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Rock Mechanics Laboratory Tests Relevant to the in-situ Stress
Measurements at the 4850-level, Homestake Mine, Lead, South Dakota
by
Peter Vigilante
A thesis submitted in partial fulfillment of
the requirements for the degree of
Master of Science
(Geological Engineering)
at the
UNIVERSITY OF WISCONSIN-MADISON
2017
i
Abstract
Laboratory rock mechanics experiments were conducted on cores taken from the
Sanford Underground Research Facility (SURF) (formerly of Homestake Mine) in Lead,
South Dakota. Strength properties and their anisotropy were investigated in order to aid the
interpretation of the hydraulic-fracturing stress measurements conducted in boreholes drilled
down from the 4850’ level (1478 meters depth) of the mine. Brazilian disc tests, uniaxial and
triaxial tests, and laboratory hydraulic fracturing tests were conducted on cores recovered
from the kISMET (Permeability (k) and Induced Seismicity Management for Energy
Technologies) project as well as those previously obtained as part of the Deep Underground
Science and Engineering Laboratory (DUSEL) program. Brazilian disc tests revealed
significantly higher tensile strength when samples were loaded normal to the foliation
compared to when the samples were loaded parallel to the foliation, indicating clear tensile
strength anisotropy. Uniaxial tests of the cores produced UCS results with an average value
of 107.4 MPa for samples loaded parallel to foliation, and 88.1 MPa for samples loaded
perpendicular to foliation. Triaxial dynamic moduli measurements conducted under
confinement equivalent to in-situ stress magnitudes indicated a 18% increase in dynamic
Young’s modulus between samples loaded parallel to foliation compared to perpendicular.
Laboratory hydrofracture tests were conducted under various triaxial stress states to see
whether potential shear failure along weak foliation planes, promoted by differential stress,
could affect the apparent hydrofracture breakdown pressure. While the observed breakdown
pressures did not indicate any clear influence of the rock anisotropy, some samples subject to
ii
differential stress showed lower breakdown pressure possibly caused by leak-off into
fractures before peak pressure is reached.
iii
Acknowledgements
I would first like to thank my advisor, Hiroki Sone. Being his first graduate student,
he showed immense patience and support throughout my two years at the University of
Wisconsin-Madison. He was always willing to take the necessary time out of his schedule to
help me with my classwork, research, and teaching. I would not have been able to complete
my Master’s without his support. I would also like to thank my other committee members,
Herb Wang and Bezalel Haimson. They both were incredible resources for my research, and
were always willing to help out when needed. I would also like to thank Seiji Nakagawa for
all his help on laboratory experiments.
I would also like to thank both the Geological Engineering and Geoscience
departments at the University of Wisconsin-Madison. I spent endless hours in both
Engineering Hall and Weeks Hall, and both departments helped me complete my degree.
Also, would like to thank the Department of Energy and the kISMET project for financial
support of my research.
Finally, endless thanks to my friends and family for the support the last two years.
My family, although far away, was always there for me when I needed them in some stress-
filled times. Friends and colleagues in the graduate school also made it a memorable two
years in Madison. Specifically, Ben Heinle and Elliott Andelman, who kept me sane at all
times.
iv
Contents
Abstract ..................................................................................................................................... i
Acknowledgements ................................................................................................................ iii
Contents .................................................................................................................................. iv
List of Figures ...........................................................................................................................v
List of Tables .......................................................................................................................... ix
1. Introduction ..........................................................................................................................1
2. New Laboratory Measurements of Rock Properties at kISMET Field Site...................2
2.1 Brazilian Disc Test ...................................................................................................5
2.2 Triaxial Dynamic Moduli Test...............................................................................19
2.3 Uniaxial Moduli and Unconfined Compressive Strength (UCS) Test ...................24
2.4 Laboratory Hydrofracture Test ..............................................................................36
3. Conclusions and Future Work ..........................................................................................52
4. References ...........................................................................................................................55
Appendix .................................................................................................................................59
v
List of Figures
Figure 1. a) Brazilian Disk sample preparation schematic b) Brazilian Disk schematic
representing post experiment. Black lines show rock foliation, and red line shows tensile
fracture created from the testing c) Displacement vs Load Brazilian Test results from (Wang
and Xing, 1999) ........................................................................................................................6
Figure 2. Grouped Brazilian Disc Samples plotting Normalized Load (kN/cm) vs axial
displacement (mm). The schist samples were grouped together according to what core run
and associated depth they were recovered from, as well as quartz and rhyolite samples
grouped together separately .......................................................................................................8
Figure 3. Post testing images of two separate schist Brazilian disc samples. On the left,
sample 41A2 shows the expected vertical fracture (tensile crack) within the disc. On the
right, sample 65B3 shows unexpected fracture angled away from the axial load (which is
vertical in both photos) ............................................................................................................10
Figure 4. Plot representing the angle formed between the vertical axial load of the Brazilian
Disc test and the foliation of the disc sample vs the tensile strength of each sample clarifies
(MPa). Solid blue data points represent true tensile strengths of samples, while blue unfilled
data points represent lower bounds of those samples tensile strength. All samples are
Poorman Schist, and raw data are shown in Table 2 ...............................................................13
Figure 5. Anisotropy of Ultimate Strength in Uniaxial Direct-Pull Tension of Lyons
Laminated Sandstone. (Kwaśniewski, 2009; original data from Youash, 1966) .....................17
vi
Figure 6. Anisotropy of Ultimate Strength in Uniaxial Direct-Pull Tension of Morrow Point
mica schist. T is the tensile strength (MPa) and B is the Angle Between the Loading
Direction and the Samples Foliation from (Kwaśniewski, 2009; original data from Olsen,
1967) ........................................................................................................................................18
Figure 7. Seismic P-wave velocity measurements taken (a) around the circumference of
samples and (b) along the length of samples from the kISMET field site. Velocity anisotropy
is apparent for the entire length of the cores from (Oldenburg et al., 2016) ...........................23
Figure 8. Stress vs Strain curves for all eight Schist triaxial samples tested. Note: no radial
strain data was acquired for sample 56H (bottom left) prior to bringing sample to failure
during testing. Also, “depth” is depth in feet from the 4850’ level of the Homestake Mine ..29
Figure 9. Images of triaxial samples taken after they were brought to failure in UCS testing.
Samples with foliation normal to sample axis are on the top row, and samples with foliation
relatively parallel to sample axis are the bottom row ..............................................................30
Figure 10. Anisotropy of Unconfined Compressive Strength (Kwaśniewski 2009) ...............33
Figure 11. Dependence of Differential Stress (y-axis) at Shear Failure on the Orientation of
the Weakness Plane (x-axis) in a Sample of Anisotropic Rock Model from (Paterson and
Wong, 2005; Produced by Jaeger, 1960) .................................................................................35
Figure 12. (above) Cross-section of lab hydrofracture sample and (below) detailed
description of stainless steel high-pressure tubing inserted into lab hydrofracture samples
(also seen in Figure 13). O-ring was attached to tubing pieces using the o-ring groove, and
vii
then the tube was epoxied into the 0.125” holes of the samples to seal the hydrofracture
testing zone to the high-pressure tubing in the system ............................................................37
Figure 13. Schematic of lab hydrofracture set up. Not depicted to scale, but dimensions of
hydrofracture sample and tubing detailed ................................................................................38
Figures 14-20. Schematic of lab hydrofracture set up. Not depicted to scale, but dimensions
of hydrofracture sample and tubing detailed ..................................................................... 41-44
Figure 21. Axial Stress (Max. Principal Stress) Applied to Hydraulic Fracturing Samples vs
The Breakdown Pressure of that Sample and Fracture Reopening Pressure for Samples
Recovered from Core Run 64 ..................................................................................................45
Figure 22. Axial Stress (Max. Principal Stress) Applied to Hydraulic Fracturing Samples vs
The Breakdown Pressure and Fracture Reopening Pressure of that Sample for Samples
Recovered from Core Run 53 ..................................................................................................46
Figure 23. Reproduced with Expected Breakdown Pressures (Pb) shown as Overlaid Red
Box ...........................................................................................................................................49
Figure 24. Sample 53-B Pressure vs Time Plot Showing Pressure Increase in Test Zone
Deviates from Linearity (Red Line) to Help Explain Outlier Breakdown Pressure Value .....50
Figure 25. Map View of Cross Section A to A’ (red line) which is shown in cross sectional
view in Figure 26 From (ARUP, 2015) ...................................................................................60
Figure 26. Cross sectional view and formations of the Homestake mine. 4850L represented
by solid red line. From (Denver Region Exploration Geologists’ Society) .............................61
viii
Figure 27. General Geology Overview of 4850L. Blue Dashes are General Foliation
Orientation and Red Dashes are Rhyolite Dikes. From (Golder Associates Final, 2010a) .....62
Figure 28. Range of UCS values for rock types at 4850L from (Lachel Felice, 2009) ...........69
Figure 29. Comparison of Ultimate Joint Shear Strength (Represented as Red Triangle Data
Points) to Intact Rock Uniaxial Compression and Brazilian Tensile Strength (Represented as
Blue and Green Curves, Respectively) From (RESPEC 2010) ...............................................73
Figure 30. Image of borehole breakout at 4850 level of Homestake Mine. From (Golder
Associates, 2010a) ...................................................................................................................84
Figure 31. Inclination of Breakout in Borehole Drills from the Ventilation Drift (Borehole
Advanced at an Azimuth of Approximately 310°) from (Golder Associates, 2010b) ............85
Figure 32. Vertical Stress Gradients vs Depth in the Homestake Mine, SD. Sources from
Pariseau (1985), Johnson et al. (1995), and Golder Associates (2010a) .................................88
Figure 33. Stress Data Points from Bond (1970), Hooker et al. (1972), Johnson et al. (1995)
and Golder Associates (2010a) at Respective Depths, as well as Gradients from Pariseau
(1985) .......................................................................................................................................89
Figure 34. Estimated Minimum Borehole Pressure Needed at 4850L for Hydraulic Fracturing
(1985) .......................................................................................................................................92
ix
List of Tables
Table 1. Record of all arbitrary sample names, borehole sample was recovered from,
borehole size, what test was conducted on the sample, the depth along the recovered core
length the sample was taken from, as well as a brief description of the core at the recovered
depth. (All samples are Poorman schist unless designated *=quartz samples and **=rhyolite
samples) ....................................................................................................................................3
Table 2. Brazilian Disc Samples tested. * indicates Schist samples. “Qtz” indicates samples
are quartz. “Rhy” indicates samples are rhyolite samples. “>” indicates samples which did
not fracture vertically and centered, thus not reaching the samples true maximum tensile load
..................................................................................................................................................11
Table 3. Breakdown of average normalized load (kN/cm) for the angle between foliation and
vertical axial load for 0°, 45°, and 90° .....................................................................................14
Table 4. P-wave and S-wave velocities for triaxial samples tested, calculated dynamic
moduli, and UCS data (discussed in the next section). No velocity data were recorded for
sample 56H prior to breaking the sample. M (P-wave modulus), G (Shear), were calculated
from acquired velocity measurements. ....................................................................................21
Table 5. All uniaxial samples with UCS values along with descriptions ...............................25
Table 6. Average UCS for samples of perpendicular foliation. “V” Samples have foliation-
parallel to cylindrical sample axis. “H” Samples have foliation-normal to the cylindrical
sample axis. ..............................................................................................................................26
x
Table 7. Calculated Young’s Modulus and Poisson’s Ratio for all eight triaxial samples. Both
calculated using stress vs strain curves provided in Figure X (the stress strain curves) .........27
Table 8. Raw data for the successful lab hydrofracture tests. All tests had a minimum
principal stress of 22 MPa, and the fracture reopening pressures are an estimate due to
multiple fracture re-openings for the tests ...............................................................................46
Table 9. Average unconfined compressive strength (UCS) values for rock types at 4850 level
from (Lachel Felice, 2009) ......................................................................................................68
Table 10. Original Anisotropic Rock Property Data (*C=Compressive Strength (UCS),
T=Tensile Strength; The 1- and 3-directions are parallel to the schistosity; the 2-direction is
perpendicular to the schistosity. From (Pariseau, 1985) .........................................................70
Table 11. Modified Anisotropic Rock Property Data (*C=Compressive Strength (UCS),
T=Tensile Strength; The 1- and 3-directions are parallel to the schistosity; the 2-direction is
perpendicular to the schistosity). From (Pariseau, 1985) ........................................................70
Table 12. Compressive and Tensile Strength for Yates amphibolite and Rhyolite from
(RESPEC 2010) .......................................................................................................................71
Table 13. Comparison of Intact and Residual Mohr-Coulomb Strength Parameters for Joints
in Amphibolite from (RESPEC 2010) .....................................................................................72
Table 14. Modified Anisotropic Rock Property Data (*The 1- and 3-directions are parallel to
the schistosity; the 2-direction is perpendicular to the schistosity. All units are labeled MPa
except for Poisson’s ratio (unitless)). E=Young’s Modulus; v= Poisson’s Ratio; G= Shear
Modulus. from (Pariseau, 1985) ..............................................................................................75
xi
Table 15. In-situ stress data at Homestake Mine, including data sources, stresses, magnitudes,
and directions based on Bond (1970), Hooker et al. (1972), and USBM (1984) ....................77
Table 16. Principal stresses, orientations, and elastic properties (SI units) where SM-02 to
SM-07 was in Yates amphibolite unit and SM-08 and 09 are results from rhyolite dike. From
(Golder Associates, 2010a) ......................................................................................................80
Table 17. Vertical and horizontal components, octahedral, and deviatoric stresses (SI Units)
where SM-02 to SM-07 was in Yates amphibolite unit and SM-08 and 09 are results from
rhyolite dike along 4850L. From (Golder Associates, 2010a) .................................................81
Table 18. Summary of In Situ Stress Measurements from (Golder Associates, 2010b) .........82
Table 19. Data used in Equation 9 to Determine Estimated Minimum Borehole Pressure
Needed at 4850L for Hydraulic Fracturing ..............................................................................90
Table 20. Estimated Minimum Borehole Pressure Needed at 4850L for Hydraulic Fracturing.
..................................................................................................................................................91
1
1. Introduction
The primary section of this report details the laboratory tests run on samples from the
4850-foot level (4850L) of the Homestake Mine, South Dakota, in contribution to the
collaborative research project kISMET (Permeability (k) and Induced Seismicity
Management for Energy Technologies). The four tests conducted for this report were the
Brazilian disc tensile strength test, triaxial dynamic moduli test, uniaxial moduli and
unconfined compressive strength (UCS) test, and the laboratory hydrofracture test for peak
breakdown pressure under different in-situ lab conditions (Vigilante et al., 2017). The main
focus of these laboratory tests was to observe the effect of anisotropy on the strength of the
rocks recovered from the kISMET field site. These results will help support conclusions
made from the kISMET stress measurements, made at the 4850L in August, 2016 (Wang et
al., 2017). These laboratory results may also be helpful in interpretation of the in-situ stress
state from wellbore failures and future field measurements made at the Homestake Mine.
