Comparison of corrected joint normal and shear stiffness between crystalline and carbonate rock joints

Abstract

The importance of discontinuity geomechanical properties is increasing as the use of numerical models with explicit or discrete rockmass structure becomes the state of practice. These numerical inputs are typically measured from laboratory testing and in the case of joint normal and shear stiffness this is measured from direct shear testing. This paper presents practical guidelines to correct direct shear testing data for machine influences with regards to normal and shear stiffness by accounting for system deformation and separating out the fracture deformation component. In this study, the joint normal stiffness of 23 rough granite, 10 smooth ground granite, and 6 rough limestone specimens are measured using a hyperbolic law. Joint shear stiffness is measured on 19 rough granite, 4 smooth ground granite, and 6 rough limestone specimens. This data set is used to compare the measured joint stiffnesses based on lithology and topology.

Full text

Comparison of corrected joint normal and shear
stiffness between crystalline and carbonate rock
joints
Packulak, T.R.M., Day, J.J.
Department of Geological Sciences and Geological Engineering – Queen’s
University, Kingston, Ontario, Canada
ABSTRACT
The importance of discontinuity geomechanical properties is increasing as the use of numerical models with explicit or
discrete rockmass structure becomes the state of practice. These numerical inputs are typically measured from laboratory
testing and in the case of joint normal and shear stiffness this is measured from direct shear testing. This paper presents
practical guidelines to correct direct shear testing data for machine influences with regards to normal and shear stiffness
by accounting for system deformation and separating out the fracture deformation component. In this study, the joint normal
stiffness of 23 rough granite, 10 smooth ground granite, and 6 rough limestone specimens are measured using a hyperbolic
law. Joint shear stiffness is measured on 19 rough granite, 4 smooth ground granite, and 6 rough limestone specimens.
This data set is used to compare the measured joint stiffnesses based on lithology and topology.
RÉSUMÉ
L’importance des propriétés géomécaniques des discontinuités est grandement mise en évidence par l’utilisation
croissante des modèles numériques avec implémentation explicite ou discrète des éléments structuraux dans les massifs
rocheux. Ces paramètres sont en général obtenus à partir de tests en laboratoire alors que les coefficients de rigidité
normal et de cisaillement sont mesurés à l’aide de cellules de cisaillement. Le présent papier présente une série de
recommandations pratiques pour corriger l’influence des composantes mécaniques de la machinerie d’essais sur les
coefficients de rigidité normal et de cisaillement. Les corrections sont faites en considérant la déformation du système en
place et en isolant les composants de déformation des fractures. Dans cette étude, le coefficient de rigidité normal de 23
spécimens de granites rugueux, 10 spécimens de granites lisses, et 6 spécimens de de calcaire rugueux a été obtenu et
la relation établie à l’aide d’une loi hyperbolique. Le coefficient de rigidité en cisaillement a été mesuré pour 19 spécimens
de granite rugueux, 4 spécimens de granite lisse machinés, et 6 spécimens de calcaire rugeux. Les données sont utilisé
afin de comparer les mesures basé sur la lithologie et la topographie
1 INTRODUCTION
The rockmass is composed of two components: intact rock
and discontinuities. In many cases, the rockmass
behaviour for surface and near surface engineering
projects is governed by the discontinuity component. For
rock engineering design associated with these projects,
laboratory direct shear testing is a critical but expensive
tool used to characterize and measure stiffness, strength,
and dilative behaviour of rock joints and other fractures.
These measured geomechanical properties are the basic
inputs to numerical models with explicit structures.
For the average geotechnical commercial testing
laboratory, readily available machines from laboratory
testing equipment suppliers are a cost-effective option.
One of the limitations of these machines is that they may
not be stiff or rigid enough, causing deformation while
applying normal and shear loads and providing laboratory
results that may not solely reflect the joint specimen. This
paper presents practical guidelines to correct direct shear
deformation testing data in order to facilitate the
measurement of joint normal and joint shear stiffness. In
addition, the measured joint normal stiffness and joint
shear stiffness from granite and limestone are compared.
2 ACCOUNTING FOR SYSTEM STIFFNESS
All materials possess the property of elasticity and rock
joints are no exception. The elastic deformations
associated with rock joints was first described by Goodman
et al. (1968) where joint stiffness was separated into two
components, a normal stiffness (kn) and a shear stiffness
(ks). Joint normal stiffness (kn) is defined as the normal
stress increment required for a small closure of a joint or
fracture at a level of effective stress and joint shear
stiffness (ks) is the elastic deformation response in shear
(Barton, 2007).
Direct shear machines, while being sophisticated
laboratory equipment, are not without their limitations. This
is especially evident with regards to the measurement of
joint deformation as solely based on the location of
installed instruments (e.g. linear variable differential
transformers (LVDTs)). LVDTs placed on the machine but
away from the fracture surface and in a location such as
the outside of the specimen holder will measure
deformations associated with the rock, encapsulating
material (e.g. grout), and steel housing. Throughout this
paper the following terms are used to describe the
stiffnesses and deformations associated with different
components of the direct shear test.

