isrm-eurock-1996-020_influence of particle size on the shear behaviour of rock joints
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Eurock '96,Barla (ed.) 1996 Balkema, Rotterdam. ISBN 90 54108436
Influence of particle size on the shear behaviour of rock joints
Influence de Ia dimension des grains de Ia roche sur Ie comportement en cisaillement
des joints
Del' Einfluf del' Partikelkomgrofse auf das Scherverhalten von Kluftflachen
K. K. Kabeya - Rock Engineering, CSIR, Miningtek, Pretoria. South Africa
T. F. H. Legge - Department of Civil Engineering, Rand Afrikaans University, Johannesburg. South Africa
ABSTRACT: In order to study the influence of particle grain size on the shearing behaviour of rock joints, a series
of tilt and shear tests using a model material has been conducted in the laboratory. The average particle size index
has been suggested to be the most appropriate parameter to represent the particle size distribution as compared
to the geometric mean particle size. It has been found that the joint roughness coefficient, as well as the peak and
residual friction angles increase with the average particle size index while the base friction angle does not.
However, it has also been shown that the residual friction angle can differ from the base friction angle with
increase in the particle size and, in this case the residual friction angle can be expressed as a function of the base
friction angle and the average particle size index.
RESUME: L'inlluence de la dimension des grains de la roche sur Ie comportement en cisaillement des joints a
ete etudie en laboratoire. Deux types d'essais a savoir I'essai de basculement et I'essai de cisaillement en boite ont
ere realises sur un rnateriau synthetique. L'indice moyen de dimension des grains a ete propose com me etant Ie
meilleur index pour definir la distribution des grains au sein de la roche, ceci en comparaison avec la moyenne
geometrique des grains. Les resultats ont montre que Ie coefficient de rugosite du joint, l' angle de frottement
residuel ainsi que l'angle de frottement en pic augmentent avec la dimension moyenne des particules exprimee
par I' indice moyen de dimension des grains, tandis que I'angle de frottement de base est independant de ce
parametre. L'etude a aussi rnontre que I'angle de frottement residuel peut etre different de I'angle de frottement
de base a cause de la dimension des grains. Dans ce cas, il est alors possible d'exprimer I'angle de frottement
residuel en fonction de l'angle de frottement de base et de I'indice moyen de dimension des grains.
ZUSAMMENFASSUNG: Urn den Einflul3 der Partikelkomgrolle auf das Scherverhalten von Kluftflachen zu
untersuchen, wurde eine Reihe von Neigungs- und Scherversuchen unter Verwendung eines Modellmaterials im
Labor ausgefiihrt. Zur Beschreibung der Partikelgrollenverteilung hat sich der mittlere Partikelgrofsenindex im
Vergleich zu der mittleren geometrischen Partikelgrolle, als der geeignetere Parameter erweisen. Experimente
haben gezeigt, daf sowohl die Rauhigkeitskoeffizient der Kluftflachen wie auch der Maximum- und
Restreib'ungswinkel mit zunehmendem mittleren Partikelgrobenindex ansteigen, wahrend der
Grundreibungswinkel unabhangig vom Index ist. Mit zunehmender Partikelgrofse kann jedoch der
Restreibungswinkel von Grundreibungswinkel abweichen, so daf in diesem Fall der Restreibungswinkel als eine
Funktion des Grundreibungswinkels und des mittleren Partikelgrolienindex ausgedriikt werden kann.
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I. INTRODUCTION
The behaviour of a rock mass is determined
principally by the shear strength of the jointing system,
which in turn is influenced predominantly by the
roughness of the joint surfaces. The standard shear
tests on joints indicate the presence of a peak shearstrength followed by the residual shear strength. This
behaviour is predominantly due to the dilation that
takes place during the displacement due to joint
roughness.
