International Journal of Rock Mechanics & Mining Sciences 64 (2013) 258–269

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International Journal of
Rock Mechanics & Mining Sciences
journal homepage: www.elsevier.com/locate/ijrmms

Technical Note

Damage stress and acoustic emission characteristics

of the Beishan granite
X.G. Zhao a,n, M. Cai b, J. Wang a, L.K. Ma a
a
CNNC Key Laboratory on Geological Disposal of High-level Radioactive Waste, Beijing Research Institute of Uranium Geology, Beijing 100029, China
b
Bharti School of Engineering, Laurentian University, Sudbury, Ontario, Canada P3E 2C6

art ic l e i nf o

Article history:
Received 12 October 2012
Received in revised form
*Highly valued paper for AE concept
8 June 2013
Accepted 1 September 2013
Available online 10 October 2013

1. Introduction compression were found less dependent on loading conditions.

The two stress thresholds have been considered as key para-
Safe disposal of high-level radioactive waste (HLW) is an meters to describe rock mass responses around underground
important issue and also a challenging task for all countries openings [10,11].
utilizing nuclear energy. Due to long half-life and high toxicity, Based on a comparison of the crack initiation measured in
the HLW is required to be isolated from the biosphere until its laboratory uniaxial compression tests with the spalling strength of
hazard is reduced by radioactive decay so that there is no crystalline rocks in the field, Martin and Christiansson [12]
significant risk to human and the environment. In the interna- suggested that the crack initiation stress could provide a lower
tional nuclear energy community, deep geological disposal has bound limit for the spalling strength. Using the cracking initiation
been considered as a suitable way to deal with HLW. An HLW stress and peak strength, Cai [13] suggested a method to estimate
repository can be constructed in a host rock at a depth of several the tensile strength and Hoek–Brown strength parameter mi.
hundred meters below the ground surface. Different rock types, Hence, it is important to know the characteristic and critical stress
such as granite, tuff, rock salt, and clay, are being considered as levels such as crack initiation stress during rock deformation for
potential host rocks of HLW repositories and extensive laboratory engineering design and application.
and field studies have been conducted [1–5]. Beishan granite is a Description of rock failure process using only conventional
preferred candidate host rock for the construction of an HLW stress and strain measurements is not sufficient. The rock failure
repository in the Beishan area, China [6,7]. A better understanding process is associated with acoustic emission (AE). AE can be
of the mechanical behaviors of the host rock is essential to long- defined as the transient elastic wave generated by the rapid
term stability evaluation and engineering optimization of the release of energy from a source within a material [14]. Due to its
radioactive waste disposal system in the rock. high sensitivity to crack initiation, propagation, and coalescence in
Peak rock strength is required in rock mechanics design, and rocks subjected to loading, AE monitoring provides a powerful tool
the International Society for Rock Mechanics (ISRM) suggests that for investigating brittle rock failure and this technique has been
uniaxial and triaxial compression tests can be used for its widely used in rock mechanics studies and engineering applica-
determination. Two peak strength criteria, i.e., the linear Mohr– tions [15–18]. In general, AE event counts, AE count rates scaled
Coulomb failure criterion and the nonlinear Hoek–Brown failure with the stress–strain relationship, and source location of the
criterion [8], are widely used in rock engineering. Martin [9] events, are frequently used by researchers to study the rock failure
indicated that the peak strength of granite was not a unique characteristics under different loading conditions. In addition,
material property but was loading condition (such as the load- some waveform parameters involved in the generation of an AE
ing rate) dependent. The crack initiation stress (sci) and crack event such as ring-down count, energy, peak amplitude, rise-time
damage stress (i.e., long-term strength scd,) during uniaxial and event duration also provide useful information to further
investigate rock cracking mechanisms associated with macro-
scopic deformation and failure. For example, amplitude distribu-
n
Corresponding author. Tel.: þ 86 10 64932892. tions of AE signals have been used to infer the relationship
E-mail address: xingguang100@126.com (X.G. Zhao). between variations of AE event magnitudes and failure processes

1365-1609/$ - see front matter & 2013 Elsevier Ltd. All rights reserved.
http://dx.doi.org/10.1016/j.ijrmms.2013.09.003
 X.G. Zhao et al. / International Journal of Rock Mechanics & Mining Sciences 64 (2013) 258–269 259