• Composite Deformation and Stiffness: Deformations
associated with all components of the direct shear
test subject to measurement by machine
instrumentation, including the steel platens, steel
housing, encapsulating material (e.g. grout, resin),
rock AND the fracture test specimen
• System Deformation and Stiffness: Deformations
associated with all components of the direct shear
test subject to measurement by machine
instrumentation, including the steel platens, steel
housing, encapsulating material (e.g. grout, resin),
and rock but EXCLUDING the fracture test specimen
• Fracture Deformation and Stiffness: Deformations
associated with the fracture test specimen ONLY
To quantify the deformations associated with the
system components, an additional direct shear test is
conducted with an intact rock specimen of the same
lithological characteristics. The normal deformation
resulting from this direct shear test on the system is then
subtracted from the composite normal deformation. This
leaves a deformation curve representing the fracture only
(Figure 1), which is then used to measure joint normal
stiffness. The same process is undertaken to correct shear
deformation data using measured shear displacements on
the specimens as a result of applied shear stress.
Figure 1: Normal stress – Normal displacement curve of
the fracture deformation compared to system and
composite response curves.
3 DETERMINATION OF STIFFNESS PROPERTIES
Joint normal stiffness and joint shear stiffness are
measured using displacement and stress data prior to yield
and were first introduced by Goodman et al. (1968) as a
response to the need to quantify the pre-yield elastic
behaviour in finite element and finite difference numerical
models that were beginning to use explicit structural
elements.
3.1 JOINT NORMAL STIFFNESS (KN)
The joint normal stiffness deformation property is
measured during the initial loading stage of the direct shear
test. This initial loading stage is where the normal stress is
increased to the target starting stress for both constant
normal stress and constant normal stiffness tests. During
this stage, shear displacement is held constant at zero.
The original normal stiffness law was proposed by
Goodman et al. (1968). This law was linear in nature and
specifically created for use in numerical modelling. As
research on rock joints and discontinuities continued, the
non-linear behaviour of rock joints became an important
area of study (e.g. Shehata, 1971; Goodman, 1974; Bandis
et al., 1983; Swan, 1983; Evans et al., 1992). Based on
these studies, a series of joint normal stiffness laws were
proposed including hyperbolic equations (Goodman, 1974;
Bandis et al., 1983), power law equations (Swan, 1983),
and semi-logarithmic equations (Bandis et al., 1983; Evans
et al., 1992). In more recent times with the continued
improvement of computing systems and iterative fitting
functions, complex normal deformation models have been
proposed (e.g. Malama and Kulatilake, 2003; and Li et al.,
2016).
For this study, the normal closure data used to fit the
test data is the Bandis et al. (1983) hyperbolic law. The
Bandis et al. (1983) hyperbolic law is dependent on two
parameters, maximum joint closure (Vm) and initial normal
stiffness (kni). The Bandis et al. (1983) hyperbolic model is
mathematically described in Equations 1 and 2, where
Equation 1 is the normal deformation equation and
Equation 2 is the instantaneous normal stiffness equation.
=




