Document Actions

IJEGE-11_BS-Hotta

background image
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
319
DOI: 10.4408/IJEGE.2011-03.B-037
PORE WATER PRESSURE DISTRIBUTIONS OF GRANULAR MIXTURE
FLOW IN A ROTATING MILL
n
oRifumi
HOTTA
(*)
(*)
Graduate School of Life and Environmental Sciences, University of Tsukuba (1-1-1 Tennodai, Tsukuba, Ibaraki 3058577, Japan)
size, specific weight,friction coefficient, and coeffi-
cient of restitution) and sediment concentration. Thus,
many different kinds of debris flows are possible, such
as boulder debris flow (t
akaHasHi
, 1977; t
subaki
et
alii, 1982; e
GasHiRa
et alii, 1989), hyper-concentrated
flow (a
Rai
& t
akaHasHi
, 1986; w
inteRweRP
et alii,
1990), and mud flow (o’b
Rien
& J
ulien
, 1988; Shan-
mugam, 1996). These flows are usually classified
based on phenomenal behavior without a clear defini-
tion of the mechanics.
The basic nature of debris flow as a multiphase
flow can be described using constitutive equations
(t
akaHasHi
, 1977; t
subaki
et alii, 1982; e
GasHiRa
et alii, 1997), which have been derived from simple
modeling of the laminar motion of sediment particles,
focusing on the stress structure of the particles and the
pore fluid. These equations have been experimentally
validated, for example, by comparing theoretical and
experimental velocity distributions (i
toH
& e
GasHiRa
,
1999) and flow resistance (a
Rattano
& f
Ranzi
, 2004).
However, those indices as measures of velocity dis-
tributions and flow resistance were merely compre-
hensive indices that resulted from the internal stress
structure. Few studies have succeeded in directly
measuring internal stresses, with some exceptions in-
cluding b
aGnold
(1954)
and
m
iyamoto
(1985) who
measured the pressure component due to particle-to-
particle collisions in granular flows.
R
iCkenmann
(1991) and t
akaHasHi
& k
obayasHi
(1993) investigated how increasing fluid viscosity
ABSTRACT
We measured the pore water pressure distributions
in miniature debris flows to assess the validity of the
related constitutive equations. Our experiments used
a rotating mill that allowed steady flows to be main-
tained easily and a Pitot tube to measure pore pressure
accurately. Plastic and glass beads with particle sizes of
1–6 mm were used to simulate the debris flows. Since
laboratory debris flows within a rotating mill give flow
fields that differ from those of in situ debris flows, the
flow characteristics in the rotating mill were also in-
vestigated. The experimental results showed that the
pore water pressure was greater than the hydrostatic
pressure. Although Stokes drag also appeared in the
excess pore pressure in tests of small particle sizes due
to infiltration flow caused by the inherent fluid field
of the granular mixture flows in the rotating mill, pore
water pressure in the case of 6-mm particles could be
induced by Reynolds stress. The observed excess pore
water pressure in the debris flows with 6-mm particles
corresponded closely to theoretical values, supporting
the use of constitutive equations for evaluating shear
stress in the pore fluid of debris flows.
K
ey
words
: constitutive equation, debris flow, pore pressure,
Reynolds stress, rotating mill
INTRODUCTION
Debris flows exhibit various fluidities, due to the
material condition of the contained sediment (e.g.,
background image
N. HOTTA
320
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
water pressure in debris flows. Even in the laboratory
setting, accurate measurements of pore water pressure
distributions in an open channel are difficult, because
collisions of sediment particles with pressure gauges
can influence measurements. To avoid this, H
otta
&
o
Hta
(2000) used a rotating mill to measure pore wa-
ter pressure distributions in laboratory debris flows.
Rotating mills (also known as tumbling mills) have
been used frequently for laboratory abrasion experi-
ments (k
Rumbein
, 1941; k
uenen
, 1956). The debris
flow within a rotating mill can be maintained in a
relatively stationary manner. Although internal parti-
cles are agitated within the rotating mill, the effect of
particle collisions with sensing instruments is greatly
reduced compared with that in an open channel. Ad-
ditionally, a steady flow can be easily maintained in
the rotating mill with only slight fluctuations in flow
surface, allowing steady measurement of pore water
pressure. However, H
otta
et alii (1998) noted that
the measured pore water pressure might be affected
by factors other than Reynolds stress, including cen-
trifugal force and infiltration flow, so laboratory debris
flows produced in rotating mills may have a differ-
ent nature from actual debris flows. In this study, we
measured pore water pressure distributions in labora-
tory debris flows in a rotating mill to investigate the
internal stresses of debris flows. First, differences
in flow fields were specified between debris flows
in the rotating mill and actual debris flows to obtain
adequate experimental conditions for measuring pore
water pressure. Based on these experimental results,
we assessed the validity of constitutive equations for
debris flows, which assume pore water pressure based
on related stress components
PORE-WATER PRESSURE IN DEBRIS
FLOWS
Pore water pressure in a debris flow pw can be
expressed as follows:
where p
h
is the hydrostatic pressure and p
f
is the
Reynolds stress from turbulent mixing in pore water.
