Post on 29-Apr-2023
Editorial Manager(tm) for Geotechnique Manuscript Draft Manuscript Number: 10-P-005R2 Title: Rheological behaviour of reconstituted pyroclastic debris flow Article Type: General Paper Corresponding Author: Anna Scotto di Santolo Corresponding Author's Institution: University of Naples Federico II, Naples, Italy First Author: Anna Scotto di Santolo Order of Authors: Anna Scotto di Santolo;Anna Maria Pellegrino;Aldo Evangelista;Philippe Coussot Manuscript Region of Origin: ITALY Abstract: An experimental study of the rheological behavior of three natural pyroclastic soils with different depositional processes remixed with water was carried out with the help of a rotational rheometer and inclined plane tests. A homogeneous fluid-like behavior is obtained only within a very narrow range of concentrations, typically not more than 10%. Below this range the material sedimentates rapidly, above this range it behaves like a solid. In the fluid-like range the typical rheological behavior of these suspensions is that of a yield stress fluid exhibiting a static yield stress larger than its dynamic yield stress. This effect likely finds its origin in a "local" sedimentation effect, i.e. the particles sedimentate just as necessary to form a structure more jammed than the structure during flow. As a result the flow of such materials is usually unstable: they will start to flow beyond a critical stress but just beyond this value will reach a high shear rate associated with a high flowing velocity. The static and dynamic yield stresses of these materials widely increase from very low to very large values (several orders of magnitude). Inclined plane tests were shown to provide reasonable though still approximate values for the static and dynamic yield stresses. These results suggest that in the field a small change in solid fraction will cause a slight decrease of the static yield stress, readily inducing a rapid flow which will stop only when the dynamic yield stress is reached, namely on a much smoother slope. This can explain the in situ observed post-failure behaviour of pyroclastic debris flows, which are able to flow over very long distances even on smooth slopes. Number of words in main text: 7744; number of table: 1; number of illustrations: 8 Suggested Reviewers: Serge Leroueill Laval University Serge.Leroueil@gci.ulaval.ca expert Dieter Rickenmann Mountain Hydrology and Torrents dieter.rickenmann@wsl.ch expert Nicolas Roussel LCPC
Data of initial submission: 28/12/2009
Data: 12/11/2010 revised2
Title: Rheological behaviour of reconstituted pyroclastic debris flow
Full name and qualifications of the authors:
o Anna Scotto di Santolo, Assistant Researcher (1)
o Anna Maria Pellegrino, Ph. D student (1)
o Aldo Evangelista, full professor (1)
o Philippe Coussot, responsable de l’Equipe Imagerie et Matériaux de l’UR Navier (2)
Position or affiliation of the authors:
(1) University of Naples Federico II, Hydraulic, Geotechnical and Environmental Engineering, Naples, Italy
(2) LMSGC/Navier, 2 Allée Kepler, 77420 Champs sur Marne, France
Contact address, telephone and e-mail address of the submitting author:
Anna Scotto di Santolo,
University of Naples Federico II, Hydraulic, Geotechnical and Environmental Engineering, Naples, Italy
Via Claudio 21, 80125 Naples, ITaly
e-mail: anscotto@unina.it
tel : +39 081 7683543
Number of words in main text: 6031; number of table: 1; number of illustrations: 8.
Cover Letter
We thank again the referee for his/her work. Taking into account all his/her comments
made it possible to improve further the manuscript.
Abstract
True. We deleted the sentence part “due to rainfall”.
1. Introduction
The sentence has been deleted.
We have added e.g. Laigle
The meaning is common.
Pag. 3 references:
We have added some reference
Pag. 4. yes
Pag. 5 We have added some reference:
2. Investigated pyroclastic material
Pag 5 They are the data of the landslides: we have added “occurred on”
Pag 6 We clarified the sentence and added a sentence.
3.1 Rheometerical tests
is this the first application of this approach to this type of material and processes?
As far as we know the first was in Scotto di Santolo et al 2009
not yet defined : We added some explanation in the text why? any reason? Because the possible correction to data in the case of yield stress fluids
has generally a minor effect on the shape of the flow curve. We added this explanation.
sweep test
at the maximum stress value
3.2 Incline plane
can you give any range of values for the thickness and its deviation?
We added this text : The measured thickness ranged from 0.5 to 20mm, and the maximum
deviation observed in the series of measurements for one test was 1mm.
4. Behaviour evolution with the solid fraction
*Response to Reviewer and Editor CommentsClick here to download Response to Reviewer and Editor Comments: Scotto_di_Santolo_Answers_to_Referees_2.doc
references?
It a quite obvious result that dense particles sedimentate in water, as long as they are not
packed to each other. So we do not think necessary to find a reference for that.
in which time interval? This is not a question of velocity here, but of displacement, so there is no time interval to
specify.
why?
Because the circumstances were such that we had not a sufficient amount of the appropriate sieved sample in hand at the time we realized it was useful to make this test.
unclear how this values has been measured?
We added this explanation: The current solid fraction is computed by assuming that the
total sample amount has simply been reduced of the solid front displacement length to
the container height ratio.
5. Rheometer results
5.1 Sweep tests
tco or tau co?
tc1 and tc2
5.3 does this agree with findings from other authors?
Yes we added two references about that.
We corrected various points in the rest of the manuscript in agreement with the referee’s comments.
In particular we removed the non accessible Italian references.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
1
ABSTRACT
An experimental study of the rheological behavior of three natural pyroclastic soils with
different depositional processes remixed with water was carried out with the help of a
rotational rheometer and inclined plane tests. A homogeneous fluid-like behavior is obtained
only within a very narrow range of concentrations, typically not more than 10%. Below this
range the material sedimentates rapidly, above this range it behaves like a solid. In the fluid-
like range the typical rheological behavior of these suspensions is that of a yield stress fluid
exhibiting a static yield stress larger than its dynamic yield stress. This effect likely finds its
origin in a “local” sedimentation effect, i.e. the particles sedimentate just as necessary to
form a structure more jammed than the structure during flow. As a result the flow of such
materials is usually unstable: they will start to flow beyond a critical stress but just beyond
this value will reach a high shear rate associated with a high flowing velocity. The static and
dynamic yield stresses of these materials widely increase from very low to very large values
(several orders of magnitude). Inclined plane tests were shown to provide reasonable though
still approximate values for the static and dynamic yield stresses. These results suggest that
in the field a small change in solid fraction will cause a slight decrease of the static yield
stress, readily inducing a rapid flow which will stop only when the dynamic yield stress is
reached, namely on a much smoother slope. This can explain the in situ observed post-
failure behaviour of pyroclastic debris flows, which are able to flow over very long distances
even on smooth slopes.
