experimental study on the rheological behaviour of debris ﬂow · gulf of naples gulf of salerno...

Nat Hazards Earth Syst Sci 10 2507ndash2514 2010wwwnat-hazards-earth-syst-scinet1025072010doi105194nhess-10-2507-2010copy Author(s) 2010 CC Attribution 30 License

Natural Hazardsand Earth

System Sciences

Experimental study on the rheological behaviour of debris flow

A Scotto di Santolo A M Pellegrino and A Evangelista

Department of Hydraulic Geotechnical and Environmental Engineering University of Naples ldquoFederico IIrdquo Italy

Received 27 December 2009 ndash Revised 29 August 2010 ndash Accepted 30 August 2010 ndash Published 7 December 2010

Abstract A model able to describe all the processes in-volved in a debris flow can be very complex owing to thesudden changing of the material that turns from solid intoliquid state The two phases of the phenomenon are analysedseparately referring to soil mechanics procedures with regardto the trigger phase and to an equivalent fluid for the post-failure phase The present paper is devoted to show the exper-imental results carried out to evaluate the behaviour assumedby a pyroclastic-derived soil during the flow A traditionalfluid tool has been utilized a standard rotational rheometerequipped with two different geometries The soils tested be-long to deposits that cover the slopes of the Campania regionItaly often affected by debris flows The influence of solidconcentrationCv and grain size distribution was tested thesoils were destructurated sieved and mixed with water start-ing from the in situ porosity All material mixtures showed anon-Newtonian fluid behaviour with a yield stressτy that in-creases with a solid volumetric concentration and decreasesfor an increase of sand fraction The experimental data werefitted with standard model for fluids A simple relation be-tweenCv andτy was obtained The yield stress seems to be akey parameter for describing and predicting the post-failurebehaviour of debris flows These results suggest that in thefield a small change in solid fraction due to rainfall willcause a slight decrease of the static yield stress readily in-ducing a rapid flow which will stop only when the dynamicyield stress is reached namely on a much smoother slopeThis can explain the in situ observed post-failure behaviourof debris flows which are able to flow over very long dis-tances even on smooth slopes

Correspondence toA Scotto di Santolo(anscottouninait)

1 Introduction

Debris flows represent serious hazards on the slopes of theNorth-western Campania region (southern Italy) Thereforethe evaluation of constitutive laws for the material involvedrepresents a key requirement for the hazard mitigation Tra-ditionally debris flows have been regarded as homogeneousfluids and flow behaviour has been considered to be con-trolled by the properties of the ldquomatrixrdquo a mixture of finesediment and water in which coarse particles are dispersed(Costa and Williams 1984 Johnson 1984) Existing physi-cal theories to describe flow and depositional process of de-bris flows are mainly divided into theories which are based onthe treatment of the material as one single phase (rheologicalapproaches) (OrsquoBrien and Julien 1984 Phillips and Davies1991 Major and Pierson 1992 Coussot and Piau 1994) oras two or more phases (Coulomb mixture approaches) (Sav-age and Hutter 1989 Iverson 1997) The Coulomb mix-ture approach specifies distinct constitutive equations for thesolid phase the liquid phase and the interaction forces phaseConversely using a rheological approach the bulk mixturebehaviour can be characterised by a limited number of pa-rameters relating shear stress and viscosity to shear rate Thepresent study focuses on the results obtained by means of arheological point of view

11 Debris flow rheology

Natural debris flows are often classified on the relative con-centration of fine and coarse sediments that are used to char-acterize the main flow regime behaviour (Takahashi 2007)Above a critical solid concentrationClowast

v a particle-friction-collision regime dominates the flow process Models basedon the work of Bagnold (1954) are used to describe the flowbehaviour of such mixtures If the solid concentration is lessthan the critical one the flow behaves like a Non-Newtonian

Published by Copernicus Publications on behalf of the European Geosciences Union

2508 A Scotto di Santolo et al Experimental study on the rheological behaviour of debris flow

20

1

Figure 1 2

3

4

5

6

7

8

9

10

11

12

13

14

15

(1) Newtonian fluids behaviour(2) Shear thinning behaviour (Pseudoplastic fluids)(3) Shear thickening behaviour (Dilatant fluids)

(4) Shear thinning yield stress fluids (viscoplastic fluids)

(5) Bingham plastic fluids

a) b)




a) b)

Fig 1 (a)Flow curves(b) Viscosity curves

fluid They are also called time-independent fluids and aresubdivided into several groups (Fig 1) Generally the de-bris flow mixtures behave like viscoplastic fluids as indi-cated in curve (4) Fig 1 It is considered that for sucha fluid an abrupt change in flow behaviour exists around agiven shear stress value the yield stressτy which needs tobe overcome before flow takes place The viscoplastic char-acter of debris flow mixtures has often been reported in liter-ature (OrsquoBrien and Julien 1984 1988 Phillips and Davies1991 Major and Pierson 1992 Coussot and Piau 1995Contreras and Davies 2000 Ancey and Jorrot 2001 Schatz-mann 2005 Kaitna et al 2007) Phenomenological lawslike the Bingham generalized model (or Herschel amp Bulk-ley model) are usually used to describe the rheological be-haviour of such mixtures (Major and Pierson 1992 Nguyenand Boger 1992 Coussot 1997) The mathematical expres-sion can be written as

τ = τy +k middot γ n (1)

In Eq (1)τy is the yield stressγ is the shear ratek is theconsistent coefficient [Pa sn] andn is the pseudoplastic indexWhen the indexn is equal to the unity the Eq (1) becomesthe Bingham model and the coefficientk becomes the Bing-ham viscosityηB (curve (5) in Fig 1)

2 Experimental setup and procedures

21 Rheometer apparatus

In order to ensure the validity of rheometrical measurementsand to reduce the risk of misinterpretation the rotationalrheometer AR 2000ex (TA Instruments) equipped with twodifferent geometry systems (parallel plates ndash PP and vanerotor ndash VR) has been utilized (Fig 2) The parallel platesgeometry is composed of a lower stationary steel plate andan upper rotational one with a 4 mm diameter The distancebetween two plates (the gapH ) must be at least ten times the

21

1

Figure 2 2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

Ω

Ω

Ω

Ω

Fig 2 The rotational rheometer AR 2000ex (TA Instruments) andthe two rheometrical system used parallel plates and vane rotorsystem

maximum particles diameterdmax (Chhabra and Richardson1999) Because of the variability in the grain size distributionof the material the gap has been fixed (H equal to 1 mm) andthe maximum diameter has been established according to theprevious relation (dmaxle 01 mm) The shear rate and theshear stress are evaluated with the following equations