Turbulence in the pore space of debris flows is strong-
ly affected by particle shearing. Based on Prandtl’s
mixing length theory, p
f
can be rewritten as:
with clay suspensions affected the fluidity of debris
flows containing coarse particles, in which the viscous
coefficient of pore fluid altered the total shear stress.
e
GasHiRa
et alii (1989) investigated boulder debris
flows in which pore fluid can be treated as clear water
by formulating Reynolds stress in the pore fluid as a
component of shear stresses, based on the idea that
pore fluid is turbulent, resulting from strong shear in-
duced by sediment particles, although sediment parti-
cles themselves descend in a laminar motion.
While excess pore pressure in debris flows, in-
cluding fine sediment, has been examined (s
avaGe
&
i
veRson
, 2003; i
veRson
et alii, 2010), pore water pres-
sure in boulder debris flows has often been regarded
as hydrostatic. This should not be the case when Rey-
nolds stress is present as shear stress. Assuming an
isotropic turbulent condition in the pore fluid of debris
flows makes it possible to consider pore pressures to
be greater than hydrostatic pressure, due to Reynolds
stress being the same as the shear stress. i
veRson
(1997), i
maizumi
et alii (2003), and m
C
a
Rdell
et alii
(2007) observed excess pore pressure from hydro-
static pressure in mature debris flows. Their results
incorporated the presence of the Reynolds stress com-
ponent in pressure. This is noteworthy because meas-
uring pore water pressure makes it possible to esti-
mate the shear stress component of Reynolds stress,
which is considered to be present to the same extent
as described above. Above all, measuring pore water
pressure may explain the stress structure of debris
flows. e
GasHiRa
et alii (1997) proposed a constitu-
tive equation for debris flow, which consisted of stress
terms relating sediment particle-toparticle collisions,
friction between sediment particles, and Reynolds
stress due to pore fluid mixing. Because the sum of the
three stress components equals the external force, and
the stress from particle-to-particle collisions among
the three stresses can be validated (m
iyamoto
, 1985),
measuring either of the two unknown stresses experi-
mentally can reveal total stress.
Pore water pressure measurements are difficult
for debris flows under various conditions during field
observations or in large scale experiments. Even if
they are attempted, it is particularly difficult to as-
sess the internal structure of debris flows, because
only basal pore water pressure can be measured in
such debris flows. Consequently, laboratory testing is
the most suitable method for measuring detailed pore
(1)
background image
PORE WATER PRESSURE DISTRIBUTIONS OF GRANULAR MIXTURE FLOW IN A ROTATING MILL
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
321
tions of debris flow (H
otta
& m
iyamoto
, 2008),
ρ
m
is the mass density of the debris flow, g is the ac-
celeration due to gravity, )θ is the inclination, and h is
the flow depth. Assuming a uniform sediment concen-
tration, the velocity profile can be given by integrating
eq. (6) as follows:
Equation (7) exhibits the typical velocity profile
for a dilatant fluid in an open channel (t
akaHasHi
,
1977) and can be rewritten using the mean velocity
u
m
as follows:
Differentiating eq. (8) and substituting into eq. (5)
yields the following expression for the theoretical p
f
profile:
According to eq. (9), pf distributes linearly from
the flow surface to the bed, and p
f
increases in propor-
tion to the square of d and u
m
, respectively, when the
sediment concentration profile is uniform.
EXPERIMENTAL METHODS AND MATE-
RIALS
The rotating mill was 4 cm wide and 20 cm in
diameter; it was constructed of an acrylic cylinder
and discs (Fig. 1). Glass beads (4 mm in diameter)
p is the density of pore water, u’ is the fluctuat
i
on
velocity of pore water, l is the mixing length in the
pore space, and u is the mean velocity of pore wa-
ter, which is assumed to correspond with debris flow
velocity. Note that this is a very simple assumption
as pore water in debris flows is strongly sheared by
particles. In debris flows, l is defined by the scale of
the pore space. a
sHida
et al. (1985) proposed the fol-
lowing expression for l:
where k
f
is the ratio between shape parameters for
the sediment particle and the pore space in the range
of 0.16-0.25 (a
sHida
et alii, 1985; e
GasHiRa
et alii,
1989), c is the sediment concentration, and d is the
diameter of sediment particles. a
sHida
et alii (1985)
expressed kf as:
where k
p
and k
v
are the shape coefficient of sedi-
ment particles and pore space, respectively, V
p
and V
v
are the volumes of sediment particles and pore space
in unit volume, and L is the length scale of the pore
space. Substituting eq. (3) into eq. (2) yields the fol-
lowing expression for p
f
:
The vertical velocity profile appears in eq. (5).
Although the constitutive equations should be solved
to obtain an exact velocity profile for debris flows, an
approximation for boulder debris flows can be read-
ily generated. When steady and uniform debris flows
descend with a uniform sediment particle size and uni-
form sediment concentration profile, shear stress τ is
balanced with external force as follows:
where k(c, d) is the function of c and d,
which is derived from the constitutive equa-
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
Fig. 1 - Sketch of the experimental setup
background image
N. HOTTA
322
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
scribed previously. Because the volume of the beads
and water was known, comparison of the projected
areas enabled estimation of the mean concentration of
the granular mixture flow, assuming a uniform concen-
tration in the debris flow part (H
otta
& o
Hta
, 2000).
