
Iverson, R.M., and Vallance, J.W., 2001. New views of granular mass
flows.
Geology, 29: 115-118.
Jaeger, H.M., Nagel, S.R., and Behringer, R.P., 1996. Granular
solids, liquids, and gases. Reviews of Modern Physics, 68:
1259-1272.
Lowe, D.R., 1976. Grain flow and grain flow deposits. Journalof
Sedimentary
Petrology,
46: 188-199.
Major, J.J., 1997. Depositional processes in large-scale debris-flow
experiments. Journalof Geology, 105: 345-366.
Major, J.J., and Iverson, R.M., 1999. Debris-flow deposition—Effects
of pore-fluid pressure and friction concentrated at flow margins.
Geological
Society of America Bulletin, 111: 1424-1434.
Middleton, G.V., 1970. Experimental studies related to problems of
flysch sedimentation.
Geological
Society of Canada Special
Paper,
7:
253-272.
Middleton, G.V., 1993. Sediment deposition from turbidity
currents. Annual Review of Earth and Planetary Sciences, 21:
89-114.
Mohrig, D., Whipple, K.X., Hondzo, M., Ellis, C, and Parker, G.,
1998.
Hydroplaning of subaqueous debris flows. Geological Society
of America Bulletin, 110: 387-394.
Parker, G., Fukushima, Y., and Pantin, H.M., 1986. Self-accelerating
turbidity currents. Journatof Fluid Mechanics, 171:
145-181.
Pouliquen, C, Delour, J., and Savage, S.B., 1997. Fingering in
granular flows. Nature, 386: 816-817.
Savage, S.B., and Hutter, K., 1989. The motion of a flnitc mass of
granular material down a rough incline. Journal of Fluid Mechanics,
199:
177-215.
Simpson, J.E., 1987. Gravity currents in the environment and the
laboratory. Chichester: Ellis Horwood Limited.
Vallance, J.W., and Savage, S.B., 2000. Particle segregation in granular
flows down chutes. In Rosato, A., and Blackmore, D. (eds.).
Segregation in Granular Flows. Dordrecht: International Union of
Theoretical and Applied Mechanics, pp.
31-51.
Vreugdenhil, C.B., 1994. Nutnerical Methods for Shallow-water Flow.
Dordrecht: Kluwer Academic.
Cross-references
Debris Flow
Grading, Graded Bedding
Grain Fiow
Liquefaction and Fluidization
Physics of Sediment Transport
Turbidites
GUTTERS AND GUTTER CASTS
The term "gutter cast" was coined by Whitaker (1973) for
elongate downward-bulging, deep, narrow erosional structures
on the base of sandstone beds. The overlying bed may be a
small fraction of the thickness of the gutter cast to several
times its thickness or, in cases, the gutter casts are isolated
scour-fills surrounded by mudstone or shale. These represent
the casts of small-scale erosional channels cut into consoli-
dated mud. A wide variety of sizes and shapes have been
described for these features using many different terms,
including priels, furrows, rinnen, erosionrinnen, large groove
casts,
rills, etceteras (see Myrow, 1994). The term gutter cast is
preferred and is in general use. The wide range of size, shape,
lithology and internal structures of these erosional structures
suggest that their origin is polygenetic. The sizes and
geometries of gutter casts are likely a function of many
variables including the intensity and nature of the eroding
flows, length of time that erosion takes place, and the grain size
and diagenetic history (e.g., degree of compaction or lithifica-
tion) of the underlying eroded substrate.
Gutter casts occur in association with pot casts, which are
cup-shaped to cylindrical pillars of sandstone that formed
from the infilling of potholes, or rounded nonlinear erosional
depressions. They range in shape from discs to rounded
loatlike forms to tall pillars, and in size from
1
cm to 20 cm in
diameter or more. The bottoms of pot casts are commonly
deepest around the outside, with a central erosional high. Pot
casts have geometries and markings that indicates vertically
oriented vortex flow (Myrow, 1992a) similar to that which
forms potholes in bedrock in glaciated regions (Alexander,
1932).
Gutter casts are generally composed of sandstone but in
some cases they contain conglomeratic lags. Internal structures
include normal grading, parallel lamination, and wave-
generated stratification including small-scale hummocky
cross-stratification and 2d wave ripple lamination. The cross-
sectional shapes of these gutter casts range from symmetrical
to strongly asymmetrical, and include u-shaped, bilobate, v-
shaped, semicircular, fiat-based and wide, shallow forms (see
Myrow, 1992a). The plan-view shapes of gutter casts are highly
variable in width, and range from straight to sinuous to highly
irregular. Some gutter casts bifurcate and pinch out along
strike. Sinuous gutter casts may have geometries comparable
to modern meandering rivers with steep to overhanging walls
on the outside of meander bends. Sole markings are common
features along the sides and bases of these gutter casts, and
include groove marks, prods, and fiute marks, and post-
depositional trace fossils. The presence of delicate groove
marks on the sides of gutter casts indicates that sand-sized
sediment may have aided in their erosion as an abrasive agent.