In rock engineering practice, the design against
failure of a potential sliding surface can be
accomplished either by use of the Mohr-Coulomb
failure criterion, which combines the normal stress
with the base friction angle and cohesion in a linear
manner, or by using a normal stress dependant
empirical law that corrects the base friction angle inorder to take account of the microstructure of the
sliding surfaces. In this regard, various parameters
have been proposed using different approaches to
characterise analytically the joint roughness. One can
cite the root mean square of the first slope (Myers,
1962); the roughness angle (Patton, 1966); the joint
roughness coefficient, (Barton and Choubey, 1978);
the fractal dimension (Carr and Warriner, 1987, Tse
and Cruden ,1979, Lee, 1988, Huang et al 1992); the
modi fied root mean square of the first derivative and
the average roughness inclination (Kulatilake et al1995). All these empirical laws can be expressed in a
general form which resembles to the earlier Patton
equation (Patton 1966), where r is the strength, a is
the norrnal stress, < P b is the base friction angle, andiis
the roughness angle of the joint:
r = 0 tan ( C 1 Jb
+i ) (1)
In the above-mentioned equation, it is possible to
differentiate the roughness characteristics representedby the parameter i, which, in fact, is mainly influenced
by geological properties such as the mineral
composition; the type of cement and the degree of
cementation; grain sizes; and the secondary minerals.
It is noteworthy topic of that most of the work done on
the surface roughness has always studied the surface
roughness by its "effect" which is the roughness itself
observed on the joint, whereas the "causes" which have
created such roughness, are frequently ignored.
Assuming that these geological parameters can be
grouped in three categories, namely the type of
mineral; the grain sizes, and the matrix material, as
shown in Fig 1, the philosophy used in t his
investigation is based on characterising the surface
roughness using these three parameters as inputs.
Pelton (i)
ertcn-Choubey (JRC)T'ae and Cruden (Z2)
Lee, Kliche (D)
Kulatikale et al (I,D,Z2')
"IG r'FlOW CIHlAR,: SHEA.j~ S JIl.IENG H
It follows that these three parameters are
independent variables compared to the surface
roughness which is regarded as a dependent variable.
In order to study the influence of anyone of the
independent variable it is necessary to keep constantthe other two variables. For instance, the influence of
the minerals on the joint roughness coefficient requires
that the grain size and the matrix material be kept
constant throughout the investigation. In this case it is
also assumed that there is only one type of mineral in
the rock type used. The same reasoning can be applied
when studying the grain size or the matrix in order to
assess their impact on the surface roughness.
However, in the real world, it is impossible to
find a rock type that complies with virtually allthese requirements. The model material would seem to
be the answer to the problem, in the sense that it will
facilitate the study of one particular variable while the
others are hold constants. It is also true that using only
a model material is not the perfect solution because the
behaviour of these parameters may differ from the
model to the rock material. Due to the complex nature
of the natural rock, a combination of these two
approaches is found more appropriate. For a given
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minerals, the grain size is the best parameter to
investigate because it can be easily measured.
Granular materials have been studied in soil
mechanics, and it has been found that the friction angle
increases with the grain sizes, and the relative density
(Kaibori and Tokudome 1993, Sadana et al 1994). It is
accepted that the shear behaviour of rock joints is
influenced by the grain size. Generally, fine grained
rock tend to have a lower friction angle, while the
coarse grained rocks have higher friction angles
(Willie, 1993). No analytical relationship has been
produced in which geological characteristics have
been related to the shear strength of rock joints.
The objective of this investigation is therefore
to study by the use of experimental and numerical
techniques, on a model material, the influence of
particle size on the surface roughness of rock joints,
and to develop subsequent correlation between the
particle size and the shear strength parameters.
2. TESTING PROGRAMME
The testing programme comprises both tilt and
shear tests performed on the model material and on
natural rock (prototype). Thin section result was made
available for the natural rock tested during the
investigation. The surface roughness was characterised
Using Barton's joint roughness coefficient (JRC)
obtained by the tilt tests or back-calculated from the
shear tests (Barton &Choubey 1977).
3. MACROSCOPIC FAILURE MECHANISM
Assuming that the surface roughness is made of
Particle grains embedded in a matrix, the shear failure
mechanisms of a joint can be described in three
different ways:
-dilation by sliding over the particle grains (asperities)
-shearing through the particle grains (asperities)
-Ploughing of asperities by tearing of particle grains
and eventual sliding over particle grains.
The welding is the fourth type of deformation process,
in which joints undergo a complete plastic deformation
Where a rearrangement at microscopic level of the rock
itself can occur. It is generally an exothermic process.
This type of failure is of less interest because it only
OCCurswhen the normal stresses are very high.