of rocks [19]. Based on frequency-spectra analysis of the full-wave 3. AE characteristics of the Beishan granite
AE data, He et al. [20], and Zhao et al. [21] correlated the
frequency–amplitude of AE signals with the characteristics of 3.1. Testing facilities
rockburst stages. A schematic illustration of these AE event wave-
form parameters is shown in Fig. 1, and definitions of the Uniaxial and triaxial compression tests were carried out using a
terminologies can be found in [22]. computer controlled servo-hydraulic compression system. The test
In the present study, experimental investigations into the system has a maximum load capacity of 2000 kN and can supply a
engineering properties of the Beishan granite have been executed. maximum confining stress of 60 MPa. The axial and lateral strains
The objectives of the experiments are to determine damage stress of the sample during loading were acquired automatically by a
characteristics and to understand the failure process of the rocks pair of extensometers located in the middle height of the rock
using the AE monitoring technique in combination with strain
measurement. Real-time spatial distributions of AE events in the
rock during uniaxial compression and triaxial compression tests
are captured. The identification methods of crack initiation and
crack damage thresholds are discussed, and the relationships
between confining stress and crack initiation stress and crack
damage stress are analyzed. The obtained results will be used in
establishing constitutive models for use in numerical codes for the
rock response prediction around underground excavations in the
site characterization and evaluation of a potential HLW repository
in the Beishan area.

2. Description of rock specimens

Drill cores with a diameter of 63 mm were taken from bore-

hole BS06 in the Xinchang rock block in the Beishan area. The
sampling depth was from 450 to 460 m below the ground
surface. The granite used in the laboratory test was fine-
medium-grained (Fig. 2a), and was relatively isotropic in texture
and composition with low porosity and water content. The rock
density was 2.69 g/cm3, and the average P-wave velocity was
5239 m/s. Based on cross-polarized light observations, a typical
photomicrograph of a thin section of the rock was obtained and it
showed the microstructure and mineralogical composition of the
rock (see Fig. 2b). The rock displayed granular mosaic texture,
and was mainly composed of approximately 52% plagioclase,
17% quartz, 15% alkali feldspar, 12% biotite, 3% albite, and o 1%
myrmekite. Accessory minerals primarily consisted of sphene,
apatite, zircon, and magnetite. A total of 42 core-based cylindrical
rock specimens with a diameter of 50 mm were prepared.
The specimen length was twice the diameter. The tolerance of
perpendicularity and flatness of the specimens met the specifica-
tions of the ISRM Suggested Method [23]. In particular, the ends
of all the specimens were carefully polished to minimize the end Fig. 2. Fine-medium-grained Beishan granite (a), and a photomicrograph showing
effect during loading. the main mineralogical composition of the rock (b).

Fig. 1. Features of transient AE waveform generated from rock sample loaded. Modified from (http://www.vallen.de).
260 X.G. Zhao et al. / International Journal of Rock Mechanics & Mining Sciences 64 (2013) 258–269

