ISRM-8CONGRESS-1995-074_A Comprehensive Peak Shear Strength Criterion for Rock Joints
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Eurock '96, Barfa (ed.)!$;) 1996 Ba fkema, Ro tterdam. ISBN 90 5 41 08 43 6
Rock joint shear mechanical behavior with 3D surfaces morphology
and degradation during shear displacement
Comportement mecanique avec modelisation 3D d 'un joint en cisaillement
Das mechanische Verhalten und die 3D-Modellierung der Morphologie der
Oberflachen und ihrer Beschadigung in Direcktschnitt-Proben
Guy Archambault &Rock Flarnand - Centre d' Etudes sur les Ressources Minerales, Universite du Quebecd Chicoutimi. Que .. Canada
Sylvie Gentier - BRGM. Direction de /0 Recherche. Or/eons, France
Joelle Riss - Centre de Developpement des Geosciences Appliquees, Universite de Bordeaux I, Talence, France
Colette Sirieix -ANTEA, Direction de /0 Geotechnique, Orleans, France
ABSTRACT: Joint shear behavior is analyzed in relation with profiles 20 statistical description, 3D statisticalmodelling of asperities angularity, geostatistical analysis and krigeage modelling to detect superposed structuresand restitute surfaces topography of a joint roughness morphology on replicas of a natural fracture submitted to
direct shear tests performed under various normal stresses and stopped at defined shear displacements. Theshear processes and progressive degradation on the replicas joint surfaces as well as their evolution are evaluatedthrough measurements of the damaged areas using image analysis. The evolution of the size and location of thedamaged areas arc analyzed in relation with normal stress for given shear displacement.
RESUME: Le comportement d'un joint en cisaillement est analyse en fonction de la description stanstique 20des profils, de la rnodelisation statistique 3D de l'angularite des asperites, de l'analyse geostatistique et dukrigeage permenant de detecter la superposition de structures et de restituer la topographie des surfaces de lamorphologie de la rugosite du joint, sur des repliques d'une fracture naturelle sollicitees en cisaillement directsous diverses contraintes normales et pour des deplacernents en cisaillement definis. Les mecanismes de cisail-Iernent et la degradation progressive des surfaces du joint sur les repliques, ainsi que leur evolution sont cvaluesen rnesurant les aires endornmagees a I'aide de la technique d'analyse images. L'evolution de la dimension et dela localisation des aires endornrnagees sont analysecs en fonction de la contrainte norrnale appliquee pour des
deplacements en cisaillemcnt definis.
ZUSAMMENFASSUNG: Das Verhalten von Kluftscherung wird analysiert in Benzug auf 2D-statitischeBeschreibung del' Profile, 3D-statitische Modellisierung del' Winkel von Asperiten, geostatitische Analyzen undKrigeagemodellierung, urn aufeinandcrgereihte Strukturen einer rauhen Kluftmorphologie auf Bausteinmodelleelnes naturlichen Bruches, festzustellen. Scheversuche an diesen Modellisierungsversuch wurden unterverscheidene norma Ie Spannungen ausgefuhrt und bei hestimmten Scherdeplacierungen angehalten. Del'Scherungsprozess und progressive Degradierung del' Kluftflachen des Bausteinrnodels wurden in den gestortcnZonen durch lmageanalysierung ausgewertet. Die Entwicklung del' Grosse und genaue Stellung diesel'Storlingszonen wurden analysiert in Bezung auf Norrnalspannung fur einen bestimmten Scherungswert.
fNTRODUCTION
The prolific literature on characterization and behavior
of single, irregular rock joints submitted to various
normal and direct shear loading conditions, to eva-
luate the needed mechanical and hydraulic parameters
In hydromechanical stability analysis of workings in
fractured rock masses (Stephansson 1985; Barton &
Stephansson 1990; Myel' et al. 1995; to cite only the
three organized symposium of the .ISRM commission
On rock joints) show their inextricable complex
behavior and characteristics. These numberless
research works on various rock joints problems
Confirm Scholtz (1990) statement that there is noconstitutive law for friction quantitatively built upon
micromechanical framework because of the com-
plexity of shear contacts, the topography of con-
tacting surfaces and the evolving surfaces topography
during sliding. A recent review of the literature onrock joints testing and modelling (Stephansson &
ling 1995) pointed out that there is still a large
number of problems to solve before having an overall
understanding of the phenomenon, particularly the
roughness morphology and the difficulty of its
characterization and modelling.
