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Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
313
DOI: 10.4408/IJEGE.2011-03.B-036
CHARACTERIZATION OF FRICTION ANGLES FOR STABILITY AND
DEPOSITION OF GRANULAR MATERIAL
a
ndRea
M. DEGANUTTI
(*)
,
P
ia
R. TECCA
(*)
&
R
inaldo
GENEVOIS
(**)
(*)
CNR-IRPI - Corso Stati Uniti, 4 - 35127 Padova
(**)
University of Padua - Dept. of Geosciences - Via Gradenigo, 6 - 35100 Padova
many other ways to measure friction angles (in partic-
ular by classical geotechnical apparatuses) the authors
propose this way that is closer to the natural slope con-
dition where granular mass flows originate.
K
ey
words
: granular material, friction angle, deposition pro-
cess, yielding process
INTRODUCTION
The friction angle of a granular mass is of funda-
mental importance among the rheological parameters
that rule the initiation, the resistance to motion and the
deposition of a flowing mass composed by granules,
with or without the presence of an interstitial fluid.
The term friction angle comes from the well es-
tablished Coulomb equation (for dry non cohesive
materials):
t
= s tan F
(1)
where the term tan(F) is a parameter which, express-
ing the ratio of tangential and direct stresses, repre-
sents the friction among two bodies in contact. Ini-
tially referred to a solid body laying on a surface this
empirical relation was extended to granular media
(C
asaGRande
, 1936) both in static/quasi-static (e.g. in
soil mechanics) and in dynamic conditions (e.g. H
un
-
GR
& m
oRGensteRn
, 1984) even if very different phys-
ical phenomena are involved in the two situations.
In spite of the simplicity of eq. (1), very often
scholars and designers use the term “friction angle”
with different adjectives, especially in earth sciences
ABSTRACT
The concept of friction angle as a measure of fric-
tion among bodies in static or dynamic conditions,
is almost ubiquitous in Earth sciences. In spite of its
importance, there is not a general agreement on its
definition or standardization on the way to measure it.
This study goes back to the fundamentals of fric-
tion among granular particles, presenting results from
laboratory tests performed in order to measure the
friction angles of particles of different shape, density
and material, getting indications on the role of inter-
particle friction on the stability of a mass of granular
material and on its depositional features.
Several granular materials of different nature, nat-
ural and artificial, are studied in laboratory by means
of a tilting flume. The aim of the performed tests is to
measure the characteristic friction angles, both depo-
sitional (or repose) and stability limit (critical) taking
into account the material characteristics: size, shape,
density and roughness.
The granular materials are heaped inside the
flume which is then tilted until destabilization of the
mass and the gradient of the new deposition surface
is then measured by means of a lab-size laser scanner
and a digital still camera; video shots of the motion of
granules while sliding have been taken as well.
The study shows that characteristic friction angles
depend on size and shape of grains while when mixing
granules of different size a sorting mechanism arises
with less clear deposition angles. Although there are
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A.M. DEGANUTTI , P.R. TECCA & R. GENEVOIS
314
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
tions; here we propose a methodology that reproduces
in laboratory the natural conditions of loose granular
rock materials (such as scree) on a slope, conditions
potentially able to originate debris flows. In this sense
authors’ proposed methodology is strictly related to
superficial instability, where there is no confinement
pressure and the granules are free to move and to di-
late (R
eynolds
, 1885); in order to test the effect of a
vertical load on the tested material, authors have per-
formed some shear box tests as well.
Some recent developments (d
aeR
& d
ouady
,
1999; GdRm
i
d
i
, 2004; J
oP
et alii, 2006) on dense
granular flows are focused on some particular labo-
ratory tests in which artificial granular material (gen-
erally glass beads) is poured on a tilted rough plane;
in that particular experimental settings (in which the
material is far from a natural one, given the ability
to rotate and the very low particle-to-particle friction
of glass spherical beads) those scholars found that
there is a relation between the plane inclination and
the thickness of granular material that remains stable
on the plane. In that case the surface of the grain pile
is parallel to the plane. While that finding is impor-
tant for its relation to industrial applications in which
dense granular flows are involved, present paper’s ap-
proach is more focused on yielding and deposition of
the superficial layer of a pile of granular material (that
is not parallel to plane bottom) for its relation to natu-
ral conditions, e.g. of a mountain scree slope.
