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Decay mechanism of fracture induced electromagnetic pulses

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  • Technological College Beer Sheva, Israel

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In this article we consider the rise and fall time (which were earlier shown experimentally to be the same) of electromagnetic radiation (EMR) from propagating cracks. This feature is shown theoretically to be inversely proportional to the pulse frequency ω and to the fourth degree of the absolute temperature. It is shown experimentally that in glass and in glass ceramics, which are not porous, and in granite, whose porosity is of the order of 5%, τ is indeed inversely proportional to ω. In chalk, whose porosity is as high as 40%, however, this relation is not observed. We argue that the latter result is due to the interaction between the cracks which emit the EMR and the pores of the material and specifically to the spread of ensuing temperatures of the cracks caused by this interaction. © 2003 American Institute of Physics.
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Decay mechanism of fracture induced electromagnetic pulses
A. Rabinovitcha)
Department of Physics, Ben-Gurion University of the Negev, Beer Sheva84105, Israel
and The Deichmann Rock Mechanics Laboratory of the Negev, Beer Sheva, Israel
V. Frid and D. Bahat
Department of Geological and Environmental Sciences, Ben-Gurion University of the Negev,
Beer Sheva 84105, Israel and The Deichmann Rock Mechanics Laboratory of the Negev, Beer Sheva, Israel
J. Goldbaum
Department of Physics, Ben-Gurion University of the Negev, Beer Sheva84105, Israel
and The Deichmann Rock Mechanics Laboratory of the Negev, Beer Sheva, Israel
Received 20 August 2002; accepted 28 January 2003
In this article we consider the rise and fall time which were earlier shown experimentally to be the
sameof electromagnetic radiation EMRfrom propagating cracks. This feature is shown
theoretically to be inversely proportional to the pulse frequency
and to the fourth degree of the
absolute temperature. It is shown experimentally that in glass and in glass ceramics, which are not
porous, and in granite, whose porosity is of the order of 5%,
is indeed inversely proportional to
. In chalk, whose porosity is as high as 40%, however, this relation is not observed. We argue that
the latter result is due to the interaction between the cracks which emit the EMR and the pores of
the material and specifically to the spread of ensuing temperatures of the cracks caused by this
interaction. © 2003 American Institute of Physics. DOI: 10.1063/1.1562752
I. INTRODUCTION
Electromagnetic radiation EMRfrom propagating
cracks was observed by Stepanov in 1933 in fractured KCl
crystals.1In 1973 Misra2detected alternating magnetic fields
in the form of decaying pulses while fracturing some metals
and alloys in tension. In 1975 Nitsan3measured EMR during
his experiments of fracturing quartz-containing rocks. In the
1980’s and 1990’s a lot of fracture experiments, in which
EMR was detected, were carried out in various materials,
e.g., ionic crystals,4rocks,5–12 ice13,14 and glass.15 Various
tests were
used to obtain fracture by tension and compression, by ap-
plying uniaxial,5,7,8 triaxial,10–12 bending6and impact6meth-
ods. It was found that the EMR intensity depends on the
elastic rigidity of the material fractured12,16 and the new frac-
tured area,17 but is not affected by the fracture mode, i.e.,
tension or shear.17 In spite of all measurements to date, the
origin of EMR is still not completely understood. Existing
models are unable to quantitatively explain the phenomenon.
Rabinovitch, Frid, and Bahat9carried out parametriza-
tion of EMR pulses. They showedthat the shape of an indi-
vidual EMR pulse can be described by the formula
At
A0sin
tt0
1exp
tt0
;t0tT
¯
A0sin
tt0
1exp
T
¯
t0
exp
tT
¯
;tT
¯
.1
Here A(t) is the pulse intensity as a function of time, t0is
the time of pulse origin,
is the rise and fall time which turn
out to be the same,A0is the amplitude of the pulse enve-
lope maximum, T
¯
is the time when the amplitude is maxi-
mal, and
is the pulse frequency. An example of a pulse
with fitted parameters and their errors is shown in Fig. 1. As
can be seen, the fit is quite good with very low errors. This
kind of fit was achieved for all pulses with errors in the
parameters of less than 5% except for
, whose errors are
usually 2%, but infrequently can be as large as 30%.It
has been found that TT
¯
t0, the time from the pulse ori-
gin to its maximum, is proportional to the crack length, L,
TL/vcr where vcr is the crack velocity, while
is in-
versely proportional to the crack width, b,
vR
b.2
aAuthor to whom correspondence should be addressed; electronic mail:
avinoam@bgumail.bgu.ac.il
JOURNAL OF APPLIED PHYSICS VOLUME 93, NUMBER 9 1 MAY 2003
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Here vRis the Rayleigh velocity.
