A Comparison of Short-Circuited Streaming
Potentials in Westerly Granite From Changes in
the Rock's Volume, Shape, Saturation, and
Fracture Under Unconfined Uniaxial
Compression
by
Elizabeth Annah Jensen
Submitted to the Department of Earth, Atmosphere, and Planetary
Science
in partial fulfillment of the requirements for the degree of
MASSACHUSETTS INSTI U E
Master of Science in Geosy stems
at the
TECHNOLOG1999
MASSACHUSETTS INSTITUTE OF TECHNOLOG x
May 1999
LW49-w
@ Massachusetts Institute of Technology 1999. All rights reserved.
Author
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Department of Earth, Atmosphere, and Planetary Science
April 23, 1999
trtified by
I
Frank Dale Morgan
Professor
Thesis Supervisor
rtified by...................................................
Chris J. Marone
Professor
Thesis Supervisor
A ccepted by ......................................................
Ronald G. Prinn
Department Head
A Comparison of Short-Circuited Streaming Potentials in
Westerly Granite From Changes in the Rock's Volume,
Shape, Saturation, and Fracture Under Unconfined
Uniaxial Compression
by
Elizabeth Annah Jensen
Submitted to the Department of Earth, Atmosphere, and Planetary Science
on April 23, 1999, in partial fulfillment of the
requirements for the degree of
Master of Science in Geosystems
Abstract
An experiment was designed to gain some insight into the phenomena of electrical
charge in the uniaxially stressed environment of a sample of Westerly granite. Varying properties of size, shape, saturation, and stress rate of the Westerly granite, a
tentative set of physical relationships were measured. For instance, there is a strong
suggestion that the amount of acoustic energy released when the sample fractures is
proportionately related to the amount of charge that moves into or out of the sample,
the net charge, over the period of the experiment. Increasing the concentration of
the saturating solution increased the amount of charge that moved into or out of the
sample. With all the samples that were dry, more charge move in than out over the
period of the experiment. The few samples that were alike in every way before and
after they fractured had a difference in charge and acoustic energy by a magnitude
of their measured net charge and acoustic energy.
Thesis Supervisor: Frank Dale Morgan
Title: Professor
Thesis Supervisor: Chris J. Marone
Title: Professor
Acknowledgments
I would like to thank:
Deborah Jensen, Edward Jensen, and Patricia Chapela for their unparalleled emotional, financial, and editing support;
Zhenya Zhu for his careful and patient instruction in the experimental setup procedure;
Dale Morgan for strategic guidance and research support;
Chris Marone for allowing me to use (and occasionally break) all the equipment I
needed in his lab;
Steve Karner and Karen Mair for their assistance in helping me to avoid damage
to the biax and in processing load data;
Karyn Green, Toby Kessler, and Robert Fleming for technical support and tracking down obscure references;
Kate Lehetola and Mary Krasovec for helping me keep a sane mind in a sound
body;
Youshun Sun for all the support and guidance a former Geosystems student could
give;
Philip Reppert for filling in the gaps of my knowledge while I was writing my
thesis;
and most especially, Rebecca Saltzer, for giving me both good advice and information about where to find good advice on the Geosystems program elements.
Biographical Note
Education
Massachusetts Institute of Technology 1998-1999 SM Geosystems
Texas A&M University 1993-1998 BS Geophysics
Texas A&M University Honors
F. Vilas, E. A. Jensen, and L. A. McFadden. Extracting Spectral Information about
253 Mathilde Using the NEAR Photometry. Icarus, 129(2):440+, 1997.
F. Vilas, E. A. Jensen, D. L. Domingue, L. A. McFadden, and C. R. Coombs. An
Unusual Photometric Signature Detected on Lunar Complex Crater Rims at the South
Pole. In Lunar and PlanetaryScience XXIX, Lunar and Planetary Institute, Houston
(CD-ROM).
E. A. Jensen.
Satellite Observations of Oceanic Shelf-Slope Exchange.
Graduate Research Fellows Thesis, Texas A&M University, 1997.
University
Contents
1 Introduction
2
6
1.1
Background Description of Sample Material
1.2
Characteristics of Westerly Granite in Electrolytic Solutions ....
1.3
Compression of Core Samples ...................
. .............
6
.
...
Methods and Materials
8
10
17
2.1
Sample Selection and Preparation . ..............
2.2
Collection of Data ..............
.
. . . . .
.
........
..
17
20
3 Results
22
4
29
5
Discussion
4.1
Qualitative Differentiation ...................
4.2
Other Electrical Sources . ..................
4.3
The Piezoelectric Problem ...................
.....
......
.....
Conclusions
5.1
Future Investigations ...................
32
32
33
35
........
36
A Calculation of the Resistance of Saturated Westerly Granite
37
B Sample Preparation
39
C Streaming Potentials
41
D Experiment Data
43
Chapter 1
Introduction
Before the Ms (surface wave magnitude) 7.1 Loma Prieta, CA earthquake in 1989,
Fraser-Smith, Bernardi, McGill, Ladd, Helliwell, and Villard (1990) [6] recorded several anomalous magnetic (EM) signals. Peaks were detected on September 16-17,
followed by a rise in background noise on October 6 and an EM spike on October 17
approximately 3 hours before the quake. The regional stress prior to the earthquake
changed by less than 1 pbar[18].
Park, Johnston, Madden, Morgan, and Morri-
son (1993) review the history of looking for a possible link between generation of
anomalous EM signals and a subsequent earthquake. The study of how electricity
is generated and transfered in a rock is required. The objective of this research is
to study the generation of electrical charge in Westerly granite before and during
uniaxial fracture.
1.1
Background Description of Sample Material
Granite rocks are igneous in origin, comprising of interconnected crystals of quartz,
feldspar, mica and other minerals of various concentrations. Because granite is formed
in the crust, the uplifting and release of pressure compounded with exposure to the
atmosphere causes the rock to crack, with cracks even developing between the crystals
themselves (Figure 1-1). The core samples used in this study were Westerly granite,
which comes from Westerly, Rhode Island. It is composed of 27.5% quartz, 35.4%
Figure 1-1: Wong, Fredrich, and Gwanmesia (1989) show a view of what the crack
surface areas look like. This is also typical in that the cracks often occur on grain
boundaries.
microcline, 31.4% plagioclase (with 17% anorthite), and 4.9% biotite [1]. The distribution of minerals in Westerly granite is virtually homogenous, which makes it a
popular specimen for rock mechanics experiments.
There is also extensive information about the microstructure of Westerly granite.
The cracks between the grains occupy about 0.9% of the space. Labeled as a low
porosity rock, Westerly granite also does not have much connectivity between the
cracks, thus making it a low permeability rock as well [1].
