ROCKENG09: Proceedings of the 3rd CANUS Rock Mechanics Symposium, Toronto, May 2009 (Ed: M.Diederichs and G.Grasselli)
Estimation of rock block strength
M. Pierce
Itasca Consulting Group, Inc., Minneapolis, MN, USA
M. Gaida
Kennecott Utah Copper Corporation, Rio Tinto, Salt Lake City, UT, USA
D. DeGagne
Itasca Consulting Group, Inc., Minneapolis, MN, USA
ABSTRACT: Empirical relations exist for the estimation of rock block strength at scales larger
than standard core sizes. Two recently published relations account for the significant impact that
microflaws (pores, open cracks, veins) and weathering/alteration can have on scale effect. These
relations were used to estimate the rock block strength of heavily microfractured quartzite from
the Bingham Canyon Mine. Predictions were compared to the results of Uniaxial Compressive
Strength (UCS) tests conducted on cylindrical core samples of varying microfracture intensity
and diameter. The comparison confirms the sensitivity to microfracturing suggested by existing
relations and suggests that they would benefit from more detailed consideration of microfracture
strength, density and persistence over a range of scales. The results of a numerical study illustrate how Synthetic Rock Mass (SRM) modeling techniques could be used to complement empirical data in the development of such relations.
1 INTRODUCTION
The intact strength of rock blocks larger than standard core sizes (i.e. 50 mm diameter) is often
of interest in rock engineering, particularly in underground mines where insufficient natural or
blasted fragmentation may lead to large rock blocks and associated difficulties with handling
and comminution. It is well established that the intact strength of rock decreases with increasing
scale and several quantitative empirical relations have been published for estimation of rock
block strength as a function of scale. Two recently published relations consider the impact of
microfracturing and alteration on scale effect and were used to estimate rock block strength for
heavily microfractured quartzite from the Bingham Canyon Mine near Salt Lake City, Utah.
These predictions are compared to the results of Uniaxial Compressive Strength (UCS) tests
conducted on cylindrical core samples of quartzite exhibiting varying microfracture intensity
and a range in diameter from 63 mm to 240 mm. A numerical study employing Synthetic Rock
Mass (SRM) modeling techniques was conducted in parallel to analyze the impact of microfracture/vein strength on rock block strength and scale effect relations in more detail.
2 PUBLISHED RELATIONS
Hoek & Brown (1980) developed an empirical scale effect relation for intact strength on the basis of laboratory testing conducted by a number of different researchers on homogenous hard
rock samples (i.e. samples lacking significant microfracturing or alteration). Their relation,
which is still widely used in the mining industry, is shown in Figure 1 and takes the form:
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σ c = σ c.50 ( d / 50 )
−0.18
(1)
where σc.50 is the uniaxial compressive strength of a cylindrical specimen with diameter d = 50
mm, and σc is the uniaxial compressive strength of a specimen with an arbitrary diameter, d (10–
200 mm).
Figure 1. Scale effect relation for intact rock UCS proposed by Hoek & Brown (1980).
Yoshinaka et al. (2008) note a similarity in the form of Hoek & Brown’s function to the relation between strength and volume of a solid that may be derived from Weibull’s statistical
theory:
−1
σ c = σ c 0 (V / V0 ) m
(2)
where V is the volume of a specimen, m is a material constant called the Weibull modulus, and
V0 is the volume of a standard-size specimen. In order to compare test results on samples of
shapes and sizes that differ from the standard 2:1 cylindrical core sample, Yoshinaka et al. suggest a scale effect equation that employs equivalent length, de = V1/3 , and an exponent, k, as follows:
σ c / σ c ⋅0 = ( d e / d e 0 )
−k
(3)
Using the above equation, Yoshinaka et al. (2008) were able to compare the results of testing
conducted in both the laboratory and in situ on a wide range of rock types, strengths, sample
shapes and sample sizes. The results of their analyses show that the value of the exponent k is
strongly influenced by presence of microflaws (i.e. pores, open cracks, veins, etc.). They report
that k ranges from about 0.1 to 0.3 for homogeneous hard rock, and from about 0.3 to 0.9 for
weathered and/or extensively microflawed rock. These relations are plotted in Figure 2 along
with Hoek & Brown’s relation. The comparison suggests that Hoek & Brown’s relation should
only be used to estimate the strength of relatively homogeonous hard rock blocks; use of the relation for extensively microflawed rock is likely to result in a significant overprediction of rock
block strength.