RESULTS
VELOCITY PROFILE
Figure 2 shows the velocity profiles of the granu-
lar mixture flows in the rotating mill. The velocity of
the glued beads to simulate bed roughness, which was
equal to the speed of rotation, was set at zero. Although
in some cases a velocity deficit appeared near the flow
surface, velocity profiles of both plastic and glass beads
corresponded well with the theoretical velocity profile
of a boulder debris flow, described in eq. (8).
To visualize internal flow in the water phase, metal
powder was placed in the rotating mill in some experi-
ments (see Fig. 3 for an overview). The dominant cur-
rent in the water phase was induced at the meeting point
of the debris flow front and the bed surface. Because
these two motions were in opposite directions, the colli-
sions generated a complex current circulating in the wa-
ter phase. A current also emerged from the debris flow
surface, generated by debouched pore water (Fig. 3).
were glued inside the cylinder to simulate bed rough-
ness. The rotating mill was connected to a motor via
a gear box, and the rotating speed was controlled by
changing the power supply voltage. The Pitot tube
used to measure pore water pressure was constructed
of a stainless tube (1.5 mm external diameter, 1.0 mm
bore diameter). The end of this tube was closed and
an opening (0.8 mm in diameter) was made in both
lateral faces near the end. The Pitot tube was placed
into the rotating mill vertically with the opening fac-
ing perpendicular to the flow direction to measure the
static pore water pressure profile. Although the rotat-
ing mill reduces the influence of particle collisions
with the Pitot tube, it remains possible that the Pitot
tube itself disturbs the surrounding flow, which will
affect the measurements. However, no apparent dis-
turbance was observed under the experimental condi-
tions in this study.
Table 1 lists the materials used in the experi-
ments. Each type of material (50 cm
3
) was mixed with
water (130 cm
3
) to form a mixture (180 cm
3
). Based
on the mixing ratio, the concentration of the mixture
was 0.28, but the granular mixture flow maintained
in the rotating mill resulted in separation of the water
phase and the mixture phase in the front part (see Fig.
1), resulting in a mean concentration greater than 0.28
for the debris-flow part.
After the mixture was poured into the mill, the
pore water pressure profile was measured during a
constant rotational speed. Pore water pressure was
measured vertically at the center line of the rotating
mill at heights of every 2 or 3 mm, with the bed sur-
face set as the bottom (0 mm). The speed of rotation
was recorded and checked before and after measure-
ments to confirm the flow was steady.
After experiments were completed, the velocity
profile and mean concentration of each granular mix-
ture flow was examined by analyzing images recorded
by a video camera. The velocity profile was obtained
by chasing the trajectories of particles passing through
the measuring section. The mean concentration was
obtained from the ratio between the projected area of
the debris flow phase (mixture phase) and the water
phase, which are separated in the rotating mill, as de-
Tab. 1. Materials used in the experiment.
Fig.2 - Nondimensional velocity profiles measured in the
rolling mill. The velocity of the glued beads of bed
roughness, which was equal to the rotating speed,
was set as zero. Solid curve indicates theoretical
velocity profile for boulder debris flows
background image
PORE WATER PRESSURE DISTRIBUTIONS OF GRANULAR MIXTURE FLOW IN A ROTATING MILL
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
323
converted into water height (mm). Figure 5a also shows
the p
f
distribution for clear water flow as a control.
While the p
f
in clear water was nearly zero, resulting
in hydrostatic pressure at any depth in the flow, the pf
in all granular mixture flows began to increase from the
flow surface to the bed, indicating greater pore water
pressure than hydrostatic pressure. The distribution had
a roughly linear shape in most cases, while some cases
resulted in a parabolic profile with moderate increases
in pf near the bed (Fig. 5d). The pore water pressure
observed in real debris flows is often high enough to
support the total pressure of debris flow (i
maizumi
et
alii, 2003; m
C
a
Rdell
et alii, 2007; i
veRson
et alii,
2010), resulting in a fully liquefied state. However, the
excess pore pressure shown in Figure 5 is too low to
support the weight of the beads completely, indicating
that internal stresses due to particles are dominant in
these experimental conditions.
When the type of material remained constant, pf
was greater with faster rotating speeds. When the rotat-
ing speed remained constant, 6-mm plastic beads had a
greater pf than 6-mm glass beads (Fig. 5de), although
similar pf values were observed when 4-mm particles
MEAN CONCENTRATION
Mean concentrations of granular mixture flows
varied due to the differing materials and the rotat-
ing mill’s speed of rotation. Figure 4 shows the re-
lationship between mean concentration and speed
of rotation (rps, revolutions per second); it also in-
dicates the minimum mean concentration (c = 0.28)
derived simply from the mixing ratio of the mixture.
The figure shows that granular mixture flows had a
higher mean concentration of glass beads than plas-
tic beads. For glass beads with a comparable speed
of rotation, the highest concentrations were observed
when 2-mm particles were used, and no significant
difference was detected between glass beads of 4
mm and 6 mm. In contrast, mean concentrations in
mixtures of plastic beads were higher for 6-mm par-
ticles than for 4-mm particles. Mixtures of glass and
plastic beads both exhibited the same trend of lower
concentrations during faster speeds of rotation
PORE-wATER PRESSURE
Figure 5 shows the vertical distribution of excess
pore water pressure from hydrostatic pressure, with pf
Fig. 3 - Schematic illustration of internal flows in water
phase
Fig. 4 - Relationship between speed of rotation (rps) and
mean concentration in laboratory debris flows
Fig. 5 - Excess pore water pressure distributions
background image
N. HOTTA
324
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
were used.