In this paper, an approach is reviewed for geo-
metrical description of joint surfaces morphology on
the basis of a 3D statistical description and modelling.
A contribution to the characterization of damaged
areas in relation with shear displacement under
constant normal stress is also presented, in which theevolution and geometrical characteristics of the
damaged zones are evaluated in relation with the
normal stress magnitude, for given shear displace-
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Table I. Classical linear roughness coefficients measured on profiles parallel to the shear direction.
Profile RL Z2 Z3 8rcgrcssion S /x mm2 Z4
z=f(x)
A B A B A B A B A B A B
I 1.029 1.029 0.251 0.246 0.547 0.608 1059 1063 0.108 0.092 0.089 0.190
2 1.030 1.031 0.249 0.254 0.528 0.551 00
5 6 00
6 4 0.281 0.286 0.111 0.220
3 1.033 1.033 0.263 0.264 0.597 0.581 - 007 4 - 007 6 0.327 0.321 -0.018 0.0244 1.041 \ .036 0.300 0.283 0.611 0.521 0
005 0002 0.585 0.552 0.057 0.101
5 1.022 1.030 0.212 0.254 0.448 0.56\ -1088 -1068 0.702 0.637 -0.017 0.048
6 1.042 1.043 0.300 0.306 0.556 0.590 - 00
3 4 - 00
3 7 0.493 0.485 0.136 0.103
248
damaged zones are evaluated in relation with the
normal stress magnitude, for given shear displace-
ment.
2 JOINT ROUGHNESS CHARACTERIZATION
Joint walls morphology characterization means here
that a 3D quantitative description of roughness evolu-
tion on the joint surfaces was done during laboratory
shear tests performed on a series of identical replicas
from the walls of a natural fracture in a granite
(Gueret, France) for which a detailed study of the
morphology was done (Gentier 1986; Riss & Gentier
1990, 1995). The replicas were submitted to direct
shear tests under three different normal stress and
each shear test was stopped at a defined shear dis-
placement for five displacements (Flamand et a!'
1994). This procedure permits a control on theevolution of the joint wall surfaces morphology with
shear displacement.
The shear stress, shear displacement, normal
stress and normal displacement being available at the
end of each test; a morphological analysis was
performed using five profiles, z=f(x,y), recorded on
the joint wall surfaces 15.26 rnm apart in four direc-
tions, digitized at a constant step (L'l.x=0.5 rnrn) and
kept constant for all shear tests (Flamand et a!' 1994;
Riss et a!' 1995). The analysis of these data consists
first in the deduction of parameters characterizing the
whole set of recorded points, i.e. the joint wallsurface expanding in a 3D space and, secondly, in
detailed distribution analysis of the 82 angles between
a reference plane and a line segment linking two
successive points on the recorded profiles. This
analysis is fundamental to restore the true 3D colati-
tude (83) distribution of elementary plane facets
composing the joint wall surfaces before and after
testing and correcting by the same way the bias intro-
duced by the profiles.
2. I Statistical description and analysis of the joint
surfaces
The overall analysis of the joint wall surfaces gives a
global view of the morphology and depends on
wheter we are interrested in the 3D spatial reality of
each joint wall surface or to each joint wall surface
recording directions related respectively to:
a) the total variance of all profiles set of points,
the residual variance and correlation coefficient after
linear regression of the altitudes z in function of the
coordinates (x,y) on the reference plane, the azimuthand colatitude in a given reference system of the
regression plane and of the principal plane resulting
from the diagonalization of variance and covariance
matrices of the whole set of points; or
b) the linear roughness coefficient RL, the z2, z3
and z4 coefficients and the linear regression parame-
ters (8rcgrcssion and residual variance ~.~).As the total variance is an invariant for a given
set of points (x, y, z referred to given reference
systems: VI01al = V x+Vy+V z) the spatial dispersion of
the set of recorded points and its evolution during
shear displacement can be measured and comparedproviding profiles are recorded at the same positions
on each wall surfaces of the fracture replica and kept
constant in each shear test. Taking into account both
variances and covariances, it is also possible to
compute estimations of the local mean plane of the
fracture that could be slightly different from the
regional one. They are based firstly on a linear
regression of z on x and y and secondly on deriving
the first principal plane from the diagonalization of the
variance-covariance matrix. The following analysis
performed on the joint wall surfaces under study
permits to establish that the local mean plane dipsslightly (5) in a direction perpendicular to the shear
direction, that the upper wall dips slightly more than
the lower one and that the lower wall is rougher than
the upper one. The detail of these analyses and
computations are given in Riss et a!' (1995).