Main TextClick here to download Main Text: Scotto di Santolo Text R2.doc
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
2
List of notations:
GS the specific gravity of soil particles
γd dry weight of soil per unit volume
γ total weight of soil per unit volume
n the porosity
Sr the degree of saturation.
the solid concentration
TV the total volume of the sample
SVthe volume of solid in the sample
1R the blade radius of the vane
L the blade height of the vane
2R the radius of the cylindrical cup in which the vane is immersed
the shear stress
the shear rate
the angular velocity
T the torque
0hthe initial layer thickness of the sample in the inclined plane test
ci the critical angle in the inclined plane test
fhthe final layer thickness of the sample in the inclined plane test
the volume fraction
1 the lower bound of the volume fraction
2 the upper bound of the volume fraction
c the yield stress
1c the static yield stress
2c the dynamic yield stress
B the Bingham viscosity
the soil density
i the plane slope in the inclined plane test
g the acceleration due to gravity
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
3
List of three Keywords: pyroclastic soils, yield stress, instability
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
4
1. INTRODUCTION
A significant part of the world’s surface is covered by pyroclastic deposits generated by
the explosive activity of volcanoes. Such materials cover both flat and sloping areas,
reaching thicknesses up to many tens of metres. For example, the Campania region is
covered by pyroclastic deposits generated by different volcanic centres, the most famous of
which are the Phlegrean Fields and the Somma-Vesuvius, which are still active inside the
so-called Campanian Volcanic Zone. The cover is cohesionless and poses severe slope
stability problems. As a result of the ceaseless growth and spreading of urbanised areas and
infrastructures, the risk of landslides increased enormously, as testified by hundreds of
victims of flowslides in the last fifty years (e.g. Scotto di Santolo, 2002; Cascini and
Sorbino, 2003) with the most catastrophic event of 1998 which made more than 150 victims
(Del Prete et al., 1998; Crosta and Dal Negro, 2003). Despite the relevance of the problem, a
comprehensive geotechnical classification of these deposits is still lacking. There are other
regions throughout the world which are severely affected by this kind of problem, such as
the lahars of very large volumes which occurred during 6 years at several tens of kilometres
from the Pinatubo following its eruption in 1991 (van Westen and Daag, 2005).
Although the soil characteristics have already been explored (Picarelli et al., 2007) there
are almost no studies focused on the properties of the “post-failure” material, i.e. the rapidly
moving material as a result of some kind of liquefaction. Within the frame of a fluid
mechanics treatment the rheological characteristics of the flowing material would be useful
for better understanding the flow characteristics of such events. Rheological models thus
obtained may indeed be input in numerical simulations to predict the characteristics of
debris flow events and map hazard areas (e.g. Laigle et al., 2003; Rickenmann et al., 2006).
Here we assume that we can get interesting information in that field by studying the
rheological characteristics of a dry soil re-mixed with different amounts of water.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
5
Such an approach is in fact similar to what has generally been done for debris flows or
mudflows occurring in ordinary mountains streams. In that case typical materials contain
water, clay, silt, sand and pebbles in various relative fractions. Initially two very different
approaches were developed for the rheology of debris flows. The first one (Takahashi,
2007), relying on the suggestion of Bagnold (1954) assumed that the granular character was
predominant, with lubricated interactions at low shear rates and collisions at sufficiently
high shear rates inducing in that case a stress varying with the square of the shear rate. The
second one (Johnson and Rodine, 1984) assumed that the frictional or colloidal interactions
were dominant so that the basic property of a debris was considered to be its yield stress.
This approach has the advantage to provide a straightforward explanation to the shape of
materials deposits over steep slopes after flow stoppage. Various works went into this
approach in depth (see the review in Coussot, 1997).
Nevertheless the determination of the rheological properties of debris flow material
remains a difficult subject. Specific rheometers have been developed (Phillips and Davies,
1991; Major and Pierson 1992; Coussot and Piau 1995; Schatzmann et al., 2009) but
measurements on large volumes of suspensions including coarse dense particles implies
many experimental artefacts such as migration, sedimentation, wall slip, heterogeneities, etc.
Note that the same problematic exists in the field of concrete rheology. In addition there is
still some difficulty to deduce the behavior of the complete material containing sometimes
particles up to a few meters large from measurements with particles smaller than a few
millimetres. In addition, Iverson (1997) showed the possible role of interstitial pressure
within flowing granular suspensions. This indicates that there might be a need for different
models associated with different material types. The problem to identify the appropriate
model and to determine its parameters for natural flows led some people to consider that
empirical approaches may be more appropriate (Hungr, 1995; Rickenmann, 1999; Scotto di
Santolo & Evangelista, 2009). There was some attempt of clarification and classification in
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
6
Coussot (1996) but this was only a preliminary work. More recent works have for example
shown that granular debris flow materials (with a low clay fraction) may be considered at
first sight as simple yield stress fluids but in fact exhibit some original flow curve with a
minimum which is the hallmark of some flow instability (Sosio and Crosta, 2009).