All aspects of this model except
were experimentally
confirmed.9–12,17 In this article
is considered in detail.
II. EXPERIMENTAL PROCEDURE
A. Experimental equipment and sample preparation
A triaxial load frame TerraTeck stiff press model FX-S-
33090, axial pressure up to 450 MPa, confining pressure up
to 70 MPa, stiffness 5109N/m), combined with a closed-
loop servocontrol, was used for the measurement. The servo-
control linearity 0.05%was used to maintain a constant
axial piston displacement rate. The load was measured by a
sensitive load cell LC-222M maximum capacity 220 kN,
linearity 0.5% full scale. Acantilever set, consisting of axial
and lateral detectors, was used to measure the sample strains
in three orthogonal directions parallel to the principal
stresses. A magnetic one-loop antenna with a diameter of 3
cm EHFP-30 Near Field Probe set, Electro-Metrics Penril
Corporationwas used for the EMR detection. The signals
were amplified by means of a low-noise microsignal ampli-
fier Mitek Corporation Ltd., frequency range 10 kHz-500
MHz, gain 600.5 dB, noise level 1.40.1 dB across the
entire frequency bandand transferred to a Tecktronix TDS
420 digital storage oscilloscope. The latter was connected to
an IBM PC by means of a general purpose interface bus, so
the signals were stored on the computer hard disk for further
processing. The antenna was placed 2 cm away from the
center of the loaded sample, its normal pointing perpendicu-
lar to the cylinder axis. The EMR was monitored with an
overall sensitivity of 1
V.
To reduce the background noise level, the following
means were employed: 1the measurements were carried
out in a thick-wall steel pressure vessel; 2special radio
frequency filters were used; 3the amplifier power supply
was independent of the industrial net; 4the antenna was
connected to the oscilloscope via the amplifier by means of
special double-screen cables Alpha wire Corporation Ltd..
The samples had a cylindrical shape, with standard
length of 100 mm and standard diameter of 53 mm. The
experiments were carried out on: 1. chalk samples taken
from the Horsha Foundation in the Beer Sheva syncline18 all
samples were cut from the same layer with the same orien-
tation within the rock, 2. Eilat granite,10 3. soda-lime glass
and 4. glass ceramics.10,19 Also included in the analysis are
some of the results obtained in our drilling experiments of
glass and granite.20
B. Measurement of pore radii distribution in chalk
The distribution of pore radii was experimentally mea-
sured in a thin cut of chalk 2030 mm area, 30
m thick-
ness. It was examined under a microscope with an enlarge-
ment of 100. The cut was placed on a table that was moved
by means of a computer program Automatic Point Meter
steps 300
m in the ‘‘horizontal’ direction and 600
min
the ‘‘vertical’’ directionso that different pieces of the cut
were sequentially seen, and at each measuring instance the
radius of the pore situated at the same point of the image was
measured. Thus, as a result of a large number of measure-
ments, pore-radii distribution was obtained. The measure-
ment was carried out by means of a micrometer with accu-
racy of 5
m, which is actually a ‘‘ruler’ of 1 mm divided
by 100 equal parts, 10
m each.
A photograph of the cut, where pores can clearly be
seen, is shown in Fig. 2.
III. RISE AND FALL TIME
A. Theoretical considerations
We assume that EMR is originated by surface atomic
ionicvibrations21 caused by bonds rupture, similar to Ray-
leigh waves or surface optical phonons. It has been shown
elsewhere22 that surface waves decay as a result of interac-
tion with bulk phonons. We therefore consider
to be the
relaxation time of such a surface Rayleigh-likewave,
which interacts with a bulk phonon, leading to the creation of
another bulk phonon a three-phonon process, and use Eq.
13of King and Sheard23 to characterize the process. The
rate of occurrence of the process per unit time, or its transi-
tion probability, is given by the golden rule formula24 Pi
f
2
/
f
H3
i
2
(EfEi), where the initial and the final
states are
i
nR,nb1,nb2
,
f
nR1,nb11,nb21
,
where H3is the time dependent anharmonic part of the crys-
FIG. 1. An experimental EMR pulse emitted from chalk and its numerical
fit. The fitted parameters are: A0.0410.002 mV,
31070.27
108s, t0⫽⫺2.68310791010 s, T
¯
3.41072108s,
6.591071105s1.
FIG. 2. Microscope photograph of a thin section of chalk; the real width of
the picture is 1.2 mm. Large white spots are plankton skeletons calcite;
black spots are pores the one shown by arrow is 84
m in diameterand
partly iron oxide; gray structure is micrite, or cryptocrystals very fine grains
of carbonate, less than 10
m; small white spots are microsparite, fine to
medium size grains about 10–50
mof calcite.
