Rock joint compliance tests for compression and shear loads

Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. Vol. 22. No. 4, pp. 197-213, 1985

Printed in Great Britain

0148-9062 85 S3.00 + 0.00 Pergamon Press ktd

Rock Joint Compliance Tests for Compression and Shear Loads Z. SUN*'++ C. G E R R A R D + O. S T E P H A N S S O N *

A series of compression and shear tests were conducted at large scale on joint surfaces in granite and slate specimens, with special equipment being used to isolate the deformations of the joints from those of the rock material. The matrix of compliance components for a rock joint is discussed in relation to these standard tests and it is shown that one pair of compliance components can be determined from a compression test and a second pair from a shear test. Any attempt to base predictions of rock mass behaviour opt the combined use of these two pairs of components should take into account the different stress paths to which they relate. The nature of the contacts between the asperities on adjacent joint surfaces is considered as a means of suggesting the form of the stress-deformation relations, both in compression and shear. This approach is shown to be of great assistance in helping to explain the test results and fit the observed compliance characteristics. For the compression tests, the test results indicate a pattern of decreasing compliance with load, an increase in compliance with initial aperture, and high levels of recoverabili O' of deformation. In the shear tests, the curves for the relative displacements indicate there are three zones of different behaviour, elastic, transition and sliding. There appear to be links between the way in which forces are transferred at asperities and the typical patterns of observed compliance.

INTRODUCTION In practical situations, rock masses are often subject to stress increments due to man-made construction and/or excavation. The resultant deformations will be determined by the mechanical properties of both the rock material and the sets of discontinuities contained within the rock mass. The deformations can be divided into those that can be recovered if the stress increment is removed or reversed, i.e. elastic, and those that are not recoverable, i.e. plastic or brittle behaviour of the rock material and separation or slippage on the discontinuities. Failure accompanied by gross deformation will result in either the rock material or the discontinuities if the stress increments, when added to any pre-existing initial stresses, fulfil the respective failure criteria, It is generally recognized that while the mechanical properties of the rock material are much better understood than those of the discontinuities it is usually the latter that dominate the response of the rock mass. The results reported here are aimed at contributing to the redress of this imbalance. * Lulefi University of Technology, Division of Rock S-951 87 Lule& Sweden. + C.S.I.R.O. Division of Building Research, P.O. Box Victoria 3190, Australia. Present address: Central-South Institute of Mining lurgy, Mining Department, Changsha, Hunan, Peoples" China. RMMS

224

A

Mechanics, 56, Highett, and MetalRepublic of 197

The discontinuities in rock masses can take many forms, e.g. faults, joints, bedding and fractures. They may occur in the form of persistent sets that can be regarded as continuous over the zone of interest. Alternatives to this are where the discontinuities terminate when they encounter a more persistent discontinuity or simply terminate within the rock material. In the first two cases, the discontinuities are inter-connected but then are not in the last case. In reality, rock masses often contain both inter-connected and uninter-connected discontinuities. The deformation processes that influence the stability of the rock mass are the separation and sliding of inter-connected discontinuities and, to a lesser extent, the fracture propagation of uninter-connected discontinuities. Such propagation ultimately leads to interconnection, at which stage separation and sliding completely dominate. It has been observed in practice that, in many rock masses, a self-stabilizing process can develop if movement on discontinuities is restricted at the time of the imposition of an increment of stress. The manner in which this occurs appears to be linked to the pre-failure stress-deformation properties of the discontinuities. Knowledge of these properties is essential to take full advantage of this behaviour. In addition, several mathematical models have now been developed to model jointed rock masses and reinforced jointed rock masses,

198

SUN et al.: ROCK JOINT COMPLIANCE TESTS

e.g. Cundall e t al. [1], Zienkiewicz and Pande [2], Pande and Gerrard [3]. For input data, these models require information on both the stress-deformation and strength properties of the discontinuities. In the past, emphasis has been placed on the measurement of the strength of rock discontinuities, with relatively recent interest being placed on the stress-deformation properties that are discussed herein. With regard to the shear strength of joints, it is now well established that the strength increases with the level of the normal compressive stress, although at a decreasing rate as this compressive stress increases, Hoek and Brown [4], Barton and Choubey [5], Gaziev and Lapin [6]. The last two papers also present data showing that the dilation rate of the joints during shear failure decreases with increasing normal stress, apparently on the assumption that the joints are initially mated. The stress--deformation properties of discontinuities in rock masses have been studied by separately considering the behaviour in compression, and the behaviour in shear accompanied by constant compressive stress. For compression, Goodman [7, 8] has suggested a hyperbolic relation between increasing compressive stress and the normal displacement of one surface of the joint relative to the other. The inherent non-linearity was largely attributed to crushing of asperities leading to the conclusion that the normal relative displacements would be largely irrecoverable on unloading. Hungr and Coates [9] anticipated finding this hyperbolic relation between normal stress and relative normal displacement but their measurements plotted in an essentially linear fashion. They concluded that this was due to the test stresses not exceeding the field pre-compression on the discontinuities. An alternative view of the major mechanism involved in the compression of rock discontinuities has been presented by Swan [10], and is based on elastic Hertzian contact theory. Non-linear behaviour derives from the increasing contact areas and the increasing number of contacts. The results presented later in this paper suggest that this mechanism had a more dominant role to play in producing deformation than the crushing of the asperities. The results of shear tests on rock discontinuities, typically reported in the literature, indicate a shear stress-relative shear displacement characteristic that exhibits initial hardening and a near constant residual value. A maximum rate of relative normal displacement (dilation) is often associated with the relative shear displacement at which peak shear stress occurs. "Peaked" behaviour appears to be at a maximum for small test specimens of fresh, rough joints at low normal stress and also for tests of wet surfaces [11]. However, it does not appear to be an essential characteristic in the mechanism of the shearing of discontinuities since it is absent in many cases. These include (a) the triaxial behaviour of discontinuities that are generated during testing, and direct shear tests of relatively smooth surfaces [11, 12], (b) surfaces that are rough but "old" [13],

