International Journal of Geosciences, 2011, 2, 240-247
doi:10.4236/ijg.2011.23026 Published Online August 2011 (
Copyright © 2011 SciRes. IJG
The Effect of Micro-Structure on Fatigue Behaviour of
Intact Sandstone
Manoj N. Bagde1*, Vladimir Petroš2
1Central Institute o f Mining and Fuel Research, Regional Centre, MECL Complex, Nagpur, India
2Faculty of Mining and Geology, VŠB-TU, Ostrava, Czech Republic
E-mail: *
Received January 4, 2011; revised May 8, 2011; accepted June 11, 2011
With advent of servo-controlled stiff testing machines, it is now possible to conduct tests on a rock in the
laboratory under different variable controlled conditions. In this paper, cyclic fatigue behaviour of intact
sandstone obtained from the rock burst prone coal mine in the Czech Republic were presented. Tests were
conducted on MTS- 816 rock test system in the laboratory on intact rock samples of L/D ratio 2 under cyclic
loading frequency of 0.1, 1, 3, 5, 7 and 10 Hz at amplitude of 0.1 mm under displacement control mode until
failure of the samples in uni-axial compression. From, the primary results it was observed that at low loading
frequency range of 0.1 to 3 Hz, there was degradation of the rock samples in terms of fatigue strength and
modulus. While, at higher frequency rose-up in strength and deformation properties were observed. It was
observed that the machine behaviour in terms of amplitude at higher loading frequencies might be affecting
the results. It seemed that machine behaviour of servo-hydraulic testing system was also dependent on rock
type under investigation.
Keywords: Cyclic Loading, Fatigue, Micro-Structure, Machine Behaviour, Rock Memory
1. Introduction
During different mining operations such as excavation,
blasting, drilling and cutting, surrounding rock or rock
mass subjected to alternating or cyclic stresses. Different
researchers studied this type of rock behaviour generally
referred as “Fatigue” under cyclic conditions in the labo-
ratory. From the reported literature, it was found that
intact and failed models of jointed rock were extremely
susceptible to cyclic fatigue failure. Fatigue strength was
typically between 50 and 70 per cent of the static strength
of rock [1-4]. It were reported that different materials
showed different responses in cyclic loading conditions
and cyclic fatigue behaviour in rock was a complex
phenomena. For the detailed literature review on the
subject refers to author’s paper [5-6].
We have investigated the fatigue behaviour of sand-
stone samples from a rock burst prone coal mine in
Czech Republic. Laboratory tests were conducted using
MTS-816 rock test system at cyclic loading frequencies
from 0.1 to 10 Hz. The tests were carried out at displace-
ment control mode until sample failure. The machine
behaviour in terms of amplitude at higher loading fre-
quencies might have affected the results. It seemed that
machine behaviour of servo-hydraulic testing system was
also dependent on rock type under testing. The fatigue
behaviour of sandstone samples and effect of machine
behaviour on obtained results were also discussed and
presented herewith. This study is the continuation of our
previous investigations [5-8] on the fatigue properties of
sandstones. We have discussed the fatigue properties of
sandstones in terms of rock microstructure and stress
memory effects.
2. Testing Programme
In Czech Republic hard coal underground mines, the
highest safety risk evolves from the anomalous geo-
mechanical events, especially rock bursts. Thus, enginee-
ring interest in the Czech Republic is related to the desire
and need to predict and control such phenomena as a
means of ensuring safety. Problems of the genesis of
occurring rock bursts and influencing parameters are
under settlement through various organized research in
the laboratory and through seismic monitoring etc. The
work presented herein extends consideration to dynamic
cyclic load in the laboratory to improve the understand-
ing of damage mechanisms of rock subjected to severe
dynamic fatigue loads. Dynamic cyclic loading influence
fatigue in rock and has great significance in predicting
rock behaviour in excavation systems prone to rock burst
loading. With this aim, the testing programme were de-
signed and discussed in the following.
The tested sandstone samples were from borehole C
62-01 (then referred as C1) obtained from the rock burst
prone CSA-Jan-Karel coalmine from Ostrava-Karvina
coal basin in Czech Republic. Sandstone from borehole
C1, were light to medium coarse grained with small par-
ticles of the coal detritus and small amounts of muscovite
on the jointing surfaces. The test specimen contained
small amounts organic detritus, coal clasts, muscovite
and pyrite etc. The samples were of 1:2 diameter to
length ratio with average diameter of 47.6 mm.