5086 J. Appl. Phys., Vol. 93, No. 9, 1 May 2003 Rabinovitch
et al.
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tal Hamiltonian, nR,nb1and nb2are the numbers of surface
phonons, and initial and final bulk phonons, respectively. Ei
and Efare the initial and the final energies of the three-
phonon system, so that EfEi(
b2
R
b1), where
the
-sdenote the related frequencies. The relaxation time is
obtained from the golden rule formula 1/
being propor-
tional to the transition probabilityusing the explicit expres-
sion for H3Eq. 6.47in Srivastava22, the displacement
field due to the surface modes written in second quantized
notation Eq. 8.26op. cit.22, and integrating over the states
of the initial and final bulk phonons b1 and b2; one obtains
Eq. 8.36op. cit.22
1
R
RT4
3vR
2,3
where Tis the temperature,
is the material density, and vR
as mentioned beforeis the Rayleigh wave velocity. The
proportionality coefficient contains data of bulk phonons and
of the crystallographic orientation and is considered to be
constant for the same material. Note that Tis the local tem-
perature at the crack tip. It is much higher than room tem-
perature. See, e.g., Ref. 25.
In a developing crack, a surface wave propagates along
the crack surfaces.21 Its emitted EMR frequency is the same
as that of the oscillating ions of the crack sides,9
. There-
fore we equate
R.
B. Experimental results and analysis
We have analyzed EMR pulses of chalk, granite, glass
and glass ceramics by fitting them to Eq. 1and deriving
their parameters in particular
and
. Figure 3ashows
the dependence of
on
for glass, glass ceramics and gran-
ite. The slopes on a logarithmic scale are within 10.1,
with R20.96, 0.85 and 0.91, respectively, agreeing with the
theoretical prediction Eq. 3兲兴. For chalk, however, an ‘‘ef-
fective’’ slope of 0.7 is obtained Fig. 3b兲兴. It cannot be
attributed to the low accuracy of the fitting parameters: the
error for
ranges between 2% and seldom30%, which is
quite small in a logarithmic scale, while the error for
does
not exceed a few percent, and is usually only a fraction of a
percent. We would like to attribute this ‘‘change of slope’’to
the spread in temperatures of the small cracks there.
The distribution of (
)1/4, which according to Eq. 3
should be proportional to the absolute temperature, for small
and large crack widths in granite is shown in Figs. 4aand
4b, respectively. We denote (
)1/4 values henceforth as
‘‘temperatures.’ The mean values of the crack temperatures
in relative units are, respectively, 0.67 and 0.65 for small and
large cracks, which are considered to be the same within the
accuracy for temperature values 10%. Similar distributions
for chalk are shown in Figs. 5aand 5b. Here, however,
the mean values are different, being 0.47 for small crack
widths and 0.67 for large ones. As mentioned, the error for
is not more than a few percent, mostly a fraction of a percent,
while for
it ranges between 2% and 30%. Thus the error of
(
)1/4 may be estimated as 10%, yielding temperatures
of 0.470.05 for small cracks and 0.670.07 for large
cracks.
Figure 6 shows the distribution histogramof log(1/
)
where 1/
should be proportional to crack widths, Eq. 2兲兴
FIG. 3. Rise and fall time
as a function of frequency
: the points are the
experimental results of individual pulses, and the line is the power law
fitting result: afor glass triangles, fitting
1.87
0.95 short-dashed
line; for glass ceramics squares, fitting
28.1
1.1;solid linefor
granite (xs), fitting
2.23
0.93 long-dashed line;bfor chalk
circles, fitting
1.87
0.7.
FIG. 4. Frequency counts of temperatures (
)1/4 for cracks in granite: a
short cracks; blong cracks.
5087J. Appl. Phys., Vol. 93, No. 9, 1 May 2003 Rabinovitch
et al.
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for small and large cracks. We denote by small cracks those
cracks which have
values larger than 2107s1e.g.,
Fig. 3b兲兴. By large cracks we denote those with
values
smaller than 2107s1. If one assumes the Rayleigh veloc-
ity in chalk to be26 1200 m/s, then the calculated small crack
widths in chalk by Eq. 2兲兴 range between 52.5 and 130
m.
For large cracks the corresponding range is from 130
mto
1.8 cm.
IV. DISCUSSION
It has been shown that the temperature of dynamically
propagating cracks rises.25 The actual temperature rise de-
pends on crack velocity and on material properties.27 The
spread of experimental points in Fig. 3acan be attributed to
a spread in crack velocities that causes a spread in tempera-
tures. Since we assume that 1/
T4, the dependence on
temperature is very strong. However, cracks in glass and in
glass ceramics which are not porousand in granite the
porosity of which is about 5%lead to almost uniform dis-
tribution of crack temperatures around their mean see Fig.
