Environ Earth Sci (2017) 76:364

DOI 10.1007/s12665-017-6696-4

ORIGINAL ARTICLE

An experimental study on deformation and failure mechanical

behavior of granite containing a single fissure under different
confining pressures
Sheng-Qi Yang1 • Yan-Hua Huang1

Received: 14 January 2017 / Accepted: 4 May 2017 / Published online: 13 May 2017
Ó Springer-Verlag Berlin Heidelberg 2017

Abstract Fissures in natural rocks play an important role containing a single fissure under conventional triaxial
in determining the strength, deformability and failure compression. Finally, a series of X-ray microcomputed
behavior of rock mass. However in the past, triaxial com- tomography (CT) observations were conducted to analyze
pression experiments have rarely been conducted for rock the internal damage mechanism of granite specimens with
materials containing three-dimensional (3-D) fissures and respect to various fissure angles. Reconstructed 3-D CT
the failure mechanical behavior of fissured rocks is not well images indicate obvious effects of confining pressure and
known due to the difficulty of conducting triaxial experi- fissure angle on the crack system of granite specimens. The
ments on fissured rocks. Therefore in this research, con- study helps to elucidate the fundamental nature of rock
ventional triaxial compression experiments were performed failure under conventional triaxial compression.
to study the strength, deformability and failure behavior of
granite specimens with one preexisting open fissure. Keywords Granite  Triaxial compression  Single fissure 
Thirty-one specimens were prepared to perform conven- Strength  Crack damage threshold  X-ray micro CT 
tional triaxial compression tests for intact and fissured Crack
granite. First, based on the experimental results, the effects
of the confining pressure and the fissure angle on the elastic
modulus and the peak axial strain of granite specimens are Introduction
analyzed. Second, the influence of the confining pressure
on the crack damage threshold and the peak strength of Fissures in natural rocks play an important role in deter-
granite with respect to various fissure angles are evaluated. mining the strength, deformability and failure behavior of
For the same fissure angle, the crack damage threshold and rock masses (Wong and Chau 1998; Li et al. 2005; Pru-
the peak strength of granite both increase with the con- dencio and Van Sint Jan 2007; Park and Bobet 2009; Lee
fining pressure, which is in good agreement with the linear and Jeon 2011; Yang and Jing 2011; Yang et al.
Mohr–Coulomb criterion. With increasing fissure angle, 2008, 2012a). Figure 1a illustrates a typical granite rock
the cohesion of granite first increases and later decreases, mass with a steep slope at the Three Gorges Project (TGP)
but the internal friction angle is not obviously dependent on located in Yichang city, Hubei province, China (modified
the fissure angle. Third, nine crack types are identified to after Shi 2006). It is clear that the granite rock mass
analyze the failure characteristics of granite specimens developed by wedge failure due to the effect of two larger
fissures. Therefore, it is significant to investigate the failure
mechanical behavior of fissured rocks to assure the stability
& Sheng-Qi Yang and safety of fissured rock slopes in such applications as
yangsqi@hotmail.com high slope engineering and deep tunnel engineering.
1
The simplified geometry of a single fissure is often
State Key Laboratory for Geomechanics and Deep
adopted to investigate the effect of fissure angle and fissure
Underground Engineering, School of Mechanics and Civil
Engineering, China University of Mining and Technology, length on the failure mechanical behavior of all kinds of
Xuzhou 221116, People’s Republic of China rock material (Fujii and Ishijima 2004; Lu et al. 2008;

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(a) Wedge failure along (b)

the fissure surface

Fissure

Fig. 1 Three Gorges Project located in Yichang city, Hubei province, China. a Granite rock mass high slope (modified after Shi 2006);
b double-lane five-step ship lock (after Fan et al. 2015)

Wong and Einstein 2009; Lee and Jeon 2011; Yang and To evaluate the stability and safety of the steeply sloping
Jing 2011; Zhang and Wong 2012). Fujii and Ishijima lock channel, many experiments have been performed on
(2004) performed uniaxial compression tests on sandstone the granite specimens from the TGP. Yu and Yin (2004)
specimens with an inclined slit or an inclined initial frac- compared the energy dissipation characteristics of TGP
ture from the specimen surface. The experimental results granite under four different loading modes (3-point bend-
showed the crack from the inclined slit from the specimen ing, Brazilian tension, uniaxial compression and triaxial
surface grew at a small angle to the initial direction and compression) and determined that a 3-point bending
curved slightly toward the free surface in all cases for specimen dissipated minimum energy, a Brazilian tension
sandstone specimens. Lu et al. (2008) conducted an specimen dissipated much more energy than a 3-point
experimental study on cylindrical red sandstone (50 mm in bending specimen but less than a uniaxial compression
diameter and 100 mm in length) containing one preexisting specimen, and a triaxial compression specimen dissipated
fissures under chemical action, which investigated the maximum energy. Zhu et al. (2007) conducted conven-
influence of water chemistry on the mechanical behavior of tional triaxial compression tests on the TGP granite, which
pre-cracked sandstone. Wong and Einstein (2009) investi- showed that the crack initiation stress of the granite gen-
gated the cracking behaviors in modeled gypsum and erally occurred between 25 and 50% of the peak strength.
Carrara marble specimens containing a single open fissure In addition to experimental results on granite from the
under uniaxial compression. Yang and Jing (2011) con- TGP, Zhao et al. (2013) experimentally studied the defor-
ducted uniaxial compression experiments for brittle sand- mation, peak and post-peak strength characteristics of
stone specimens containing a single fissure. Based on the granite from Beishan area (a preferable region for high-
experimental results of axial stress–strain curves, the level radioactive waste disposal in China) under uniaxial
influence of fissure length and fissure angle on the strength, and triaxial compression. Using a three-dimensional (3-D)
deformation and cracking behavior of sandstone specimens acoustic emission (AE) monitoring system, Chen et al.
has been analyzed in detail. They found that the uniaxial (2014) experimentally studied the cracking process of
compressive strength, elastic modulus, deformation mod- Beishan granite under compressive stress condition and its
ulus and peak strain all decrease with the increase in fissure effect on the hydro-mechanical properties. Sun et al. (2015)
length, but first decrease then increase with increasing investigated the physical and mechanical behaviors of
fissure angle. Nine different crack types were identified granite specimens after high-temperature treatment under
based on the geometry and crack propagation mechanism uniaxial compression.
in their study. However, the above experimental studies are However, previous triaxial compression experiments
mainly limited under uniaxial compression stress state. have rarely been conducted for granite materials containing
As many people know, the TGP is the largest hydro- 3-D fissures, and the failure mechanical behavior of fis-
power project in the world and has a double-lane five-step sured granites is not well known due to the difficulty of
ship lock, as shown in Fig. 1b (Fan et al. 2015). The side conducting triaxial experiments on fissured rocks. Further,
slopes of the lock are characterized by great height X-ray computed tomography (CT) is an effective nonin-
(170 m), steepness (70 m in height of upright slope) and vasive nondestructive method to detect the internal fracture
length (over 7000 m in total length). All of the rocks in the in a material. In recent years, CT scanning has been applied
TGP are all granite with different amounts of weathering. to explore the internal damage behavior of rock (Jia et al.