Wong, Fredrich, and
Gwanmesia (1989) [21] found that Westerly granite has crack apertures that vary
from 0.7 to 0.002 micrometers in width. The crack surface area per volume (Sv)
was measured to be approximately 7.98 mm 2 /mm 3 . The distribution of cracks in
this range corresponded to a fractal dimension of 2.84 with the smallest apertures
occurring with the greatest frequency. The mean crack aperture is 0.015 micrometers.
1.2
Characteristics of Westerly Granite in Electrolytic Solutions
When Westerly granite is saturated, the connected pore space is filled with fluid.
When the fluid is an aqueous electrolytic solution, some of the ions adsorb to the
grain surfaces around the cracks and some of the ions on the surfaces of the cracks
dissolve into the solution. Because most of the molecules that make up granite consist
of SiO 2 1
Revil and Glover (1997) [19] argue that there are five chemical species that occur
on the surface of Si0 2 mineral lattices (where > refers to the mineral lattice): >SiOH,
> SiO-, > SiOH-, and >SiONa (in the presence of high pH values).
The adsorbtion of the ions make a net negative electrical charge on the grain
surfaces around the cracks. Different solutions react to the static electrical charge in
different ways.
Figure 1-2 of Morgan, Williams, and Madden (1989) [14] illustrates the adaptation
of the current view of how ionic charge distribution on the surface of the cracks with
respect to SiO2 surfaces depending on the nature of the aqueous soltion with respect
to the composition of the rock. The negative electrical charge on the surface of the
rock is neutralized by positive ions in the electrolytic saturating solution. Because
the ions have diameters, only a limited number can reach the charged surface. As
a result, it takes more than one layer in most cases for the negative potential to
be neutralized. The negative charge is at first linearly reduced by several layers of
positive ions, then it decays exponentially with distance from the Inner Helmholtz
1
It is observed that the solution used to saturate Westerly granite changes in composition after
saturation. The solution conductivity measurements were made before and after the Westerly was
saturated with tap water were different; the conductivity decreased from 200 pS to 8 pS. Other ions
are probably involved in the development of the double layer [15]:
1. quartz is essentially pure SiO2
2. microcline KA1Si 3 08
3. plagioclase (17% CaA12 Si 2 08, 83% is NaAISi 3 0s)
4. biotite K 2 (Mg,Fe)3 A1Si 3Olo(OH,O,F)2
$
S
7
O(STANCE
•
7<
Figure 1-2: "S" corresponds to the slipping plane. The fixed layer where the electrical
potential decreases linearly is inside the slipping plane. The diffuse layer where the
electrical potential decreases exponentially is outside the slipping plane. Morgan,
Williams, and Madden (1989).
Layer. The plane where this behavior changes corresponds to the Outer Helmholtz
Layer. Within a short distance outside of the Outer Helmholtz Layer, ions can move.
This is labeled the slipping plane. The region outside of the slipping plane where
potential electrical energy is still decaying is labeled the diffuse layer. The region
inside the slipping plane is labeled the fixed layer. The zeta potential is defined as
the electrical potential that exists at the slipping plane.
This situation becomes a little more complex as the smallest crack apertures of
.002 micrometers occur more frequently. The diffuse layer in some solutions is greater
than half this value. In this situation, the double layer will overlap in a manner
described by Hunter [8]. The repulsion between the double layers on either side of
the crack creates an osmotic pressure. In a confining pressure situation, this adds to
the pore pressure of the system.
Movement of ions outside of the slipping plane has been studied for several decades.
When a pressure is applied, a physical current displaces ions in the diffuse layer. This
is called a streaming or convective electrical current. The physical flow of ions which
had kept the surface charge neutral begins to concentrate in some areas and dilute in
others. This causes a current of ions, labeled the conduction current, to be induced
in the opposite direction.
When a steady state is achieved, ions physically flow
in both directions. An electrical potential field forms that is labeled the streaming
potential. This is quantitatively described by the Helmholtz-Shmoluchowski equation
(derivation from streaming current in a capillary shown in (Appendix D):
A(P)
A(V)
c
aov
P=physical pressure
V=voltage in the streaming potential
( =zeta potential
E =dielectic constant
a =conductivity of the electrolytic solution
v =viscosity of the liquid
1.3
Compression of Core Samples
As the rock sample is compressed uniaxially, those cracks that are easiest to close are
closed. As the compression continues to increase past 50% of the fracture strength
of the rock, new cracks open and old cracks dilate to wider apertures [1] (Figure
1-3). The dilating effect tends to follow a particular orientation that develops into
a fracture in the rock [12] (Figure 1-4). Scholz [20] (Figure 1-5) explained that the
fracture mode for unconfined samples is an elongated fracture in the direction of
compression extending through the sample. Jaegar [10] (Figure 1-6) showed that
the stronger platens above and below the sample affect how the uniaxial pressure is
distributed in the sample. This distribution tends to follow two cones with their bases
on the platens, and their tips touching in the middle of the sample. It is not surprising
that the acoustic activity in Lockner's samples was first localized in the middle of the
sample. Furthermore, the rupturing highlighted the side of the pressure cone as the
sample approached failure. This is probably due to the high pressure gradient on
the side of the cones in unconfined samples. The inside of the cone has the pressure
load, while the outside experiences only atmospheric pressure. The samples in this
r
i
II
Cracks in the sample
are closing
Axial
>
Cracks in
the sample
are dialating
Tra nsverse
'
1
i
,I
,
Percent of fracture
IXII^IIII
w
100O
50
stress
Figure 1-3: Brace and Orange (1968) measured the changes in resistivity of Westerly
granite under uniaxial compression. The results they found was an increase in resistivity followed by a decrease in resistivity. This was due to the closing and widening
of cracks in the process of stressing the rock.
experiment exhibited behavior that was either conical or a combination of conical and
elongated.
__:___ _;. ~Yi~i~_i
....................................................................
Perpendicular
to the plane
of fracture
.
\ ''" i
L
I
L
..........
""
24
~r
•
4
i
i
Looking at
plane of
fracture
face on
b
d
Figure 1-4: Lockner, Byerlee, Kuksenko, Ponomarev, and Sidorin (1991) measured
acoustic emissions from uniaxially compressed Westerly granite sequentially over time.
At first the acoustic waves are distributed through out the sample. Then they begin
to concentrate on the plane of the developing fracture.
12
il
Figure 1-5: Scholtz (1990) illustrates three modes of fracturing seen in rocks. Arrows
indicate the direction of stress. (a) tensile fracturing. (b) triaxial fracturing. (c)
uniaxial fracturing.
Figure 1-6: Jaegar and Cook (1969) illustrate how pressure is distributed in a rock
under uniaxial compression. A saddle point occurs in the middle where pressure
increases toward the platens and decreases on all other sides.