4, resulting in the almost exact
const relation of Fig.
3a.In chalk, however,
const. The ‘‘temperature distri-
bution’’ histogramsfor small and large cracks are given in
Figs. 5aand 5b. It can be seen that temperatures of small
cracks are significantly lower than those of large cracks.
We assume that this temperature difference in chalk is
due to the interaction between the propagating cracks and the
existing material pores. Chalk is the only material of the four
analyzed that has large porosity of about 40%. The pore
radii in chalk range28 between 0.05 and 100
m. The results
of our measurements see Sec. IIB, together with their ex-
ponential fitting, are given in Fig. 7. Note that although the
range of observed pore sizes was between 2 and 210
m,
their three-dimensional 3Dfitting, being exponential, in-
cludes all pores, also those of lower sizes see Eqs. 5and
6below. The cracks in chalk encounter one or more pores
during their development. Thus crack heat can be partially
spent on raising the temperature of the air inside the pores; in
addition, air from the pore can enter the crack and expand
adiabatically, which process could also lower the latter’s
temperature. Although all cracks in chalk are cooled down in
this way, small sized cracks’temperatures are more strongly
influenced by these processes than large cracks, since the
final temperature depends on the ratio between the pores’
volume and the volume of the crack. The greater this ratio,
the stronger is the temperature decrease. Note that the only
EMR emitting objects are the cracks and the influence of the
pores is only a passive one, namely changing the temperature
of these cracks. While the volume of the interacting pores is
proportional to the area of the crack as will be shown pres-
ently, the crack volume is proportional both to the crack
area and to its aperture; the latter, however, depends on crack
length in the form of a power law29
kx
,4
FIG. 5. Frequency counts of temperatures (
)1/4 for cracks in chalk
columnsand calculated solid lineusing Eq. A19:afor short cracks;
bfor long cracks; crack aperture is assumed to behave as ␧⬃kx
, where x
is the crack half width; the parameters obtained are Tp0.32, Tcr0.9,
0.22, k25
m1
, both for aand b. Parameters found by best fit.
FIG. 6. Frequency counts for log(
1)(
1is proportional to crack widths,
b
vR/
) in chalk.
FIG. 7. Measured pore radii distribution in chalk, fitted to P(r)
a2rexp(ar); best fit obtained for a0.1060.004
m1(R20.98).
5088 J. Appl. Phys., Vol. 93, No. 9, 1 May 2003 Rabinovitch
et al.
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where is the aperture and xis the crack half width mea-
sured cracks had approximately equal widths and lengths.
Crack volume is thus proportional to x2
and small cracks
are cooled more than large ones when intersecting pores.
The distribution of pore radii in the sample volume can
be approximated by a negative exponential
Praexpar.5
However the distribution of pore radii that cross a chosen
plane does not have the same form. Simmons30 showed that
the cracks’ distribution obtained by means of a thin section
needs corrections in order to get a 3D distribution. These
corrections are included here see the Appendix. The distri-
bution of pore radii that cross a chosen plane is thus given by
Pra2rexpar,6
which fits the experimentally measured pore distribution
quite well Fig. 7.
To show the self-consistency of our assumptions, we
have theoretically derived the probability distribution of final
temperatures see the Appendix. The comparison of the de-
rived distribution with the experimental result is carried out
by fitting the following parameters of the former: the power
and the proportionality coefficient kof Eq. 4, and the
initial temperatures of the pore and of the crack, Tpand Tcr .
The best fitting parameters both for small and large cracks
are
0.22, Tp0.32, Tcr0.9, and k25
m1
. The ex-
perimental and the calculated Eq. A19兲兴 distributions of
final temperatures for small and large cracks are shown in
Figs. 5aand 5b. The agreement is adequate.
V. SUMMARY
The rise and fall time
is theoretically shown to be
inversely proportional to the pulse frequency
and to the
fourth degree of temperature T. Experimentally for glass and
glass ceramics, which are not porous, and for granite, whose
porosity is as low as 5%, the
1relation is shown to
hold while for chalk, whose porosity is of the order of 40%,
this relation is not fulfilled. We conjecture that the latter fact
is due to the temperature difference between small and large
cracks: the temperature of cracks drops when encountering
pores since heat emanating at the crack tip is spent on heat-
ing both the crack and the air in the pore; and the tempera-
ture decrease is larger for small cracks. Results show ad-
equate agreement between experimental and calculated
values.