The appendix of this thesis, is a critical review prepared for the kISMET project. It is
a compilation of previous rock mechanics tests and in-situ stress measurements relevant to
the Sanford Underground Research Facility (SURF) in the Homestake Mine, South Dakota.
The goal of the kISMET field work at SURF was to conduct in-situ hydraulic fracturing
experiments which allowed for interpretation of the stress field (Haimson, 1978), learning
how the local rock fabric affects hydraulic fracturing, and to use geophysical methods to
locally monitor the hydraulic fracturing process at close distance compared to typical field
operations. Results from the August, 2016 kISMET field work can be found in Oldenburg et
2
al. (2016) and Wang et al. (2017). The critical review was prepared to aid the design of these
field experiments.
2. New Laboratory Measurements of Rock Properties at kISMET Field
Site
In conjunction with the field testing, I conducted laboratory rock mechanics tests on
the cores retrieved from the kISMET field site (Homestake Mine, SD). The intent of this
portion of the project was to measure the retrieved rock’s properties and influence of
anisotropy in order to aid the interpretation of the hydraulic-fracturing stress measurements.
The borehole (kISMET-003) where the cores were recovered penetrated Poorman Formation,
which is a dark grey banded foliated phyllite to schist formation, and described in more detail
in Section 2 of this thesis (Oldenburg et al., 2016). Furthermore, kISMET-003 is the borehole
in which hydraulic fracture stress measurements were conducted (Wang et al., 2017). Quartz
veins, ranging in size from a few millimeters to centimeters, were also apparent sporadically
throughout the recovered core. The strong texture detailed from the recovered core suggests
the presence of significant mechanical and strength anisotropy of the rocks in the Poorman
Formations.
The four laboratory tests I conducted are detailed in this section of the report.
Brazilian disc test for tensile strengths, triaxial tests for dynamic moduli, uniaxial tests for
static moduli and unconfined compressive strengths, and hydraulic fracturing tests for
hydraulic breakdown pressure. The four lab experiments used cores recovered from the
3
kISMET field site, as well as cores recovered from the Deep Underground Science and
Engineering Laboratory (DUSEL) program, a previous project which took place at the 4850’
level of the Homestake Mine. A main emphasis for the Brazilian disc and triaxial and
uniaxial tests was on how the orientation of the foliation in the schist relative to the loading
direction affects the respective strengths of the rocks. As for the lab hydrofracturing test, the
primary goal was to perform a laboratory stimulation of the breakdown pressures and
fracture reopening pressures of all the samples.
Due to multiple rock tests conducted on rocks recovered from the same field site,
Table 1 contains the arbitrary names given to all the samples, the borehole the sample was
recovered from, the depth in the borehole the sample was taken from (not the depth in the
mine), what test was conducted on the sample, and a brief description of the core where the
sample was taken from. The arbitrary names often include a number which corresponds to a
core run of the borehole it was recovered from. However, for future referencing the depth at
which the sample was taken from is recorded.
Table 1. Record of all arbitrary sample names, borehole sample was recovered from,
borehole size, what test was conducted on the sample, the depth along the recovered
core length the sample was taken from, as well as a brief description of the core at the
recovered depth. (All samples are Poorman schist unless designated *=quartz samples
and **=rhyolite samples)
Arbitrary
Sample
Name
Borehole
Sample was
Recovered
from
Diameter
of
Borehole
Test
Conducted
on Sample
Depth
(along
core
length) Description
56A1
kISMET-
003 NQ2
Brazilian 278’
No intense microfolding.
Plenty of brown/gold
4
56A2
kISMET-
003 NQ2
Brazilian 278’
coloration. Foliation
consistent throughout.
56B1
kISMET-
003 NQ2
Brazilian 278’
56B2
kISMET-
003 NQ2
Brazilian 278’
41A2
kISMET-
003 NQ2
Brazilian 202.5’
Lighter portion of the core.
Whitish hue.
Intense folding and possible
quartz veins present.
41C1
kISMET-
003 NQ2
Brazilian 202.5’
41C3
kISMET-
003 NQ2
Brazilian 202.5’
41C2
kISMET-
003 NQ2
Brazilian 202.5’
63A1
kISMET-
003 NQ2
Brazilian 312.5’
Not as apparent foliation.
Homogenous looking portion
of the core.
63A3
kISMET-
003 NQ2
Brazilian 312.5’
63B2
kISMET-
003 NQ2
Brazilian 312.5’
65B1
kISMET-
003 NQ2
Brazilian 320’
Darker gray portion of the
core.
Intense microfolding.
65C3
kISMET-
003 NQ2
Brazilian 320’
65C2
kISMET-
003 NQ2
Brazilian 320’
65B3
kISMET-
003 NQ2
Brazilian 320’
Qtz2* DUSEL J HQ Brazilian N/A Pure quartz vein.
No foliation to test
anisotropy.
Qtz4* DUSEL J HQ Brazilian N/A
Qtz5* DUSEL J HQ Brazilian N/A
rhy2** DUSEL J HQ Brazilian 226.5’ Pure rhyolite portion of core.
Whitish-gray with darker
specks.
No foliation to test
anisotropy.
rhy3** DUSEL J HQ Brazilian 226.5’
rhy4** DUSEL J HQ Brazilian 226.5’
rhy5** DUSEL J HQ
Brazilian 226.5’
41V
kISMET-
003
NQ2 Triaxial
and
Uniaxial 204’
Lighter portion of core.
Intense folding. 41H
kISMET-
003
NQ2 Triaxial
and
Uniaxial 204’
49V
kISMET-
003
NQ2 Triaxial
and
Uniaxial 242.5’
Foliation is folding but
consistent. Dark bands in
foliation.
5
49H
kISMET-
003
NQ2 Triaxial
and
Uniaxial 242.5
56V
kISMET-
003
NQ2 Triaxial
and
Uniaxial 279.5’
Foliation relatively
perpendicular to axis. Not
much folding. 56H
kISMET-
003
NQ2 Triaxial
and
Uniaxial 279.5’
63V
kISMET-
003
NQ2 Triaxial
and
Uniaxial 313’
Foliation relatively
consistent. Normal Poorman
grayish color. 63H
kISMET-
003
NQ2 Triaxial
and
Uniaxial 313’
64-E
kISMET-
003
NQ2 Lab
Hydrofrac 318.5’
Foliation ~20° off vertical.
No intense folding.
64-C
kISMET-
003
NQ2 Lab
Hydrofrac 319’
Some folding, but foliation
about 10°-20° off vertical
53-C
kISMET-
003
NQ2 Lab
Hydrofrac 262.3’
Intense microfolding.
Foliation relatively normal to
vertical axis.
53-D
kISMET-
003
NQ2 Lab
Hydrofrac 262’
Intense microfolding. Shiny
white/silver areas.
53-B
kISMET-
003
NQ2
Lab
Hydrofrac 262.6’
Intense microfolding.
Foliations goes from
horizontal to vertical
orientation.
531111-A
kISMET-
003
NQ2 Lab
Hydrofrac 263.3’
Not as clear foliation.
Foliation dips ~10°-40°
531-A
kISMET-
003
NQ2 Lab
Hydrofrac 264’
Not as clear foliation.
Foliation dips ~10°-40°
2.1 Brazilian Disc Test
Methods - Brazilian Disc Test
The initial laboratory test conducted on the Homestake Mine cores was the Brazilian
Disc test. To prepare the Brazilian disc samples, the first step was to core 2.54 cm diameter
cylinders from the recovered rock samples. The 2.54 cm. specimens were cored parallel to
6
the general foliation direction on both HQ sized core (63.5 mm or 2.5 in. diameter core) and
NQ2 sized core (50.5 mm or 1.99 in diameter core). These 2.54 cm diameter and 5.08 cm –
6.35 cm length cores were then sliced into disc shaped test specimens using a rock saw
(depicted in red in Figure 1a). The suggested thickness to diameter ratio for the Brazilian
Disc test is 0.5 to 0.6 (Ulusay and Hudson, 2007). Due to constraints on the amount and size
of the rock cores, the average thickness of the 22 Brazilian disc samples we tested was 1.14
cm or 0.45 in.
Figure 1. a) Brazilian Disk sample preparation schematic b) Brazilian Disk
schematic representing post experiment. Black lines show rock foliation, and red line
shows tensile fracture created from the testing c) Displacement vs Load Brazilian Test
results from (Wang and Xing, 1999)
The Brazilian disc test allows the study of anisotropy effects by varying the angle
between the force applied on the discs and the foliation within the rock disc. This is depicted
in Figure 1b, where the angle between the diametrically applied force on the disc shaped
sample and the foliation in the rock can be varied between 0°-90°. The “Triaxial Platens” are
7
the surfaces that the sample sits on (the bottom platen) and the surface that exerts the axial
load on the sample (top platen). An example of how the Brazilian disc test allows the study
of anisotropy is that a sample with foliation parallel to the vertical axial load of the testing
apparatus would have 0° angle between axial load direction and foliation, and a sample with
foliation normal to the vertical axial load would have a 90° angle between axial load
direction and foliation. With the recovered kISMET cores, as well as the previously drilled
DUSEL cores, we were able to produce groups of Brazilian Disc samples from four separate
depths in the Poorman Formation (foliated phyllite to schist), one group of disc samples from
the quartz veins, and one more group of samples from the DUSEL cores which penetrated a
rhyolite dyke. In total, 22 Brazilian disc samples were tested. A GCTS RTR-1000 Triaxial
Testing System was used for all of the Brazilian Disc testing. Force-displacement data were
recorded during the experiment and failure of the sample was identified as the frame load
dropped suddenly to a residual value. After the destructive testing, samples were then
observed to identify the failure plane.
Results - Brazilian Disc Test
Plots of the Brazilian disc tests conducted in this report are in Figure 2. The results
are presented in a Normalized load (kN/cm) vs piston displacement (mm) curve for all of the
samples. The normalized load is defined by the force from the triaxial machine imposed on
the disc sample divided by the thickness of the sample. Calculating the normalized load was
necessary for eventually calculating tensile strength using the Brazilian test formula. This
formula calculates the tensile strength (using the parameters peak applied load (P),
8
diameter of the disc sample (D), and thickness of the sample (L), and is shown below in
equation 1 (Ulusay and Hudson, 2007):
𝜎𝑡 = 2 ∗ 𝑃/(𝜋 ∗ 𝐷 ∗ 𝐿) (𝟏)
Figure 2. Grouped Brazilian Disc Samples plotting Normalized Load (kN/cm) vs axial
displacement (mm). The schist samples were grouped together according to what core
run and associated depth they were recovered from, as well as quartz and rhyolite
samples grouped together separately.
9
These load-displacement curves were then grouped together by rock type and depth
of sample recovery. Core runs 41, 56, 63, and 65 are all Poorman Schist sample groups, and
the Quartz group and Rhyolite group samples are separate. The load-displacement curve is a
good indication that the elastic stiffness (represented by the slope of the curve) is anisotropic.
This anisotropic effect can be seen clearly in CoreRun 56. In CoreRun 56 the Schist seems
stiffest loaded parallel to foliation (0°), and then decreases in stiffness as the angle between
the vertical axial load and the foliation increases to 30°, 60°, and then 90°. These load
displacement curves are also necessary in calculating the tensile strength, because the curves
give us the peak applied load (or P in equation 1 above).
Figure 3 below includes two of the Poorman schist Brazilian disc samples post
failure. These images show the difference in how the Brazilian disc samples fractured. The
sample on the left, 41A2, fractured vertically almost perfectly along the axial load axis. This
type of fracture indicates the sample fractured in tension so that the peak load represents the
true tensile strength of the sample. However, many of the samples fractured similarly to the
sample shown in the right of Figure 3. In this image, the axial load axis is still represented as
a vertical line through the center of the sample, however, the fracture is angled and off
center. Samples which fractured along such diagonal plane likely underwent shear failure
before the tensile stress at the center of the sample reached the true tensile strength of the
sample. Therefore, the tensile strengths inferred form the peak load observed during such
tests are only lower bounds of the actual tensile strength of the rocks.
10
Figure 3. Post testing images of two separate schist Brazilian disc samples. On the left,
sample 41A2 shows the expected vertical fracture (tensile crack) within the disc. On the
right, sample 65B3 shows unexpected fracture angled away from the axial load (which
is vertical in both photos)
Table 2 shows information from all of the Brazilian Disc samples and tests. Table 2
also shows the normalized peak load (kN/cm) taking into account the thickness of all the
samples, and the tensile strength of the sample (MPa) determined by the maximum peak load
reached during the Brazilian Test. Because a tensile fracture at the center of the disc was not
produced in many samples, the tensile strength is written as a lower limit using the “>”
symbol for those samples that did not produce a load-parallel tensile fracture.
11
Table 2. Brazilian Disc Samples tested. * indicates Schist samples. “Qtz”
indicates samples are quartz. “Rhy” indicates samples are rhyolite samples. “>”
indicates samples which did not fracture vertically and centered, thus not reaching the
samples true maximum tensile load.
Sample Borehole Depth Description Axial
load to
foliation
angle
(deg)
Normalized
Peak Load
(kN/cm)
Tensile
Strength
(MPa)
56A1* kISMET-
003
278’ No intense
microfolding.
Plenty of
brown/gold
coloration.
Foliation
consistent
throughout.
0 1.9 4.1
56A2* kISMET-
003
278’ 45 >2.3 >4.9
56B1* kISMET-
003
278’ 90 >3.7 >7.9
56B2* kISMET-
003
278’ 90 >5.6 >12.0
41A2* kISMET-
003
202.5’ Lighter
portion of the
core. Whitish
hue.
Intense
folding and
possible
quartz veins
present.
0 1.5 2.7
41C1* kISMET-
003
202.5’ 30 >1.3 >2.5
41C3* kISMET-
003
202.5’ 60 2.2 4.7
41C2* kISMET-
003
202.5’ 90 >2.7 >5.8
63A1* kISMET-
003
312.5’ Not as
apparent
foliation.
Homogenous
looking
portion of the
core.
0 2.4 4.7
63A3* kISMET-
003
312.5’ 45 >2.8 >6.3
63B2* kISMET-
003
312.5’ 90 3.6 7.6
12
65B1* kISMET-
003
320’ Darker gray
portion of the
core.
Intense
microfolding.
0 1.9 4.8
65C3* kISMET-
003
320’ 0 1.8 3.9
65C2* kISMET-
003
320’ 45 >3.4 >7.9
65B3* kISMET-
003
320’ 90 >3.5 >8.6
Qtz2 DUSEL
J
4850’ Pure quartz
vein.
No foliation
to test
anisotropy.
N/A 2.8 6.0
Qtz4 DUSEL
J
4850’ N/A 5.8 15.8
Qtz5 DUSEL
J
4850’ N/A 4.2 9.1
rhy2 DUSEL
J
4850’ Pure rhyolite
portion of
core.
Whitish-gray
with darker
specks.