Actually we can remark that, whatever the material type, we are dealing with a mixture of
water and grains of different sizes. As a consequence, it is relevant to overview our current
knowledge of the behavior of such materials in the field of physics and in particular recent
progress in that field. In the absence of sedimentation suspensions of non colloidal particles
in a Newtonian liquid are Newtonian as long as the concentration is not close to the
maximum packing fraction with a viscosity increasing with the solid fraction. Around the
maximum packing fraction the rheological behavior is much more complex due to the
possibility of lubrication, frictional and migration effects (Ancey and Coussot, 1999; Huang
et al., 2005; Ovarlez et al., 2006). Roughly speaking we are dealing with a material which
may behave like a simple yield stress fluid at low shear rates (when interparticle contacts
dominate) and like a simple liquid if the particles have just been well dispersed. With very
small particles another effect may occur, namely shear thickening, in which the material
behaves like a Newtonian fluid up to a critical shear rate at which the viscosity diverges
(Fall et al., 2009). this effect seems to find its origin in that at a sufficiently high shear rate
the particles have not enough time to rearrange and facilitate the flow so that the structure
tends to jam.
On the other side we have colloidal suspensions for which particles develop interactions
at distance within the liquid. Clay suspensions are typical examples of such materials. When
the interactions are relatively low the suspension behaves as a simple yield stress fluid
without significant thixotropic effect (e.g. kaolin suspensions). When there are strong
attractive colloidal attractions the suspension is significantly thixotropic so that its apparent
yield stress increases with the time at rest (Mewis and Wagner, 2009). This effect was
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
7
shown to be associated with shear-banding (Ovarlez et al., 2009). In fact it was shown that
shear-banding is a very common property of concentrated suspensions of various types. It
was even shown to occur in suspensions of non-colloidal grains (Fall et al., 2009).
Recently there has also been significant progress in the field of dry granular flows. It was
in particular shown that it is possible to describe complex flows at moderate velocities with
the help of a “frictional” model (GDR Midi, 2004; Jop et al., 2008), which couples the usual
yield stress model form with a Coulombian property, i.e. yield stress proportional to the
normal stress.
The rheological behaviour of pyroclastic deposits remixed with water has not been
studied often (e.g. Iverson and Vallance, 2001). From preliminary rheometrical tests Scotto
di Santolo et al. (2009) found that they behave as a non-Newtonian fluid with a yield stress
varying with the solid concentration. In this paper we report results of more detailed
rheological experiments on three pyroclastic deposits. We determine the flow curves of
these materials from sweep tests. We show that each material exhibit a static yield stress,
associated with flow start, significantly larger than the dynamic yield stress, associated with
flow stoppage. This means that there is an hysteresis in the flow curve, associated with some
flow instability and likely shear-band below a critical shear rate. We also compare the
results obtained from conventional rheometry and from inclined plane tests.
2. INVESTIGATED PYROCLASTIC MATERIALS
The materials tested were collected from the source area of three debris flows in the
Campania region (southern Italy). Material I was sampled in Nocera, Salerno (occurred on
March 2005). Material II was from Monteforte Irpino, Avellino (occurred on May 1998).
Material III was from Astroni, Naples (occurred on December 2005). The soil type, in a
thickness of about a metre, depends on the most recent pyroclastic deposits deriving from
the volcanic activity of Mount Somma/Vesuvius for materials I and II and from the volcanic
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
8
activity of the Phlegrean Fields for material III. The grain size distributions of the collected
samples are reported in Figure 1. Soil I and soil II are sandy silt with a small clay fraction,
and soil III is gravely silty sand. The bedrock underlying the soil is volcanic tuff for material
III and limestone for materials I and II. Main physical properties are reported in Table 1.
In order to respect at best the continuum assumption it is necessary to have a material
thickness during rheometrical tests much larger than the particle size in the material. Here
the material thickness was larger than 5 mm. As a consequence, we chose to perform tests
on the soil fraction with a particle diameter less than 0.5 mm. The ratio of the material
thickness to the maximum particle size was thus larger than 10 but it grows up to almost 100
if one uses the mean particle diameter (about 0.06 mm). These conditions are expected to be
sufficient for the continuum assumption to be valid. Doing so we keep about 50 to 70% of
the whole grain size distribution, as shown in Figure 1. Since the rest of the particles which
are contained in the whole material are not colloidal, when they are mixed with the paste to
get the complete mixture they can be expected to essentially increase the values of the
rheological parameters but do not affect the behaviour type. Thus, we believe that if we were
working with the whole mixtures we would get similar qualitative trends as described below
but in different ranges of solid fractions for the fluid-like region identified in Section 4.
We carried out all experiments with mixtures of dry soils with different amounts of water.
The solid concentration is described with the help of the solid volume fraction , i.e., the
ratio of the volume of solids, SV, to the total volume TV (water plus solids) of the sample,
defined as TS VV. This parameter is preferred to a weight fraction as it gives a more
straightforward indication of the way the solid particles are jammed or dispersed in water,
and it thus provides relevant information for a comparison between materials of different
types.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
9
For each material tested, we prepared material mixtures of about 500 ml, mixing soils and
distilled water with an electronic mixer (at about 30 rpm) for 15 minutes. Then we used a
sample volume of about 30 ml for each test at a constant temperature (23°C).
3. EXPERIMENTAL PROCEDURES
3.1 Rheometrical tests
We used a rotational rheometer CVOR (Bohlin Instruments) equipped with a vane rotor
geometry system, which consists of four thin blades arranged at equal angles around a small
cylindrical shaft. The blade radius was 1R =13 mm, and the blade height was L 48 mm.
The vane rotor was immersed in the sample (the sample volume was roughly 27 ml)
contained in a cylindrical cup of radius 2R 18.5 mm. During the test, a part of the material
is trapped in the blades so that as a first approximation the flow characteristics are similar to
those between two solid coaxial cylinders, with the inner radius equal to that of the blade
(Nguyen and Boger, 1985). The interest of this geometry is that no slip at the inner wall may
be feared since there is no solid-paste interface. In that case, under usual assumptions (no
inertia effects, negligible normal stress differences) one can estimate the shear stress and
the shear rate within the material from the following formulae:
)( 121 RRR and LRT2
12 . Note that these equations neglect the stress
heterogeneity which leads to a heterogeneity of the shear rate within the rheometer gap,
namely the stress decreases with the distance from the center. The consequence is that there
is some uncertainty on the exact value of the shear rate when using the above equation for
the shear rate. This effect is especially critical at low shear rates. However this does not
affect significantly the qualitative shape of the flow curves and the critical stress levels:
indeed the stress plateau values associated with the yielding behavior (see below) are not
affected by this problem. Within the frame of this study it did not seem useful to be more
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
10
precise because the possible correction to data in the case of yield stress fluids has generally
a minor effect on the shape of the flow curve. We can also define the deformation undergone
by the material from the initial time: at time t , it is equal to t
dt
0
.