Chapter 2
Methods and Materials
2.1
Sample Selection and Preparation
All samples except one were cored from the same block of Westerly granite to ensure
uniformity of chemical makeup and crystal distribution in the samples. Core samples
were obtained from the Westerly granite by using a drill press, then slicing the column
to various lengths using saws. Then the core samples were polished on the ends with
a diamond drill while squeezing on the sides of the sample with a conical base to
ensure that the ends were also parallel. The samples varied in size and ranged from
1870 mm 3 to 37800 mm 3 .
The samples were subsequently wrapped with an insulated wire, size #18 19/30,
attached to the lengthwise surface of the core by conductive glue, DuPont conductor
composition 4929N, submitted to different atmospheric pressures and humidities, and
soaked in different solutions before being submitted to uniaxial stress. The acoustic
transducer marked the time range for recording the electrical signals produced during
fracture of the core samples.
Figure 2-1 shows how the wires were placed onto the samples using 2 different
methods. The experimental setup is drawn out in Figure 2-2 in terms of what the
electrical circuit of the experiment consists of.
Sample
2~
'p
Mlethod I
This was the first method used for
wrapping the wires around the
sample. Conductive glue was
brushed around the wires.
Wires
S00-
lmll
)
Method 2
This was the second method
that was used to wrap the wires
amund the sample. Conductive
glue was rubbed on to the
sample around the wires.
Wres
Figure 2-1: Methods used for wrapping wires around the samples
Current
to wund
Impedance>> 1 mega-ohm
Figure 2-2: Experimental setup using GageScope as an Ammeter
2.2
Collection of Data
The electrical signals resulting from fracture of the samples were recorded with a
GageScope, an IBM PC-software based oscilloscope. The current passed through the
wire wrapped around each sample with a 1 mega-ohm impedance, which has to be less
than the impedance of saturated Westerly granite (Appendix A) [2] for the Gagescope
to work as an ammeter. The signal was recorded in terms of volts with a sample rate
of 200 kilohertz. The system accepted an external trigger source from an acoustic
transducer which measures pressure waves in terms of electrical volts. 5 milliseconds of
time requires 30 kilobytes of memory. This sort of precision is necessary to get enough
points into the electrical waves produced by the sample at the amplitudes before and
after fracture. Maintaining this precision for the duration of the experiment would
require 24.3 megabytes of memeory for 8.5 minutes. At least 4 files were produced
for each run. The acoustic transducer signal was processed through an amplifier to
increase the voltage of the signal to positive or negative 5 volts. The voltage was
recorded with the oscilloscope both before and after the trigger signal of positive 5
volts, so 512 points were recorded for each sample both before and after the signal
making a total of 1024 points.
The core samples were fractured using a biaxial system produced by Downhold
Piston
Plastic Film
Top Probe
Middle Probe
Bottom Probe
...
.
Sample
..
.....................
Plastic Film
Acoustic Transducer
PlasticPlastic FilmFIm
Figure 2-3: This is the experimental setup used in fracturing the samples of Westerly
granite. The plastic film was used to isolate the sample from the ground. Each of
the probes have 1 MQ impedance.
Systems, Inc. following plans drawn up by E. Sholtz in 1993.
The loadcell and
LVDT recordings of displacement over time were recorded by Superscope II Macintosh
program with the sampling rate at 1 hertz. The samples were lined up with a manual
laser placed in the loadcell to ensure radial symmetry of the samples before they were
fractured . Plastic film was placed above steel blocks on the sample and below the
sample itself. The uniaxial system grounded the probes that connected the wires on
the sample to the computer. The acoustic transducer produced electrical disturbances
from pressure waves interacting with its bladder. The plastic film acted as an electrical
insultator for the sample by preventing the electrical energy from passing straight to
the ground rather than through the 1 mega-ohm probe (Figure 2-3).
Chapter 3
Results
An integration to calculate the number coulombs which had moved through the acoustic transducer and the probes in any particular direction was used 1. The' Acoustic
versus Net Charge (Figure 3-1) shows a rough increasing relationship between the
acoustic total charge in coulombs and the net charge of coulombs flowing through the
Westerly granite. This plot uses all the experimental data that has been collected by
Morgan and Zhu (1998) and Jensen (this report). The increasing relationship is also
in samples that had a net influx of positive electrical charge. An influx of positive
electrical charge is negative, and these samples were not plotted in Figure 3-1.
When plotting the Net Acoustic energy versus the Volume of all the different
samples (Figure 3-2). There are three ranges of acoustic energy that appear. The
topmost range, Region 1, exists above 8X10 -
1
Coulombs.
Region 2 ranges from
1The data collected from the probes and the acoustic energy were received in terms of volts. To
find the current at each point in time, the values were divided by the 1 mega-ohm resistance. For
some, a smoothing function was applied. This took the form of a running average of 10 points. For
these, the values were buffered on the ends by 10 points. In order to compare how much the values
changed in the integration to total up the the moving charge, an average was taken of the beginning
of each spectra. The average used the first 200 points for the Poland Spring data and the first 100
for the data collected by Morgan and Zhu (1998). This average was then used to set the zero level.
The caculation of how much charge had moved added the electrical current multiplied by the change
in time to the previous calculation of electrical current by change in time. Then the value from this
calculation for each probe were summed together. This was the net flow of charge in the sample.
If it was negative, in the case of all the dry samples, then this meant that more positive electrical
charge had flowed into the sample. If it was positive, more positive electrical charge had flowed out
of the sample. The value for the Relative Acoustic Energy was calculated as the root-mean-square
of the acoustic signal.
10-'
108
"
U
E
-"
oa 0 10'
1 0 -14
1 0 -' 3
0-
2
1 0-"
10- 0
Acoustic Relative Energy
Figure 3-1: Net charge shows an increase with respect to the acoustic relative energy
1.4E-10 -r
1.2E-10
IE-10
U
8E-11
6E-11
1A
4E-1 1
2E-11
I
2
0.OOE+00
2.00E+04
4.00E+04
6.00E+04
8.00E+04
1.00E+05
U
1.20E+05
1.40E+05
1.60E+05
Yolume (mm^3)
Figure 3-2: The acoustic relative energy is unrelated to volume. With respect to
Figure 3-1, the net charge is unrelated to volume.
5X10 - 12 and 2X10 - 11 Coulombs. Region 3 lies below. This strongly suggests that
there is no relationship between the volume of the sample and the relative acoustic
energy that the sample produces when it fractures. This in turn argues that there is
no relationship between volume and the net electrical charge flux.
In Region 1, there are only three points. Two are 25mm diameter by 50.8mm
length dry samples which were broken at a loading rate of 100 um/sec. The third is
a 25mm diameter by 50.8mm length sample that was saturated in 200 uS tap water
and broken at a loading rate of 100 um/sec. The most remarkable point to make
in Table 3.1 is that the saturated sample produced as much as a magnitude more
coulombs of net charge than the dry samples.