The occurrence ofthese mechanisms depends upon
the normal stress acting on the joint and the relative
toughness of the particle grains and matrix. For
instance, at low normal stress, strong particle grains
forming strong asperities within a strong matrix will
result in a sliding of surfaces giving rise to dilation.
In general, the failure shearing mechanism of natural
joints is a combination of two of the three basic failure
mode described above. Fig 2 illustrates the different
possibilities of failure shearing mechanisms for this
model.
4. MODEL MATERlAL
[- ~Strong l".ill. w ] r. Diiation+slid.,'arl. Gr l
I~a.~ 2 . S he a i o g
Sim g
I ~_Soft [ - l " . J O v : ] 3 Shearing~Parl. Grl
~.".hie~ 4. Shearing
lMatrix]
Stw~! -['" r ; ; ; : ; ] S. Ploughing~ +clilation.
~ i/illJ 6. Ploughing.
s O f l l " { ' " low] t, S caring[Pari. G! - [._:::;]
1, hip,hJ &. Plastic welding
[Sofl
FiG 2: AllLURE SEEA\RING MECHANISMS
4.1 Composition design
The composition design presents the grading process
of the model material. From norite, the prototype rock
type, eight fractions, namely 0.075, 0.15, 0.3, 0.6, 1.18,
2.36, 4.75, 6.7mm of crushed particle grains were
obtained by sieving. Two concepts, the fraction and
composition need to be clarified: A fraction is defined
as the mass of sieved material reatianed for any sieve
opening. It is expressed in terms of a percentage of the
total mass of the aggregates. It is assumed that the
eight fractions are all different from one another and
there is no repetition of particle grains of any size in
two successive fractions. Composition is the
combination of eight fractions in any given proportion.
A composition is defined by the average particle size
index, As and the geometric mean particle size, M;
The process of proportioning different fractions
within any composition was carried out randomly on
trial basis. Five compositions have been selected taking
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into account the following guidelines: Grading had to
spread as much as possible, lying from the very fine to
the very coarse. Fine composition means that there isa
significant proportion of fine grained particles while
coarse composition is the reverse. Expressed in
percentages, the sum of combined proportions of all
eight fractions yield 100% for each composition. The
average particle size index had to be firstly determined
in order to get an near linear increase of the index (I to
5) whilst the grading passes from fine to coarse
composition. In the second stage, the geometric mean
particle size was then calculated.
The average particle size index As has been
calculated in the same way as the Fineness Modulus in
concrete technology. The index measures the average
particle size based on a purely empirical classification,
and furthermore, It does not describe the grading itself
(Fulton 1977, 1986). The average particle size index As
is given as follows:
A =_l_t (Pk)
s 100 k:1(2 )
where k is the number of fractions and P k is the total
mass percentage retained on each fraction (sieve).
The geometric mean particle size M, has been
obtained by summing the products of the geometric
mean of sieve openings and the corresponding
percentage of the fraction.
M=(X1
)*p+t(tx *X*p) (3)s 2 1 k:2 V k r L k k
where: X , =First and smallest sieve opening 0.075 mrn
PI =corresponding proportion (percentage)
k= fraction number (1 to 8)
P k =proportion in mass of kth fraction
(percentage)
X, =kth sieve size opening
Table I gives the grading of the different compositions
retained tor the study and Fig 3 the grading curves.
4.2 Preparation and curing procedure
Polyester resin (Crystic 900 PA) has been chosen
as a matrix material because of its strong bonding
capacity that is almost similar to that observed in the
norite. Plaster of Paris and cement were not used
because of their soft bonding characteristics.
Plate I: Joints obtained after splitting
~ 100
:
/
.I
L-- 7V1--'"
eziiiII)
Q.w
~zw
~WQ.
W>
~:J
:Ii!:JU
80
60
40
20
o0.01 0.1 1
SIZE OPENING (mm)
10
___ Cl C2 .....C3 C4 ....CS
FIG 3: PARTICLE SIZE ANALYSIS
GRADING CURVES
Table I: Particle size analysis: grading curves
GROUP C JlfVU QJMl'nl'I1lIJt.I
rlACTW1S U 1l1'1~"IN(l
" ,-,
" " " " "f--- uI.