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Environ Earth Sci (2017) 76:364 Page 3 of 22 364

2013; Zhao et al. 2014; Lu et al. 2015; Wang et al. 2015; machined the granite specimens along the same direction in
Yang et al. 2015, 2017; Zhao et al. 2017). However, X-ray order to avoid the influence of anisotropy on the experi-
CT observations have rarely been applied to fissured mental results for the granite. At the same time, machined
granites under triaxial compression. Therefore, in this granite specimens were observed and carefully selected to
paper, we report the results of a series of conventional produce specimens suitable for testing. To obtain the exact
triaxial compression tests on granite containing a single results as well as the best comparison, all the experiments
fissure under different confining pressures ranging from 0 were performed in natural and dry conditions.
to 20 MPa. Based on the experimental results, we first According to the method suggested by the International
investigate the influence of the angle of a single fissure on Society for Rock Mechanics (ISRM) (Fairhurst and Hud-
the deformation parameters of granite material to evaluate son 1999), the length-to-diameter ratio of tested specimens
the crack damage threshold and peak strength behavior of should be in the range of 2.0–3.0 to minimize the influence
granite containing a single fissure under conventional tri- of the end friction effects on the testing results. Therefore,
axial compression. Then, we analyze the effects of the all tested granite specimens are cylinders of 38 mm in
angle of the single fissure and the confining pressure on the diameter and 80 mm in length. As a result, all tested
crack types of granite. Finally, using an X-ray microCT specimen have a length-to-diameter ratio of 2.1 to ensure a
scanning system, the internal damage characteristics of the uniform stress state within the specimens. The strength
deformed granite specimens containing a single fissure are behaviors of specimens under conventional triaxial com-
analyzed in detail. pression tests are also determined according to the method
suggested by the ISRM.
The geometry of a granite specimen containing a pre-
Experimental methodology existing single fissure is illustrated in Fig. 3. The fissure
length is 2a, and the fissure angle (the angle between the
Granite material fissure and the direction of the confining pressure) is a. To
simplify the present analysis, the fissure length 2a is fixed
To investigate the mechanical behavior of rock with one at 14 mm. A high pressure water-jet cutting technique was
preexisting open fissure, the granite material located in used to cut 3-D open single fissure in the intact specimens.
Quanzhou city of China was chosen for the experimental The machined fissure width is approximately 1.8–2.0 mm.
study in this research. The granite has a crystalline and To investigate the effect of preexisting crack geometry on
blocky structure (Fig. 2) and is macroscopically very the strength and deformation behavior of granite under
homogeneous with an average unit weight of approxi- different confining pressures, five fissure angles (a = 0°,
mately 2730 kg/m3. The mineral components of the tested 30°, 45°, 60° and 90°) were chosen for this study. Detailed
granite material are muscovite (46.04%), quartz (10.32%), descriptions for granite specimens with different fissure
labradorite (37.69%) and hornblende (5.95%) according to geometries are listed in Table 1.
XRD analysis.
In this research, thirty-one granite specimens were pre- Testing equipment and procedure
pared to perform uniaxial and conventional triaxial com-
pression tests with the confining pressure equal to 0, 5, 10, Uniaxial and conventional triaxial compression experiments
20 and 30 MPa. The specimens were drilled from one big for intact and fissured granite specimens were all performed
rectangular block. During the process of drilling, we on rock servo-controlled triaxial equipment. The equipment

Fig. 2 Microscopic structure of

granite used in this research.
a Optical microscopy, and
b SEM photograph

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Fig. 3 Granite specimen

containing preexisting 3-D σ1
single fissure

Upper fissure tip

Pre-existing 3-Dopen fissure thickness
is approximately 1.8~2.0 mm

2a=14mm
σ3 σ3
α
80 mm

38 mm
Under fissure tip

2 a cos α Pre-existing 3-D open

σ1 single fissure pattern

Table 1 Preexisting single

Fissure geometry Specimen number D/mm L/mm 2a/mm r3/MPa
fissure geometries of granite
specimens Intact specimen I2# 38.2 78.4 N/A 0
#
I3 37.9 76.5 N/A 5
I7# 38.2 76.4 N/A 10
I11# 38.1 76.4 N/A 20
I13# 38.1 73.8 N/A 30
a = 0° A0-1# 38.3 80.0 14 0
A0-6# 38.5 80.1 14 0
A0-2# 38.4 80.0 14 5
A0-3# 37.9 78.7 14 10
A0-4# 38.3 80.5 14 20
a = 30° A30-1# 37.7 80.5 14 0
#
A30-16 38.0 79.8 14 0
A30-2# 38.3 80.0 14 5
A30-3# 38.2 81.0 14 10
A30-5# 38.4 80.9 14 10
A30-7# 38.3 78.9 14 20
a = 45° A45-1# 38.2 80.1 14 0
#
A45-3 38.0 80.8 14 5
A45-6# 38.0 80.9 14 10
A45-5# 38.0 81.3 14 20
a = 60° A60-1# 38.0 80.7 14 0
A60-2# 38.0 79.8 14 0
#
A60-6 37.9 81.0 14 5
A60-4# 38.1 80.4 14 10
A60-5# 38.0 80.4 14 20
a = 90° A90-1# 38.0 81.0 14 0
A90-6# 38.0 80.0 14 0
#
A90-3 38.4 79.4 14 5
A90-2# 38.0 80.3 14 10
A90-4# 38.0 81.6 14 20
A90-5# 38.0 79.1 14 20
D diameter, L length

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Environ Earth Sci (2017) 76:364 Page 5 of 22 364

