ASTM D4015-92(2000)
(Test Method)Standard Test Methods for Modulus and Damping of Soils by the Resonant-Column Method
Standard Test Methods for Modulus and Damping of Soils by the Resonant-Column Method
SCOPE
1.1 These test methods cover the determination of shear modulus, shear damping, rod modulus (commonly referred to as Young's modulus), and rod damping for solid cylindrical specimens of soil in the undisturbed and remolded conditions by vibration using the resonant column. The vibration of the specimen may be superposed on a controlled ambient state of stress in the specimen. The vibration apparatus and specimen may be enclosed in a triaxial chamber and subjected to an all-around pressure and axial load. In addition, the specimen may be subjected to other controlled conditions (for example, pore-water pressure, degree of saturation, temperature). These test methods of modulus and damping determination are considered nondestructive when the strain amplitudes of vibration are less than 10-4 rad (10-4 in./in.), and many measurements may be made on the same specimen and with various states of ambient stress.
1.2 These test methods cover only the determination of the modulus and damping, the necessary vibration, and specimen preparation procedures related to the vibration, etc., and do not cover the application, measurement, or control of the ambient stress. The latter procedures may be covered by, but are not limited to, Test Methods D2166 or D2850.
1.3 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.
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Designation:D4015–92(Reapproved 2000)
Standard Test Methods for
Modulus and Damping of Soils by the Resonant-Column
Method
This standard is issued under the fixed designation D4015; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (e) indicates an editorial change since the last revision or reapproval.
1. Scope D2850 Test Method for Unconsolidated, Undrained Com-
pressive Strength of Cohesive Soils in Triaxial Compres-
1.1 These test methods cover the determination of shear
sion
modulus, shear damping, rod modulus (commonly referred to
D4767 Test Method for Consolidated-Undrained Triaxial
as Young’s modulus), and rod damping for solid cylindrical
Compression Test on Cohesive Soils
specimens of soil in the undisturbed and remolded conditions
by vibration using the resonant column. The vibration of the
3. Terminology
specimen may be superposed on a controlled ambient state of
3.1 Definitions of Terms Specific to This Standard:
stress in the specimen. The vibration apparatus and specimen
3.1.1 ambient stress—stresses applied to the specimen,
may be enclosed in a triaxial chamber and subjected to an
during the test, that do not result from the vibration strains.
all-around pressure and axial load. In addition, the specimen
These test methods do not cover the application and measure-
may be subjected to other controlled conditions (for example,
ment of ambient stresses; however, the ambient stress at the
pore-water pressure, degree of saturation, temperature). These
time of measurement of the system resonant frequency and
test methods of modulus and damping determination are
systemdampingshallbemeasuredandrecordedinaccordance
considerednondestructivewhenthestrainamplitudesofvibra-
−4 −4
with the final section of the paper.
tion are less than 10 rad (10 in./in.), and many measure-
3.1.2 apparatus model and constants—therigidityandmass
ments may be made on the same specimen and with various
distribution of the resonant column shall be as required in the
states of ambient stress.
followingsectioninorderfortheresonant-columnsystemtobe
1.2 These test methods cover only the determination of the
accurately represented by the model shown in Fig. 1. The
modulus and damping, the necessary vibration, and specimen
apparatus constants are the mass of the passive-end platen, M
preparationproceduresrelatedtothevibration,etc.,anddonot
P,includingthemassofallattachmentsrigidlyconnectedtoit;
cover the application, measurement, or control of the ambient
the rotational inertia of the passive-end platen, J , including
P
stress. The latter procedures may be covered by, but are not
the rotational inertia of all attachments rigidly connected to it;
limited to, Test Methods D2166 or D2850.
similar mass, M , and rotational inertia, J , for the active-end
A A
1.3 This standard does not purport to address all of the
platen and all attachments rigidly connected to it, such as
safety concerns, if any, associated with its use. It is the
portions of the vibration excitation device; the spring and
responsibility of the user of this standard to establish appro-
damping constants for both longitudinal and torsional springs
priate safety and health practices and determine the applica-
and dashpots (K , K , ADC , ADC ); the apparatus resonant
SL ST L T
bility of regulatory limitations prior to use.
frequencies for longitudinal vibration, f , and torsional vibra-
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2. Referenced Documents tion, f ; the force/current constant, FCF, relating applied
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vibratory force to the current applied to the longitudinal
2.1 ASTM Standards:
excitation device; the torque/current constant, TCF, relating
D2166 Test Method for Unconfined Compressive Strength
applied vibratory torque to the current applied to the torsional
of Cohesive Soil
excitationdevice;andthemotiontransducercalibrationfactors
D2216 TestMethodforLaboratoryDeterminationofWater
(LCF , RCF , LCF , RCF )relatingthetransduceroutputsto
A A P P
(Moisture) Content of Soil and Rock
active- and passive-end longitudinal and rotational motion.
