ISRM-EUROCK-1996-020_Influence of Particle Size on the Shear Behaviour of Rock Joints

8/12/2019 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

-" - >-


7/8

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

Barton, N. & Choubey, V. 1978. The shear strength

of rock joints in theory and practice. Norwegian

Geotechnical Institute. 169: 3-54.

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Carr, 1 . R. & Warriner, 1 . B. 1987. Rock mass

classification using a fractal dimension. 28th

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Fulton, S. F. 1977 &1986. Concrete technology, A

South African Handbook. Portland Cement Institute:

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Huang, S. L.; Oelfke, S. M. & Speck, R. C. 1992.

Applicability of fractal characterisation and modelling

to rock joint profiles. Int. J Rock. Mech. Min. Sci. &

Geomech. Abstr. 29: 89-98.

Hsiung, S. M.; Goshi, A.; Chowdhury A. H.; &

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Ivicsics, L. 1975. Hydraulic models. Water Resour-

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Kaibori, M. & Tokudome Y. 1993. Study on the

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Patton, F. D. 1966. Multiple modes of shear failure in

rock. Proc. 1st Int. Congo on Rock Mechanics I,

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Stacey, T. R. 1980. A simple device for the direct

shear strength testing of intact rock. Journal of the

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Singh, S. K. 1988. Relationship among fatigue

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271-276.

Stimpson, B. 1970. Modelling materials for

engineering rock mechanics. Int.. J . Rock Mech. Min.

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Tse, R.& Cruden, D. M. 1979. Estimating joint

roughness coefficient. Int. J Rock Mech. Min. Sci.

&Geomech. Abstr; 16: 303-307.

Van Jaarsveld, A, P. 1972. High alumina cement

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