1、Designation: D 4015 07Standard Test Methods forModulus and Damping of Soils by Resonant-ColumnMethod1This standard is issued under the fixed designation D 4015; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revis
2、ion. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (e) indicates an editorial change since the last revision or reapproval.1. Scope*1.1 These test methods cover the determination of shearmodulus, shear damping, rod modulus (commonly referred toas Youngs modulus)
3、, and rod damping for solid cylindricalspecimens of soil in the undisturbed and remolded conditionsby vibration using the resonant column. The vibration of thespecimen may be superposed on a controlled ambient state ofstress in the specimen. The vibration apparatus and specimenmay be enclosed in a t
4、riaxial chamber and subjected to anall-around pressure and axial load. In addition, the specimenmay be subjected to other controlled conditions (for example,pore-water pressure, degree of saturation, temperature). Thesetest methods of modulus and damping determination areconsidered nondestructive wh
5、en the strain amplitudes of vibra-tion are less than 104rad (104in./in.), and many measure-ments may be made on the same specimen and with variousstates of ambient stress.1.2 These test methods cover only the determination of themodulus and damping, the necessary vibration, and specimenpreparation p
6、rocedures related to the vibration, etc., and do notcover the application, measurement, or control of the ambientstress. The latter procedures may be covered by, but are notlimited to, Test Methods D 2166 or D 2850.1.3 All recorded and calculated values shall conform to theguide for significant digi
7、ts and rounding established in PracticeD 6026.1.3.1 The procedures used to specify how data are collected/recorded and calculated in this standard are regarded as theindustry standard. In addition, they are representative of thesignificant digits that should generally be retained. The proce-dures us
8、ed do not consider material variation, purpose forobtaining the data, special purpose studies, or any consider-ations for the users objectives; and it is common practice toincrease or reduce significant digits of reported data to becommensurate with these considerations. It is beyond the scopeof thi
9、s standard to consider significant digits used in analysismethods for engineering design.1.3.2 Measurements made to more significant digits orbetter sensitivity than specified in this standard shall not beregarded a nonconformance with this standard.1.4 The values stated in SI units are to be regard
10、ed as thestandard. Reporting test results in units other than SI shall beregarded as conformance with these test methods.1.5 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-p
11、riate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2D 653 Terminology Relating to Soil, Rock, and ContainedFluidsD 2166 Test Method for Unconfined Compressive Strengthof Cohesive SoilD 2216 Test Methods
12、for Laboratory Determination of Wa-ter (Moisture) Content of Soil and Rock by MassD 2850 Test Method for Unconsolidated-Undrained Tri-axial Compression Test on Cohesive SoilsD 3740 Practice for Minimum Requirements for AgenciesEngaged in the Testing and/or Inspection of Soil and Rockas Used in Engin
13、eering Design and ConstructionD 4767 Test Method for Consolidated Undrained TriaxialCompression Test for Cohesive SoilsD 6026 Practice for Using Significant Digits in Geotechni-cal Data3. Terminology3.1 Definitions: For definitions of other terms used in thisTest Method, see Terminology D 653.3.2 De
14、finitions of Terms Specific to This Standard:3.2.1 ambient stressstresses applied to the specimen,during the test, that do not result from the vibration strains.These test methods do not cover the application and measure-ment of ambient stresses; however, the ambient stress at the1These test methods
15、 are under the jurisdiction ofASTM Committee D18 on Soiland Rock and are the direct responsibility of Subcommittee D18.09 on Cyclic andDynamic Properties of Soils.Current edition approved Sept. 1, 2007. Published October 2007. Originallyapproved in 1981. Last previous edition approved in 2000 as D 4
16、015 92 (2000).2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.1*A Summary of Changes section appears at the e
17、nd of this standard.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.time of measurement of the system resonant frequency andsystem damping shall be measured and recorded in accordancewith the Report section of these test methods.3.2.2
18、 apparatus model and constantsthe rigidity and massdistribution of the resonant column shall be as required in thefollowing section in order for the resonant-column system to beaccurately represented by the model shown in Fig. 1. Theapparatus constants are the mass of the passive-end platen, MP, inc