 + 
[1]
= 1 
 + 

[2]
3.2 JOINT SHEAR STIFFNESS (KS)
Joint shear stiffness is measured prior to yield at the start
of the shear loading stage of a direct shear test, under the
specified normal stress. The joint shear stiffness is
measured as the slope of the linear-elastic portion of the
shear stress data with respect to shear displacement. This
linear component represents the test from the onset of
shear displacement to yield shear stress. To measure the
shear stiffness, two methods are commonly used: the
secant (peak) method (Goodman, 1970) and the tangent
(yield) method (Hungr and Coates, 1978). Other joint shear
stiffness models include the Kulhaway (1975) hyperbolic
model and the Day et al. (2017) best fit chord
measurement.
4 SPECIMEN DESCRIPTION
Specimens used in this study are a combination of polished
saw cuts, machine breaks, and natural fractures through
NQ (47.6 mm diameter) and NQ3 (45 mm diameter) size
drill core of gneissic tonalite, pink granite, leucogranite, and
limestone. For this study, the geology has been separated
into two major units: (i) the Pointe Du Bois Granites and
Gneisses and (ii) the Cobourg Limestone.

4.1 POINTE DU BOIS GRANITES AND GNEISSES
Specimens of gneissic tonalite, pink granite, and
leucogranite units from the Canadian Winnipeg River
Complex within the Pointe Du Bois Batholith (Figure 2)
were obtained from drill core sourced from the Pointe Du
Bois Generating Station, in Pointe Du Bois, Manitoba.
Machine breaks and joints were distinguished by the
characteristics of the fracture: natural joints typically had a
trace mineral coating of calcite or iron oxide, while machine
breaks had rough, irregular profiles and fresh fracture
faces. The tonalites and granites are equigranular, medium
to coarse grained, and unfoliated to weakly foliated. The
joints are smooth to semi-rough, planar to sub-planar, and
generally fresh with trace mineral coating.
Figure 2: NQ3 (45 mm diameter) Pointe Du Bois core: (a)
smooth ground specimen, and (b) fracture specimen.
4.2 COBOURG LIMESTONE
Specimens of the Cobourg limestone were obtained from
rock blocks sourced from near surface at the St. Mary’s
Cement Bowmanville quarry near Bowmanville, ON. The
Cobourg limestone sourced from the Bowmanville quarry
is argillaceous and nodular, where light grey nodules of
calcite-rich limestone are surrounded by tortuous layers of
dark grey, clay rich rock (Figure 3). Discontinuities tested
in Cobourg Limestone specimens are typically smooth to
semi rough, sub-planar to wavy, and fresh.
Figure 3: 50 mm diameter Cobourg Limestone core
fracture specimen.
5 DIRECT SHEAR TESTING PROGRAM
Normal and shear joint deformation was measured through
a direct shear testing program completed at the Advanced
Geomechanics Testing Laboratory (AGTL) at Queen’s
University using a commercially available GCTS RDS-200
Servo-Controlled Rock Direct Shear System. The RDS-200
system consists of the following:
• GCTS DSH-150 direct shear apparatus with a double
acting ± 100 kN capacity shear load actuator with 25
mm stroke and single acting 50 kN capacity normal
load actuator with 25 mm stroke.
• RDS-SERVOPAC hydraulic servo control package.
• SCON-1500 microprocessor based digital servo
controller and acquisition system.
All reported direct shear tests were conducted under
constant normal stress (CNL*) or constant normal stiffness
(CNS) boundary conditions while being compliant with the
International Society of Rock Mechanics Suggested
Method for Laboratory Determination of the Shear Strength
of Rock Joints: Revised Version (Muralha et al., 2013).
Direct shear tests were completed using the sample
preparation procedures as outlined by Day et al. (2017)
and Ahmed Labeid et al. (2019). The direct shear testing
program consisted of single stage tests that were
completed at a normal stress (σn) of 2, 4, 8, 16, or 20 MPa
with a normal loading rate of 10 kPa/s and a shear
displacement rate of 0.2 mm/min for the granite specimens.
Limestone specimens were tested at normal stresses of 2,
3, or 8 MPa with a normal loading rate of 10 kPa/s and a
shear displacement rate of 0.2mm/min. Fracture and
smooth ground specimens were subjected to three normal
loading-unloading cycles and sheared approximately 8-10
mm.
For specimens tested under CNS boundary conditions
(granite only), the normal stiffness of the machine was
determined based on the equation by Packulak et al.
(2021). Specimens were tested at a machine stiffness of
(KNM) of 1.5, 3, 6, or 12 kN/mm. For consideration of the
analysis within this study, the CNS boundary condition has
no effect compared to the CNL* conditions during the
normal loading stage and varying degrees of effect during
the pre-yield shear stage of the direct shear test as based
on the specified KNM. As the normal load-dilation feedback
is present during the shear stage of the CNS direct shear
test, only specimens tested under the CNL* boundary
condition were included in from the joint shear stiffness
analysis.
6 DATA CORRECTION AND STIFFNESS
MEASUREMENT PROCEDURE
For direct shear tests conducted in the AGTL, the following
process is used to isolate the fracture deformation from the
measured composite deformation. To isolate the fracture
deformation, a separate intact specimen from the same
lithological unit with the same dimensions is tested to
measure the elastic deformation of the system.
Through the testing of intact and fracture specimens,
two distinct behaviours are present in both the normal
loading and shear loading data (Figure 4) for both the
composite and system loading curves: (i) a distinct non-
linear behaviour at low stresses (<1 MPa) that transitions
to (ii) linear to linear behaviour at higher stresses. The non-
linear behaviour at lower stresses is due to the machine
seating, as the components in the machine are machined