included a loading system, constant-stability pressure equip- Axial LVDT

ment, a hydraulic pressure transfer system, a pressure cham-
ber, a hydraulic pressure system, and an automatic data
collection system. The most important part of this equipment
is the self-equilibrium triaxial pressure chamber system,
Rock
which consists of three high precision pumps controlling axial
specimen
pressure, confining pressure, and pore pressure. The maxi- Circumferential
mum capacity of confining pressure and pore pressure is strain transformer
60 MPa. However, the maximum capacity of axial pressure
can reach approximately 800 kN. Due to the auto-compen-
sation system, the axial pressure generated by axial pressure
pump is transmitted entirely as deviatoric stress. The testing
equipment can be used to perform all controlled tests, and the
data acquisition and analysis by computer and automatized Fig. 4 Strain measurement of granite in the present study
operations ensure that the tests are conducted safely and pre- the axial strain and the circumferential strain, respectively.
cisely and performed in a timely manner. The data are col- In this research, a positive value for the strain means
lected automatically by the digitized computer configuration. compressive deformation and a negative value means
This equipment can be used to perform hydrostatic pressure dilatation deformation. From Fig. 5, the standard devia-
tests, conventional triaxial compression tests under drained or tions of the elastic modulus, axial peak strain and triaxial
undrained conditions, triaxial seepage tests, triaxial creep compressive strength under axial compression for a = 90°
tests, and chemical corrosion tests, etc. are 1.98 GPa, 0.3815 9 10-3 and 2.96 MPa, while they
The triaxial compression experiment procedure is descri- are 1.985 GPa, 0.0745 9 10-3 and 2.49 MPa under a
bed as follows: The confining pressure was first applied to the confining pressure of 20 MPa for a = 90°. It can be seen
specimen at a constant rate of 0.5 MPa/s, which ensured that that specimen variability has a minimal influence on the
the specimen was under uniform hydrostatic stresses; then, the deformation behavior of fissured granite specimens.
axial deviatoric stress was applied to the surface of the rock Therefore, based on a series of conventional triaxial test
specimen at a 0.04 mm/min displacement control rate until results of fissured granite specimens, we can analyze the
the failure occurred. During the entire uniaxial and triaxial influence of the confining pressure and the fissure angle on
compression experiment, loads and deformations of the tested the deformation parameters of the tested granite material.
granite specimens were recorded simultaneously. Moreover,
two rigid steel cylinders (38 mm in diameter and 20 mm in Deformation behavior of granite containing a single
length) were placed between the loading frame and the rock fissure
specimen, which distinctly decreased the influence of the end
friction effects on the testing results of granite specimens with Axial deviatoric stress–strain curves of granite containing a
a length-to-diameter ratio of *2.0. During a test, the axial single fissure with different fissure geometries under con-
displacement was measured with two linear variable differ- ventional triaxial compression are shown in Fig. 6, in
ential transformers (LVDTs), as shown in Fig. 4, which were which the numbers give the confining stress in MPa. From
fixed between the bottom and top surfaces of the specimen Fig. 6, we can conclude that the yielding stress (the stress
inside the triaxial cell. The circumferential strain transformer value that begins to depart from the linear elastic phase in
was wrapped around the central region of the specimen. the axial stress–strain curve) and TCS (triaxial compressive
strength) of intact and fissured specimen increase gradually
with the confining pressure.
Triaxial experimental results of granite containing In accordance with Fig. 6, the axial deviatoric stress–
a single fissure strain curves of intact and fissured granite at the lower
confining pressures initially show nonlinear deformation,
To analyze the discreteness of the tested granite specimens, and this usually results from the closure of open microc-
we repeated tests with several specimens under the same racks (Yang et al. 2012b). It is known that a minor load
experimental conditions. Figure 5 presents a typical effect may result in a large deformation due to the closure of open
of specimen variability on the triaxial stress–strain curves microcracks in the rock specimen, and thus, the macro-
of granite containing a single fissure (a = 90°). scopic stress–strain curve is nonlinear. Moreover, this stage
In Fig. 5, r1 and r3 represent the major principal stress of microcrack closure depends on the confining pressure.
and the confining pressure, respectively. e1 and e3 represent With the increase in confining pressure, the stage of

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Fig. 5 Typical effect of (a)  σ1 / MPa (b) 

heterogeneity on axial
deviatoric stress–strain curves 
of granite containing preexisting  A90-6 #
single fissure for a = 90°. 
A90-6 # A90-5 #
a r3 = 0 MPa. b r3 = 20 MPa A90-1 # # A90-5 #
 A90-1  A90-4 #
A90-4 #




 
             
ε3 /10 -3 ε1 / 10 -3 ε3 / 10 -3 ε1 / 10 -3

Fig. 6 Axial deviatoric stress– (a)  

σ1 -σ3 / MPa (b) σ1 -σ3 / MPa
strain curves of granite
containing a single fissure with σ3 =30MPa σ3 =20MPa
 
various fissure angles. a Intact
specimen. b a = 0°. c a = 30°. 20MPa
d a = 45°. e a = 60°. f a = 90°   10MPa

 
10MPa
5MPa 5MPa
 
0MPa
0MPa
 
           
ε3 / 10 -3 ε1 / 10 -3 ε3 / 10 -3 ε1 / 10 -3

 
(c) σ1 -σ3 / MPa σ1 -σ3 / MPa
(d)
 
σ3 =20MPa σ3 =20MPa




 10MPa
10MPa
 5MPa
5MPa 

 0MPa 0MPa


 
            
ε3 / 10 -3
ε1 / 10 -3
ε3 / 10 -3 ε1 / 10 -3

 
(e ) σ1 -σ3 / MPa σ1 -σ3 / MPa
(f)



 σ3 =20MPa
 σ3 =20MPa

10MPa 
 10MPa
5MPa


0MPa 5MPa
 
0MPa
 
               
ε3 / 10 -3 ε1 / 10 -3 ε3 / 10 -3 ε1 / 10 -3

initially nonlinear deformation becomes less and less dis- of deformation. After the stage of microcrack closure, the
tinct. This is likely to be a result of the confining pressure stage of elastic deformation dominates the linear portions
acting to close the preexisting microcracks prior to the start of the stress–strain curves. With continuous increase in

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axial deformation, the stress–strain curves begin to depart Fig. 7c. However, for fissured granite, the failure axial
from the linear behavior, which marks the yielding of the strain usually ranges from 0.20 to 7.86% and increases
specimens. However, when the peak strength is reached, nonlinearly with increasing r3 for the same angle of single
there is an obviously brittle drop. It should be noted that the fissure, as shown in Fig. 7d; the value of failure axial strain
granite specimens have no clear residual strength. In the is significantly dependent on the cracking mode in the
stress–strain curves, there are many stress drops, which fissured specimens under different confining pressures.
result from the initiation and propagation of cracks inside
the granite specimen; however, the location and numbers of Crack damage threshold and peak strength
stress drop are closely related to the fissure angle. of granite containing a single fissure
Based on the experimental results shown in Fig. 6,
Table 2 lists the deformation parameters of granite speci- A typical evolution of the volumetric strain of a fissured
mens containing a single fissure under conventional triaxial granite specimen under conventional triaxial compression
compression. In Table 2, ES is the elastic modulus, which is shown in Fig. 8. ev refers to the volumetric strain, which
is confirmed by the slope of the approximately linear part is calculated from the sum of e1 and twice e3 (i.e., ev =
of the stress–axial strain curve (Yang et al. 2008). e1c is the e1 ? 2e3). The crack damage threshold (rcd) of the speci-
peak axial strain value at rupture in terms of the stress– men (Wong et al. 1997; Fairhurst and Hudson 1999; Heap
axial strain curve. et al. 2009) is defined as the corresponding axial deviatoric
According to ES and e1c values listed in Table 2, Fig. 7 stress at which the volumetric deformation of the specimen
illustrates the effect of confining pressure on the elastic switches from compaction-dominated to dilatancy-domi-
modulus and the peak axial strain of granite containing a nated. The peak strength (rp) is obtained by the maximum
single fissure with various fissure angles. From Fig. 7a, we stress value in the deviatoric stress–strain curves. The crack
conclude that the elastic modulus of an intact granite damage thresholds and the peak strengths of granite spec-
specimen decreases from 43 to 32.74 GPa as r3 increases imens with respect to various fissure angles are listed in
from 0 to 5 MPa. This can be explained as follows. Table 2.
Compared with uniaxial compression, the axial deforma- To investigate the effect of confining pressure on the
tion of the granite specimen is larger than the circumfer- strength and crack damage behavior of granite specimens
ential deformation under a 5 MPa hydrostatic pressure, with various fissure angles, a common Mohr–Coulomb
which results in the decrease in ES. However, the elastic criterion is adopted in the present study. The linear Mohr–
modulus increases linearly from 32.74 to 50.11 GPa as r3 Coulomb criterion can be expressed with the following
increases from 5 to 30 MPa because the confining pressure equation:
increases the stiffness of the granite due to the increasing 2C cos u þ r3 ð1 þ sin uÞ
closure of many pores and fissures in the specimen. rS ¼ M þ Nr3 ¼ ð1Þ
1  sin u
In addition, from Fig. 7b and Table 2, it can be con-
cluded that the elastic moduli of fissured specimens are all where rS is the maximum axial supporting capacity of the
smaller than those of intact specimens, which can be rock; M and N is the material parameters, which are related
explained as follows. Due to the heterogeneity of the rock to the cohesion C and the internal friction angle u of the
material, the existence of a single fissure in the specimen rock material.
results in the increase in the slipping interface; therefore, In accordance with Mohr–Coulomb criterion Eq. (1),
the slippage of fissured specimen also increases in the the influences of the confining pressure on the crack
process of axial compression, which reduces the elastic damage threshold and the peak strength for granite speci-
modulus of fissured granite. Moreover, because the crack mens are presented in Figs. 9 and 10, respectively. It is
evolution modes in the fissured granite specimen vary very clear that there are good linear regression coefficients
greatly with the fissure angle, the elastic modulus of fis- of R = 0.932–0.998 for the crack damage threshold, and
sured granite has no quantitative relation with the fissure R = 0.972–0.998 for the peak strength. Tables 3 and 4 list
angle. However, except for uniaxial compression, the the crack damage and the peak strength parameters,
elastic modulus of fissured granite increases nonlinearly respectively, in accordance with the linear Mohr–Coulomb
with increasing confining pressure, and the increasing criterion.
amplitude is slower than for an intact specimen. Based on Figs. 9, 10 and Tables 3, 4, it is clear that
The intact granite specimens failed at an axial strain of M and N are 152.24 MPa and 7.75, respectively, for the
approximately 0.50–1.16% under different confining pres- crack damage threshold, while M and N are 149.24 MPa
sure, which is greater than that of the fissured granite and 10.13, respectively, for the peak strength; these
specimens. Moreover, we find that e1c of an intact speci- observations result in the following conclusion. The Ccd of
men increases linearly with increasing r3, as shown in intact granite is 27.34 MPa, which is higher than CP of