From the computed linear roughness coefficient
(RL) (Table I), dependent on 82 distributions, and on
the basis of experimental 20 colatitudes distributions
characteristics, it is observed that probabilities of 82
is slightly higher than for the negative 82, but the
mean values of the latter are smaller than the other
one. In
average, there are more asperities in thepositive direction than in the opposite one but these
asperities are smoother than in the negative direction.
On the whole, repartitions of positive and negative
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angles can be considered as identical for wall A and
slightly more dispersed for wall B. Experimental 20
colatitudes (82) for both walls are quite similar and
the mean fW > is 10.310 for wall A and 10.080 for wallB while 8~-) is -11.910 and -12.490 for wall A and8respectively. Also, from Table I, the parameters
8rcgrcssion and residual variance S;.x indicate the trend
of the profiles to dip and the latter measures the part
of the elevations z that are not explained by the global
dip of the fracture replica. The dipping trend of
profiles can indicate probable zones of contact where
asperities may be damaged, particularly for the
profiles dipping towards the shear direction and
against the sense of shear displacement while, for
oppositc dipping, there will be a trend of the surfaces
to separate in creating voids between them. But these
situations depend also on asperities heights (CLA or
RS), profile roughness (RL), roughness dispersion
(S;.x) and other linear coefficients, So, looking at
one of them without taking into account informationsfrom the others can introduce large errors and biased
informations on the morphology of the surfaces.
Moreover, 20 roughness parameters are insufficient
to describe adequately the joint wall surfaces
IllOllJhology changing from to point to point.
2.2 Statistical modelling in 3D of roughness
angularities
Digitized profiles look like polygonal lines and a
polygonal surface results from a joint wall inter-
section wih a set of contiguous hexagonal prismsorthogonal to the mean regional plane. Then, the
surface is subdivided into small facets, small enough
to be considered as planar (Fig. IA). Angles between
the normal to facets and z axis are the real colatitudes
(83). As shear direction is parallel to the local mean
plane horizontal direction, it is assumed that 20
colatitudes (82), measured in vertical planes in this
direction, can represent any colatitude measured in a
plane perpendicular to the local mean plane. Using
classical method of 3D colatitude reconstruction
(Gentier 1986), inference of the 3D colatitudes distri-
butions is done (Fig. IB). The reconstructed distri-butions are not strictly similar for each wall, like the
20 distributions. Then areal roughness (RA) is
computed from these distributions in order to
evaluate, by comparison, the reconstructed distribu-
uons F(83) using RA values deri ved from a stereo-
logical method. The F(83) distributions being
acceptable, then theoretical models must be fi t to them
In order to have an expression useful for further
developments such as a simulation of the fracture wall
Surfaces and for estimating RA. Inference is done
either by fitting the 3D empirical distribution derived
frOIll the 20 (82) distribution to a model or by fillingthe 20 experimental (82) to a 20 distribution from a
3D model (Riss & Gentier 1989, 1990). The 3D
mOdels used are generalized axial distributions:
A)
Section
(prOfil~eFacet
Line of "'-reference T 8] I
rue ang e8,
Apparenl angle
B)3.5
3.0
(IN l(Jc
1.0
'" ~ 25.c
o0 .20
'0'
~.~ 1.5 .o
1.0
0.75
0.5
0.25
0.5
o
6010 20 30 403D Cotaliludes
50
K ~ R
A I M o d e l fhWaliA 16.58 1.10 1.0634 13
I
1611
WallB 15.08 1.25 1.0625 [ 13 15'96
A+B 12.06 1.65 1.0632 13 1588
I
Figur-e I. AlDcfinitions of 02 and 03 and stercogrnphic projection showing
the dependence of 02 on 03 the direction of the vertical section plane; ll) 3D
r ec onstruc te d distr ibutions and models for colatitudcs 83 with characteristics
of the filled models for 3D distribution.