The testing equipment was MTS-816 rock test system.
The MTS controller consists of hardware components
and software applications that provide closed-loop con-
trol of servo-hydraulic test equipment. The details about
the equipment were provided elsewhere [5-7]. The tests
were conducted with axial displacement controlling
loading system and the cyclic load specified was a ramp
cyclic compressive. In the beginning of the test, the axial
displacement target set point was set equal to the ampli-
tude simulated. The tests were conducted at loading fre-
quencies from 0.1 to 10 Hz with simulated amplitude of
0.1 mm. The illustration of loading condition on time-
displacement curve throughout the uniaxial cyclic load-
ing is shown in Figure 1. The room temperature was
20˚C during these tests.
The segment command process was a command that
controls a servo-valve. It was produced via segment
shape and it could be sine, ramp or square. A cyclic com-
Figure 1. Time-displacement curve illustrating uniaxial
dynamic cyclic loading condition (example for 0.1 Hz fre-
quency and 0.1 mm amplitude).
mand created waveforms by assembling two single seg-
ments and repeating them continuously for a number of
cycles. The cycle command always went first to end
level 1 and then end level 2. For example the sine seg-
ment shape, the starting level was wherever the last
process ended or wherever the current output on the ac-
tive control mode happened to be rate defined the dura-
tion of a single cycle (or segment) with the rate type as
time, frequency or rate. Time specified the time to exe-
cute one segment. Frequency specified the time to exe-
cute a two-segment cycle (even though a single segment
was executed), and rate specified a constant rate between
the starting level and the end level. A rate value repre-
sented the amount the control mode changed in one time
unit. Rate was typically associated with a ramp. Peak/
Valley data acquisition in cyclic loading were recorded
data when the master channel signal detected a peak or
valley. The sensitivity could be set to ignore peaks and
valleys that fall below a certain range of amplitudes. The
certain parameters associated with cyclic loading as il-
lustrated in Figure 1 could be defined as follows:
Loading frequency could be defined as,
tt (1)
where, f was frequency in Hz and tp and tv was the time(s)
at corresponding peak and valley data series.
Amplitude could be defined as,
All  (2)
where, A was the amplitude in mm and lp and lv was
the displacement in mm at corresponding peak and val-
ley data series.
Though simulated amplitude for given testing condi-
tions was supposed to be constant, it was observed that
the machine failed to produce simulated amplitude at
higher cyclic loading frequencies (i.e. 3 Hz and more in
this case). The machine performance for simulated am-
plitude of 0.1 mm at varying frequencies is shown in Fig.
2. It could be seen that the amplitude decreased with rise
in the loading frequencies. This affected the results as
discussed later.
3. Experimental Results and Discussion
The data from the cyclic loading tests were analysed to
obtain peak fatigue strength (
fp), valley fatigue strength
fv), average fatigue strength (
f), Young’s modulus
from peak (Eavp) and valley (Eavv) curves, secant modulus
from peak (Esp) and valley (Esv) curves, and average val-
ues were calculated from obtained peak and valley and
also reported here. The stress-strain curves were ana-
lysed for strength and deformation properties using a
computer programme developed in MATLAB. An illus-
Copyright © 2011 SciRes. IJG
tration of stress and modulus computation from peak-
valley data is shown in Figure 3. Since the data were
recorded in peak-valley mode in dynamic cyclic loading,
peak and valley curves were obtained separately and
analysed independently using MATLAB programme to
calculate strength and modulus values as shown in Fig-
ure 3.
Peak fatigue strength (
fp) was the maximum stress
sustained by the rock specimen and obtained from the
peak curve. Valley fatigue strength (
fv) was the maxi-
mum stress obtained from valley curve. The average fa-
tigue strength (
f) was the average obtained from the
peak fatigue strength (
fp) and valley fatigue strength
fv). Thus, it could be defined as:
 (3)
f was the average fatigue strength,
fp was the
peak fatigue strength obtained from the peak curve and
fv was the valley fatigue strength from the valley curve.
The different modulus parameters were obtained from
peak-valley data using MATLAB software and could be
defined as:
avavp avv
EEE 2
where, Eav was the average Young’s modulus and Eavp
and Eavv was the average Young’s modulus obtained
from peak and valley curve respectively.