We mainly carried out stress sweep tests which consist to measure the apparent flow
curves by applying an increasing-decreasing shear stress ramp. In such tests the shear stress
was continuously increased in a logarithmic way from 0.1 Pa to a large (maximum) value,
and the corresponding shear rate measured. The maximum stress value was specifically
determined for each sample from independent (rheometrical) tests under similar technical
conditions so as to get a fast flow in the liquid regime without fluid expulsion out of the
geometry. Then the shear stress was decreased down to the initial value following exactly
the same stress path. The total duration of this sweep was 120s.
The complete procedure consists to set up the material inside the geometry and
immediately impose a preshear at the maximum stress value above described during 30
seconds, then start the sweep test. It is hoped that this preshear homogenizes the sample. In
some cases (mentioned below) the material was left at rest some time between the end of
preshear and the beginning of the sweep test.
Some creep tests were also carried out, which consist to impose a constant stress and
measure the induced deformation of the material in time. Deformation is expressed in terms
of angle of rotation of the inner cylinder since the initial time of application of the stress. A
complete test consists to impose various values of stress, preparing again each sample in the
same initial state before each new stress value.
3.2 Inclined plane tests
The inclined plane test consists to analyze the fluid depth over an inclined plane in
rheological terms. The mixture was first spilled on a horizontal rough plane in order to
obtain a wide layer of material. Then a very thin graduated ruler was inserted into the fluid
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
11
at different places in the central region of the layer, say at a distance of the edges larger than
3 times the thickness. The initial layer thickness ( 0h) was computed as the average of about
ten such measures. Then the plane was progressively inclined until a critical angle ( ci ) for
which we could observe a significant motion of the layer front. Then we wait for the full
stoppage of the material over this slope and we measure the final thickness ( fh) according to
the same procedure as above. The measured thickness ranged from 0.5 to 20mm, and the
maximum deviation observed in the series of measurements for one test was 1mm. The test
duration, from the initial spreading to the end of the final one was less than 3 min.
4. BEHAVIOUR EVOLUTION WITH SOLID FRACTION
4.1 Three different possible material states
The first step of our study was to have an overview of the behavior of our materials as a
function of the solid concentration, in order to identify the range of concentrations in which
they may be considered as fluids and thus characterized with usual rheological tools. Three
different possible states appeared.
For sufficiently low solid volume fractions ( 1 , see the values for 1 below), the particles
rapidly (within a few seconds) settle down, leading to an apparent phase separation. This
comes from the fact that in this situation the suspended particles, which are much denser
than water, do not interact at distance via colloidal interactions (or these interactions are
negligible at such distances). There is thus no force to counterbalance the action of gravity
force until the particles are packed to each other at the bottom of the container. As a
consequence, in the very first instants after preparation, i.e. when the particles are still
dispersed in water and the concentration is approximately homogeneous, the system
certainly exhibits an apparent Newtonian behavior described by the usual theories for
suspensions of non-colloidal particles (see a review in Coussot, 2005). We were obviously
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
12
unable to carry out rheometrical tests with such materials but for solid fractions in the ranges
defined below these theories predict a viscosity of the order of few times that of pure water.
When the particles have settled, we are no longer dealing with a homogeneous material, and
nothing can be said about its viscosity.
For high volume fractions ( 2 ), the suspension obtained is in fact a kind of paste of high
strength, which easily breaks like a solid when it is deformed. Such a material cannot be
considered as a fluid able to undergo reversible large deformations without changing its
basic properties. We were also unable to carry out with such materials rheometrical tests
appropriate for fluids.
For intermediate volume fractions ( 21 ), we could observe some slight sedimentation
after significantly longer times of rest, say typically of the order of 10 min. The material thus
remains homogeneous over a reasonable time of observation and can flow like a liquid. This
is in these “fluid-like” intervals 21; that studied the rheological behaviour of our
materials. In the next Section we discuss in more details the possible impact of this
sedimentation on measurements.
The lower bound 1 is 32% for material I, 30% for material II and 35% for material III. In
general, for non-colloidal grains much denser than water, sedimentation occurs rapidly as
long as the solid fraction is smaller than the maximum packing fraction. We emphasize that
in our case the values for 1 are significantly lower than the maximum packing fraction of
non-colloidal grains, which is typically of the order of 60% for uniform spheres and
increases above this value when the grain size distribution is widened. This means that there
are likely some slight colloidal interactions, acting at relatively short distances, between
some of the solid particles in our materials, which can counterbalance the settling tendency
and make smaller the apparent maximum packing fraction before getting a solid.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
13
The upper bound 2 is 42% for material I, 38% for material II and 42% for material III.
Surprisingly, the range of solid concentrations in which the material mixtures can be
considered as “fluid-like” is rather narrow for each material tested. This contrasts with clay-
water systems, for example, for which one may get homogeneous fluids in a range from one
percent to several tens of percents.
4.2 Impact of sedimentation
In order to evaluate the impact of sedimentation on the rheometrical tests we performed an
experiment providing an estimation of the characteristic time of sedimentation. We put a
sample in a graduated cylinder (with a volume of 250 ml) and observed the aspect of the
fluid in time. As usual with concentrated suspensions sedimentation leads to the formation
of a region of transparent water at the top of the sample above a non-transparent region of
material containing all the solid particles. It is generally considered that in this process the
solid particles sedimentate more or less in mass through the liquid independently of their
size, as a result of a collective effect. As a consequence it is relevant to follow the
displacement of the pure water-concentrated suspension interface in time, which gives an
indication of the increase of solid concentration within the bottom region. Note that this is a
“macroscopic sedimentation” effect that we can observe here: if the particles move of a
distance proportional to the height above the container bottom the displacement of most of
them is much larger than their size.