(c) surfaces that are rough, new, and have a relatively large area [14]. Because of the way in which stress-deformation tests are conducted on rock discontinuities, the measured properties can be best described in terms of compliance rather than stiffness which is the inverse of compliance. The various compliance components can be evaluated as either ratios or gradients relating the resultant relative displacements to the causal applied stress. To date, the compliance components of rock discontinuities have only been measured in "standard" compliance tests. following well defined stress paths. The results from such tests can be used as indices in order to compare the mechanical properties of different discontinuity surfaces. However, since the stress-deformation properties of discontinuities are stress-path dependent, so also will be their compliance components. This means that compliance components determined in one "standard" test do not necessarily relate to those determined in a second "standard" test, having a different stress path to the first, Ultimately, the objective is to develop a theory capable of predicting compliance components for general stress paths, thereby providing essential input for advanced mathematical models of boundary value problems of discontinuous rock masses. It is considered that the results of the "standard" compliance tests provided in this paper can provide part of the background information essential to the formulation of generalized stress-deformation theories for rock discontinuities. The literature on the measurement of the compliance of rock discontinuities is somewhat confused because several writers have attempted to derive stiffness components from what are essentially compliance tests. The distinction is trivial when the respective matrices only contain non-zero terms on their leading diagonals. However, this is rarely the case for rock discontinuities. For example, Hungr and Coates [9] give examples of both positive and negative values of the compliance component that relates the relative normal displacement to the shear stress, this behaviour being consistent with some of the discontinuities being initially unmated. These authors report their results in the form of "apparent" stiffness components. However. components of the stiffness matrix can only be determined by inversion of a complete matrix of compliance components. While each column in the compliance matrix is directly derived from each "'standard" compliance test, the process of matrix inversion ensures that no such association can be made for any row or column of the resultant stiffness matrix. It would appear that the development of a general compliance theory for rock discontinuities will depend on describing the interaction between stress path, surface wear, surface topography, and initial displacement conditions. The body of this paper contains four main sections in which rock joints are taken as a typical example of the more general term, rock discontinuity, as used in the above introductory comments. In the first section, the concept of the compliance of rock joints is developed

SUN et al.: ROCK JOINT COMPLIANCE TESTS and related to the surface topography of these discontinuities. Expressions are advanced to describe the compliance components involved in the standard compliance tests for compression and shear. The second part describes the test equipment, the test methods, and the specimens tested. The last two parts describe, in terms of compliance, the results of the compression tests and shear tests, respectively. DEFINITION OF COMPLIANCE COMPONENTS This section discusses the connection between the compliance of rock joints and the experimental methods used to evaluate the mechanical behaviour of such joints. Throughout this work the term stress is used to mean the average force per unit plan area of the joint. Hence, this does not represent the true stress at the contact points. The deformation of the joint is in the form of relative displacements of one of the joint surfaces with respect to the other surface. Through the interaction of the asperities of one joint surface with those of the other it is possible for these relative displacements to be either recoverable or irrecoverable. In general, there are three stresses (tractions) that can be applied to a rock joint, a one normal stress and two shear stresses. They may produce one or more of the three possible relative displacements of the joint, & analogously consisting of one relative normal displacement and two relative shear displacements. A 3 × 3 compliance matrix can be defined for the joint such that when it is post-multiplied by the 3 x 1 matrix of applied stresses it gives the 3 x 1 matrix of relative displacements, a =Ca. (1) A 3 × 3 stiffness matrix can also be defined such that, a =Ka,

(2)

and it therefore follows that, K = C

1.

(3)

When the compliance matrix only has non-zero components on its leading diagonal, the stiffness matrix will also only have non-zero components on its leading diagonal, the values of which are given simply as the inverses of the corresponding components of the compliance matrix. However, non-zero off-diagonal compliance components are commonly observed in tests of rock joints so that the relations between the stiffness and compliance components will be more complex than simple inverses. For example, in the two dimensional case the relations will be,

KII- D

= C22,

Kj2" D =

- - C21,

K21" D = - Cp.,

K~2' D = CI1, where D = Clt C22

-

CI2C21 •

(4)

199

In interpreting and predicting the behaviour of rock joints, the use of compliance is preferred to stiffness for two main reasons, (a) rock joint tests are usually of the type where one stress is varied while the other two are kept constant. One or more of the relative displacements are measured. Components of the compliance matrix for that particular stress path are directly determined by simply dividing the relative displacements by the applied stress. However, as explained earlier, components of the stiffness matrix can only be determined by inversion of a complete compliance matrix. As a result, none of the stiffness components can be directly linked to a particular "standard" test of the rock joint. To obtain components of the stiffness matrix directly, tests would need to be conducted where one relative displacement was varied while the other two were held constant. The stresses generated in such tests, when divided by the relative displacement, would directly provide stiffness components. (b) It is observed that, in practical field situations, shear failure of rock joints is usually accompanied by dilation. Since rock joint properties are stress-path dependent, it is therefore considered that the properties measured in "compliance" tests will be more representative of field conditions than those measured in "stiffness" tests. The main purpose of considering rock joint compliance is to facilitate subsequent analysis and prediction of the behaviour of jointed rock masses. Depending on the nature of these analyses and predictions, decisions can be made on whether to use the tangent or secant forms of the compliance. In the former, incremental changes in stresses and relative displacements are considered in place of the total values used in the secant approach. Throughout this paper the tangent compliance will be referred to as C' and the secant compliance as CL The two dimensional case is relevant to the test results discussed in later sections of this paper. If we choose axis .,q as the normal to the joint plane and axis x2 as the direction of shear within the joint plane, then a "normal" compliance test will enable the determination of the compliance components, C~ and C > Since the first of these, i.e. CH, relates the relative normal displacement to the normal stress, it is referred to as the normal compliance component. The second component, i.e. C2~, relates the relative shear displacement to the normal stress and is hence referred to as the shear/normal compliance component. In an analogous way a "shear" compliance test enables the determination of the two compliance components, C12 and C:2. Consistency of terminology requires these to be known as the normal/shear and the shear compliance components, respectively. The two pairs of compliance components, CI~,C,~ and CI>C= relate to different stress paths. As mentioned earlier, great caution should be exercised when they are used together to predict the behaviour of a rock joint subject to a general stress path. A general theory of stress-deformation needs to be developed to cover this case.

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MECHANICS AND SURFACE

The power law distribution is more generai m ~ts application to various stress levels and the following analogous relations apply.

TOPOGRAPHY RELATED TO

JOINT COMPLIANCE In general, the matrix of compliance components of a rock joint is a function of joint surface topography, the initial displacement condition of the joint, and the stress levels and paths. With regard to the normal compliance component, Cn, these factors can be taken into account through the application of the Hertzian contact theory. For example, Greenwood and Williamson [15] have examined the case of a rough surface being compressed against a smooth surface and have derived the following relation,

(Z -- d)3/2e~(z)dz,

~1 = g f l l / 2 r l E '

cr~ = (61/bo) l~b'.

c,

~Sb)

b0b,(0,] ~,b<)

(8c)

where b0 and b~ are constants. As an example of the application of the power law, ~t can be shown that, if q~ is assumed to be uniform, then equation (5) gives,

(5)

61 oc a~'3,

(9a)

d

where

while equation (6) gives,

B is the mean peak radius, r/is the peak density, E" is an effective modulus, z applies to the rough surface and is the distance from a peak to its reference plane, d is the distance between this reference plane and the smooth surface, and q~(z) is the probability density function of the asperity peak height distribution. The analogous relation for two rough surfaces being compressed together has been given by Greenwood and Tripp [16] as,

hi oc a~q

The above results indicate how non-linear behaviour can be predicted from the application of Hertzian theory even though linear elasticity is assumed. The effect of initial displacement of the joint, as measured by the initial aperture, ~ , on its normal compliance has been examined by Swan [10]. In applying the exponential law to Offerdal slate, tested over the range 0~
oO

o"1

C~I = 6il/al ~, constant.