γR

= γ (R) = middotR

H(2)

τ(γ

R

)=

3T

2πR3+

γR

2πR3middot

dT

dγR

(3)

whereR is the upper plate radiusH is the gap is therotation velocity (rads) andT is the torque (Coussot 1997)

The vane rotor geometry consists of four thin blades ar-ranged at equal angles around a small cylindrical shaft theblades radius is 14 mm and the blades height is 42 mm It isimmersed in the sample contained in a cylindrical cup with15 mm in radius The vane is rotated around its axis at agiven rotational speed and the torqueT is measured Dur-ing the test the material is trapped in the blades and the shearis achieved around a fictitious cylinder within the mixtureThe shear stress and shear rate are

γ = middotR1

R2minusR1(4)

τ =3middotT

2middotπ middotR21 middotL

(5)

whereR1 andR2 are respectively the blades radius and thecup radiusL is the material depth The Eqs (4) and (5) areusually applied when the ratioR1R2 is close to the unity(Coussot 1997) in our caseR1R2 is equal to 0933

Nat Hazards Earth Syst Sci 10 2507ndash2514 2010 wwwnat-hazards-earth-syst-scinet1025072010

A Scotto di Santolo et al Experimental study on the rheological behaviour of debris flow 2509

22

1

Figure 3 2

3

4

5

6

7

8

9

10

11

12

13

14

Gulf of Naples

Gulf of Salerno

Volcanic Systems

Calcareous bedrock covered by pyroclastic materials

Bedrock covered by ashes pyroclastic materials

Bedrock covered by ashes and pumices pyroclastic materials

Bedrock on flysch

Somma - Vesuvio

Island of Ischia

Phlegrean Fields

Roccamonfina

Piedmont Plans

Plans on pyroclastic

Plans on Ignimbrite

B

A

C

Campania

Gulf of Naples

Gulf of Salerno

Volcanic Systems




Bedrock on flysch

Somma - Vesuvio

Island of Ischia

Phlegrean Fields

Roccamonfina

Piedmont Plans


Plans on Ignimbrite

B

A

C

Campania

0

10

20

30

40

50

60

70

80

90

100

0000 0001 0010 0100 1000 10000 100000

Particle diameter d (mm)

Pe

rce

nt

fin

er

()

Material A

Material B

Material C

Clay Silt Sand Gravel

a)

b)

Gulf of Naples

Gulf of Salerno

Volcanic Systems




Bedrock on flysch

Somma - Vesuvio

Island of Ischia

Phlegrean Fields

Roccamonfina

Piedmont Plans


Plans on Ignimbrite

B

A

C

Campania

Gulf of Naples

Gulf of Salerno

Volcanic Systems




Bedrock on flysch

Somma - Vesuvio

Island of Ischia

Phlegrean Fields

Roccamonfina

Piedmont Plans


Plans on Ignimbrite

B

A

C

Campania

0

10

20

30

40

50

60

70

80

90

100

0000 0001 0010 0100 1000 10000 100000


Pe

rce

nt

fin

er

()

Material A

Material B

Material C


a)

b)

Fig 3 (a)Location of the studied debris flows and distribution of the main deposits (Modified from di Gennaro et al 1998)(b) Grain sizedistribution of the tested debris flow materials

22 Materials

The materials tested have been collected from the source areaof three debris flows which are originated in pyroclastic-derived terrains occurred in Campania region (southernItaly) Fig 3a Material A has been sampled in NoceraSalerno (event of March 2005) material B in Monteforte Ir-pino Avellino (event of May 1998) material C in AstroniNaples (event of December 2005) The soil type derivedfrom the most recent deposits produced by the volcanic activ-ity of mount SommaVesuvius for materials A and B and bythe volcanic activity of the Phlegrean Fields for material CThe grain size distributions of the undisturbed samples arereported in Fig 3b Soil A and soil B are sandy silt with asmall clay fraction while soil C is gravely silty sand Theclay part is slightly plastic though only in the Vesuvian de-posits The gravel part mainly consists of pumices and to aminor extent of scoriae and lapilli The particles are mainlysiliceous Their structure is amorphous and porous there is adouble porosity system inter- and intra-particle (the latter notconnected to the surface) Porosity exceeds 70 for Vesu-vian deposits while it is lower for the Phlegrean depositsThe cover is partially saturated the level of saturation variesaccording to weather conditions Mean physical propertiesare reported in Table 1 (GS is the specific gravity of soil par-ticlesγd andγ are the dry and total weight of soil per unitvolume respectivelyn is the porosity andSr is the degree ofsaturation) The geotechnical properties of such materials arewell documented in literature (eg Scotto di Santolo 2000ab Ruopolo 2006 Papa 2007 Picarelli et al 2007) Thenature of the substratum underlying the soil is volcanic formaterial C and carbonatic for materials A and B (Fig 3a)

23 Laboratory procedures

The analysed debris flow mixtures have been tested in rate-controlled mode at a constant temperature (20plusmn 05C) Theflow curves (τ γ ) have been determined by applying a suc-cessive shear rate level ranging from 0014 to 1400 1s

For each level of shear rate the duration of the experi-ment has been imposed long enough to obtain a simple shearsteady regime In order to certify the reproducibility of theexperiment each test has been repeated at least three timesand the averaged values of the experimental results have beenconsidered Due to the geometry dimension of the usedrheometer only the flow curves of fine material with grainsizes smaller than 01 mm have been derived The experi-ments have been carried out with mixtures of different watercontent The solid volumetric concentrationCv ie the ratioof the amount of solids to the total mixture has been consid-ered The total solid volumetric concentrationCv is definedas

Cv =Vs

Vs+Vw(6)

whereVw andVs are respectively the volumes of water andsolid in the sample In order to consider a significant rangeof the sediment concentration for the material tested mix-tures withCv changing from 20 to 40 have been pre-pared These values correspond to the variation of porosityin situ (n ranging from 60divide 80) Two grain size distribu-tions were analysed for each material the first with a maxi-mum particle diameter equal to 01 mm and the second witha maximum diameter equal to 05 mm respectively defined

wwwnat-hazards-earth-syst-scinet1025072010 Nat Hazards Earth Syst Sci 10 2507ndash2514 2010


Table 1 Main physical properties of the tested debris flow materials

Debris flow Substratum Material GS γd γ n Sr

(1) (kNm3) (kNm3) (1) (1)