19、luding the mass of all attachments rigidly connected to it;the rotational inertia of the passive-end platen, JP, includingthe rotational inertia of all attachments rigidly connected to it;similar mass, MA, and rotational inertia, JA, for the active-endplaten and all attachments rigidly connected to
20、it, such asportions of the vibration excitation device; the spring anddamping constants for both longitudinal and torsional springsand dashpots (KSL, KST, ADCL, ADCT); the apparatus resonantfrequencies for longitudinal vibration, foL, and torsional vibra-tion, foT; the force/current constant, FCF, r
21、elating appliedvibratory force to the current applied to the longitudinalexcitation device; the torque/current constant, TCF, relatingapplied vibratory torque to the current applied to the torsionalexcitation device; and the motion transducer calibration factors(LCFA, RCFA, LCFP, RCFP) relating the
22、transducer outputs toactive- and passive-end longitudinal and rotational motion.3.2.3 moduli and damping capacitiesYoungs modulus(herein called rod modulus), E, is determined from longitudinalvibration, and the shear modulus, G, is determined fromtorsional vibration. The rod and shear moduli shall b
23、e definedas the elastic moduli of a uniform, linearly viscoelastic (Voigtmodel) specimen of the same mass density and dimensions asthe soil specimen necessary to produce a resonant columnhaving the measured system resonant frequency and responsedue to a given vibratory force or torque input. The str
24、ess-strainrelation for a steady-state vibration in the resonant column is ahysteresis loop. These moduli will correspond to the slope of aline through the end points of the hysteresis loop. The sectionon calculations provides for computation of rod and shearmoduli from the measured system longitudin
25、al and torsionalresonant frequencies. The energy dissipated by the system is ameasure of the damping of the soil. Damping will be describedby the rod damping ratio, DL, and the shear damping ratio, DT,which are analogous to the critical viscous damping ratio, c/cr,for a single-degree-of-freedom syst
26、em. The damping ratiosshall be defined by:DL5 0.5hv/E! (1)where:h = viscous coefficient for rod motion, Ns/m2,v = circular resonant frequency, rad/s, andE = rod modulus, Pa.and by:DT5 0.5v/G! (2)where: = viscous coefficient for torsional motion, N-s/m2, andG = shear modulus, Pa.3.2.3.1 Values of dam
27、ping determined in this way willcorrespond to the area of the stress-strain hysteresis loopdivided by 4p times the elastic strain energy stored in thespecimen at maximum strain. Methods for determining damp-ing ratio are prescribed later. In viscoelastic theory, it iscommon to use complex moduli to
28、express both modulus anddamping. The complex rod modulus is given by:E* 5 E1 1 2iDL! (3)and the complex shear modulus is given by:G* 5 G1 1 2iDT! (4)where i =21.3.2.4 resonant-column systema system consisting of acylindrical specimen or column of soil that has platens attachedto each end as shown in
29、 Fig. 1. A sinusoidal vibrationexcitation device is attached to the active-end platen. The otherend is the passive-end platen. It may be rigidly fixed (thecriterion for establishing fixity is given later) or its mass androtational inertia must be known. The vibration excitationdevice may incorporate
30、 springs and dashpots connected to theactive-end platen, where the spring constants and viscousdamping coefficients are known. Vibration excitation may belongitudinal or torsional. A given apparatus may have thecapability of applying one or the other, or both. The mass androtational inertia of the a
31、ctive-end platen and portions of thevibration excitation device moving with it must be known.Transducers are used to measure the vibration amplitudes foreach type of motion at the active end and also at the passiveend if it is not rigidly fixed. The frequency of excitation will beadjusted to produce
32、 resonance of the system, composed of thespecimen and its attached platens and vibration excitationdevice.3.2.5 specimen strainfor longitudinal motion, the strain,e, is the average axial strain in the entire specimen. Fortorsional motion, the strain, g, is the average shear strain in thespecimen. In
33、 the case of torsion, shear strain in each crosssection varies from zero along the axis of rotation to aFIG. 1 Resonant-column SchematicD4015072maximum at the perimeter of the specimen, and the averageshear strain for each cross section occurs at a radius equal to 80percent the radius of the specime
34、n. Methods for calculatingspecimen strain are given later in the calculations section.3.2.6 system resonant frequencythe definition of systemresonance depends on both apparatus and specimen character-istics. For the case where the passive-end platen is fixed,motion at the active end is used to estab