4.74 fl~/2q2E" ~(z~ - e)Saq~(z~)dz~,

(6)

~t

a I oc diit.

where

Swan [10] has examined the application of equations (5) and (6) from cases where the distributions of peak asperity heights were either assumed or actually measured. In both cases it was possible to produce predictions of the variation of normal relative displacement with normal stress that compared well with experimentally measured curves. There were three assumed distributions that were found by Swan to be of considerable use, the exponential, the power law, and the Gaussian forms. The exponential distribution is easiest to manipulate and is more applicable to low to medium stress ranges. It gives rise to the following relations between al, 6~, and C]~, 61 = a0 + al In al, (7a) al = exp ( ~ ) , /'t~1

--

C~, = a,/a, =a,/exp~----~

a0\

),

(10)

Comparison with equation (7c) gives rise to,

e

z~ is the sum of the heights of the two surfaces, e is the distance between the reference planes of the two surfaces, and ~b~(z~) is the distribution of the summed heights.

(9b)

(11)

The shear/normal compliance component, C2,, was not measured in the tests reported herein and also does not appear to have been measured previously. It is unclear at this stage as to what importance should be attached to it and resolution of the matter requires further research. The deformational processes involved when shear loads are applied to rock joints, can be illustrated by considering the contacting hemispherical asperities shown in Fig. 1. With the normal force, F,, kept constant we initially consider the case where the shear force F2 is just sufficient to produce a resultant force that acts along the line joining the centres of the two spheres. This resultant will be, F'~ = F, sec i,

(12)

where i is the angle of inclination of the contact plane.

(7b)

If F2 is now increased by AF2 so that sliding begins to occur it can be shown that,

(7c)

Ft sec i cosec i AF2 = cot q5 cot i - 1"

where a0 and al are constants determined experimentally.

(13)

The resultant forces acting on the contact are the shear

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201

R O C K JOINT C O M P L I A N C E TESTS

xl Fig. 1. Normal and tangential asperity forces during shearing of a rock joint.

stress, F;. and the increment of normal stress, AF'~. These are given by, F;= AFI =

F 1 cosec i cot q~ cot i - 1' F~ sec i cot ~b cot i - 1"

C'~ = -

(14)

(%

-

-

mo)m , (15a)

or

r, -

"

62

m~ + m~62

~- too,

(15b)

while those involving the relative normal displacement, 6~, are, 61 = no + nl z~2, (16a) OF

r , = ( -6~- n ~ ° ' ] ~'"2 \ n~ / '

(ml + m262)2 ml [1 - -

ml

(16b)

(17a)

(Z 2 - - m o ) m 2 ] 2'

{6~-,,&' Ct12 = n~ n2 T"2: - l = n l n2 | - - /

k

It can be seen that prior to sliding there will be a tendency for F~ to produce positive increments of 62 apd negative (extensile) increments of 6~ while AF~ will tend to produce positive increments of both 6~ and @ The sign of the resultant increments of 6~ will depend on the relative magnitudes of q~ and i. Once sliding commences the increments of 62 will be positive and those of 6~ will be initially negative. For both the elastic and the sliding behaviour the application of shear stress produces both normal and relative shear displacements. Based on the above discussion, several empirical relations are advanced for shear tests of rock joints to describe the variation between the applied shear stress and the resultant normal and shear relative displacements. The ways in which these relations can be "fitted" to experimental data are discussed in a subsequent section of this paper. The empirical relations involving the relative shear displacements, 62, are, 62 = i -- ('r 2 - - m o ) m 2'

These empirical relations give rise to the tangent compliance components of,

nl

/

1°(17b)

The quantity m0 is intended as a zero correction and so its value is relatively small. Since 62 must always increase when r: increases, it follows that both rn~ and m2 must be positive. From equation (17a) it can be seen that the initial value of C~:, i.e. when 62 ---0, is given by mj and is a minimum. As 62 (or r2) is increased, the value of C;, gradually increases to reach an infinite value when re =mo + l/m2, i.e. when z2 ~ l/m2, on the basis of m0 being small. Peaked behaviour of the stress strain curve is not considered and, after the point of infinite compliance is reached, it is assumed that there can be no further increase in shear stress. The secant shear compliance can be derived from equation (15b), C~2 --

(ml + m262)02 mo(ml + m:62) +/L"

(18)

It will be shown later that for many practical cases the values of m0, m~ and m2 are such that equation (18) can be closely approximated by making the secant shear compliance, C~z, directly proportional to the relative shear displacement, 6z. The expressions for the rock joint compliance components described above will be discussed in relation to experimentally observed behaviour in later sections of this paper. Emphasis will be placed on determining the values of the constants involved in these expressions.

ROCK JOINT TESTING TECHNIQUES This section discusses the equipment, the specimen preparation, and the test procedures for both the normal compliance tests and the shear compliance tests.

202

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et al.:

ROCK JOINT COMPLIANCE TESTS

(b)

L~__/Norrnot loading cylinder

Fig. 2. Large scale shear rig, (a) photograph, (b) diagrammatic representation.

The compliance components of rock joints in normal normal displacement, A6,, and relative shear displaceand shear tests were measured in the direct shear rig ment, A6,, for the rock joint are, shown in Fig. 2. The shear box was 0.5 m long and A3. = (AUa + AUO/2, 0.35 m wide with the applied normal and shear forces A6s = (AUa - AUO/2 tan a. (19) being generated by a hydraulic system and measured by load cells. The maximum possible values of these forces were 1500 and 3000 kN, respectively, with the accuracy The accuracy of displacement measurement is of the of measurement being of the order of _+0.5 kN. During order of +0.004 mm. Three different types of rock were involved in the rock the test, the upper part of the shear box was held fixed joint tests, coarse grained red granite, medium grained and the lower part was pulled in the direction indicated grey granite, and Offerdal slate. The joint surfaces of the in Fig. 2b. The relative velocity between the two halves of the shear box was usually about 0.5 mm/min, with the grey granite were relatively rough, being generated by maximum being 2 mm/min. The maximum possible rela- fracturing in tension. The surfaces involved in the red granite specimen were artificially created and relatively tive shear displacement was 100 mm. The measurement of the relative displacements be- smooth, but with each having a different roughness. tween the joint surfaces in direct shear tests is often Since the granite specimens had been previously tested subject to errors, as discussed by Rosso [17]. In the tests in direct shear tests their surfaces should be considered reported here such errors were minimized by conducting as "old", as discussed by Jaeger and Cook [19]. The joint measurements as close as possible to the joint surface. surfaces of the slate specimen were created along a The apparatus used is shown in Fig. 3 and was designed cleavage plane and the resultant joint roughness was by Larsson [18] to operate within a hole drilled normal variable. The strength and deformational properties of to the joint plane through the centre of its area. The the rock material for each of three types are summarized lower part of this apparatus is fixed within the lower in Table 1. Photographs of the test surfaces for the red granite rock block and contains two planes that are inclined at angles of + ~ and - • with respect to the direction of and grey granite specimens are shown in Fig. 4, where relative shear displacement of the joint plane. The upper the trace lines for the profile measurements are evident. part is fixed within the upper rock block and includes The surface areas of the joint surfaces tested were two linear displacement transducers (LVDTs), each of 731 cm 2 for red granite, 1009cm 2 for grey granite, and which is in contact with one of the inclined planes 630 cm 2 for the slate. The compression tests on the rock joints were conduccontained in the lower part of the apparatus. If A Ua and ted in the absence of shear stress. On the other hand, for AUb are the incremental changes in lengths measured by the shear tests, there was a pre-applied and constant the two LVDTs, then the increments of the relative

SUN et al.:

ROCK J O I N T C O M P L I A N C E TESTS

Fig. 3. Apparatus for normal and shear relative displacement measurements of rock joints, (a) disassembled apparatus, (b) assembled apparatus, (c) installed apparatus.