Laubscher & Jakubec (2001) provide guidelines for estimation of rock block strength for both
homogenous and veined/fractured rocks. Since only a single estimate is provided by their methodology, it is presumed that this represents the strength for blocks larger than 200-300 mm;
above this size, the relations of Hoek & Brown (1980) and Yoshinaka et al. (2008) both suggest
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that the rock block strength remains relatively constant. Laubscher & Jakubec (2001) suggest
that the strength of a homogenous rock block is 80% of the mean intact strength obtained from
testing standard (i.e. 50 mm diameter) core samples. This corresponds well with the asymptote
(at large block sizes) for k = 0.1, which is the least dramatic scale effect relation for homogenous
rock suggested by the work of Yoshinaka et al. (2008) For rock blocks containing veins and
open fractures, Laubscher & Jakubec (2001) suggest a scaling factor that combines the 80%
“size factor” with a second adjustment that considers the vein/fracture hardness and the
vein/fracture frequency. The nomogram they provide for estimating rock block strength is
shown in Figure 3. The maximum value for the second adjustment is 60%; this could result from
open fractures exhibiting a frequency of 40/m or healed veins at an even higher frequency.
When this maximum vein frequency/hardness factor of 60% is multiplied by the size factor of
80%, an overall maximum scaling factor of 48% is suggested. This corresponds well with the
asymptote (at large block sizes) for k = 0.3, which is the least dramatic scale effect relation for
weathered or extensively microflawed rock suggested by the work of Yoshinaka et al. (2008).
Overall, the Laubscher & Jakubec (2001) relations result in higher rock block strengths than
what the relations of Yoshinaka et al. (2008) suggest may be possible in heavily weathered
and/or microfractured rock.
Figure 2. Scale effect relations for intact rock UCS proposed by Yoshinaka et al. (2008). The relation of
Hoek & Brown (1980) is also shown for comparison.
Figure 3. Nomogram for estimation of rock block strength based on Intact Rock Strength (IRS) developed
by Laubscher & Jakubec (2001).
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Laubscher & Jakubec (2001) note that careful consideration must be given to the selection of
representative standard core strengths when applying their scaling relations in practice. They
suggest that when intercalations of weaker material are present in the rock, a sampling bias is often introduced because the stronger sections of core tend to be selected for testing. In this case,
they suggest a downgrading of intact rock strength based on the relative proportions and
strengths of weak and strong material that are present. The downgraded intact rock strength is
obtained via the nomogram reproduced in Figure 4. Yoshinaka et al. (2008) also point out that
statistical analysis of a large number of tests is generally required to establish a valid baseline
core strength due to the fact that strength results on standard-sized cores tend to exhibit a wide
degree of scatter, particularly with heterogeneous, weathered and/or altered rock.
Figure 4. Nomogram developed by Laubscher & Jakubec (2001) for estimation of Intact Rock Strength
(IRS) when intercalations of weaker material are present.
3 CASE STUDY - BINGHAM CANYON QUARTZITE
A study of rock block strength was conducted for the quartzite lithology present at the Bingham
Canyon Mine, a porphyry copper-gold-molybdenum deposit located in the Oquirrh Mountains,
just 30 km southwest of Salt Lake City, Utah in the USA. The mine is owned and operated by
Kennecott Utah Copper Corporation (KUCC), a subsidiary of Rio Tinto. At over 3 km wide and
more than 900 m deep, it is one of the world’s largest open pit mines. The purpose of the study
was to estimate the strength of rock blocks that might be produced during potential cave mining
of the rock mass beneath the existing pit. A number of UCS tests were conducted on core samples of varying size to quantify the scale effect. The results of these tests were then compared to
the published relations discussed in the previous section.