A comparison by particle size revealed that in ex-
periments using glass beads, the greatest p
f
appeared for
particles sized 1 mm and 2 mm, and p
f
tended to de-
crease with increasing particle diameter. However, the
p
f
for 6-mm particles was greater than that for 5-mm
particles. For experiments using plastic beads, the p
f
for
6-mm particles was greater than that for 4-mm particles
at a rotational speed of 1.0 rps, although the difference
was not large.
The p
f
data for glass beads (1-6 mm) was com-
pared using rotational speeds of 1.0 rps and 1.1 rps
to investigate the effect of particle size to pf value.
Although the mixture volume was identical in these
experiments, flow depths of the laboratory debris
flows differed according to the experimental condi-
tions. To remove the difference in flow depth, a pf
gradient was used; this was derived using the pf value
at the bed (z = 0) divided by the flow depth (∂ p
f
/∂z)
assuming a linear profile of p
f
Figure 6 shows the
relationship between ∂p
f
/∂z and particle size; it also
shows the theoretical ∂ p
f
/∂z obtained by substituting
the experimental results (u
m
, c, h) into eq. (9) at z =
0 and dividing this by flow depth h. The experimen-
tal ∂p
f
/∂z decreased with increasing particle diameter
when diameters ranged from 1-5 mm, while the ∂p
f
/∂z
increased when the diameter increased from 5 mm
to 6 mm. In contrast, the theoretical ∂p
f
/∂z increased
with increasing particle diameter for all diameters, as
expressed in eq. (9), where p
f
increases in proportion
to squared d, due to Reynolds stress. As a result, the
experimental and theoretical values for p
f
did not only
differ greatly, but also showed the opposite trends in
relation to diameter, with the exception of the experi-
ments using 5- and 6-mm particles, when the p
f
values
were relatively similar.
DISCUSSION
PORE wATER PRESSURE IN LABORATORY DE-
BRIS FLOwS IN A ROTATING MILL
Before investigating pore water pressure, it was
important to determine whether the properties of
granular mixture flows in the rotating mill sufficiently
reproduced the nature of actual debris flows. Debris
flows can be roughly classified into several types using
the relative flow depth (h/d) (t
akaHasHi
, 2007; H
otta
& m
iyamoto
, 2008). According to the h/d range, the
granular mixture flows we studied should be similar
to boulder debris flows. However, actual debris flows
never have a uniform particle size. It is noteworthy
how the great diversity in particle size, especially fine
sediment in pore fluid, affects the pore water pressure
in actual debris flows. In addition, the flow mecha-
nisms differ, even between a granular mixture flow
maintained in a rotating mill and a steady uniform de-
bris flow in an open channel in several ways.
In an open channel, the driving force is balanced
with flow resistance at any part of the steady uniform
debris flow. However, a rotating mill can only main-
tain a steady state, and the debris flow is necessarily
non-uniform. As the granular mixture flow in the ro-
tating mill descends on the side wall of cylinder, the
bed inclination varies with location, resulting in an
entirely non-uniform debris flow. Additionally, par-
ticles in the debris flow circulate within the rotating
mill and counterchange between the upper and lower
layers at the front and rear edges, respectively. Parti-
cles on the bed move with the rotating bed roughness
and are released at the rear edge with a steep slope,
‘falling’ to the front part. This flow mechanism means
that granular mixture flows within a rotating mill dif-
fer from actual debris flows, so the fundamental nature
of the debris flow in a rotating mill might also differ
from a typical debris flow evaluated by the constitu-
tive equations.
However, the differing flow mechanisms between
debris flows do not significantly affect the Reynolds
stress in interstitial waterflow mechanisms. Interstitial
water in debris flows is exposed to strong shearing by
particles, and Reynolds stress is considered to be gov-
Fig. 6. - Comparison
be-
tween
measured
(open circle) and
calculated (closed
circle) excess pore
water pressure gra-
dient (∂pf/∂z)
background image
PORE WATER PRESSURE DISTRIBUTIONS OF GRANULAR MIXTURE FLOW IN A ROTATING MILL
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
325
Although the velocity at the bed surface was regarded
as zero for experimental purposes (Fig. 2), the bed and
the flow part near the bed did actually move with the
rotation of the mill. If the debris flow in the rotating mill
was influenced by this rotation, centrifugal force might
act as inertial force in addition to gravity, thereby in-
creasing the pore water pressure. Considering the cen-
trifugal force, hydrostatic pressure can be written as:
where u
r
(z) is the profile of the rotational speed in the
debris flow and R(z) is the distance from the center axis
of the rotating mill. For example, Figure 7 compares
the measured distribution of excess pore water pres-
sure with the calculated distribution by substituting
the experimental conditions into eqs. (10) and (11).
Although basal pore water pressure values were com-
parable between measured and calculated results (Fig.