It appears that the sedimentation process within Material II only starts to be significant after
a time of the order of 3 min (see Figure 2), i.e. the interface remains close to the free surface
of the sample during that time. Then the interface starts to move downward significantly.
We unfortunately could not carry out this test with material I but our qualitative observations
in particular during the preparation of the material strongly suggest that its behaviour is very
similar to that of Material II. As a consequence, since the duration of rheometrical and
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
14
inclined plane tests is smaller than 3 min we believe that macroscopic sedimentation with
Materials I and II did not affect our results.
Material III exhibits a different behaviour: macroscopic sedimentation starts as soon as the
fluid has been put inside the container (as may be seen from Figure 2). The current solid
fraction is computed by assuming that the total sample amount has simply been reduced of
the solid front displacement length to the container height ratio. After 3 min the variation is
such that the mean solid fraction within the material below the interface has been increased
by a factor of the order of 1.1, which constitutes a very significant variation within the
range 21; . As a consequence the impact of macroscopic sedimentation during a
rheometrical test for material III may be significant.
5. RHEOMETRY: RESULTS AND DISCUSSION
5.1 Sweep tests
Typical results of sweep test are shown in Figure 3. Note that we removed data points for
shear rate estimated from measurements of too small deformations over the usual time step
and thus leading to a large uncertainty. In our results, for increasing stress, there is first an
apparent flow curve rapidly increasing with shear rate, with a slope of about 1 (see for
example the curve part on the bottom left in Figure 3). Actually this does not correspond to a
flow of the material in its liquid regime. This part of the curve varies with the timing for
stress increase, and the total deformation undergone by the material is very low. The rest of
the flow curve is supposed to correspond to the material behaviour in the liquid regime: the
transition to the liquid regime is associated with the rapid increase of the shear rate at some
critical value (stress plateau) of the stress. At larger stresses, the curve slope increases (on a
logarithmic scale) and seems to approach a straight line of slope 1. The plateau thus obtained
for the stress increase is associated with the static yield stress ( 1c ) of the material.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
15
For decreasing stress the curve falls along the increasing curve only down to some shear rate
value. Then the decreasing curve is below the increasing curve and follows approximately a
stress plateau until flow stoppage.
Thus the decreasing curve differs significantly from the increasing curve; there is a
hysteresis. This trend is more marked for high solid fractions (see Figure 3): in that case the
initial stress plateau associated with the solid-liquid transition is almost perfectly horizontal
and the increasing and decreasing parts of the curves well superimpose over a range of shear
rates which exactly starts at the end of the plateau. For lower solid fractions this effect is less
marked: the stress “plateaus” are not horizontal and the transition to the liquid regime in the
increasing curve does not correspond exactly to the range of good superimposition of the
increasing and decreasing curves. In that case obviously our estimation of the static ( 1c ) and
dynamic ( 2c ) yield stress values are more approximate. The method for estimating the
static and dynamic yield stress values and the critical shear rate are as follows: the static
yield stress is associated with the inflexion point in the increasing stress curve; the dynamic
yield stress is taken where the decreasing stress curve tends to a plateau before decreasing
faster at very low shear rates, this slight stress decrease at low shear rates being likely due to
artifacts.
5.2 Thixotropy
The hysteresis found in our sweep tests are reminiscent of thixotropic effects for colloidal
suspensions. The material is initially in some structured state associated with some apparent
yield stress; after flow at large velocities the material is destructured so that its apparent
yield stress for flow stoppage is smaller than the static yield stress. Note that here, although
there is no time of rest after preshear, the time needed to increase the stress from 0.1 Pa to
the static yield stress (between 30 and 60 seconds depending on material) might allow some
restructuration of the material in its solid regime. In order to clarify this aspect we carried
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
16
out tests by leaving the material at different times of rest between the end of preshear and
the beginning of the stress ramp. We observe that for Material I and Material II the impact of
a time of rest up to 300s on the apparent static yield stress was negligible: within the
uncertainty on our measurements (say typically 10%) there was no observable change of the
static yield stress with the time of rest. This is in contradiction with a usual thixotropic
character, which basically implies an increase of the static yield stress with the time of rest.
This means that for these materials the hysteresis observed in our standard sweep tests does
not find its origin in a thixotropic effect.
On the contrary, for Material III and for each solid fraction within 21; we observed a
significant variation of the static yield stress with the time of rest (see Figure 4), while the
decreasing curve remains independent of the time of rest. These trends are fully consistent
with a thixotropic behavior: qualitatively similar trends were for example observed with
well-known thixotropic materials (bentonite suspensions) (Coussot, 2005). However,
considering that for this material sedimentation is significant over a time scale of a few
minutes we believe that these effects are due to macroscopic sedimentation: as the time of
rest increases the material becomes more concentrated in the bottom layers and exhibits a
higher global strength; during a flow at a high shear rate the material is “resuspended” (i.e.
the solid particles are re-dispersed homogeneously). This explanation also seems consistent
with the observation that the time of rest has no impact on the hysteresis for Materials I and
II which precisely do not exhibit sedimentation over a time scale of a few minutes (see
Section 4.2).
5.3 Further interpretation of results
In our context it is natural to consider that the hysteresis effect observed for Material I and II
is in some way related to the particulate character of the fluids which leads to macroscopic
sedimentation. A recent work (Fall et al., 2009) focused on the behavior of model
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
17
concentrated granular suspensions exhibiting similar characteristics suggests that there may
be a “local sedimentation” effect which takes place over very short time scales and which, in
contrast with macroscopic sedimentation, does not yield macroscopic density
heterogeneities. This is due to the fact that, as a result of gravity, particles denser than the
interstitial liquid may enter in contact and even locally jam after a short displacement of the
order of the particle size. In this recent work (Fall et al., 2009) an inspection of the flow
characteristics inside the materials also showed that they exhibit a critical shear rate below
which they cannot flow steadily, an effect leading to shear-banding when an apparent shear
rate is imposed below this value (Ovarlez et al., 2009).
We believe that with our materials we have here the same trends: the static yield stress
corresponds to the stress needed to unjam the locally settled structure, then the dispersed
suspension flows more easily. In consistence with this scheme we expect that along the
stress plateau associated with the static yield stress the material shear-bands and starts to
flow homogeneously only beyond the critical shear rate marking the end of this plateau.
obviously this description is more approximate for low concentrations when the plateaus are
less clear.