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Table 2 Mechanical parameters of granite specimens containing a single fissure under conventional triaxial compression
Fissure geometry Specimen number r3/MPa ES/GPa e1c/10-3 rcd/MPa rsd/MPa rP/MPa rS/MPa

Intact specimen I2# 0 43.00 4.982 152.96 152.96 155.60 155.60

I3# 5 32.74 6.876 181.08 186.08 183.95 188.95
I7# 10 37.54 8.512 232.98 242.98 245.94 255.94
I11# 20 44.33 10.086 270.64 290.64 329.49 349.49
I13# 30 50.11 11.583 362.00 392.00 424.89 454.89
a = 0° A0-1# 0 21.51 2.821 43.08 43.08 46.39 46.39
A0-6# 0 26.03 2.011 39.22 39.22 43.52 43.52
A0-2# 5 23.44 5.032 57.95 62.95 73.82 78.82
A0-3# 10 29.69 3.678 85.42 95.42 85.87 95.87
A0-4# 20 31.03 5.292 129.54 149.54 129.99 149.99
a = 30° A30-1# 0 31.33 2.827 – – 70.22 70.22
A30-16# 0 23.14 4.036 55.74 55.74 70.44 70.44
A30-2# 5 20.24 5.385 52.85 57.85 84.99 89.99
A30-3# 10 28.75 4.557 72.83 82.83 96.77 106.77
A30-5# 10 25.01 4.249 91.18 101.18 93.38 103.38
A30-7# 20 31.84 6.825 120.95 140.95 159.09 179.09
a = 45° A45-1# 0 37.54 4.112 83.16 83.16 100.44 100.44
A45-3# 5 28.77 5.611 76.33 81.33 113.69 118.69
A45-6# 10 30.05 5.845 94.21 104.21 124.02 134.02
A45-5# 20 36.69 7.599 193.02 213.02 195.81 215.81
a = 60° A60-1# 0 33.26 4.610 68.05 68.05 89.15 89.15
A60-2# 0 30.93 3.848 74.53 74.53 86.10 86.10
A60-6# 5 29.47 4.270 95.8 100.80 102.95 107.95
A60-4# 10 34.45 5.526 133.14 143.14 145.67 155.67
A60-5# 20 35.86 7.349 153.41 173.41 183.78 203.78
#
a = 90° A90-1 0 33.10 4.422 83.36 83.36 110.12 110.12
A90-6# 0 29.14 5.185 72.57 72.57 104.21 104.21
A90-3# 5 31.84 4.916 111.9 116.90 127.30 132.30
A90-2# 10 33.87 5.681 103.38 113.38 156.22 166.22
A90-4# 20 44.81 7.862 226.1 246.10 271.79 291.79
#
A90-5 20 40.84 7.713 219.17 239.17 266.82 286.82

intact granite (23.45 MPa), whereas the ucd of intact that of an intact specimen, and the value of ucd is also
granite is 50.48°, which is lower than uP of intact granite lower than that of an intact specimen except when a = 90°.
(55.12°). However, for fissured granite, M ranges from From Fig. 11, it is clear that with the increase in the fissure
39.84 to 74.88 MPa for crack damage threshold, while angle, the value of Ccd of fissured granite specimen first
from 46.66 to 97.16 MPa for the peak strength. Meanwhile, increases nonlinearly from 8.52 to 16.26 MPa as a
N lies between 4.55 and 8.16 for the crack damage increases from 0 to 60°, and then decreases to 12.33 MPa
threshold, and between 5.16 and 9.25 for the peak strength. as a increases from 60° to 90°. But, the value of ucd of
The values of cohesion (C) and internal friction angle (u) fissured granite specimens has a nonlinear variance with
calculated according to the crack damage threshold and the the increase in fissure angle, and at a = 90°, the value of
peak strength of granite specimens with a single fissure at ucd is approximately 51.41°, which is approximate to that
five angles are presented in Fig. 11. of an intact specimen (50.48°).
Table 3 shows that the values of Ccd range from 8.52 to In Table 4, the values of CP range from 10.25 to
16.26 MPa, while the values of ucd are between 39.76° and 18.96 MPa, while the values of uP are between 42.48° and
51.41°. The above analysis indicates that the values of Ccd 53.60°. The above analysis shows that the values of CP and
and ucd are significantly dependent on the angle of the uP are significantly dependent on the angle of the single
single fissure in the specimen. Generally, the value of Ccd fissure in the specimen. Generally, the values of CP and uP
of a fissured granite specimen is considerably lower than of fissured granite specimens are all considerably lower

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Environ Earth Sci (2017) 76:364 Page 9 of 22 364

Fig. 7 Effect of confining (a)  (b)  α=0°; α=30°; α=45°;

pressure on elastic modulus and α=60°; α=90°
peak axial strain of granite  
containing a single fissure with
various fissure angles. a Elastic 

E S / GPa
ES / GPa

modulus of intact specimen.
b Elastic modulus of fissured 

specimen. c Peak axial strain of 
intact specimen. d Peak axial

strain of fissured specimen 

 
        
σ3 / MPa σ3 / MPa
(c)
 (d)  α=0°; α=30°; α=45°;
α=60°; α=90°




εc / 10-3
εc / 10-3




 
        
σ3 / MPa σ3 / MPa

σ1-σ3 / M Pa 180 σp to 45°, and then decreases to 15.97 MPa as a increases from
45° to 90°. However, the value of uP of fissured granite
150
Dilatancy specimen ranges from 42.48° to 45.52° as a varies between
120 0 and 60°, but at a = 90°, the value of uP is 53.60°, which is
σcd
90 close to that of an intact specimen (55.12°). Furthermore,
the cohesion of fissured granite obtained by the crack
α =30° 60 Compaction
σ3 =20MPa damage threshold is lower than that obtained by the peak
30 strength, but the internal friction angle of fissured granite
obtained by the crack damage threshold is approximately
0
-10 -8 -6 -4 -2 0 2 4 equal to that obtained by the peak strength.
εv / 10-3