Nocera Carbonatic A 262 908 1135 066 035Monteforte Irpino Carbonatic B 257 711 1211 071 071Astroni Pyroclastic C 254 899 984 067 024

Table 2 Experimental program

Material Mixture Test Cv Geometry system

Parallel plate Vane rotor

1

A

FPA-FP-20 20 A-FP-20-PP A-FP-20-VR

2 A-FP-30 30 A-FP-30-PP3 A-FP-40 40 A-FP-40-PP

4LP

A-LP-20 20 A-LP-20-PP A-LP-20-VR5 A-LP-30 30 A-LP-30-PP6 A-LP-40 40 A-LP-40-PP

7

B

FPB-FP-20 20 B-FP-20-PP B-FP-20-VR

8 B-FP-30 30 B-FP-30-PP B-FP-30-VR9 B-FP-40 40 B-FP-40-PP B-FP-40-VR

10LP

B-LP-20 20 B-LP-20-PP B-LP-20-VR11 B-LP-30 30 B-LP-30-PP B-LP-30-VR12 B-LP-40 40 B-LP-40-PP B-LP-40-VR

13

C

FPC-FP-20 20 C-FP-20-VR

14 C-FP-30 30 C-FP-30-VR15 C-FP-40 40 C-FP-40-VR

16LP

C-LP-2017 C-LP-3018 C-LP-40

(FP maximum diameter 01 mm LP maximum diameter 05 mmminus = not investigated)

fine (FP) and coarse (LP) in the following The experimentalprogramme performed is shown in Table 2

3 Experimental results

31 Preliminary evaluations

The choice of the measurement geometry depends on theexpected rheological properties of the mixture Becausethe rheological properties are unknown a priori preliminarymeasurements are absolutely necessary

Disturbing effects due to material properties and rheomet-rical geometry features could lead to erroneous data inter-pretation (Major and Pierson 1992 Coussot and Piau 1995Coussot 1997 Kaitna et al 2007) Depending on the ge-ometry apparatus shear conditions (related to samples vol-ume) and disturbing effects (related to geometry features andfluid types) change in a different way Data obtained by dif-

ferent facilities should be in agreement only if the materialtested has been homogeneously sheared as predicted by the-ory (Major and Pierson 1992 Coussot 1997)

In order to understand how the geometry system influencesthe experimental results preliminary tests on a typical New-tonian fluid (τ = η middot γ in which η is the viscosity) liquidparaffin on sale withη equal to 001 Pa s have been carriedout with parallel plates and vane rotor Figure 4 reports theflow curves of the liquid paraffin obtained using the men-tioned geometries A quantitative difference between theexperimental results obtained using the parallel plates sys-tem and the experimental data obtained using the vane rotorsystem has always been noted Comparing the theoreticaland the measured viscosity values an overestimate of therheological parameters has been observed when the parallelplates geometry has been used A scale factor from the re-sults obtained with the parallel plates system to the resultsobtained with the vane rotor system has been evaluated byconsidering the Newtonian behaviour of the liquid paraffin



23

1

2

3

Figure 4 4

0

05

1

15

2

25

3

0 20 40 60 80 100

Sh

ear st

ress

(P

a)

Shear rate (1s)

Parallel Plates

Vane Rotor

0001

001

01

1

0 20 40 60 80 100

Vis

cosi

ty (P

a s)

Shear rate (1s)

Parallel Plates

Vane Rotor

a)

b)

b)

23

1

2

3

Figure 4 4

0

05

1

15

2

25

3

0 20 40 60 80 100

Sh

ear st

ress

(P

a)

Shear rate (1s)

Parallel Plates

Vane Rotor

0001

001

01

1

0 20 40 60 80 100

Vis

cosi

ty (P

a s)

Shear rate (1s)

Parallel Plates

Vane Rotor

a)

b)

b)

Fig 4 Liquid paraffin on sale Comparison of parallel plates resultsand vane rotor results

For a Non-Newtonian fluid like the mixtures tested quan-titative and qualitative differences have been observed InFig 5 for material A withCv equal to 20 the flow curvesobtained with the two geometric facilities have been re-ported At a small shear rate a minimum in the flow curvesattained by the tests carried out using the vane rotor systemhas been noted the shear stress decreases with shear ratefollowed by a subsequent increase at larger shear rate valuesSuch behaviour for concentrated suspensions with a mini-mum to low shear rate has been reported by several authors(Nguyen and Boger 1985 Alderman et al 1991 Major andPierson 1992 Pignon et al 1996 Coussot 1997 Anceyand Jorrot 2001 Kaitna et al 2007) and only the increas-ing part of the flow curves has been considered Moreoverthe vane rotor response is higher than the parallel plates re-sponse after a shear rate value equal to 50 1s Regardlessof the solid volumetric concentrations considered after thisvalue of shear rate the mixtures analysed behave like a Non-Newtonian fluid In the following only these experimentalresults have been analysed

Probably some disturbing effects have occurred duringthe tests like the changing of the material free surfaceedgecrack effects heterogeneities in particle distribution(particle settling and migration due to particle inertia andsecondary flow) and the phenomenon of wall slip The oc-currence of some disturbing effects has been evaluated Instatic experiments gravity forces are in competition with theBrownian forces To estimate the sedimentation of the sam-ples of spherical particles the ratio between gravity (set-tling) and Brownian forces (thermal) should be greater than1 (Macosko 1994)

001

01

1

10

100

0 200 400 600 800

Shea

r stre

ss (P

a)

Shear rate (1s)

Parallel PlateVane rotor

Critical Shear rate

Yield Stress

001

01

1

10

0 20 40 60 80 100Sh

ear s

tress

(Pa)

Shear rate (1s)


Fig 5 Material A Cv = 20 Comparison between the experi-mental results obtained with the parallel plates and the vane rotorsystem

gravitymiddot force

Brownianmiddot force=

(ρdminusρc) middotg middota3

kB middotTa(7)

whereρd andρc are the densities of the disperse and contin-uous phaseg is the acceleration of gravitya is the particleradiuskB is the Boltzmannrsquos constantT is the absolute tem-perature