ACKNOWLEDGMENTS
The authors are thankful to E. Shimshilashvili and Pro-
fessor V. Samoilov for their help in conducting microscopic
measurements, and to Professor Thieberger and B. Gold-
baum for useful discussions. This research No. 98/02-01 was
supported by the Israel Science Foundation.
APPENDIX: CALCULATION OF DISTRIBUTION OF
CRACK TEMPERATURES AFTER THEIR
INTERACTION WITH PORES
The temperature of a crack after encountering poresis
assumed to be given by the heat exchange between the air in
the crack ‘‘volume’ and the pores
TTpVcr
VcrVpores TcrTp,A1
where Tcr and Tpare the initial temperatures of the crack and
the pores, and Vcr and Vpores are, respectively, their volumes.
Our assumptions are: 1pores are homogeneously distrib-
uted in the sample and have a spherical shape; 2cracks are
rectangular of dimensions of 2x2x;3the crack aper-
ture depends on the crack width in the form of a power law
Eq. 4兲兴;4all the cracks and all the pores have identical
initial temperatures Tcr and Tp, respectively; 5porosity is
taken as 40% for all samples.
Porosity
is the ratio between the volume of all the
pores to the total sample volume. Let us ascribe to a pore of
volume Va volume Vunit , so that
V/Vunit ; the radius of
this volume is
r
3
.A2
Then the concentration of the pores number of pores per
unit volumein the sample is given by
n1
Vunit
V.A3
Pore radii distribution is taken as see above,
PraexparA4
and the concentration of pores with radii between rand r
dr is
nrdrnPrdr.A5
The number of pores of radius rthat intersect a chosen plane
per unit areais equal to the number of pores of radius r,
whose centers are situated in a layer of thickness 2raround
the plane, per unit area
nr2rnr2rnPr2narexparnPr,
A6
where nis the total number of pores that cross the chosen
plane per unit area
n
0
nrdr2n
a.A7
Thus the probability distribution of radii of pores that cross
the plane is
Pra2rexpar.A8
When a pore of radius r, the center of which is situated
at a distance yfrom the plane, cuts the latter, the area ‘‘oc-
cupied’’by it in the plane is the area that is cut from it by the
volume of radius
Eq. A2兲兴 ascribed to the pore
Sr,y
2y2
r2
2/3y2.A9
5089J. Appl. Phys., Vol. 93, No. 9, 1 May 2003 Rabinovitch
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The average area of the plane that is occupied by a pore of
radius ris
S
¯
r
0
rSr,yPydy
0
r
r2
2/3y2dy
r
r2
1
2/3 1
3
C
r2,
A10
where the probability distribution, P(y), of the pore center
from the plane is assumed to be homogeneous, i.e.,
Pydydy
rA11
and
C
2/31
3.A12
Hence the number of pores of average radius r, which inter-
act with a crack of width 2x,is
Nr4x2
S
¯
r
A13
and the volume of these encountered pores is
VporesrVrNr4
3
r34x2
C
r216rx2
3C.A14
The crack volume Eq. A1兲兴 is
Vcr4x24kx2
A15
and thus the final temperature after crack–pores interaction
is
TTpk
k4r
3Cx
TcrTp
Tpk
kC1r
x
TcrTp.A16
Now we have to calculate the probability distribution of the
final temperatures based on the following results: a. Tis only
a function of zr/x
all other parameters are assumed to be
constant; b. the distribution of pores radii is given by P(r)
Fig. 7and c. the distribution of crack half widths is given
by P1(x) for both short and long cracks Figs. 6aand 6b兲兴.
We first calculate the distribution of z31
PzP
r
x
ixi
Pxi
zP1xi
xi
ia2xi
2
zexpaxi
zP1xix.A17
Now from the relations
zk
C1
TcrT
TTp;dz
dT⫽⫺ k
C1
TcrTp
TTp2A18
we obtain the temperature distribution
PTPzT
dz
dT
a2
k
C1
2TcrT
TTp
TcrTp
TTp2
i
xi
2
exp
axi
k
C1
TcrT
TTp
Pxixi
.
A19
A comparison of Eq. A19with the distribution of tempera-
tures or rather (
)1/4) evaluated from the EMR measure-
ments for both the small and the large cracks is shown in
Fig. 5.
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5090 J. Appl. Phys., Vol. 93, No. 9, 1 May 2003 Rabinovitch
et al.
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... Also it is vulnerable to the high-frequency interference from mechanical and electrical equipment [20]. However, low-frequency electromagnetic wave can propagate a longer distance (around 3.5 km), with a small attenuation [21], and will be less affected by mining equipment. So, it is very important to study the characteristics of low-frequency EMR from coal under dynamic loading, to develop monitoring and early warning technology for coal and rock mines. ...