No foliation
to test
anisotropy.
N/A 8.6 19.6
rhy3 DUSEL
J
4850’ N/A 10.3 22.9
rhy4 DUSEL
J
4850’ N/A 11.6 24.7
rhy5 DUSEL
J
4850’ N/A 9.7 22.2
In Figure 4, the data in Table 2 above are plotted to represent both the “true” tensile
strength data points, as well as the lower bound tensile strength points. The solid blue circle
data points represent the “true” tensile strength data points, meaning the disc sample broke in
tension along a near vertical fracture. The blue unfilled circle data points represent the lower
bound tensile strength samples. For these samples, they often fractured at an angle away from
13
vertical, and thus were considered to be a lower limit of the tensile strength of the sample,
and not the true, higher tensile strength of that sample.
Figure 4. Plot representing the angle formed between the vertical axial load of
the Brazilian Disc test and the foliation of the disc sample vs the tensile strength of each
sample clarifies (MPa). Solid blue data points represent true tensile strengths of
samples, while blue unfilled data points represent lower bounds of those samples tensile
strength. All samples are Poorman Schist, and raw data are shown in Table 2.
Table 3 below summarizes the anisotropy of tensile strengths observed from the
results in Table 2 and Figure 4. Table 3 shows the average peak normalized load (kN/cm),
average tensile strength (MPa), and standard deviation of tensile strength data points of the
Brazilian disc samples of each rock type, and how the foliation affected these averages.
However, for these values, the “lower limit” values were not included in the averages. For
0
2
4
6
8
10
12
14
0 20 40 60 80
Ten
sile
Str
engt
h (
MP
a)
Axial Load to Foliation Angle
Axial Load to Foliation Angle of Brazilian Disc Samples vs Tensile Strength (MPa)
Actual Tensile Strengths Lower Bound Tensile Strengths
14
the Poorman Schist samples, multiple samples were conducted where the foliation was
angled at 0°, 45°, and 90° to the applied load. Although only a limited number of samples
produced actual tensile strength measurements, the average tensile strength of the disc
samples increased as the angle between the axial load and the foliation increased. The
average tensile strength increased from 4.1 MPa to 8.4 MPa as the angle between the
foliation and applied load increased from 0° to 90°. Both the rhyolite and quartz samples did
not show strength anisotropy. The average tensile strength of the rhyolite samples was the
highest of the three rock types at 22.3 MPa, and the quartz vein samples were stronger than
the Poorman Schist but weaker than the rhyolite, with an average tensile strength of 10.3
MPa.
Table 3. Breakdown of average normalized load (kN/cm) for the angle between foliation
and vertical axial load for 0°, 45°, and 90°
Axial Load to
Foliation Angle -
Rock Type
# of
Successful
Samples
Avg. Peak
Normalized
Load (kN/cm)
Avg. Tensile
Strength (MPa)
Std. Dev.
(MPa)
0° - Poorman Schist 5 1.9 4.1 0.9
45° - Poorman Schist 0 N/A N/A N/A
90° - Poorman Schist 1 3.8 7.6 N/A
N/A - Rhyolite 4 10.0 22.3 2.1
N/A -Quartz 3 4.3 10.3 5.0
15
Discussion - Brazilian Disc Test
The Brazilian disc test and its calculated indirect measurement of tensile strength is
important because the failure point during hydrofracturing tests is directly affected by the
tensile strength of the rock in the borehole. The minimum tangential stress around a vertical
borehole is given by:
𝜎𝜃𝜃𝑚𝑖𝑛 = 3𝑆ℎ𝑚𝑖𝑛 − 𝑆𝐻𝑚𝑎𝑥 − 2𝑃0 − ∆𝑃 (𝟐)
Where Shmin is the minimum horizontal stress, SHmax is the maximum horizontal stress,
P0 is the pore pressure (which is ~zero at the 4850L), ∆P is the difference between the
injected fluid pressure in the borehole and the formation pore pressure (Zoback, 2007). Note
that here we do not take into account the thermal stress. In a laboratory triaxial setting which
we conduct our hydraulic fracturing tests under, the equation can be simplified to the
Equation 3 below where Pb is the minimum pressure needed to create a vertical fracture in the
borehole, PC is confining pressure and T is tensile strength:
𝑃𝑏 = 2𝑃𝐶 + 𝑇 (𝟑)
The Laboratory results showed the apparent Brazilian disc tensile strengths ranged
between 3-8.5 MPa when samples were loaded foliation-parallel, whereas the strengths were
about 8 MPa for the one successful sample loaded foliation-normal. Comparing these results
to Pariseau (1985) tensile strength results, both are in a similar range of tensile strength
values. Pariseau (1985) cited two sets of anisotropic rock property data, an original data set
and a modified rock property data set. The tensile results in this report are closer to
Pariseau’s (1985) original data set, which produced tensile measurements in three orthogonal
directions with values of 11.9 MPa, 6.9 MPa, and 14.0 MPa. Their modified data set
produced tensile measurements in three orthogonal directions of 20.6 MPa, 5.7 MPa, and
16
13.2 MPa, which are slightly higher than our tensile results on average compared to their
original data set. RESPEC (2010) also conducted tensile strength tests, but these were
conducted on the Yates amphibolite and the rhyolite rock. The mean tensile strength for 13
rhyolite samples RESPEC tested was 10 MPa, while our 4 rhyolite disc samples averaged
22.3 MPa for tensile strength. This shows a clear discrepancy between previous RESPEC
(2010) rhyolite tensile strength results and this reports results.
The data of the tensile strengths associated with their foliation direction compared to
the axial load clearly indicate tensile strength anisotropy in the Poorman schist rocks. The
best supporting argument for this is looking at all of the apparent tensile strength (MPa)
measurements, including the samples which produced tensile fractures as well as shear
failure. For samples with a 0° between the vertical axial load and the foliation plane is 4.1
MPa, for 45° samples there was an average tensile strength of 6.4 MPa, and for 90° samples
there was an average tensile strength of 8.4 MPa. This clear increase in average tensile
strength as the angle between the vertical axial load and the foliation of the sample increases
indicates strong strength anisotropy in the Poorman schist.
Previous tensile strength tests on foliated rocks have also been conducted using
uniaxial direct tensile measurement techniques. These results can show possible similarities
or differences between Brazilian testing and direct testing results. Youash (1966) tested well
bedded and laminated sandstones, shales, and gneiss samples while altering the direction of
loading to the foliation angle in his direct tensile strength tests. Youash found that samples
tested with an angle between 0°-30° from the loading direction and foliation fractured across
the foliation and had the highest tensile strengths, and samples tested with angles between
45°-90° between the loading direction and foliation fractured along planes of weakness, and
17
had lower tensile strength values (Youash, 1966). These results are shown in Figure 5, and
agree with the general trend of tensile strength anisotropy of our results from the Homestake
Mine samples. However, the one difference which must be taken into account when viewing
the data sets is that our samples were tested using the Brazilian disc method which causes
tensile failure under compressional forces, rather than direct tension. So, the data will look
flipped between the two data sets, but the same tensile strength anisotropy is apparent.
Figure 5. Anisotropy of Ultimate Strength in Uniaxial Direct-Pull Tension of
Lyons Laminated Sandstone. T is the tensile strength (MPa) and is the Angle
Between the Loading Direction and the Samples Foliation from (Kwaśniewski, 2009;
original data from Youash, 1966)
Olsen (1967) also conducted a similar direct tensile strength test on Morrow Point (II)
mica schist. Olsen varied the angle between the loading direction and the foliation of the rock
18
from 15°-65°, and similar trend in tensile strength anisotropy was consistent with our data
and Youash’s (1966) data. As Olsen increased the angle between the loading direction and
the foliation of the sample, the apparent tensile strength of the samples decreased. This is
shown in Figure 6.
Figure 6. Anisotropy of Ultimate Strength in Uniaxial Direct-Pull Tension of
Morrow Point mica schist. T is the tensile strength (MPa) and is the Angle Between
the Loading Direction and the Samples Foliation from (Kwaśniewski, 2009; original data
from Olsen, 1967)
19
2.2 Triaxial Dynamic Moduli Test
Methods – Triaxial Dynamic Moduli test
The second laboratory test conducted was the triaxial tests to obtain dynamic moduli.
The cores retrieved from the kISMET project, as well as the DUSEL project, show intense
folding and microfolding within its foliation. Ideally, dynamic elastic properties should be
measured at various loading directions against the foliation plane, but the small core diameter
and intense variability of the rock texture posed difficulty in producing multiple triaxial
samples from similar depths with consistent rock texture. Therefore, the focus in preparation
of this test was to obtain a pair of 2.54 cm diameter cylindrical cores from adjacent portions
of the core with perpendicular foliation to one another.
Similar to the initial step in producing the Brazilian disc samples, coring
perpendicular to the axis of the NQ2 (50.5 mm or 1.99 in. diameter) core was used to obtain
some of the triaxial samples. To obtain sets of samples with perpendicular foliation to one
another, other samples were often cored axially to obtain cores in the opposite orientation.
Four pairs of cylindrical samples were obtained after coring from the original NQ2 sized
cores. For each pair of cylindrical samples from the same depth, the axis of the cylindrical
sample was either parallel or normal to the foliation. We refer to the former as a vertical (V)
foliation samples, and the latter as a horizontal (H) foliation samples in the tables and figures
of this report. Once coring of these samples was completed, ends of the cylindrical cores
were ground using a surface grinder to produce parallel surfaces, necessary for the triaxial
tests and subsequent uniaxial testing.
20
Same as for the Brazilian disc test, the GCTS RTR-1000 Triaxial Testing System was
used for the triaxial testing. The test began with an initial pressurization of the confining
pressure to 21 MPa, which is representative of the in-situ minimum horizontal stress
measured at the 4850’ level of the Homestake Mine (Oldenburg et al., 2016). Axial
differential stress of 21 MPa was then applied, held for a three-hour creep step while
ultrasonic measurements were taken in order to obtain dynamic elastic moduli, and then the
axial differential stress was finally unloaded. Axial differential stress of 21 MPa was chosen
to match the approximate value estimated from the stress measurements (Oldenburg et al.,
2016).
Results – Triaxial Dynamic Moduli Test
Dynamic and static elastic properties were measured under triaxial stress conditions.
The average density of the Poorman schist samples was 2.75 g/cm3, which was used for
calculating dynamic moduli from the p-wave and s-wave velocity measured during the
triaxial testing. Table 3 shows the p- and s-wave velocities (in m/s). The average p-wave
velocity for the eight samples was 4772 m/s, and the average s-wave velocity for the eight
samples was 2848 m/s. The anisotropy effect was not as clearly shown in the velocity
measurements when comparing the foliation direction of the samples. The p wave velocity
average was 4672 m/s for foliation-normal samples (vertical samples), and 4847 m/s for
foliation-parallel samples (horizontal samples). The s-wave velocity average was 2860 m/s
for foliation-normal samples, and 2838 m/s for foliation-parallel samples. Using the velocity
measurements, Shear (G) and M modulus were also calculated. The average shear (G)
modulus for the eight samples was 22.5 GPa. The raw velocity data and the calculated
21
moduli are in Table 4 below. Lawrence Berkeley National Laboratory (LBNL) also produced
velocity data on cores retrieved from the kISMET field site. However, they used a different
testing technique which utilized immersion transducers to calculate ultrasonic P wave
velocity measurements in a submerged water tank environment. This data and its significance
are discussed further below in the uniaxial/triaxial discussion section.
Table 4. P-wave and S-wave velocities for triaxial samples tested, calculated
dynamic moduli, and UCS data (discussed in the next section). No velocity data were
recorded for sample 56H prior to breaking the sample. M (P-wave modulus), G (Shear),
were calculated from acquired velocity measurements.
Sampl
e
Borehol
e
Dept
h Description
p wave
velocit
y (m/s)
s wave
velocit
y (m/s)
M
Modulus(GPa
)
Shear
Modulu
s (GPa)
41V kISMET
-003 204’ Lighter
portion of
core. Intense
folding.
4962 2909 69.2 23.8
41H kISMET
-003 204’ 4470 2929 56.4 24.2
49V kISMET
-003
242.5
’
Foliation is
folding but
consistent.
Dark bands
in foliation.
4709 2747 60.6 20.6
49H kISMET
-003 242.5 4988 2896 68.0 22.9
56V kISMET
-003
279.5
’
Foliation
relatively
perpendicula
r to axis. Not
much
folding.
4495 2628 54.9 18.8
56H kISMET
-003
279.5
’ N/A N/A N/A N/A
63V kISMET
-003 313’ Foliation
relatively 4561 2603 56.8 18.5
22
63H kISMET
-003 313’
consistent.
Normal
Poorman
grayish
color.
4559 2757 55.7 20.4
Discussion – Triaxial Dynamic Moduli Test
The triaxial portion of the test was when velocity measurements were taken to
calculate dynamic moduli on the samples. Stress-strain data were acquired when the
additional axial load was applied. These data are stored in the GCTS RTR-1000 machine and
could be interpreted for static modulus. The velocity measurements did not show as clear of
an anisotropic effect as the UCS rock strength data. The average P-wave velocity for
foliation-parallel samples was 4682 m/s, while the average P-wave velocity for foliation-
normal samples was 4672 m/s. The P-wave velocity measurements for foliation-parallel
samples ranged 467.35 m/s, while the foliation-normal samples ranged 517.46 m/s. The S-
wave velocities were also quite similar in magnitude, with foliation-parallel samples
producing an average S-wave velocity of 2722 m/s, and foliation-normal samples producing
an average S-wave velocity of 2860 m/s. The range for S-wave velocities for foliation-
parallel samples was 305.5 m/s, while foliation-perpendicular samples was 172.3 m/s.
Lawrence Berkeley National Laboratory (LBNL) also conducted velocity
measurements on cores retrieved from the kISMET site (Oldenburg et al., 2016). Differing
form our velocity measurements, clear anisotropy was seen in the data produced by LBNL.
Figure 7 produced by LBNL shows the velocity measurements of two core types, long core
and short core, tested for velocity around the circumference of the samples, and along the
length of the samples. Both show clear anisotropy in that the velocity measurements are not
23
constant around and along the samples. However, this anisotropy which is not apparent in our
data set could be due to the confining pressure applied during our testing. Our samples were
under 21 MPa confining pressure within a triaxial set up while velocity measurements were
recorded, and LBNL’s samples were tested immersed in a water bath with no confining
pressure. With confining pressure, foliation planes may close, and thus diminish the
anisotropic effect that may be prevalent in an unconfined situation.
Figure 7. Seismic P-wave velocity measurements taken (a) around the circumference of
samples and (b) along the length of samples from the kISMET field site. Velocity
anisotropy is apparent for the entire length of the cores from (Oldenburg et al., 2016)
Due to low contrast between the velocity measurements for foliation-parallel and
foliation-perpendicular samples, calculated shear modulus (G) results were similar between
both types of foliated samples. Preliminary full waveform sonic logs with calculated dynamic
elastic constants were produced during the kISMET field work, and presented in the
24
“kISMET Field Work Results” portion of this report. The field results produced P wave
velocities ranging from around 4500 m/s to 5500 m/s, and S wave velocities ranging from
around 2750 m/s to about 3375 m/s (Oldenburg et al., 2016). Our results for both P-wave and
S-wave velocities fall into a similar range of values, thus showing consistency between the
two velocity data sets for field and lab data.
