1、Designation: D4015 07D4015 15Standard Test Methods forModulus and Damping of Soils by Resonant-ColumnMethodFixed-Base Resonant Column Devices1This standard is issued under the fixed designation D4015; the number immediately following the designation indicates the year oforiginal adoption or, in the
2、case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.1. Scope*1.1 These test methods cover the determination of shear modulus, shear damping, rod modulus
3、 (commonly referred to asYoungs modulus), and rod damping modulus and shear damping as a function of shear strain amplitude for solid cylindricalspecimens of soil in the undisturbed intact and remolded conditions by vibration using the resonant column. column devices. Thevibration of the specimen ma
4、y be superposed on a controlled ambientstatic state of stress in the specimen. The vibration apparatusand specimen may be enclosed in a triaxial chamber and subjected to an all-around pressure and axial load. In addition, thespecimen may be subjected to other controlled conditions (for example, pore
5、-water pressure, degree of saturation, temperature).These test methods of modulus and damping determination are considered nondestructive when the shear strain amplitudes ofvibration are less than 1042 rad % (1044 in. in./in.), in.), and many measurements may be made on the same specimen andwith var
6、ious states of ambientstatic stress.1.2 Two device configurations are covered by these test methods: Device Type 1 where a known torque is applied to the topof the specimen and the resulting rotational motion is measured at the top of the specimen, and Device Type 2 where anuncalibrated torque is ap
7、plied to the top of the specimen and the torque transmitted through the specimen is measured by a torquetransducer at the base of the specimen. For both devices, the torque is applied to the active end (usually top) of the specimen andthe rotational motion also is measured at the active end of the s
8、pecimen.1.3 These test methods cover only are limited to the determination of the shear modulus and shear damping, the necessaryvibration, and specimen preparation procedures related to the vibration, etc., and do not cover the application, measurement, orcontrol of the ambient stress. axial and lat
9、eral static normal stresses. The latter procedures may be covered by, but are not limitedto, Test MethodsMethod D2166D2850, D3999/D3999M, D4767, D5311/D5311M, or D2850D7181.1.4 Significant DigitsAll recorded and calculated values shall conform to the guide for significant digits and roundingestablis
10、hed in Practice D6026.1.4.1 The procedures used to specify how data are collected/recorded and calculated in this standard are regarded as the industrystandard. In addition, they are representative of the significant digits that should generally be retained. The procedures used do notconsider materi
11、al variation, purpose for obtaining the data, special purpose studies, or any considerations for the users objectives;and it is common practice to increase or reduce significant digits of reported data to be commensurate with these considerations.It is beyond the scope of this standard to consider s
12、ignificant digits used in analysis methods for engineering design.1.4.2 Measurements made to more significant digits or better sensitivity than specified in this standard shall not be regarded anonconformance with this standard.1.5 UnitsThe values stated in SI units are to be regarded as the standar
13、d. Reporting standard. The values given in parenthesesare mathematical conversions to inch-pound units, which are provided for information only and are not considered standard.Reporting of test results in units other than SI shall not be regarded as conformancenonconformance with these test methods.
