Journal of Rock Mechanics and Geotechnical Engineering.

2012, 4 (2): 168–176

Laboratory creep tests for time-dependent properties of a marble in

Jinping II hydropower station
Xiaojun Zhao1, Bingrui Chen2*, Hongbo Zhao1, Binghui Jie3, Zhengfang Ning4
1
School of Civil Engineering, Henan Polytechnic University, Jiaozuo, 454003, China
2
State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, 430071,
China
3
Ertan Hydropower Development Co., Ltd., Chengdu, 610051, China
4
School of Civil Engineering, Southwest Jiaotong University, Chengdu, 610031, China
Received 14 November 2011; received in revised form 27 February 2012; accepted 2 May 2012

Abstract: In order to investigate the time-dependent behaviors of deep hard rocks in the diversion tunnel of Jinping II
hydropower station, uniaxial creep tests were carried out by using the triaxial testing machine RC-2000. The axial compressive
load was applied step by step and each creep stage was kept for over several days. Test results show that: (1) The lateral
deformation of rock specimens is 2–3 times the axial compressive deformation and accelerates drastically before damage, which
may be employed as an indicator to predict the excavation-induced instability of rocks. (2) The resultant deformation changes
from compression to expansion when the Poisson’s ratio is larger than 0.5, indicating the starting point of damage. (3) In the
step-loading stages, the Poisson’s ratio approximately remains constant; under constantly imposed load, the Poisson’s ratio
changes with elapsed time, growing continuously before the specimen is damaged. (4) When the applied load reaches a certain
threshold value, the rock deteriorates with time, and the strength of rocks approximately has a negative exponent relation with
time. (5) The failure modes of the deep marble are different in long- and short-term loading conditions. Under the condition of
short-term loading, the specimen presents a mode of tensile failure; while under the condition of long-term loading, the specimen
presents a mode of shear failure, followed by tensile failure.
Key words: time-dependent mechanical behaviors; marble; long-term strength; the Poisson’s ratio of rocks; rock creep

2011). Most importantly, indoor test results on

1 Introduction time-dependent properties are the basis of the model

to reflect time-dependent mechanical behaviors of
The time-dependent mechanical behavior of rocks rocks in field, and provide important information for
is one of the important topics in rocks, especially for numerical simulations and stability analysis of
the long-term stability of rock engineering. In recent geotechnical engineering.
years, major hydropower engineering projects in Xu et al. (2005) conducted triaxial compression
western China are frequently encountered, rheological tests on greenschist specimens taken
characterized by more and more complicated from the site of Jinping I hydropower station, and it
geological environments. Based on this, many was observed that local non-uniform failure of rocks
scholars have conducted various indoor or field tests, had a large influence on lateral deformation of rocks,
and interesting results were obtained (Li, 1995; Yang, but less on the axial deformation of rocks. The axial
1995; Munson, 1997; Maranini and Brigndi, 1999;
and lateral rheological processes of rocks before
Sun, 1999, 2007; Zhao et al., 2003; Li et al., 2004;
damage have two stages: initial rheological rate stage
Fabre and Pellet, 2006; Fan et al., 2007; Zhang et al.,
and steady rheological rate stage. In the failure stage,
the lateral rheology shows initial and steady
Doi: 10.3724/SP.J.1235.2012.00168 rheological rate stages, but the axial one presents the
*Corresponding author. Tel: +86-27-87198805;
E-mail: brchen@whrsm.ac.cn initial, steady and accelerative rheological rate stages.
Supported by the National Natural Science Foundation of China
(50909092), the Open Research Fund of State Key Laboratory of Grain and cleavage sliding are observed in the
Geomechanics and Geotechnical Engineering, Institute of Rock and Soil rheological process. Fu et al. (2007) conducted
Mechanics, Chinese Academy of Sciences (Z000802), and the Natural
Science Foundation of Hubei Province (2009CDB120) triaxial compression rheological tests on oil
Xiaojun Zhao et al. / J Rock Mech Geotech Eng. 2012, 4 (2): 168–176 169

