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

nicolas.roussel@lcpc.fr expert of rheology of suspensions Opposed Reviewers:

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.

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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

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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

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List of three Keywords: pyroclastic soils, yield stress, instability

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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.

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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

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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

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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

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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.

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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

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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

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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

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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.

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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

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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.

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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

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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

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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

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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

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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

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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.

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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

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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.

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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