7), increases in calculated pressure do not appear in the
upper part (heights greater than 10 mm from the bed) of
the granular mixture flow, so the profiles disagree. Also,
based on eqs. (10) and (11), when centrifugal force in-
creases the pore water pressure, the basal pore water
pressure should increase to at least the same extent in
experiments using the same rotating speed; this did not
occur (see Fig. 5). Thus, centrifugal force does not ex-
plain the differing pore water pressures for the different
particle sizes (Fig. 6).
It is important to note that the effect of the centrifu-
gal force on pore water pressure (Fig. 7) was calculated
based on the velocity profile derived from eq. (8). Al-
though results indicated that eq. (8) fit with the actual
velocity profile in the rotating mill (Fig. 2), they did not
assure that the velocity of interstitial water correspond-
erned by particle motion around the interstitial water.
Consequently, the Reynolds stress can be treated in
the same manner for velocity profiles in a rotating mill
and in an open channel.
Figure 2 shows that the velocity profiles for both
glass and plastic beads were in good agreement with
the typical velocity profile for a boulder debris flow
over a rigid bed in an open channel. Thus, the pore
water pressure in the laboratory debris flow in the
rotating mill exhibits the value described in eq. (9).
However, when experimental and theoretical pore
water pressures are compared across the particle di-
ameters of glass beads (Fig. 6), the measured pore
water pressure did not correspond with the calculated
value derived from eq. (9), especially under condi-
tions of small-diameter beads. Thus, we investigated
the source of this disagreement. Other than Reynolds
stress, the following three candidates might be respon-
sible for increasing pore water pressure in granular
mixture flows within a rotating mill.
A) Increasing pore water density, due to release of
internal particle-to-particle stress.
B) Centrifugal force, due to rotation.
C) Pressure gradient induced by an internal flow
of interstitial water different from the track of particles.
Candidate A might result in increased pore water
pressure when a debris flow descends as a turbulent
flow. In a turbulent debris flow, the internal particle-
to-particle stress is released as particles in the debris
flow are actively mixed. A stress equivalent to the re-
leased particle-to-particle stress should be supported
by interstitial water, resulting in increased apparent
density. This increase in the apparent density of inter-
stitial water can be observed as increased pore water
pressure. However, in this study the velocity profile
(Fig. 2) confirmed that particles in the granular mix-
ture flow moved in a laminar fashion and no mixing
of particles (even small particles) occurred, except
in the front and rear edges. Figure 4 reveals slightly
higher concentrations under conditions of smaller par-
ticles. This finding indicates that inter-particle contact
is more dominant with smaller particles, supporting
the hypothesis that debris flows with small particles
should be also regarded as laminar, because particle
mixing does not appear to occur under these condi-
tions. Therefore, Candidate A can be rejected as a fac-
tor affecting the increased pore water pressure.
Candidate B is inherent in the use of a rotating mill.
(10)
(11)
Fig.7 - Comparison be-
tween distribu-
tions of measured
and centrifugal-
ly-driven excess
pore water pres-
sures
background image
N. HOTTA
326
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
cussion of increased pore water pressure, because the
former generally treats the interstitial flow as laminar.
By setting the velocity difference between the par-
ticles and interstitial water in the z direction as v in the
granular mixture flow within the rotating mill, the drag
force on single particle D can be expressed as
where D
s
is the Stokes drag, D
I
is the inertial drag, and
μ is the viscosity coefficient of water. D
s
is dominant in
flows with a small Reynolds number, while D
I
exceeds
D
s
in flows with a large Reynolds number. Equation
(12) can be rewritten as a pressure gradient using sedi-
ment concentration c as:
From the right side of eq. (15), increased pore
water pressure (derived based on Candidate C) is ex-
pressed in inverse proportion to d-squared or d. Be-
cause the excess pore water pressure is expressed in
proportion to d-squared in eq. (9), a combination of
eq. (9) and (15) can reproduce experimental results
(Fig. 6). Substituting representational experimental
conditions from Fig. 6 (rotating speed: 1.0 rps, c: 0.4)
into eqs. (9) and (15), relationships between particle
diameter and gradient of excess pore water pressure
can be obtained (see Fig. 8). Figure 8 also shows the
ed exactly to the particle velocity. Figure 3 shows that
in the granular mixture flow, a clear water part was ob-
served in front of the complex internal flow. An emerg-
ing flow was maintained from the debris flow surface,
suggesting that the flow lines of particles and intersti-
tial water did not correspond. That is, the effect of the
centrifugal force might be more limited for pore water
than for particles. Considering the factors discussed
above, Candidate B can also be rejected as a cause of
increased pore water pressure. However, as mentioned
above, centrifugal force might affect particles in granu-
lar mixture flows in a rotating mill: centrifugal force
is equal to roughly K to ½ the gravity near the bed of
the rotating mill. Consequently, when investigating
particle-to-particle stresses in debris flows in a rotating
mill, the influence of centrifugal force should be taken
into consideration
Candidate C should be considered when the flow
lines of particles and interstitial water disagree. In the
granular mixture flow in the rotating mill, an emerging
flow occurred from the debris flow surface (Fig. 3) and
the surfaces of the interstitial water and the debris flow
also disagreed at the rear edge of the debris flow where
the particles were dragged above the water surface by
the bed of the rotating mill, resulting in temporary un-
saturation. These results Fig. 8. Relationship between
particle diameter and gradient of excess pore water
pressure. Open circle indicates the measured excess
pore water pressure gradient (;p
f
/;z). Solid line indicates
eq. (9), broken line indicates eq. (15) divided by flow
depth, and dashed line indicates the sum of these. high-
light the disagreement between the flow lines of parti-
cles and interstitial water in the granular mixture flow
induced in the rotating mill. Because both flow lines
usually correspond in a debris flow in an open chan-
nel, Candidate C is also an inherent issue related to the
use of a rotating mill. Generally, the interactive force
acts in such a way as to produce a difference in velocity
between particles and interstitial water. When particles
are sufficiently dense to be treated as porous media, this
difference in velocity can be interpreted as an infiltra-
tion flow, where the interactive force is described as
a pressure loss. In contrast, when the phenomenon is
interpreted as the sum of single-particle motion in the
fluid, the interactive force can be described as the drag
force of the particles. Although the interactive force
can be expressed as the pressure gradient of fluid in
both situations, the latter is more applicable to this dis-
(12)
(13)
(14)
(15)
Fig.8 - Relationship
be-
tween particle diam-
eter and gradient of
excess pore water
pressure. Open circle
indicates the meas-
ured excess pore
water pressure gra-
dient (;pf/;z). Solid
line indicates eq.