The secant modulus were obtained from peak (Esp) and
valley (Esv) curves, and average secant values (Es) were
calculated from obtained peak and valley and also re-
ported here. Thus, it could be defined as:
EEE 2
where, Es was the average secant modulus and Esp and
Esv was the secant modulus obtained at 50% of the
maximum stress sustained in the case of peak and valley
curve respectively.
3.1. Strength and Deformation Behaviour of the
The uniaxial compressive strength determined from static
tests of sandstone rock was 148 MPa and average Young’s
modulus was 20 GPa.
The peak, valley and average fatigue strength was
plotted against loading frequencies as shown in Figure 4.
Results showed a general trend of decrease in fatigue
strength till 3 Hz loading frequency. Then sudden rose-
up in values were observed at 5 and 7 Hz loading fre-
quency. Drop in fatigue strength was observed at 10 Hz
loading frequency.
In the case of the Young’s modulus (Figure 5) and
secant modulus (Figure 6) of the rock, also showed
similar trend as discussed in the case of fatigue strength.
It showed first decreasing trend with increase in fre-
quency till 3 Hz and then rose-up at 5 and 7 Hz loading
frequencies and then dropped at 10 Hz loading fre-
The drop in values at 10 Hz loading frequency could
be related to sample disturbance since this particular
tested sample was having coal intrusion. But rose-up in
values at 5 and 7 Hz loading frequencies were mostly
related to machine behaviour as discussed earlier and as
shown in Figure 2, where machine failed to produce
simulated amplitude at these frequencies. Another ex-
planation could be given as at higher loading frequencies
crack propagation might not be allowed to develop in the
rock specimen, thus increase in strength of the rock. The
optical microscopic observation made on thin sections
prepared from failed samples suggested that at higher
loading frequencies propagation of cracks were not al-
lowed to develop compared to that at low loading fre-
quencies and thus rock specimen at higher frequencies
continued to support increased in load up until its final
Figure 2. Machine performance behaviour in cyclic loading
Figure 3. Typical stress-strain curve with illustrating com-
putation of fatigue strength and modulus from peak valley
data in uniaxial dynamic cyclic loading condition and vio-
lent failure of the rock samples as soon as peak fatigue
strength is reached.
Copyright © 2011 SciRes. IJG
Figure 4. Fatigue strength with cyclic loading frequency.
Figure 5. Young’s modulus w i th cyclic loading frequency.
Figure 6. Secant modulus with cyclic loading freque n cy.
failure. At low loading frequency the development of
shear and axial cracks lead to a violent-explosive brittle
failure (refer Figure 3). It was found that sandstone
samples failed violently and even thrown away from the
loading platen basement at high velocity.
According to Martin and Chandler [9], both the loads
and stable crack length were increased up to the critical
moment at which the strain-energy release rate equalled
or exceeded that of energy absorption. At this stage crack
propagation becomed unstable, and the material reached
its peak strength. For heterogeneous materials such as
rock, the propagating crack would most likely encounter
material that was stronger or weaker (an area of pre-ex-
isting stable cracks) than the mean strength. In either
case, after the propagating crack advanced through the
softer or harder material, there was an excess energy
released that was converted to kinetic energy that was
available to do work against the remaining uncracked
material. It was here that the volume of the sample and
the stiffness of the testing machine played a critical role
because the stored energy in the total system dictated the
energy release rate. Peng [10] questioned the view that a
violent fracture was characteristic property of a material.
He had suggested that such a phenomenon could be
caused by the in-ability of the servo-machine to follow
the certain rock fracture. According to him, there exists a
critical crack propagation velocity such that within the
particular machine response time, it reduces the load-
carrying capacity of the fractured specimen to extent that
the machine cannot follow. According to Peng [10] al-
though closed-loop servo-controlled testing machine is a
versatile tool for studying rock fracture, the testing ma-
chine has a finite response time, which is often slow for
extremely brittle rocks. Li et al. [11] also reported that
cracks were initiated with a low velocity and the rate of
increase of the loading rate depended primarily on the
rock type. They were of the opinioned that the softer
rocks were more sensitive to the rate effect.