3.1 Geology
At Bingham Canyon, a sequence of folded and faulted Paleozoic quartzites and lesser limestone,
calcareous siltstone and sandstone were intruded by a series of Eocene igneous rocks known as
the Bingham Intrusive Complex (Fig. 5). The oldest and largest unit in the complex is an equigranular monzonite that hosts a significant portion of the deposit. A later intrusion of quartz
monzonite porphyry is spatially and temporally associated with mineralization. This case study
addresses the UCS of the quartzite sequence.
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3.2 Core logging
Diamond drilling is performed at the Bingham Canyon Mine in order to better characterize the
resource for potential mining extensions and to improve the understanding of the geological and
geotechnical settings for future mine designs. All diamond drill core is photographed and logged
both geologically and geotechnically according to standard company procedures. This logging
includes detailed characterization of the lithology, alteration, fracture style, fracture intensity
and fracture orientation. The logging information of particular relevance to rock block strength
is the estimation of microdefect intensity and microdefect strength. Microdefects are defined at
Bingham Canyon Mine as healed fractures that appear as fine (<1 mm thick) lines in the core
and do not exhibit significant mineral filling. These are considered distinct from veins, which
are defined as healed features >1mm in thickness that contain mineral filling.
Figure 5. East west cross section through Bingham Canyon Mine, looking north (Modified from Babcock
et al. 1997)
Microdefect intensity is characterized descriptively as “non-existent”, “minor (spacing >10
cm)”, “moderate (spacing 1 cm to 10 cm)” or “heavy (spacing <1 cm)”. See Figures 6 & 7 for
examples. The strength of the microdefects is characterized via drop testing of the core from a
0.2 m height; the microdefect strength is rated as “always breaks (2)”, “sometimes breaks (1)”,
“never breaks (0)”, or “no pieces of core large enough to perform a drop test on (-1)”. More than
180 km of diamond drilled quartzite core has been logged at Bingham Canyon Mine to date.
The explicit logging of microdefects was initiated several years ago, and now microdefects have
been characterized in 31 km of quartzite core. Of the quartzite that has been logged for microdefects, 7% of has either no microdefects or a minor microdefect intensity, 39% has a moderate
microdefect intensity and 54% has a heavy microdefect intensity.
Microdefect intensity is generally much greater than vein intensity in the quartzite. Veins are
typically spaced at more than 10 cm, whereas microdefects are most commonly spaced at less
than 1 cm. The most frequently logged vein types within the quartzite are sulphide, quartz sulphide and pyrite. A sulphide fill typically consists of some combination of pyrite, chalcopyrite,
bornite and molybdenum.
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Figure 6. Quarztite with minor microdefect intensity.
Figure 7. Quartzite with heavy microdefect intensity.
3.3 Laboratory testing
While attempts are made to select core samples for testing at regular intervals, the need for a
continuous piece of core with a minimum length of 150 mm and the tendency to select samples
with fewer pre-existing defects means that some sampling bias is present. This can be quantified, however, by comparing the microdefect intensity of tested samples to the range of microdefect intensity derived from core logging. Samples are packaged carefully and shipped to an
external testing laboratory for uniaxial compressive, tensile and triaxial testing. The number of
samples available for strength testing may be reduced due to damage in transmit or while being
machined for testing.
UCS tests are performed to ASTM standards on selected samples. The sample is photographed prior to testing; testing results include sketches of the failure path and classification of
the failure mode. If the core break follows a clear structure, it is classed as a “structural” break.
A core break that appears jagged, with the failure path both along existing flaws and through
solid rock, is classified as a “both” break. If no contributing structure is observed, the test is
classified as an “intact rock” failure.