mudstone, and considered that the lateral acceleration 2.2 Rock samples
creep stage occurred earlier than the axial The rock samples taken from the auxiliary tunnel
acceleration creep stage and the Poisson’s ratio had a of Jinping II hydropower station are gray-white,
nonlinear relationship with creep. Cui and Fu (2006) medium-fine crystalline marbles of Baishan group
conducted uniaxial compression rheological tests on (T2b), the sampling location is shown in Fig. 2. The
red freestone, and observed that in the failure stage, rocks are hard, brittle and compact. Elasticity
the lateral creep was evident than the axial creep, and modulus of the marble varies from 25 to 40 GPa, and
the lateral acceleration creep stage appeared earlier the deformation modulus is 8–16 GPa. No palpable
than the axial stage. Fujii et al. (1999) believed that infilling materials, filling belt or structural plane in
marbles can be observed with naked eyes.
the lateral deformation was larger than the axial
Homogeneous lithology shows that the components
deformation. In this regard, the lateral deformation
of minerals are mainly composed of quartz, potash
can be used as an index of rock damage in creep tests
feldspar, calcite, mica, chlorite and smectite. The
of rocks.
cylinder rock samples, with a diameter of 50 mm and
Most rocks in the diversion tunnel of Jinping II
height of 100 mm, are obtained by drill-and-blast
hydropower station are composed of marble (Chen et
method. In addition, the two end faces of rock
al., 2010; Li et al., 2011; Wu et al., 2011). The in-situ
samples are polished smoothly. Processing accuracy
stress of 60-70 MPa after excavation is observed in
of the test is controlled properly in accordance with
field. Rock falling caused by time-dependency and
specification (2007).
time-delayed rockbursts are the two main
engineering disasters in Jinping II hydropower
station. In this paper, by using deep marble samples
taken 2 500 m below the surface, axial compression
Sampling location
creep test is conducted to analyze the time-dependent
property, deformation and damage of marble after
tunnel excavation.

2 Testing device and procedures

2.1 Testing device
Tests of marbles were carried out with the servo- Fig. 2 Sampling location.
controlled triaxial rheological testing machine
RC-2000 (Fig. 1). The system of the testing machine 2.3 Test procedures
adopts digitally servo-controlled device of EDC, The tests are conducted in a special laboratory,
which is fabricated by DOLI Corporation in where indoor temperature is controlled at (20±0.5) C
Germany. The loading system adopts servo- to reduce the impact of thermal factors on testing
controlled motor and ball screw systems. Both axial results. First, the rock sample is placed between the
and lateral strains are measured by the extensometers. upper and lower pressure heads, and the rock sample
Measuring range of the axial deformation is 0–8 mm, is amounted with high-quality rubber sleeve to
and that of the lateral deformation is 0–5 mm. The prevent oil leakage. Then, the extensometer (Fig. 1)
measurement error is controlled within ±1%. The is installed in the testing machine. When the rock
maximum axial load applied by the testing machine samples are placed on the testing machine, we can
connect the extensometer with microcomputer
can reach 2 000 kN, and the normal confining
interface, and thus the extensometer can be debugged
pressure can be controlled at 70 MPa.
timely. The test can start at the moment that
Extensometer
debugging is completed. The load is applied step by
step, and the first-grade load is considered to be 0.6
times the uniaxial compressive strength (UCS) of
rocks. The following loading steps of imposed loads
are gradually increased with a magnitude of 20.4,
10.2 and 5.1 MPa, respectively. If rock failure
Fig. 1 Rock servo-controlled triaxial rheological testing doesn’t occur at the moment that the third level of
machine RC-2000. load is applied on the sample, an increasing load of
170 Xiaojun Zhao et al. / J Rock Mech Geotech Eng. 2012, 4 (2): 168–176