From the presented results, it seemed that machine
performance behaviour had a markedly different effect
on fatigue properties of the rock tested than higher load-
ing frequencies and sample disturbance. The system
performance was affected by the hydraulic power supply,
servo-valve, actuator and load frame type and specimen
compliances to name only the most critical components.
It was found that when original simulated amplitude
dropped well below to its 2 %, the machine performance
behaviour started affecting the behaviour of the tested
rock. According to Helešic [12], whenever the feedback
was felled lower than the command value, it caused a
phase lag between them and thus distorting the feedback
wave-shape. This was a typical appearance of “pseudo-
control” condition and the system would not be able to
fulfil the demands. According to him whenever the feed-
back falls below 2% of the command amplitude, the sys-
tem goes in “pseudo-control” mode.
From the presented and discussed results it was ob-
served that machine performance behaviour in terms of
drop in amplitude, affected the obtained results and
found to depend on rock type under investigation. The
stiffer the rock would be, the earlier sensitivity to the
machine behaviour would be. From this it could be con-
cluded that cyclic loading was very susceptible to rock
type and particularly to microstructure of the rock. From
this it was put forward that machine sensitivity to rock
type could be used as a basis in identification of the rock
burst prone rocks. Earlier the sensitivity of machine to
rock type in terms of dropped in amplitude and affected
the results; more prone would be the rock-to-rock burst.
The effect of machine behaviour and mechanical proper-
ties of intact sandstone under static and dynamic uni-
axial cyclic loading was discussed in detailed in authors’
Copyright © 2011 SciRes. IJG
paper [7]. The difference between two studies was that in
earlier one tested samples were from different mine and
of L/D ratio 1 and results presented therein were at
higher loading frequencies ranging from 10 to 100 Hz.
According to Stavorgin and Tarasov [13], the reason
for sharp rise in strength lies in the mechanics of energy
transmission to the tip of the rupture crack; at high rates,
not all of the energy reaches the crack tip. Giving an
example of BP sandstone and NBP sandstone, where BP
sandstone was having higher total porosity compared to
that NBP sandstone, they were of the opinioned that the
mechanical characteristics of these sandstones could not
serve as dependable criteria in defining the “burst pro-
neness”. According to them in such cases, petrographic
indices and permeability characteristics are the depend-
able criteria. According to Braunner [14] as to the petro-
graphic composition, a high percentage of durain seems
to be somewhat conductive to bursting. According to him
most of the seams overlain by strong and massive strata
also could be considered potentially burst-prone.
3.2. Effect of Loading and Unloading Path in
Cyclic Loading on Fatigue Strength of
To study the effect of cyclic loading on rock in terms of
change in its microstructure, it was decided to conduct a
test using loading-unloading path. First identical rock
specimen were tested at 1 Hz and 0.1 mm amplitude
loading condition till failure of the sample to know num-
ber of cycles and peak fatigue strength at failure. The
obtained peak fatigue strength for this tested sample was
130 MPa and number of cycles required to caused failure
was approximately 230. Then another test was under-
taken on another sample of similar kind at same loading
conditions with difference that deformation was cycled
in stages and after each stage load was completely
unloaded. It was decided to load the sample in four
stages of 50 cycles each and unload it completely after
each stage subsequently. In very stage-I cycled deforma-
tion was for total number of 50 cycles and unloaded
completely, then in stage II sample loaded and cycled for
another 50 number of cycles (i.e. cumulative number of
cycles were 100 in this case) and unloaded again com-
pletely, so in similar way in stage III (cumulative cycles
150) and stage IV (cumulative number of cycles 200)
procedure was repeated. In final stage V, specimen was
loaded till failure (stage V) and in this case total numbers
of cycles were 210 at failure (actual number of cycles).
The load history illustration of this type of test on stress-
strain curve is shown in Figure 7. The obtained results
peak, valley and average fatigue strength is plotted
against different loading stages used and is shown in
Figure 8.
Figure 7. Stress-strain curve showing load history in load-
ing and unloading stages in cyclic loading (stage II and III
Figure 8. Fatigue strength with loading and unloading
stages in cyclic loading.
The peak fatigue stresses for the 1st, 2nd , 3rd and 4th
loading stages were 18, 41, 42, and 60 MPa, respectively.