3.1.3 moduli and damping capacities—Young’s modulus
(hereincalledrodmodulus), E,isdeterminedfromlongitudinal
ThesetestmethodsareunderthejurisdictionofASTMCommitteeD18onSoil
and Rock and are the direct responsibility of Subcommittee D18.09 on Soil
vibration, and the shear modulus, G, is determined from
Dynamics.
torsional vibration. The rod and shear moduli shall be defined
Current edition approved May 15, 1992. Published September 1992. Originally
as the elastic moduli of a uniform, linearly viscoelastic (Voigt
published as D4015–81. Last previous edition D4015–87.
Annual Book of ASTM Standards, Vol 04.08. model) specimen of the same mass density and dimensions as
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
D4015
G* 5 G~1 12iD ! (4)
T
where i= =21.
3.1.4 resonant-column system—a system consisting of a
cylindricalspecimenorcolumnofsoilthathasplatensattached
to each end as shown in Fig. 1. A sinusoidal vibration
excitationdeviceisattachedtotheactive-endplaten.Theother
end is the passive-end platen. It may be rigidly fixed (the
criterion for establishing fixity is given later) or its mass and
rotational inertia must be known. The vibration excitation
device may incorporate springs and dashpots connected to the
active-end platen, where the spring constants and viscous
damping coefficients are known. Vibration excitation may be
longitudinal or torsional. A given apparatus may have the
capability of applying one or the other, or both. The mass and
rotational inertia of the active-end platen and portions of the
FIG. 1 Resonant-column Schematic
vibration excitation device moving with it must be known.
Transducers are used to measure the vibration amplitudes for
each type of motion at the active end and also at the passive
the soil specimen necessary to produce a resonant column
endifitisnotrigidlyfixed.Thefrequencyofexcitationwillbe
having the measured system resonant frequency and response
adjusted to produce resonance of the system, composed of the
due to a given vibratory force or torque input.The stress-strain
specimen and its attached platens and vibration excitation
relation for a steady-state vibration in the resonant column is a
device.
hysteresis loop.These moduli will correspond to the slope of a
3.1.5 specimen strain—for longitudinal motion, the strain,
line through the end points of the hysteresis loop. The section
e, is the average axial strain in the entire specimen. For
on calculations provides for computation of rod and shear
torsionalmotion,thestrain, g,istheaverageshearstraininthe
moduli from the measured system longitudinal and torsional
specimen. In the case of torsion, shear strain in each cross
resonant frequencies. The energy dissipated by the system is a
section varies from zero along the axis of rotation to a
measureofthedampingofthesoil.Dampingwillbedescribed
maximum at the perimeter of the specimen, and the average
by the rod damping ratio, D , and the shear damping ratio, D ,
L T
shearstrainforeachcrosssectionoccursataradiusequalto80
which are analogous to the critical viscous damping ratio, c/c ,
r
percent the radius of the specimen. Methods for calculating
for a single-degree-of-freedom system. The damping ratios
specimen strain are given later in the calculations section.
shall be defined by:
3.1.6 system resonant frequency—the definition of system
D 50.5~hv/E! (1)
resonance depends on both apparatus and specimen character-
L
istics. For the case where the passive-end platen is fixed,
motion at the active end is used to establish resonance, which
where:
is defined as the lowest frequency for which the sinusoidal
h = viscous coefficient for rod motion, N·s/m ,
excitationforce(ormoment)isinphasewiththevelocityofthe
v = circular resonant frequency, rad/s, and
active-end platen. For the case where the passive-end platen
E = rod modulus, Pa.
mass (or passive end platen rotational inertia) is greater than
100 times the corresponding value of the specimen and is not
rigidly fixed, resonance is the lowest frequency for which the
and by:
sinusoidal excitation force (or moment) is 180° out of phase
D 50.5~µv/G! (2)
T
withthevelocityoftheactive-endplaten.Otherwise,motionat
the passive end is used to establish resonance, which is the
where: second lowest frequency for which the sinusoidal excitation
µ = viscous coefficient for torsional motion, N-s/m , and force (or moment) is in phase with the velocity of the
G = shear modulus, Pa.
passive-end platen. (The lowest frequency for this condition is
3.1.3.1 Values of damping determined in this way will
not used because it does not produce significant strains in the
correspond to the area of the stress-strain hysteresis loop
specimen.) In general, the system resonant frequency for
divided by 4p times the elastic strain energy stored in the
torsional excitation will be different from the system resonant
specimen at maximum strain. Methods for determining damp-
frequency for longitudinal excitation.