to fit with some leeway. Loading will remove any slack in
the components.
Figure 4: Example granite test data. (A) Non-truncated
normal loading data (B) Non-truncated shear loading data.
The following steps were taken to isolate the normal
component of fracture deformation:
1. Conduct three (3) normal loading-unloading cycles on
the intact specimen.
2. Record the second (2nd) and third (3rd) cycle normal
deformation. The use of the 2nd and/or 3rd cycle
deformation behavior is dependent on inspection of
the recorded data for repeatability.
3. Determine the normal transition stress (σnT). This is
based on where the loading curve transitions from a
machine seating response to an elastic response.
4. Using the system deformation data, derive a
representative mathematical function.
5. Calculate the fracture deformation by subtracting the
system deformation from the composite deformation.
Like the steps taken to isolate the fracture’s normal
closure, the following steps are used to isolate the shear
component of the fracture’s closure (Ahmed Labeid, 2019).
It should be noted that the data for analysis and
determination of joint shear stiffness is only corrected prior
to the yield point, which is the elastic portion of the shear
loading stage.
1. Conduct a direct shear test on the intact specimen up
to the peak shear displacement of jointed samples
tested under the same normal stress without yielding
the intact specimen to determine the system shear
deformation response.
2. Determine the shear transition stress (τT). This is based
on where the loading curve transitions from a machine
seating response to an elastic response.
3. Fit a linear trendline into the test data;
4. Using the function of the linear trendline, obtain the
elastic shear displacement at desired shear stress
values.
5. Calculate the fracture component of shear
displacement by subtracting the system deformation
from the composite deformation.
Fracture deformation curves are analyzed with some
assumptions about the system behaviour. These
assumptions include:
• The composite stiffness cannot be stiffer than the
system stiffness;
• The system stiffness can vary between tests;
• The measured stiffness of the system is linear up to
the point where machine components start to fail (e.g.
grout); and
• The linear portion of the composite deformation curve
at very high confinements must represent the point at
which the joint closure response becomes asymptotic
and therefore the upper end linear value in these high
confinement tests must also represent the system
stiffness (if it is higher that the nominal value).
As the normal stiffness laws used in this study are non-
linear, the fracture normal deformation curve needs to be
offset in order to provide a more representative normal
stress vs. normal displacement curve where maximum joint
closure influences the measured joint normal
stiffness. The steps used in this study to offset the
fracture normal deformation curve are as follows (and
illustrated in Figure 5).
A
B
00.2 0.4 0.6 0.8 11.2 1.4 1.6 1.8 22.2 2.4 2.6 2.8 3
0
1
2
3
4
5
6
7
8
Normal Stress, σn (MPa)
Normal Displacement, δn (mm)
Composite Deformation
System Deformation
Fracture Deformation
TG-TH3-R5-NQ-F-CD
σn = 8 MPa KNM = 6 kN/mm
00.2 0.4 0.6 0.8 11.2 1.4 1.6 1.8 22.2 2.4
0
2
4
6
8
10
12
14
16
Shear Stress, τ (MPa)
Shear Displacement, δ
s
(mm)
Composite Deformation
System Deformation
Fracture Deformation
GI-BH3-R10-NQ-F-DE
σ
n
= 8 MPa KNM = 0 kN/mm