sample, and the measurement ranges for the axial and lateral AE distribution in the complete process of rock deformation. This
extensometers were 72.5 mm and 6 mm, respectively. meant that the measurement technique was able to provide a
In all tests, AE transducers (type Micro30, from American feasible means to study AE characteristics of rock failure under
Physical Acoustics Corporation) and a six channel AE signal confined conditions.
processing system (PCI-2) were used to record AE data. AE signals
obtained from the AE transducers were amplified by a gain of 3.2. Testing results
40 dB in order to filter out the background noise. The trigger
threshold of AE was set to 40 dB for each test, and full waveform 3.2.1. Uniaxial compression test
data were recorded with a data collection rate of 0.5 MHz. In the Fig. 4 shows the complete stress–strain relationships and
uniaxial compression test, AE transducers were in direct contact associated AE characteristics for a rock sample (i.e., BS06MD-01)
with the rock sample except that a thin layer of Vaseline was tested in uniaxial compression. Several characteristic stress levels
applied to provide a good acoustic coupling. could be identified using AE data in combination with the stress–
The minimum number of transducers forming an array is strain curves. scc was the crack closure stress level, which was
determined by the spatial dimension to be measured. In general, indicated by the end of the initial concave part in the axial stress–
if the wave velocity of the rock is known and constant, a minimum strain curve. In this stage, there was often an initial flurry of
of N þ 1 sensors are required in the array for an N-dimensional acoustic emissions due to seating and loading adjustment, as well
problem [24]. For a cylindrical rock specimen, at least four as crack closure. It is also likely that small cracks may form at a low
transducers are required. Six transducers were used in the present stress level in areas already weakened prior to or during the
study to increase AE source location accuracy. Three AE transdu- sampling process [25]. As shown in Fig. 4b, the relationship
cers were treated as a group and installed evenly in a plane 10 mm between AE hit and axial stress illustrates that the accumulative
away from the end of the specimen as shown in Fig. 3. An AE hit counts increased rapidly when load was applied, and the AE
unsymmetrical layout of the two groups of transducers was rate decreased subsequently to a constant level when linear elastic
adopted to have a better coverage of the rock volume. deformation took place (from scc to sci).
In the present experiment, the AE transducers could not with- The crack initiation stress sci was defined by the onset of stable
stand high pressure in the triaxial compression cell. Therefore, in crack growth or dilation. AE rate changed at sci and it gradually
the triaxial compression test, the AE transducers with a similar increased as more new cracks were generated and the existing
distribution as that in the uniaxial compression test were magne- cracks extended their lengths (see Fig. 4b). sci could be identified
tically attached to the wall surface of the triaxial cell. It should be as the point where the AE curve departed from linearity. AE hits
noted that the elastic waves generated from rock damage needed started to increase systematically when the applied stress was
to pass the Teflon heat-shrink jacket wrapped tightly around the above sci. In the test result, a marked increase in AE rate occurred
specimen first, and subsequently the hydraulic oil and the steel at a stress level of 0.5sc, where sc was the uniaxial compressive
wall of the triaxial cell before reaching the transducers. Conse- strength of the rock. The important feature of stable crack growth
quently, the strength of the recorded AE signals was reduced due is that cracks propagate parallel to the axial stress direction,
to the existence of these three media. This meant that the leading to a decreased velocity of elastic waves in the direction
measured AE hits might be less than those obtained from attach- perpendicular to the loading direction [9,13]. Subsequently in our
ing the AE sensors directly to the rock sample, which was test, AE hits increased drastically when scd was reached, as
impractical for the triaxial test in our study. Fortunately, based presented in Fig. 4b. From this moment, the crack density was
on the acquired AE monitoring data, we found that the measure- high enough so that cracks started to interact with the neighbor-
ment method used in our experiment had a negligible impact on ing ones, leading to crack coalescence and formation of tensile
judging the characteristic stress thresholds and on capturing the spalls when loading continues. In addition, the volumetric strain
reversal occurred and unstable crack growth began. For this rock
sample, the onset of crack damage started at a stress level of 0.8sc.
When the stress was increased from scd to sc, the volumetric
strain change was not large, which meant that rock dilation before
the peak stress was relatively small. The maximum AE hit rate was
reached when the rock sample entered its post-peak deformation
stage (see Fig. 4a). The accumulated AE hit counts in the post-peak
deformation stage increased about 5 times compared with the AE
hit counts at the peak stress. As the sample was further deformed,
the volumetric dilation continued at a high rate because there was
no confinement to limit the dilation process. As the specimen
gradually disintegrated due to fracture propagation and coales-
cence, the AE hit rate decreased gradually.
It should be pointed out that the use of AE hits in combination
with stress–strain measurements cannot exhibit damage evolution
visually within the rock. To further reveal failure characteristics of
the Beishan granite at different loading stages, real-time source
locating technique was used to find the AE event locations as
shown in Fig. 5. The spatial distributions of AE events revealed a
good picture of microcrack evolution during the deformation
process. It is seen that the local spalling failures in the rock served
as sources of stress concentration. As the rock was further
deformed, more cracks were generated and the AE event cloud
expanded gradually and covered the right side and both ends of the
sample, leading to densely distributed splitting fractures. In addi-
Fig. 3. The designed positions of AE transducers in the uniaxial compression test. tion, the rock sample tended to present dispersive mircocracking
 X.G. Zhao et al. / International Journal of Rock Mechanics & Mining Sciences 64 (2013) 258–269 261

Fig. 4. Complete stress–strain curve associated with AE hit characteristics showing different deformation stages of the Beishan granite in uniaxial compression test (a), and a
zoomed-in relationship between AE hit count and axial compression stress for identifying crack initiation and crack damage stresses (b).

throughout each loading stage, indicating that certain amount of determine the crack initiation and crack damage stresses, as
the rock's cohesion strength was lost. Due to space limitation, AE shown in Fig. 6b.
distribution maps for other rock samples cannot be presented but The 3D locations of accumulated AE events were used to
the test results are very consistent. visualize the gradual formation of the shear band (see Fig. 7).
Before the peak strength, there were no clusters of AE events, and
AE events were randomly distributed in the sample. The relatively
3.2.2. Triaxial compression test uniform and diffuse distribution of AE events throughout the
The triaxial compression tests were carried out under different sample indicated that strain localization was a post-peak phenom-
confining pressures (i.e., 1.0, 2.0, 3.5, 5.0, 10.0, 15.0, 20.0, 30.0 and enon. The number of AE events was high when the crack damage
40.0 MPa). Observation of the failed rock samples revealed that stress was reached; thus it was easier for adjacent cracks to
when the confining stress was increased, there was a gradual interact with each other when the stress is higher than the crack
change of macroscopic failure modes from axial splitting at low damage stress. Once the peak stress was experienced, more events
confinements to shear localization at high confinements. At low were generated and the cracks concentrated on or near a potential
confinements (0–2 MPa), the failure mode was dominated by shear plane (Fig. 7d). Subsequently, the crack density in this region
splitting or spalling failure, accompanied by a large dilation as increased drastically, starting first at the lower right end and then
previously described in the results of uniaxial compression tests. expanding to the top left corner of the sample (Fig. 7e). As a
When the confining stresses were further increased, a transition consequence, a macroscopic shear fracture was formed (Fig. 7f–h).
from axial splitting to shear failure occurred. Without loss of A detailed examination of the shear plane revealed that the shear
generality, the relationship between axial stress, strain, AE hit fracture was formed due to the coalescence of many axially aligned
counts and AE source locations of a rock sample (BS06MD-24) at a microcracks (Fig. 7i), which were tensile in nature. This supports
confinement of 10 MPa was used to analyze the deformation the notion that shear failure in brittle rocks is in fact caused by
process of shear failure, as presented in Figs. 6 and 7. tensile damage accumulated in the rock during deformation.
The development of AE hit counts during rock deformation was It should be noted that the location accuracy of AE events in the
similar to that in the uniaxial compression test. The accumulated confined test was not high due to the fact that the four different
number of AE hits before the peak stress was small compared with media (rock, Teflon, silicone oil, and steel) had different wave
that recorded at the post-peak stage where large rock dilation took velocities. As a result, the AE signals were sensed from an
place, especially during the process of strain localization. When “anisotropic” material. In addition, the used AE system only
the load reached the residual strength, the AE hit rate was more allowed the user to input the wave velocity parameter for a single
or less constant and the volumetric dilation rate eventually medium. Hence, there existed a small error in the AE locations
approached zero (see Fig. 6a). A zoomed-in plot was used to when compared with those in the unconfined test. Although the
262 X.G. Zhao et al. / International Journal of Rock Mechanics & Mining Sciences 64 (2013) 258–269