2.3 Uniaxial Moduli and Unconfined Compressive Strength (UCS) Test
Methods – Uniaxial Moduli and Unconfined Compressive Strength (UCS) Test
The same samples used for the triaxial test to measure the dynamic moduli were also
used for the uniaxial static moduli as well as the UCS test. This was done because in one test
using the triaxial set up, the sample could undergo the triaxial conditions and have the
velocity measurements recorded, and then all the pressures applied to the sample could be
released, and the axial stress could be increased until sample failure. This second “step” in
the test run was the Uniaxial static moduli and UCS test.
Following the triaxial test, the sample had no confining pressure or axial pressure
applied to the sample. With this unconfined stress state, UCS was then measured by applying
axial load with no confining pressure until rock failure. While the axial load was increased,
strain gauges which were applied to all the samples recorded strain data which then produced
stress strain curves below in Figure 8. The final step in the uniaxial test was loading until
sample failure occurred, and this is the data used for our UCS measurements.
25
Results - Uniaxial Moduli and Unconfined Compressive Strength (UCS) Test
For the strength of the samples, unconfined compressive strength tests were
conducted on all eight triaxial samples after the ultrasonic velocities were measured at
triaxial stress conditions. Table 5 shows the maximum stress each sample endured prior to
failure. These values are thus the UCS of each of the eight samples. The average UCS of the
eight samples of the Poorman schist was 96.4 MPa. The anisotropy effect on the strength of
the samples was also obtained by comparing the strength of the samples with different
foliation directions. The average UCS for foliation-parallel vertical samples was 107 MPa,
and the average UCS for foliation-normal horizontal samples was 88.1 MPa. These data are
shown in Table 6. In general, the samples with foliation parallel to the sample axis had a
higher average UCS than the samples with foliation normal to the sample axis.
Table 5. All uniaxial samples with UCS values along with descriptions
Sample
Borehole
Depth
Description
UCS
(MPa)
41V
kISMET-
003
204’ Lighter portion
of core. Intense
folding.
89.5
41H
kISMET-
003
204’
94.0
49V
kISMET-
003
242.5’ Foliation is
folding but
consistent. Dark
bands in
foliation.
88.5
49H
kISMET-
003
242.5
89.8
26
56V
kISMET-
003
279.5’ Foliation
relatively
perpendicular to
axis. Not much
folding.
121.9
56H
kISMET-
003
279.5’
69.9
63V
kISMET-
003
313’ Foliation
relatively
consistent.
Normal
Poorman
grayish color.
110.7
63H
kISMET-
003
313’
98.6
Table 6. Average UCS for samples of perpendicular foliation. “V” Samples have
foliation-parallel to cylindrical sample axis. “H” Samples have foliation-normal to the
cylindrical sample axis.
Foliation of Sample Avg. UCS (MPa)
"V" samples 107.4
"H" samples 88.1
Young’s modulus and Poisson’s ratio were also calculated for the samples under
uniaxial conditions. The stress (MPa) vs strain (E) curves for the samples (Figure 8 below)
were used to make these calculations. Results of these calculations are presented in Table 7
below. The average Young’s Modulus for the eight samples was 58.0 MPa, and the average
Poisson’s ratio was 0.22. Anisotropy seemed to have an effect on the Young’s modulus of
the samples, but not as much on the Poisson’s ratio. The average Young’s modulus for
foliation-normal horizontal samples was 52.3 MPa, while the average for foliation-parallel
vertical samples was 63.4 MPa. The average Poisson’s ratio of foliation-normal horizontal
27
samples was 0.22, and that of foliation-parallel vertical samples was 0.22. The difference in
Young’s Modulus for the different foliation angles was a 18% difference, while the Poisson’s
ratio was only 2.7%, a significantly smaller difference.
Table 7. Calculated Young’s Modulus and Poisson’s Ratio for all eight triaxial samples.
Both calculated using stress vs strain curves provided in Figure X (the stress strain
curves).
Sample Young's Modulus
(GPa)
Poisson's
Ratio
41V 87.2 0.20
41H 45.1 0.28
49V 57.0 0.22
49H 60.1 0.21
56V 53.1 0.20
56H 56.0 N/A
63V 57.3 0.24
63H 47.9 0.18
28
29
Figure 8. Stress (MPa) vs Strain (E) curves for all eight Schist triaxial samples
tested. Note: no radial strain data was acquired for sample 56H (bottom left) prior to
bringing sample to failure during testing. Also, “depth” is depth in feet from the 4850’
level of the Homestake Mine.
Figure 8 are images of all eight samples tested under uniaxial/triaxial conditions for
this thesis. All of these pictures show the samples post-testing, so they are post-failure
samples. The top row of the samples is the “H” samples, or samples with foliation normal to
the vertical applied load for UCS tests. The bottom row is the “V” samples, of the samples
with foliation parallel to the vertical applied load for UCS tests. The rock appears shiny or
slightly saturated because they all came into contact with some amount of confining oil post-
testing. Fractures are clearly seen in all eight of the samples, however, their orientations and
lengths vary significantly.
30
Figure 9. Images of triaxial samples taken after they were brought to failure in
UCS testing. Samples with foliation normal to sample axis are on the top row, and
samples with foliation relatively parallel to sample axis are the bottom row.
Discussion – Uniaxial Moduli and Unconfined Compressive Strength (UCS) Test
The unconfined compressive strength (UCS) destructive test also indicated a certain
degree of anisotropic behavior. Strength anisotropy was shown in the UCS test data, and
static and elastic property anisotropy was shown in the triaxial portion of the test. It is also
important to note that the foliation in these pairs of samples was not perfectly perpendicular
to one another. With limited core to work with, the sample pairs in the uniaxial tests were a
best approximation for samples with foliation perpendicular to one another.
31
The rock samples tested in the UCS test produced data which were broken down to
compare samples with foliation-parallel and foliation-normal orientation to the vertical axial
load to show strength anisotropy. The average strength for the samples with foliation-parallel
to the vertical axial load was 107.4 MPa, and the average strength for the samples with
foliation-normal to the vertical axial load was 88.1 MPa. This showed that the average
strength of samples with foliation-parallel to the vertical axial load was on average almost 20
MPa higher than the triaxial samples with foliation-normal orientation. This shows clear
strength anisotropy in the eight samples which we tested for this portion of the test. However,
the range for foliation-parallel samples was 33.4 MPa and the range for foliation-normal
samples was 28.7 MPa, both quite significant. If a higher number of Poorman Schist UCS
tests were run focusing on the varying foliation between samples, it would help confirm this
significant strength anisotropy.
Figure 9 shows images of all eight samples post UCS test and fracturing. The top row
shows the foliation-normal samples, and the bottom row shows the foliation-parallel samples.
An observation on the foliation-normal samples is that fractures often were at a higher angle
(sometimes close to 45°) compared to the foliation-parallel samples, and show rough non-
planar fractures which mostly do not extend through the entire sample and to the bottom of
the samples. The foliation- normal samples seemed to chip off corners of the cylindrical
sample upon fracturing. The foliation-parallel samples (which had a higher average UCS)
tended to show failure planes which are more planar and extend through the entire length of
the samples. The foliation clearly affected the morphology of the fractures and thus also the
resulting UCS of the samples.
32
A possible source of error in our UCS data may come from the 2:1 ratio of
differential stress introduced to the samples during the creep portion of the triaxial tests. This
could have potentially damaged the samples to an extent, which could have biased the UCS
to lower values. However, the maximum horizontal stress applied to the samples during this
creep step was 42 MPa, which is less than half the average UCS of our samples. The
Poorman schist is a relatively hard rock, and believed to have been under similar in-situ
conditions before being recovered from the mine. Thus, hopefully possible weakening of the
samples did not occur before the UCS was measured.
Previous research has also conducted similar UCS testing to determine the effect of
anisotropy. Kwaśniewski (2009) conducted UCS tests on Zloty Stok crystalline mica schist.
Similar to the previously cited papers who focused on direct tension tests, Kwaśniewski also
altered the angle between the direct compressional load of the UCS test and the foliation of
cylindrical triaxial samples. Kwaśniewski altered the angle between the load and foliation of
the sample between 0°-90° by 15° increments. What he found was the highest UCS values
when the foliation of the cylindrical samples were 0° from the compressional load (or the
foliation was parallel to the load direction), then the UCS values decreased to a certain angle
(about 30° for his data) and then increased again to 90°, creating a parabolic curve. This
curve for mean UCS values at differing angles between the load and foliation is shown below
in Figure 10.
33
Figure 10. Anisotropy of Unconfined Compressive Strength (C of Zloty Stok schist as
, the angle between the axial load and samples foliation, is altered between 0°-90° from
(Kwaśniewski, 2009)
However, the average UCS at 90° was about 57 MPa lower than at 0° for this data set.
This ratio of samples with an angle of 90° between the axial load and sample foliation and
samples with an angle of 0° between the axial load and sample foliation was 0.66 (111.4
MPa/168.6 MPa). Due to constraints on cores used for testing and the intense folding within
those cores, we were only able to test samples on the two extremes of 0° between loading
direction and foliation and 90° between loading direction and foliation. Because of this we
cannot confirm that our samples acted in the same parabolic UCS curve with varying the
angle between axial load and foliation, but we can confirm that samples with 0° between
axial load and foliation had a higher average UCS than samples with 90° between axial load
34
and foliation. From our UCS data set, samples with 0° between the axial load and sample
foliation averaged 107.4 MPa while samples with 90° between the axial load and sample
foliation averaged 88.1 MPa. This ratio of UCS averages for the two end points is 0.82,
which is higher than Kwaśniewski (2009) results of 0.66.
Although both our data and Kwaśniewski (2009) showed greater UCS values at 0°
between the sample foliation and axial load compared to 90°, past theories predict that the
two end members of 0° and 90° in UCS tests should produce similar UCS values. Jaeger
(1960) assumed that the plane of weakness in a rock sample would have one set of values for
cohesion and internal friction, and that any other plane in the rock would have another set of
values for cohesion and internal friction. Using these assumptions and the Coulomb theory to
“calculate the resistance to failure on the plane of weakness and on the most favored plane
intersecting it, in terms of the principal stress” led to the theory that compressive strength is
dependent on orientation, and produced Figure 11 below (Paterson and Wong, 2005).
35
Figure 11. Dependence of Differential Stress (y-axis) at Shear Failure on the
Orientation of the Weakness Plane (x-axis) in a Sample of Anisotropic Rock Model from
(Paterson and Wong, 2005; Produced by Jaeger, 1960)
Using the stress-strain data plotted in Figure 8 of the uniaxial test results, Young’s
modulus and Poisson’s ratio were calculated for the triaxial samples. This stress strain data
was recorded during the uniaxial test portion of the uniaxial/triaxial test. Anisotropy was
greater in the Young’s Modulus compared to the Poisson’s ratio. The preliminary full
waveform sonic logs produced from the kISMET field work also produced Young’s Modulus
and Poisson’s ratio data for the kISMET-003 well in which our samples were recovered from
and the field stress measurements were conducted. The preliminary full waveform sonic logs
produced Young’s modulus results which ranged from about 55 GPa to 85 GPa, and
Poisson’s ratio which ranged from about 0.05 to 0.28. Our results showed an average
Young’s Modulus of 58 GPa and a range between 45 GPa and 87 GPa. This average and
range show consistency with the field moduli results. Our laboratory Poisson’s ratio results
produced an average of 0.22 and a range of values between 0.18 and 0.28, which also fall
between the Poisson ratios determined from the kISMET-003 borehole.
A key observation which supports the consistency of our data is apparent in groups 41
and 49 samples, where the sample with the larger P-wave velocity measurement (samples
41V and 49H) also had the higher Young’s Modulus result compared to the groups other
samples (41H and 49V). This same trend could have been true for sample group 56, but lack
of data made it impossible to compare. Sample group 63 produced P-wave velocity
measurements which were nearly identical, but their moduli differed, so we did not see the
36
agreement for this sample group. This general agreement between the static moduli and
dynamic moduli support the credibility of our data set. Also, the consistency and range of
Poisson’s ratio values throughout the samples is promising as well.
2.4 Laboratory Hydrofracture Test
Methods - Laboratory Hydrofracture Test
The fourth test conducted was the lab hydraulic fracturing test (Avasthi, 1981). The
primary goal of the lab hydrofracture testing was to determine if premature shear failure
along weak foliation planes affect the breakdown pressure of the Poorman formation
samples. Another goal of the testing was to document the initial hydraulic breakdown
pressure for all the samples, as well as the fracture reopening pressure, and see how these
compare with the field results.
The same NQ2 (50.8 mm or 1.99 in. diameter) recovered core was used for the lab
hydrofracture test as the Brazilian disc and triaxial test and uniaxial tests. The NQ2 diameter
core was cut with a rock saw, and although the sample lengths varied, the average
hydrofracture sample was 7.874 cm length, and 5.05 cm diameter. A total of twelve
hydrofracture samples were initially produced. The next step was to remove a smaller
diameter hole in the center of the samples, which would eventually be used to inject the
water for the testing. A 0.3175 cm coring bit was used to core out a 4.1275 cm long hole
centered in the middle of one end of the sample, as shown in Figure 12.
High pressure steel tubing pieces 5.0165 cm long and slightly smaller than 0.3175 cm
diameter were inserted into the small borehole. These tubing pieces were manufactured with
37
a groove at one end, which would be used to hold an o-ring in place to seal off the injection
zone for the hydrofracture testing. Low viscosity epoxy was also poured between the steel
tubing and the borehole to secure the o-ring and seal off the injection zone. A schematic of
the cross section of the hydrofracture sample and the high-pressure steel tubing pieces are
depicted below in Figure 12.
Figure 12. (above) Cross-section of lab hydrofracture sample and (below) detailed
description of stainless steel high-pressure tubing inserted into lab hydrofracture
samples (also seen in Figure 13 below). O-ring was attached to tubing pieces using the o-
38
ring groove, and then the tube was epoxied into the 0.3175 cm holes of the samples to
seal the hydrofracture testing zone to the high-pressure tubing in the system.
Following steps to introduce the steel tubing and epoxy into the drilled-out hole,
which included chamfering the opening of the borehole and applying some silicone grease to
allow the tubing to fit, the epoxy was poured and settled, and the tubing was now attached
into the hole and the injection zone was sealed off. The remaining tubing sticking out of the
sample would be inserted into the sample holder platen where it is sealed off with another o-
ring.
Figure 13. Schematic of lab hydrofracture set up. Not depicted to scale, but dimensions
of hydrofracture sample and tubing detailed.