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Dynamic loads provided by the SHPB test system were applied to coal specimens, and the TEM signals that emerged during coal rupture were recorded by the TMVT system. Experiments on coal-mass blasting rupture in excavating workface were also carried out, and the emerged TEM signal was analyzed. The results indicate that the low-frequency TEM signals were detected close to the coal specimens under high strain dynamic load applied by the SHPB, initially rising sharply and dropping rapidly, followed by a small tailing turbulence. And the field test results obtained during coal blasting process coincided with the results from the SHPB tests. Furthermore, its initial part shaped like a pulse cluster had a more pronounced tail and lasted even longer. And the generation mechanism of the low-frequency TEM effect was analyzed. It suggests that the low-frequency TEM effect of coal during dynamic rupture is contributed by the fractoemission mechanism and the resonance or waveguide effects. Because its wavelength is longer than the higher ones, the low-frequency TEM has a good anti-interference performance. That can expand the scope and performance of the coal-rock dynamic disaster electromagnetic monitoring technique.
... According to Fig. 4 the corresponding crack velocity v cr is 2209 m/s (calculated for c s = 3330 m/s). Now, it was shown [19] that τ is a function of the pulse frequency ω and for glass can be obtained from ...
Article
Our model of electromagnetic radiation (EMR) emanated from fracture implies that EMR amplitude is proportional to crack velocity. Soda lime glass samples were tested under uniaxial tension. Comparison of crack velocity observed by Wallner line analysis and the peak amplitude of EMR signals registered during the test, showed very good correlation, validating this proportionality.
... Here A 0 is the maximum amplitude of the pulse, t 0 is its onset time and T is the time to reach the maximum value of the amplitude; ω is the pulse frequency, τ 1 and τ 2 are the rise and the fall times respectively. It has been shown [16] that the rise and fall times of the same pulse are equal, τ 1 = τ 2 = τ . The model implies that the time elapsed from the pulse onset to its maximum, which is denoted by T = T − t 0 , is proportional to the crack length L [10], ...
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As shown at the Laboratory of Rock Mechanics, electromagnetic radiation (EMR) emitted by propagating fractures provides relatively accurate information on the dimensions of the cracks emitting it. In this paper we demonstrate that this method (i.e.?EMR analysis) can also be advantageously used for obtaining the exact time sequence of double or triple pulses when they appear simultaneously and, hence, the sequence of the relevant cracks. The method is first used to analyse the time sequence of a triple fracture during failure and for a double fracture in relaxation of a glass ceramic sample. The analysis is in good agreement with the actual fractography of the sample. A similar procedure applied to fracture of chalk enabled us to show that most large fractures are, in fact, double, and to find the specific time sequences involved.
Article
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This technical note portrays that one of the main reasons for the lack of progress in the application of the Fracture induced ElectroMagnetic Radiation (FEMR) method for the stress field assessment in underground conditions is the lack of a single measurement methodology/protocol. Three FEMR parameters (frequency range, intensity/sensitivity and activity) are analyzed in relation to micro-crack dimensions and rock elastic properties. Two seismic acoustic parameters (seismic moment and b-factor) are considered from the perspective of FEMR application in underground. It is proposed that the combined use of intensity, activity, b-factor and calculated seismic moment FEMR, together with the proposed FEMR instrument sensitivity and frequency range, be entered into the future FEMR measurement protocol as mandatory parameters for the FEMR instruments design for the successful assessment of the stress state in the vicinity of mine workings.
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Chapter
Originating from the field of geophysics science, electromagnetic emission analysis is a nondestructive measurement technique to monitor crack formation and propagation. Similar to acoustic emission analysis, the electromagnetic emission method is capable of providing real-time information on microscopic failure mechanisms on a qualitative basis. In both cases the reliability of quantitative information still hinges on the lack of a detailed understanding of the correlation between the source mechanism and the measured signal. Therefore, electromagnetic emission analysis is currently considered a method under development and is mostly limited to applications in materials research and has not yet been used for structural health monitoring applications. In this chapter the principle of operation of electromagnetic emission is presented first. Subsequent to that, aspects of the source mechanism, the detection systems and some applications of the method used as in situ technique are introduced. Due to the novelty of the method, some applications are demonstrated to monitor failure of reference materials such as polymers and carbon fibers to elucidate basic relationships between failure mechanisms and the EME phenomenon. At the end of the chapter the established approaches are than extended to applications monitoring failure of fiber reinforced composites.