Gutter casts are described from ancient deposits with
paieoenvironments that range from tidal fiat to submarine
fan (Whitaker, 1973). Most gutter casts are described from
shallow-marine rocks, and are considered to be storm-
generated features (e.g., Aigner and Futterer, 1978; Kreisa,
1981;
Aigner, 1985; Myrow, 1992a,b). Currents responsible for
their erosion were likely highly variable. Unoriented (Allen,
1962) to bidirectional (Bloos, 1976; Aigner, 1985) prod marks
on gutter casts indicating erosion by multidirectional and
bidirectional currents/waves or combined fiows (Aigner, 1985;
Duke, 1990). The occurrence of spiraling or ropelike pattern of
grooves on the soles of gutter casts has led to the suggestion
that some formed by horizontal helical flows (Whitaker, 1973;
Myrow, 1992a). In many cases, gutters were likely formed by
powerful unidirectional flows that characterize the initial
stages of deposition of tempestites (Myrow, 1992a). Aigner
and Futterer (1978) suggested that gutters are produced by
currents interacting with obstacles forming horseshoe hollows
that were later developed into channels in a downstream
direction. This is not readily apparent from most ancient
deposits, although evidence for such and origin would likely be
lost during continued erosion of the gutter. A series of
laboratory experiments on fine-grained cohesive sediment are
needed to constrain the nature of flows that could potentially
be responsible for gutter erosion, and thus help constrain their
conditions of formation within storm depositional models.
The long axes of gutter casts are generally oriented
perpendicular to shoreline (e.g., Daley, 1968; Myrow,
1992a,b) although some studies indicate shore-parallel orienta-
tions (Aigner, 1985; Aigner and Futterer, 1978). Gutter cast
354
GUTTERS
AND
CUTTER CASTS
orientation can vary within depositional sequences. McKie
(1994) shows a shift from shore-parallel orientations in
transgressive systems tracts that were dominated by geos-
trophic flow to shore-normal orientations in highstand
deposits that reflect downwelling flows in friction-dominated
conditions. Gutter casts have also been shown to develop at
the base of highstand systems as a result of forced regression
(Graham and Ethridge, 1995). They are also known from
nearshore areas of sediment bypass under thick sediment-laden
flows (Myrow, 1992b). tn these cases, isolated gutter casts (or
those connected by very thin overlying beds) are up to orders
of magnitude thicker than intercalated tempestites and
represent sediment that accumulated almost exclusively in
the gutters during bypass to deeper shelf environments.
Paul Myrow
Bibliography
Aigner,
T.,
1985. Storm depositional systems. Lecture Notes in Farth
Sciences,
3. New
York: Springer-Verlag, 174pp.
Aigner,
T., and
Futterer,
E.,
1978. Kolk-topfe
und
-rinnen
(pot and
gutter casts)
im
Muschelkalk
-
anzeger fiir Wattermeer?
Neues Jahrbuch
Fiir
Geologie Und
Pataontologie
Abhandlungen,
156:
285-304.
Alexander,
H.S., 1932.
Pothole erosion. Journal
of
Geology,
40:
305-337.
Allen,
P.,
1962.
The
Hastings Beds Deltas: recent progress
and
Easter
field meeting report. Proceedings of the Geologists Association,
73:
219-243.
Bloos,
G., 1976.
Untersuchungen uber
Bau und
Entstehung
der
feinkornigen Sandsteine des schwarzen Jura alpha (Hettangian
und
tiefstes Sinemurian)
im
schwabischen Sedimentationsbereich.
Ar-
beiten Institut
Fiir
Geologie Paleontologie University Stuttgart,
N.F.,
71:
1-296.
Daley,
B.,
1968. Sedimentary structures from
a
non-marine horizon
in
the Bembridge Marls (Oligocene)
of
the Isle
of
Wight, Hampshire,
England. Journalof Sedimentary
Petrology,
38:
114-127.
Duke, W.L., 1990. Geostrophic circulation
or
shallow marine turbidity
currents?
the
dilemma
of
paleoflow patterns
in
storm-influenced
prograding shoreline systems. Journalof Sedimentary
Petrology,
60:
870-883.
Graham,
J., and
Ethridge, F.G., 1995. Sequence stratigraphic implica-
tions
of
gutter casts
in the
Skull Creek Shale, Lower Cretaceous,
northern Colorado. The Mountain Geologist,
32:
95-106.
Kreisa,
R.D., 1981.
Storm-generated sedimentary structures
in
subtidal marine facies with examples from Middle
and
Upper
Ordovician
of
southwestern Virginia. Journal
of
Sedimentary
Petrology, 51: 823-848.
McKie,
T.,
1994. Geostrophic versus friction-dominated storm flow:
paleocurrent evidence from
the
Late Permian Brotherton Forma-
tion, England. Sedimentary Geology, 93: 73-84.
Myrow,
P.M.,
1992a.
Pot and
gutter casts from
the
Chapel
Island Formation, southeast Newfoundland. Journal
of
Sedimen-
tary Petrology, 62: 992-1007.
Myrow,
P.M.,
1992b. Bypass-zone tempestite facies model
and
proximality trends
for an
ancient muddy shoreline
and
shelf.
Journal of Sedimentary
Petrology,
62:
99-115.
Myrow,
P.M., 1994. Pot and
gutter casts from
the
Chapel Island
Formation, southeast Newfoundland—reply. Journal
of
Sedimen-
tary Research, A64: 706-709.
Whitaker, J.H. McD., 1973. 'Gutter casts',
a
new name
for
scour-and-
fill structures: with examples from
the
Llandoverian
of
Ringerike
and Malmoya, Southern Norway. Norsk Geologisk Tidsskrift.
53:
403-417.
Cross-references
Bedding
and
Internal Structures
Coastal Sedimentary Facies
Paleocurrent Analysis
Parting Lineation
and
Current Crescents
Scour, Scour Marks
Storm Deposits
Tool Marks