Figure 5: (a) Truncated normal stress vs. normal displacement fracture deformation curve (b) zeroed fracture deformation
curve (c) Bandis et al. (1983) hyperbolic law is fit to the fracture data, noting the initial normal stiffness (kni) (d) extrapolate
the normal stress-normal displacement line from (0,0) to negative transition stress, measuring what the change in normal
displacement is at the transition stress (e) offset the fracture deformation data by the measured normal displacement from
the previous step (f) fit normal closure laws to the corrected fracture deformation data.
0246810 12 14 16
0.0
0.1
0.2
0.3
0.4
Normal Displacement, δn (mm)
Normal Stress, σn (MPa)
TG-TH2-R16-NQ-A3
σ
n
= 16 MPa KNM = 0 kN/mm
Hyperbolic (Bandis et al., 1983)
A B
C D
0 2 4 6 8 10 12 14 16
0
0.1
0.2
0.3
0.4
Normal Displacement, δn (mm)
Normal Stress, σn (MPa)
TG-TH2-R16-NQ-A3
σ
n
= 16 MPa KNM = 0 kN/mm
0 2 4 6 8 10 12 14 16
0
0.1
0.2
0.3
0.4
Normal Displacement, δn (mm)
Normal Stress, σn (MPa)
TG-TH2-R16-NQ-A3
σ
n
= 16 MPa KNM = 0 kN/mm
E F
0 2 4 6 8 10 12 14 16
0
0.1
0.2
0.3
0.4
Power (Swan, 1983)
Hyperbolic (Bandis et al., 1983)
Semi-Log (Bandis et al., 1983)
Semi-Log (Evans et al., 1992)
Normal Displacement, δn (mm)
Normal Stress, σn (MPa)
TG-TH2-R16-NQ-A3
σ
n
= 16 MPa KNM = 0 kN/mm
Model
Equation
n
V
m
k
ni
Hyperbolic (Bandis et al., 1983)
(V
m
*s
n
)/((V
m
*k
ni
)+s
n
)
0.41487 ± 0.0033
22.1616 ± 0.18239
-2 0 2 4 6 8 10 12 14 16
-0.1
0
0.1
0.2
0.3
0.4
Normal Displacement, δn (mm)
Normal Stress, σn (MPa)
TG-TH2-R16-NQ-A3
σ
n
= 16 MPa KNM = 0 kN/mm
Extrapolated δ
n
- σ
n
Line
(1, 0.045)
Reference Line
Transition Stress (σ
nT
)
-2 0 2 4 6 8 10 12 14 16
-0.1
0.0
0.1
0.2
0.3
0.4
Normal Displacement, δn (mm)
Normal Stress, σn (MPa)
TG-TH2-R16-NQ-A3
σ
n
= 16 MPa KNM = 0 kN/mm
Hyperbolic (Bandis et al., 1983)
Extrapolated δ
n
- σ
n
Line
(-1, -0.045)
Reference Line
Negative Transition Stress ( − σ
nT
)