To get an idea as to how much variation there is in samples that are identical
experiments, three sets of data were compared. The samples used in the data set
include:
Table 3.1: The three highest acoustic
Acoustic Relative Energy Charge (coulombs)
1.28E-10
-2.05E-09
1.04E-10
-1.38E-09
1.04E-10
1.13E-08
relative energy samples
sample style
dry
dry
wet
1. The dry samples from Table 3.1
2. Two 25mm diameter by 50.8mm length Region 2 samples that were saturated
with 200pS tap water and broken at a 100 pm/sec loading rate
3. Two 25mm diameter by 76.2mm length Region 3 samples that were saturated
with 225pS Poland Springs water and broken at a 1 pm/sec loading rate
It is important to note that the experiment was identical for these samples except
in the way that they fractured. The Fracture Variation plot (Figure 3-3) demonstrates
that a relationship may exist between the Acoustic energy produced during rupture
and the fracture type. Six samples were compared. Four Poland Springs saturated
samples broken at 1 um/sec and two tap water samples broken at 100 um/sec were
plotted against each other depending on which fracture type they followed (Figure
3-4). There are two main fracture types with some variations. The first fracture type
is a fault extending from upper portion of one side of the sample to the lower portion
of the other side. The second fracture type is a combination of the first type but
with the development of a second fault on the other side that propagates through the
sample at least part way. An example of other fracture types is pictured as well, but
other fracture types did not occur in the samples used in the plot. For the samples
which were broken at the 1 pm/sec loading rate, a strong relationship is suggested
between the acoustic energy and the way the sample fracture. At the 100pm/sec
loading rate, this trend does not appear to be present.
In Region 2, there are two samples which are identical in every way except in the
conductivity of the solutions that they were saturated in. Shown in the Conductivity
versus Net Charge plot (figure 3-5), the 450 and 820 pS samples are 25mm diameter
by 50.8mm length, broken at the same 100 pm/sec loading rate, and produced similar
1
10
I
S100 um/sec
10-* [
*
fracture 1-1urn/sec
*
fracture 2-1um/sec
100 um/sec
U.
1o10
10-11
i
10
-
i
10-1
1 014
1
0-12
I
1 0-11
1 0-1
Acoustic Relative Energy
Figure 3-3: Fracture versus Stress Rate (Positive Charge)
Fracture Type 1
Fracture Type 2
Other types of
fractures
Figure 3-4: These are the most common ways that the Westerly granite samples
fractured.
2.00e-9
1.00e-9
2j -1.OOe-9
E
a-
SO.OOe+O
Wires Method 1
using electrodes
-1.0e-9
'
I 02
103
Solution Conductivity (uS)
Figure 3-5: Solution Conductivity versus Charge and Electrode Placement
amount of Net Charge. They indicate a general increasing trend in the Net Charge
produced and the conductivity of the saturating solution.
More variation may be in seen in how the electrical energy is drawn off of the
sample. The conductivity samples varied somewhat in this respect. The 450 and 820
pS saturated samples had electrodes placed as seen in Figure 3-6(a). The Conductivity versus Net Charge plot also shows the 590 AS saturated sample. The electrodes
on this sample were place with 1 vertical as used in the 450 and 820 AS saturated
samples and with 2 electrodes placed around the length of the sample which is somewhat similar to Method 1 (Figure 3-6b). Although the 590 /S saturated sample lines
up with the 450 and 820 AS saturated samples, it appears that the electrodes in this
formation did not collect as much electrical charge. The 570 S saturated sample had
electrodes placed on it almost identical to the wires in Method 1. The electrodes in
(b)
(a)
C
>E3
EI1
El
E(
/ El
Morgan and Zhu (1998) placed
electrodes on the Westerly
granite samples in this way
Morgan and Zhu (1998) placed
electrodes on the Westerly
granite sample in this way
for the sample saturated in the
590 microsiemens solution.
for the samples saturated in
450 and 820 microsiemens
solutions.
Figure 3-6: Variations in electrode placement
this formation detected even less charge (Figure 3-5). Method 2 for placing the wires
onto the samples was meant to take advantage of the geometry of having a conducting loop wrapping around the sample, as well as cover much more of the sample with
conducting wires to collect any local charges. The raw data plot from sample 101
(following the appendicies) shows that the current was moving in opposite directions
through wires that were next to each other on the sample.
Chapter 4
Discussion
The phenomenon of piezoelectricity in a quartz crystal is the release of electrical energy when the crystal is compressed. There is 25.7% quartz in a Westerly granite; this
is a source of some electricity. Quartz is a very hard mineral, 7 on the hardness scale.
For this reason, many cracks in the Westerly granite develop between the quartz
grains and the plagioclase grains and along the cleavage planes of the plagioclase. As
the granite is loaded, these cracks are among those closed. As the faulting begins, it
will tend to go around the quartz crystals; however, when a faulting plane propogates,
enough inertia is built up that it will pass through the crystals and break them. The
dangling bonds on the new cracks become a new electrical field for adsorbing ions.
Electricity that is produced by breaking quartz minerals or through piezoelectricity [16][17] has two ways of passing through the rock to the wires surrounding it:
through the grains themselves, and through any sort of fluid in the cracks. With
the impedance of dry Westerly being greater than 1 mega-ohm (Appendix A), the
preferred vector for the propogation of electrical energy is through any fluid in the
cracks. Since the percentage of quartz in Westerly granite is constant, a voltage increase in the maximum amplitude of the amperes may be initially detected between
a dry granite and a granite that is saturated with a conductive solution. However, as
the conductance of the solution increases, the finite energy source of the electricity
prevents it from contributing more than a constant value to the voltage readings.
Morgan and Zhu (1998) broke four samples that were 25mm diameter by 50.8mm
i/
I
Figure 4-1: Matijevic (1974) illustrates the effect of increasing the concentration of
the aqueous solution on the zeta potential. cl and c2 are solutions with increasing
molarities. x is the distance from the surface wall.
in length. Electrodes were glued onto the sample in the manner shown in Figure
3-6. When the results are plotted against the conductivity of the saturating solution,
there is an increasing trend that becomes visible (Figure 3-5).
One aspect of the behavior of the system described by the Helmholtz-Shmoluchowski
equation argues that the greater the molarity of a solution, the less the amperage of
the streaming current should be.
This is because the greater conductivity of the
solution decreases the amount of charge in the diffuse layer by concentrating it in
the fixed layer which decreases the zeta potential [8] (Figure 4-1). The streaming
current depends on the zeta potential through a logarithmic relationship. The other
variables which effect the streaming potential, geometry, conductivity of the solution,
and viscosity, are relatively constant in comparison to the zeta potential.
If the piezoelectric effect were at work, the electrical relationship should be a flat
line; if the streaming current effect were taking place, the line should be decreasing.
Because this is not the behavior observed in Figure 3-5, neither of these phenomena
are producing the increasing electricity with concentration.