14、1.5.1 The converted inch-pound units use the gravitational system of units. In this system, the pound (lbf) represents a unit offorce (weight), while the unit for mass is slugs. The converted slug unit is not given, unless dynamic (F = ma) calculations areinvolved.1.5.2 It is common practice in the
15、engineering/construction profession to concurrently use pounds to represent both a unit ofmass (lbm) and of force (lbf). This implicitly combines two separate systems of units; that is, the absolute system and thegravitational system. It is scientifically undesirable to combine the use of two separa
16、te sets of inch-pound units within a single1 These test methods are under the jurisdiction of ASTM Committee D18 on Soil and Rock and are the direct responsibility of Subcommittee D18.09 on Cyclic andDynamic Properties of Soils.Current edition approved Sept. 1, 2007Oct. 1, 2015. Published October 20
17、07November 2015. Originally approved in 1981. Last previous edition approved in 20002007as D4015 92D4015 07. (2000). DOI: 10.1520/D4015-07.10.1520/D4015-15.This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made
18、to the previous version. Becauseit may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current versionof the standard as published by ASTM is to be considered the official document.*A Sum
19、mary of Changes section appears at the end of this standardCopyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1standard. As stated, this standard includes the gravitational system of inch-pound units and does not use/present the slug unit
20、 formass. However, the use of balances or scales recording pounds of mass (lbm) or recording density in lbm/ft3 shall not be regardedas nonconformance with this standard.1.6 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibilit
21、yof the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatorylimitations prior to use.2. Referenced Documents2.1 ASTM Standards:2D653 Terminology Relating to Soil, Rock, and Contained FluidsD2166D2166/D2166M Test Method for Unconfine
22、d Compressive Strength of Cohesive SoilD2216 Test Methods for Laboratory Determination of Water (Moisture) Content of Soil and Rock by MassD2850 Test Method for Unconsolidated-Undrained Triaxial Compression Test on Cohesive SoilsD3740 Practice for Minimum Requirements for Agencies Engaged in Testing
23、 and/or Inspection of Soil and Rock as Used inEngineering Design and ConstructionD3999/D3999M Test Methods for the Determination of the Modulus and Damping Properties of Soils Using the Cyclic TriaxialApparatusD4753 Guide for Evaluating, Selecting, and Specifying Balances and Standard Masses for Use
24、 in Soil, Rock, and ConstructionMaterials TestingD4767 Test Method for Consolidated Undrained Triaxial Compression Test for Cohesive SoilsD5311/D5311M Test Method for Load Controlled Cyclic Triaxial Strength of SoilD6026 Practice for Using Significant Digits in Geotechnical DataD7181 Test Method for
25、 Consolidated Drained Triaxial Compression Test for Soils3. Terminology3.1 DefinitionsFor definitions of other terms used in this Test Method,these test methods, see Terminology D653.3.2 Definitions of Terms Specific to This Standard:3.2.1 ambient stressstresses applied to the specimen, during the t
26、est, that do not result from the vibration strains. These testmethods do not cover the application and measurement of ambient stresses; however, the ambient stress at the time of measurementof the system resonant frequency and system damping shall be measured and recorded in accordance with the Repo
27、rt section ofthese test methods.3.2.1 apparatus model anddamping capacity D constantsunitless, typically expressed in %,nthe rigidity and massdistribution of the resonant column shall be as required in the following section in order for the resonant-column system to beaccurately represented by the m
28、odel shown in Fig. 1. The apparatus constants are the mass of the passive-end platen, Min P,including the mass resonant column systems, of all attachments rigidly connected to it; the rotational inertia of the passive-endplaten,is related to the component of the dynamic shear JmodulusP, including th
29、e rotational inertia of all attachments rigidlyconnected to it; similar mass, that lags the MA, and rotational inertia, JA, for the active-end platen and all attachments rigidlyconnected to it, such as portions of the vibration excitation device; the spring and damping constants for both longitudina
30、l andtorsional springs and dashpots (KSL, KST, ADCL, ADCT); the apparatus resonant frequencies for longitudinal vibration, f oL, andtorsional vibration, foT; the force/current constant, FCF, relating applied vibratory force to the current applied to the longitudinalexcitation device; the torque/curr
31、ent constant, applied shear stress by 90 degrees. TCF, relating applied vibratory torque to thecurrent applied to the torsional excitation device; and the motion transducer calibration factors (LCFA, RCFA, LCF P, RCFP)relating the transducer outputs to active- and passive-end longitudinal and rotati
32、onal 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 from torsional vibration. The rod and shear moduli shall be defined as the elasticmoduli of a uniform, linearly viscoelastic