1. Plot resultant fracture deformation data once the
system deformation has been subtracted from the
composite deformation curve (Figure 5a)
2. Zero the fracture deformation curve by taking the
fracture data normal stress at each data point and
subtract the transition stress (σnT) (Figure 5b)
3. Fit the Bandis et al. (1983) hyperbolic law (Equation
1) to the fracture data noting the measured initial
normal stiffness (kni) (Figure 5c)
4. Using the measured initial normal stiffness,
extrapolate a line back to the negative transition
stress (Figure 5d)
5. Offset the fracture normal deformation curve using
the extrapolated normal deformation, calculated in
step 4. Once shifted upwards, return the fracture
deformation curve to its original normal stress
positions by adding back the transition stress to each
data point (Figure 5e)
6. Fit fracture deformation data with normal closure laws
(Figure 5f)
Because the fracture shear deformation curves are
being fitted with linear shear stiffness laws the offset
procedure is not required.
7 TEST RESULTS
The objective of this analysis are to remove the influence
of the system deformation and isolate the fracture
deformation to determine fracture stiffness properties.
Comparisons between the fracture deformations and their
measured stiffness responses associated with smooth
joints in granite, rough fractures in granite and rough
fractures in limestone are presented in this section.
7.1 JOINT NORMAL STIFFNESS (KN)
The normal stiffness response of specimens tested in this
study were analyzed using the Bandis et al. (1983)
hyperbolic relationship.
In total, twenty-three (23) direct shear tests on rough
fractures in granite, ten (10) direct shear tests on smooth
ground specimens in granite, and six (6) direct shear tests
on fractures in limestone were incorporated into the results
of this study. The Bandis et al. (1983) hyperbolic law is non-
linear and therefore does not have a constant normal
stiffness as the value is dependent on the instantaneous
normal stress. A compilation of normal stiffness results for
all tested specimens is shown in Table 1 and Figure 6.
Table 1: Range of measured normal stiffness values for
fracture and smooth ground specimens in granite and
fracture specimens in limestone.
Specimen Type
Normal Stiffness (k
n
)
(GPa/m)
Granite – Rough
16 – 1 600
Granite – Smooth Ground
13 – 140
Limestone – Rough
16 – 1 060
Figure 6: Normal stiffness results for all tested specimens
used in this study.
7.2 JOINT SHEAR STIFFNESS (KS)
Joint shear stiffness is measured during the second stage
of the direct shear test, after normal loading in the first
stage is complete. The shear stiffness values for all
specimens were measured using a linear relationship
where the shear stiffness is the slope of the shear stress
with respect to shear displacement.
Many specimen behaviours were linear, with some
exhibiting non-linear behaviour at the start of the shear
stage, even though the data was corrected only for shear
stresses exceeding 1 MPa. In addition to the samples
showing non-linear behaviour at the start of the shear
stage, some specimens when tested at high stresses,
above 8 MPa, show a non-linearity immediately before
peak shear stress (Figure 7).
In total, nineteen (19) rough granite fracture, four (4)
smooth ground granite fracture, and six (6) rough limestone
fracture direct shear tests are included in the shear
stiffness results. Only CNL* direct shear tests are included
in the fracture results. The number of available smooth
ground specimens is limited as most of the specimens
yielded at a shear stress of approximately 1 MPa. Due to
the correction process being applied to data starting at 1
MPa, this resulted in a lack of suitable data to properly fit
any shear stiffness relationships. A compilation of shear
stiffness results for all tested specimens is shown in Table
2 and Figure 8.
0246810 12 14 16 18 20
10
100
1000
Fracture (Granite)
Fracture (Limestone)
Smooth Ground (Granite)
Normal Stiffness, K
n
(GPa/m)
Normal Stress, σ
n
(MPa)