5.1 MPa should be considered till rocks fail in the When a certain stress level is reached, stable creep
form of rheological acceleration. A loading rate of rate increases remarkably. When the deformation
0.1 MPa/s is adopted for all loading stages. The axial increases rapidly, rock samples present creep failure.
stress keeps constant after load reaches the preset The three stages of attenuation, stabilization and
threshold value, and then the next loading stage can acceleration can be evidently captured on rock
be considered when the lateral deformation of rocks samples. The results of axial and lateral creep strains
becomes stable under previous loading stage. of rocks at different stress levels are shown in Table 1.
Recording is stopped when rock sample is damaged. In Table 1, the instantaneous elastic strain is not
included in either the axial strain or the lateral strain.
3 Time-dependent mechanical pro-
perties of marble Table 1 Axial and lateral creep strains of rocks at different
stress levels.
Time-dependent properties of marble are strongly 1 1 2 v
 1 / 1  2 /  2  2 / 1
affected by various stress levels on the axial or lateral (MPa) 6
(10 ) 6
(10 ) (106)
deformation. Under low stress levels, the two stages
84.7 33 101 169 0.031 0.04 3.06
of attenuation and stabilization are reflected to some
105.1 55 126 186 0.052 0.05 2.29
extent on axial and lateral creeps of rock samples.
115.3 66 162 258 0.062 0.063 2.45
The duration of attenuated stage is very short and the
120.4 53 143 206 0.049 0.056 2.7
stable stage of rock creep comes quickly. With the
125.5 88 190 292 0.083 0.074 2.16
increase in stress level, instantaneous elastic strain
comes up observably and rock creep decreases 130.6 175 405 635 0.165 0.159 2.31

rapidly with time, which is called the attenuated 135.7 588 1 425 3 309 0.556 0.558 2.42

stage of rock creep. In addition, there is an increasing Note:  1 is the total axial creep strain,  2 is the total lateral creep

trend for the duration of attenuated stage with strain, 1 is the axial creep strain, 2 is the lateral creep strain, and v is the
volumetric strain.
increase in stress level, which can be observed on the
representative results shown in Figs. 3 and 4. As
3.1 Variation in axial and lateral strains of time-
shown in Fig. 3, compressive strain is positive and
dependent properties of rocks
expansive strain is negative. Duration of attenuated
At different stress levels, the axial and lateral
creep is defined from the end of instantaneous elastic
strains of rocks exhibit different time-dependent
strain to the start of constant creep rate.
properties. The increment in lateral creep is larger
than that of axial creep under the same stress level,
Axial creep strain
0.4 i.e. the lateral creep strain is 2–3 times the axial creep
Lateral creep strain 135.7 MPa
0.3
115.3 MPa 120.4 MPa125.5 MPa
130.6 MPa strain. From this point of view, with the increase in
105.1 MPa
0.2 84.7 MPa stress level, the increment in lateral creep becomes
Strain (%)

0.1 larger than that in axial creep at the same stress level.
0.0
084.7 MPa50 100 150 200 250 300 350
The reason may be interpreted that with the increase
0.1 105.1 MPa 115.3 MPa Time (hour)
120.4 MPa
in stress level, rocks begin to appear damage and
125.5 MPa 130.6 MPa
0.2 dilatation, which will result in the gradually
135.7 MPa
0.3 dominant role of the lateral strain. And it can be
Fig. 3 The axial and lateral creep strain curves of marble attributed to the increase in the volumetric strain. In
under uniaxial compression test (UCT).
the failure stage, the lateral steady creep rate is
evidently larger than the axial one, the lateral strain
35
30 increases rapidly, and its increment is much larger
Time (hour)

25
20
than that of axial strain.
15 From Table 1, it can also be observed that with the
10
5 increase in stress level, both the axial and lateral
0 creep strains exhibit an increasing trend. For
80 90 100 110 120 130 140
Stress (MPa) instances, at the stress level of 84.7 MPa and after
Fig. 4 Curve between the duration of attenuated stage under 38.45 hours from the instantaneous strain, the
uniaxial compression creep and axial stress levels. increment in axial creep is 33×106, and that in
Xiaojun Zhao et al. / J Rock Mech Geotech Eng. 2012, 4 (2): 168–176 171

lateral creep is 101×10–6. At the stress level of 135.7

84.7 MPa
0.1 105.1 MPa

Volumetric creep strain (%)

