ASTM D3148-96
(Test Method)Standard Test Method for Elastic Moduli of Intact Rock Core Specimens in Uniaxial Compression
Standard Test Method for Elastic Moduli of Intact Rock Core Specimens in Uniaxial Compression
SCOPE
1.1 This test method covers the determination of elastic moduli of intact rock core specimens in uniaxial compression. It specifies the apparatus, instrumentation, and procedures for determining the stress-axial strain and the stress-lateral strain curves, as well as Young's modulus, E, and Poisson's ratio, v
Note 1—This test method does not include the procedures necessary to obtain a stress-strain curve beyond the ultimate strength.
1.2 For an isotropic material, the relation between the shear and bulk moduli and Young's modulus and Poisson's ratio are:
Equation 1
G =
E
2(1 + v)
Equation 2
K =
E
3(1 - 2v)
where:
G = shear modulus,
K = bulk modulus,
E = Young's modulus, and
v = Poisson's ratio.
The engineering applicability of these equations is decreased if the rock is anisotropic. When possible, it is desirable to conduct tests in the plane of foliation, bedding, etc., and at right angles to it to determine the degree of anisotropy. It is noted that equations developed for isotropic materials may give only approximate calculated results if the difference in elastic moduli in any two directions is greater than 10 % for a given stress level.
Note 2—Elastic moduli measured by sonic methods may often be employed as preliminary measures of anisotropy.
1.3 The test method given for determining the elastic constants does not apply to rocks that undergo significant inelastic strains during the test, such as potash and salt. The elastic moduli for such rocks should be determined from unload-reload cycles, which is not covered by this test method.
1.4 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.
General Information
Standards Content (Sample)
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Designation: D 3148 – 96
AMERICAN SOCIETY FOR TESTING AND MATERIALS
100 Barr Harbor Dr., West Conshohocken, PA 19428
Reprinted from the Annual Book of ASTM Standards. Copyright ASTM
Standard Test Method for
Elastic Moduli of Intact Rock Core Specimens in Uniaxial
Compression
This standard is issued under the fixed designation D 3148; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (e) indicates an editorial change since the last revision or reapproval.
1. Scope * responsibility of the user of this standard to establish appro-
priate safety and health practices and determine the applica-
1.1 This test method covers the determination of elastic
bility of regulatory limitations prior to use.
moduli of intact rock core specimens in uniaxial compression.
It specifies the apparatus, instrumentation, and procedures for
2. Referenced Documents
determining the stress-axial strain and the stress-lateral strain
2.1 ASTM Standards:
curves, as well as Young’s modulus, E, and Poisson’s ratio, n.
D 2216 Test Method for Laboratory Determination of Water
NOTE 1—This test method does not include the procedures necessary to
(Moisture) Content of Soil and Rock
obtain a stress-strain curve beyond the ultimate strength.
D 4543 Practice for Preparing Rock Core Specimens and
1.2 For an isotropic material, the relation between the shear
Determining Dimensional and Shape Tolerances
and bulk moduli and Young’s modulus and Poisson’s ratio are:
E 4 Practices for Load Verification of Testing Machines
E 691 Practice for Conducting an Interlaboratory Study to
E
G 5 (1) 4
Determine the Precision of a Test Method
2~11n!
E
3. Summary of Test Method
K 5 (2)
3~1 2 2n!
3.1 A rock core sample is cut to length, and the ends are
where: machined flat. The specimen is placed in a loading frame and,
G 5 shear modulus, if required, heated to the desired test temperature. Axial load is
K 5 bulk modulus,
continuously increased on the specimen, and deformation is
E 5 Young’s modulus, and
monitored as a function of load.
n5 Poisson’s ratio.
4. Significance and Use
The engineering applicability of these equations is decreased
if the rock is anisotropic. When possible, it is desirable to
4.1 The elastic constants are used to calculate the stress and
conduct tests in the plane of foliation, bedding, etc., and at right
deformation in rock structures.
angles to it to determine the degree of anisotropy. It is noted
4.2 The deformation and strength properties of rock cores
that equations developed for isotropic materials may give only
measured in the laboratory usually do not accurately reflect
approximate calculated results if the difference in elastic
large-scale in situ properties, because the latter are strongly
moduli in any two directions is greater than 10 % for a given
influenced by joints, faults, inhomogeneities, weakness planes,
stress level.
and other factors. Therefore, laboratory values for intact
specimens must be employed with proper judgment in engi-
NOTE 2—Elastic moduli measured by sonic methods may often be
neering applications.
employed as preliminary measures of anisotropy.