4.1
Qualitative Differentiation
Three types of fractures were observed (Figure 3-4). The first type is a fracture
extending through the sample to the other side. The second type was characterized
by curved structures that did not always pass through the center of the sample. The
third type consisted of the loading surface of the sample breaking through as if two
type one fractures on either side met up at the top of the sample. There appears to
be different acoustic energy generated with the different fracture types (Figure 3-3).
4.2
Other Electrical Sources
Another electrical potential field exists at the contact points between the wires and
the metal in the conductive glue. This probably does produce some electricity. The
purpose of the glass experiment was to determine what the magnitude of this would
be. An amorphous glass sample cored from a block of Corning glass was broken
using the setup described for the Poland Springs saturated sample. The glass sample
of dimensions (19mm by 54mm) was loaded to a significantly higher pressure than
the sample of Westerly granite of the same dimensions was because it took twice as
long for the sample to rupture. When it broke, it produced a popping sound about
four times before shattering. Table 4.1 shows that some electrical energy was detected
after the sample ruptured. The postive results was surprising. Because of the positive
detection of electrical energy, samples of the same magnitude of electrical energy are
suspect.
Morgan and Zhu's (1998) data for the conductivity experiments confirms the concept that the measured electrical signal is not due to the wires alone because electrodes
were place on the sample instead of glued wires. The signal that he measured could
not have been produced by the electrical potential field between the glue and the
wires because neither were present.
Much of Morgan and Zhu's (1998) data which measured the effects of loading rates
and piezoelectric trends used wires rather than electrodes placed on the sample in the
manner shown in the description of sample zhu. In order to be able to use Morgan
and Zhu's (1998) data in this thesis for comparing amplitudes and frequencies, it was
necessary to use the same placement of wires on the sample. Some minor variations
were used as shown in Figure 2-1. The geometry is similar to zhu's, yet more surface
area of the sample is covered with glue and electrical wires. This was the best way
to measure how the electrical signal varied between volumes of the sample that were
wrapped by the wires. Rather than a wire measuring a circle in the volume, the
volume itself was measured.
4.3
The Piezoelectric Problem
Ogawa, Oike, and Miura (1985)[17] and Nitsan (1977)[16] similarly measured electricity produced from fracturing rocks. Although neither author discusses how their
experimental samples were prepared, they measure little to no electrical activity in
samples which lack piezoelectrical minerals. Enomoto and Hashimoto (1990) [5] used
samples of different minerals for their fracturing tests. The electrical signals that
Enomoto and Hashimoto measured depended on the moisture content of the rocks
they were fracturing. They detected electrical energy in fracturing saturated rocks
that lack piezoelectric minerals.
Table 4.1:
Experimental
Data
sample
volume mm 3
4.83E+04
91
6.12E+04
101
6.12E+04
102
1.50E+05
110
1.50E+05
120
6.12E+04
140
9.97E+04
450
9.97E+04
570
9.97E+04
590
9.97E+04
820
1.50E+05
zhu
splayed wires 1.50E+05
9.97E+04
RD
9.97E+04
RG
9.97E+04
RI
9.97E+04
RJ
9.97E+04
RK
9.97E+04
RL
9.97E+04
RM
Acoustic Energy
sum of abs
fracture
sample style
1.13017E-12
6.91819E-12
2.01123E-13
8.63303E-14
1.229E-12
1.78488E-13
7.26319E-12
8.51587E-12
5.44736E-12
6.2775E-12
1.7149E-12
6.02616E-12
1.27559E-10
1.03589E-10
8.96146E-11
1.03589E-10
6.05045E-13
6.02523E-13
6.50963E-12
2.8953E-11
2.0946E-09
3.4867E-11
1.4322E-11
1.6761E-10
2.1E-11
1.5311E-10
7.7034E-11
2.1256E-10
1.1445E-09
1.4451E-11
6.5764E-10
2.0495E-09
1.3841E-09
9.3363E-09
1.1272E-08
2.8541E-09
2.9075E-09
2.3481E-09
1
2
1
1
2x
Poland
Poland
Poland
Poland
Poland
glass
450 uS
570 uS
590 uS
820 uS
dry
1
1
1 or 2
1
2
1
dry
dry
200
200
200
200
200
uS
uS
uS
uS
uS
Spring
Spring
Spring
Spring
Spring
load rate (pm/sec)
1
1
1
1
1
1
100
100
100
100
100
1
100
100
100
100
1
100
100
Chapter 5
Conclusions
Both the piezoelectric effect and the streaming potential effects for the production of
the energy fail to explain why the energy increases with molarity of the saturating
solution in Morgan and Zhu's (1998) conductivity experiment. This leaves taking a
closer look at the whole system and what assumptions have been made. The most
significant assumption is that the layer inside the slipping plane is fixed. This is true
in a steady state, but in the system of a rock under stress, this possibly fails. As
cracks get smaller the repulsion between double layers increases. A lot of charge is
accumulated in a small area. When the crack closes, much of this charge is pushed
out into the adjoining cracks, and the charges unbalance the charge distribution in
the adjoining decreasing crack widths. The movement of this energy is closer to the
charge stored in the surface potential on the grain surfaces.
The acoustic energy is proportional to how much charge moves through the rock
in any particular direction for the duration of the measurement.
In general, the
more acoustic energy the sample breaks with, the greater the amount of net charge
has passeed through. This includes such effects as piezoelectricity. There is some
deviation, however.
The samples that were broken at a 100pm/sec loading rate
were far more dependent on this relationship than samples that were broken at a 1
pm/sec loading rate. For the 1 pm/sec loading rate samples, there was a significant
variation in the way that the samples fractured whenever they were being loaded.
The fracture variation contributed to the increasing net charge with acoustic energy
relationship. Whenever this was taken into account, the samples depended much less
on the acoustic energy in the amount of net charge moving through them.
The movement of electrical energy through the rock appears to be a localized effect
but with a net magnitude and direction for the whole of the sample. The raw data
from sample 101 shows this. Even though the middle and bottom probes literally had
wires right next to each other on the sample, they each had current passing in opposite
directions through the wire. Although it may only be coincidental, it is interesting
to note that all of the dry samples produced negative net electrical charges.
5.1
Future Investigations
Placing multiple small electrodes around the sample in a similar run could provide a
resolved view of just how localized the direction of charge movement is in the sample.
There is even the possibility that observations may be made of how the charge is
flowing with respect to how the rock is fracturing in this type of experiment. However,
the method of data collection would need to be altered.
Continuously taking data through the 1 mega-ohm probes may provide some interesting data on how the system of the saturated sample behaves in a temporal way.
Maintaining this precision for the duration of the experiment would take up 24.3
megabytes for 8.5 minutes. At least 4 files are produced for each run. There is no
reason to assume that there are no significant electrical signals being produced with
longer wavelengths.
