ISRM-EUROCK-1996-031_Rock Joint Shear Mechanical Behavior With 3D Surfaces Morphology and...

8/12/2019 ISRM-EUROCK-1996-031_Rock Joint Shear Mechanical Behavior With 3D Surfaces Morphology and Degradation Dur

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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-

247


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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

249


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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

250


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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.

251


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7/8

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).

253


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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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