(9), broken line indi-
cates eq. (15) divided
by flow depth, and
dashed line indicates
the sum of these
background image
PORE WATER PRESSURE DISTRIBUTIONS OF GRANULAR MIXTURE FLOW IN A ROTATING MILL
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
327
by Reynolds stress in experiments using particles with
a 6-mm diameter. Excess pore water pressure was
measured and calculated using eq. (9) for all data of
6 mm particles. Figure 9 compares the measured and
calculated values, which were in good agreement, al-
though different trends appeared in the distributions
between glass beads and plastic beads. Calculated val-
ues were greater than measured values for glass-bead
experiments, while measured values were greater for
plastic-bead experiments.
When rotational speeds were identical, the pore
water pressure measured in plastic-bead experiments
was greater than that in glassbead experiments (Fig.
5de). This can be explained by the lower concentra-
tions of plastic beads than glass beads (Fig. 4), as the
excess pore water pressure shown in eq. (9) increases
with increasing mixing length, and the mixing length
increases when concentration decreases. The experi-
mental results revealed higher pore water pressure
in the granular mixture flow of plastic beads, which
had lower specific weight than glass beads. This is
an important finding with regard to the internal stress
structure of debris flows. It suggests that stress in the
pore water of a debris flow behaves independently
from particle-to-particle stresses that are related to the
specific weight of the particles, and is primarily deter-
mined by the structure of the pore space. This finding
might also support the assumption when modeling the
constitutive equations of debris flow that internal en-
ergy dissipation occurs independently, depending on
space: particle-to-particle collisions consume energy
inside the beads, friction between particles consumes
energy on the particle surface, and Reynolds stress
due to pore fluid mixing consumes energy in the pore
fluid (e
GasHiRa
et alii, 1989).
The differing experimental and theoretical values
between glass and plastic beads (Fig. 9) appear to be
related to the shape of the pore space when the particle
concentration changes. Assuming no increases in pore
water pressure due to the infiltration flow under condi-
tions of 6-mm particles, differences between the meas-
ured and theoretical pore water pressure can thus be
considered to be caused by Reynolds stress, as shown
in eq. (9). Equation (9) simply uses mixing length
based on shape parameters for sediment particles and
pore space, as described in eq. (4). The effective space
for the mixing length can be derived from eq. (4) with-
out considering the effect of particle concentration,
results from Figure 6 and the sum of eqs. (9) and
(15). The value for v in eq. (15) was obtained as 4
(cm/s) by setting eqs. (9) and (15) to cross at a 5-mm
diameter, referring to the plot distribution shown in
Figure 6. This value of 4 cm/s for the velocity dif-
ference between particles and interstitial water does
not differ greatly from the roughly-observed velocity
of the emerging flow from the surface of the granular
mixture flow, supporting the theory that a combination
of eqs. (9) and (15) reproduced the results shown in
Figure 6 Based on Figure 8, Candidate C can explain
the measured increase in pore water pressure: the
pressure gradient due to the internal flow, in addition
to Reynolds stress, increased the pore water pressure
in the rotating mill. Some issues remain to be exam-
ined, such as whether pore pressure can be increased
simultaneously based on eqs. (9) and (15) and how
infiltration velocity is determined by experimental
conditions. In addition, .the infiltration flow emerging
from the flow front (Fig. 3) implies that a longitudinal
gradient of excess pore-water pressure exists within
the flow, at least in the case with small particles. It is
unclear how the presence of this gradient might bias
the pore-pressure measurements, which were made
along a single vertical transect.
However, the most remarkable finding at this point
is that the expressions for eqs. (9) and (15) are quite
different as functions for d. The pressure gradient due
to infiltration flow (Candidate C) and Reynolds stress
can independently reproduce the increased pore water
pressure for conditions of small and large particles,
respectively. That is, although a factor other than
Reynolds stress can increase pore water pressure in a
granular mixture flow in a rotating mill, this factor’s
effect can be eliminated by increasing the particle di-
ameter. In this study, pore water pressure measured
using experiments with 6-mm particles increased due
to Reynolds stress, based on the results shown in Fig-
ure 8. Additionally, eqs. (9) and (15) are different with
regard to dependence on c. Reynolds stress increased
with decreasing concentrations and excess pore water
pressure due to Candidate C increasing with increas-
ing concentration. Both factors responded oppositely
to the scale of the pore space.