Splitting fracture

Fig. 5. Accumulative spatial distribution of AE events in the rock sample at different stress levels under uniaxial compression condition. (a)–(j) respectively correspond to
points scc to si in the complete stress–strain curve shown in Fig. 4a, and tested rock sample (k) indicates spalling failure (l) and splitting fractures approximately parallel to
the direction of axial stress (m).
 X.G. Zhao et al. / International Journal of Rock Mechanics & Mining Sciences 64 (2013) 258–269 263

Fig. 6. Complete stress–strain curve associated with AE hit characteristics showing different deformation stages of the Beishan granite at a confinement of 10 MPa (a), and a
zoomed-in relationship between AE hit count and axial compression stress for identifying crack initiation stress and crack damage stress thresholds (b).

shear failure under confined conditions is captured reasonably before and after the crack damage threshold. Thus, the AE method
well using the proposed method, further efforts are needed to is less objective compared with the volumetric strain method, and
produce innovative design for conducting direct AE measurements the error introduced might be high. When the stress–strain
inside the triaxial cell. relationships are not available, the AE measurement can be
employed to determine the crack damage stress threshold in
compression tests. In the following discussion, the crack damage
4. Damage stress of the Beishan granite stresses obtained from the volumetric strain method are used.
Over the last 40 years, various methods have been proposed to
4.1. Identification of crack initiation and crack damage stresses establish crack initiation threshold in laboratory compression tests
involving stress and strain measurements [22,27–31]. Compared
In the experimental results presented in Section 3, the crack with the methods for crack damage threshold identification, the
initiation, crack damage and peak stresses at different confine- methods for identifying the crack initiation threshold for hard
ments were obtained. Among the three characteristic stress rocks are less accurate and continued research is on-going to
thresholds, the peak strength is the easiest to be determined and address the problem. At present, the ISRM has established a
this task can be achieved even without strain measurement. The commission on rock spalling, and one of the important objectives
crack damage stress can be determined either from the reversal of the commission is to develop suggested guidelines for deter-
point on the volumetric strain–axial strain plot or from the mining the crack initiation threshold of rocks. Recently, Nicksiar
intersection of the cumulative AE hit lines that clearly defines and Martin [32] proposed a new method, which is called Lateral
two constant AE rates before and after the crack damage thresh- Strain Response (LSR) method, for the determination of crack
old, as shown in Figs. 4 and 6. The crack damage stresses initiation stress. Meanwhile, they also utilized different strain
determined by the two methods for the uniaxial and triaxial based methods to evaluate the crack initiation threshold of Äspö
compression tests are presented in Fig. 8a and b, respectively. It diorite in uniaxial compression, and showed that any of the strain-
is seen that both methods produce consistent scd values with based methods provided statistically accurate results.
acceptable deviations. This conclusion is in agreement with that It should be noted that the volumetric strain [27], the lateral
drawn from the triaxial compression test results of rock salt in strain [28,29] and the instantaneous Poisson's ratio [31] methods
which both methods were used to determine scd [26]. Compared depend strongly on user's judgment because the curves associated
with the AE technique, the volumetric strain method tends to be with the strains are often strongly nonlinear (see Fig. 9b, c, d and
more objective because scd can be precisely registered from the f). Some errors due to subjectivity can occur when picking the
maximum volumetric strain point whereas the AE method crack initiation stress from the drawn tangential lines, especially
requires the user to define two lines that have constant AE rates when the quality of the stress–strain relationship is poor and the
264 X.G. Zhao et al. / International Journal of Rock Mechanics & Mining Sciences 64 (2013) 258–269

Fig. 7. Spatial distribution of accumulated AE events in the rock sample at different stress levels under a confining stress of s3 ¼ 10 MPa. (a)–(j) respectively correspond to
points sci to sh in the complete stress–strain curve shown in Fig. 6a, and the sample fails in shear (i).