115.3 MPa
MPa and after 20.9 hours, creep failure of rock 120.4 MPa
125.5 MPa
A
0.0
occurs, and the axial creep increases to 588×10–6, 0 50 100 150 200 250 300 350
Time (hour) 130.6 MPa
55.58% of the total axial creep; the lateral creep 0.1
increases to 1 425×10–6, 55.84% of the total lateral
135.7 MPa
creep. During the failure stage, the lateral and axial 0.2

creep strains account for more than half of the total

0.3
creep strain. This indicates that the creep strain of
Fig. 5 Volumetric creep strain of marble vs. time.
hard rocks mainly occurs during the stage of failure.
This phenomenon can be explained as follows:
(1) With the increase in stress level and the load generation of microcracks. Thus, this critical point,
history of rocks, initial cracks occur in the internal i.e.  v  0 , can be treated as a starting point of rock
parts of rocks. When the stress reaches the of damage.
threshold value of failure, abrupt changes will occur Fig. 5 shows that the volumetric strain experiences
in rocks, resulting in a large deformation. In a two stages: compression and expansion. In a low
common sense, we can find that the lateral creep stress level, it is deemed as a compression state.
strain is usually 2–3 times the axial creep strain. Along with the increase in stress, it gradually
(2) With the increase in stress level, the difference transfers from compression to expansion state. In the
between the lateral and axial creep strains failure stage, rock volume increases sharply,
approximately exhibits an increasing trend. When it accounting for 2 262×106, about 78.08% of the total
reaches the last two stress levels, this gap increases expansion before failure. From Fig. 5, it is clear that
drastically. in the first 5 stress levels, rock compression has a
Conclusions can be drawn from the above analysis linear relation with the increase in applied stress and
that the lateral creep strain is a better indicator for its acting duration. At the sixth stress level, the point
predicting the trend of deformation of rocks. A in Fig. 5, where rock volumetric strain  v equals
Therefore, using lateral deformation to control the zero and rock damage begins, can be regarded as the
trend of rock deformation is of better controllability. starting point of stress transferring from compression
By doing so, more precious time can be saved before to expansion. At this point, the applied stress does
the occurrence of engineering disasters. not exceed the rock strength of deterioration, about
3.2 Time-dependency of volumetric strain 96% of rock strength at creep damage. From that
Volumetric strain of rocks can be calculated by the
point on, after a short period of time, the expansion
lateral and axial strains, which can be written as
rate slows down and gradually becomes stable. With
 v  1  2 2 (1) an increase in stress at the next stress level, new
The volumetric strain curve of marble is shown in cracks are generated and the expansion rate of old
Fig. 5. Rock dilation is a gradually developing cracks increases. As a result, rock volumetric
process, which has a close relationship with stress expansion rate is obviously larger than that of the last
levels and duration of the imposed stress. Under a low stress level. With the elapsed time, rock strength
stress level, the existing microcracks inside the rocks further decreases till it reaches the currently applied
will be gradually closed with time, and no damage stress. Then, the rock creep failure occurs.
occurs. Thus, no cracks are generated as a result of 3.3 Evolution law and time-dependent properties
volumetric compression. Rock damage and new of the Poisson’s ratio
crack are generated as a result of increase in stress According to the definition of Poisson’s ratio
level and applied stress with time. With a further    2 / 1 , the variation in the Poisson’s ratio
increase in stress level and duration of applied stress, during loading creep test is illustrated in Fig. 6. As
new cracks propagate and expand continuously, and for the heterogeneous geotechnical materials, there
thus the rock volume will increase. At last, various exist various defects inside, such as microcracks and
cracks will connect, and rock volume increases voids. With the increase in load and creep time, the
sharply, which will lead to the failure of rocks. From defects inside the rock will form nucleus that
the above analysis, we know that the transferring of coalescences and grows to be a larger crack till a
rock volumetric creep from compression to macroscopic fracture penetrates through the rock
expansion is a result of damage inside the rocks and sample. In this process, a mechanical quantity
172 Xiaojun Zhao et al. / J Rock Mech Geotech Eng. 2012, 4 (2): 168–176