Most samples are from HQ core, and are approximately 63 mm in diameter. Distinct populations are seen when the data from UCS testing of this core is broken out by the failure mode
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(Fig. 8). It is clear that the sample UCS decreases at this scale when there is increasing structural
control in the failure. The negative impact of microdefect intensity on intact strength can be seen
in Figure 9. When the samples are group by microdefect intensity (as logged for the sampling
interval) mean intact strengths of 79 MPa and 43 MPa are calculated for moderately microdefected quartzites (21 samples) and heavily microdefected quartzites (19 samples), respectively.
These correspond closely to the mean strengths of 73 MPa and 43 MPa calculated for samples
exhibiting the combined and structurally controlled failure modes, respectively (Fig. 8).
UCS tests were also performed on larger 140 mm and 240 mm diameter quartzite core samples in an attempt to quantify the effect of sample size on strength (Call & Nicholas 2008). All
of these samples exhibited failure through intact rock as well as failure along pre-existing
veins/fractures (i.e. “both” failure mode). For the larger core sizes, it was sometimes necessary
to test samples with a height:width ratio less than 1 (Fig. 10) and so the effective sample length
(de) of Yoshinaka et al. (2008) was employed to account for sample shape effects. When the
UCS results for these samples are compared to the results of tests on 63 mm diameter core that
exhibited the same failure mode, a strong size effect is suggested (Fig. 11).
Boxplot of 63 mm Quartzite Strength by Failure Mode
250
UCS (MPa)
200
150
109
100
74
50
41
0
Intact Rock
Both
Failure Mode
Structural
Figure 8. UCS of 63 mm diameter quartzite samples as a function of observed failure mode.
Quartzite UCS Comparison by Microdefect Intensity
250
UCS (MPa)
200
150
100
50
0
Microdefect Intensity
M
or
in
er
od
M
Failure_Mode
R
ct
ta
n
I
e
at
k
oc
a
He
vy
y
e
or
at
av
in
er
M
He
d
o
M
th
Bo
y
e
or
at
av
in
er
M
He
d
o
M
a
ur
ct
ru
t
S
l
Figure 9. UCS of 63 mm diameter quartzite samples as a function of failure mode observed during testing and microdefect intensity. Black dots are individual sample strengths while bars represent mean UCS.
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Figure 10. The 240 mm diameter core before and after testing (Call & Nicholas 2008).
Figure 11. UCS exhibited by quartzite samples as a function of equivalent sample length.
3.4 Comparison to published relations
The first step in using the published relations is to remove any sampling bias that may be
present in the standard-sized (63 mm diameter) test. The results of UCS testing indicates that the
intact strength is a function of microdefect intensity; the mean strength is 79 MPa in samples
with moderate microdefect intensity (39% of logged core) and 43 MPa in samples with heavy
microdefect intensity (54% of logged core). A weighted averaging based on the proportion of
each type within the logged core suggests a baseline intact strength of 58 MPa for the 63mm diameter samples. This was compared to the value estimated using the nomogram (Fig. 4) of
Laubscher & Jakubec (2001), which considers the relative proportion and strength of weak rock
(heavily microdefected quartzite) and strong rock (moderately microdefected quartzite). The
UCS of the heavily microdefected rock is approximately 55% of the moderately defected rock
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and comprises 55% of the logged core. Using the nomogram in Figure 4, an adjusted intact rock
strength of 51 MPa (65% of the moderately defected rock strength) was estimated. This is lower
than the value of 58 MPa obtained through the previous weighted averaging approach.
In order to estimate rock block strength using the Laubscher & Jakubec (2001) relation, the
corrected baseline strength is multiplied by the size factor (80%) and the vein frequency/hardness factor, which is determined using the nomogram in Figure 3. The microdefect frequency ranges from 10/m-100/m in the moderately defected quartzite and is greater than 100/m
in the heavily microdefected quartzite. A weighted averaging based on the proportion of each
type within the logged core suggests an approximate average microdefect frequency of 80/m.