Fig. 8. Estimation of the crack damage stress from cumulative AE hit number and volumetric strain in an uniaxial (a) and a triaxial (s3 ¼10 MPa) compression tests (b) based
on Figs. 4 and 6, respectively.

nonlinearity of the curve is strong. The less subjective crack volumetric strain from the total volumetric strain. A shortcoming
volumetric strain method [30] attempts to find sci by plotting of this method is that the determination of sci relies on the elastic
the crack volumetric strain versus the axial strain (see Fig. 9e). The constants (i.e., Young's modulus E and Poisson's ratio v), and this
crack volumetric strain is calculated by subtracting the elastic method is especially sensitivity to the Poisson's ratio [25].
 X.G. Zhao et al. / International Journal of Rock Mechanics & Mining Sciences 64 (2013) 258–269 265

Fig. 9. Determinations of crack initiation stress threshold based on various methods respectively proposed by different researchers. (a) Stress–strain curve of the Beishan
granite (BS06MD-21) in triaxial compression at a confinement of 5 MPa. (b) Volumetric strain method [27], (c) lateral strain method [28], (d) extensional strain method [29],
(e) crack volumetric strain method [30], (f) instantaneous Poisson's ratio method [31], (g) lateral strain response (LSR) method [32] and (h) AE hit line method.
266 X.G. Zhao et al. / International Journal of Rock Mechanics & Mining Sciences 64 (2013) 258–269

Compared with other strain methods, an advantage of the newly available, AE monitoring is an alternative approach for identifying
proposed LSR method [32] is that it removes the user's subjective the crack initiation stress. It is observed from Fig. 9 that the sci
judgment (see Fig. 9g). However, the use of the LSR method values obtained from seven different methods are reasonably close
depends on accurate determination of the crack damage stress to each other. This supports the conclusion arrived by Nicksiar and
and on having a fitting equation to find the maximum LSR value Martin [32], although they used only data from uniaxial compres-
and the associated sci. sion tests without AE measurement. Presently, the ISRM has not
In the present study, sci can be determined easily by using the provided a suggestion for the determination of sci during rock
linear AE hit line method to identify the inflection point in the AE deformation in both unconfined and confined compression tests.
hit-axial stress plot, as presented in Fig. 4b, Fig. 6b, and Fig. 9h. As According to the suggestion in [13], strain in combination with AE
mentioned above, when the stress–strain relationships are not should be used to evaluate crack initiation stress whenever

Table 1
Determinations of characteristic parameters of the Beishan granite in unconfined and confined compression tests.

Sample no. s3 (MPa) E (GPa) v sc (MPa) Crack initiation stress sci (MPa) scd (MPa) sci/sc scd/sc sci/scd

VS AE LSR Mean SD Cov (%)

BS06MD-01 0 62.45 0.18 129.61 60.22 64.57 64.97 63.25 2.63 4.17 103.75 0.49 0.80 0.61
BS06MD-02 62.12 0.12 127.25 77.34 78.99 80.18 78.84 1.43 1.81 119.81 0.62 0.94 0.66
BS06MD-03 65.76 0.14 156.63 77.00 84.73 88.34 83.36 5.79 6.95 134.55 0.53 0.86 0.62
BS06MD-04 64.05 0.15 152.50 64.05 62.50 66.36 64.30 1.94 3.02 105.44 0.42 0.69 0.61
BS06MD-05 65.08 0.15 155.29 71.80 84.8 81.84 79.48 6.81 8.57 118.91 0.51 0.77 0.67
BS06MD-06 61.48 0.12 154.66 65.93 69.57 64.79 66.76 2.50 3.74 99.93 0.43 0.65 0.67

Mean 63.49 0.14 145.99 69.39 74.19 74.41 72.67 2.84 3.91 113.73 0.50 0.78 0.64
BS06MD-07 1 66.80 0.16 158.01 65.15 65.83 79.30 70.09 7.98 11.39 124.33 0.44 0.79 0.56
BS06MD-08 65.83 0.12 166.10 71.24 74.35 81.37 75.65 5.19 6.86 118.24 0.46 0.71 0.64
BS06MD-09 65.90 0.16 160.72 75.55 78.94 72.12 75.54 3.41 4.51 134.60 0.47 0.84 0.56
BS06MD-10 66.16 0.15 136.49 71.14 64.02 68.78 67.98 3.63 5.34 97.06 0.50 0.71 0.70
BS06MD-11 61.55 0.15 151.82 70.18 85.97 75.53 77.23 8.03 10.40 109.73 0.51 0.72 0.70