As shown by Larson (1999) sedimentation certainly oc-curred for1ρ difference between the densities of the dis-perseρd and the continuous phaseρc equal to 103 kg mminus3

and particles or aggregates larger than 1 microm radius For ourmixtures these differences are equal to 1600 the experimen-tal flow condition should be adjusted so that during the ex-perimental time the sedimentation does not play an impor-tant role It is possible to estimate the influence of settlingthrough the calculation of the experimental timetexp requiredfor a single sphere of radiusa to migrate over a lengthl (l isequal toH the gap height) as in the following

texp=9

2middot

ηc middot l

1ρ middotg middota2(8)

whereηc is the viscosity of the continuous phase (for water10minus3 Pa s)1ρ is the difference between the densities of thedisperseρd and the continuous phaseρc g is the accelerationof gravity anda is the radius of the particle with maximumsize in the mixtures (Macosko 1994) For our mixtures thistime is equal to 0115 s for fine mixtures and equal to 0005 sfor coarse mixtures



Particle inertia can also influence the results of experi-ments With the particle Reynolds numberRe

Pan estimation

of the inertial effects is possible

ReP

=ρc middot γ middota2

ηc(9)

In this equationγ andηc are the shear rate and the viscosityof the continuous phase respectively For a maximum diam-eter used (radiusa equal to 005 mm and 025 mm) and for ashear rate equal to 50 1s particle inertia occurred because theRe

Pis 0125 and 3125 greater than 10minus1 (Macosko 1994)

In the following due to the presence of these phenomenathe flow curves for the shear rate more than 50 1s have beenshown and interpreted

32 Experimental results and model fitting

The flow curves for each analysed material have been re-ported in Fig 6 It is noted that all the investigated debrisflow mixtures behave like a non-Newtonian fluid and in par-ticular like yield stress fluids shear stress non-linearly in-creases with the increase of shear rate after a yield stress thatrepresents the value ofτ required to initiate the flow (valueof τ asγ goes to zero)

The influence of the solid volumetric concentrationCv onthe rheological behaviour of fine debris flow material mix-tures tested has been evaluated Proportionally higher valuesof shear stress with the increasing of the solid volumetricconcentration have been noted Moreover at equal solid vol-umetric concentration the shear stresses of material B arehigher than materials A and C The rheological parametersof C mixtures are the lowest due to the different volcanicparticle nature (Phelegrean Field) and the higher grain size(Fig 3b)

The best fitting model of the experimental data is the Bing-ham generalized (Eq 1) The theoretical flow curves are re-ported as a solid line in Fig 6 Table 3 shows the relativerheological parameters The obtained yield stressτy is plot-ted versus the solid volumetric concentrationCv in Fig 7It can be observed that the yield stressτy exponentially in-creases with the increase of solid volumetric concentrationCv According to some previous study (OrsquoBrien and Julien1984 1988 Phillips and Davies 1991 Major and Pierson1992 Coussot and Piau 1995 Coussot 1997 Kaitna et al2007) the following relation can be used

τy = α middoteβmiddotCv (10)

whereα andβ are material parameters Their values for allthe tested material mixtures have been reported in Table 4

In order to evaluate the influence of larger particles mix-tures with the same solid volumetric concentration and witha maximum diameter of 05 mm were tested using a vane ro-tor Figure 8 shows for instance the comparison betweenfine and coarse particle mixtures of the materials B for asolid volumetric concentration equal to 30 A decrease of

25

1

Figure 6 2

01

1

10

100

50 200 350 500 650 800

Shear rate (1s)

Shear

str

ess (

Pa)

Cv 020

Cv 030

Cv 040

01

1

10

100

50 200 350 500 650 800

Shear rate (1s)

Shea

r str

ess (

Pa

)

Cv 020

Cv 030

01

1

10

100

50 200 350 500 650 800

Shear rate (1s)

She

ar

str

ess (

Pa

)

Cv 020Cv 030Cv 040

a)

b)

c)

Fig 6 Experimental data and theoretical flow curves at differentvolumetric concentrationCv (a) material A(b) material B(c) ma-terial C

26

1

Figure 7 2

3

Figure 8 4

5

1

10

100

50 200 350 500 650 800

shea

r st

ress

(P

a)

shear rate (1s)

Fine particle mixture Cvf 03 CvL 00

Large particle mixture Cvf 02 CvL 01

001

01

1

10

100

10 100Solid volumetric concentration ()

Yie

ld s

tre

ss (

Pa

)

Material A

Material B

Material C

20 30 40

Fig 7 Yield stressτy vs solid volumetric concentrationCv

yield stress is observed This reduction may be justified by adecrement of finer content the yield stress tends to disappeardue to a reduction of the fine fraction (clean water)

This behaviour is in agreement with the experimental re-sults of Ancey and Jorrot (2001) on coarse particles withina clay dispersion with a parallel plates system When thelarge particle fraction is small compared to the amount offine particle fraction the colloidal fine fraction determinesthe rheological features of the mixture



Table 3 Bingham generalized model parameters

Material Solid Mixture Yield Consistent Pseudoplastic Determinationvolumetric stress coefficient index coefficientconcentration() (Pa) (Pa sn) (1) (1)

A 20 Fine particle 04431 02756 06116 0988A 30 Fine particle 09169 05227 06116 0979A 40 Fine particle 32398 29569 06116 0991

B 20 Fine particle 35465 18708 02553 0999B 30 Fine particle 145960 67207 02553 0998B 30 Coarse particle 555 17351 03653 0955

C 20 Fine particle 0080 000105 06842C 30 Fine particle 01910 00914 06842 0999C 40 Fine particle 06744 02302 06842 0999

26

1

Figure 7 2

3

Figure 8 4

5

1

10

100

50 200 350 500 650 800

shea

r st

ress

(P

a)

shear rate (1s)



001

01

1

10

100


Yie

ld s

tre

ss (

Pa

)

Material A

Material B

Material C

20 30 40

Fig 8 Material B effect of maximum particle diameter forCvequal to 30

Instead as observed in different studies led using non-conventional rheometers on material mixtures rheologicalproperties are altered by addiction of larger particles (up toseveral centimeters) to the viscous fluid (Coussot and Piau1995 Contreras and Davies 2000 Schatzmann 2005) Thusrheological parameters determined by debris flow material oflimited grain size with a conventional rheometer do not rep-resent the bulk rheological behaviour of the complete natu-ral material Therefore further tests are necessary on mix-tures including sand and gravel fraction according to the nat-ural grain size distribution This activity is being undertakenthrough the development of a new type of equipment that ispresently being tested

4 Conclusions

In order to evaluate the rheological behaviour of debris-flowmaterial laboratory tests involving soils taken in the sourceareas of three debris flows occurred in Campania region(southern Italy) were carried out Mixtures with varying con-centration of fine sediment with maximum diameter less than01 mm (fine particle mixture) and less than 05 mm (coarse