39
The lab hydrofracture test was again conducted in the GCTS RTR-1000 Triaxial
Testing System. The lab hydrofracture testing set up included a ISCO 100DM syringe pump
to supply the constant water flow for the testing, a vacuum to eliminate any air bubbles in the
high-pressure tubing setup. A schematic of the lab hydrofracture set up is depicted above in
Figure 13.
Specialty platens were made for the lab hydrofracture testing. The platens were 5.08
cm in diameter, slightly larger than the 5.08 cm diameter samples. The bottom platen was
manufactured with an injection hole on the side to carry the high-pressure water to the
sample (seen in Figure 13). The base of the platen, or the portion of the bottom platen where
the sample is placed on, is equipped with a 0.3175 cm hole and another o-ring, used to seal
off the other end of the high-pressure tubing which was epoxied into the samples. With this
set up complete, making sure all connections were sufficiently tightened for high-pressures,
the samples were then ready to be tested.
The tests were run in a triaxial testing set up to be able to replicate the in-situ
conditions of the samples. The first step of the lab hydrofracture testing was to increase the
confining pressure to 22 MPa. This value was chosen because it was representative of the
minimum horizontal stress near the 4850’ level of the Homestake mine (Oldenburg et al.,
2016). The next step was to increase the axial load to a desired force. This desired force was
then converted into additional pressure applied axially to the sample, and was deemed as the
axial stress on the sample. This pressure was varied, to conduct different samples under
different in-situ conditions. The reason for this was to see if there was any correlation in
varying the axial stress and the samples breakdown pressures.
40
Before all test runs, to eliminate any air bubbles in the high-pressure tubing and to
ensure the testing zone was filled purely with water, the pore pressure lines were vacuumed.
Once the high-pressure tubing system was vacuumed and the desired in-situ conditions for a
given sample were met within the triaxial testing system, the ISCO syringe pump was
operated and monitored for pressure to determine sample breakdown pressures. For all tests,
the pump was run at a constant flow rate of 0.5 mL/min. The LabVIEW software produced a
plot showing the increasing hydraulic pressure in the system with increasing time as the flow
rate stayed constant. Using this real-time plot, it helped decipher when the sample fractured
due to the significant drop in pressure in the system. Upon initial breakdown and obtaining
the peak breakdown pressure for the sample, the fluid pressure was released to complete the
first injection cycle, and then multiple injection cycles were performed using the same flow
rate to observe the fracture re-opening pressure.
Results - Laboratory Hydrofracture Test
Of the 13 prepared hydrofracture samples, 7 of them produced results which were
acceptable. The samples which were not considered acceptable were altered by unstable axial
load controls as well as leakage in the injection fluid. Similar to both the Brazilian and
uniaxial/triaxial tests, the hydrofracture samples were grouped together depending on what
depth in the core they were recovered from. In the title of all of the hydrofracture plots, an
initial number indicates what core run the sample was taken from. The subscript numbers and
letters in the sample names were solely for naming purposes when handling the cores. The
axial stress the samples were tested under are in parentheses for all samples. The pressure
(MPa) vs time (s) plots for all 7 successful test runs are shown below.
41
0
10
20
30
40
50
60
0 50 100 150 200 250
Pre
ssu
re, M
Pa
Time (s)
64-E (Max. Principal Stress 27 MPa)
Test Zone
0
10
20
30
40
50
60
0 500 1000 1500 2000 2500 3000 3500
Pre
ssu
re,
MP
a
Time (s)
Sample 64-C (Max. Principal Stress 44 MPa)
TestZone
42
0
10
20
30
40
50
60
0 200 400 600 800 1000
Pre
ssu
re,
MP
a
Time (s)
53-C (Max. Principal Stress 23 MPa)
Test Zone
0
10
20
30
40
50
60
0 200 400 600 800 1000
Pre
ssu
re,
MP
a
Time (s)
53-D (Max. Principal Stress 33 MPa)
TestZone
43
0
10
20
30
40
50
60
0 200 400 600 800
Pre
ssu
re,
MP
a
Time (s)
53-B (Max. Principal Stress 44 MPa)
TestZone
0
10
20
30
40
50
60
0 200 400 600 800 1000
Pre
ssu
re,
MP
a
Time (s)
Sample 531111-A (Max. Principal Stress 55 MPa)
TestZone
44
Figures 14-20. Pressure (MPa) vs Time (s) plots for all 7-successful lab
hydrofracture experiments. Title describes what core run the sample came from and
the axial stress on the sample during hydrofracture testing.
Although we only have 7 samples with data deemed acceptable, 5 of those samples
came from one testing group and thus all were tested with different axial stress magnitudes.
The other 2 samples were from a different core depth, and the axial stress was altered
between those two samples as well. The breakdown pressure vs axial stress plots are below in
Figures 21 and 22. In these figures, the fracture reopening pressure for these samples was
also plotted. The hydraulic breakdown pressure is plotted in blue, and the fracture reopening
pressure is in orange for both figures. The raw data for breakdown pressures and fracture
reopening pressures are below in Table 8.
0
10
20
30
40
50
60
0 200 400 600 800 1000
Pre
ssu
re,
MP
a
Time (s)
Sample 531-A (Max. Principal Stress 66 MPa)
Test Zone
45
Figure 21. Axial Stress (Max. Principal Stress) Applied to Hydraulic Fracturing
Samples vs The Breakdown Pressure of that Sample and Fracture Reopening Pressure
for Samples Recovered from Core Run 64
0
10
20
30
40
50
60
0 10 20 30 40 50
Pre
ssu
re,
MP
a
Max. Axial Stress (MPa)
Run 64 Breakdown Pressure and Fracture Reopening Pressure vs Max. Axial Stress
Max. HydraulicPressure (MPa)
FractureReopeningPressure (MPa)
Linear (Max.Hydraulic Pressure(MPa))
Linear (FractureReopeningPressure (MPa))
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
0 10 20 30 40 50 60 70
Pre
ssu
re,
MP
a
Max. Axial Stress (MPa)
Run 53 Breakdown Pressure and Fracture Reopening Pressure vs Max. Axial Stress
Max. HydraulicPressure (MPa)
Fracture ReopeningPressure (MPa)
Linear (Max.Hydraulic Pressure(MPa))
Linear (FractureReopeningPressure (MPa))
46
Figure 22. Axial Stress (Max. Principal Stress) Applied to Hydraulic Fracturing
Samples vs The Breakdown Pressure and Fracture Reopening Pressure of that Sample
for Samples Recovered from Core Run 53
Table 8. Raw data for the successful lab hydrofracture tests. All tests had a minimum
principal stress of 22 MPa, and the fracture reopening pressures are an estimate due to
multiple fracture re-openings for the tests.
Sample
Borehole
Depth
Description
Max.
Principal
Stress
(MPa)
Max.
Hydraulic
Pressure
(MPa)
Fracture
Reopening
Pressure
(MPa)
64-E
kISMET-
003
318.5’
Foliation
~20° off
vertical. No
intense
folding. 27 43.3 ~21
64-C
kISMET-
003
319’
Some
folding, but
foliation
about 10°-
20° off
vertical 44 48.5 ~27.6
Run 53-C
kISMET-
003
262.3’
Intense
microfolding.
Foliation
relatively
normal to
vertical axis. 23 47.4 ~21.5
Run 53-D
kISMET-
003
262’
Intense
microfolding.
Shiny
white/silver
areas. 33 52.9 ~23.5
47
Run 53-B
kISMET-
003
262.6’
Intense
microfolding.
Foliations
goes from
horizontal to
vertical
44 34.8 ~22.7
Run 531111-A
kISMET-
003
263.3’
Not as clear
foliation.
Foliation
dips ~10°-
40° 55 58.4 ~22.2
Run 531-A
kISMET-
003
264’
Not as clear
foliation.
Foliation
dips ~10°-
40° 66 50.0 ~21.9
Discussion - Laboratory Hydrofracture Test
The laboratory hydrofracture experiment was on a different scale than the field
hydrofracturing test, so comparing results of the two tests is not entirely possible. With the
relatively small hydrofracture samples which were produced due to limited core size, the goal
was to maximize the difference between the borehole diameter and the sample diameter to
have the confining pressure act as far field stress. We were still able to create a test where an
interval of the rock was isolated and allowed for the buildup of hydraulic pressure to induce
fracturing. In this environment, it provided the capability to differ the stresses on the samples
to see if this had any effect on the samples.
The average hydraulic breakdown pressure for the 2 core-run 64 samples was 45.9
MPa, with the sample tested under 27 MPa axial stress having a breakdown pressure of 43.3
MPa, and the other sample tested under 44 MPa axial stress having a breakdown pressure of
48.5 MPa. There is a trend of increasing hydraulic breakdown pressure with increasing axial
48
stress here, but with a small sample size of only two samples it is difficult to conclude that
this is a general trend.
The average hydraulic breakdown pressure for the five core run 53 samples was 48.7.
These five samples with varying axial stresses resulted in hydraulic breakdown pressures of
47.4 MPa, 52.9 MPa, 34.8 MPa, 58.4 MPa, and 50.0 MPa in the increasing order of axial
stress magnitudes. There does not seem to be a clear trend in the breakdown pressure against
axial stress, however, a linear fit to the data does show a slightly positive slope, meaning the
average breakdown pressure may possibly be increasing with increasing axial load.
As for the fracture reopening pressures, for both group of samples from core run 64
and 53, no clear trend with increasing axial stress is observed and all values are close to 22
MPa, which is the confining pressure used for all samples tested. In general, from these
observations, we see that there is no strong dependence of the breakdown and reopening
pressures with the axial stress applied on these samples.
As stated previously in equation 3, the expected breakdown pressure at the borehole
wall in a laboratory triaxial is Pb=2PC+T. This is a simplification of the equation for
breakdown pressure in the field (Pb=3Shmin-SHMax+T) because Shmin and SHMax are equal to
one another in a triaxial set up, due to the confining pressure being equal in all directions
besides the vertical axial load. Using the equation for breakdown pressure in the borehole for
a laboratory setting, we expected to see a range of breakdown pressures between 47 MPa and
56 MPa. The confining pressure used for all the lab hydraulic fracturing tests was 22 MPa, so
that is PC, and we know tensile strength (T) ranged between 3 MPa to 12 MPa from our
Brazilian disc results. Plugging these values in is how the expected range of breakdown
49
pressures is calculated. Below in Figure 23 it shows the expected range of breakdown
pressures (47-56 MPa) as a red box for the core run 53 sample group. This shows that four of
the five samples fall into the expected range or are very close, while one sample is a clear
outlier and shows a much lower breakdown pressure.
Figure 23. Reproduced with Expected Breakdown Pressures (Pb) shown as Overlaid
Red Box.
The clear outlier of the core run 53 samples was sample 53-B with a breakdown
pressure of about 35 MPa, and was conducted under 44 MPa of axial stress. This figure is
presented again below in Figure 24. Looking at the sample 53-B, and comparing it to the other
successful hydrofracture lab samples, it is apparent that the increase of pressure in the sample’s
test zone was non-linear. This is shown in Figure 24 by showing how the increase in pressure
in the test zone up until the breakdown pressure deviates from linearity (shown as a red line
50
here). This shows that there was a clear dissipation of pressure in the test zone prior to the
breakdown pressure. This could have been due to fluid leakage into a preexisting or shear-
induced fracture at the test zone. This shows evidence that if there is a source for premature
leak off of the test zone, then the breakdown pressure could be lowered significantly compared
to a sample that overcomes the true breakdown pressure anticipated for a completely intact
rock.
Figure 24. Sample 53-B Pressure vs Time Plot Showing Pressure Increase in Test Zone
Deviates from Linearity (Red Line) to Help Explain Outlier Breakdown Pressure Value
Back to Figure 23 (axial load vs pressure) above it is also important to note that the
fracture reopening pressures average around 22 MPa. This is shown by the orange data points
and the near horizontal trend line between all five of the fracture reopening pressure values.
0
10
20
30
40
50
60
0 200 400 600 800
Pre
ssu
re,
MP
a
Time (s)
53-B (Max. Principal Stress 44 MPa)
TestZone
51
Although the breakdown pressures mostly fell into the predicted range of values (besides the
one outlier explained above), these fracture reopening pressure are not consistent with what
we had expected from our laboratory measurements. The equation for fracture reopening
pressure should be the same as the breakdown pressure in the lab (Pb=2PC+T) but without the
tensile strength. So, our expected fracture reopening pressure would thus be 44 MPa (Pb=
2*22 MPa = 44 MPa). However, the average fracture reopening pressure is about 22 MPa,
which is equal to the confining pressure being applied to all the samples. We interpret that
the fluid pressure is reopening the fracture that has propagated beyond the stress
concentration produced around the borehole, thus equation (3) is not valid in this case to
predict the fracture reopening pressure.
Studying the hydrofracture orientations, and how the fractures form and propagate
from the borehole is also imperative in interpreting the laboratory and field hydrofracture
experiments. Although we have not successfully image the fractures from the laboratory
samples, we did see other aspects of our results which may indicate how the Poorman schist
altered hydrofracture results. The tensile strength anisotropy which we clearly saw from the
Brazilian disc test is the main indicator from our results that the hydrofracture orientations
may have been altered due to the rock properties and local foliation. Similar to Figure 3 (two
samples with actual and lower bound tensile strength), which saw evidence that certain
samples seemed break at pressures lower than the pressure necessary to cause a true tensile
fracture vertically down the sample, the laboratory and field hydrofractures also may have
formed before overcoming the pressure needed to form a vertical hydraulic fracture which
had to overcome the true tensile strength contributing toward the breakdown pressure. This
52
would suggest that hydrofractures may have formed along a weak plane, thus showing a
lower apparent breakdown pressure.
Contributing factors which may indicate that hydraulic fractures formed prematurely
is that the foliation is not consistent throughout our core of Poorman schist. With the foliation
changing drastically throughout the core, it is difficult to determine how the fracture formed
relative to the foliation. The hydrofracture is supposed to form in the direction of SHMax and
perpendicular to the Shmin, but if the local foliation alters this and the hydrofracture forms
along a weak plane, then the fracture may not form perfectly in this orientation.
3. Conclusions and Future Work
Past laboratory research had been conducted on cores recovered from multiple
locations of the Homestake mine. However, the cores tested for this thesis were recovered
directly from the kISMET field site, and thus support rationalizing the field results. All three
of the laboratory tests presented in this report were chosen to acquire specific rock property
data to compare with past laboratory data and the field data to see similarities or
discrepancies. The updated and spatially relevant rock property data in this thesis may be
used for future research that may take place at the kISMET site location.
One of the main conclusions from our laboratory work was clear strength anisotropy
from both tensile and UCS strength. Brazilian disc data showed that as the samples were
rotated from foliation parallel to the axial load to foliation normal to the axial load, the
apparent tensile strength of the samples increased. For UCS, samples with foliation parallel
to the axial load had a significantly higher average strength than foliation normal to the axial
53
load. More samples for both tests would certainly increase our understanding of how strong
these anisotropic effects actually are. Future work for both the Brazilian and UCS test would
include samples tested at more foliation angles than in our testing. For example, for the UCS
test, it would be beneficial to test samples with foliation between foliation parallel and
foliation normal.