This description also seems consistent with data from creep tests. Indeed we observe that
for stresses lower than some critical stress the deformation vs time curve remains concave
with a slope continuously decreasing in time on a logarithmic scale and exhibits an apparent
horizontal asymptote. Thus, the deformation seems to be limited, and the instantaneous
shear rate continuously decreases to lower values, so that no steady state is reached. Finally,
the material apparently stops moving. This should correspond to the solid regime of the
material. For stress values higher than the critical value the initial slope of the curve is
similar to that under smaller stresses, but after some time, there is an inflection point, and
the curves tend to reach an inclined straight line gradually with a slope equal to 1. In that
case, the deformation increases at a constant rate, which means that the apparent shear rate is
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
18
constant, and a steady state flow has been reached. These curves correspond to the liquid
regime of the material, as is usually observed for simple yield stress fluids (Coussot et al.,
2006). However the transition from the solid to the liquid regime is abrupt (see Figure 5):
For a stress just above the yield stress, the material rapidly reaches a shear rate level that is
relatively high (typically on the order of or larger than 1 s-1
). This suggests some viscosity
bifurcation effect associated again with a critical shear rate below which no steady flow can
be observed, as was already observed for colloidal thixotropic materials (Coussot et al.,
2002). Note that the apparent critical shear rate may depend on the flow history, which can
explain a slight difference between the value deduced from Figure 5 and that found from our
specific procedure for sweep tests.
The important consequence of these results is that the flow of such materials is unstable:
when a stress is imposed while they are at rest they will not flow until the static yield stress
has been reached and just beyond this value will soon flow at a shear rate larger than the
critical shear rate, so that in practice the apparent velocity will be large. Then if the stress is
progressively decreased they will go on flowing and will stop only when the dynamic yield
stress is reached. This contrasts with simple yield stress fluid (identical static and dynamic
yield stress) for which there is a smooth increase of the shear rate (and thus the velocity)
with the increasing stress above the yield stress, and a stoppage as soon as the applied stress
falls below the yield stress.
5.4 Behavior evolution with solid fraction
It is especially interesting to look at the variations of the static and dynamic yield stresses
with the solid fraction (see Figure 6). We see that for each material the two yield stresses
increase in a similar way with solid fraction, the two sets of data being simply identical by a
vertical translation by a constant factor (between 1.4 and 2). Moreover the variations of one
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
19
yield stress type with solid fraction for the different materials are roughly similar. The
straight lines of Figure 6, which roughly follow the increase of these different parameters
with solid fraction are almost identical. The impressive point is that the yield stresses
increase by two orders of magnitude over the very narrow range of concentration (less than
10%) in which they behave as homogeneous fluids. This finally ensures some continuity
between the range (below 1 ) for which the material is apparently a simple liquid (just after
homogenization) and the range (above 2 ) for which the material is a solid. Also note that
the critical shear rate increases more or less like the yield stress, which implies that as the
solid fraction increases the material strength increases but its apparent velocity when it starts
to flow increases proportionally.
Note that as for usual yield stress fluids a Herschel-Bulkley model may be fitted to the flow
curve obtained for decreasing stress. However it is interesting to remark that the flow curve
at large shear rates seems to tend to a straight line of slope 1, as if the material was tending
to a Newtonian fluid. As a consequence we thought appropriate to simplify the problem and
fit a Bingham model to our flow curves (the decreasing part) (see Figure 3):
Bc 2 .
In some cases the fit is not perfect but this has the strong interest to introduce only one new
rheological parameter. It is worth noting that for all material types the Bingham viscosity
increases in the same way along the fluid-like solid fraction range. This is illustrated by the
fact that all the data fall along a single straight line when the Bingham viscosity is plotted as
a function of the solid fraction scaled by the lower bound of the solid fraction range (see
Figure 7). Finally, the fact that the stress is the sum of a yielding term and a simple viscous
term suggests that there is a kind of liquefaction beyond the yielding, so that the viscous
stress is essentially due to the shear flow of a Newtonian concentrated suspension. However
we have no explanation for the variation of this Bingham viscosity as a function of the solid
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
20
fraction. It indeed strongly depends on the grain configuration within the flowing granular
suspension.
6. INCLINED PLANE RESULTS
Under the usual so-called “lubrication assumption”, i.e., that the material thickness ( h ) is
much smaller than its longitudinal extent (see, e.g., Coussot, 2005), so that the velocity
components parallel to the solid plane are the dominant ones, and in the absence of inertia
effects, a simple momentum balance provides the shear stress distribution within the
material. In particular, it follows that the wall shear stress is given as igh sin , in which
is the soil density, i the plane slope and g the acceleration due to gravity. As a consequence
we can interpret the flow start at a critical slope as a measure of the static yield stress:
cc igh sin01 . Also the flow stoppage over the inclined plane can be interpreted as a
measure of the dynamic yield stress: cfc igh sin2 . Note that for material III a significant
sedimentation occurred during the tests, leading to a material apparently unable to flow like
a fluid over the inclined plane. So we do not report any corresponding data.
In Figure 8 we compare the data obtained from inclined plane tests with those obtained
from rheometry (sweep tests) for the different yield stresses. We see that as a first
approximation the data obtained with the different techniques are consistent: the data are
globally around the identity line. However on average the inclined plane data are situated
above the rheometrical data by a significant factor of about 1.4. This means that the inclined
plane test can provide an overestimate of the value of the yield stress, which nevertheless
varies in the same way with the solid fraction.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
21
7. CONCLUSION
We have studied the rheological behavior of three natural pyroclastic soils with different
depositional processes remixed with water. A homogeneous fluid-like behavior is obtained
only within a very narrow range of concentrations, typically not more than 10%. Below this
range the material sedimentates rapidly and soon becomes heterogeneous. Above this range
it behaves more like a solid, which breaks beyond a critical stress. In the fluid range there is
still some (macroscopic) sedimentation but with a characteristic time larger than the duration
of rheometrical tests so that its impact is negligible. The typical rheological behavior of
these suspensions is that of a yield stress fluid exhibiting a static yield stress larger than its
dynamic yield stress. This effect likely finds its origin in a “local” sedimentation effect, i.e.
the particles sedimentates just as necessary to form a structure more jammed than the
structure during flow. As a result the flow of such materials are usually unstable: they will
start to flow beyond a critical stress but just beyond this value will reach a high shear rate
associated with a high flowing velocity. At last it was shown that in the fluid range of solid
fractions the yield stresses widely increase from very low to very large values (several
orders of magnitude).