Table 4 Material parameters

Material α β

A 02464 01215B 01333 01909C 00089 01066

particle mixtures) and distilled water were prepared Suchmixtures were investigated in a standard rheometer with twodifferent geometries the parallel plates system and the vanerotor system in order to distinguish disturbing effects Thevane geometry seems to be an appropriate rheometrical toolfor quantitative evaluation of the rheological behaviour of de-bris flow materials Instead by using the parallel plates sys-tem only some qualitative ideas about their behaviour can beobtained The comparison between the results of the two ge-ometry configurations allows checking the range of shear ratewhere there are no disturbing effects and misleading evalua-tions In this range of shear rate all the tested debris flow mix-tures behave like a non-Newtonian fluid with a yield stressτy that increases with solid volumetric concentrationCv anddecreases for sand fraction increase The experimental datawere fitted with the theoretical Bingham generalized modelin the range of the evaluated shear rate A simple relationbetweenCv andτy was obtained

These results suggest that in the field a small change insolid fraction due to rainfall will cause a slight decreaseof the yield stress inducing a flow rapidly reaching a shearrate larger than the critical shear rate associated with a rapidflow Then the flow will stop only when the material reachesa much smoother slope This might explain the in situ ob-served post-failure behaviour of debris flows which are ableto flow over very long distances even over smooth slopes

The rheological parameters determined for flows of lim-ited grain size with a conventional rheometer do not represent



the bulk rheological behaviour of the complete natural mate-rial Further tests are necessary on mixtures including sandand gravel fraction reflecting the natural grain size distribu-tion This activity is being undertaken through the develop-ment of a new equipment under test The yield stress seemsto be a key parameter for describing and predicting the post-failure behaviour of debris flows but further experimentalvalidation is required

AcknowledgementsWe thank Renzo Pepi for assisting in carryingout rheometer tests at the Dept of Chemical Science and Technol-ogy and Biosystems University of Siena and the TA Instrumentsfor having lent the Rheometer AR 2000EX

Edited by G G R IovineReviewed by A Bartosik and two anonymous referees

References

Alderman N J Meeten G H and Sherwood J D Vane rheom-etry of bentonite gels J Non-Newton Fluid 39 291ndash310 1991

Ancey C and Jorrot H Yield stress for particle suspensionswithin a clay dispersion J Rheol 45(2) 297ndash319 2001

Bagnold R A Experiment on a gravity-free dispersion of largesolid sphere in a Newtonian fluid under shear Proc of The RoyalSociety London Series A 49ndash63 1954

Chhabra R P and Richardson J F Non-Newtonian Flow in theProcess Industries Butterworth-Heinemann Oxford 436 pp1999

Contreras S M and Davies T H R Coarse-Grained DebrisFlows Hysteresis and Time-Dependent Rheology J HydraulEng-Asce 126 938ndash941 2000

Costa J E and Williams G P Debris flow dynamics (videotape)US Geological Survey Open file 84ndash606 22 min available athttpwwwpubsusgsgovof1984ofr84-606 1984

Coussot P and Piau J M On the behaviour of fine mud suspen-sions Rheol Acta 33 175ndash184 1994

Coussot P and Piau J M A large-scale field cylinder rheometerfor the study of the rheology of natural coarse suspensions JRheol 39(1) 105ndash123 1995

Coussot P Mudflow Rheology and Dynamics IAHR MonographSeries A A Balkema Rotterdam 1997

di Gennaro A Terribile F Basile A Aronne G BuonannoM De Mascellis R and Vingiani S I suoli delle aree di crisidi Quindici e Sarno proprieta e comportamenti in relazione aifenomeni franosi 2 Rapporto informativo dellrsquoUnita Operativa421N del CNR ndash GNDCI Lrsquoinstabilita delle coltri piroclas-tiche delle dorsali carbonati che in Campania Primi risulatati diuno studio interdisciplinare 1998

Iverson R M The physic of debris flow Rev Geophys 35 245ndash296 1997

Johnson A M Debris flow Topics in Slope Instability edited byBrunsdenm D and Prior D B Wiley New York 257ndash3611984

Kaitna R Rickenmann D and Schatzmann M Experimen-tal study on rheological behaviour of debris flow material ActaGeotech 2 71ndash85 2007

Larson R G The Structure and Rheology of Complex Fluids Ox-ford Univ Press New York 1999

Major J J and Pierson T C Debris flow rheology experimen-tal analysis of fine ndash grained slurries Water Resour Res 28(3)841ndash857 1992

Macosko C W Rheology Principles Measurements and Appli-cations Wiley-VCH Inc 1994

Nguyen Q D and Boger D V Direct yield stress measurementwith the vane method J Rheol 29 335ndash347 1985

Nguyen Q D and Boger D V Measuring the flow properties ofyield stress fluids Annu Rev Fluid Mech 24 47ndash88 1992

OrsquoBrien J S and Julien P Y Physical properties and mechanicsof hyperconcentrated sediment flow Proc of the Specialty Con-ference on Delineation of landslide flash flood and debris flowhazard in Utah Utah Water Research Laboratory General SeriesUWRLG-8503 260ndash278 1984

OrsquoBrien J S and Julien P Y Laboratory analysis on mudflowproperties J Hydraul Eng-Asce 144 877ndash887 1988

Papa R Indagine sperimentale di una copertura piroclastica di unversante della Campania PhD thesis University of Naples ldquoFed-erico IIrdquo 2007

Phillips C J and Davies T R H Determining rheological pa-rameters of debris flow material Geomorphology 4 573ndash5871991

Picarelli L Evangelista A Rolandi G Paone A NicoteraM V Olivares L Scotto di Santolo A Lampitiello S andRolandi M Mechanical properties of soils in Campania Re-gion Proc Int Int Workshop on Characterisation amp Engineer-ing Properties of Natural Soils edited by Tan Phoon Hight andLeroueil Singapore 29 Novemberndash1 December 2006 Taylor ampFrancis Group London 4 2331ndash2383 2007

Pignon F Magnin A and Piau J M Thixotropic colloidal sus-pension and flow curve with a minimum identification of flowregimes and rheometric consequence J Rheol 40 573ndash5871996

Ruopolo S Analisi dei fenomeni franosi nella coltre piroclasticanon satura del cratere degli Astroni Graduate thesis Departmentof Geotechnical Engineering University of Naples ldquoFederico IIrdquo2006