PORE PRESSURE AS REYNOLDS STRESS
As discussed in the previous section, the increased
measured pore water pressure appeared to be induced
background image
N. HOTTA
328
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
i.e., that is the mixing length changes in proportion to
the concentration regardless of the changing shape of
the pore space. However, because pore space deforms
with increasing concentration, reducing the mixing
length due to the decreased effective volume of the
pore space, shape parameters should be expressed as
functions of concentration. s
uzuki
et alii (2003) re-
ported that when a debris flow has a low concentration,
it is preferable to use 0.08 kf rather than 0.16-0.25 k
f
, as
was previously proposed by a
sHida
et alii (1985) and
e
GasHiRa
et alii (1989). e
GasHiRa
et alii (1989) also
reported that a constant k
f
overestimates mixing length
l in case of lower sediment concentration c, and s
uzuki
(2007) proposed k
f
as a function of c. Together, these
results suggest that mixing length is overestimated in
glass beads with higher concentrations, and underesti-
mated in plastic beads with lower concentrations, re-
sulting in the differing results from measurement and
calculation (Fig. 9).
The structure of pore space in a granular mixture
flow might also affect the pore pressure profile. In this
study, two types of excess pore water pressure profiles
appeared: linear and parabolic (Fig. 5). The parabolic
profile was obtained in cases with higher pore water
pressure. Pore water pressure increased with increas-
ing rotating speed for identically-sized particles with
same specific weight. Because the mean concentration
of the debris flow decreased with increasing rotating
speed (Fig. 4), not only um but also c affected the in-
creased pore water pressure, as shown in eq. (9). In eq.
(9), p
f
increases linearly when c is vertically uniform,
while p
f
profile differs from a straight line when c is
non-uniform. Figure 10 shows the theoretical p
f
pro-
files derived feom eq. (9) using three different types
of c profiles. The gradient of c from surface to the bed
was steeper when the mean concentration was lower.
Figure 10 reproduces the shape of the pf profile, which
changes from linear to parabolic when the the c profile
inclines. Although this study did not measure concen-
tration profiles, Figure 10 may explain the results in
Figure 5, implying that the concentration profiles in-
clined with decreasing mean concentrations due to an
increasing speed of rotation.
CONCLUSIONS
This study measured pore water pressure distri-
butions in granular mixture flows in a rotating mill to
investigate the internal stresses of debris flows. The ex-
perimental results revealed that the pore water pressure
was greater than the hydrostatic pressure. The results
imply that a Reynolds stress model best fits the data
when only larger particles are present, whereas an “in-
filtration flow” drag model best fits the data when only
smaller particles are present. A combination of the two
models provides the best fit to the full dataset. The data
are inconclusive as far as determining which model
might work best for real debris flows with a great di-
versity of particle sizes.
The observed excess pore water pressure in de-
bris flows using 6-mm particles corresponded closely
to theoretical values, supporting that the theory that
constitutive equations can also evaluate shear stress in
pore fluid of debris flows with uniform grain size.
Differing pore water pressure profiles could be ex-
plained by the differing sediment concentration gradi-
ents, which appeared to induce uneven mixing lengths.
Observed pore water pressure was greater for debris
flows consisting of particles with lower specific grav-
ity, indicating that the stress components of pore fluid
behaves independently from those of sediment parti-
Fig. 9 - Relationship between measured and calculated
basal pore water excess pressure from hydrostatic
pressure
Fig.10 - Relationship between concentration profile and
excess pore water pressure distribution
background image
PORE WATER PRESSURE DISTRIBUTIONS OF GRANULAR MIXTURE FLOW IN A ROTATING MILL
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
329
sure measurements and the background of the con-
stitutive equations of debris flows. This research was
partially supported by the Ministry of Education, Sci-
ence, Sports and Culture, Grant-in-Aid for Scientific
Research, 22780140, 2010.
cle interactions, and are determined by the pore-space
structure of debris flows.
ACKNOWLEDGEMENTS
I express sincere thanks to Prof. Miyamoto (Uni-
versity of Tsukuba) for his comments on the pore pres-
REFERENCES
a
Rai
m. & t
akaHasHi
t. (1986) - The mechanics of mud flow. Proceedings of the Japan Society of Civil Engineers, 375 (II-6):
69-77. (in Japanese with English summary)
a
Rattano
m. & f
Ranzi
l. (2004) - Analysis of different water-sediment flow processes in a mountain torrent, Natural Hazards
and Earth System Sciences, 4: 783-791.
a
sHida
k., e
GasHiRa
s., k
amiya
H. & s
asaki
H. (1985) - The friction law and moving velocity of a soil block on slopes. Annals
of the Disaster Prevention Research Institute, Kyoto University, 28 (B-2): 297-307. (in Japanese with English summary)
b
aGnold
R.a. (1954) - Experiments on a gravity-free dispersion of large solid spheres in a Newtonian fluid under shear. Pro-
ceedings of the Royal Society of London, Series A, Mathematical and Physical Sciences, 225: 49-63.
e
GasHiRa
s., a
sHida
k., y
aJima
H. & t
akaHama
, J. (1989) - Constitutive equations of debris flow. Annals of the Disaster Preven-
tion Research Institute, Kyoto University, 32 (B-2): 487-501. (in Japanese with English summary)
e
GasHiRa
s., m
iyamoto
k. & i
toH
t. (1997) - Constitutive equations of debris flow and their applicability. Proceedings of the 1st
International Conference on Debris-Flow Hazards Mitigation, 340-349.