Since the microdefects do not contain significant mineral infillings, it is not possible to assign a
mineral hardness. However, the adjustment factor is relatively insensitive to this parameter when
frequency is large. When the inverse of hardness over the complete range of 1 to 5 is multiplied
by the microdefect frequency, the nomogram indicates a vein frequency/hardness factor ranging
from 60% to 65%. When multiplied by the size factor of 80%, a total adjustment factor of approximately 50% is suggested. Using the baseline strength of 51 MPa, an approximate rock
block strength of 25 MPa results. This is larger than the UCS measured for the largest 240mm
diameter core (18 MPa) but corresponds reasonably well with the overall trend of lab-derived
strengths shown in Figure 11.
In order to compare to the relations of Yoshinaka et al. (2008), the results of all tests were
normalized to the baseline strength of 58 MPa (calculated via weighted averaging as above). Although the number of samples tested at the larger scales in limited (three 140 mm diameter samples; one 240 mm diameter sample), a relatively strong scale effect is suggested that is consistent with the range suggested by Yoshinaka et al. (2008) for weathered and/or heavily
microflawed rocks (Fig. 12).
Figure 12. Comparison of laboratory-derived intact strengths for Bingham quartzite to the scale effect relations proposed by Hoek & Brown (1980) and Yoshinaka et al. (2008). quartzite strengths have been
normalized to the mean bias-corrected value for 63 mm diameter samples.
Although the study would benefit from testing on a greater number of large scale samples, it
appears likely that the relation of Hoek & Brown (1980) would over predict the strength of large
blocks of quartzite. This is attributed to the fact that the relation was derived from tests on relatively homogenous rocks. This study also highlights the significant control that microfractures
exert on the scale effect, which is considered in the empirical relations of Laubscher & Jakbuek
(2001) and Yoshinaka et al. (2008). Both of these relations provide predictions that correspond
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reasonably well with the measured strengths. The relation of Laubscher & Jakbuek (2001) considers the mineralogy and frequency of the microfractures but only provides a single estimate,
presumed to be valid for blocks exceeding 200 mm to 300 mm in diameter. The relations of Yoshinaka et al. (2008) allow for the estimation of rock block strength over a wider range of scales
but do not offer guidelines for the selection of the k exponent based on the nature and frequency
of microfracturing. The next section discusses the results of numerical modelling studies aimed
at developing such guidelines.
4 SYNTHETIC ROCK MASS (SRM) MODELLING OF SCALE EFFECTS IN VEINED
INTACT ROCK
The case study presented in the previous section reaffirmed the importance of considering the
presence and nature of microfracturing/veining within the rock when trying to estimate the
strength of rock blocks larger than the standard core scale. Although it was demonstrated that
some existing empirical relations consider these effects, there remains scope for developing
quantitative guidelines for selection of the exponent k in the scale effect equation (Equation 3)
of Yoshinaka et al. (2008) so that the impacts of microfracture/vein strength, frequency and persistence on rock block strength can be predicted over a wider range of scales than offered by the
relation of Laubscher & Jakubec (2001).
A series of Synthetic Rock Mass (SRM) tests were conducted to assess the feasibility of developing such guidelines. The SRM approach was originally developed to model large-scale
jointed rock masses (Pierce et al. 2007; Mas Ivars et al. 2007) and involves the embedment of
discrete planar fractures into a bonded-particle model of the intact rock, developed in this case
using the Particle Flow Code (PFC3D). In this approach, intact rock is represented by an assembly of spherical particles with “parallel” bonds at their contacts (Potyondy & Cundall 2004).
Particles and bonds to act in parallel at the contact level and provide a connection that can resist
tension, shear and bending. The microstiffnesses (normal and shear) of the particles and bonds
and the micro strengths (normal and shear) of the bonds can be adjusted to achieve realistic macroscopic rock properties, including intact strength and modulus. A discrete fracture is included
in the bonded-particle assembly by locating contacts between particles on opposite sides of a user-defined plane and debonding them. A “smooth joint” contact model is installed at these contacts to reorient them parallel to the plane (thereby removing the “bumpiness” associated with
the discrete assembly) and to enforce a Mohr-Coulomb shear criterion.