GRAVl;L A (,'ll IIlU rm 11M ) lUll II.T,V
0' ." . " v s 'U, "Ef---"f--- ER
C
' " ' " . " . " "' -tn ',
E
N
' 1 0 " . . ." " lOBT
SAND
"
u(,(I
'" " " "
11M
A
SU}U . , ., ie un . . ,s,
lIn s tN ou " " 10
t--- G
I---
~NE nun "' '" '" '" '"
COMI'OSITION PARAMETERS
A VERAGF. PARTICLE SIZE INDEX A. lilA 21(,
'" "" ""GEOMETRIC MEAN PART SIZE " . nH U( un ' ' 6 ru
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Specimens were prepared by mixing aggregates for
each composition (C I, C2, C3, C4, C5) together with
the polyester. A round mould in mild steel of 54.5 mm
diameter and 260mm height was used for casting and
a vibrating table for compaction. Manual mixing was
found to be appropriate for the preparation. The setting
process, which is in fact part of the curing procedure
for the resin, has been performed at laboratory
temperatue (250 and 50% humidity). The average age
of specimens at testing was 28 days. The fresh joints
were obtained by simultaneously loading core at four
different points in order to induce a splitting tensile
fracture. Plate I shows split faces of specimens for
different composition C I, C2, C3, C4, and C5.
4.3 Mechanical properties of the model material
Preliminary tests have shown that the suitable resin-
aggregates ratio to be used for mixing different
compositions (CI, C2, C3, C4, C5) was 35%. Table 2
gives the four mechanical characteristics determined
in order to assess the similitude requirements
(Stimpson 1970, Van Jaarsveld 1972). Nevertheless, it
appeares that each these four properties decreases as
the average particle size index increases.
Table 2: Mechanical properties: norite, resin, and
model material
Comp, A. ucs [MPal E [GP.J UllJ IMP.] DOSS [MP'J
Nor ite 4.5 243.7 102.0 14.9 23.1
Resin 105.3 3.1 47.3 32.0
CI 1.08 122.0 15.0 21.9 20.5
C2 2.16 114.3 15.0 20.4 15.2
C3 3.12 93.4 13.0 16.0 15.9
C4 4.10 70.0 9.0 9.1 16.6
C5 5.40 61.8 5.3 6.9 11.4
UCS: Uniaxial Compression Test, E: Young's
mOdulus, UTB: Uniaxial Tensile Strength by Brazilian
method DDSS: Double Direct Shear Strength
(Punching test, Stacey, 1980).
4.4 Similitude requirements
Dimensional analysis applied to the data in Table 2
gives three sets of similitude parameters in Table 3.
7t1 = UCSIUTB, 7t2= EIUCS, 7t3= DDSSIUTBIt can be seen that the similitude parameters 7t1, 7t2 are
not consistent. The main reason for that is the resin
used in the modelling process which tends to model
more the macro mechanical failure mechanism as
observed on the prototype rock than other properties.
This can also be explained using the distortion theory
which allows a certain distortion on other similitude
parameters than the one for which the problem has
been modelled (Van Jaarsveld 1972, Ivicsics, 1975).
In fact, the similitude parameters 1t1, 7t2 appears to be
less relevant to the study than 1t3 which is the ratio
between the double direct shear strength and the tensile
strength.
Table 3: Similitude requirements.
Composition A."
rr
"Nor itc 4.5 16.4 418.5 1.55
CI 1.08 5.6 122.9 0.94
C2 2.16 5.6 131.2 0.75
C3 3.12 5.8 139.2 0.99
C4 4.10 7 .7 128.6 1.82
C5 5.40 9.0 85.8 1.65
5. DISCUSSION AND INTERPRETATION OF
RESULTS
5.1 Joint roughness coefficient
The joint roughness coefficient (JRC), as well as
the shear test results are summarised in Table 4. The
JRC values measured by tilt test and those back
calculated evidence the same trend. The coarseness of
the particle grain increases with the JRC value. The
larger the average particle grain size, the higher the
joint roughness coefficient. It is also noticed that, the
JRC values estimated by the tilt test are lower than
those obtained by back calculation from the shear tests.