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Understanding tensile fracture in rocks provides an important key for the interpretation of many problems in structural geology. This book presents a multidisciplinary approach to tensile fracture in rocks (faulting is briefly addressed), starting with an introduction to fracture physics and progressing through tectonofractographic features, characterized both in experimental settings and in geological outcrops. Four examples of sedimentary rocks and two of granites have been chosen to demonstrate the principles and problems in fracture geology. Principles of fracture mechanics and rock mechanics are applied throughout the book, which also explores current understanding about electromagnetic radiation induced by fractures and how such radiation can be used to monitor and predict earthquakes and hazardous collapses in mines. The monograph serves not only as a manual on how to handle specific problems and their solutions in fractual geology but also as a starting point for researchers and graduate students interested in the field of rock fracturing. © Springer-Verlag Berlin Heidelberg 2005. All rights are reserved.
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High time resolution monitoring of radon (=222Rn) in three boreholes, 4, 10 and 53 m deep, along a 0.6 km transect is carried out in massive granite in southern Israel. Three components of variation occur in the measured signal (MS) - seasonal radon (SR - periodic), multiday (MD), and daily radon (DR - periodic). Temporal variation of the components suggests an association between the overall level of the long-term variation and the amplitude of the daily variation. The daily mean level of radon and the daily standard deviation vary periodically throughout the year. Time offsets occur among time series of the MS and were investigated also for the MD and DR components, using consecutive 20-day intervals spanning +900 days. The resulting time series show that systematic time offsets occur, whereby the radon signal always occurs first at the easternmost site. The MD shows a gradually varying lag of 0-12 h, and the DR a stable 1-3 h lag. Spectral analysis shows that diurnal (24-h) and semidiurnal (12-h) periodic components characterize the DR. The amplitudes of these components exhibit regular temporal variation having a seasonal pattern. The ratios of co-occurring amplitudes of these components define a linear pattern indicating a fundamental statistical property in the frequency domain of the radon time series. The results indicate that unrecognized dynamic processes are driving the radon signal in the subsurface regime of the pluton, suggesting new prospects for radon behavior in the frame of interacting geodynamic (tectonic?) and Earth-Sun system related processes.
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We have accurately measured and parametrized individual pulses of electromagnetic radiation (EMR) obtained during a fracture experiment. Analysis of the parameters shows that they follow a log-normal distribution. Results indicate no dependence between fracture lengths and widths.
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We have carefully analysed the amplitude-frequency relation of the electromagnetic radiation pulses emitted during the fracture of chalk, granite and glass ceramic under compression. The results show the amplitudes to be inversely proportional to the frequencies in all cases.
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A study has been made of the electromagnetic radiation (EMR) emitted during triaxial compression of granite. Changes in EMR activity with loading are shown to be strongly correlated with changes in Poisson's ratio but not with Young's modulus.
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Frid, V., Bahat, D., Goldbaum, J., Rabinovitch, A. 2000. Experimental and theoretical investigations of electromagnetic radiation induced by rock fracture. Isr. J. Earth Sci. 49: 9-19. There is a general agreement in the literature that the technique of measuring electro- magnetic radiation (EMR) emitted from cracked rock is a good candidate for forecast- ing of earthquakes. Our immediate objective in pursuing this goal is to correlate EMR with crack dimensions in micro-scales (mm-cm), coupling it with the understanding of atomic-scale phenomena for coherently understanding the EMR process. We review some of the results obtained in this laboratory. They include the isolation, both experimentally and theoretically, of an individual EMR pulse. Individual EMR pulse parameters are correlated with crack dimensions: the time from pulse origin up to its maximum is proportional to the crack length, and the frequency of the EMR pulse relates to the crack width. Individual EMR pulses are classified both according to their length and according to their location on the stress-strain curve. We find that the key elastic parameter for EMR characterization during triaxial compression is the Poisson ratio: the lower the Poisson ratio, the higher the EMR activity. Amplitudes of EMR and their changes with loading are shown to be independent of crack mode (tensile vs. shear), they are only dependent on the entire crack area. In order to experimentally overcome load limitations we introduce a new sample shape, the truncated cone, that fails more readily than standard cylindrical samples.