Poisson’s ratio and axial

0.35 strain relation curve 1.0
1.0 Poisson’s ratio
Lateral strain and axial Creep
0.30 0.9 Volumetric strain 0.1
strain relation curve
0.8 0.8

Volumetric strain (%)

135.7 MPa

Poisson’s ratio
0.25
Lateral strain (%)

Loading 0.7 0.0

Poisson’s ratio
0.6 0.6
0.20
120.4 MPa 130.6 MPa 0.5 0.1
0.15 125.5 MPa 0.4
Creep 0.4 0.3 0.2
115.3 MPa
0.10 105.1 MPa 0.2
84.7 MPa 0.1 0.3
0.2
0.05 0.0
0 50 100 150 200 250 300 350
0.00 0.0 Time (hour)
0.10 0.15 0.20 0.25 0.30 0.35
Fig. 7 Evolution law of Poisson’s ratio and volumetric strain
Axial strain (%)
Fig. 6 The relation between the lateral strain, the Poisson’s with time.
ratio and the axial strain.
loading step, which can reflect that the growth rate of
lateral creep deformation is larger than that of axial
(Wang, 2007) similar to the Poisson’s ratio needs to
creep deformation. The Poisson’s ratio becomes
be introduced to describe the lateral deformation of
rock sample. Thus, the Poisson’s ratio herein does larger than 0.5 when the applied load on the rock
not have the same meaning as that in the elastic range. specimen lasts for 225 hours, and when the
It includes the range of viscoelastic-plasticity in volumetric deformation  v is zero and the stress of
consideration of the time effect. the rock is 130 MPa. It is basically consistent with
From Fig. 6, it is observed that the relation curve the time point when the volumetric deformation
of lateral strain and axial strain increases stepwise shifts from compression to expansion, which shows
and the curves at each step consist of two parts: the initial damage development of rock specimen.
approximately straight line segment and slope- The micro-fissures begin to reproduce and expand
increasing curve segment, i.e. the loading and creep when damage occurs in the rock specimen. With the
stages. The Poisson’s ratio in the two stages is elapsed time, the micro-fissures increase and
defined as loading Poisson’s ratio and creep propagate, resulting in the Poisson’s ratio larger than
Poisson’s ratio, respectively. Evidently, the lateral 0.5. Sometimes, the Poisson’s ratio could exceed 1.0
creep has approximately a linear relation with the at the failure of the rock specimen.
axial creep, which shows that the loading Poisson’s The tendency of the variation in the Poisson’s ratio
ratio can be roughly regarded as a constant during the with stress, under uniaxial compression and uniaxial
loading process. When the axially applied load keeps compression creep, is shown in Fig. 8. It can be seen
constant and the rock specimen reaches the creep that:
stage, the relation curve of lateral and axial creep (1) Under uniaxial compression, the Poisson’s
gradually transfers from straight line segment to ratio decreases slightly with the increase in stress and
curve segment. The slope of the curve increases it can be regarded as a constant since the decreasing
gradually and keeps steady finally, which is related amplitude is very small. When the applied stress
to the creep loading process, i.e. the rock specimen reaches 68 MPa, the Poisson’s ratio begins to
first reaches the decayed creep stage and then increase. When the imposed stress reaches 83 MPa,
develops to the steady creep. The slopes of the curves the Poisson’s ratio increases to 0.66 drastically and
and the Poisson’s ratio increase gradually at the stage the rock specimen is damaged. Under the condition
of decayed creep, while the slopes of the curves and of low stress level, the cracks inside the rock
the Poisson’s ratio keep constant at the stage of specimen are coalesced and the axial deformation is
steady creep. It indicates that the creep Poisson’s larger than the lateral deformation, which results in
ratio has experienced the evolution from fluctuant to the decrease tendency of the Poisson’s ratio. When
steady state, not constant. the stress reaches the threshold that the damage
The evolution law of the Poisson’s ratio is shown occurs in the specimen, the crack inside the specimen
in Fig. 7. In a global sense, the variation in loading begins to develop and the lateral deformation
Poisson’s ratio is small and keeps nearly constant. becomes larger than the axial deformation, which
The loading Poisson’s ratio varies under different results in increase in the Poisson’s ratio. When the
stress levels. At the stage of creep, the creep stress reaches the critical failure stress, the internal
Poisson’s ratio increases continuously at each crack propagates and expands sharply. The lateral
Xiaojun Zhao et al. / J Rock Mech Geotech Eng. 2012, 4 (2): 168–176 173