Exp (Kcos~83)F(e3) =f l sin 03
o Exp(Kt~)dtModels derived from the fitting process are shown in
Figure IB with the parameters used and the charac-
teristics deduced for RA, the mode and the mean (8 3).The most important result is that the 3D elementary
facets dip in any direction with a mean angle of 16
and this angle is obviously greater than the 20 mean
angle of individual segments (Riss et al. 1995).
These statistical analyses and deduced physical
conditions of the joint walls permit to establish that a
perfect matching between the surfaces is highly
improbable with the differential variation between
walls dipping and roughness as well as between 20and 3D colatitudes (82 and 83) or asperities slopes
distributions on both walls. Moreover, Gentier
(1986), in its evaluation of voids between the joint
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walls, has illustrated a series of profiles of both walls
adjusted together in which large void spaces and few
contact areas could be seen between them. 3D analy-
sis of enclosed void spaces between the fracture
surfaces to evaluate voids morphology, either by
statistical simulation or casting of voids, show also
few contact areas between joint surfaces (Gentier &Riss 1990). These studies also show that most of the
contacts seem to be located on the slopes of asperities
and it even may happen that on particular profiles no
contact can be seen. Equally, an anisotropic joint
shear behavior with shear direction and sense may be
deduced from the previous analyses and be attributed
to the slight dip (5) of the tested joint local mean
plane perpendicular to the shear direction used, the
dip variations of the profiles with the recorded direc-
tion, the variability in roughness of each joint wall
and the dissymmetry between the positive and nega-
tive colatitudes (82) on the profiles.
2.3 Geostatistical analysis a/joint sur/aces
Even with all these quantitative statistical analyses and
the more sophisticated 3D statistical modelling and
characterization of joint roughness angularities giving
a more realistic figure than the 2D statistical evalua-
tion, no spatial structural information is given
regarding asperities structures (shape, size, jogs,
waviness and others) for an adequate modelling of
joint shear deformation and strength. Asperities spa-
tial distribution and shape on joint wall surfaces arenot necessarily at random and the presence of super-
posed structures cannot be detected on 3D angularities
distribution (Fig. IB) and the presence of a major
structure like a jog showing high angularity (>45),
this will not change appreciably the distribution
shown. But the mechanical shear behavior will be
greatly affected by this structure which will control
the joint shear strength and the related dilatancy
behavior. Various methods are available to do it and
among them geostatistics with which variograms and
variographic analysis of profiles permit to characterize
the size of asperities structures (range) related to theheights, curvature radii and angularity distributions
while krigeage modelling and simulation can restitute
the topographic surfaces (Fig. 2) (Gentier 1986;
Gentier &Riss 1990).As an example, the variograms analyses applied
to heights, curvature and angularity statistical
distributions on various samples of Gueret granite
joint surfaces show at least two overlapping asperity
structures: 4 to 6 rnrn and 18 to 20 mm, and also a
large one (40 mm) causing a 5 dipping of the joint
plane sample. The chosen shear direction was
parallel to the principal structure, so that only theroughness morphology represented by the 3D
colatitudes (83) distributions (Fig. IB) are controlling
the joint shear behavior.