The peak fatigue strength was 125 MPa and number of
cycles at failure was approximately 210 (last stage till
failure). From stress-strain curve (in case of stage V)
presented in Figure 7, it could be seen that failure of the
rock after experiencing such loading path also, had failed
in sudden and violent manner after reaching its ultimate
strength. Also it was found that peak fatigue strength and
average Young’s modulus of this specimen after cycled
in stages and then allowed to fail for given loading con-
dition were 125 MPa and 18 GPa respectively and that of
specimen without such loading stages were 130 MPa and
18.5 GPa. Thus, it could be concluded that first two
stages were had a significant effect and here restructur-
ing of the grain of the rock specimen took place chang-
ing original geometry of the rock specimen thus making
it more compact. During third stage of loading it had just
re-produced stress it had experienced through in second
stage of loading. This suggested that rock had a stress
memory it had sustained during earlier loading history
and needed to overcome it when reloaded and cycled
again. This phenomenon is called as Kaiser Effect (KE)
in the rock and studied extensively using Acoustic Emis-
sions (AE) methods [15-17].
Memory properties of rocks are the ability of rocks to
accumulate, to keep and to reproduce information about
Copyright © 2011 SciRes. IJG
the stresses, which they experienced earlier. The best
studied memory effects are the memory effect in AE,
known as Kaiser Effect, and the deformation memory
effects, or memory effects in strain, which make a phy-
sical basis of the Deformation Rate Analysis (DRA)
stress measurement method. Both kinds of effects take
place while the rock is cyclically loaded to stress levels,
increasing from cycle to cycle [15]. Both deformation
and acoustic emission memory effects are due to the de-
velopment of irreversible micro-fractures in rock sub-
jected to cyclic loading [9,18]. According to Filimonov
et al., [15] this leads to the absence of crack growth and
sliding processes (dislocation movements) at stress val-
ues smaller than the maximum previously applied stress.
As soon as this “memorized” stress value is attained,
crack propagation is again initiated, which is accompa-
nied with AE pulses and non-linear inelastic strain de-
velopment. Memory effects are related to irreversible,
stress-induced changes in the rock’s structure occurring
in the first cycle loading. Therefore, the elastic limit pre-
sents a natural threshold for memory formation. This is
confirmed by the tests in which the first stage cycle axial
stress was smaller than the elastic limit for the given
loading condition. In second stage cycle stress and defor-
mation of such specimen were similar to those of “fresh”
specimen, which did not undergo any first cycle loading.
This was due to the absence of micro-fracture damage
below the elastic limit, which could form a stress mem-
ory. Distinct memory effects in the third stage cycle took
place where the maximum axial stress exceeded the elas-
tic limit took place in the second stage cycle. From the
Figure 7, it can be seen that in final stage of cycling and
loading, rock has followed the same path experienced in
stage II and III loading path. A more detailed study of
the stress memory effect under dynamic cyclic loading
could be carried out in the future.
According to Smith et al., [19] often cyclic loads are
not repetitive, i.e. cyclic stress or deformation does not
have constant amplitude or frequency. According to
them it is necessary therefore to know how irregularity in
loading sequences affects accumulation of damage. Here
to study the effect of loading sequence, test was designed
on the sandstone rock specimen of L/D ratio 2 such as
amplitude and target set point was changed in increments
of 0.05 mm, starting from 0.05 to 0.25 mm (referred as
up-loading sequence) and then decreasing from 0.25 to
0.05 mm (referred as reverse loading sequence). The
target set point was also set equal to amplitude simulated
during each increment of loading sequence. The fre-
quency of loading was kept at 0.5 Hz and deformation
was cycled for approximately 25 numbers of cycles for a
given amplitude and displacement target set point during
each increments. The test was carried out continuously
on the same rock specimen with changing amplitude and
target set point from one transition increment phase to
another. The load history on time-displacement curve for
this designed test is as shown in Figure 9 and scattered
data therein represent transition phase from one incre-
ment stage to another. Basically this type of test was
rheological fatigue test, since amplitude and target set
point was maintained constant during each incremental
stage for approximately 25 numbers of cycles.