35、lish resonance, whichis defined as the lowest frequency for which the sinusoidalexcitation force (or moment) is in phase with the velocity of theactive-end platen. For the case where the passive-end platenmass (or passive end platen rotational inertia) is greater than100 times the corresponding valu
36、e of the specimen and is notrigidly fixed, resonance is the lowest frequency for which thesinusoidal excitation force (or moment) is 180 out of phasewith the velocity of the active-end platen. Otherwise, motion atthe passive end is used to establish resonance, which is thesecond lowest frequency for
37、 which the sinusoidal excitationforce (or moment) is in phase with the velocity of thepassive-end platen. (The lowest frequency for this condition isnot used because it does not produce significant strains in thespecimen.) In general, the system resonant frequency fortorsional excitation will be dif
38、ferent from the system resonantfrequency for longitudinal excitation.4. Summary of Test Method4.1 In the resonant column test, a cylindrical soil specimenis subjected to an imposed ambient stress condition. Onceequilibrium at the imposed stress condition is achieved, tor-sional or longitudinal, or b
39、oth, sinusoidal vibrations are appliedto the soil specimen and the specimen motions (strains)resulting from the imposed vibrations are measured. Thefrequency of excitation is varied until resonance is achieved asdescribed in Section 3.2.6. Given the geometry, mass andsystem parameters, the shear and
40、 longitudinal moduli andmaterial (hysteretic) damping may be determined at a mea-sured strain value. The amplitude of vibration is typicallyvaried to measure the variation of moduli and damping as afunction of strain. Since the test is usually conducted at strainlevels between 0.00001 and 0.5% strai
41、n leaving the specimenrelatively intact, the test is often conducted at several differentsets of ambient stress conditions to measure the variation ofmoduli and damping with ambient stress.NOTE 1The quality of the results produced by this standard isdependent on the competence of the personnel perfo
42、rming it, and thesuitability of the equipment and facilities. Agencies that meet the criteriaof Practice D 3740 are generally considered capable of competent andobjective testing/sampling/inspection/etc. Users of this standard are cau-tioned that compliance with Practice D 3740 does not in itself as
43、surereliable results. Reliable results depend on many factors; Practice D 3740provides a means of evaluating some of those factors.5. Significance and Use5.1 The modulus and damping of a given soil, as measuredby the resonant-column technique herein described, dependupon the strain amplitude of vibr
44、ation, the ambient state ofeffective stress, and the void ratio of the soil, temperature, time,etc. Since the application and control of the ambient stressesand the void ratio are not prescribed in these methods, theapplicability of the results to field conditions will depend onthe degree to which t
45、he application and control of the ambientstresses and the void ratio, as well as other parameters such assoil structure, duplicate field conditions. The techniques usedto simulate field conditions depend on many factors and it is upto the engineer to decide on which techniques apply to a givensituat
46、ion and soil type.6. Apparatus6.1 GeneralThe complete test apparatus includes theplatens for holding the specimen in the pressure cell, thevibration excitation device, transducers for measuring theresponse, the control and readout instrumentation, and auxil-iary equipment for specimen preparation.6.
47、2 Specimen PlatensBoth the active-end and passive-endplatens shall be constructed of noncorrosive material having amodulus at least ten times the modulus of the material to betested. Each platen shall have a circular cross section and aplane surface of contact with the specimen, except that theplane
48、 surface of contact may be roughened to provide for moreefficient coupling with the ends of the specimen. The diameterof platens shall be equal to or greater than the diameter of thespecimen. The construction of the platens shall be such thattheir stiffness is at least ten times the stiffness of the
49、 specimen.The active-end platen may have a portion of the excitationdevice, transducers, springs, and dashpots connected to it. Thetransducers and moving portions of the excitation device mustbe connected to the platen in such a fashion that they are to beconsidered part of the platen and have the same motion as theplaten for the full range of frequencies to be encountered whentesting soils. The theoretical model used for the resonant-column system represents the active-end platen, with allattachments, as a rigid mass that is attached to the specimen;this mass m