1.3 The test method given for determining the elastic
5. Apparatus
constants does not apply to rocks that undergo significant
5.1 Loading Device—The loading device shall be of suffi-
inelastic strains during the test, such as potash and salt. The
cient capacity to apply load at a rate conforming to the
elastic moduli for such rocks should be determined from
requirements specified in 9.5. It shall be verified at suitable
unload-reload cycles, which is not covered by this test method.
time intervals in accordance with the procedures given in
1.4 This standard does not purport to address all of the
Practices E 4 and comply with the requirements prescribed
safety concerns, if any, associated with its use. It is the
therein. The loading device may be equipped with a displace-
ment transducer than can be used to advance the loading ram
at a specified rate.
This test method is under the jurisdiction of ASTM Committee D-18 on Soil
and Rock and is the direct responsibility of Subcommittee D18.12 on Rock
Mechanics. Annual Book of ASTM Standards, Vol 04.08.
Current edition approved Oct. 10, 1996. Published April 1997. Originally Annual Book of ASTM Standards, Vol 03.01.
published as D 3148 – 72. Last previous edition D 3148 – 95. Annual Book of ASTM Standards, Vol 14.02.
*A Summary of Changes section appears at the end of this standard.
D 3148
−6
5.2 Elevated-Temperature Enclosure—The elevated tem- resolution of at least 25 3 10 strain and an accuracy within
−6
perature enclosure may be either an enclosure that fits in the 2 % of the value of readings above 250 3 10 strain and
−6
loading apparatus or an external system encompassing the accuracy and resolution within 5 3 10 for readings lower
−6
complete test apparatus. The enclosure may be equipped with than 250 3 10 strain, including errors introduced by excita-
humidity control for testing specimens in which the moisture tion and readout equipment. The system shall be free from
content is to be controlled. For high temperatures, a system of noncharacterizable long-term instability (drift) that results in
−8
heaters, insulation, and temperature measuring devices are an apparent strain of 10 /s.
normally required to maintain the specified temperature. Tem-
NOTE 4—The user is cautioned about the influence of temperature on
perature shall be measured at three locations, with one sensor
the output of strain and deformation sensors located within the heated
near the top, one at midheight, and one near the bottom of the
environment.
specimen. The average specimen temperature based on the
5.5.1 Axial Strain Determination—The axial deformations
midheight sensor shall be maintained to within 61°C of the
or strains may be determined from data obtained by electrical
required test temperature. The maximum temperature differ-
resistance strain gages, compressometers, linear variable dif-
ence between the midheight sensor and either end sensor shall
ferential transformers (LVDTs), or other suitable means. The
not exceed 3°C.
design of the measuring device shall be such that the average
of at least two axial strain measurements can be determined.
NOTE 3—An alternative to measuring the temperature at three locations
along the specimen during the test is to determine the temperature
Measuring positions shall be equally spaced around the cir-
distribution in a dummy specimen that has temperature sensors located in
cumference of the specimen close to midheight. The gage
drill holes at a minimum of six positions: along both the centerline and
length over which the axial strains are determined shall be at
specimen periphery at midheight and at each end of the specimen. The
least 10 grain diameters in magnitude.
temperature controller set point shall be adjusted to obtain steady-state
5.5.2 Lateral Strain Determination—The lateral deforma-
temperatures in the dummy specimen that meet the temperature require-
tions or strains may be measured by any of the methods
ments at each test temperature (the centerline temperature at midheight
shall be within 61°C of the required test temperature, and all other mentioned in 5.5.1. Either circumferential or diametric defor-
specimen temperatures shall not deviate from this temperature by more
mations (or strains) may be measured. A single transducer that
than 3°C). The relationship between controller set point and dummy
wraps around the specimen can be used to measure the change
specimen temperature can be used to determine the specimen temperature
in circumference. At least two diametric deformation sensors
during testing provided that the output of the temperature feedback sensor
shall be used if diametric deformations are measured. These
(or other fixed-location temperature sensor in the triaxial apparatus) is
sensors shall be equally spaced around the circumference of the
maintained constant within 61°C of the required test temperature. The
specimen, close to midheight. The average deformation (or
relationship between temperature controller set point and steady-state
specimen temperature shall be verified periodically. The dummy specimen
strain) from the diametric sensors shall be recorded.
is used solely to determine the temperature distribution in a specimen in
NOTE 5—The use of strain gage adhesives requiring cure temperatures
the triaxial apparatus; it is not to be used to determine elastic constants.
above 65°C is not allowed unless it is known that microfractures do not
5.3 Temperature Measuring Device—Special limits-oferror develop at the cure temperature.
thermocouples or platinum resistance thermometers (RTDs)
6. Safety Precautions
having accuracies of at least 61°C with a resolution of 0.1°C.