Fig. 8 Confirmation of crack damage threshold and peak strength of

fissured granite specimen
Cracking behavior of granite containing a single
fissure
than those of intact specimen, even for a = 90°. From
Fig. 11, it is clear that with the increase in the fissure angle, Figure 12 shows the failure modes of intact granite speci-
the value of CP of fissured granite specimens first increases mens without any preexisting fissures from our conven-
nonlinearly from 10.25 to 18.96 MPa as a increases from 0 tional triaxial compression experiments. The confining

Fig. 9 Influence of the (a) 500 (b) 300

confining pressure on the crack
damage threshold of fissured 400 α=0°; α=30°
granite specimens. a Intact α=45°; α=60° α=90°
200
σsd / MPa

σsd / MPa

specimen. b Fissured specimen 300

200
100

100

0 0
0 10 20 30 0 5 10 15 20
σ3 / MPa σ3 / MPa

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364 Page 10 of 22 Environ Earth Sci (2017) 76:364

Fig. 10 Influence of the (a) 500 (b) 300

confining pressure on the peak α=0°; α=30°
strength of fissured granite 400 α=45°; α=60° α=90°
specimens. a Intact specimen.
200
b Fissured specimen

σS / MPa

σS / MPa
300

200
100
100

0 0
0 10 20 30 0 5 10 15 20
σ3 / MPa σ3 / MPa

Table 3 Crack damage parameters in accordance with the linear mode, and several axial tensile cracks were observed in the
Mohr–Coulomb criterion direction of major principal stress. However at confining
Fissure geometry M/MPa N Ccd/MPa ucd/° R pressures between 10 and 30 MPa, the granite specimens
all demonstrated a typical shear fracture mode. At
Intact specimen 152.24 7.75 27.34 50.48 0.992 r3 = 10 MPa, in addition to two main shear fracture
a = 0° 39.84 5.46 8.52 43.66 0.998 planes, several axial and lateral tensile cracks were also
a = 30° 46.74 4.55 10.96 39.76 0.959 observed. At r3 = 20 MPa, two shear cracks were
a = 45° 60.67 6.83 11.61 48.12 0.932 observed; the angle of the left shear fracture plane was
a = 60° 74.88 5.30 16.26 43.04 0.979 approximately 68°, and the angle of right shear fracture
a = 90° 70.42 8.16 12.33 51.41 0.968 plane was approximately 72°. At r3 = 30 MPa, the granite
specimen took on a single shear fracture mode. Further-
more, the angle of the shear fracture plane at r3 = 30 MPa
was approximately 60°, lower than for r3 = 10 MPa (ap-
Table 4 Peak strength parameters in accordance with the linear proximately 68°).
Mohr–Coulomb criterion
Fissure geometry M/MPa N CP/MPa uP/° R Crack types of granite containing a single fissure

Intact specimen 149.24 10.13 23.45 55.12 0.998 In granite specimens containing a single fissure, crack
a = 0° 46.66 5.18 10.25 42.56 0.996 initiation, propagation and coalescence modes are all
a = 30° 64.60 5.16 14.22 42.48 0.972 observed from the upper and lower tips of the preexisting
a = 45° 91.38 5.81 18.96 44.94 0.974 fissure (Figs. 13, 14), and they are obviously dependent on
a = 60° 86.69 5.98 17.73 45.52 0.992 the confining pressure and the fissure angle. Therefore, in
a = 90° 97.16 9.25 15.97 53.60 0.986 this section, a systematic evaluation is presented on the
cracking behavior in granite specimens containing a single
fissure under conventional triaxial compression.
Nine different crack types (Fig. 15) were identified
pressure exerted a significant influence on the failure mode. based on their geometry and crack propagation mechanism
At confining pressures between 0 and 5 MPa, our granite (tensile, shear and far-field crack) by analyzing the ultimate
specimens all demonstrated a typical axial splitting fracture failure modes of granite specimens containing a single

Fig. 11 Influence of fissure 20 55

angle on crack damage and peak
Ccd / MPa, CP / MPa

strength parameters of granite 16

45
specimens
φ cd / °, φ P / °

12
35
8
obtained by peak strength obtained by peak strength
obtained by crack damage threshold 25 obtained by crack damage threshold
4

0 15
0 15 30 45 60 75 90 0 15 30 45 60 75 90
α/ ° α/ °

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Environ Earth Sci (2017) 76:364 Page 11 of 22 364

Shear crack
Shear crack

Tensile crack

Shear crack
Tensile crack Shear crack
Tensile crack

(a) (b) (c) (d) (e)

Fig. 12 Ultimate failure mode of intact granite specimen without any preexisting fissures. a r3 = 0 MPa. b r3 = 5 MPa. c r3 = 10 MPa.
d r3 = 20 MPa. e r3 = 30 MPa

fissure (Figs. 13, 14). According to Fig. 15, one can see crack and preexisting fissure are usually coplanar.
that four of them (crack types Tw, Ts, Ta and Tas) are tensile, However, the main shear crack usually propagates
three of them (crack types Sm, Ss and Sa) are shear crack, toward the end surface of the specimen along an angle
and two of them (crack types Ft and Fs) are far-field. The inclined approximately 70° to the minimum principal
crack types can be categorized as follows: stress.
6. Crack type Ss The secondary shear crack initiates from
1. Crack type Tw A tensile wing crack initiates from the
the upper or lower tip of the single fissure, which
upper or lower tips of the single fissure or at a certain
usually follows after Tw. The secondary shear crack
distance from the fissure tips. The tensile wing crack
usually propagates toward the end surface of the
usually initiates and propagates along the direction of
specimen along the direction of the maximum princi-
the major principal stress toward the end surface of the
pal stress.
specimen. Moreover due to the influence of crystal
7. Crack type Sa The anti-shear crack initiates from the
grains in granite material, this propagation path of a
upper and lower tip of the single fissure. Although Ta
tensile wing crack Tw is not very smooth.
propagates along the direction of the maximum
2. Crack type Ts The crack is a secondary tensile crack,
principal stress, Sa propagates toward the corners of
which often initiates from upper or lower tip of the
the specimen at a smaller angle with the direction of
single fissure. The crack usually initiates after Tw and
maximum principal stress. Furthermore, Sa propagates
propagates along the direction of the major principal
in a shear failure mode.
stress toward the end surface of the specimen, which is
8. Crack type Ft The far-field tensile crack does not
usually the same direction as Tw.
usually initiate from the tips of the single fissure.
3. Crack type Ta The crack propagation is opposite to that
Moreover, the far-field tensile crack propagation path
of crack type Tw, and therefore, this is called as ‘‘anti-
is not very smooth, and it may be vertical or horizontal
tensile crack.’’ The anti-tensile crack also initiates
tensile depending on the loading process.
from the upper or lower tip of the single fissure and
9. Crack type Fs The far-field shear crack does not
develops along the direction of the axial stress.
usually initiate from the tips of the single fissure.
4. Crack type Tas The crack propagation follows after Ta,
Moreover, the far-field shear crack coalescence path is
which is called an ‘‘anti-tensile secondary crack.’’ This
not very smooth, and it may have an inclined angle
crack also initiates from the upper or lower tip of the
with the direction of the major principal stress.
single fissure and develops along the direction of the
maximum principal stress. In accordance with the above nine crack types, one can
5. Crack type Sm The main shear crack initiates from the analyze the ultimate failure mode and cracking process of
upper or lower tip of the single fissure, and the crack granite specimens containing a single fissure under triaxial
initiation path is approximately parallel to the direction compression (Figs. 13, 14). It is clear that all of the
of the preexisting fissure. The initiating main shear macroscopic failure mode of granite specimens containing