LABORATORY APPARATUS
The laboratory tests have been performed using
an apparatus (Fig. 1), constituted by a 2 m long and
1.5 m wide tilting plane with an adjustable slope up to
38° from the horizontal. A 232 mm wide flume with
one glass side wall was installed on the plane. The tilt-
ing plane was hinged to a fixed horizontal plane (1.5
m long and 1.5 m wide). To avoid slippage of material,
coarse sand paper was glued on the flume bottom
The tilting movement of the plane was control-
led by a synchronous electric motor which provides a
constant (slow) rate of tilting (around 2.5x10
-3
rad s
-1
)
through a robust rotating screwed bar; this system has
proved to be very good for the smoothness of move-
ment and for the absence of vibrations on the plane
itself, both characteristics of great importance for the
kind of test that have been performed.
The morphological measures on materials were
(e.g. repose, dynamic, static, critical, internal, natural,
stopping, residual, neutral, bulk, etc.; (e.g. f
isCHeR
et
alii, 2008; P
udasaini
& H
utteR
, 2007; C
alvetti
et alii,
2000; H
olz
& k
ovaCs
, 1981) with different meanings,
according to different physical situations, following
their field of interest. In other words, it is not possible
to find in literature a univocal, unambiguous definition
of friction angle for the different conditions. Moreover
a generic “angle of internal friction” referred to bodies
in static or quasi-static conditions can assume different
values following the Coulomb equation as the shear
and normal stresses can assume different values de-
pending on the state of bodies in contact.
With reference to granular materials, where the
influence of the packing state makes things more
complicated than the simple case of a block slide, the
terminology relative to friction among granules and
to friction angle abounds with no standardization (e.g.
m
etCalf
, 1965; b
aGnold
, 1966; C
undall
& s
tRaCk
,
1979; m
etHa
& b
aRkeR
, 1994). This aspect is rel-
evant especially with regard to the special situations
(or limit situations) in which a granular media can be
found and in those that are of most interest in engi-
neering design and natural hazard studies like the an-
gle of deposition (or repose) and the angle of incipient
movement for a mass of granular media.
Given the importance of friction parameters in
the development of models for debris flow runout
prediction (H
unGR
et alii, 2002; R
iCkenmann
, 2005)
many different ways to measure various types of fric-
tion angles for granular materials have been proposed
by various scholars (e.g. m
etCalf
, 1965; H
utteR
&
k
oCH
, 1991; P
udasaini
& H
utteR
, 2007). Thus the
values of measured friction angles for a certain mate-
rial generally differ from a study to another and are
significant for the particular context in which those
values were found.
The authors of the present work take into consid-
eration the deposition (or repose) friction angle de-
fined as the uniform angle at which a granular material
arranges itself on a inclined slope coming at a stop af-
ter being mobilized and a critical (or yielding) friction
angle defined as the gradient at which a granular mass
becomes unstable and start to slide down. A measure
of critical friction angles for movement initiation and
for movement ceasing has already been proposed by
d
eGanutti
& s
Cotton
(1997) by means of a cone and
plate rheometer in controlled normal stress condi-
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CHARACTERIZATION OF FRICTION ANGLES FOR STABILITY AND DEPOSITION OF GRANULAR MATERIAL
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
315
grained sub-angular gravel particles, obtained by
crushing limestone rocks, with equivalent sizes rang-
ing on the whole from 16.0 to 4.0 mm and density
between 2600 and 2700 kg m
-3
.
Materials m12, m14 and m16 are represented by
graded sands with equivalent sizes ranging on the
whole from 2.0 to 0.075 with a few fines (less than
5-6%); m14 is the finer fraction of m12.
Materials m8, m11 and m12 result by mixing dif-
ferent grain size classes: m8 by 20% of each a, b, c,
d and e size class; m11 by 50% of c and d size class;
m12 by 50% of g and h size class.
Material m17 is a coarse grained material ob-
tained by mixing in equal proportions rounded and
sub-angular gravels to have a grain size distribution
from 4.0 to 2.0 mm (mean density 2650-2700 kgm
-3
).
The roundness grade is based on the classification
of P
oweRs
(1953).
METHODS
Some authors consider as “friction angle” of a
granular material the maximum slope at which a heap
of loose material will come to rest when dumped on
a slope, but this way to measure the friction angle is
subject to the way the granular material is dumped,
and to the roughness of the surface on which the mate-
rial is poured. Tests were then performed by accumu-
lating a heap of dry material in the rising end of the
flume, not considering the angle at which the material
stopped. The plane was slowly and continuously tilted
performed by a laboratory class laser-scanner which
was attached to a frame able to move along the flume
and adjustable in height through a spherical joint; in
this way the position of the measuring instrument was
adjustable in every direction for the best accuracy of
measurements. This instrument had just been added
to the laboratory equipment and thanks to its ability
to scan an object surface with millimetric precision
proved to be very useful for the planned measurement
where a mathematical definition of the granular sur-
face easily yielded the average surface angle to the
horizontal (with exclusion of the tests with fine ma-
terial, see later in the text). The irregularities on the
grain surfaces were generally within 2 particle diam-
eters. In those experimental conditions the use of me-
chanical measuring devices would have been not easy
and more time consuming.