Experiments with increasing the conductivity of the saturating solution should
be performed. At greater magnitudes of conductivity, a problem may arise with the
resistance of the rock decreasing into the the range of one mega-ohm. If this is the
case, a new experimental setup would need to be considered.
The behavior of saturated rocks that lack piezoelectric minerals should be explored. The experiments performed by Ogawa, et al(1985)[17], Nitsan (1977)[16],
and Enomoto and Hashimoto (1990) [5] argue that this is an important direction for
more research.
Appendix A
Calculation of the Resistance of
Saturated Westerly Granite
The porosity of Westerly granite is approximately 0.009.
The conductivity of the Poland Springs water was measured to be 225 pS. Morgan
and Zhu's greatest solution conductivity was 820 pS. Using Archie's Law, the resistance of the rock before the experiment was a magnitude greater than the impedance
on the probe. It is improtant to note that the porosity and the level of saturation are
altered at the time of fracture when measurements are made [1].
I
V
where
I = Amperes
V = volts
The resistance of the soltion is
Rsolution =
where
R= Q
If the solution had a shape, a similar volume's resistance could be measured as
R=p
1
A
where
p = Qmeters
1 = meters
A = meters 2
According to Archie's Law
Prock = Psolution
- 2
where
0 = porosity
So the resistance of the rock is calculated as
A
Rrock = Rsolution A-2
1
so
Rrock =
0.009-2
The resistance of a rock saturated in 820pS NaC1, Rrock = 1.2X107
magnitude greater than the impedance of the Gagescope probes.
, is about a
Appendix B
Sample Preparation
The insulated wire wrap size #18 19/30 contains 19 fine wires that were split roughly
in half and wrapped around sample zhu and glued with the conductive glue. The
sample was baked in a vacuum for 30 minutes. One hour later in 22% humidity and
23.5 degrees Celsius, it was loaded and broken in the lab at a piston displacement
rate of 100 microns/sec.
The splayed wire sample had 16 wires around the top, 18 around the middle, and
12 around the bottom. With generous amounts of glue, this sample sat in room
humidity (greater than 22%) for several weeks before being broken in the lab at a
rate of 1 micron/sec.
Samples 91, 101, 102, 110, and 120 were placed in a vacuum for two days. After
this period of time, the samples were placed in 204 microsiemens solution of Poland
Springs water for two days to saturate and moved to the lab while immersed in the
solution. The wires for the samples were placed while still immersed in the solution.
As the stress was being applied to the sample, the conductive glue was being applied to
the wires as well. Compression of all samples was applied at the rate of 1 micron/sec.
Each sample was removed from solution only when the time came for stress to be
applied.
Sample 140 consisted of cored glass from a block of Corning amorphous glass. The
sample had always been in 22% humidity. Wires were placed on the sample, and the
sample was placed under stress as the glue was being applied.
Table B.1: Experimental methods used for preparing samples
Wire Method Prep Procedure
sample
3
2
91
3
2
101
3
2
102
3
2
110
3
2
120
3
2
140
Electrodes 1 1
450
1
Electrodes 4
570
1
Electrodes 2
590
1
1
Electrodes
820
1
1
zhu
2
splayed wires 2
1
1
RD
1
1
RG
1
1
RI
1
1
RJ
1
1
RK
1
1
RL
1
1
RM
Appendix C
Streaming Potentials
I,
=
---
7rr2 p
The pressure p that causes movement of ions on the slipping plane causes an
electrical or streaming current I,. I, then induces a conductive current Ic in the
opposite direction.
Figure C-1 illustrates the geometry of a capillary with radius, r, and length, 1.
Fluid, of viscosity v, in the capillary moves under an induced pressure, p. Adsorbtion
of ions on the surface of the capillary produces a double layer with a slipping plane
conductivity of ao and a zeta potential C. The conductivity with respect to the
distance r towards the slipping plane is described by a,.
7r r2 Vuo
le =
1
The balance of electrical charge between the currents causes the streaming potential V.
I, + Ic = 0
V
_
pHunter [8].
See Hunter [8].
r
T
I
Capillary Surface
Figure C-1: Diagram of capillary geometry with P as the direction of a pressure
gradient
Appendix D
Experiment Data
Integration Sample RM
Fracture 1
r
le-9
D/L=25/50.8 mm
Top Probe
Oe+O
Middle Probe
-e
-le-9
Bottom Probe
III
-0.1
-2e-9 '
-U. 2
0.1
0.0
0.2
Time (sec)
Integration
Sample "zhu"
Fracture 1
D/L=25/76.2 mm
2e-12 I
Top Probe
Oe+O
-2e-12
Middle Probe
-4e-12
-6e-12
Bottom Probe
-8e-12 '
-u.003
I
I
I
I
-0.002 -0.001 -0.000 0.001
Time (sec)
I
0.002
0.003
Integration Sample 101
Fracture 2
D/L =19/57 mm
le-9
-
Top Probe
0
1e-9
E
o le-9
0
8e-10 0
6e-10
Middle Probe
4e-10
0 2e-10
Oe+O
S-2e-10
'
'
'
'
Bottom Probe
'
-u.003-0.002-0.001-0.000 0.001 0.002 0.003
Time (sec)
Integration
-
E
Sample 102
Fracture 1
D/L=19/57 mm
2e-11
Top Probe
0
o le-ll
0
& Oe+
Probe
-Middle
c
0 -le-ll
-2e-1 1
-u.003-0.002-0.001-0.000 0.001 0.002 0.003
S)
Bottom Probe
Time (sec)
Integraition
Sample 110
Fracture 1
D/L=25/76.2 mm
- le-ll
E
Top Probe
0
0
0
Oe+O
Middle Probe
c-
Bottom Probe
1
11
-u.003-0.002-0.001-0.000 0.001 0.002 0.003
Time (sec)
Integratiion
Sample 120
Fracture 21(
D/L=25i/76.2 mm
a 8e-11
E
Top Probe
0
S 6e-11
0
0
4e-11
I
Middle Probe
I
a 2e-11
Oe+O
Bottom Probe
-2e-11
-U.
003-0.002-0.001-0.000 0.001 0.002 0.0 03
Time (sec)
Integr ation
.
E
0
-s
0
a
Sample 140
Fracture ?
D/L=19/54 mm
le-ll
Top Probe
Oe+O
0
Middle Probe
."-1e-11
Bottom Probe
z
-u.003- 0.002-0.001-0.000 0.001 0.002 0.003
Time (sec)
Integration
-
E
Sample 450
Fracture ?
D/L=251/50.8 mm
2e-11
O0e+O
Electrode 1
0
0 -2e-11
&-4e-1 1
Electrode 2
. -6e-11
Electrode 3
S-8e-11
z
-le-10
-u.I 002
-0.001
-0.000
0.001
Time (sec)
0.0 02
Integration
Sample 570
Fracture ?