Mean 65.25 0.15 154.63 70.65 73.82 75.42 73.30 2.43 3.31 116.79 0.48 0.75 0.63
BS06MD-12 2 66.88 0.17 171.64 80.18 74.97 89.24 81.46 7.22 8.86 123.58 0.47 0.72 0.66
BS06MD-13 61.98 0.12 166.25 75.46 65.42 85.13 75.34 9.86 13.08 120.18 0.45 0.72 0.63
BS06MD-14 62.05 0.12 172.36 70.68 85.65 72.49 76.27 8.17 10.71 125.54 0.44 0.73 0.61
BS06MD-15 67.00 0.18 145.08 68.70 72.40 64.36 68.49 4.02 5.88 115.21 0.47 0.79 0.59

Mean 64.48 0.15 163.83 73.76 74.61 77.81 75.39 2.13 2.83 121.13 0.46 0.74 0.62
BS06MD-16 3.5 68.79 0.14 185.56 86.01 73.43 97.45 85.63 12.01 14.03 145.92 0.46 0.79 0.59
BS06MD-17 68.62 0.13 184.66 86.38 79.90 99.27 88.52 9.86 11.14 150.93 0.48 0.82 0.59
BS06MD-18 76.10 0.16 183.33 85.01 92.40 86.34 87.92 3.94 4.48 139.82 0.48 0.76 0.63
BS06MD-19 62.76 0.12 176.19 90.24 83.67 102.40 92.10 9.50 10.32 153.35 0.52 0.87 0.60

Mean 69.07 0.14 182.44 86.91 82.35 96.37 88.54 7.15 8.07 147.51 0.49 0.81 0.60
BS06MD-20 5 67.10 0.18 212.01 91.10 88.04 91.99 90.38 2.07 2.29 156.95 0.43 0.74 0.58
BS06MD-21 75.69 0.17 206.72 98.28 102.44 108.72 103.15 5.26 5.10 163.14 0.50 0.79 0.63
BS06MD-22 76.50 0.20 209.09 84.25 94.25 96.58 91.69 6.55 7.14 154.29 0.44 0.74 0.59
BS06MD-23 65.53 0.15 199.80 89.33 82.26 114.90 95.50 17.17 17.98 169.52 0.48 0.85 0.56

Mean 71.21 0.18 206.91 90.74 91.75 103.05 95.18 6.83 7.18 160.98 0.46 0.78 0.59
BS06MD-24 10 77.98 0.19 245.40 99.18 113.75 104.24 105.72 7.40 7.00 171.53 0.43 0.70 0.62
BS06MD-25 72.39 0.18 258.27 97.22 104.58 114.69 105.50 8.77 8.31 180.28 0.41 0.70 0.59
BS06MD-26 70.50 0.20 226.01 92.54 117.11 108.76 106.14 12.49 11.77 195.46 0.47 0.86 0.54

Mean 73.62 0.19 243.23 96.31 111.81 109.23 105.79 8.30 7.85 182.42 0.44 0.75 0.58
BS06MD-27 15 72.13 0.20 274.23 114.34 128.53 124.01 122.29 7.25 5.93 198.04 0.45 0.72 0.62
BS06MD-28 68.62 0.17 275.18 119.38 135.50 133.37 129.42 8.76 6.77 209.67 0.47 0.76 0.62
BS06MD-29 79.55 0.20 245.10 126.40 104.94 112.28 114.54 10.91 9.52 191.67 0.47 0.78 0.60
BS06MD-30 74.15 0.18 260.44 124.24 135.80 143.90 134.65 9.88 7.34 218.93 0.52 0.84 0.62
BS06MD-31 75.42 0.21 300.11 125.84 105.96 119.65 117.15 10.17 8.68 207.86 0.39 0.69 0.56

Mean 73.97 0.19 271.01 122.04 122.15 126.64 123.61 2.63 2.13 205.23 0.46 0.76 0.60
BS06MD-32 20 81.90 0.22 339.27 148.33 118.00 170.20 145.51 26.21 18.02 271.22 0.43 0.80 0.54
BS06MD-33 70.51 0.21 331.27 147.85 99.14 147.73 131.57 28.09 21.35 246.67 0.40 0.74 0.53
BS06MD-34 74.38 0.17 343.94 144.70 130.74 174.23 149.89 22.20 14.81 265.08 0.44 0.77 0.57
BS06MD-35 81.41 0.22 311.16 145.17 146.94 171.68 154.60 14.82 9.59 278.31 0.50 0.89 0.56