2.0
1.0 1.8 130.6 MPa
1.6 125.5 MPa
0.8 120.4 MPa
1.4

Creep rate (105)

Poisson’s ratio

135.7 MPa
1.2 115.3 MPa
0.6 130.6 MPa Creep
125.5 MPa 1.0
Loading 105.1 MPa
0.4 120.4 MPa 0.8
115.3 MPa 84.7 MPa
105.1 MPa 0.6
0.2 84.7 MPa
0.4
Creep
Loading 0.2
0.0
50 60 70 80 90 100 110 120 130 140 0.0
Axial stress (MPa) 0 10 20 30 40 50 60 70
(a) The relationship between Poisson’s ratio and stress. Time (hour)

0.8
Fig. 9 The evolution laws of deformation rate and time under
different loads.
0.6
Poisson’s ratio

From Fig. 10, in the failure stage, the axial and

0.4 lateral creep rates show different behaviors in
comparison with those of the former stress levels.
0.2
Besides the creep’s first two stages, the accelerated
creep stage is also observed in this stage. In the early
0.0
0 20 40 60 80 100 stage of decayed creep stage, the rock’s creep rate
Stress (MPa)
decreases to be approximately a constant in a short
(b) The relationship between Poisson’s ratio and stress under conventional
uniaxial compression.
period of time, which means that the creep of rocks is
Fig. 8 The relationship between Poisson’s ratio and stress in a stable creep stage. In the stable stage, the creep
level.
remains increasing with time, and the creep rate of
rocks grows sharply in a very short period of time at
deformation increases markedly and the lateral a certain critical point, resulting in the creep damage
of rock sample. Both the axial and the lateral creep
deformation is much larger than the axial deformation,
resulting in the sharp increase in the Poisson’s ratio. rates of rock sample hold the same creep property.
(2) In the whole process of uniaxial compression However, the lateral creep rate is larger than the axial
creep test, the Poisson’s ratio first increases slowly creep rate. A larger creep rate in the last stress level
and then decreases at a low speed during the loading is illustrated in Fig. 10.
stage. This variation is very small and almost can be
0.035
considered to be constant. But the variation trend of Axial creep rate
0.030 Lateral creep rate
the Poisson’s ratio is contrary, compared with
conventional uniaxial compression at a UCS of 18 0.025
Creep rate (%)

MPa. It shows that creep greatly affects the Poisson’s 0.020

ratio and the effect needs further study. 0.015
3.4 Evolution laws of creep rate vs. time A
0.010
The rock’s creep rate is an important index in
B
stability evaluation of rock engineering structure. Fig. 9 0.005