The time-stress plot obtained from this test is shown in
Figure 10. It was found that up loading cycling sequence
resulted in larger stress accumulation than that reverse
loading sequence. It could be seen that in such kind of
test only peak stress was cycled and valley stress was
constant during the whole test and all incremental load-
ing sequences. From reverse loading it could be seen that
rock was able to reproduce earlier cycled stress in the
case of 0.2 and 0.15 mm cycled earlier during up loading
sequence. Though cycled stress reproduce was less in the
case of reverse loading than that during up loading se-
quence, again suggested that rock had a memory and to
overcome the earlier experienced stress, it should un-
dergo again the same experienced stress. Since rock has
experienced more stress during up-loading sequence, it
was unable to reproduce it in the case of 0.05 and 0.1
mm incremental cases during reverse loading sequence
where it was levelled of with minimum or valley cycled
stress. These results suggested that to overcome earlier
experienced stress by the rock, it need to go through it
The same rock specimen experienced incremental
loading sequence as above, tested at cyclic loading con-
dition of 0.5 Hz and 0.05 mm till failure. The peak fatigue
Figure 9. Axial displacement vs. time showing the load
history for an incremental cyclic loading test performed on
a sandstone (sample C2) of L/D ratio 2 at 0.5 Hz loading
frequency and amplitude and target set point was varied in
increments from 0.05 to 0.25 mm.
Copyright © 2011 SciRes. IJG
Figure 10. Axial stress vs. time showing the stress accu-
mulated during an incremental cyclic loading test per-
formed on a sandstone (sample C2) of L/D ratio 2 at 0.5 Hz
loading frequency and amplitude and target set point was
varied in increments from 0.05 to 0.25 mm.
strength and average Young’s modulus obtained was 151
MPa and 19 GPa respectively, while rock specimen
tested without experiencing such loading condition pro-
duced peak fatigue strength of 164 MPa and average
Young’s modulus 21 GPa. The difference in values was
very negligible and might be related to sample distur-
bance, thus it could be concluded that any stress cycling
made the rock compact, restructure its geometry in the
form of grain re-distribution and thus made it more
stiffer. Hence, it could be concluded that cyclic loading
was very susceptible to rock geometry in terms of its
mineralogy, structure and texture etc. Eberhardt [18]
revealed through his cyclic loading tests study that the
rate at which damage accumulates in the sample could be
controlled through the load path used.
4. Conclusions
In this paper, cyclic fatigue behaviour of intact sandstone
rock samples obtained from the rock burst prone coal
mine in the Czech Republic were discussed. Tests were
conducted under cyclic loading frequencies of 0.1, 1, 3, 5,
7 and 10 Hz at amplitude of 0.1 mm under displacement
control mode untill failure of the sample in uniaxial
compression. From the presented results, it was observed
that at low loading frequency range of 0.1 to 3 Hz, there
was degradation of the rock properties in terms of fatigue
strength and modulus. At higher frequency, rock had
showed increase in strength and deformation properties
under investigation. It was observed that machine be-
haviour in terms of amplitude at higher loading fre-
quencies might be affecting the results. It seemed that
machine behaviour of servo-hydraulic testing system was
also dependent on rock type under testing and found to
be very susceptible to microstructure of the rock. This
was also confirmed through studies conducted to study
effect of loading and unloading path in cyclic loading on
fatigue strength of sandstone. During stress cycling the
re-distribution of grains makes the rock more compact.
Hence, the specimen becomed stiffer. The cyclic loading
response of the rock appeared to be sensitive to sample
geometry and mineralogy. More in-depth studies were
suggested before drawing any final conclusions.
5. Acknowledgements
This work has been performed with financial grant No.
105/01/0042 from Grant Agency of the Czech Republic.
The first author would like to take this opportunity to
thank the Czech Government for providing a scholarship
to pursue his doctoral study in the Czech Republic. Also,
he takes this opportunity to thank all his teachers and
friends for their continuous encouragement. Particular
thanks go to Dr. Alexander Lavrov; Dr. Erik Eberhardt;
and others who provided literature and suggestions.
Thanks are due to Doc. Ing. P. Konečný from Institute of
Geonics, ASCR, Ostrava for his valuable criticism and
suggestions and Dr. J. L. Jethwa for his editing help and
suggestions. Thanks are due to the libarary staff who
were of great help. Thanks are also due to my friend Ing.
Miloš Daniel for his programming help and to Ing. P.
Michalčík and Ing. O. Špinka for their help in carrying
out experiments. I also wish to thank my wife Shaila and
son Anurag for living without me and taking pain in their
stride and for their encouragement throughout this study.
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