Besides we also showed that the inclined plane test provides reasonable though still
approximate values for the static and dynamic yield stresses. This consistency also implies
that in the field the conditions for incipient flow over steep slopes can be well described
from the knowledge of the static yield stress, the flow characteristics can be well described
with the decreasing stress flow curve and in particular the flow stoppage conditions can be
described with the dynamic yield stress.
These results suggest that in the field a small change in solid fraction, due to rainfall for
instance, will cause a slight decrease of the static yield stress, inducing a flow rapidly
reaching a shear rate larger than the critical shear rate associated with a rapid flow. Then,
since the dynamic yield stress is significantly smaller than the static yield stress the flow will
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
22
stop only when the material reaches a much smoother slope. This might explain the in situ
observed post-failure behaviour of pyroclastic debris flows, which are able to flow over very
long distances even over smooth slopes.
References
Ancey, C. and Coussot, P. (1999). Frictional-viscous transition for concentrated suspensions. C.R. Acad. Sci.,
Paris 327, 515-522.
Bagnold, R.A. (1954). Experiment on a gravity-free dispersion of large solid sphere in a Newtonian fluid under
shear. Proc. of The Royal Society London, Series A, 49-63.
Cascini, L. and Sorbino, G. (2003). The contribution of soil suction measurements to the analysis of flowslide
triggering. Proc. Int. Workshop on Occurrence and Mechanisms of Flows in Natural Slopes and Earthfills –
IW-Flows2003, Sorrento, 77-86.
Coussot, P. and Meunier, M. (1996). Recognition, classification and mechanical description of debris flows.
Earth-Science Reviews 40, 209-227.
Coussot, P. (1997). Mudflow Rheology and Dynamics. IAHR Monograph Series, Rotterdam: A.A. Balkema.
Coussot, P., Laigle, D., Arattano, M., Deganutti, A.M. and Marchi, L. (1998). Direct determination of
rheological characteristics of debris flow. J of Hydraulic Engineering 124, 865-868.
Coussot, P. (2005). Rheometry of Pastes, Suspensions and granular materials: Application in Industry and
Environment. New York: John Wiley & Sons, Inc., Publications.
Coussot, P., and Piau, J.M. (1995). A large-scale field coaxial cylinder rheometer for the study of the rheology
of natural coarse suspensions. J. Rheol. 39, 105-124.
Coussot, P., Nguyen, Q.D., Huynh, H.T., and Bonn, D., (2002). Avalanche behavior in yield stress fluids,
Physical Review Letters 88, 175501.
Coussot, P. Tabuteau, H., Chateau, X., Tocquer, L., and Ovarlez, G., (2006). Aging and solid or liquid
behavior in pastes. J. Rheol. 50, 975-994.
Crosta, G.B., and Dal Negro, P. (2003). Observations and modelling of soil slip-debris flow initiation
processes in pyroclastic deposits: the Sarno 1998 event. Natural Hazards and Earth System Sciences 3, 53-
69.
Del Prete, M., Guadagno, F.M., Hawkins, A.B. (1998). Preliminary report on the landslides of 5th
May 1998,
Campania, Southern Italy. Bull. Eng. Geol. Environ. 57, 113-129.
Fall, A., Bertrand, F., Ovarlez, G., Bonn, D. (2009). Yield stress and shear-banding in granular suspensions.
Physical Review Letters 103, 178301.
GDR Midi. (2004). On dense granular flows. European Physical Journal E. 14, 367-371.
Huang, N., Ovarlez, G., Bertrand, F., Rodts, S., Coussot, P., Bonn, D. (2005). Flow of wet granular materials.
Physical Review Letters 94, 028301.
Iverson, R.M. (1997). The physics of debris flow. Reviews of Geophysics 35, 245-296.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
23
Iverson, R.M. and Vallance, J.W. (2001). New views of granular mass flows. Geology 29, no. 2, 115–118.
Johnson, A.M. and Rodine, J.R. (1984). Debris flow. In: D. Brunsden and D.B. Prior (Editors), Slope
Instability. Ch.8, New York: Wiley.
Jop, P., Forterre, Y., Pouliquen, O. (2006). A constitutive law for dense granular flows. Nature 441, 727-730.
Laigle, D., Hector, A.F., Hübl, J., Rickenmann, D. (2003). Comparison of numerical simulation of muddy
debris-flow spreading to records of real events. Proc. 3rd
Int. Conf. Debris-Flow Hazards Mitigation, Davos,
Debris-Flow Hazard mitigation: mechanics, prediction and Assessment, 635-646.
Major, J.J. and Pierson, T.C. (1992). Debris flow rheology: Experimental analysis of fine-grained slurries.
Water Resources Research 28, 841-857.
Mewis, J. and Wagner, N.J. (2009). Thixotropy. Advances in Colloid and Interface Science 147-148, 214-227.
Nguyen, Q.D. and Boger, D.V. (1985). Direct yield stress measurement with the vane method. Journal of
Rheology 29, 335-347.
Ovarlez, G., Bertrand, F., Rodts, S. (2006). Local determination of the constitutive law of a dense suspension
of noncolloidal particles through MRI. Journal of Rheology 50, 259-292.
Ovarlez, G., Rodts, S., Chateau, X. and Coussot, P. (2009). Phenomenology and physical origin of shear
localization of the shear banding in complex fluids. Rheologica Acta 48, 831-844.
Phillips, C.J. and Davies, T.R.H. (1991). Determining rheological parameters of debris flow material.
Geomorphology 4, 101-110.