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364 Page 12 of 22 Environ Earth Sci (2017) 76:364

α = 0° α = 30° α = 45° α = 60° α = 90°

(a)

α = 0° α = 30° α = 45° α = 60° α = 90°

(b)
Fig. 13 Ultimate failure mode of granite specimens containing a single fissure at lower confining pressures (r3 = 0 and 5 MPa). a Under
uniaxial compression (r3 = 0 MPa). b At a confining pressure of 5 MPa

a single fissure (Figs. 16, 17) are mixtures of several cracks be noted that at the upper fissure tip for a = 30°, no Ts
among the nine various crack types. For example, the cracks are observed from the same position as Tw. For
failure mode of the specimen with a = 30° and a = 90°, no Ts cracks are observed from the upper and
r3 = 5 MPa is a mixture of cracks Tw, Ts, Ta and Sa. It lower fissure tips, but the crack Ta is initiated from the
should be noted that typical surfaces of the tensile and upper fissure tip and develops toward the bottom boundary
shear cracks shown in Figs. 18 and 19 also support initiated of the specimen along the direction of the maximum
crack types depicted in Figs. 16 and 17. principal stress. Moreover, one Ft is observed for a = 30°,
Table 5 summarizes the initiated crack types of granite and several Ft for a = 60° and 90°, which means that it is
specimens containing single fissure with different fissure easier to emanate more far-field tensile cracks with larger
angles in response to the applied axial loads. As indicated fissure angles.
in Table 5, under uniaxial compression (see Fig. 16a), Tw At r3 = 5 MPa, the crack modes in granite specimens
is often the first crack and Ts is often a secondary crack that containing a single fissure are different from those under
is initiated after Tw. Usually, Tw is initiated from the tips of uniaxial compression. For a = 0°, Tw is initiated from the
preexisting fissure. However, sometimes Tw is initiated at a tips of the single fissure and propagates to the boundaries
distance away from the tips of the single fissure, but this is of the specimen, and several cracks Ft are also observed
observed only in this case of a = 0°, which possibly results during the failure. For a = 30°, one crack Tw is initiated
from the low fissure angle (Yang and Jing 2011). It should from the upper fissure tip, but the other crack Tw is initiated

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Environ Earth Sci (2017) 76:364 Page 13 of 22 364

α = 0° α = 30° α = 45° α = 60° α = 90°

(a)

α = 0° α = 30° α = 45° α = 60° α = 90°

(b)

Fig. 14 Ultimate failure mode of granite specimens containing a single fissure at higher confining pressures (r3 = 10 and 20 MPa). a At a
confining pressure of 10 MPa. b At a confining pressure of 20 MPa

at a distance away the lower fissure tip. Although Ts and Ta from near the right crack Ta. However, for a = 90°, two
are observed from the same lower fissure tip, the directions wing tensile cracks Tw are observed from the upper and
of Ts and Ta are reversed. The anti-shear crack Sa is lower fissure tips. At the lower fissure tip, two secondary
observed from the upper fissure tip and propagates toward tensile cracks Ts are initiated from the lower fissure tip and
the right boundary of the specimen along the direction develop toward the bottom boundary of the specimen along
perpendicular to the preexisting fissure, and the shear the direction of the maximum principal stress. Further-
slippage surface is very clear as shown in Fig. 19. For more, three far-field tensile cracks are also observed.
a = 45°, one tensile wing crack Tw is initiated from the At r3 = 10 MPa, the crack modes in granite specimens
upper fissure tip and develops as far as the top boundary of containing a single fissure are different from those at
the specimen along the direction of the major principal r3 = 0–5 MPa. For a = 0°, Tw is initiated from the middle
stress, and two shear cracks (Sm and Ss) are observed from position of the single fissure and propagates toward the
the lower and upper fissure tip, respectively. The fracture bottom boundary in the direction of the major principal
surfaces of shear cracks are also illustrated in Fig. 19. For stress. However, due to the initiation of two cracks from
a = 60°, the anti-tensile crack Ta is observed from the the upper and lower fissure tips, the crack Tw only propa-
upper and lower fissure tips and propagates to the boundary gates for a short distance. At the same time, in this speci-
of the specimen. At the same time, four far-field tensile men, two anti-tensile secondary cracks Tas are also
cracks are observed, and one far-field shear crack emanates observed. Accompanying the ultimate failure, the specimen

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364 Page 14 of 22 Environ Earth Sci (2017) 76:364