D/L=25/50.8 mm
-0 le-ll
E
. Oe+O
Electrode 1
o
o -le-11
-2e-1 1
cc-3e-1 1
Electrode 2
S-4e-11
" -5e-11
-6e-11
-u.002
-
-0.001
-0.000
0.001
Electrode 3
0.002
Time (sec)
Integration
Sample 590
Fracture ?
D/L=25/50.8 mm
-0 2e-10
E
0
Electrode 1
o
o
a le-10
Electrode 2
Oe+O
Electrode 3
-le-10
-u.002
Integration
.
E
-0.001
-0.000
0.001
Time (sec)
Sample 820
Fracture ?
0.002
DIL=25/50.8 mm
5e-10
0
- 4e-10
0
Electrode 1
o 3e-10
o 2e-10
I
Electrode 2
I
I-
.c
le-10
m Oe+O
4~
Electrode 3
4I~
-u.002
-0.001
-0.000
Time (sec)
0.001
0.0 02
Integra tion
Sample RD
Fracture ?
D/L=25/ 50.8 mm
Sle-9
E
Top Probe
0
o Oe+O
Middle Probe
-le-9
-2e-9
0
Bottom Probe
Z
-U.2
-u.2
Integration
-0.1
0.0
Time (sec)
Sample RG
0.1
Fracture ?
0. 2
D/L=25/50.8 mm
"5e-10
E
Top Probe
0
0
2o Oe+O
a)
Middle Probe
-5e-10
.
Bottom Probe
z
-le-9
-u.2
Integr ation
0
E
-0.1
0.0
Time (sec)
Sample RI
0.1
0.2
D/L=25/50.8 mm
Fracture ?
6e-9
Top Probe
5e-9
0 4e-9
3e-9
Middle Probe
2e-9
le-9
W
Bottom Probe
Oe+0O
_'
9_
-U .2
I
-0.1
I
0.0
Time (sec)
I
0.1
0.2
Integr ation
6e-9
.
E
. 5e-9
Sample RJ
I
D/L=25/50.8 mm
Fracture ?
I
I
Top Probe
o 4e-9
0 3e-9
0
&- 2e-9
(
Middle Probe
le-9
j Oe+O
z l~ 9
-u2
Bottom Probe
I
I
-0.1
I
0.0
0.1
0.2
Time (sec)
Integration
Sle-9
E
Sample RK
I
Fracture 1
D/L=25150.8 mm
I
0
Top Probe
o
2 Oe+O
Middle Probe
0)
-le-9
.~
Bottom Probe
z
I
-U.2
I
0.0
-0.1
0.1
0. .2
Time (sec)
Integr -ation Sample RL
.0
Fracture 2
D/L=25/50.8 mm
4e-9
E
0
S 3e-9
Top Probe
0
0
2e-9
I
Middle Probe
I
Oe+O
z
Bottom Probe
_tI,-
-U.2
-0.1
0.0
Time (sec)
0.1
0.2
Sample 101
Fracture 2
D/L=19/57 mm
0
0
O
I0
0
-9
-u.003 -0.002 -0.001 -0.000 0.001
0.002
0.003
-u.003 -0.002 -0.001 -0.000
0.001
0.002
0.()03
-u.003 -0.002 -0.001 -0.000 0.001
0.002
0.0 03
0.002
0.0 03
o
O
00
0
o.
.l
b
-f
-u.003 -0.002 -0.00 L-0.0 00 0001
ime (sec
Sample 102
Fracture 1
D/L=19/54 mm
- 0.07
0
> 0.06
.0 0.05
0
CL 0.04
o 0.03
0.02
-u.003 -0.002 -0.001 -0.000 0.001
0.002
0.003
0.002
0.003
S0.02
S0.01
0
& 0.00
.-0.01
2 -0.02
-u.003 -0.002 -0.001 -0.000 0.001
(A
m 0.00
I
I
0
0
Q-0.01
E
o
0
M .0.02
---
-u.003 -0.002 -0.001 -0.000
0.3
0.2
0.1
0.0
-0.1
-0.2
-0.3
0.001
00
-. 02-00
-U. 003 -0.002 -0.00
L-r0.00 c.0
Time(sec)
01
0.002
0.0 03
0.02
000
0.002
0.003
Sample 110
Fracture 1
D/L=25/76.2mm
0.04
.0
0 0.03
0.02
I0.01
-u.003 -0.002 -0.001 -0.000 0.001
0.002
0.003
0.002
0.003
0.002
0.003
0.002
0.003
0.03
0.02
S-0.01
0.00
'a-.01
2 -0.02
-u.003 -0.002 -0.001 -0.000 0.001
0.01
S0.0
0
, -0.01
-u.003 -0.002 -0.001 -0.000 0.001
o
0.2
S0.1
Fn 0.0 -
n -0.1
0
S-0.2
-u.003 -0.002 -0.00L-n ngn
I me (secT
001
Sample 120
-0.14
o 0.12
0.10
.0 0.08
0
0.06
I
Fracture 2X
I
D/L=25/76.2 mm
I
I
I
0.001
0.002
0.003
-u.003 -0.002 -0.001 -0.000 0.001
0.002
0.003
0.002
0.003
C.0.04
o 0.02
0.00
-U.
0
.0
0
mm0
L
003 -0.002 -0.001 -0.000
0.3
0.2 I
0.1
0.0
0
e0
0.4
0.3
N
0.2
0.1
0o
0
0.0
-u.003 -0.002 -0.001 -0.000 0.001
11
e
0 -
0
-2'
I
I
I
-u.003 -0.002 -0.00Ln
cn
Iime (secl
I
0.002
0.001
0.003
Fracture ?
Sample 140
D/L=19/54 mm
0.022
0.021
0.020
0.019
0.018
0.017
0.016
1
0.015
-u.003 -0.002 -0.001 -0.000
0.001
0.002
0.003
0.001
0.002
0.003
0.001
0.002
0.003
0.03
Q)
O
0
F
n ni I
-U.0 03 -0.002 -0.001 -0.000
I
I
-1I
S0.02
S0.01
.
0
-
0.00
I -0.01
E -0.02
0
w-0.03
0
S-0.0404
-u.003 -0.002 -0.001 -0.000
o
I
0.4
_
S0.2
u) 0.0
0 -0.2
o
o -0.4
-u.003 -0.002 -0.00 rr
m
n
N
N
on
Tme (secT
l
0.002
0.003
0.001
Sample 450
Fracture ?
D/L=25/50.8 mm
0.1
0
I
II
I
I
O
0>
a)
0.0
O
LU
-0.1
-U. 002
0
-0.001
-0.000
0.001
0.002
-0.001
-0.000
0.001
0.0 02
0.2
0.1
0
C)
O
0.0
-U. 002
0.1
0.0
a)
--
iMY
-U. 002
-0.001
-0.1
-0.2
6
4
\r
-0.000
0.001
0.0 02
.0
.0
I
I
2
0
-2
00
001
-.