Picarelli, L., Evangelista, A., Rolandi, G., Paone, A., Nicotera, M.V., Olivares, L., Scotto di Santolo, A.,
Lampitiello, S. and Rolandi, M. (2007). Mechanical properties of pyroclastic soils in Campania Region.
Proc. Int. Workshop on Characterisation & Engineering Properties of Natural Soils, Singapore, 2331-2383.
Rickenmann, D. (1999). Empirical relationships for debris flows. Natural Hazards 19, 47-77.
Rickenmann, D., Laigle D., McArdell, B.W., Hubl, J. (2006). Comparison of 2D debris-flow simulation
models with field events. Computational Geosciences 10, 241-264.
Schatzmann, M., Bezzola, G.R., Minor, H.E., Windhab, E.J., Fischer, P. (2009). Rheometry for large-
particulated fluids: analysis of the ball measuring system and comparison to debris flow rheometry.
Rheologica Acta 48, 715-733.
Scotto di Santolo, A. (2002). Le colate rapide, 118, Benevento: Helvelius Edizioni.
Scotto di Santolo, A. and Evangelista, A. (2009). Some observations on the prediction of the dynamic
parameters of debris flows in pyroclastic deposits in the Campania, region of Italy. Journal of Natural
Hazards 50, 605-622.
Scotto di Santolo, A., Pellegrino, A. M. & Evangelista, A. (2009). Experimental study on the rheological
behaviour of debris flow material in Campania region. Proc. 5th Int. Conf. Computational and Experimental
Methods in Multiphase and Complex Flow, New Forest 1, 305-316.
Sosio, R. and Crosta, G.B. (2009). Rheology of concentrated granular suspensions and possible implications
for debris flow modelling. Water Resources Research 45, W03412.
Takahashi, T. (2007). Debris Flows: Mechanics, Prediction and Countermeasures. London: Taylor and
Francis.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
24
van Westen, C.J. and Daag, A.S. (2005). Analyzing the relation between rainfall characteristics and lahar
activity at Mount Pinatubo, Philippines. Earth Surface Processes and Landforms 30, 1663-1674.
Debris flow
Site Material
GS
γd
(kN/m3)
γ
(kN/m3)
n
Nocera (SA) I 2.61 9.08 11.35 0.66
Monteforte
Irpino (AV) II 2.57 7.11 12.11 0.71
Astroni (NA) III 2.53 8.99 9.84 0.67
Table 1: Main physical properties of the tested debris flow materials: GS is the specific gravity
of soil particles, γd and γ are the dry and total weight of soil per unit volume respectively, n is
the porosity.
TableClick here to download Table: Table 1_Scotto di Santolo.doc
List of figures:
Figure 1: Grain size distribution of our different materials.
Figure 2: Sedimentation in Material II (squares) and Material III (stars): height of the interface
between pure liquid and concentrated suspension as a function of time.
Figure 3: Sweep tests with Material I (a) at %38 (circles) and %42 (squares) and
Material II (b) at %32 (circles) and %38 (squares). The continuous line corresponds
to the Bingham fitted to data using the static yield stress value determined as described in the
text.
Figure 4: Apparent flow curves from sweep tests for Material III after different times of rest
following preshear: 5s (circles), 300s (stars), 1200s (squares).
Figure 5: Creep tests for Material III (40%). Deformation vs time for different stress levels:
(from bottom to top) 1, 3, 5, 7, 8, 10, 15, 20, 30, 40Pa.
Figure 6: Rheological characteristics of Material 1 (squares), Material 2 (diamond), and
Material 3 (circles) as a function of solid fraction: static yield stress (empty symbols), dynamic
yield stress (filled symbols), and critical shear rate (half-filled symbols). The straight lines are
guides for the eyes.
Figure 7: Bingham viscosity as a function of the ratio of solid fraction to the lower bound of
the fluid-like range for Material I (squares), Material II (diamonds), and Material III (circles).
Figure 8: Inclined plane static (empty symbols) and dynamic (filled symbols) yield stresses as
a function of the corresponding values determined from flow curves for Material 1 (squares)
and Material 2 (circles).
FigureClick here to download Figure: List of figures.doc
0
10
20
30
40
50
60
70
80
90
100
0,000 0,001 0,010 0,100 1,000 10,000 100,000
Particle diameter d (mm)
Pe
rce
nt fin
er
(%)
Material I
Material II
Material III
Clay Silt Sand Gravel
Figure 1: Grain size distribution of our different materials.
FigureClick here to download Figure: Figure 1_Scotto di Santolo.doc
100 101 102 103 1045
6
Inte
rface
pos
ition
(cm
)
Time (s)
5.5
FigureClick here to download Figure: Scotto di Santolo Fig 2.EPS
10-2 10-1 100 101 102
101
102
2c
1c
c
She
ar s
tress
(Pa)
Shear rate (1/s)
FigureClick here to download Figure: Scotto di Santolo Fig 3a.EPS
10-2 10-1 100 101 102
101
102
c
Shear rate (1/s)
She
ar s
tress
(Pa)
2c
1c
FigureClick here to download Figure: Scotto di Santolo Fig 3b.EPS
10-2 10-1 100 101 102
101
102
She
ar s
tress
(Pa)
Shear rate (1/s)
FigureClick here to download Figure: Scotto di Santolo Fig 4.EPS
10-1 100 101
10-2
10-1
100
101
102
Ang
le o
f rot
atio
n (r
ad)
Time (s)
FigureClick here to download Figure: Scotto di Santolo Fig 5.EPS
30 32 34 36 38 40 42
100
101
102
Yie
ld s
tress
(Pa)
and
Crit
ical
she
ar ra
te (1
/s)
Solid fraction (%)
FigureClick here to download Figure: Scotto di Santolo Fig 6.EPS
1,0 1,1 1,2 1,3
0
1
2 (Pa.s) B
1
FigureClick here to download Figure: Scotto di Santolo Fig 7.EPS
101 102
101
102
Incl
ined
pla
ne y
ield
stre
ss (P
a)
Flow curve yield stress (Pa)
FigureClick here to download Figure: Scotto di Santolo Fig 8.EPS