ing ratio are prescribed later. In viscoelastic theory, it is
common to use complex moduli to express both modulus and
4. Significance and Use
damping. The complex rod modulus is given by:
4.1 The modulus and damping of a given soil, as measured
E* 5 E~1 12iD ! (3)
L by the resonant-column technique herein described, depend
upon the strain amplitude of vibration, the ambient state of
and the complex shear modulus is given by: effectivestress,andthevoidratioofthesoil,temperature,time,
D4015
etc. Since the application and control of the ambient stresses be connected to the platen in such a fashion that they are to be
and the void ratio are not prescribed in these methods, the considered part of the platen and have the same motion as the
applicability of the results to field conditions will depend on platenforthefullrangeoffrequenciestobeencounteredwhen
the degree to which the application and control of the ambient testing soils. The theoretical model used for the resonant-
stresses and the void ratio, as well as other parameters such as column system represents the active-end platen, with all
soil structure, duplicate field conditions. The techniques used attachments, as a rigid mass that is attached to the specimen;
tosimulatefieldconditionsdependonmanyfactorsanditisup this mass may also have massless springs and dashpots
to the engineer to decide on which techniques apply to a given attached to it as shown in Fig. 1. If springs are used, the
situation and soil type. excitation device and active-end platen (without the specimen
in place) form a two degree-of-freedom system (one-degree-
5. Apparatus
of-freedom system for devices designed for only longitudinal
5.1 General—The complete test apparatus includes the oronlytorsionalmotion)havingundampednaturalfrequencies
platens for holding the specimen in the pressure cell, the for longitudinal motion, f , and torsional motion, f . The
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vibration excitation device, transducers for measuring the device shall be constructed such that these modes of vibration
response, the control and readout instrumentation, and auxil- are uncoupled. The passive-end platen may have a mass and
transducersrigidlyattachedtoitoritmayberigidlyfixed.The
iary equipment for specimen preparation.
5.2 Specimen Platens—Boththeactive-endandpassive-end passive-end platen may be assumed to be rigidly fixed when
the inertia of it and the mass(es) attached to it and the stiffness
platens shall be constructed of noncorrosive material having a
modulus at least ten times the modulus of the material to be of the support of the mass(es) provide a dimensionless fre-
quencyfactorwithin1%ofthedimensionlessfrequencyfactor
tested. Each platen shall have a circular cross section and a
plane surface of contact with the specimen, except that the for the passive-end inertia ratio equal to infinity. (Use Fig. 2
andthecalculationssectiontogetthedimensionlessfrequency
planesurfaceofcontactmayberoughenedtoprovideformore
efficient coupling with the ends of the specimen. The diameter factor.)
of platens shall be equal to or greater than the diameter of the 5.3 Vibration Excitation Device—This shall be an electro-
specimen. The construction of the platens shall be such that magnetic device capable of applying a sinusoidal longitudinal
their stiffness is at least ten times the stiffness of the specimen. vibration or torsional vibration or both to the active-end platen
The active-end platen may have a portion of the excitation towhichitisrigidlycoupled.Thefrequencyofexcitationshall
device, transducers, springs, and dashpots connected to it. The be adjustable and controlled to within 0.5%. The excitation
transducers and moving portions of the excitation device must device shall have a means of measuring the current applied to
FIG. 2 (a) Dimensionless Frequency Factors
D4015
FIG. 2 (b) Dimensionless Frequency Factors (continued)
the drive coils that has at least a 5% accuracy. The voltage recorder with appropriate response time and chart speed or an
drop across a fixed, temperature-and-frequency-stable power oscilloscope and camera or a digital oscilloscope may be used
resistor in series with the drive coils may be used for this for this purpose.
purpose. The force/current and torque/current factors for the
5.6 Support for Vibration Excitation Device—For the spe-
vibration excitation devices must be linear within 5% for the
cialcasewherethepassiveendofthespecimenisrigidlyfixed
entire range of operating frequencies anticipated when testing
and the vibration excitation device and active-end platen are
soils.
placed on top of the specimen, it may be necessary to support
5.4 Sine Wave Generator—The sine wave generator is an
alloraportionoftheweightoftheplatenandexcitationdevice
electric instrument capable of producing a sinusoidal current
to prevent excessive axial stress or compressive failure of the
with a means of adjusting the frequency over the entire range
specimen. This support may be provided by a spring, counter-
of operating frequencies anticipated. This instrument shall
balance weights, or pneumatic cylinder as long as the support-
provide sufficient power to produce the required vibration
ing system does not prevent axial movement of the active-end
amplitude, or its output may be electronically amplified to
platen and as long as it does not alter the vibration character-
provide sufficient power. The total distortion of the signal
istics of the ex
...
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