Table I. Rock material properties

Rock type Red coarse-grained granite

Uniaxial compression strength qu (MPal

Young's modulus E (GPa)

233.9

67.9

Grey medium-grained granite

207.5

E, = 60.2" E S= 50.7 b

Slate

320.0

68.0

Poisson's ratio v

Reference

0.29

Bjurstr6m [20]

v~= 0.22 a v~ = 0.14 b 0.20

~E,, v~= tangent Young's modulus and tangent Poisson's ratio. hE, v~ = secant Young's modulus and secant Poisson's ratio.

Stillborg and Swan [21]

203

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ROCK JOINT COMPLIANCE TESTS ..............

-

-

Profile before t e ~ Profiie

offer

Test

E ~o -.1= .o, ¢u I"

0 iO 0

200

400

Profile

600

800

t000

'1200

length(ram)

Fig. 5. Normal stress-normal relative displacement curves for Red granite during shear tests. Profile measurements were made of the surfaces of the joints before and after conducting the shear tests, as shown for the grey granite specimen in Fig. 5. The equipment and procedures discussed above related directly to the experimental measurement of t h e stress--displacement behaviour of rock joints outlined in the next section.

COMPRESSION TEST RESULTS

The results presented here are for tests in which the normal (compressive) stress applied to the joint was varied in the absence o f any shear stress. Measurements Fig. 4. Photographs showing surface texture of rock joint specimens. were made of the relative normal displacements but not (a) Red granite, (b) Grey granite. of the relative shear displacements. This meant that the normal compliance component, CH, could be evaluated normal stress. The specimen was sheared at three or four but not the shear/normal compliance component, C2~. levels of normal stress. The procedure was to first apply This latter component is only relevant for unmated the initial level of normal stress and then to apply shear joints and, as discussed earlier, the degree of its practical stress until the shear strength of the joint was fully significance in describing the mechanical behaviour of mobilized. The shear stress was then unloaded followed rock joints is unknown at this stage. by unloading of the normal stress. The relative displaceFor the compression tests of joints the typical curves ment state attained at this stage provided the starting of normal stress vs normal relative displacements show point for the next test cycle. In this fashion, one series a consistent pattern of a decrease in the rate of normal of shear tests were conducted on the slate specimen and relative normal displacement as the normal relative two series conducted on both the red granite and grey displacement increases. Since the curves are monotonic granite specimens. For the tests on the slate joint, and this means that the normal compliance decreases with for the first series of tests for the red and grey granite, increase in either the normal stress or normal relative the compression load was successively increased for each displacement. There appear to be two reasons why the test in the series. However, for the second series of shear normal compliance should decrease at higher displacetests on the grey granite, the first test was conducted at ments, a compressive stress of 4.0 MPa, the second at 2.0 MPa, (a) for points initially in contact, the area of contact and the third at 6.0 MPa. In a similar fashion, the second will have significantly increased, and series of shear tests on the red granite commenced with (b) new points of contact will have been gradually a test at a compressive stress of 8.2 MPa, followed by brought into action. further tests at compressive stress levels of 5.5, 2.8 and 11.1 MPa, respectively. The pattern of decreasing normal compliance with In the compression tests, the relative normal displace- increasing normal relative displacement can be best seen ment of the joint was measured during the loading cycle. from the monotonic loading results for red granite, as In the shear tests, both the relative shear displacement shown in Fig. 6, and to a lesser extent from the results and the relative normal displacement, extensile or com- for grey granite shown in Fig. 7. For the red granite both pressive, were measured. During each shear test, a the exponential and power laws, equations (7a) and 8(a), relative shear displacement of the order of 3 mm was respectively, could be made to closely fit the experirequired to fully mobilize the shear strength of the joint, mental data, using least squares regression analysis. For after which the shear stress remained sensibly constant. the first series of tests, test 12-15, the respective corThis relative displacement was small in comparison with relation coefficients were 0.98 and 0.998. For the power the length of the test specimens, about 35 cm, so that law, the exponent b~ in equation (8a) is shown in Table there was little change in the effective area of a specimen 2 for each of these tests.

ROCK

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COMPLIANCE

205

TESTS

Table 2. Exponent in power lau [equation (Sa)] for Red granite specimens

Relative Fig. 6. Joint surface

normal

profile

displacement

of Grey granite testing.

(mm

before

1

and after

shear

The exponent, b,, decreases over the range ot 0.560.41 with increase in normal stress over the range 2.7-l I .3 MPa. These values compare well with those theoretically derived in equation (9). i.e. 213 for a rough

Test no.

Maximum normal stress (MPa)

12 13 14 15

2.7 5.5 8.4 11.3

Exponent h, 0.53 0.51 0.41

. Nominal normal

8 6 -

A

E ‘0 z

d

. .

.

n 2-.

0 .

:

v. -. 0,

Od

.

.

.

002

0 08 -.

stress-normal

6

0 E k Z

006-

Aa

o

I

x

0

.

0 O0

:

. a 000

Relative

Fig. 7. Normal

I

0.

n .O

004

I

(b)

010-x

a E z

0

~~;~.f./

0

maximum applied sfre~s MPa

087 nll

e X0

d

0.998 0.996 0.999 0.998

surface in contact with a plane and 2’5 for two rough surfaces in contact. Further normal loading tests were ccnducted subsequent to the application and removal of shear loads. tests 60, 63, 66 and 69. In these cases, the correlation coefficients for curve fitting by the exponential and power laws were 0.99 and 0.96 respectively. The values of the tangential normal compliance. C:,, were computed from the fitted curves using equations (7~) and (8~) and are plotted in Fig. 8a, for samples 12-15. and in Fig. 8b for the remainder. It can be seen that a hyperbolic relation, such as that suggested by equation (7c), is a good approximation. As mentioned previously, the red granite specimen consisted of two dissimilar surfaces and hence could never be considered to be in a mated position. However, because of the way in which it was produced, it was possible to place the grey granite specimen in the mated position. The test results for this case are shown in Fig. 7, for test 21. For tests 23, 24 and 25 the test specimen was subject to an initial relative shear displacement before the conduct of the normal compliance test, these

(a)

0

R’

0.56

006

normal

008

displacement

relative

granite,

010

displacement

012

0 14

(mm)

curves

for Grey

f

f

0

2

4

Normol

Fig. 8. Tangential granite. (a) power

I

I

I

6

8

10

stress

12

(MPa)

normal compliance-normal stress curves for Red law fitted to test 12-15. (b) exponential law fitted to tests 60, 63, 66 and 69.