H
otta
n., m
iyamoto
k., s
uzuki
m. & o
Hta
t. (1998) - Pore-water pressure distribution of solid-water phase flow in a rolling
mill. Journal of the Japan Society of Erosion Control Engineering, 50 (6): 11-16. (in Japanese with English summary)
H
otta
n. & o
Hta
t. (2000) - Pore-water pressure of debris flows. Physics and Chemistry of the Earth (B), 25 (4): 381-386.
H
otta
n. & m
iyamoto
k. (2008) - Phase classification of laboratory debris flows over a rigid bed based on the relative flow
depth and friction coefficients. International Journal of Erosion Control Engineering, 1 (2): 54-61.
i
maizumi
f., t
suCHiya
s. & o
Hsaka
o. (2003) - Flow behavior of debris flows in the upper stream on mountainous debris torrent.
Journal of the Japan Society of Erosion Control Engineering, 56 (2): 14-22. (in Japanese with English summary)
i
toH
t. & e
GasHiRa
s. (1999) - Comparative study of constitutive equations for debris flows. Journal of Hydroscience and Hy-
draulic Engineering, 17 (1): 59-71.
i
veRson
R.m. (1997) - The physics of debris flows. Review of Geophysics, 35 (3): 245-296.
i
veRson
R. m., l
oGan
m., l
a
H
usen
R.G. & b
eRti
m. (2010) - The perfect debris flow? Aggregated results from 28 large-scale
experiments, Journal of Geophysical Research, 115: F03005.
k
Rumbein
w. C. (1941) - The effects of abrasion on the size, shape and roundness of rock fragments. Journal of Geology, 49:
482-520.
k
uenen
P.H. (1956) - Experimental abrasion of pebbles 2. Rolling by current. Journal of Geology, 64: 336-368.
m
C
a
Rdell
b.w., b
aRtelt
P. & k
owaRski
J. (2007) - Field observations of basal forces and fluid pore pressure in a debris flow.
Geophysical research letters, 34: L07406.
m
iyamoto
k. (1985) - Mechanics of grain flows in Newtonian fluid. Ph.D.-thesis presented to Ritsumeikan University, Japan.
(in Japanese).
o’b
Rien
J.s. & J
ulien
P.y. (1988) - Laboratory analysis of mudflow properties. Journal of Hydraulic Engineering, 114 (8):
877-887.
R
iCkenmann
d. (1991) - Hyperconcentrated flow and sediment transport at steep slopes. Journal of Hydraulic Engineering, 117
(11): 1419-1439.
s
avaGe
s.b. & i
veRson
R.m. (2003): Surge dynamics coupled to pore-pressure evolution in debris flows. Debris-flow Hazards
Mitigation: Mechanics, Prediction and Assessment, R
iCkenmann
d. & C
Hen
C.l. eds., Millpress, Rotterdam, 503-514.
s
HanmuGam
G. (1996) - High-density turbidity currents: Are they sandy debris flows? Journal of sedimentary Research, 66 (1): 2-10.
s
uzuki
t., H
otta
n. & m
iyamoto
k. (2003) - Influence of riverbed roughness on debris flows. Journal of the Japan Society of
Erosion Control Engineering, 56 (2): 5-13. (in Japanese with English summary)
background image
N. HOTTA
330
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
s
uzuki
t. (2007) - Flow mechanics of debris flows on the roughness boundary. Ph.D.-thesis presented to the University of Tokyo,
Japan. (in Japanese).
t
akaHasHi
t. (1977) - A mechanism of occurrence of mud-debris flows and their characteristics in motion. Annals of the Disaster
Prevention Research Institute, Kyoto University, 20 (B-2): 405-435. (in Japanese with English summary)
t
akaHasHi
t. (1978) - Mechanical characteristics of debris flow, Journal of Hydraulic Engineering, 104, HY8: 1153-1169.
t
akaHasHi
t. (2007) - Debris flows: Mechanics, Prediction and Countermeasures, Taylor and Francis / Balkema, 448p.
t
akaHasHi
t. & k
obayasHi
k. (1993) - Mechanics of the viscous type debris flow. Annals of the Disaster Prevention Research
Institute, Kyoto University, 36 (B-2): 433-449. (in Japanese with English summary)
t
subaki
t., H
asHimoto
H. & s
uetsuGi
t. (1982) - Grain stresses and flow properties of debris flows. Proceedings of the Japan
Society of Civil Engineers, 317: 79-91. (in Japanese)
w
inteRweRP
J.C.,
de
G
Root
m.b., m
astbeRGen
d.R. & v
eRwoeRt
H. (1990) - Hyperconcentrated sand–water mixture flows over
flat bed, Journal of Hydraulic Engineering, 116 (1): 36-54.
Statistics