33、 (Voigt model) specimen of the same mass density and dimensions as the soil specimennecessary to produce a resonant column having the measured system resonant frequency and response due to a given vibratoryforce or torque input.The stress-strain relation for a steady-state vibration in the resonant
34、column is a hysteresis loop.These moduliwill correspond to the slope of a line through the end points of the hysteresis loop. The section on calculations provides forcomputation of rod and shear moduli from the measured system longitudinal and torsional resonant frequencies. The energydissipated by
35、the system is a measure of the damping of the soil. Damping will be described by the rod damping ratio, DL, andthe shear damping ratio, DT, which are analogous to the critical viscous damping ratio, c/cr, for a single-degree-of-freedom system.The damping ratios shall be defined by:DL 50.5/E! (1)2 Fo
36、r referencedASTM standards, visit theASTM website, www.astm.org, or contactASTM Customer Service at serviceastm.org. For Annual Book of ASTM Standardsvolume information, refer to the standards Document Summary page on the ASTM website.D4015 152where: = viscous coefficient for rod motion, Ns/m2, = ci
37、rcular resonant frequency, rad/s, andE = rod modulus, Pa.and by:DT 50.5/G! (2)where: = viscous coefficient for torsional motion, N-s/m2, andG = shear modulus, Pa.3.2.3.1 Values of damping determined in this way will correspond to the area of the stress-strain hysteresis loop divided by 4times the el
38、astic strain energy stored in the specimen at maximum strain. Methods for determining damping ratio are prescribedlater. In viscoelastic theory, it is common to use complex moduli to express both modulus and damping. The complex rod modulusis given by:E*5E112iD L! (3)and the complex shear modulus is
39、 given by:G*5G112iDT! (4)where i5=21.3.2.2 resonant-column systemDevice Type 1, DT1, na system consisting of a cylindrical specimen or column ofin resonantcolumn systems, soil that has platens attached to each end a resonant column system as shown in Fig. 1. A sinusoidal vibrationexcitation device i
40、s attached to the active-end platen. The other end is the passive-end platen. It may be rigidly fixed (the criterionfor establishing fixity is given later) or its mass and rotational inertia must be known. The vibration excitation device mayincorporate springs and dashpots where the passive end plat
41、en is directly connected to the active-end platen, where the springconstants and viscous damping coefficients are known. Vibration excitation may be longitudinal or torsional. A given apparatusmay have the capability of applying one or the other, or both. The mass and rotational inertia of the activ
42、e-end platen and portionsof the vibration excitation device moving with it must be known. Transducers are used to measure the vibration amplitudes for eachtype of motion Fixed Base (no torque transducer), a calibrated vibratory torque is applied to the active end, and rotation ismeasured at the acti
43、ve end and also at the passive end if it is not rigidly fixed. The frequency of excitation will be adjusted toproduce resonance of the system, composed of the specimen and its attached platens and vibration excitation device.end.For Device Type 1, no torque transducer is needed and the Passive End P
44、laten is connected to the Fixed Base.FIG. 1 Resonant-column SchematicResonant-Column Schematic for Both Device Types 1 and 2D4015 1533.2.2.1 DiscussionThe vibration excitation device may incorporate springs and dashpots connected to the active-end platen, where the springconstants and viscous dampin
45、g coefficients must be known. The rotational inertia of the active-end platen and portions of thevibration excitation device moving with it must be known.3.2.3 Device Type 2, DT2, nin resonant column systems, a resonant column system as shown in Fig. 1 where the passive endplaten is connected to a t
46、orque transducer, an uncalibrated torque is applied to the active end, torque is measured by the torquetransducer at the passive end, and rotation is measured at the active end.3.2.3.1 DiscussionThe vibration excitation device may incorporate springs and dashpots connected to the active-end platen,
47、but the spring constantsand viscous damping coefficients are not needed. The rotational inertia of the active-end platen and portions of the vibrationexcitation device moving with it also are not needed.3.2.4 dynamic shear modulus, G* FL-2, nin resonant column systems, is the ratio of shear stress t
48、o shear strain undervibratory conditions (also known as complex shear modulus).3.2.5 equivalent elastic shear modulus G FL-2, nin resonant column systems, is the component of the dynamic shearmodulus that is in-phase with the applied shear stress.3.2.6 resonant-column system, na system as shown in F
49、ig. 1 consisting of a cylindrical specimen or column of soil enclosedwith a flexible membrane that has platens attached to each end and where a sinusoidal vibration excitation device is attached tothe active-end platen and where the other end is the passive-end platen that is rigidly fixed.3.2.7 specimen strainshear strain , unitless, frequently expressed as %,nfor longitudinal motion, the strain, , is theaverage axial strain in the entire specimen. For torsional motion, the strain, , in resonant column systems, is the average