206

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oppJecN l °mtn(MPon°rmal °sltress m°xlmum)No 1st test series ! No 2nd test 59

25

•

05]

4 0

24

•

03 i

ROCK JOINT COMPLIANCE TESTS ~ties

z~ []

]

o4j

2 0

o

i

n ~9

~, 0 0 6 -

E

Io 0OOOOo

(,J

°

-

8t #

8oo4-

~

~ 002

• Loading x U nloadlng

m

6

§

o O0

7o000

,~-m-..~

,

2

, 8

,

4

6

Normal stress (MPo)

6 E Z

5

Z

4'

OX OX

Fig. 9. Tangential normal compliance-normalstress curves for Grey granite.

2

oOx ox x ix Vexx

I

displacements being 0.5, 2.5 and 4.2 mm, respectively. These increasing initial shear displacements were associated with increasing initial normal displacements of a dilatant nature, or in other words increasing initial joint aperture. The test results in Fig. 7 clearly indicate the close correlation between softer behaviour and increasing initial joint aperture, thereby providing support for relations such as equation (10), that suggest proportionality between normal compliance and initial joint aperture. Curve fitting techniques were applied to tests 24, 25 and the second series of tests, 03, 04 and 05, also shown on Fig. 7. The tangential normal compliances thereby derived are shown in Figure 9. The behaviour of the joints for unloading and repeated loading of normal stress was also examined to some extent. For example, the loading and unloading curves for an unmated joint of slate are shown in Fig. 10. Although it was evident that there was some damage to the asperities on the joint surfaces it was significant

10"

0~

0 0

0 'I

Relative

Oi 2

normal

displacement ( m m )

Fig. I 1. Repeated normal loading and unloading of the Red granite joint. that as much as 72yo of the relative normal displacement was recoverable. Repeated loading was applied to the dissimilar surfaces of the red granite specimen and the results for two of the loading/unloading curves are shown in Fig. 11. The specimen was first subject to loading up to 2.7 MPa and unloading. Although a small amount of hysteresis is evident, unloading was associated with the recovery of 87°/o of the total normal relative displacement. Subsequently, the specimen was subjected to an increased normal stress of 11 MPa. A second cycle of stress was applied at this level and on unloading 93~ of the relative normal displacement was found to be recoverable. The main observed aspects of the behaviour of joints when subject to compression were found to be, (i) an increase in normal compliance with decrease in normal stress [see equation (10)], (ii) an increase in normal compliance with increase in initial aperture [see equation (10)], and (iii) the high degree of recoverability of relative normal displacement when the normal stress is removed.

O_

Loodmq

Unloading

E

00

,..d~ t"

4-

SHEAR TEST RESULTS

Z

2.

0

O0

02

Relative normal

04 displacement

06 (mm)

Fig. |0. Normal loading and unloading of an unmated slate joint.

When shear loads are applied to joints there are basic mechanisms involved in the production of recoverable and irrecoverable deformations. These mechanisms result in the production of relative normal displacements (dilatancy) as well as shear relative displacements. This aspect was discussed earlier and illustrated in Fig. 1. In the shear tests, conducted under constant normal stress, measurements were made of both of these relative

SUN et al.:

ROCK JOINT COMPLIANCE TESTS

207

Shear Normal dlspl, displ. (ram} (ram) Shear I

o

:

l

d i s p l curve

Grey

g ra n it e

04

.eO

g ra n it e

70

Normal

d~spl, curve

M Pa 70

d J

|"-

0

u " - - i

.

1

.

.

.i .

.

.

i

i

2

i

3

Shear

i

u

4

i

!

i

5

stress ( M P a )

Fig. 12. Three zones in the relative displacement curves for shear tests on joints. displacements. This enabled the direct determination of the shear compliance component, C22, and the normal/shear compliance component, C~2. In this section of the paper, the variations of the two relative displacements with shear stress are firstly considered together, in order to better understand the basic mechanisms involved during the application of shear loads to rock joints. Subsequently, details of the variations of each of the relative displacements are considered separately, with the results of fitting the empirical relations given in equations (15), (16), (17) and (18). Finally, discussion is centred on the components of the frictional strength of joints. Typical variations of both the normal relative displacement and the shear relative displacement are shown in Fig. 12. These curves relate to tests on the red granite specimen having dissimilar surfaces and the grey granite specimen that initially had mated surfaces. It is suggested that the curves can be divided into three distinct zones, indicated on Fig. 12. The first zone is typified by low compliance components with the relative displacements remaining comparatively small even when the shear stress reaches a high proportion of its ultimate value. This behaviour is apparently elastic in nature since the magnitude of the relative displacements is of the same order of that occurring during the eventual removal of the shear load. The relative shear displacement varies linearly with the shear stress and has the same sign, while the relative normal displacement is compressive and exhibits a curved characteristic. The explanation for this behaviour is linked to the mechanism illustrated in Fig. 1 and described by equations (14), in terms of the forces F; and AF;. In particular, for the resultant normal relative displacement to be compressive, as observed in the tests, it means that the elastic compressive relative displacement produced by AFI must exceed the elastic extensile relative displacement produced by F;. The second zone of the relative displacement curves is

a transition from essentially elastic behaviour to essentially sliding behaviour. The point at which the second zone commences, when expressed as a proportion of the ultimate shear stress, is higher for mated joints than for other joints. For mated joints, this point varies between 85 and 95% of the ultimate shear stress. The higher figure is associated with low normal stress and hence minimal surface damage. The lower figure is for cases of relatively high normal stress, where hardening accompanies relative displacement as a result of the wear and damage that the joint surfaces suffer. When the normal stresses are high and the joint surfaces rough, the second zone is relatively large compared with the case of low stress and smooth surfaces. This is because the high normal stresses produce the hardening effect mentioned above, while for rough surfaces the shearing of asperities can produce peak values of shear stress that are higher than the ultimate values. Such peaks rarely occurred in this series of tests and are not evident in Fig. 12. When they did occur the magnitude of the difference between the peak and ultimate stress levels was small. In the third zone, sliding is fully underway as indicated by a plateau being reached in the shear stress, with only minor fluctuations occurring with further increase in the relative shear displacement. These fluctuations appear to be due to the surface topography of the joint surfaces and the damage they sustain. In this regard the results from both the red granite specimen and grey granite specimen, as shown in Fig. 12, are in close agreement. However, in this third zone, the two specimens display markedly different patterns of behaviour for the relative normal displacement. The grey granite specimen is strongly dilatant and develops comparatively high values of relative normal displacement. On the other hand, the relative normal displacements developed by the red granite are small and oscillatory in nature, firstly being dilatant, then contractile, and then dilatant again. The reason for this difference is considered to lie in the nature