Savage S B and Hutter K The motion of a finite mass of granularmaterial down a rough incline J Fluid Mech 199 177ndash2151989

Schatzmann M Rheometry of large particle fluids and debrisflows PhD Dissertation No 16093 ETH Zurich Switzerland2005

Scotto di Santolo A Analisi geotecnica dei fenomeni franosi nellecoltri piroclastiche della provincia di Napoli PhD thesis Univer-sity of Naples ldquoFederico IIrdquo and Rome ldquoLa Sapienzardquo 2000a

Scotto di Santolo A Analysis of a steep slope in unsaturatedsoils Proc Asian Conference on Unsaturated Soils SingaporeBalkema Rotterdam 569ndash574 2000b

Scotto di Santolo A and Evangelista A Some observations on theprediction of the dynamic parameters of debris flows in depositsin the Campania region of Italy Int J Nat Hazards 50 605ndash622 2009

Takahashi T Debris flow Mechanics Prediction and Countermea-sures Taylor and Francis Group London 35ndash38 2007



20

1

Figure 1 2

3

4

5

6

7

8

9

10

11

12

13

14

15




a) b)




a) b)

Fig 1 (a)Flow curves(b) Viscosity curves

fluid They are also called time-independent fluids and aresubdivided into several groups (Fig 1) Generally the de-bris flow mixtures behave like viscoplastic fluids as indi-cated in curve (4) Fig 1 It is considered that for sucha fluid an abrupt change in flow behaviour exists around agiven shear stress value the yield stressτy which needs tobe overcome before flow takes place The viscoplastic char-acter of debris flow mixtures has often been reported in liter-ature (OrsquoBrien and Julien 1984 1988 Phillips and Davies1991 Major and Pierson 1992 Coussot and Piau 1995Contreras and Davies 2000 Ancey and Jorrot 2001 Schatz-mann 2005 Kaitna et al 2007) Phenomenological lawslike the Bingham generalized model (or Herschel amp Bulk-ley model) are usually used to describe the rheological be-haviour of such mixtures (Major and Pierson 1992 Nguyenand Boger 1992 Coussot 1997) The mathematical expres-sion can be written as

τ = τy +k middot γ n (1)

In Eq (1)τy is the yield stressγ is the shear ratek is theconsistent coefficient [Pa sn] andn is the pseudoplastic indexWhen the indexn is equal to the unity the Eq (1) becomesthe Bingham model and the coefficientk becomes the Bing-ham viscosityηB (curve (5) in Fig 1)

2 Experimental setup and procedures

21 Rheometer apparatus

In order to ensure the validity of rheometrical measurementsand to reduce the risk of misinterpretation the rotationalrheometer AR 2000ex (TA Instruments) equipped with twodifferent geometry systems (parallel plates ndash PP and vanerotor ndash VR) has been utilized (Fig 2) The parallel platesgeometry is composed of a lower stationary steel plate andan upper rotational one with a 4 mm diameter The distancebetween two plates (the gapH ) must be at least ten times the

21

1

Figure 2 2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

Ω

Ω

Ω

Ω

Fig 2 The rotational rheometer AR 2000ex (TA Instruments) andthe two rheometrical system used parallel plates and vane rotorsystem

maximum particles diameterdmax (Chhabra and Richardson1999) Because of the variability in the grain size distributionof the material the gap has been fixed (H equal to 1 mm) andthe maximum diameter has been established according to theprevious relation (dmaxle 01 mm) The shear rate and theshear stress are evaluated with the following equations

γR

= γ (R) = middotR

H(2)

τ(γ

R

)=

3T

2πR3+

γR

2πR3middot

dT

dγR

(3)

whereR is the upper plate radiusH is the gap is therotation velocity (rads) andT is the torque (Coussot 1997)

The vane rotor geometry consists of four thin blades ar-ranged at equal angles around a small cylindrical shaft theblades radius is 14 mm and the blades height is 42 mm It isimmersed in the sample contained in a cylindrical cup with15 mm in radius The vane is rotated around its axis at agiven rotational speed and the torqueT is measured Dur-ing the test the material is trapped in the blades and the shearis achieved around a fictitious cylinder within the mixtureThe shear stress and shear rate are

γ = middotR1

R2minusR1(4)

τ =3middotT

2middotπ middotR21 middotL

(5)

whereR1 andR2 are respectively the blades radius and thecup radiusL is the material depth The Eqs (4) and (5) areusually applied when the ratioR1R2 is close to the unity(Coussot 1997) in our caseR1R2 is equal to 0933



22

1

Figure 3 2

3

4

5

6

7

8

9

10

11

12

13

14

Gulf of Naples

Gulf of Salerno

Volcanic Systems




Bedrock on flysch

Somma - Vesuvio

Island of Ischia

Phlegrean Fields

Roccamonfina

Piedmont Plans


Plans on Ignimbrite

B

A

C

Campania

Gulf of Naples

Gulf of Salerno

Volcanic Systems




Bedrock on flysch

Somma - Vesuvio

Island of Ischia

Phlegrean Fields

Roccamonfina

Piedmont Plans


Plans on Ignimbrite

B

A

C

Campania

0

10

20

30

40

50

60

70

80

90

100

0000 0001 0010 0100 1000 10000 100000


Pe

rce

nt

fin

er

()

Material A

Material B

Material C


a)

b)

Gulf of Naples

Gulf of Salerno

Volcanic Systems




Bedrock on flysch

Somma - Vesuvio

Island of Ischia

Phlegrean Fields

Roccamonfina

Piedmont Plans


Plans on Ignimbrite

B

A

C

Campania

Gulf of Naples

Gulf of Salerno

Volcanic Systems




Bedrock on flysch

Somma - Vesuvio

Island of Ischia

Phlegrean Fields

Roccamonfina

Piedmont Plans


Plans on Ignimbrite

B

A

C

Campania

0

10

20

30

40

50

60

70

80

90

100

0000 0001 0010 0100 1000 10000 100000


Pe

rce

nt

fin

er

()

Material A

Material B

Material C


a)

b)


22 Materials





Cv =Vs

Vs+Vw(6)






(1) (kNm3) (kNm3) (1) (1)





1

A



4LP


7

B



10LP


13

C



16LP

C-LP-2017 C-LP-3018 C-LP-40











23

1

2

3

Figure 4 4

0

05

1

15

2

25

3

0 20 40 60 80 100

Sh

ear st

ress

(P

a)

Shear rate (1s)