Figure 7: Shear stage where non-linear is behaviour is
exhibited at an approximate shear stress of 5 MPa and
immediately prior to peak shear stress above 19 MPa.
Table 2: Range of measured shear stiffness values for
fracture and smooth ground specimens in granite and
fracture specimens in limestone.
Specimen Type
Shear Stiffness (k
s
)
(GPa/m)
Granite – Rough
9 - 250
Granite – Smooth Ground*
20 - 40
Limestone – Rough**
2 – 18
*Specimens tested between 16 – 20 MPa
**Specimens tested between 2 – 8 MPa
Figure 8: Shear stiffness results for all tested specimens
used in this study.
8 DISCUSSION
Joint stiffness is measured using the direct shear test and
is separated into two components: joint normal stiffness
and joint shear stiffness. In order to obtain the best
measurement of joint stiffness, deformation
instrumentation should be installed directly on the fracture
specimen. In many cases, this is neither practical nor
feasible.
The method presented in this paper provides guidelines
for the correction of deformation data through the
subtraction of all the system deformations from the
composite deformation, resulting in normal and shear
stress vs. displacement data for the fracture itself.
The resultant measurements of normal stiffness of
fractures in the limestone exceed that of fractures in the
granite samples, and the smooth ground granite fractures
are softest in normal stiffness (Figure 6). While at first the
data set may seem counterintuitive based purely on
mechanical properties of the intact rock, the lithology is
accounted for in the data curve correction and largely
accounted for as part of the system. In essence, the main
factor that is not accounted for and unique to the fracture
is the fracture topology. Rough granite fractures were
found to have back calculated joint roughness coefficients
(JRC) typically ranging near the middle to high end of the
scale (13-20), limestone specimens were much smoother
and generally undulating with measured JRCs in the
middle of the scale with two fractures having a JRC of 18
(10-18) and the smooth ground granite fractures by design
have a JRC of 0. In the study conducted by Hopkins et al.
(1990), an analysis of six fracture surfaces with varying
degrees of roughness undergoing increasing normal stress
concluded that rougher fractures have lower measured
stiffnesses than smoother fractures, as the change in
overall contact area as normal stress increases is at a
smaller rate than smoother fractures which reach
maximum contact area quickly. This trend is observed in
this study between the rough limestone and granite
fractures; however, this does not hold true for the smooth
ground specimens which have much lower measured
normal stiffnesses than the other two specimen types. It is
hypothesized that during preparation of the smooth granite
specimens, microfractures may have been introduced
during the saw cutting and subsequent polishing, which
effectively softened the surface. These additional
microfractures would not be accounted for in the system
deformation data and further study is required to
understand any damage that may have occurred during
sample preparation.
The shear stiffness results show that the rough granite
specimens have a larger measured shear stiffness than the
smooth ground granite specimens and the rough limestone
fractures. As fracture specimens become smoother and
from irregular to undulating, the number of asperities
diminishes. In the case of rough granite fractures, the high
degree of interlocking prevents deformation until a critical
number of asperities have either failed or started to slip. If
fractures become smoother, the relative number of
asperities preventing movement will decrease and the
angle of the asperities will become smaller, providing less
resistance to shear deformation.
0 2 4 6 8 10 12 14 16 18 20
1
10
100
1000
Tangent
Fracture (Granite)
Fracture (Limestone)
Smooth Ground (Granite)
Shear Stiffness, Ks (GPa/m)
Maximum Applied Normal Stress, σn (MPa)

9 CONCLUSION
The research presented in this paper covers a concept that
is not widely considered in commercial laboratory testing
for engineering projects. By adding the intact specimen
into direct shear testing programs, fractures can be
corrected for system deformations. This study also
highlights that joint stiffness is not necessarily dependent
on lithology. Variation of the measured joint normal
stiffness and joint shear stiffness is attributed to the
difference in topology (roughness) of the fracture.
These measured stiffnesses can then be used as inputs
into numerical models where explicit or discrete rockmass
structures are being simulated. However, fractures
typically exhibit non-linear normal deformation behaviour
and a stress-dependent stiffness value should be used
when available for numerical modelling applications.
ACKNOWLEDGEMENTS
The Natural Sciences and Engineering Research
Council of Canada through a Post-graduate Scholarship
held by Timothy R. Packulak, P.Eng., P.Geo. and the
Nuclear Waste Management Organization of Canada have
financially supported this research. Thank you to Manitoba
Hydro for supplying the rock core samples.
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