208

SUN et al.:

ROCK JOINT COMPLIANCE TESTS

of the joint surfaces, the grey granite was initially mated, while the red granite specimen consisted of two dissimilar surfaces. The joint that starts its deformation from a mated position is forced to undergo dilation if sheared in any direction. However, the joint of dissimilar surfaces can be considered equivalent to a joint that was originally mated but has undergone significant shear movements to the extent that the respective joint surfaces become unrelated. In this condition it is possible for relative normal displacements, of small magnitude, to occur in either extension or contraction. The test results shown in Fig. 12 can be expressed in terms of the tangential shear compliance component, C~2, and the tangential normal/shear compliance component, C~2. These are plotted in Fig. 13 for the red granite and Fig. 14 for the grey granite. The typical curve fitting techniques used in this process are discussed later in this section. The main features of Figs 13 and 14 are, (i) the shear compliance component is initially low and increases gradually with shear stress to approach extremely large values at ultimate conditions, and (ii) the normal/shear compliance component initially may have a greater magnitude than the shear compliance component indicating a strong initial tendency towards compressive relative displacements. At higher levels of shear stress its magnitude decreases as shown. Test results ~ndicate that as ultimate shear stress levels are approached, C~2, will usually pass through a zero value and will either become highly negative (grey granite) or will oscilliate around zero (red granite). There has been no attempt to fit the compliance curves in Figs 13 and

I

041

comphoi ce

Sheor

C~Z

"~ component,

~T~

- -

7 5 o"t :

E 0 Q.

°2i

E

o E p-o

I /

0.1-

I

/ J ~,~

~

O0

Normal

/

,

,

comphonce

shear

C:2

component,

,

,

',

,

4

2

0

Shear

6

stress ( M P a )

Fig. 14. Comparison of the shear and the normal/shear compliance for Grey granite.

14 to this last, highly complex and variable, aspect of the characteristic of the relative normal displacement during shear testing. However, the described behaviour can be clearly seen by reference to Fig. 12. Having discussed the way in which the basic shearing mechanism is best understood by considering together ~. : 10 9 MPo

5 6MPo _o ,,,~"~o o

6

Shear compliance component, C~2

o°o °°°°°

70

°°°°

:

8

15

2

MPa

03

O0oOOCOO%061 0o GO

E

._,2 1

2 ~d P 0

:

i I i I I I I

E

.-r

A 0 n

104 ~4

03~f

o CL (3

--6 7 ~ t " 2 8 MPo - - ' - - 70 °1 " 11 1 MPo

04"

~--

oOo 0

/ /

0.2

E o r~

f

i

Q)

3

"

~ ~

o°

13

i

J~ (I)

g

2

lit

o~ :

0 ~x

xx

Xx

x

01

¢

/'/

k /I /

2 7

1 t /

---}-(1 st x Ao 2 nd

ser,es

0.0

4

6

stress ( M P o )

Fig. 13. Comparison of the shear and the normal/shear compliance components for Red granite.

)

Nomber on

curve

testnumber

0 0

Shear

of tests

series of fesfs

indicates

2

MPo

67

I

D

0

MPQ

55

I 0

20

30

(ram) Fig. 15. Plots of shear stress vs shear relative displacement for Red granite. Relative

shear

displacement

S U N et al.:

ROCK JOINT COMPLIANCE TESTS

(o)

26 a t :7

05

MPa

4

25 .4

209

Granite

) 000000

O0

05

2'5

Category a~:

one

60MPa

a I : 5 9 MPo A 0 n

0 0 n

~

24 .,,A ~ ' ~ ' ~ ' ~ ' ' ~ '

,, , ~ m ~ .

~,~a~-o

03

~'1 = 4 0 M

/

(.f)

b) 3 ¸

2

"G

Pa

t

two

0-I : 5 5

MPa

r-. ~

=2.0MPa

u3

23 zx ~ . x

Category

x

0

~

XxxxXX

04

2.5 1 St s e r i e s

"I A o

of

2 nd

series

Number

on

indicates

tests of

20 1.5 f

tests

curve

testnumber

]

o

I

0

I I

Granlte 0 3 Category three 0-I = 4.0 M P a

0.5

0

1

2

3 0.0

Relative

shear

displacement

(mm)

Fig. 16. Plots of shear stress vs shear relative displacement for Grey granite.

O.0 1 '0 2'.0 Relative shear displacement

(mm)

Fig. 17. Three categories of curves of shear stress vs shear relative displacement.

the characteristics of the relative normal and shear E displacements, attention will now be drawn to each E characteristic separately, particularly from the viewpoint (a) of fitting the empirical relations given in equations (15), _~ o o (16), (17) and (18). For example a series of plots of shear stress vs relative shear displacement are given in Fig. 15, 02 o for the red granite specimen, and in Fig. 16 for the grey x xx x x x x E granite specimen. As discussed earlier, peaked behav~' o 4 E iour, i.e. a decrease in shear stress with increased relative ,2 06 shear displacement, was not observed to any significant o lID extent. Bandis et al. [14] have concluded that "peaked" w behaviour is essentially a scale effect, and on this basis, (b) xx , x * x xx x x x x x x )~xx the absence of peaks could be anticipated for the relaxxx tively large scale tests reported here. 4 0 The shape of the shear stress-shear relative displacement curves can be classed as belonging to one of three categories, with typical examples of each of these being shown in Fig. 17. The essential difference between these categories is the relative shear displacement at which 95°0 of the ultimate shear stress is reached. This is m smallest for category 1 and greatest for category 3, ~ 2o effectively meaning that category 1 is least compliant and category 3 most compliant. This variation in shear ffl i compliance appears to have the same basis as was the 1 st test | I 0 c~1=8 7 MPo case for normal compliance, i.e. increasing compliance is 2 nd t e s t associated with both a decrease in the effective area of asperity contacts and a decrease in their number. It O0 appears that if the two surfaces of joint are in juxtal o I 2 3 position such that a dilatant response accompanies the Relative shear displacement (mm) initiation of sliding, then least compliant behaviour is Fig. 18. Link between increased shear compliance and compressive produced (i.e. category 1). At the other extreme, if joint normal relative displacements.

210

SUN et al.:

R O C K J O I N T C O M P L I A N C E TESTS

Table 3. Regression analyses relating to the shear compliance curves

no.