Mean 77.05 0.21 331.41 146.51 123.71 165.96 145.39 21.15 14.55 265.32 0.44 0.80 0.55
BS06MD-36 30 82.69 0.19 365.10 177.51 148.29 192.17 172.66 22.34 12.94 300.00 0.47 0.82 0.58
BS06MD-37 70.64 0.22 402.14 161.91 171.21 191.92 175.01 15.36 8.78 301.29 0.44 0.75 0.58
BS06MD-38 76.40 0.20 411.69 159.73 184.82 163.43 169.33 13.54 8.00 278.60 0.41 0.68 0.61
BS06MD-39 82.54 0.22 371.66 166.45 157.98 171.68 165.37 6.91 4.18 278.31 0.44 0.75 0.59

Mean 78.07 0.21 387.65 166.40 165.58 179.80 170.59 7.99 4.68 289.55 0.44 0.75 0.59
BS06MD-40 40 80.03 0.21 437.17 183.74 195.50 200.16 193.13 8.46 4.38 324.52 0.44 0.74 0.60
BS06MD-41 75.94 0.22 458.90 193.96 218.36 204.83 205.72 12.22 5.94 326.75 0.45 0.71 0.63
BS06MD-42 75.31 0.20 446.47 189.97 198.64 203.16 197.26 6.70 3.40 329.39 0.44 0.74 0.60

Mean 77.09 0.21 447.51 189.22 204.17 202.72 198.70 8.24 4.15 326.89 0.44 0.73 0.61

Note: E–Young's modulus, v–Poisson's ratio.

 X.G. Zhao et al. / International Journal of Rock Mechanics & Mining Sciences 64 (2013) 258–269 267

initiation and crack damage stresses increase with increasing

confining stress. The best-fit crack initiation threshold for all the
tested rocks over a confinement range of 0–40 MPa can be written
in the form of
s1 ¼ 0:51sc þ 3:21s3 : ð1Þ
In the splitting zone (s3 ¼ 0–2 MPa), an envelope that better
represents the crack initiation stress threshold can be expressed
by
s1 ¼ 0:50sc þ 1:36s3 ð2Þ
The major difference between Eqs. (1) and (2) is that the envelope
represented by the later has a smaller slope in the principal stress
space, indicating that crack initiation stress is less sensitive to
confinement under low confinement conditions. It is seen that the
slopes of the two crack initiation thresholds have a negligible
impact on the threshold levels in the splitting zone. However, with
the increase of confining stresses, the crack initiation threshold
becomes more sensitive to confinement. For example, when s3 is
equal to 1 MPa, the crack initiation stresses obtained from Eqs.
(1) and (2) are 77 and 74 MPa, respectively. Whereas when s3 is
increased to 20 MPa, the crack initiation stresses obtained from
Eqs. (1) and (2) are 138 and 100 MPa, respectively.
Field observations demonstrate that brittle failure around
underground openings in hard rocks often occurs in the form of
spalling or slabbing. Some researchers [12,32,33] suggested that
crack initiation stress from laboratory uniaxial compressive tests
could be used as a lower-bound value for evaluating the onset of
in situ spalling strength. Near the underground excavation bound-
ary, the confining stress is low, generally in a range of 0 to a few
MPa; hence, the slope of the crack initiation surface is of
Fig. 10. Average SD (a) and CoV values (b) of the crack initiation stresses obtained
from three different methods under various confinement conditions.
subordinate importance [10]. To estimate the depth of brittle
failure around tunnels excavated in moderately jointed to massive
hard rock masses, Martin et al. [34], based on the Hoek–Brown
possible. Hence, three different methods, i.e., volumetric strain (VS) failure criterion, proposed a m-zero damage initiation criterion:
method [27], LSR method [32], and AE hit line method, are used to 1
s1 s3 ¼ sc : ð3Þ
establish the crack initiation stress in the following analysis. 3
Using the three selected methods described above, the crack The fundamental assumption in using the m-zero damage initia-
initiation stresses at different confinements were determined and tion criterion is that the failure process around the tunnel is
the interpreted results for all tested samples are listed in Table 1. To dominated by cohesion loss associated with rock mass fracturing.
reveal the dispersion degree among the crack initiation stresses It must be pointed out that this approach is only valid when used
obtained from the three methods and their means, we calculated with an elastic analysis utilizing the strength factor concept to
the standard deviation (SD) and coefficient of variation (CoV) for the estimate the maximum depth of failure at low confinement condi-
dataset. It is observed from Table 1 that the cases with SD values tions. When using the laboratory crack initiation stress to establish
less than 10 MPa and 15 MPa account for 70% and 85% of the all in situ spalling strength, caution should be taken when using Eq. (3)
experiments (42 samples with 10 confinement levels), respectively. to predict the brittle failure of hard rocks. This is due to the fact that
In addition, the cases with CoV values less than 15% accounts for when those researchers tried to link the crack initiation stress to
90% of the total, indicating that regardless of the methods used for in situ rock strength, some important factors such as gradual failure
identifying the crack initiation stress at a given confinement, the process due to tunnel face advance and complex excavation
results are generally good and consistent. Based on the mean sci boundary conditions were not properly considered. As argued in
values estimated from each method, the average SD and CoV values Cai et al. [10], the in situ strength could be significantly higher if the
at different confinements were calculated and the results are actual tunnel excavation geometrical condition were honored. This
presented in Fig. 10. It is seen that the average SD and CoV values was further explained using the Mine-by tunnel case history in
are less than 10 MPa and 10%, respectively, with an exception for Canada [35].
s3 ¼20 MPa which shows a SD value of 23 MPa and a CoV value of Compared with the crack initiation stress, the crack damage
15%. This demonstrates that each method determines the crack stress is more sensitive to confinement as a high slope of the
initiation stress reasonably well, and the use of either method for envelope can be seen (Fig. 11a). Similar to the crack initiation
determining sci is not confinement dependent. Without loss of stress thresholds, two crack damage thresholds, one for the
generality, we will use the average crack initiation stresses obtained splitting confinement zone and the other for the whole confine-
from the three selected methods in the following discussion. ment zone, can be expressed as