pressures (0–10 MPa) are restricted; the main-shear and

σ1
anti-shear cracks dominate the ultimate failure mode of the
granite specimen. For a = 0° and 30°, two anti-shear
Tf Ss
cracks that emanate from the fissure tips dominate the
Tf Ts
Tw
Tw=Tensile wing crack; ultimate failure of the specimen. For a = 45°, two main
Ts=Secondary tensile crack; shear cracks results in the shear slippage fracture of the
Ss=Secondary shear crack;
T as Ta Sm=Main shear crack; specimen. For a = 60°, one anti-shear crack is initiated
Sm
σ3 σ3
Ta=Anti-tensile wing crack; from the lower tip of the single fissure and propagates to
Tas= Anti-tensile secondary crack;
Sm Sa=Anti-shear crack; the top boundary of the specimen, whereas one anti-tensile
T a Sa
Ft=Far-field tensile crack; crack is initiated from the upper tip of the single fissure and
Fs=Far-field shear crack;
Ts Tw
propagates toward the bottom boundary of the specimen. It
Sf should be noted that at this fissure angle, one far-field shear
crack emanates from the right bottom region of this spec-
imen and one far-field tensile crack is observed in the
σ1 region under the preexisting fissure. The tensile and shear
failure mechanism is also validated from Figs. 18 and 19,
Fig. 15 A sketch of initiated crack types of granite specimens respectively. However for a = 90°, one main shear crack
containing a single fissure under conventional triaxial compression passes through the entire specimen from the top boundary
(modified after Yang and Jing 2011 and Yang et al. 2012a)
to the bottom boundary. One tensile wing crack is also
observed from the upper tip of fissure and propagates to the
top boundary in the direction of the major principal stress.
has several far-field tensile cracks. For a = 30°, two tensile
At the same time, one far-field shear crack is observed in
wing cracks are initiated from the upper and lower fissure the left middle region accompanying the ultimate failure of
tips, and the initiating direction is perpendicular to the
the specimen.
preexisting fissure. Then, Tw propagates in the direction of
It should be noted that shear crack Sa and Sm are usually
the major principal stress. Afterward, with the increase in easier to initiate and nucleate for larger confining pressures,
axial deformation, two secondary tensile cracks are
e.g., the confining pressure is 20 MPa. However, for
observed from the same position as Tw and propagate in the
r3 = 5 MPa, only the specimen with a = 45° initiates
direction of the major principal stress. Accompanying the shear cracks Sm and Ss, and the specimen for a = 30°
ultimate failure of the specimen, two far-field tensile cracks
initiates shear cracks Sa. Tensile cracks Tw and Ts are easier
are also observed. For a = 45°, two anti-tensile wing
to emanate for lower confining pressure (0–10 MPa), but
cracks emanate from the upper and lower fissure tips. The
for a = 90°, the tensile wing crack Tw is observed in all of
left crack Ta does not propagate to the top boundary of the
the specimens. It is very clear that Ts often accompanies
specimen, but the right crack Ta propagates to the bottom
with Tw toward the same direction. Ta is usually easier
boundary of the specimen and the propagation path is not
under the action of confining pressure, except for a = 90°.
smooth. Accompanying the ultimate failure of the speci-
In accordance with Table 5, the anti-tensile secondary
men, two far-field tensile cracks are observed in the left top
crack Tas is rare, observed only for a = 0° and
region of the specimen, and one far-field shear crack is
r3 = 10 MPa. However, far-field tensile cracks initiate in
observed in the right bottom region of the specimen. For
most of the specimens containing a single fissure, and far-
a = 60°, the crack mode is very simple; only two anti-
field shear cracks initiate only under the larger confining
tensile wing cracks are observed from the upper and lower
pressures.
fissure tips, and they propagate to the boundaries of the
From Figs. 16 and 17, it can also be observed that
specimen along the direction of the major principal stress.
several wing tensile cracks Tw appear to stop at a certain
One tensile wing crack is also observed from the lower
distance from the upper and lower boundaries of the
fissure tip. However, for a = 90°, the crack modes are
specimen, which is probably related to the confining stress
approximately the same as those at r3 = 0–5 MPa, which
induced by the friction between the specimen and the steel
indicates that for this fissure angle, the crack mode does not
plates at r3 = 0 MPa or the constriction of applied con-
depend on the confining pressure.
fining pressure. The tensile fracture and shear fracture of
At r3 = 20 MPa, the crack modes in granite specimens
granite specimens under conventional triaxial compression
containing a single fissure are simpler compared to those at
can be further inferred from microscopic observations on
r3 = 0–10 MPa. Furthermore, under higher confining
the fracture surface of the failed specimen, as shown in
pressure of 20 MPa, the tensile wing and secondary tensile
Figs. 18 and 19. The microscopic structure images were
cracks that are easily initiated under lower confining
obtained using KH-8700E optical microscopic machine.

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Environ Earth Sci (2017) 76:364 Page 15 of 22 364

α = 0° α = 30° α = 45° α = 60° α = 90°

Ft
Tw Tw Ft
Tw Ft
Ft Ft
Ts Tw
Ts
Ts Tw

Ft
Ft
Ts
Ts
Tw Ts Ts
Tw Tw Ta
Tw
Tw Ft
Ft

(a)

Ft
Tw Ft Ft
Tw Tw
Ta Ft
Ft Tw
Ft
Ss Ta
Ft Ft
Sa
Fs
Ts Tw Ta
Tw Ft
Sm Ts Tw
Ft Ts

(b)
Fig. 16 Crack types of granite specimens containing a single fissure at lower confining pressures (r3 = 0 and 5 MPa). a Under uniaxial
compression (r3 = 0 MPa). b At a confining pressure of 5 MPa

The tensile fracture is very rough, but the grains keep accelerating voltage was 140 kV, and the scanning time
relatively intact (Fig. 18). However, the shear fracture is was 4 s. The degree of X-ray attenuation depends on the
very smooth, and slippage powders can be seen (Fig. 19). density and the atomic number of the materials in the
specimens. Material with higher density and higher atomic
Internal crack characteristics of granite by X-ray number generally causes higher attenuation of the X-rays.
microCT observation X-ray projection data from various directions are obtained
by the 360° rotation of the X-ray source. We collected 2-D
X-ray CT scanning of the granite specimen was carried out images at intervals of 0.18°, and thus 2000 slice images
using a Nanotom 160 high-resolution microCT at a spatial could be obtained for one specimen. A 2-D image repre-
resolution of 30 lm. The X-ray beam penetrating the senting the linear distribution of X-ray attenuation was
specimen was measured by an array of detectors. The reconstructed using Fourier transformation of the projec-
X-ray was produced by electrons striking a Mo–W alloy tion data. A 3-D data set of the specimen was obtained by
target in an X-ray tube. The electron current was 80 lA, the stacking consecutive 2-D images.

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364 Page 16 of 22 Environ Earth Sci (2017) 76:364

α = 0° α = 30° α = 45° α = 60° α = 90°

Ft
Ft
Ft Ft
Ft Ft
Ta
Ft
Ta Tw Tw
T as Ts

Ta

Tw Ft
Tw Tw Ft
Ta Ta
Ts Ta Tw
T as Fs
Ft

(a)

Ft
Sm Tw
Sa Sm
Sa
Sa

Ta
Sa Fs

Sa Ft
Sm Fs Sm

(b)
Fig. 17 Crack types of granite specimens containing a single fissure at higher confining pressures (r3 = 10 and 20 MPa). a At a confining
pressure of 10 MPa. b At a confining pressure of 20 MPa

It should be noted that a cylinder only 38 mm diameter uniaxial compression has a typical axial splitting failure
and 68 mm length can be regarded as the scanning region, mode, which is also identical to the surface fracture shown
as shown in Fig. 20a, b. Figure 20a, b shows the compar- in Fig. 12a. However, the failure mode of the intact granite
ison of the X-ray CT scanning surface images and the specimen after triaxial compression failure is different
actual surface crack photographs of granite specimen from that after uniaxial compression failure. At a confining
containing a single fissure after uniaxial compression fail- pressure of 10 MPa, the specimen shows a shear failure
ure, where the black regions represent cracks, and other mode with two shear cracks, along with several localized
regions indicate no surface failure. In Fig. 20, the X-ray CT lateral tensile cracks. However, at a confining pressure of
scanning surface images approximate the actual surface 20 MPa, the specimen takes on a single shear failure mode.
crack photographs, which demonstrate that X-ray microCT By rotating the image of the specimen, the trace of the
scanning can be used to explore the internal damage in shear fracture may be perceived as not a plane but a curve.
granite materials. In contrast, once there exists one preexisting fissure, the
Figure 21 shows 3-D CT images of failed granite granite specimen emanates different crack modes, as
specimens. In the 3-D images, the fracture regions are shown in Fig. 21e, f. The 3-D fracture of a fissured granite
black, and the other regions are transparent. From Fig. 20, specimen results mainly from the propagation and coales-
the intact granite specimen without any fissures under cence of 3-D cracks near the tips of the single fissure.