Normal stress (MPa)

11 13 14 15 61 64 67 70 75

2.7 5.5 8.4 11,3 8.2 5.5 2.8 11,1 5.6

23 24 25 26 03 04 05

2.0 4.0 6.0 7,1 4.0 2.0 6.0

Test

Red

granite

Grey granite

Chosen

Determined

Correlation coefficient

m0

ml

rn~

- 1.5 - 1.5 -1.5 0.0 . . - 1.6 -0.1 -3.0 -0.7

0,018 0.011 0.0035 0.0034 . . 0.0037 0,023 0.0016 0.014

031 0.20 0,15 0.15 0.18 0.42 0.10 0.19

0,983 0,993 0,991 0.926 t),616 0,973 0,987 0,980 0.970

-0.3 -0,3 -0.3 +2.0 -0.2 - 0.1 -0.3

0.051 0,012 0.0062 0,044 0,040 0,068 0.025

0.50 0.28 0.21 0.24 0.32 0.48 0.18

0,993 0.970 0.995 0.990 0.987 0.985 0,987

closure is associated with the initiation of sliding then the most compliant behaviour results (i.e. category 3). This tendency is illustrated in Fig. 18 where, for two tests on the red granite specimen, both the shear stress and the relative normal displacement are plotted against the relative shear displacement. High levels of compressive relative displacement are associated with high levels of shear compliance, thereby suggesting the basis of a possible relation between C~2 and C22. The empirical relation suggested for the variation of relative shear displacement with shear stress (equation 15) can be made to provide a very good fit to the category 1 and category 2 curves. The correlation coefficient in these cases is between 0.97 and 0.99. For the category 3 cases, the fit is at a lower level of correlation but still satisfactory for practical purposes. In all cases, the basis of the regression analysis is to choose a value of m0 that will maximize the correlation coefficient. The values of m0, ml, and m2 resulting from these analyses are given in Table 3. The value of m0 in Table 3 is usually small in relation to the ultimate shear stress. It therefore follows from equation (15b) that this ultimate shear stress is given to a close approximation by the value of 1/m~_.

Having evaluated m0, m, and m2 the tangent shear compliance values can be evaluated from equation (17a). Typical curves of the shear compliance vs shear stress, for different values of normal stress, are shown in Fig. 19, for the red granite specimen. In accordance with the Mohr-Coulomb type of shear failure criterion, these show proportionately higher ultimate shear stresses with higher normal stresses. Additionally, they show lower pre-failure compliances with higher normal stresses. t Tangent compl~ance, C22

~

20

X 0 X

•

O • X O • x •

1 5

•

~eu "0 c

Normal

~@ • •

I 0

stress

•

%

(MPo)

~/

m

A

0

20

67 0"1 : 8 MPo 7 0 ~t =11 1 M P o 6 MPo 7 5 ~t

Q.

05 el

~ o o

O0

o o

2.0

u

o

o

08

Is

~

40

,a

0.0 0

( M P a ) No O20 x40

0.5

~oOO

° I

•

23 24

06 0 25 Secant comptlonce , C22

00,

,

,

,

,

,

,

,

1

2'

3

4

5

6

7

Sheer

Normal stress test

II

/"

o

F--

(b, ~ Grey gromte

~

Ii

I

04

c o m p l i a n c e ,C22

X

.~ co

i i i i i

1 2-

o u

c

i I

E o

8

Secant c o m p h o n c e , C ~ 2

¢

E I

test No

0 836 '14 • 5 5 2 43 x 2 7 4 44

v

Tangent t m--

~a) Red gramte

stress ( M P o )

Fig. 19, Tangential shear compliance vs shear stress for Red granite.

0,O Shear Fig. 20. Secant

05

'~O

displacement

and tangential relative

(ram)

shear compliance displacement.

components

vs shear

SUN et al.: ROCK JOINT COMPLIANCE TESTS Table 4. Regression analyses relating to the normal/shear compliance component Normal Test stress Chosen Determined Correlation no. (MPa) no n~ n: coefficient 64 5.5 0.15 0.022 0.95 0.996 Red 67 2.7 0. l 1 0.023 0.57 0.996 granite 70 11.2 0.16 0.015 0.63 0.993 75 5.8 0.15 0.027 0.63 0.991 03 4.0 0.13 0.014 1.16 0.995 Grey 04 2.0 0.035 0.047 0.97 0.992 granite 05 6.0 0.086 0.050 0.72 0.997

The tangent shear compliance, C~2 [equation(17a)], and the secant shear compliance, C~2 [equation (18)], have been plotted against relative shear displacement in Fig. 20, for both the red granite and grey granite specimens. The approximately linear relation between the secant shear compliance and the relative shear displacement is clear, thereby confirming the suggestion made earlier in the discussion following the presentation of equation (18). It is also significant from these plots that while the secant shear compliance decreases significantly with increase in normal stress, the tangent shear compliance is essentially independent of the normal stress. The relative shear displacement at which the tangential shear compliance reaches a value of 1 m/GPa varies over a relatively small range of 0.35 for the grey granite to 0.4-0.5 for the red granite. For the relative normal displacements developed during shear testing, it has been previously suggested that the power law [equation (16)] will provide a reasonable description of the variation with shear stress. As mentioned early in this section, no attempt is made to fit the curve to the relative normal displacement behaviour at levels of shear stress near ultimate. The regression analysis relating to equation (16a) proceeds by initially solving for no. The results of the analysis for ranges of tests on red granite and grey granite are given in Table 4, with the correlation coefficients being at a satisfactorily high level. Typical fitted curves and experimental data are compared in Fig. 21. Having determined the values of no, nl and n2, equation (17b) can be used to determine the tangential normal/shear compliance component, C'12. Typical values for both the red granite and grey granite specimens,

O0 F

E

t

Sohd l i n e - F i t t i n g

curve

} Expenmenlol

211

derived in this way, have been shown previously in Figs 13 and 14, respectively. The results of the shear tests of rock joints confirm the contention that the effective friction angle can be considered to consist of three components as given by the following relation, /% = tan(~b + i + co),

(20)

where #u is the ultimate coefficient of friction, ~b is the friction angle for smooth undamaged surfaces, i is the slope of the contact plane, and co is wear "angle" corresponding to the frictional resistance produced by wear. Being a material property, q5 is independent of the joint surface roughness or the applied normal stress. The effect of i can be seen from Fig. 1 where the effective friction angle is given by adding i to ~b. It should be appreciated that in the case illustrated the shear couple is clockwise and the acute angle dip direction of the contact plane is clockwise from the vertical. This produces an "uphill" condition in which the geometric component of friction is additive. However, a "downhill" condition will be produced if either the shear couple is anticlockwise or the dip direction is anticlockwise. In such cases, the geometric component will be subtractive. The geometric component of the frictional resistance will be maximum for rough surfaces and low normal stress. Its effect will be increasingly suppressed as the normal stress is increased. The wear component of friction derives from damage to the joint surfaces. Its influence will be minimal for smooth joints and low normal stress, and maximum for rough joints with high normal stress. The main aspects contained in this section on shear testing were, (i) discussion of the mechanisms involved in shear through considering the three characteristic zones exhibited by the curves of relative shear and normal displacement, (ii) curve fitting of the variations of the relative displacements with shear stress in order to derive the shear and the normal/shear compliance components, and (iii) suggestions of the components of the frictional strength of rock joints. DISCUSSION AND CONCLUSIONS

doto

In summary, the following points are the most important aspects arising from this work.

c o

.6 ~ 0 m> o cc

2I

OC

| 0

"~eO gronite 64 I I

I stress

• • • I 3

2 Shear

Fig. 21. Normal

O". 5 5~MpO~ ' ~ •

I 4

(MPo)

relative displacement vs shear stress---comparison of experimental data and fitted curves.