6.1 Many rock types fail in a violent manner when loaded to
5.4 Platens—Two steel platens are used to transmit the axial
failure in compression. A protective shield should be placed
load to the ends of the specimen. They shall have a hardness of
around the test specimen to prevent injury from flying rock
not less than 58 HRC. One of the platens should be spherically
fragments. Elevated temperatures increase the risks of electri-
seated and the other on a plain rigid platen. The bearing faces
cal shorts and fire.
shall not depart from a plane by more than 0.015 mm when the
platens are new and shall be maintained within a permissible
7. Sampling
variation of 0.025 mm. The diameter of the spherical seat shall
be at least as large as that of the test specimen but shall not 7.1 The specimen shall be selected from the cores to
exceed twice the diameter of the test specimen. The center of represent a valid average of the type of rock under consider-
the sphere in the spherical seat shall coincide with that of the ation. This can be achieved by visual observations of mineral
bearing face of the specimen. The spherical seat shall be constituents, grain sizes and shape, partings and defects such as
pores and fissures, or by other methods, such as ultrasonic
properly lubricated to ensure free movement. The movable
portion of the platen shall be held closely in the spherical seat, velocity measurements.
but the design shall be such that the bearing face can be rotated
8. Test Specimens
and tilted through small angles in any direction. If a spherical
seat is not used, the bearing faces of the platens shall be
8.1 Preparation—Prepare test specimens in accordance
parallel to 0.0005 mm/mm of platen diameter. The platen
with Practice D 4543.
diameter shall be at least as great as the specimen but shall not
8.2 Moisture condition of the specimen at the time of test
exceed the specimen diameter by more than 1.50 mm. This
can have a significant effect upon the deformation of the rock.
platen diameter shall be retained for a length of at least
Good practice generally dictates that laboratory tests be made
one-half the specimen diameter.
upon specimens representative of field conditions. Thus, it
5.5 Strain/Deformation Measuring Devices—The strain/ follows that the field moisture condition of the specimen
deformation measuring system shall measure the strain with a should be preserved until the time of test. On the other hand,
D 3148
OTE 8—Loading a high-strength specimen to failure in a loading
there may be reasons for testing specimens at other moisture N
frame that is not stiff will often result in violent failure, which will tend to
contents including zero. In any case, the moisture content of
damage the strain/deformation measuring devices.
the test specimen should be tailored to the problem at hand and
reported in accordance with 11.1.3. If the moisture content of
10. Calculation
the specimen is to be determined, follow the procedures given
10.1 The axial strain, e , and lateral strain, e , may be
a l
in Test Method D 2216.
obtained directly from strain-indicating equipment, or may be
8.3 If moisture content is to be maintained, and the elevated
calculated from deformation readings, depending on the type
temperature enclosure is not equipped with humidity control,
of apparatus or instrumentation employed.
seal the specimen using a flexible membrane or apply a plastic
10.1.1 Calculate the axial strain, e , as follows:
a
or silicone rubber coating to the specimen sides.
DL
9. Procedure
e 5 (3)
a
L
9.1 Check the ability of the spherical seat to rotate freely in
where:
its socket before each test.
L 5 original undeformed axial gage length, and
9.2 Place the lower platen on the base or actuator rod of the
DL 5 change in measured axial length (negative for a
loading device. Wipe clean the bearing faces of the upper and
decrease in length).
lower platens and of the test specimen, and place the test
specimen on the lower platen. Place the upper platen on the
NOTE 9—Tensile stresses and strains are used as being positive. A
specimen and align properly. A small axial load, approximately consistent application of a compression-positive sign convention may be
employed if desired. The sign convention adopted needs to be stated
100 N, may be applied to the specimen by means of the loading
explicitly in the report. The formulas given are for engineering stresses
device to properly seat the bearing parts of the apparatus.
and strains. True stresses and strains may be used if desired.
9.3 When appropriate, install elevated-temperature enclo-
NOTE 10—If the deformation recorded during the test includes defor-
sure and deformation transducers for the apparatus and sensors
mation of the apparatus, suitable calibration for apparatus deformation
used.
must be made. This may be accomplished by inserting into the apparatus
9.4 If testing at elevated temperature, raise the temperature
a steel cylinder having known elastic properties and observing differences
at a rate not exceeding 2°C/min until the required temperature in deformation between the assembly and steel cylinder throughout the
loading range. The apparatus deformation is then subtracted from the total
is reached (Note 6). The test specimen shall be considered to
deformation at each increment of load to arrive at specimen deformation
have reached temperature equilibrium when all deformation
from which the axial strain of the specimen is computed. The accuracy of
transducer outputs are stable for at least three readings taken at
this correction should be verified by measuring the elastic deformation of
equal intervals over a period of no less than 30 min (3 min for
a cylinder of material having known elastic properties (other than steel)
tests p
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