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Environ Earth Sci (2017) 76:364 Page 17 of 22 364

Tw Ts Ft

α = 60°, σ3 = 0 M Pa α = 60°, σ3 = 0 M Pa α = 90°, σ3 = 0 M Pa

Ta Ta Ta

α = 60°, σ3 = 5 M Pa α = 45°, σ3 = 10 M Pa α = 60°, σ3 = 20 M Pa

Enlarge 50 times Enlarge 350 times

α = 60°, σ3 = 0 M Pa α = 60°, σ3 = 0 M Pa

Fig. 18 Observations on tensile crack surface of granite specimens containing a single fissure under conventional triaxial compression

Under uniaxial compression, at a lower fissure angle (e.g., angle, with the increase in confining pressure, the tensile
a = 0°), it is possible to initiate tensile cracks at a distance wing and secondary tensile cracks are restricted; the anti-
away the tips of the preexisting fissure, which was also tensile and anti-shear cracks dominate the ultimate failure
validated in the previous experimental study for fissured mode of the granite specimen. At the same time, due to the
sandstone material (Yang and Jing 2011); however, at effect of the crystal grains in the granite on crack charac-
larger fissure angles (e.g., a = 30°–90°), all of the first teristics, the path of crack propagation is not very smooth.
cracks initiate from the tips of the single fissure. The above Figure 22 further shows internal vertical CT cross sec-
analysis indicates that with the increase in the fissure angle, tions of granite specimens containing a single fissure after
the initiated position of the first cracks transfers from the uniaxial and triaxial compression failure, respectively. From
middle position to the fissure tip. For the same fissure Fig. 22, the width of the fissure is obviously greater than the

123
364 Page 18 of 22 Environ Earth Sci (2017) 76:364

Sa Ss Sm

α = 30°, σ3 = 5 M Pa α = 45°, σ3 = 5 M Pa α = 45°, σ3 = 20 M Pa

Sa Sa Fs

α = 0°, σ3 = 20 M Pa α = 60°, σ3 = 20 M Pa α = 60°, σ3 = 20 M Pa

Enlarge 50 times Enlarge 350 times

α = 45°, σ3 = 20 M Pa α = 45°, σ3 = 20 M Pa

Fig. 19 Observations on shear crack surface of granite specimens containing a single fissure under conventional triaxial compression

other positions at the left tip of the fissure because the water- good similarity. However, we note that at in the fissured
jet enlarged the hole for the time during which it penetrated granite specimen with a = 0° at r3 = 0 MPa, there is one
the specimen thoroughly (Lee and Jeon 2011). Li et al. inclined crack A, which is not observed from Fig. 22, which
(2005) found that the rounded hole has only a little influence results from the crack A is one internal crack, as shown in the
on the damage and failure of the specimen. Therefore, the horizontal cross section. Furthermore, compared Fig. 22f, g,
results on the pre-fissured specimens with a slightly larger it can be seen that for the same fissure angle, with the increase
aperture thickness at its starting point are reliable. Compared in confining pressure, the fissure aperture thickness of granite
Figs. 22 with 21, even though the crack system mode shown specimen also decreases a lot expect for the difference of
in Fig. 21 is three-dimensional CT images, they have still crack system mode.

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Environ Earth Sci (2017) 76:364 Page 19 of 22 364

Table 5 Initiated crack types

Fissure geometry r3/MPa Tw Ts Ta Tas Ss Sm Sa Ft Fs
of granite specimens containing
a single fissure under a = 0° 0 H H
conventional triaxial
compression 5 H H
10 H H H H
20 H
a = 30° 0 H H H
5 H H H H
10 H H H
20 H H
a = 45° 0 H H
5 H H H
10 H H H
20 H
a = 60° 0 H H H
5 H H H
10 H H
20 H H H H
a = 90° 0 H H H
5 H H H
10 H H
20 H H H

strain curve of fissured specimens shows an abrupt

change of slope under various confining pressures,
(a) (b) coincident with the propagation of tensile and shear
cracks at the upper and lower fissure tips. The peak
axial strain of an intact granite specimen increases
Fissure
linearly with increasing confining pressure. However,
68 mm
80 mm

for specimens containing a single fissure, the failure

axial strain usually ranges from 0.20 to 7.86% and
S canning increases nonlinearly with increasing r3 for the same
region Cracks angle of the single fissure. The failure axial strain is
significantly influenced by crack propagation in spec-
imens containing a single fissure under different
confining pressures.
2. The influence of the confining pressure on the crack
Fig. 20 Illustration of scanning region of X-ray microCT observa- damage threshold and the peak strength of granite with
tion. a Experimental specimen; b CT image respect to various fissure angles is evaluated. For the
same fissure angle, the crack damage threshold and the
peak strength of granite both increase with the
Conclusions confining pressure, which is in good agreement with
linear Mohr–Coulomb criterion. With the increase in
Conventional triaxial compression experiments were per-
the fissure angle, the cohesion of granite first increases
formed to investigate the strength, deformability and fail-
and later decreases, but the internal friction angle is not
ure behavior of granite containing a single fissure. On the
obviously dependent to the fissure angle. The cohesion
basis of the experimental results in this research, the fol-
of granite containing a single fissure obtained by the
lowing conclusion can be obtained.
crack damage threshold is lower than that obtained by
1. Compared to an intact specimen, granite specimens the peak strength, but the internal friction angle of
containing a single fissure fail with lower peak granite containing a single fissure obtained by the
strengths and crack damage thresholds and smaller crack damage threshold is approximately equal to that
elastic moduli and failure axial strains. The stress– obtained by the peak strength.

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364 Page 20 of 22 Environ Earth Sci (2017) 76:364

(a) (b) (c) (d)

(e) (f) (g)

Fig. 21 3-D CT images of intact and fissured granite specimen c Intact specimen r3 = 10 MPa. d Intact specimen r3 = 30 MPa.
containing a single fissure after uniaxial and triaxial compression. e a = 0°; r3 = 0 MPa. f a = 30°; r3 = 0 MPa. g a = 30°;
a Uncompressed intact specimen. b Intact specimen r3 = 0 MPa. r3 = 20 MPa

3. Nine different crack types are identified based on their Tw are observed in all of the specimens. Shear cracks
geometry and crack propagation mechanism (tensile, Sa and Sm are usually easier to initiate and nucleate for
shear and far-field crack) by analyzing the ultimate larger confining pressures, e.g., when the confining
failure modes of granite specimens containing a single pressure is 20 MPa. However, for r3 = 5 MPa, only
fissure under different confining pressures. Among the the specimen for a = 45° initiates shear cracks Sm and
nine crack types, four of them (crack types Tw, Ts, Ta Ss, and the specimen for a = 30° initiates shear cracks
and Tas) are tensile, three of them (crack types Sm, Ss S a.
and Sa) are shear crack, and two of them (crack types 4. A series of X-ray microcomputed tomography (CT)
Ft and Fs) are far-field. Tensile cracks Tw and Ts are observations were conducted to analyze the internal
easier to initiate for lower confining pressure damage mechanism of the granite specimens with
(0–10 MPa), but for a = 90°, the tensile wing cracks respect to various fissure angles. Reconstructed 3-D

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(a) (b) (c) (d)

Horizontal
cross-section
(e) (f) (g)

Fig. 22 Internal vertical CT cross sections of intact and fissured r3 = 0 MPa. c Intact specimen r3 = 10 MPa. d Intact specimen
granite specimen containing a single fissure after uniaxial and triaxial r3 = 30 MPa. e a = 0°; r3 = 0 MPa. f a = 30°; r3 = 0 MPa.
compression. a Uncompressed intact specimen. b Intact specimen g a = 30°; r3 = 20 MPa

CT images indicate obvious effects of the confining References

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Yang et al. (2017) investigated the deformation characteristics and failure behavior of granite under uniaxial and
triaxial compression. It is concluded that, compared to intact specimens, specimens with a single fissure fail at lower
strength and exhibit smaller elastic moduli and axial strains. Additionally, for the same fissure angle, the crack damage
stress and peak strength of granite increase with confining pressure.

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