(i) Testing techniques have been developed to enable the measurement of the mechanical properties of rock joints under conditions where, (a) the scale is large enough to overcome the worst aspects of scale effect, and (b) the deformations of the rock joint can be effectively separated from those of the rock material. (ii) The tests reported, in common with those usually conducted on rock joints, are essentially "compliance"

212

SUN et al.:

ROCK JOINT COMPLIANCE TESTS

tests, since they lead to the direct determination of compliance components. Two compliance components can be determined from a "normal" compliance test and two from a "shear" compliance test. These compliance components provide useful indices of the joint properties. However, since the compliance of rock joints is stress dependent, the two pairs of components should be used with great caution in predicting rock joint behaviour for a general stress path. Nevertheless, the compliance components are likely to be essential inputs to the future development of a comprehensive stress-deformation theory for rock joints, taking into account both stress path and the topography of the joint Surfaces. (iii) At this stage, surface topography can be considered by using contact theories for asperities to suggest the forms of the relations that are likely to exist between the relative displacements produced on joints and the stresses applied. Such relations can be used to derive expressions for the compliance components. (iv) For normal compliance tests, these contact theories provided a good prediction of the experimental observation of decreasingly compliant behaviour with increasing compressive stress. This applied despite the theories being based on elasticity, while in the experiments both elastic and plastic deformations were involved. In the relatively adverse case of first loading of an unmated joint it was found that up to 72% of the deformation was recovered, while in repeated loading of other unmated joints this figure could be as high as 92~o. These findings are at odds with the conclusions of earlier workers who considered that compressive rock joint deformations were essentially due to crushing of asperities. This crushing was felt to be the source of the non-linearity in the relative displacement-applied stress relation and led to the prediction that the deformation of the joint would be largely irrecoverable. This divergence requires further resolution. (v) The results of the tests reported here support the previously derived relation suggesting proportionality between the normal compliance and the initial joint aperture. (vi) The mechanisms by which recoverable and irrecoverable deformations develop during shear compliance tests are best understood by considering the transfer of both tangential and normal forces on the contact planes of the asperity contacts. The characteristic curves for the relative displacements can be divided into three distinct zones: an elastic zone, a transition zone, and a sliding zone. In most cases, the elastic zone extends to shear stress levels that are quite high proportions of the ultimate shear stress. The relative normal displacement is compressive, and often the normal/shear compliance component is larger than the shear compliance component. The transition zone is usually small in size, but is largest for rough joints with high normal stress. It is in this zone that there is an acceleration in the rate of increase of the shear compliance, which now becomes much greater than the normal/shear compliance, which is decreasing in magnitude. In general, "peaked" shear

strength behaviour is absent or minor. In the sliding zone, the shear compliance component tends to infinity and the relative normal displacement displays markedl,, different patterns. For surfaces that were initially mated there is a strong pattern of dilation, while for dissimilar surfaces there is an oscillatory pattern of small magnitude. (vii) Results from the shear compliance tests indicate that, (a) for given normal stress and shear stress, the shear compliance component will be greater if it is accompanied by a compressive relative normal displacement, (b) the empirical relations for the relative displacements can be fitted well to the experimental results, (c) increasing normal stress increases the ultimate shear stress and decreases the shear compliance component, (d) the tangent shear compliance component is approximately independent of relative shear displacement while there is an approximately linear relation between this displacement and the secant shear compliance component, (e) the total frictional strength of a rock joint has components due to basic friction, asperity contact plane inclinations, and wear. In conclusion, it should be emphasized that the experiments on which the above findings are based relate to artificially produced discontinuities in rock types of relatively high strength. The levels of applied compressive stress represented the lower end of the range of engineering interest and were at least an order lower than the uniaxial compressive strengths of the rock materials involved. These limitations in the experimental programme are expected to have a significant influence on the observed behavioural trends, e.g. the high degree of elastic response. Further research is required to determine the extent to which the findings reported here apply over an extended range of discontinuity types, rock material strengths, and applied loads. Acknowledgements--This paper is largely based on a part of the Doctoral Thesis entitled, "Fracture mechanics and tribology of rocks and rock joints", written by the senior author tbllowing studies at the Lule~ University of Technology, Sweden [13]. The authors also wish to express their gratitude to a number of their colleagues and sponsors. Thanks are due to Dr Graham Swan who pioneered the tribology work at the Lule~ University of Technology, to Berit Aim for her examination of joint material, Ulf Mattila for his work during the performance of the tests, Josef Forslund for his help in preparing the specimens. Generous support for the work has been provided by the Swedish Board for Technical Development, Grant Nos 81-4584, 81-4585. the Swedish Natural Science Research Council, Grant No. E-EG 3447-109, and the Faculty of Technology at the Lule~ University of Technology,

Received 1 March t984; revised 4 January 1985.

REFERENCES 1. CundaU P. A., Marta J., Beresford P., Last N. and Asqian M. Computer modelling of jointed rock masses. Tech. Rept N-78-4, U.S. Army Corps of Engineers, Waterways Experiment Station, Vicksbury, Missouri (1978).

SUN et al.:

ROCK JOINT COMPLIANCE TESTS

2. Zienkiewicz O. C. and Pande G. N. Time-dependent multilaminate model of rocks--a numerical study of deformation and failure of rock masses. Int. J. Numer. Analyt. Meth. Geomech. 1, 219-247 (1977). 3. Pande G. N. and Gerrard C. M. The behaviour of reinforced jointed rock masses under various simple loading states. Proc. 5th Congr. ISRM, Melbourne, pp. F217-F223 (1983). 4. Hoek E. and Brown E. T. Underground Excavations in Rock, revised edn, 527 pp. IMM, London (1982). 5. Barton N. and Choubey V. The shear strength of rock joints in theory and practice. Rock Mech. 10, 1-54 (1977). 6. Gaziev E. G. and Lapin L. V. Passive anchor reaction to shearing stress in a rock joint. Proc. Int. Syrup. on Rock Bolting, Abisko, pp. 101-108 (1983). 7. Goodman R. E. The mechanical properties of joints. Proc. 3rd Congr. ISRM., Denver, Vol. VIA, p. 127 (1974). 8, Goodman R. E. Methods of Geological Engineering in Discontinuous Rock, 472 pp. West, New York (1976). 9. Hungr D. and Coates D. F. Deformability of joints and its relation to rock foundation settlements. Can. Geotech. J. 15, 239-249 (1978). 10. Swan G. Determination of stiffness and other joint properties from roughness measurements, Rock Mech. Rock Engng 16, 19-38 (1983). 11. Coulson J. H. Shear strength of fiat surfaces in rock. Stability of Rock Slopes--Proc. 13th Syrnp. on Rock Mechanics, Urbana, Aug. 30--Sept. 1, 1971, pp. 77-105. ASCE, New York (1972). 12. Krahn J. and Morgenstern N. R. The ultimate frictional resistance

RMMS

22;4-- B

213

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