TESTED MATERIALS
Seventeen different types of granular cohesion-
less material, both synthetic and natural, have been
tested. The main characteristics of tested materials are
presented in Table 1.
Materials m1 and m2 are PVC cylindrical granules
whose density is respectively 1200 and 1500 kg m
-3
.
Tested materials differ as regards the origin, the
grain size distribution and the grain shape.
Materials from m3 to m8 and m15 are coarse, well
rounded river gravel particles with equivalent sizes
ranging on the whole from 31.5 to 4.0 mm and a mean
density of 2700 kg m
-3
.
Materials from m9 to m11 and m13 are coarse-
Fig. 1 - Laboratory flume and laser-scanner apparatus
testing low density PVC material
Table 1 - Tested Material - 2r, h: cylinder diameter and
height; d: particle equivalen
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A.M. DEGANUTTI , P.R. TECCA & R. GENEVOIS
316
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
granular media, are given.
The standard deviation for the values of angles
is less than one degree for around 60% of tests per-
formed for every material. Repeated tests in the same
experimental conditions gave differences generally
smaller than 2 degrees, a value which is about our ap-
paratus and measurement system accuracy range.
For comparison, a series of direct shear tests were
conducted using direct shear box tests to determine
the consolidated-drained shear strength of some of
the materials tested on the flume (Standard Refer-
ence: ASTM D 3080 - Standard Test Method for Di-
rect Shear Test of Soils Under Consolidated Drained
Conditions). PVC materials (m1 and m2), coarse natu-
ral sands (m16) and mixed rounded and sub-angular
gravels (m17) were tested.
Mohr’s failure envelopes have been obtained
using the peak stresses recorded by shear box tests.
PVC (m1 and m2) materials gave quasi-static friction
angles ranging as a mean from 30.6° to 33.9°, differ-
ences being due mainly to difficulties in obtaining the
same initial density and to the distribution of parti-
cles axis with respect to the shear plane. High val-
ues of the quasi-static friction angles were obtained
for m16 (35.0°) and m17 (46.8°) materials. In these
cases, however, the materials showed a contractive
behavior during shear that increased the initial bulk
density to quite high values and this occurred in spite
of the relatively high value of the normal stress (50
until the material slid; at this moment the plane rais-
ing motor was stopped and the slope of the flume was
measured.
Since the material was simply poured into the flume
and the heap resulted in a loose and chaotic state, the
first sliding was not considered as “natural”.
The plane was further tilted up until material slid
again and the tilting increase necessary to cause the in-
stability of the material was recorded, its value added to
the deposition angle gives the critical angle for stability
of the tested material; depending on material charac-
teristics, up to seven successive slides were obtained.
After each sliding stopped forming a uniform
slope, gradients to the horizontal (deposition or repose
angle) were measured by least squares interpolation
of the mathematical surface described by the laser
scanner (Fig. 2), along the middle longitudinal sec-
tion, in order to minimize possible disturbances due
to “side-effects” of flume walls.
The recording accuracy of the laser-scanner was
0.38 mm with a measuring range from 38 to 45 cm.
After every scan a digital photo of the material was
taken normal to the glass wall of the flume to check
angle measurement and the photos were digitally
processed to get the material slope.
RESULTS
A total of 143 tests have been done, some in the
same experimental conditions in order to check their
repeatability.
In Table 2 synthetic resulting data are reported:
for every tested material the average values of the
critical and repose angles and their difference, a delta
value which is a measure of the yield strength of the
Fig. 2 - 3-D Laser Scanner survey restitution of the sur-
face of material m3 after a slide in the flume
Table 2 - Average values of deposition and critical an-
gles.
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CHARACTERIZATION OF FRICTION ANGLES FOR STABILITY AND DEPOSITION OF GRANULAR MATERIAL
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
317
of the values shown by the single size classes, but in
different order (the deposition angle was close to the
low ones and the yielding angle was close to the high
ones) with the result that the angles “Delta” of m8,
resulting from a mixture of 20% in weight from a, b, c,
d, e class sizes, is the lowest for rounded river gravel.