Fi~urc 2. Example of krigcage of a j o in t s u r fa ce based 011 an isotropic
spherical variogram model. ({lJler Gcnticr, /986)
3 JOINT SHEAR BEHAVIOR PHASES WITH
SHEAR DISPLACEMENT
3.1 Direct shear testing and results
The direct shear test results come from a shear test
program (Flarnand et al. 1994) on joint replicas
submitted to three different constant normal stress (7,14 and 21 MPa). The 15 shear tests were performed
and stopped at various shear displacements (0.35,
0.55, 1.0, 2.0 and 5.0 rnrn) and the results are
summarized in Figure 3. In Figure 3A the shear
stress-shear displacement-dilatancy relationships arc
recorded for the shear tests done. These results arc
plotted, for the main characteristics, in a Mohr
diagram (upper part, Fig. 3B) while the lower
diagram shows the dilatancy rate (or angle) in relation
with normal stress (ON)' These results are compared
with LA DAR model (Ladanyi &Archambault 1969)
for io values of 15 and 30 and with Barton's model(Barton 1973) for JRC values of 10 and 14, values
estimated with the Z2 coefficient in Table I (Tse &
Cruden 1979). A good agreement between experi-
mental results and io values of LADAR model
between 15 and 17 very near the mean ih value of16 (Fig. IB) evaluated statistically for the 3D
angularity of asperities on the joint surfaces. The
same observation regarding dilatancy rate (or angle
dnr) behavior with the normal stress where dl~r took
values of 14.1,11.7 and 10.4 for ON= 7,14 and21 MPa respectively for very low ON/Oc (values
between 0.1 and 0.3). This also is in better
agreement with the reconstructed 3D distribution of
asperity angularity discussed in detail in Archambault
et al. (1995). A compilation of peak dilation angles
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and 1/(JN values from direct shear test results
performed on various rock joints by different workers
(Barton 1973) including Barton's own results as well
as those from Ladanyi & Archambault (1980) on
irregular tensile fractures and more in the last decade
confirm a certain trend for io values to be between IS O
and 35 limits and for dnf, variation between 0 and
25 at peak, was observed.
3.2 Shear behavior phases
The shear process and mechanisms of a joint with
irregular surfaces, on the basis of the previous
results, may be summarized in the following phases
(Fig.3A):
Pre-phase: Normal loading on the mean shear
plane of the joint concentrates the normal stress on
very few points (contact areas) with a normal closure
depending on normal load magnitude and joint
surfaces asperities morphology well studied in theliterature (Goodman 1976; Gentier 1986; Bandis et al.
1981 ) .
A
35
IV V30
" '~ 25lJl
lJl 20eV i
:;; 15
' ".c:(J)
10
5
(JNl (7 MPa)
(JN3(21 MPa)
(JN2 (14 MPa)
oo 1 234
Shear displacement (mm)
5
60 III(JNI (7 MPa)
III IV VN". . ,~ (JN2 (14 MPa)> < 40E.s: . .cc:
'" 20
]1Q
0-
0 1 2 3 4 5
Shear displacement (mm)
Phase I: Elastic mobilization of shear stress by
friction, with the shear load gradual application from
zero level causes a new closure (negative dilatancy).
It results in an increase of the real contact area until
gross slippage is imminent and it may reach three
times the initial static area without change in the
normal load. However for any two surfaces, the final
area is a numerical constant times the initial area
developed with the normal load only, so that the
proportionality between both forces (shear and
normal) at the point of slipping is maintained, and this
increase in contact area was called "junction growth"
by Tabor (1959). This phenomenon was indirectly
observed by an increase of induced interstitial
pressure (Poirier 1996) in this phase of shear
displacement on joints. This phase of increasing
shear load give rise to a transfer of the stresses on
asperities positive slopes defined by their angularity
and friction is mobilized on their inclined planes and
accompanied by their deformation. Phase 1 1 : A non-linear shear stress-shear dis-
placement-dilatancy hardening mobilization phase to
B
35 Fairhurst
30 Ladar(i = 30)
l.adar (i= 15)
~,,/' Barton (JRC=14)
/ . .,< Barton (JRC = 10),," .....;/ Basic friction
f r ; ; ~ ~ i > < ! :i ' , ' : m?{
/) - ....I. ....
25
.3.5mm
+ 5.0mm
-10I I
0 10 20 30
Normal stress (MPa)
30
25
dn20
15
10
I I - .
5 . . . . dnr al5 mm0
-v , --. ___ __ ~I~placemenl
0 10 20 30
Normal stress (MPa)
Figure 3. Direct shear lest results: A) shear srress-displnccrncnt-dilntancy relationships and U) calculated peak strength envelopes ami dilatancy
variation with nor mal stre ss ac cor ding 10 m o de ls a n d test results.