The Brazilian disc and UCS test also showed evidence that the strength anisotropy
affected the orientation of the failure planes. As pointed out for the Brazilian disc test, many
of the samples seemed to fracture at weak planes which were not vertical, tensile fractures.
These premature fractures were assumed to break at a lower load than they would have if it
fractured vertically in the middle of the disc sample. These weak planes in the sample thus
affected the apparent tensile strength of samples. Similar to the tensile strength, the UCS
samples of different orientation also fractured differently. Foliation parallel samples
produced planar fractures which extended through the ends of the samples, while most of the
foliation perpendicular samples seemed to chip or fracture at a weak plane. The results from
the Brazilian disc test and the uniaxial and triaxial tests which did not show a strong
anisotropic effect was the elastic and dynamic moduli. Other studies conducted on the
Poorman schist by Lawrence Berkeley National Laboratory showed stronger anisotropic
effect
Our hydrofracture results show the local stress state may not affect the breakdown
pressure all that much. As we saw in our results, as we altered the axial stress on the samples
drastically, the breakdown pressure remained quite constant. This may mean that a factor as
to why the samples breakdown when they do may be controlled more by local foliation or
54
other intrinsic qualities. Again, future research may be able to delve into this and hone in on
the mechanisms that truly control the hydraulic fracturing breakdown during these tests.
More work needs to be done on the hydrofracture samples in the future to determine a
greater understanding of how these samples fractured, and why certain samples may have a
higher breakdown pressure than others. Determining whether the breakdown was occurring
due to pure tensile fracturing, or a possible mix of shearing as well may indicate how the
fractures formed in the stress measurement field tests as well. To do this, future work would
include imaging the fractures. CT scans were attempted on the hydrofracture samples, but did
not result in successful imaging of the fractures. Other methods that could be used to image
the fractures could be scanning electron microscopy or injecting fluorescent epoxy into the
sample.
Another possibility for future work could be testing the size effect of the samples.
With larger Poorman schist samples, and a different hydrofracture test set up to
accommodate the larger sample. The purpose of testing larger samples would be to see if the
results are altered, and determine if there is any size effect on the testing. An example of how
size effect may affect the results is a larger sample is more likely to have natural fractures,
and thus could decrease the average breakdown pressures of the larger samples. This could
help determine how to interpret our results from this thesis.
55
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Engineering, Volume 3, Rock Testing and Site Characterization, Eds. J.A. Hudson,
1993, pp. 329–394.
Youash, Y.Y. “Experimental Deformation of Layered Rocks.” Houston Geological Soc.
Bull., vol. 8, no. 10, 1966, p. 24.
Zoback, M.D. “Reservoir Geomechanics” Cambridge University Press, 2007.
Appendix
Homestake Mine (Lead, SD) Geology and Previous Lab Data
General Geology
59
The Homestake Mine, located in the northern portion of the Black Hills, South
Dakota, is a part of a Precambrian core complex associated with an elongate domal Laramide
orogenic uplift structure that is 100 km long and 60 km wide. The region has undergone
multiple deformation events as well as continued uplift and erosion of bedrock materials
(Lachel Felice, 2009). The core complex is primarily metamorphosed greenschist or upper
amphibolite facies (Caddey et al., 1991). The metamorphosed portions of the region are
interpreted to be greater than 1.84 billion years old (ARUP, 2015). The Homestake Mine is
composed primarily of three different rock types. Oldest to youngest, these are the Poorman,
Homestake, and Ellison Formations. The gold mineralization, which was what the
Homestake Mine produced when active, occurred solely in the iron-rich Homestake
Formation. The rock formations in the Homestake are intruded by rhyolite and phonolite
dikes, which are dated to be around 53 million years old.
Figure 25 below shows a bird’s eye geologic map of the Homestake Mine and
surrounding regions. Detailed in red on the figure is a bird’s eye perspective of a cross-
sectional line which runs from arbitrary point A to point A’. The cross section of this red
cross-sectional line is depicted in Figure 26 below. The red line is depicted along the 4850’
level of the Homestake Mine in Figure 26, which is where the field work took place. Figure
27 is a view of the 4850’ level, with labeled names of locations on level, as well as overlaid
blue dashes showing the general foliation in areas, as well as red dashes which show rhyolite
dike locations. Figure 27 also shows where the DUSEL holes were drilled along the level, as
well as where the kISMET field work took place.
60
Figure 25. Map View of Cross Section A to A’ (red line) which is shown in cross
sectional view in Figure 2 From (ARUP, 2015)
61
Figure 26. Cross sectional view and formations of the Homestake mine. 4850L
represented by solid red line. From (Denver Region Exploration Geologists’ Society)
62
Figure 27. General Geology Overview of 4850L. Blue Dashes are General Foliation
Orientation and Red Dashes are Rhyolite Dikes. From (Golder Associates Final, 2010a)
Poorman Formation (Schist)
The upper member of the Poorman is made up of metasediments. The planned
locations for both the physics laboratories at the Homestake Mine and the kISMET location
are within these metasediments, referred to as the Poorman Formation Schist (ARUP, 2015).
63
The Poorman Schist’s protoliths include thinly bedded, carbonate-rich siltstones and
claystones, marl, iron formations, and dolomite. It is often described physically as dark grey
banded and laminated, micacious phyllite to schist, and mineralogically as carbonate-rich
with muscovite, biotite, pyrrhotite, graphite and garnet. The four, distinct rock lithologies, in
decreasing abundance, found in or intruding into the Poorman Formation Schist are Sericite
carbonate quartz schist, Graphitic Schist, Rhyolite, and Biotite quartz carbonate schist. Due
to their sedimentary source, the contacts among these lithologies are often gradational,
although the contacts between the rhyolite dikes and the Poorman formation are very abrupt
with little contact metamorphism and alteration (ARUP, 2015). The Poorman Formation is
described in geologic maps along the drifts of the 4850 level as both phyllite and schist. The
Poorman is said to have distinctive banding along the 4850 level, with band widths varying
from 1 to 5 cm thick. Beds of the Poorman Formation can contain “coarse-grained biotite,
with or without garnet, and varying portions of pyrrhotite” and “massive quartz bands with
pyrrhotite are common”. The Poorman is often folded on all scales due to the preservation of
multiple periods of deformation in this region (Lisenbee and Terry, 2009). The kISMET field
hydraulic fracturing stress measurement testing took place within the Poorman (schist)
Formation, and a majority of the laboratory experiments were conducted on the Poorman
cores recovered from the well where the hydrofracturing experiment took place. These
results are summarized in the field measurement and laboratory experiment sections of this
report.
Yates Unit (Amphibolite)
Both the lower (Yates unit) and upper members of the Poorman Formation are
present at the 4850’ level. The lower Yates unit consists of pillow basalts, which have been
64
metamorphosed into amphibolites with interbedded metasediments, or sedimentary rock that
has been altered by metamorphism. The Yates Unit is described as dark green, fine- to
medium-grained hornblende plagioclase schist and varies in thickness between 600 to 1,200
meters (Bachman and Caddey, 1990). The amphibolite Yates has strong compositional
layering and is fine grained (Lisenbee and Terry, 2009) and is commonly populated with
white calcite veins typically between 2 millimeters and 2 centimeters wide, and is noted to
have conformable contacts and interbeds (Bachman and Caddey, 1990). In summary, the
Yates Unit is described as “metamorphosed tholeiitic basalt with possible back-arc basin
affinities based in part of the structures that have been interpreted as relic pillows and
conformable overlying metasediments with an overall fine-grained character” (Campbell,
2004). Although the kISMET field work did not take place in the Yates Unit amphibolite,
this information may be pertinent to future research in the Homestake Mine and the 4850’
level.
Rhyolite Dikes
Rhyolite dikes have been mapped in both the Yates Unit and Poorman Formations at
the 4850L (Lachel Felice, 2009]. Their apparent widths vary from 2 to 115 feet. Along the
4850L drifts the dikes tended to strike north-northeast dipping to the east or to strike
northwest dipping steeply to the north. With certain measurement limitations, the rhyolite
dike swarm is believed to be 750 feet wide. Contacts between the rhyolite dikes and the
Yates Unit and Poorman Formation are sharp and clear, however the curvature of the
contacts is often undulating. Due to the undulating contacts, projecting the rhyolite pathways
through the formations is difficult.
65
Structural Geology
Contact Relationships
The Yates unit (amphibolite) contact with the Poorman Formation is exposed in four
separate drifts on the 4100 and 4850 level of the Homestake Mine. The contact zone of the
Yates with the Poorman is a “zone of broken rock” (Lisenbee and Terry, 2009). The contact
between the Yates unit and the rhyolite dikes are annealed, seen on the 4100 level of the
mine (expecting the contact to be similar on the 4850 level). A few inches of recrystallization
are often seen extending into the Yates amphibolite and the outer margins of the rhyolite
dikes are extremely fine-grained (porcelain-like). The contact between the Yates unit and the
rhyolite dike is undulatory, ranging from centimeters to the strike length of the dike. The
contacts seen between the Poorman (schist) formation and the rhyolite dikes are similar to the
contacts seen between the Yates unit and the rhyolite dikes (Lisenbee and Terry, 2009).
Folding
Geologic mapping has produced evidence of a series of synclines and anticlines in the
region (Lachel Felice, 2009). Folding and deformation can be seen both at small scales down
to inches, and also at larger regional scales. Due to multiple events of deformation in this
region, the structural folding is quite complex, potentially contributing to the complication of
stress measurement testing in this region.
The lead anticline plunges to the south-southwest and its axial trace is located 100-
200 feet west of the Yates shaft and bisects the 4850L. The Yates Shaft and Davis Campus of
the mine lay on the east limb of the fold (Lisenbee and Terry, 2009). According to Lachel
Felice’s 2009 mapping of the 4850 level, the fold axis is believed to be in the Exhaust Drift.
66
The Yates amphibolite is folded on several smaller scales in addition to the major anticline
fold (Golder Associates Final, 2010a). These smaller scale folds ranged from inches to feet
with plunges of 15°-30° to the East-southeast. The Yates amphibolite has much larger
wavelengths within its folding compared to the Poorman Formation (Golder Associates,
2010a).
Faulting
Faults along the 4850L were characterized by offsets across foliations and quartz veins
(Lachel Felice, 2009). Vertical offset of the faults found is often small (order of inches to
feet), and sometimes found to have graphitic inclusions. These graphitic inclusions could
promote weak shear zones, which could amplify the faults effect on local structural stability.
Rock in the region, which had been altered due to shearing displayed lower rock strength
than the surrounding host rock (ARUP, 2015). For the most part, the faults have evidence of
healed contacts with little or no shear zone along contact (Lachel Felice, 2009).
Fractures and Jointing
Discontinuities are an important aspect of the geology of the region around 4850L of
the Homestake Mine due to their effect on rock mass geomechanical properties such as
strength, deformability, and anisotropy, all of which are important for the stability of the
cavern (Lachel Felice, 2009). Lachel Felice (2009) report 1,495 data points collected during
the mapping of the 4850 Level (See Appendix A in Lachel Felice (2009) for full data set) and
three dominant fracture sets plus one random fracture set were identified. Different studies
have assessed the jointing, fracture networks, and faulting in the region for their effect on
different rock properties that are detailed in this paper. The range found for spacing between
discontinuities along the 4850L was less than 1 inch to roughly 3 feet.
67
Mine Water Level
The water level of the mine has fluctuated over time. Flooding of the Homestake
Mine first began in 2003 after gold production had previously ceased at the mine. Pumping to
maintain the water level was initiated when it reached 5,000 ft. depth and a maximum water
level of roughly 4,500 ft. was reached before levels started to decrease. The pumping then
maintained the water level at 5,700 ft. This water fluctuation is significant because water
levels did exceed the 4850L of the kISMET project. However, the existence of abundant
space and drifts along the 4850L of the mine, modern underground campuses along the
4850L, and sufficient distance from the water level and the physics experiments (over 1,000
ft. away from physics experiments), made the 4850L an ideal location for hydraulic
fracturing experiments in a mine (Oldenburg et al., 2016). The history and current condition
of the water table in the Homestake Mine is pertinent to this research project since it shows
that the pore pressure at the 4850L is zero.
Previous Unconfined Compressive Strength (UCS) and Tensile Strength
Data
Lachel Felice, 2009
UCS values for intact rock were presented in Lachel Felice (2009). Lachel Felice
(2009) notes that these UCS values are used in the absence of laboratory UCS testing of the
different rock units, and thus must not be considered direct rock measurements. The origins
of these UCS values are unclear through the sources used in this report. Appropriate values
68
for the Yates amphibolite’s rock strength ranged from 152 to 214 MPa with an average 183
MPa, the rhyolite ranged from 96.5 to 234 MPa with an average of 165.5 MPa, and in
domains that are controlled by both, the average rock strength is 172 MPa. The rock strength
values for the Poorman formation averaged 71 MPa. This is significantly less than the
strength of the Yates unit and rhyolite dikes. In transition zones of contact between the Yates
and Poorman Formation, the average rock strength used in analysis is 81.4 MPa, although the
definition of the transition zone of the Yates and Poorman formations is not clearly defined.
Table 9 below presents the UCS for rock types at the 4850L from the Lachel Felice (2009)
report, and Figure 28 shows the range of UCS values for different rock types along the
4850L.
Table 9. Average unconfined compressive strength (UCS) values for rock types at 4850
level From (Lachel Felice, 2009)
Rock Type AVG UCS (MPa) AVG UCS (psi)
Yates 182.7 26,500
Yates Contact with
Poorman
81.7 11,800
Poorman 71.0 10,300
Rhyolite 165.5 24,000
69
Figure 28. Range of UCS values for rock types at 4850L From (Lachel Felice, 2009)
Pariseau (1985)
Pariseau (1985) performed laboratory testing on drill core taken in three directions
from the Poorman, Homestake, and Ellison formation. Along with other elastic properties,
Pariseau tested for uniaxial and tensile strength in three mutually orthogonal directions in
each formation to ultimately determine the elastic and strength properties necessary to define
an orthotropic material model for each formation. Pariseau’s laboratory studies focused
solely on the Poorman formation; however, data for other formations along the 4850L and
other areas of the Homestake Mine are included for future reference. Previous knowledge on
the high degree of foliation in the Poorman formation suggests anisotropic properties within
the formation. Orthotropic models of the formations were suggested due to this high degree
of foliation in the region. To obtain data to create these orthotropic models, drill cores were
0
50
100
150
200
250
0
5,000
10,000
15,000
20,000
25,000
30,000
35,000
40,000
Yates Yates/Poorman Poorman Rhyolite
)psi
Rock Unit
Range of UCS Values at Homestake Mine [Lachel Felice, 2015]
70
taken from parallel to the down dip direction, perpendicular to the foliation and parallel to
strike, with the intention of aligning with the three principal material axes.