Parallel Plates

Vane Rotor

0001

001

01

1

0 20 40 60 80 100

Vis

cosi

ty (P

a s)

Shear rate (1s)

Parallel Plates

Vane Rotor

a)

b)

b)

23

1

2

3

Figure 4 4

0

05

1

15

2

25

3

0 20 40 60 80 100

Sh

ear st

ress

(P

a)

Shear rate (1s)

Parallel Plates

Vane Rotor

0001

001

01

1

0 20 40 60 80 100

Vis

cosi

ty (P

a s)

Shear rate (1s)

Parallel Plates

Vane Rotor

a)

b)

b)




001

01

1

10

100

0 200 400 600 800

Shea

r stre

ss (P

a)

Shear rate (1s)


Critical Shear rate

Yield Stress

001

01

1

10

0 20 40 60 80 100Sh

ear s

tress

(Pa)

Shear rate (1s)



gravitymiddot force



kB middotTa(7)




texp=9

2middot

ηc middot l






Pan estimation


ReP


ηc(9)











25

1

Figure 6 2

01

1

10

100

50 200 350 500 650 800

Shear rate (1s)

Shear

str

ess (

Pa)

Cv 020

Cv 030

Cv 040

01

1

10

100

50 200 350 500 650 800

Shear rate (1s)

Shea

r str

ess (

Pa

)

Cv 020

Cv 030

01

1

10

100

50 200 350 500 650 800

Shear rate (1s)

She

ar

str

ess (

Pa

)

Cv 020Cv 030Cv 040

a)

b)

c)


26

1

Figure 7 2

3

Figure 8 4

5

1

10

100

50 200 350 500 650 800

shea

r st

ress

(P

a)

shear rate (1s)



001

01

1

10

100


Yie

ld s

tre

ss (

Pa

)

Material A

Material B

Material C

20 30 40











26

1

Figure 7 2

3

Figure 8 4

5

1

10

100

50 200 350 500 650 800

shea

r st

ress

(P

a)

shear rate (1s)



001

01

1

10

100


Yie

ld s

tre

ss (

Pa

)

Material A

Material B

Material C

20 30 40



4 Conclusions



Material α β

A 02464 01215B 01333 01909C 00089 01066









References


































22

1

Figure 3 2

3

4

5

6

7

8

9

10

11

12

13

14

Gulf of Naples

Gulf of Salerno

Volcanic Systems




Bedrock on flysch

Somma - Vesuvio

Island of Ischia

Phlegrean Fields

Roccamonfina

Piedmont Plans


Plans on Ignimbrite

B

A

C

Campania

Gulf of Naples

Gulf of Salerno

Volcanic Systems




Bedrock on flysch

Somma - Vesuvio

Island of Ischia

Phlegrean Fields

Roccamonfina

Piedmont Plans


Plans on Ignimbrite

B

A

C

Campania

0

10

20

30

40

50

60

70

80

90

100

0000 0001 0010 0100 1000 10000 100000


Pe

rce

nt

fin

er

()

Material A

Material B

Material C


a)

b)

Gulf of Naples

Gulf of Salerno

Volcanic Systems




Bedrock on flysch

Somma - Vesuvio

Island of Ischia

Phlegrean Fields

Roccamonfina

Piedmont Plans


Plans on Ignimbrite

B

A

C

Campania

Gulf of Naples

Gulf of Salerno

Volcanic Systems




Bedrock on flysch

Somma - Vesuvio

Island of Ischia

Phlegrean Fields

Roccamonfina

Piedmont Plans


Plans on Ignimbrite

B

A

C

Campania

0

10

20

30

40

50

60

70

80

90

100

0000 0001 0010 0100 1000 10000 100000


Pe

rce

nt

fin

er

()

Material A

Material B

Material C


a)

b)


22 Materials





Cv =Vs

Vs+Vw(6)






(1) (kNm3) (kNm3) (1) (1)





1

A



4LP


7

B



10LP


13

C



16LP

C-LP-2017 C-LP-3018 C-LP-40











23

1

2

3

Figure 4 4

0

05

1

15

2

25

3

0 20 40 60 80 100

Sh

ear st

ress

(P

a)

Shear rate (1s)

Parallel Plates

Vane Rotor

0001

001

01

1

0 20 40 60 80 100

Vis

cosi

ty (P

a s)

Shear rate (1s)

Parallel Plates

Vane Rotor

a)

b)

b)

23

1

2

3

Figure 4 4

0

05

1

15

2

25

3

0 20 40 60 80 100

Sh

ear st

ress

(P

a)

Shear rate (1s)

Parallel Plates

Vane Rotor

0001

001

01

1

0 20 40 60 80 100

Vis

cosi

ty (P

a s)

Shear rate (1s)

Parallel Plates

Vane Rotor

a)

b)

b)




001

01

1

10

100

0 200 400 600 800

Shea

r stre

ss (P

a)

Shear rate (1s)


Critical Shear rate

Yield Stress

001

01

1

10

0 20 40 60 80 100Sh

ear s

tress

(Pa)

Shear rate (1s)



gravitymiddot force



kB middotTa(7)




texp=9

2middot

ηc middot l






Pan estimation


ReP


ηc(9)











25

1

Figure 6 2

01

1

10

100

50 200 350 500 650 800

Shear rate (1s)

Shear

str

ess (

Pa)

Cv 020

Cv 030

Cv 040

01

1

10

100

50 200 350 500 650 800

Shear rate (1s)

Shea

r str

ess (

Pa

)

Cv 020

Cv 030

01

1

10

100

50 200 350 500 650 800

Shear rate (1s)

She

ar

str

ess (

Pa

)

Cv 020Cv 030Cv 040

a)

b)

c)


26

1

Figure 7 2

3

Figure 8 4

5

1

10

100

50 200 350 500 650 800

shea

r st

ress

(P

a)

shear rate (1s)



001

01

1

10

100


Yie

ld s

tre

ss (

Pa

)

Material A

Material B

Material C

20 30 40











26

1

Figure 7 2

3

Figure 8 4

5

1

10

100

50 200 350 500 650 800

shea

r st

ress

(P

a)

shear rate (1s)



001

01

1

10

100


Yie

ld s

tre

ss (

Pa

)

Material A

Material B

Material C

20 30 40



4 Conclusions



Material α β

A 02464 01215B 01333 01909C 00089 01066









References




































(1) (kNm3) (kNm3) (1) (1)