Hsuing noticed the same behaviour when testing
natural joints in order to compare methods of assessment of joint roughness coefficient (Hsiung et al
1993). Once again, the issue of effectiveness of the
methodologies available for determining the joint
roughness coefficient is raised. This particular
question is beyond the purpose of this study and needs
special attention. The graph JRC =f(A,) for the tilt test
and back calculated values is given in Fig 4. The power
regression fits both sets of data, and formulas are
successively as follows. The correlation coefficients
are successively 0.90 and 0.84.
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Table 4: shear test results
Composition As M, JRC@ JRCb"ckcal- Phib",c Phi,c,' Phipc"k
Norite 4.5 LSI 6.5 [5.2] 7.8 32.3 38.5 56.6
Cl 1.08 0.34 4.2 [18.3] 6.6 33.2 33.8 49.6
C2 2.16 0.64 5.7 [7.4] 7.5 32.7 36.3 57.7
C3 3.12 0.87 5.7 [20.2] 11.0 31.3 37.1 64.6
C4 4.10 1.46 8.1 [8.1] 11.6 31.9 38.5 66.7
C5 5.40 3.18 8.0 [5.5] 11.0 32.4 39.9 65.2
Note: [] Coefficient of determination (Tilt tests)
JRC=4. 027 *A~41B (Tilt t.)
JRC=6. 313*A~3Bl (B. calc.)
U~14
>-Z
~ 12u
H :ur 10oU
~ Bur
z6 6::>o~ 4
z 1
Q
-" - >-
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angle equation is close to the base friction angle of the
model material, which is basically the same as the
natural rock (norite). It is therefore possible to write
the residual friction angle as function of the base
friction angle and the average particle size index as
follows:
(7 )
Peak friction angles are also given in Table 4. Each
value is a best fit of 5 apparent friction angles
obtained at successive normal stresses: 0.5, I, 2, 2.5, 3
MPa. For each specimen, "apparent friction angle" is
defined as a peak friction angle assuming that the strait
line passes through zero. It has been noticed that the
apparent peak friction angles as well as the peak
friction angles both increase with the average particle
size index.
The graph in Fig 5 shows the relationship between the
index As and the peak friction angle p, fitted by a
power law:
It has recently been shown by Sadana that for a
granular material the shearing resistance, expressed by
the friction angle, increases with the relative density
and as well as the particle size (Sadana et aI, 1994).
Although, it has been reported for granular material
and not for rock, this supports the above findings
which show an increase in residual and peak friction
angles with the average particle size index.
5.3 Efficiency of/he average particle size index.
The average particle size index As and the geome-
tric mean particle size M, correlate very well with the
shear parameters, namely the joint roughness
coefficient, as well as the residual and peak friction
angles. There is a poor correlation between these two
parameters and the base friction angle as shown in
Table 5. Correlations of JRC, , , < I J , against ~ are
found to be better than correlations of these parameters
agai nst M, Therefore, 4 : - is suggested as the best
parameter to use to represent the grain size
distribution.
For natural rock joints, the average particle size index
can be estimated from thin section results. The value of
4.5 has been found for the norite.
Table 5: Regression analysis: correlation coefficient.
Parameters
!R e.,,"" JRC~ .~ .(.) < 1 > .(.) < I > ( . )
A. 0.90' 0,84' 0.40" 0.99 0.88"
M.llIllll] 0.87 0.67' O.IS' 0.91" 0.70'
Note: * Power best fit, ** Logarithmic best fit.
6. CONCLUSIONS
Based on an experimental study, the influence of
particle sizes on the shear strength of rock joints has
been investigated, and the following conclusions can
be advanced:The average particle size index (As) has been proposed
as a parameter to represent the grain size distribution
for a rock joint. Test results indicates that the particle
size expressed in terms of average particle size index
increases with the joint roughness coefficient, together
with the peak and residual friction angles while the
base friction angle is not influenced by the index. A
power correlation has been found between the index
and the above-mentioned three parameters. However,
it has been shown that in some cases the residual
friction angle can differ from the base friction angle, inwhich case it is suggested that the residual friction
angle should be expressed as a function of the base
friction angle. This study was preliminary. Further
experimental test results on natural joints are under
investigation in order to assess the practicability of
these correlations.
7. ACKNOWLEDGEMENTS
This study was financially supported by the CSIR-
Ematek, Pretoria. The authors also wish to thankcolleagues at Ematek as well as in Miningtek, specially
Dr John Napier for his encouragement.
8. REFERENCES
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