0
-4
-6
U.' 002
-0.001
-0.000
Time (sec)
0.001
0.002
Sample 570
Fracture ?
0.1
D/L=25/50.8 mm
O
0.0 F
0
0
-0.1
-0.2
I0
Ll
0
'
-u.002
0.0
-0.001
-0.000
0.001
0.002
-0.001
-0.000
0.001
0.0 02
-0.001
-0.000
0.001
0.0 02
0.001
0.002
L
-0.1 F
0
0
0)
-0.2 I
-N L
-u.002
III
0.2
0
0
0.1
L
n
-u.002
6
4
o)
2
0
0
-2
0
-4 L
-6
-u.002
-0.001
T-0.000
Time (sec)
Sample 590
Fracture ?
D/L=25/50.8 mm
0.6
0
a
0
0.4
0.2
0.0
Li -0.2
-0.4
002
-0.001
-0.000
0.001
0.002
-u.4
-u.002
-0.001
-0.000
0.001
0.002
-0.001
-0.000
0.001
0.002
0.001
0.002
-U.
0.6
0
0.4
0.2
w
.10
c11
0.0
-0.2
fk A
0
I--
0
0.6
U
0
0.4
0.2
0
0.0
!--
o
0
-0.2
- -
-0.4
-0.002
cl
LLI
6
4
2
o
-2
-4
-6
-u.002
-0.001
Ti-0.0oe
Time (sec)
Sample 820
Fracture ?
D/L=25/50.8 mm
I
I
I
I
I
I
-u.002
-0.001
-0.000
0.001
-1
-u.002
-0.001
-0.000
0.001
0.002
-u.002
-0.001
-0.000
0.001
0.002
6
4
2
0
-2
-4
-6
-U.
002
0.002
|
I
I
I
I
I
I
-0.001
T-0.000
Time (sec)
0.001
0.002
Sample RD
Fracture ?
D/L=25/50.8 mm
0.4
0
0.2
0.0
0
.
-0.2
0
-0.4
0
-0.6
I-
-0.8 .2
.
-U
l
0
._
-0.1
0.1
0.2
0.0
0.1
0.2
0.0 I0.1
0.1
0.
0.0
0.1
0. 2
.
.
0.1
0.2
0.0
0.2
I
0.0
I-
-0.2
a
0
-0.4
"0
-0.6
.mr
-0.8
-U .2
-0.1
0
o0
.o
0
1.
0
0
I
-0.1
.2
0
0
6
4
2
II
-I
0
-2
.i
u
-4 p.
-6
-u .2
010.
-0.1
0.0
Time (sec)
Sample RG
Fracture ?
D/L=25/50.8 mm
1
-1
0
-1
I
-2
-U.2
-0.1
0.0
0.1
0.2
-0.1
0.0
0.1
0.2
0.3
0.2
0.1
0.0
-0.1
-0.2
-0.3
-U.2
I
.2
-0.1
I
_4
-.
.
0.0
I
0.1
0. 2
I
2
-u.2
-0.1
0.0
Time (sec)
0.1
0.2
Sample RI
Fracture ?
D/L=25/50.8 mm
2
0
1
()
O
0
o
0
-1
-2
-u.2
-0.1
0.0
0.1
0.2
-2 '
-u.2
-0.1
0.0
0.1
0.2
-2
-0.2
-0.1
0.0
0.1
0.2
.
0
L,
-o
."I
O
oa
E
E
0
6
4
l
2
0
-2
C.
-4
-6
-u.2
-0.1
0.0
Time (sec)
0.1
0.2
Sample RJ
Fracture ?
D/L=25/50.8 mm
I
I
I
-0.1
0.0
0.1
0.2
-u.2
-0.1
0.0
0.1
0.2
-2 -u.2
-0.1
0.0
0.1
0.2
23
-u.2
2
1
0-1
-
2
1
0
-1
-2
-3
-4 2
-U .2
-0
I
-0.1
I
0.0
Time (sec)
I
0.1
0.2
Sample RK
Fracture 1
D/L=25/50.8 mm
S0.01
0
o 0.00
a.
0
I-0.01
-u .2
-0.1
0.0
0.1
0.2
-0.1
0.0
0.1
0. 2
0.0
0.1
0. 2
- 0.02
.0 0.01
0
L.
Ia 0.00
S-0.01
-u .2
7 0.04
> 0.03
e 0.02
2 0.01
I
0.00
-0.01
-0.02
m -0.03
-U
.2
-0.1
o 0.0
-.
-
....- n --
C -0.1
-0.2
0
o -0.3
-t
j.2
-0.1
0.0
Time (sec)
0.1
0.2
Sample RL
-u.23
-u.2
_1 __I
-u.
-u .2
Fracture 2
D/L=25/50.8 mm
-0.1
0.0
0.1
0.0
0.1
0.2
0.0
0.1
0.2
0.1
0.2
1
-1 _'rl
-u.2
-0.1
6
4
2
0
-2
-4
-6
-U .2
1
-0.1
I
Ti 0.0
Time (sec)
0
0.1
0.2
Fracture 1
Sample RM
D/L=25/50.8 mm
S0.00
S-0.01
0
-0.02 II-0
-0.03
'
-u.2
-0.1
0.0
0.1
0.2
-0.1
0.0
0.1
0.2
-0.1
0.0
0.1
0.2
.
.I
.
0.1
0.2
0.01
o
.0 0.00
0
I-
aS-0.01
m
S-0.02-u.2
o
0.01
.0
0
. 0.00
E
0o
m -0.01
-U .2
0
0.8
•I
_ 0.6
S0.4
Cl
0.2
-
0.0
= -0.2
0
.2-.
-0.4
-0 .2
SII
-0.1
0.0
Time (sec)
Sample "zhu"
Fracture 1
D/L=25/76.2 mm
- 0.03
> 0.02
e 0.01
0 0.00
"-0.01
o -0.02
-0.03
-u.0 03 -0.002 -0.001 -0.000 0.001
0.002
0.003
o 0.04
0.02
•
-
-
:
1'* --: ' -- -- =
=" ' "--
':
:---
:
----
-
' -
- = '
'
=
L
-
o 0.00
-0.02
S-0.04
I
2 -0.06
-u. 003 -0.002 -0.001 -0.000
0.001
0.002
0.003
-u.003 -0.002 -0.001 -0.000 0.001
0.002
0.003
0.002
0.003
o 0.00
a -0 . 0 1
0
L
-0.02
E
o -0.03
0
M -0.04
o
2
-
I
I
I
I
I
1
r
.-
M
0
o
00
0
-2
-3
I
-4
-u.003 -0.002 -0.001 -0.000
0.001
Time (sec)
Bibliography
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