4.2. Confinement-dependent crack initiation and crack s1 ¼ 0:78sc þ 3:70s3 ð4Þ

damage stresses
s1 ¼ 0:84sc þ 5:54s3 ð5Þ
Fig. 11a presents the crack initiation and crack damage thresh- respectively. It is seen that the slope of crack damage envelope in
olds at different confining stresses. It is seen that the crack the high confinement zone is steeper than that in the splitting
268 X.G. Zhao et al. / International Journal of Rock Mechanics & Mining Sciences 64 (2013) 258–269

Fig. 11. Confinement-dependent crack initiation and crack damage stress thresholds (a), and variation of stress ratios with increasing confinement (b).

zone. When the load reaches the crack initiation stress level, that the AE method can be used effectively for the determination
microcracks are easy to propagate and coalesce under low confine- of crack initiation and crack damage stresses in both unconfined
ment conditions. As damage accumulates, the frictional strength is and confined compression tests. Unlike the crack damage stress
hard to be mobilized when the confinement is low. However, with which is associated with a volumetric strain reversal, the crack
increasing confining stress, the frictional strength component can initiation stress is difficult to be obtained directly from the stress–
be mobilized easily, resulting in an increase of resistance against strain curves. A statistical evaluation of the results using three
crack propagation. Hence, a higher stress is required to further different methods illustrates that each approach determines the
propagate the cracks. crack initiation stress reasonably well, and the use of either
The influence of confinement on some stress ratios (i.e., sci/sc, method for determining crack initiation stress is not confinement
sci/scd, and scd/sc) is presented in Fig. 11b. It is seen that the dependent. However, due to a lack of clear guidelines for deter-
variation of confinement has no impact on the scd/sc ratio, and this mining the crack initiation stress, it is suggested that whenever
ratio is approximately 0.76. However, the sci/scd and sci/sc ratios possible the strain method should be used in combination with
show a large confinement dependency in the splitting zone. At the the AE method to determine the crack initiation stress.
low confinement zone, the sci/scd and sci/sc ratios decrease rapidly For the tested rocks, the crack initiation and crack damage
as confinement increases. However, at the high confinement zone, stresses increase with increasing confining stress. Compared with
the two stress ratios are not affected by the confining pressure. the crack damage stress, the crack initiation stress is less depen-
dent on confinement, especially in the low confinement zone
(splitting zone). Work is being conducted to implement the
5. Conclusions obtained thresholds in numerical modeling to predict excavation
responses in the Beishan granite. It is planned to carry out more
Failure process of crystalline rocks is closely associated with triaxial tests on other Beishan granitic rocks to further study the
crack initiation, crack propagation, crack damage, and strain or influence of grain size and confining stress on their rock mechan-
damage localization. In this paper, the deformation, peak and post- ical properties.
peak strength characteristics of the Beishan granite were studied
systematically using laboratory uniaxial and triaxial compression
tests. Experimental results showed that the complete evolution of Acknowledgments
crack damage in the rock during rock deformation can be success-
fully characterized using the real-time spatial AE locations in This work has been supported by the National Natural Science
combination with the stress–strain relationships. Typical failure Foundation of China (Grant no. 11102061) and the China Atomic
modes such as splitting in uniaxial compression and shear failure Energy Authority through the Geological Disposal Program.
in triaxial compression were observed. The macroscopic failure
modes were in good agreement with the ones reckoned from 3D References
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Zhao et al. (2013) conducted the experimental investigation to study the engineering properties, damage stress
characteristics and to understand the failure process of granite rocks under uniaxial and triaxial compression. From the
findings, it is seen that with the increase of confining stresses, the crack initiation stress is less dependent and crack
damage stress is more dependent to confinement.