4.1 SRM sample creation
The SRM samples were generated using procedures similar to those employed by Mas Ivars et
al. (2008) for the creation of large jointed rock mass volumes. This includes the use of
“pbricks”, which are small, prismatic assemblies of particles, constructed in periodic space, that
can be combined to rapidly assemble large PFC3D assemblies (Itasca 2008).
The first step in the sample construction procedure involved the creation of a 1-m cube of
bonded spherical particles in equilibrium. The microstiffnesses (normal and shear) of the particles and bonds and the micro strengths (normal and shear) of the parallel bonds were adjusted
to achieve a macroscopic peak strength of 86 MPa, a Young’s Modulus of 52 GPa and a Poisson’s Ratio of 0.17 under simulated UCS testing. Table 1 provides a summary of the microproperties employed for the particles and bonds to achieve this intact block of rock.
An isotropic network of fully persistent veins was then generated using 3FLO (Darcel 2007)
with a target linear vein frequency of 20/m. In order to minimize anisotropy in the network, a
number of realizations were made and the one with the smallest average deviation from the target vein frequency (considering measures in each of the three coordinate directions) was selected for use in the analysis. The vein network was then embedded into the 1-m cube and the
strength and stiffness of the corresponding smooth joint contacts set to achieve a macroscopic
strength and modulus equivalent to the original parallel bonded material. A summary of the resulting smooth joint microproperties is provided in Table 1.
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Table 1. Summary of microproperties employed in PFC3D to represent the intact rock (via particles and
bonds)
and veins (via smooth joints). See Itasca (2008) for detailed microproperty definitions.
______________________________________________________________________
Property
Value
______________________________________________________________________
Particle microproperties
Radius
4.7-7.8mm
Density
4109 kg/m3
Elastic modulus
52.6 GPa
Friction coefficient
2.5 (68°)
Normal:shear stiffness ratio
2.5
Parallel bond microproperties
Bond:particle radius ratio
1.0
Elastic modulus
52.6 GPa
Normal:shear stiffness ratio
2.5
Normal strength
60 ± 12 MPa
Shear strength
60 ± 12 MPa
Smooth joint microproperties
Normal stiffness
2.3 TPa/m
Shear stiffness
2.3 TPa/m
Friction coefficient
0.58 (30°)
Dilation angle
0°
Normal strength
85 MPa
Shear strength
85 MPa
______________________________________________________________________
Note: PFC3D bulk porosity was assumed to be 36%.
The effect of scale on intact strength was examined by sub-dividing the 1-m-cube sample into
smaller prismatic samples with 2:1 length-to-width ratio. One hundred specimens were carved
from the original 1-m cube, comprising four different sample widths: 500 mm, 250 mm, 125
mm and 62.5 mm. For each of these sample sizes, four different relative vein strengths were employed: 100%, 50%, 33% and 25% of baseline strength. Testing samples from different locations but with equivalent vein strength and scale allowed for a measure of variability. Eight
samples were tested for each scale, except for the 500 mm diameter samples, which were
represented by a single sample. Figure 13 shows two views of one the 500 mm diameter sample.
Figure 13. Visualizations of the largest veined SRM specimen tested (500 mm wide × 1000 mm high)
emphasizing the three-dimensional veining (a) and the resulting assembly of bonded, angular, unveined
fragments comprising the sample prior to testing (b).
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4.2 SRM sample test results
The veined SRM samples were tested using procedures similar to those employed by Mas Ivars
et al. (2008) for the testing of large jointed rock mass volumes, including the use of so-called
“full-strain” testing approach rather than traditional platen-based techniques. Figure 14 shows
typical UCS tests for the same specimen scale as vein strength is decreased. Decreasing peak
strength and a residual strength of approximately 22 MPa are observed in the simulations.