1

A



4LP


7

B



10LP


13

C



16LP

C-LP-2017 C-LP-3018 C-LP-40











23

1

2

3

Figure 4 4

0

05

1

15

2

25

3

0 20 40 60 80 100

Sh

ear st

ress

(P

a)

Shear rate (1s)

Parallel Plates

Vane Rotor

0001

001

01

1

0 20 40 60 80 100

Vis

cosi

ty (P

a s)

Shear rate (1s)

Parallel Plates

Vane Rotor

a)

b)

b)

23

1

2

3

Figure 4 4

0

05

1

15

2

25

3

0 20 40 60 80 100

Sh

ear st

ress

(P

a)

Shear rate (1s)

Parallel Plates

Vane Rotor

0001

001

01

1

0 20 40 60 80 100

Vis

cosi

ty (P

a s)

Shear rate (1s)

Parallel Plates

Vane Rotor

a)

b)

b)




001

01

1

10

100

0 200 400 600 800

Shea

r stre

ss (P

a)

Shear rate (1s)


Critical Shear rate

Yield Stress

001

01

1

10

0 20 40 60 80 100Sh

ear s

tress

(Pa)

Shear rate (1s)



gravitymiddot force



kB middotTa(7)




texp=9

2middot

ηc middot l






Pan estimation


ReP


ηc(9)











25

1

Figure 6 2

01

1

10

100

50 200 350 500 650 800

Shear rate (1s)

Shear

str

ess (

Pa)

Cv 020

Cv 030

Cv 040

01

1

10

100

50 200 350 500 650 800

Shear rate (1s)

Shea

r str

ess (

Pa

)

Cv 020

Cv 030

01

1

10

100

50 200 350 500 650 800

Shear rate (1s)

She

ar

str

ess (

Pa

)

Cv 020Cv 030Cv 040

a)

b)

c)


26

1

Figure 7 2

3

Figure 8 4

5

1

10

100

50 200 350 500 650 800

shea

r st

ress

(P

a)

shear rate (1s)



001

01

1

10

100


Yie

ld s

tre

ss (

Pa

)

Material A

Material B

Material C

20 30 40











26

1

Figure 7 2

3

Figure 8 4

5

1

10

100

50 200 350 500 650 800

shea

r st

ress

(P

a)

shear rate (1s)



001

01

1

10

100


Yie

ld s

tre

ss (

Pa

)

Material A

Material B

Material C

20 30 40



4 Conclusions



Material α β

A 02464 01215B 01333 01909C 00089 01066









References


































23

1

2

3

Figure 4 4

0

05

1

15

2

25

3

0 20 40 60 80 100

Sh

ear st

ress

(P

a)

Shear rate (1s)

Parallel Plates

Vane Rotor

0001

001

01

1

0 20 40 60 80 100

Vis

cosi

ty (P

a s)

Shear rate (1s)

Parallel Plates

Vane Rotor

a)

b)

b)

23

1

2

3

Figure 4 4

0

05

1

15

2

25

3

0 20 40 60 80 100

Sh

ear st

ress

(P

a)

Shear rate (1s)

Parallel Plates

Vane Rotor

0001

001

01

1

0 20 40 60 80 100

Vis

cosi

ty (P

a s)

Shear rate (1s)

Parallel Plates

Vane Rotor

a)

b)

b)




001

01

1

10

100

0 200 400 600 800

Shea

r stre

ss (P

a)

Shear rate (1s)


Critical Shear rate

Yield Stress

001

01

1

10

0 20 40 60 80 100Sh

ear s

tress

(Pa)

Shear rate (1s)



gravitymiddot force



kB middotTa(7)




texp=9

2middot

ηc middot l






Pan estimation


ReP


ηc(9)











25

1

Figure 6 2

01

1

10

100

50 200 350 500 650 800

Shear rate (1s)

Shear

str

ess (

Pa)

Cv 020

Cv 030

Cv 040

01

1

10

100

50 200 350 500 650 800

Shear rate (1s)

Shea

r str

ess (

Pa

)

Cv 020

Cv 030

01

1

10

100

50 200 350 500 650 800

Shear rate (1s)

She

ar

str

ess (

Pa

)

Cv 020Cv 030Cv 040

a)

b)

c)


26

1

Figure 7 2

3

Figure 8 4

5

1

10

100

50 200 350 500 650 800

shea

r st

ress

(P

a)

shear rate (1s)



001

01

1

10

100


Yie

ld s

tre

ss (

Pa

)

Material A

Material B

Material C

20 30 40











26

1

Figure 7 2

3

Figure 8 4

5

1

10

100

50 200 350 500 650 800

shea

r st

ress

(P

a)

shear rate (1s)



001

01

1

10

100


Yie

ld s

tre

ss (

Pa

)

Material A

Material B

Material C

20 30 40



4 Conclusions



Material α β

A 02464 01215B 01333 01909C 00089 01066









References



































Pan estimation


ReP


ηc(9)











25

1

Figure 6 2

01

1

10

100

50 200 350 500 650 800

Shear rate (1s)

Shear

str

ess (

Pa)

Cv 020

Cv 030

Cv 040

01

1

10

100

50 200 350 500 650 800

Shear rate (1s)

Shea

r str

ess (

Pa

)

Cv 020

Cv 030

01

1

10

100

50 200 350 500 650 800

Shear rate (1s)

She

ar

str

ess (

Pa

)

Cv 020Cv 030Cv 040

a)

b)

c)


26

1

Figure 7 2

3

Figure 8 4

5

1

10

100

50 200 350 500 650 800

shea

r st

ress

(P

a)

shear rate (1s)



001

01

1

10

100


Yie

ld s

tre

ss (

Pa

)

Material A

Material B

Material C

20 30 40











26

1

Figure 7 2

3

Figure 8 4

5

1

10

100

50 200 350 500 650 800

shea

r st

ress

(P

a)

shear rate (1s)



001

01

1

10

100


Yie

ld s

tre

ss (

Pa

)

Material A

Material B

Material C

20 30 40



4 Conclusions



Material α β

A 02464 01215B 01333 01909C 00089 01066









References







































26

1

Figure 7 2

3

Figure 8 4

5

1

10

100

50 200 350 500 650 800

shea

r st

ress

(P

a)

shear rate (1s)



001

01

1

10

100


Yie

ld s

tre

ss (

Pa

)

Material A

Material B

Material C

20 30 40



4 Conclusions



Material α β

A 02464 01215B 01333 01909C 00089 01066









References





































References

































experimental study on the rheological behaviour of debris ﬂow · gulf of naples gulf of salerno...

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