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Elements of crystal symmetry: Direct lattice Reciprocal lattice Brillouin zone Crystal structure Point groups Space groups Symmetry of the Brillouin zone Jones zone Surface Brillouin zone Matrix representations of point groups. Lattice dynamics in harmonic approximation - semiclassical treatment: Introduction Lattice dynamics of a linear chain Lattice dynamics of three-dimensional crystals - phenomenological models Density of normal modes Numerical calculation of g(w) Lattice heat capacity. Lattice dynamics in the harmonic approximation - ab initio treatment: Introduction The frozen-phonon approach The linear response approach The planar force constant method. Anharmonicity: Introduction Hamiltonian of a general three-dimensional crystal Effect of anharmonicity on phonon states Effects of the selection rules on three-phonon processes Hamiltonian of an anharmonic elastic continuum Evaluation of three-phonon scattering strengths The quasi-harmonic approximation and Grueneisen's constant. Theory of lattice thermal conductivity: Introduction Relaxation-time methods Gree-Kubo linear response theory Second sound and Poiseuille flow of phonons. Phonon scattering in solids: Boundary scattering Scattering by static imperfections Phonon scattering in alloys Anharmonic scattering Phonon-electron scattering in doped semiconductors Phonon scattering due to magnetic impurities in semiconductors Phonon scattering from tunnelling states of impurities Phonon-photon interaction. Analysis of phonon relaxation and thermal conductivity results: Anharmonic decay of phonons Lattice thermal conductivity of undoped semiconductors and insulators Non-metallic crystals with high thermal conductivity Thermal conductivity of complex crystals Low-temperature thermal conductivity of doped semiconductors. Phonons in low dimensional solids: Introduction Surface vibrational modes Attenuation of surface phonons Phonons in superlattices Thermal conductivity of superlattices. Phonons in impure and mixed crystals: Introduction Localised vibrational modes in semiconductors Experimental studies of long-wavelength optical phonons in mixed crystals Theoretical models for long-wavelength optical phonons in mixed crystals Phonon conductivity of mixed crystals. Phonons in quasi-crystalline and amorphous solids: Introduction Phonons in quasi-crystals Structure and vibrational excitations of amorphous solids Vibrational properties of amorphous solids Low-temperature properties of amorphous solids. Phonon spectroscopy: Introduction Heat pulse technique Superconducting tunnel junction technique Optical techniques Phonons from Landau levels in 2DEG Phonon focusing and imaging Frequency crossing phonon spectroscopy Phonon echoes. Phonons in liquid helium: Introduction Dispersion curve and elementary excitations Specific heat Interactions between the excitations Kapitza resistance Quantum evaporation. Appendices: Density functional formalism The pseudopotential method Evaluation of integrals in sections 6.4.1.4 Negative-definitenss of the phonon off-diagonal operator ^D*L. References. Index.
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A general formula for the attenuation of a surface wave by interaction with thermal phonons at low temperatures is given and compared with the results of Maradudin & Mills (1968) for a simplified model. It is argued that the attenuation coefficient will often be qualitatively similar to that of the slow transverse wave propagating in the same direction. Approximations to our integral expression for the attenuation coefficient are discussed and numerical calculations for quartz described in detail. Good agreement with the experimental data of Salzmann, Plieninger & Dransfeld (1968) is obtained.
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The temperature rise at the tip of fast-moving cracks in polymethyl-methacrylate (PMMA) has been determined from the results of two experiments. In the first, thermocouples and a temperature sensitive liquid crystal film were used to measure the total heat evolved at points along the path of the crack. The values show a continuous increase with crack speed, the figure at 650 m s-1 reaching a value of 2.3 × 103 J m-2. In the second experiment an infrared detector monitored the radiation emitted from the heated zone at the crack tip. The results combined to give a temperature rise of approximately 500 K throughout the velocity range studied (200-650 m s-1). As the rise is constant, the increase in the quantity of heat evolved implies that the plastic deformation at the tip becomes more extensive at higher crack speeds. Some preliminary experiments on polystyrene (PS) show that a temperature rise of about 400 K occurs with this polymer, but, as the heat evolution is much smaller than for PMMA, accurate measurement is difficult. The effect of such large temperature rises on the mechanism of fracture in these materials and, in particular, the possibility of significant thermal decomposition within the heated region are considered.
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In a first attempt to understand the nature of observed electromagnetic emissions from large ice sheets and glaciers during fracture, it was hypothesized that internal microcracking played a role in causing this phenomenon. Laboratory-based experiments were conducted in search of evidence to support this view. It was determined that signals could be correlated with individual cracks within the bulk of a test sample. Three types of signal were observed: exponentially decaying signals with amplitudes under 10 m V and durations between 0.15 and 1.0 ms were produced by grain-boundary type cracks (i.e. small stable through-thickness or partial-through-thickness cracks of the order of grain diameter in length); axial splits (i.e. larger planar cracks usually running the length of the sample) caused similarly shaped signals with larger amplitudes (tens to hundreds of millivolts) and longer durations (1–10 ms); the third signal type exhibited a sinusoidally decaying form and is attributed to the complex interaction of multiple cracks within the ice. While experimental evidence strongly suggests a correlation between cracking and signal emission, more work must be done to characterize the effects of crack orientation, location and size on the polarity and magnitude of observed signals.