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4.2 Contact and damaged areas and their variation
with normal stress and shear displacement
Contact area between irregular joint plane surfaces,
after normal loading, is quite small in regards with the
total joint area (Gentier 1986). Phase I of friction
linear mobilization with the raising shear loadincreases the contact area (Tabor 1959) by a factor as
large as three times, as stated previously, while
mobilization of dilatancy in phase II reduces it
progressively to peak shear strength corresponding to
around 0.55 rnm of shear displacement. Following
this scenario the post-peak phases will show a
progressive degradation of the joint wall surfaces. To
quantify asperities degradation on the joint wall
surfaces, after each shear test performed on the fifteen
samples, an image analysis was undertaken on the
thirty images (15 replicas and 2 images per replica)
and the geometrical characteristics of the damaged
zones are measured: shape, size, position and/or
orientation. The whole process is detailed in Riss et
al. (1996). The damaged areas being defined, it was
Possible, with the sequence of five shear tests (for a
given normal stress) stopped at different shear
displacement, to analyze the evolution of the damaged
areas with shear displacement under constant normal
stress (Fig. 4). Also the evolution of damaged areas
7 MPA
50
40
te lQl
: ; : 30
Ql
Cl
te l
c:te l 20c" g0
10
0
0
are evaluated in relation with the normal stress, for
given shear displacement.
In general, there is an increasing degradation of
surfaces asperities by damage area extension with
increasing roughness, normal stress and particularly
with shear displacement. The analysis can produce a
slight underestimation of the damaged zones becauseof gouge sticking from one wall to the other without
change in color or by transfer of material without
crushing. From the analysis of results (Fig. 4), the
sequence of joint wall degradation may be summa-
rized as follow: first, for a given normal stress,
material from superficial parts of one wall is broken
away and crushed with shear displacement during
which the number of these deteriorating parts
increased and the size of the degradation zones
enlarged both depending on stress level. As normal
stress increased gouged material is crushed more
densely and sticked plastically on the surfaces with a
transfer of material from one wall to the other. The
anisotropy of the joint surfaces morphology show
degradation zones location depending on shear direc-
tion. After 5 mm of shear displacement and in rela-
tion with the applied normal stress (7, 14 and 21
MPa) the total damaged area evaluated, combining the
degraded zones of both walls (upper and lower) is at
most 23%, 33% and 58% respectively. With
21 MPA
7 M~a.
Walls% Area sheared
Upper: --Lower: -----
2 3 4 5
Displacement (mill)
Figure 4. Proportion of damaged area evaluated 011 Lipper and lower joint walls for an ::: 7, 14, 21 MPa and illustrated for three shear
displacements (0.55 111111,2 mill, 5 nun).
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increasing shear displacement, the damaged zones are
extending from the initial ones and by linking them to
become larger zones nearly perpendicular to shear
direction. More details on areas of damaged zones
and on position, orientation and spatial correlation
between upper and lower damaged areas are
discussed in Riss et al. (1996).
Observed sheared area proportions at peak shear
strength (phase III) are extremely low, between 2 and
3%, for the three aN values tested (7, 14 and 21 MPa)
(Fig. 4) and there was little variation with aNlaC in
this range varying from 0.1 to 0 .3 on them as i f aN
has no influence on sheared area. It is shown (Fig.
4) that most of asperity degradation resulting in
damaged (sheared) area occurs between peak and 3
mm of shear displacement corresponding to the
progressive softening phase IV of joint shear
behavior. Thus, at peak shear strength the normal
stress on c ontact areas is much higher than the
average joint applied normal stress, but despite this
fact for the three relatively low o-, values used, veryfew asperities were sheared off. If equating contact
and sheared areas, it means for aN =7, 14 a nd 21
MPa and contact area of I to 3 %, contact normal
stress of around 700 MPa (or 8 ac) an irrelevant
value. More appropriate values related to aN::; 2ac
means contact areas between 5 and 15%, so t he
difference must be in friction giving no damaged area
at failure.
ACKNOWLEDGEMENT
This is a BRGM contribution n 94059; this work
was financially supported by a BRGM research pro-
ject, an NSERC of Canada research grant and an
NSERC graduate student followship.
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Gentier S. 1986. Morphologie et comportement
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