Figure 14. Effect of reducing vein strength relative to host strength on the UCS of a 250 mm diameter
SRM sample (vein frequency = 20/m).
Strength was also found to decrease with decreasing sample size in the samples with 100%
vein strength. This was attributed to significant changes in resolution from the largest specimen
(40 particles across sample width) to the smallest specimen (5 particles across sample width).
Similar particle resolution effects have been noted by Potyondy & Cundall (2004) and Koyama
& Jing (2007). In order to isolate the impacts of vein strength on sample strength, the impact of
particle resolution on strength was factored out of the results. The strengths were also normalized to the mean value obtained for the smallest diameter samples, which have an equivalent
length of 78.7 mm. The scale effect relations resulting from this analysis can be seen in Figure
15. An overall power-law trend of decreasing relative strength (and decreasing variability) with
increasing sample size can be seen that is similar in form to the relations of Yoshinaka et al.
(2008). Values for k of 0.04, 0.15 and 0.22 were found from power law fits to the relative vein
strength trends for 50%, 33% and 25% of host strength, respectively. By combining these with
the average k value of 0.2 suggested by Yoshinaka et al. (2008) for homogenous rocks (Fig. 2),
k values for the complete scale effect relation of 0.24 to 0.42 are indicated for rocks with a vein
frequency of 20/m and vein strengths ranging from 25% to 50% of the host strength. Larger values of k (i.e. approaching the maximum value of 0.9 suggested by Yoshinaka et al.) might be
expected for higher vein frequencies and/or lower vein strengths.
The results of the SRM modeling are encouraging and suggest that the technique could be
used to developed quantitative guidelines for the selection of k in the scale effect relation (Equation 3) to provide a wider range of vein strength and vein frequency data. It could also be used
to investigate the impacts of vein persistence on these relations.
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Figure 15. UCS test results of relative vein strengths normalized to the mean strength of a sample with de
= 78 mm. Power curves superimposed over each relative strength data set indicate trends of decreasing
relative strength with increasing scale. This effect becomes more pronounced as vein strength decreases.
5 CONCLUSIONS
The empirical relations of Laubscher & Jakubec (2001) and Yoshinaka et al. (2008) consider the
impact that microflaws and/or weathering can have on rock block strength. Both relations suggest that the presence of such features exaggerates the scale effect, resulting in rock block
strengths at larger scales that are much lower then predicted by relations developed from tests on
homogenous rock samples (e.g. Hoek & Brown 1980). A comparison of measured versus estimated rock block strength for a heavily microfractured quartzite from the Bingham Canyon
Mine confirms the sensitivity to microflaws suggested by these relations. Existing relations
would benefit from more detailed consideration of microflaw type, strength, density and persistence over a range of scales.
The results of a numerical modeling study demonstrate that Synthetic Rock Mass (SRM)
modeling techniques can be used to relate the value of the k exponent in the scale effect relation
of Yoshinaka et al. (2008) to the strength of persistent veins. By extending the technique to examine a wider range of microflaw types (e.g. cracks, pores, veins) and properties (e.g. strength,
density, persistence) it may be possible to refine existing empirical relations for rock block
strength estimation.
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REFERENCES
Babcock, R., Ballantyne, G. & Phillips, C. 1997. Summary of the Geology of the Bingham District, Utah.
Geology and Ore Deposits of the Oquirrh and Wasatch Mountains, Utah, SEG Guidebook series, vol.
29: 113-132.
Call & Nicholas, Inc. 2008. Large Diameter Core Testing Results for KUCC, Unpublished internal report.
Darcel, C. 2007. Personal communications, Itasca Consultants S.A.S., Leon, France.
Hoek, E. & Brown, E. T. 1980. Underground Excavations in Rock. London, Instn. Min. Metall.
Itasca Consulting Group, Inc. 2008. PFC3D – Particle Flow Code in 3 Dimensions, Ver. 4.0 Minneapolis: Itasca.
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