Table 10. Original Anisotropic Rock Property Data (*C=Compressive Strength (UCS),
T=Tensile Strength; The 1- and 3-directions are parallel to the schistosity; the 2-
direction is perpendicular to the schistosity. From (Pariseau, 1985)
Property* Poorman Formation
(psi)
Homestake
Formation (psi)
Ellison
Formation (psi)
c1 74.5 117.8 86.5
c2 60.6 79.6 78.1
c3 78.5 98.3 83.0
T1 11.9 9.5 13.6
T2 6.8 7.8 4.1
T3 14.0 8.9 11.7
The original data, shown in Table 10 above, showed significant variation in the
results. Pariseau (1985) removed outliers from the original data, combined with further
laboratory testing conducted by the University of Utah (referred to as UU in Pariseau
(1985)), to produce the modified rock strength properties shown in Table 11. These tests
were conducted on specimens from the Homestake, Poorman, and Ellison Formation’s
hoping to somewhat correct the original rock property data.
Table 11. Modified Anisotropic Rock Strength Property Data (*C=Compressive
Strength (UCS), T=Tensile Strength; The 1- and 3-directions are parallel to the
schistosity; the 2-direction is perpendicular to the schistosity). From (Pariseau, 1985)
71
Property* Poorman
Formation
(MPa)
Homestake
Formation (MPa)
Ellison
Formation
(MPa)
c1 93.9 138.8 78.1
c2 68.9 79.6 78.6
c3 84.5 91.4 56.2
T1 20.6 9.5 16.2
T2 5.6 7.9 4.1
T3 13.2 13.2 11.4
RESPEC’s Geotechnical Engineering Summary for DUSEL (2010)
RESPEC conducted UCS and Tensile strength measurements on samples taken from
boreholes along the 4850L in the Yates amphibolite as well as the rhyolite. Table 12 below
presents tensile and compressive strength values for the average of two amphibolite
boreholes as well as a rhyolite core. Tensile strength data was measured using the Brazilian
test, while the compressive strength was measured in the uniaxial stress test. Due to large
coefficients of variability, the rocks in this report were considered to be isotropic for the
following UCS and tensile strength data.
Table 12. Compressive and Tensile Strength for Yates amphibolite and Rhyolite from
(RESPEC, 2010)
Rock
Type
Uniaxial Compressive Strength
(MPa) Tensile Strength (MPa)
Mean SD Low High # of
Samples Mean SD Low
Hig
h
# of
Samples
Amphibolite 115 52 33 216 36 14 7 0.2 35 36
72
Rhyolite 111 55 28 223 18 10 4 5 20 13
The RESPEC (2010) report also conducted direct shear strength tests on Yates
amphibolite intact joints to have data to compare intact and residual Mohr-Coulomb strength
parameters. Table 13 below presents the Mohr-Coulomb parameters of cohesion, So, and
angle of internal friction, ϕ, for both the intact and residual amphibolite.
Table 13. Comparison of Intact and Residual Mohr-Coulomb Strength Parameters for
Joints in Amphibolite from (RESPEC, 2010)
Rock Type Type Cohesion (MPa) Friction Angle (o)
Amphibolite Intact 12.0 47
Amphibolite Residual 3.6 42
Using this data, RESPEC (2010) used a set of equations to then calculate compressive
strength (Co) and tensile strength (To) from the cohesion, So, and angle of internal friction, ϕ
data in Table 13. Using these calculations, Figure 29 was produced to plot the initial, or
ultimate, joint failure in the amphibolites, compared to the average uniaxial compressive
strength (Co) and average tensile strength (To).
73
Figure 29. Comparison of Ultimate Joint Shear Strength (Represented as Red Triangle
Data Points) to Intact Rock Uniaxial Compression and Brazilian Tensile Strength
(Represented as Blue and Green Curves, Respectively) From (RESPEC, 2010)
Using the initial joint failure strength data and the following calculations, the average
uniaxial compressive strength (Co) is 60.9 MPa and average tensile strength (To) is 9.5 MPa.
For the intact amphibolite, the average Co was 115 MPa and the To was 14 MPa. This joint to
intact rock strength ratio is about 70%-75%, which is considerably high (RESPEC, 2010).
This may provide a rough estimate as to the joint strength of the amphibolite rock, however,
the ratios are suspect due to the fact that the rocks are nonlinear across tension-compression.
74
Previous Elastic Property Data
Pariseau (1985)
Pariseau (1985) also presented elastic property data on the Poorman, Homestake, and
Ellison formation from the Homestake Mine. These tests were conducted on cores in three
directions to obtain three mutually orthogonal directions in each formation. The purpose of
this was to ultimately determine the elastic properties necessary to define an orthotropic
material model for each formation. Similar to Pariseau’s (1985) UCS and tensile strength
results, previous knowledge on the high degree of foliation in the Poorman formation
suggests anisotropic properties within the formation. Orthotropic models of the formations
were suggested due to the high degree of foliation in the region. In the rock property data
provided by Pariseau (1985), the Shear Modulus was estimated rather than tested in the
laboratory. The Shear Modulus data in Table 14 is estimated using equation 1 below
(Pariseau, 1985).
𝑮𝒊𝒋 =𝑬𝒊
𝟐(𝟏 + 𝒗𝒊𝒋)⁄ (𝟒)
Similar to the UCS and tensile strength data presented in Pariseau (1985), the original
elastic property data showed a large amount of variation in the results. By removing outliers
from the original anisotropic rock property data, combined with supplemental data from the
University of Utah (referred to as UU in Pariseau (1985)), scatter of the results was reduced,
and produced the modified rock strength properties. The ambiguity of these results should be
noted for future referencing.
75
Table 14. Modified Anisotropic Rock Property Data (*The 1- and 3-directions are
parallel to the schistosity; the 2-direction is perpendicular to the schistosity. All units
are labeled MPa except for Poisson’s ratio (unitless)). E=Young’s Modulus; v=
Poisson’s Ratio; G= Shear Modulus. from (Pariseau, 1985)
Property* Poorman Formation
(MPa)
Homestake
Formation (MPa)
Ellison
Formation
(MPa)
E1 93,015 88,192 89,570
E2 49,608 67,522 63,388
E3 94,393 62,010 75,790
v12 0.23 0.14 0.20
v23 0.15 0.18 0.17
v31 0.22 0.19 0.15
G12 26,182 33,072 31,694
G23 26,871 26,871 28,938
G31 38,584 29,627 35,139
Previous Stress Measurements (Prior to Aug. 2016 kISMET Field Work)
Pariseau (1985)
Pariseau conducted a full-scale vertical crater retreat (VCR) case study between the
6950’-7100’ levels of the Homestake mine. The report also utilized past stress measurements
at various levels reported by Bond (1970), Hooker et al. (1972), and the Spokane Research
Center of the U.S. Bureau of Mines (USBM, 1984) for analysis. The purpose of combining
data from the VCR case study in conjunction with the previous stress measurements was to
provide reliable in-situ stress gradients along with rock property data to provide vital
76
information for the evaluation of safety and stability in the mine. The stress estimations
produced from this study were based on different locations of the mine than the kISMET
project. Due to the complex geology in the region, the stress field could vary between these
levels and the 4850L location for kISMET. This information was taken into account when
using this data set for preparing the hydraulic fracturing experiment.
Reports before Pariseau (1985) estimated in-situ stress at several levels of the
Homestake Mine. These reports include Bond (1970) along the 6200 level and Hooker et al.
(1972) on the 3050’ and the 6200’ levels, and the U.S. Bureau of Mines along the 7400 level
(1984). Pariseau (1985) found from comparing these results that there was rough agreement
in stress gradient magnitudes, but noticeably different information in the principal stress
directions. Table 15 summarizes the in-situ stress measurements sources and their values, as
well as shows magnitudes of normal stresses relative to coordinate axes parallel and
perpendicular to strike, referred to as the vein stresses. Earlier measurements (Bond, 1970;
Hooker et al.,1972) show principal directions aligned with the vertical, parallel to strike and
perpendicular to strike. USBM (1984) data along the 7400’ level show directions skewed
with respect to the vertical or gravity axis and with respect to local structure. This is
explained in the Pariseau (1985) report to be due to the presence of vertical shear stress
component at the 7400’ level. Thus, it is evident that the principal stress orientation at 7400’
level does not follow the trend above.
Table 15. In-situ stress data at Homestake Mine, including data sources, stresses,
magnitudes, and directions based on Bond (1970), Hooker et al. (1972), and USBM
(1984).
77
Principal Stresses and Directions
Source Stress* Magnitude (MPa) Bearing Dip**
Bond
(1970) -
6200
Level
Major 55.1 -- Vertical
Intermediate 35.8
N50E 0
Minor 20.0 N40W 0
Hooker et
al. (1972) -
3050
Level
Major 21.0 -- Vertical
Intermediate 25.4 N43E 0
Minor 12.7 N47W 0
Hooker et
al. (1972) -
6200
Level
Major 53.2 -- Vertical
Intermediate 36.9 N30E 0
Minor 25.0 N60W 0
U.S.B.M.
(1984) –
7400
Level
Major 55.0 N83W 53°
Intermediate 23.5 N08W 71°
Minor 13.3 N61E 43°
Pariseau (1985) notes that previous studies by Bond (1970) and Hooker et al. (1972)
were in similar locations (both took measurements along the 6200L), and thus can check one
another for consistency. The data from the 7400 level, however, had not been matched with
any other measurements at the time, so confidence in those stress measurements was not as
strong. Because of this, Pariseau ignored the vertical shear stresses encountered in his
overcoring results, and produced equations for the in-situ stresses in the mine, in part by
setting the vertical normal stress according to a conservative gravity gradient of 1.25 psi per
foot depth.
Pariseau thus formulated equations 5-7 below for vertical in-situ stress, as well as
principal in-situ stresses in the strike and dip directions of the foliation, as a function of
depth, h, in feet or meters. Again, it is important to keep in mind that these gradients were
78
based on measurements taken from different levels of the Homestake Mine than the 4850L
where the kISMET project took place.
σ𝑣 = 1.25ℎ (Vertical) (5)
σℎ1 = 2078 + 0.53ℎ (Dip direction) (6)
σℎ2 = 121 + 0.55ℎ (Strike direction) (7)
Where h = depth (ft), and stress is in psi.
Or, in SI units:
σ𝑣 = 0.02828ℎ (Vertical) (5’)
σℎ1 = 14.33 + 0.01199ℎ (Dip direction) (6’)
σℎ2 = 0.834 + 0.01244ℎ (Strike direction) (7’)
Where h = depth (m), and stress is in MPa
The Pariseau (1985) report has been influential in estimating in-situ stresses in the
Homestake Mine since many reports have used these equations to estimate stress states at
depths in the mine. Pariseau also simplified the stress gradient equations. Due to the basic
nature of these equations, they most likely represent a rough estimation of the exact in-situ
stress at depths in the mine. However, these equations were used prior to the field work for
determining the in-situ stress at the 4850L. Also, noted by Pariseau, along with most reports
79
regarding the stress state in the Homestake Mine, the complex geology of the region creates
more heterogeneity thus causing in-situ stress characterization to be difficult.
2009 Stress Measurement Program (Golder Associates, Jan. 2010)
The testing summarized in Golder Associates (2010) report was conducted in 2009
along the 4850 level of the mine. Eight new CSIRO hollow-cell overcoring measurements
were taken in three holes at the location of the DUSEL facility. CSIRO overcoring
(Worotnicki, 1993) method is described as “a reliable triaxial method of obtaining stress”
(RESPEC, 2010). Although not the exact location of the kISMET project, this study is closer
in proximity to the kISMET field site compared to previous stress measurements made in the
Homestake Mine.
Six of the reports measurements were testing the Yates amphibolite unit, and two of
the measurements were testing the rhyolite dikes. This is significant because previous stress
reports were lacking measurements taken from the Yates amphibolite and rhyolite units, but
the kISMET field location was located in the Poorman schist formation. However, this
report is still important to our field work due to the close proximity of this reports work to
our field site. This report also presents data on borehole breakouts observed in portions of the
optical televiewer logs as part of Golder’s 2009 coring program. Breakouts can provide data
on stress directions, and can also be used for quantitative stress determination (Zoback, 2007,
Ch. 8).
In their 2010 report, Golder Associates presented and summarized the 2009 stress
measurements executed by the firm, which were also presented in their preliminary report in
December 2009 titled “In-Situ Stress Measurement Deep Underground Science and
Engineering Laboratory”. Tables 16-18 below summarize the stress measurement results
80
(Golder, Dec. 2009) published in Golder Associates (2010a) reports. The stress
interpretations were calculated using solutions from Duncan-Fama and Pender (1980) who
assumed homogeneous, elastic isotropic rock when calculating stress from overcoring strains.
Tables 16 and 17 summarize principal stresses and Table 18 summarizes vertical and
horizontal components. Hypothesized results using Pariseau (1985) in-situ stress equations
(equations 5-7) for depths through the Homestake Mine are also calculated in Table 17 for
comparison. Figure 7 below is an image of a borehole breakout taken by Golder Associates
along the 4850L. Figure 8 is a photo depicting the inclination of a borehole breakout along
the 4850L. Breakouts and their significance are summarized below in the “Conclusions Made
by Golder Associates” portion of this thesis.
Table 16. Principal stresses, orientations, and elastic properties (SI units) where SM-02
to SM-07 was in Yates amphibolite unit and SM-08 and 09 are results from rhyolite
dike. From (Golder Associates, 2010a)
Principal Stresses Biaxially Measured
Rock Properties
2009
Tests
(4850
Level)
σ1 σ2 σ3 Young’s
Modulus
Poisson’
s Ratio
MPa
(kpsi) tr pl
MPa
(kps
i)
tr pl
MPa
(kps
i)
tr pl GPa
(Mpsi) -
SM-01 - - - - - - - - - 84.6
(12.3) 0.30
SM-02 43.6
(6.32) 15 18
35.2
(5.1
0)
25
6 56
30.8
(4.4
7)
115 28 67.2
(9.7) 0.29
SM-03
76.8
(11.1
4)
20
9 48
48.7
(7.0
6)
31
0 10
41.5
(6.0
2)
49 40 81.3
(11.8) 0.30
SM-04 59.7
(8.66)
22
4 31
47.9
(6.9
5)
44 59
40.3
(5.8
4)
134 0 - -
81
SM-05 43.6
(6.32)
18
5 21
27.0
(3.9
2)
27
5 1
19.0
(2.7
6)
8 69 93.7
(13.6) 0.25
SM-06 61.1
(8.86) 37 14
38.7
(5.6
1)
29
6 37
31.7
(4.6
0)
145 49 94.1
(13.6) 0.30
SM-07 34.2
(4.96)
13
3 51
27.5
(3.9
9)
35
9 30
24.9
(3.6
1)
255 23 93.0
(13.5) 0.32
SM-08 60.8
(8.82)
25
8 75
34.4
(4.9
9)
14
5 6
26.9
(3.9
0)
54 14 - -
SM-09 59.5
(8.63)
17
5 75
34.8
(5.0
5)
30
8 10
30.7
(4.4
5)
40 11 61.5
(8.9) 0.36
Averag
es
54.9
(7.96)
36.8
(5.3
3)
30.7
(4.4
6)
81.8
(11.9) 0.30
Table 17. Vertical and horizontal components, octahedral, and deviatoric stresses (SI
Units) where SM-02 to SM-07 was in Yates amphibolite unit and SM-08 and 09 are
results from rhyolite dike along 4850L. From (Golder Associates, 2010a)
Vertical and Horizontal
Components Octahedral
Stresses Deviatoric Principal
Stresses
2009 Tests (4850 Level)
σHMax σHmin σv σoct τoct S1 S2 S3
MPa
(kpsi) Dir.