shows that in the low stress levels, rock’s creep only 0.000
0 5 10 15 20 25
shows two stages: attenuation creep and steady creep. Time (hour)
Under various high load levels, the creep rate quickly Fig. 10 The relationship between creep rate and time in failure
stage of marble.
reduces to a certain value, almost constant, with time,
which means that the rock’s creep is in a steady creep
stage, but the deformation of rocks still grows. The Assuming that the transferring point from steady
duration for decayed creep of rocks continuously creep stage to accelerated creep is point A, and that
increases with the applied stress. The increasing from axial creep to steady creep stage is point B, it
applied stress of the next stress level has a can be seen from Fig. 10 that point A grows ahead of
considerable effect on the initial creep rate of rock point B, which means that the lateral deformation
sample, but the effect diminishes with time and accelerates earlier than the axial deformation before
finally disappears. rock failure. Therefore, if we pre-arrange
174 Xiaojun Zhao et al. / J Rock Mech Geotech Eng. 2012, 4 (2): 168–176

deformation observation points reasonably and 131.1

monitor the lateral deformation timely based on the 131.0
distribution of stress field during the operation of 130.9
130.8 Test result
rock engineering, much time for engineering hazards

Strength (MPa)
Fitting curve
130.7
prevention can be saved. In Fig. 11, after about 30
130.6
hours, the creep rate becomes stable. 130.5
4.0 130.4
130.3
3.5
Axial creep rate 130.2
3.0 Lateral creep rate
130.1
Creep rate (105)

2.5 2 4 6 8 10 12 14 16 18
Time (hour)
2.0 Fig. 13 Strength-time curves of marble.
1.5
1.0 When t   , the long-term strength of hard
0.5 rock can be obtained:  t =130.1 MPa.
0.0
3.6 Failure mechanism
0 10 20 30 40 50 60 70 Fig. 4 indicates that the accelerating stage of
Time (hour) rock’s creep occurs at stress level of failure stage,
Fig. 11 The evolution laws of deformation rate and time under and basically the creep failure of rocks occurs as long
applied stress of 130.6 MPa. as the applied stress level is greater than the rock’s
long-term strength. Wang et al. (2010) proposed that
3.5 Evolution law of rock strength vs. time the accelerating stage of rock creep would occur
With the creep testing data, the stress-strain when the applied stress was greater than the yield
isochronism curves at different times can be plotted stress of rocks. As the applied stress is greater than
(Fig. 12). It shows that each isochronism curve is the long-term strength of rocks, damage is observed
composed of linear and nonlinear segments with a on rock interior part, and micro-fissures begin to
turning point. As a whole, the turning point decreases propagate. With the elapsed time, damages further
slowly with time and approximates to a limit value, accumulate on interior of rocks and micro-fissures
i.e. long-term strength of rocks. Xu (1997) argued further develop, thus the rock strength begins to
that the turning point is a symbol of rocks decrease. With the development of the micro-fissures
in rocks, the rock strength reduces to a certain stress
transforming from the viscoelastic stage to
level and the rock is finally damaged. The
viscoplastic stage, where rock interior structure
acceleration of rock creep stage is believed to be
damage occurs and rock strength begins to decrease.
rapid growing and connection of micro-fissures. In
2 h4 h 12 h this moment, the lateral creep rate and the axial creep
136 6 h8 h10 h 14 h 18 h

134
rate will both increase rapidly, leading to the ultimate
damage of rock specimen. In rock projects, the start
132
Stress (MPa)

of rock accelerating creep stage means the final

130 failure of rocks. Unfortunately, the study on this
stage of rock creep failure is not of practical
128
significance and it leads to little attention to the stage
126 of rock accelerating creep failure. Many researches
124 are focused on the stage of rock accelerating creep
0.24 0.25 0.26 0.27 0.28 0.29 0.30 0.31 0.32 0.33 failure. Ma (2004) believed that under stress about
Strain (%)
Fig. 12 Stress-strain isochronism curves of marble samples.
90% of ultimate strength of rock-like material, the
accelerating creep failure will happen. Vyalov (1986)
argued that rock accelerating creep is the interior
A negative exponential relationship between rock
factor to cause microstructure change. Cruden (1974)
yield strength and time can be plotted in Fig. 13, and
showed that when the interior micro-crack density of
fitting curves agree well with the testing data. The
rocks reached a critical level that the rocks can
fitting curve can be written as endure, the stage of rock accelerating creep will
 t  130.1  1.5e 0.220 5t ( R 2  0.997) (2) occur.
Xiaojun Zhao et al. / J Rock Mech Geotech Eng. 2012, 4 (2): 168–176 175