Again, mixed angular gravel (m11) showed be-
haviour similar to river gravel, with smaller variations.
Apart from the mixed sands (m12 and m14) no
sorting mechanism or “Brazilian nut effect” (H
eR
-
Rmann
& l
udinG
, 1998) was noted for different size
grains, given the quasi-static experimental conditions.
6 - Materials m12 and m14, formed by a mixture
of sand and finer particles, showed an irregular be-
haviour with a size mechanism of separation: when
the bigger particles slid, the finer (silt) remained in
their previous position with a slope higher than the
deposited sand grains and forming a surface of irregu-
lar shape. This behaviour is probably due to an elec-
trostatic interaction (H
unGR
& m
oRGensteRn
, 1984)
among the fine particles giving them a cohesion effect.
7 - The density of material does not have an evident
role in the yielding and deposition of material with the
low density PVC having higher angles than the high
density one, both for critical and deposition conditions;
this can be explained by the higher friction showed by
the “rubbery” surface of the low density PVC granules.
8 - The amount of mobilized particles during a slide
is the minimum necessary for material to achieve the
new repose profile, an example of “natural economy”.
9 - From video shots of the granular slope failures
it was possible to recognize two failure mechanisms: a
general yielding of the slope starting from the top and,
with materials m12 and m14 (mixture of sand and silt)
the failure started from the toe climbing back the slope
in a negative wave fashion.
CONCLUSIONS
The authors presented a series of laboratory tests
in order to characterize two values of friction angles
showed by different materials in particular limit condi-
tions: a stability critical one and the deposition angle.
Critical angle measurements with an adapted tilt-
ing plane gave repeatable results within 1-2 degrees and
were not affected by the volume of employed material.
The use of natural cohesionless granular material
is of particular interest for its close relation with the
stability of scree slopes which are prone to debris-flow
kPa). The contractive behavior is the consequence of
an initial void ratio higher than the corresponding one
for that normal stress. Besides, it should be noted that
a contractive behavior has already been found for field
conditions in Acquabona site (G
enevois
et alii, 2000).
COMMENTS
1 - Apart from the mixed sands the tested materi-
als showed a regular behaviour characterized by con-
stant (in cited limits) deposition and critical angles,
with the deposited granular mass forming a regular
and uniform plane surface (Figg. 1 and 2).
2 - The lowest deposition angle was showed by high
density PVC (28.6°) due to the smoothness of grain sur-
face and to the cylindrical shape, giving to grains low
resistance to sliding and some rotation ability.
A bit surprisingly, the lowest yielding angle is
given by the size class e (4.0 < d < 8.0) rounded gravel
with 34.0°, against 35.2° of high density PVC. This
fact shows that the difference between the two char-
acteristic angles (angle “delta”) is not constant for dif-
ferent grain size.
This can be considered another proof that the
yielding and deposition processes are physically dif-
ferent and that it is generally incorrect to consider a
single generic “friction angle” when applying the
Coulomb equation to the different conditions in which
a granular mass can be.
3 - The highest value for critical angle was showed
by size c (11.2<d<16.0) angular gravel showing a high
resistance to yielding (due to its angular shape) while
its deposition angle (35.3°) is a bit higher than that
of rounded gravel of the same size (33.7°) showing
that the grain shape is relatively less important in the
deposition process.
4 - The size of grains of similar shape has the clear
effect of giving a higher stability to bigger grains: val-
ues of critical angle for rounded gravel go progres-
sively from 34.0° to 40.8° with size going from 4 to
31.5 mm. The same effect is shown by the same gravel
for the deposition angle even if with slighter varia-
tions. As a consequence, the “Delta” between yielding
and deposition angles decreases with size.
The angular gravel has a similar behaviour with
regard to yielding angles, while its deposition angles
seem to be unaffected by size.
5 - Tests with a mix of different grain size gave
results for characteristic angles which are in the range
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A.M. DEGANUTTI , P.R. TECCA & R. GENEVOIS
318
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
triggering, especially in the Dolomites area.
These angles, here defined and measured, are of
paramount importance for the rheology of granular
materials and in particular for debris flow studies,
where the consideration of a generic friction angles
(e.g. in debris flow numerical models) as character-
istic for yielding and deposition of a flowing mass,
could lead to results far from reality and in particular
to an underestimation of the maximum runout of de-
bris flows and other granular flows.
ACKNOWLEDGEMENTS
The authors are grateful to Stefano Castelli for his
competent work with laser scanner.
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i
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