MPa
(kpsi)
MPa
(kpsi)
MPa
(kpsi)
MPa
(kpsi)
MPa
(kpsi)
MPa
(kpsi)
MPa
(kpsi)
SM-02 42.7
(6.19) 17
31.9 (4.62)
35.1 (5.09)
36.5 (5.30)
5.3 (0.76)
7.1 (1.02)
-1.3 (-0.19)
-5.7 (-0.83)
SM-03 57.7
(8.36) 20
48.1
(6.98)
61.2
(8.87)
55.7
(8.07)
15.1
(2.19)
21.1
(3.06)
-7
(-1.01)
-14.2
(-2.05)
SM-04 56.6
(8.20) 44
40.2
(5.83)
51.1
(7.41)
49.3
(7.15)
7.9
(1.15)
10.4
(1.51)
-1.4
(-0.20)
-9
(-1.31)
SM-05 40.2
(5.83) 4
27
(3.92)
22.3
(3.23)
29.9
(4.33)
10.1
(1.47)
13.7
(1.99)
-2.9
(-0.42)
-10.9
(-1.58)
SM-06 50.1
(7.26) 20
44.1
(6.39)
36.1
(5.23)
43.8
(6.36)
12.4
(1.80)
17.3
(2.50)
-5.1
(-0.74)
-12.1
(-1.76)
SM-07 29.8 148 25.7 31.2 28.9 3.9 5.3 -1.4 -4
82
(4.32) (3.73) (4.52) (4.19) (0.56) (0.77) (-0.20) (-0.58)
SM-08 38.7
(5.61) 141
28.7
(4.16)
58.7
(8.51)
40.7
(5.90)
14.4
(2.09)
20.1
(2.91)
-6.3
(-0.91)
-13.8
(-2.00)
SM-09 35.8
(5.19) 141
31.5
(4.57)
57.7
(8.37)
41.7
(6.04)
12.6
(1.83)
17.8
(2.59)
-6.9
(-1.00)
-11
(-1.59)
Averages
43.9
(6.37)
34.7
(5.02)
44.2
(6.41)
40.8
(5.92)
10.2
(1.48)
14.1
(2.05)
-4
(-0.58)
-10.1
(-1.46)
Pariseau (1985)
gradient
32.1
(4.65)
19.2
(2.79)
41.8
(6.06)
Table 18. Summary of In Situ Stress Measurements from (Golder Associates Final,
2010b)
Summary of In Situ Stress Measurements
from (Golder Associates Final, Oct. 2010)
Test No. Depth m
(ft)
Vertical Stress
σ2/ σ1 ratio σ3/ σ1 ratio Value
(MPa)
Gradient
(MPa/m)
Hooker et al.
(1972)
950
(3050) 26.29 0.028 0.96 0.48
RI9446 – Site
1
1112
(3650) 28.73 0.026 0.71 0.48
RI9446 – Site
2
1112
(3650) 35.53 0.032 0.69 0.38
Hooker et al.
(1972)
1890
(6200) 53.23 0.028 0.69 0.47
Bond (1970) 1890
(6200) 55.16 0.029 0.65 0.36
NIOSH 2256
(7400) 54.92 0.024 0.75 0.59
Average 0.028 0.74 0.46
Golder Associates Stress Results
SM-02 1478
(4850) 35.1 0.024 0.81 0.71
SM-03 1478
(4850) 61.22 0.041 0.63 0.54
SM-04 1478
(4850) 51.06 0.035 0.8 0.68
83
SM-05 1478
(4850) 22.3 0.015 0.62 0.44
SM-06 1478
(4850) 38.14 0.026 0.63 0.52
SM-07 1478
(4850) 31.17 0.021 0.8 0.73
SM-08 1478
(4850) 58.67 0.04 0.57 0.44
SM-09 1478
(4850) 57.65 0.039 0.58 0.52
Borehole Breakouts (Golder Associates, Jan. 2010)
Borehole breakouts are fractures along the borehole caused by compressive stress
concentration (Golder Associates, 2010a). The bands formed along borehole walls and
breakouts are often on opposing sides of the borehole in the direction of minimum stress
normal to the borehole axis. Thus, breakouts can be a useful indicator for stress direction, and
were seen in one of the Golder Associates stress measurements holes. Based on the 2009
testing, the breakouts seemed to occur only in the Yates amphibolite close to rhyolite
contacts or in rock mass, which contains Yates amphibolite and rhyolite. An example of a
borehole breakout seen in this study is seen in Figure 30.
To further investigate which of the two sub-horizontal directions is the minor stress
direction, televiewer images were investigated in the boreholes along the 4850 level. The
televiewer images showed evidence of borehole breakouts in the holes drilled at trends near
310°, and no borehole breakouts in the boreholes oriented at trends near 40°. This would
suggest that the borehole breakouts would occur while drilling in the general direction of the
intermediate stress, which would be 310°. It is assumed that borehole breakouts would not
84
occur while drilling parallel to the minor stress axis, so the general trend of 40° can be
assumed to be the minor stress direction. These televiewer breakout images would thus
suggest that the minor principle stress is in an inferred northeast orientation (Golder
Associates, 2010b). Figure 31 below shows an image of the inclination of a borehole
breakout along a borehole, which had been drilled at an azimuth of approximately 310°.
Figure 30. Image of borehole breakout at 4850 level of Homestake Mine. From (Golder
Associates, 2010b)
85
Figure 31. Inclination of Breakout in Borehole Drills from the Ventilation Drift
(Borehole Advanced at an Azimuth of Approximately 310°) from (Golder Associates
Final, 2010b)
Conclusions made by Golder Associates (Jan. 2010(a) and Oct. 2010(b) Reports)
Below are conclusions derived from the reports by Golder Associates. It is important
to emphasize again that these conclusions are based on results from tests conducted in the
Yates amphibolite and rhyolite units of the Homestake Mine, while the kISMET project site
was located in the Poorman schist. Although units being tested differed, these conclusions
were made in regions in close proximity to the kISMET project site.
86
• Stress varied with space in the mine. The Yates amphibolite stress
measurements varied greatly, showing large degrees in variability from tests
within 1 meter of each other. The two rhyolite dikes measured showed
consistency with one another, however, was a smaller sample set than the
amphibolite.
• Data quality and Uncertainties are prevalent in this data set because the
rhyolite data is consistent because the rock is likely isotropic and the
assumptions used in analyzing the overcoring strains hold true. However, the
amphibolite data is variable because they didn’t fully characterize the
anisotropic elastic properties and strain was not properly interpreted.
• Heterogeneity Effects may also affect the rock properties determined in this
report. Heterogeneities could potentially occur on the scale of centimeters or
less, which could cause variability on a stress measurement cell. Larger scale
heterogeneities could affect results spatially. Differing rock types can also
cause stress variations due to contrasts in elastic properties.
• Comparison with Lithostatic Stress and other Stress Indicators can also be an
indicator of the quality of the data measured in the field. The vertical stress at
the 4850 level would be 40.6 MPa for rock with density of 2800 kg per cubic
meter. Pariseau’s (1985) hypothetical calculations would estimate a vertical
stress of 41.8 MPa. Golder Associates testing in 2009 produced an average
vertical stress of 44.2 MPa, and includes both the Yates unit and rhyolite dike
measurements. The rhyolite dike data had vertical stress results higher than
87
lithostatic and near vertical σ1. Alone, the Yates amphibolite’s average
vertical stress was 39.5 MPa, very close to lithostatic gradient values.
Considering horizontal stress components, figure 10 shows that orientations of
maximum horizontal stress components, σHMax, trend northeast for Yates unit
measurements except SM-07 which trends northwest along with the two
rhyolite measurements. An average of all σHMax values are close to lithostatic
stress, while σhmin are about 80% of lithostatic.
• Borehole Breakouts were seen in one of the Golder Associates boreholes
drilled for overcoring. The direction of breakouts in the borehole suggest that
the 40° was the minor stress axis direction, while 310° was the general
direction of the intermediate stress.
Preparing for kISMET Field Work
For predictive purposes and to approximate what equipment the kISMET project
would need at the 4850L to perform hydrofracture experiments, the figures below in this
preparation section represent previous results and hypotheses for vertical, maximum
horizontal, and minimum horizontal stress throughout the Homestake Mine. These gradients
are extrapolated from the available data presented in this report. This previously published
data is from Pariseau (1985), Johnson et al. (1993), and Golder Associates (Jan. 2010).
Figure 32 shows extrapolated gradients for vertical stress against depth in the Homestake
Mine, and Figure 33 shows specific stress data points from Bond (1970) along the 6200
level, Hooker et al. (1972) along the 3050 and 6200 level, Johnson et al. (1995) along the
3650 level in the Homestake and Poorman Formations, and Golder Associates (Jan. 2010)
88
along the 4850 level in the Yates Unit and Rhyolite dikes, as well as Pariseau’s (1985)
hypothesized stress gradients for horizontal stress measurements.
Figure 32. Vertical Stress Gradients vs Depth in the Homestake Mine, SD. Sources from
Pariseau (1985), Johnson et al. (1995), and Golder Associates (2010)
0
1000
2000
3000
4000
5000
0 2000 4000 6000 8000
De
pth
(ft
)
Vertical Stress (psi)
Vertical Stress (psi) vs Depth (ft) at Homestake Mine
Vertical Stress-Avgs. From[GolderAssociates,2010] in psi
Vertical Stress-from [Pariseau,1985] in psi
Lithostatic(density=2800kg/m3)
Vertical Stress-Avgs. from[Johnson et al.,1993] in psi
89
Figure 33. Stress Data Points from Bond (1970), Hooker et al. (1972), Johnson et al.
(1995) and Golder Associates (2010) at Respective Depths, as well as Gradients from
Pariseau (1985)
With tabulated stress data throughout the Homestake Mine, measuring minimum
hoop stress and predicting injection pressure for hydraulic fracturing was done. The
minimum tangential stress around a vertical borehole is given by,
𝜎𝜃𝜃𝑚𝑖𝑛 = 3𝑆ℎ𝑚𝑖𝑛 − 𝑆𝐻𝑚𝑎𝑥 − 2𝑃0 − ∆𝑃 − 𝜎∆𝑇 (𝟓)
90
where Shmin is the minimum horizontal stress, SHmax is the maximum horizontal stress, P0 is
pore pressure which is zero at 4850L due to water level maintenance, and ∆P is the
difference between the injection in the borehole and formation pressure (Zoback, 2007)
Change to Zoback. By setting the minimum compressional stress in the above equation to the
tensile strength of the rock, one can equate for the pressure in the borehole necessary to
fracture the rock by solving the above equation. Table 19 presents the maximum and
horizontal stress values used in calculating predictions for minimum borehole pressure at the
4850 level of Homestake Mine. Table 20 presents the minimum borehole pressure necessary
for hydraulic fracturing at the 4850 Level for several different instances, and Figure 34
represents this in bar chart form.
Table 19. Data used in Equation 9 to Determine Estimated Minimum Borehole Pressure
Needed at 4850L for Hydraulic Fracturing
Data Source SHmax - MPa (psi) Shmin - MPa (psi)
Golder Associates (2010a)- Averages
43.9 (6,370)
34.7 (5,030)
Golder Associates (2010a) – SM-02
42.7 (6,193)
31.9 (4,627)
Golder Associates (2010a) – SM-03
57.7 (8,369)
48.1 (6,980)
Golder Associates (2010a) – SM-04
56.6 (8,209)
40.2 (5,831)
Golder Associates (2010a) – SM-05
40.2 (5,831)
27.0 (3,916)
Golder Associates (2010a) – SM-06
50.1 (7,266)
44.1 (6,396)
91
Golder Associates (2010a) – SM-07
29.8 (4,322)
25.7 (3,727)
Golder Associates (2010a) – SM-08
38.7 (5,613)
28.7 (4,163)
Golder Associates (2010a) – SM-09
35.8 (5,192)
31.5 (4,569)
Pariseau (1985) (using gradient)
27.7 (4,020)
14.7 (2,130)
Table 20. Estimated Minimum Borehole Pressure Needed at 4850L for Hydraulic
Fracturing. (SHmax and Shmin values used for calculations are presented in Table 19
above)
Data Source Minimum Borehole Pressure
needed at 4850L – MPa (psi)
Minimum Borehole Pressure needed
at 4850L with Assumed 10 MPa
Tensile Rock Strength – MPa (psi)
Golder Associates
(2010a) - Average
60.2 (8,720)
70.2 (10,170)
Golder Associates
(2010a) – SM-02
53 (7,787)
63 (9,140)
Golder Associates
(2010a) – SM-03
86.6 (12,564)
96.6 (14,011)
Golder Associates
(2010a) – SM-04
64 (9,282)
74 (10,732)
Golder Associates
(2010a) – SM-05
40.8 (5,918)
50.8 (7,368)
Golder Associates
(2010a) – SM-06
82.2 (11,922)
92.2 (13,373)
92
Golder Associates
(2010a) – SM-07
47.3 (6,860)
57.3 (8,311)
Golder Associates
(2010a) – SM-08
47.4 (6,875)
57.4 (8,325)
Golder Associates
(2010a) – SM-09
58.7 (8,514)
68.7 (9,964)
Pariseau (1985) 16.4
(2,370) 26.4
(3,820)
Figure 34. Estimated Minimum Borehole Pressure Needed at 4850L for Hydraulic
Fracturing
From these results, it shows the Golder Associates data requires a much higher
borehole pressure to fracture the rock at the 4850L. Due to uncertainty in all previous stress
0
20
40
60
80
100
120
Min
. Bo
reh
ole
Pre
ssu
re N
ee
de
d a
t 4
85
0L
(M
Pa
)
Data Source
Predicted Minimum Borehole Pressures Needed for Hydraulic Fractuing at 4850L of Homestake
Mine, SD
Min. PressureNeeded @4850L (WithAssumed 10MPa TensileRockStrength)
Min. PressureNeeded @4850L
93
measurements done in the Homestake Mine, we prepared for the “worst case scenario” in
which the equipment was suited for the highest pressures. This is why we honored Golder
Associates data which was conducted most recent of the three data sets along the 4850 Level.
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