In this paper, it is believed that micro-fissures in

rock interior part begin to propagate with time as 1
long as the applied stress level is greater than the 1
2 2
rock’s long-term strength. When the intensity of
micro-fissures reaches a critical density, the stage of
rock accelerating creep will occur. Fig. 14 shows the (a) Creep failure of rock samples.
final failure modes of rocks at creep by conventional
UCT. In Fig. 14(a), the shear failure pattern is
presented. There is a main shear plane followed by
tensional failure, including a few spalling tensional
chips and few inconspicuous tensional cracks. This is
similar to the mode of shear-type failure of intact
deep marble described by Hou et al. (2011). On the (b) Conventional uniaxial compressive failure of rock sample.
Fig. 14 Uniaxial creep and conventional compressive test
shearing section, there are a lot of rock powder, and failures of marble.
some significant friction and sliding traces. All of
these indicate that the rheological failure of the
rocks in uniaxial compression creep exhibits a shear
samples does not take place instantaneously. With
failure in correspondence with failure of rocks in the
the accumulation of damages inside, the rock sample
conditions of unixial compression and confining
becomes anisotropic, and the defective material
pressure. That is to say, the failure type is of mostly
reaches the yield strength and fails firstly, which
ductile damage.
increases the accumulation of the damages. Through above analyses, creep failure of rocks can
Therefore, the range of the yield areas expands with be defined as follows. When the stress reaches the
the increasing defects. This circulation of failure crack damage stress threshold, which means the
mechanism goes on with time, and the rock samples Poisson’s ratio is equal to 0.5, interior microcrack
finally fail at creep. and damage will occur; if the applied stress keeps
Fig. 14(b) shows that there are several tensional constant, the cracks and voids will expand with
failure planes along the axial direction, accompanied elapsed time. Then, the crystal grains of rocks begin
by a partially penetrated shear failure plane. This to slide, and finally, there may be a new balance state
failure mode is more violent and brisk noises can be inside the rock. If the rock is approaching failure and
captured when rock is broken. In the process of the the applied stress reaches the accelerating point of
compression test, if the material of the samples is creep of rocks, the slipping of the grains will not
isotropic, there will be only shear and compressive keep the stress being balanced. Therefore, the rock
stresses, and no tensile stresses will be generated samples finally slide and fail at creep.
before rock yield strength is reached. The initial
failure of the samples is due to the shearing and 4 Conclusions
sliding effects at the beginning of yielding. Then, the
stresses are redistributed inside rocks with elapsed The time-dependent properties of rock tests of
time, and the tensional stress is presented along the deep marble under different stress levels indicate that
axial direction. With the increasingly applied load, the marble has the following characteristics:
the tensional stresses produced by stress (1) The lateral deformation is 2–3 times the axial
redistribution reach the tensile strength, and axial deformation. Before the failure of the rock specimen,
tensional failure occurs. This is the mechanism that the lateral deformation accelerates earlier than axial
there are some tensional failure planes and shear deformation, which is a better index to predict the
failure planes on rocks. Even if the tensional stress is deformation tendency of some rock and soil
large enough, the tensional failure planes will cover engineering projects. Based on this, monitoring of
the shear failure planes. the lateral deformation can be widely used to predict
Failure of hard rock under UCT mostly exhibits a deformation development, and pre-warn and prevent
tensile splitting failure as shown in Fig. 14(b). Under the disasters in geotechnical projects. It has good
the condition of confining pressure, failure type of controllability, but further studies are needed.
hard rock varies from splitting to shear with the (2) The starting of rock damage characteristics of
increase in confining pressure; while the type of hard deep marble is evident: volumetric deformation
176 Xiaojun Zhao et al. / J Rock Mech Geotech Eng. 2012, 4 (2): 168–176

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