1、Designation: D 5858 96 (Reapproved 2003)Standard Guide forCalculating In Situ Equivalent Elastic Moduli of PavementMaterials Using Layered Elastic Theory1This standard is issued under the fixed designation D 5858; the number immediately following the designation indicates the year oforiginal adoptio
2、n or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (e) indicates an editorial change since the last revision or reapproval.1. Scope1.1 This guide covers the concepts for calculating the in situequivalent layer
3、 elastic moduli can be used for pavementevaluation, rehabilitation and overlay design. The resultingequivalent elastic moduli calculated from the deflection dataare method-dependent and represent the stiffnesses of thelayers under a specific nondestructive deflection testing (NDT)device at that part
4、icular test load and frequency, temperature,and other environmental and site-specific conditions. Adjust-ments for design load, reference temperature, and other design-related factors are not covered in this guide. The intent of thisguide is not to recommend one specific method, but to outlinethe ge
5、neral approach for estimating the in situ elastic moduli ofpavement layers.1.2 This guide is applicable to flexible pavements and insome cases, rigid pavements (that is, interior slab loading), butis restricted to the use of layered elastic theory2as the analysismethod. It should be noted that the v
6、arious available layeredelastic computer modeling techniques use different assump-tions and algorithms and that results may vary significantly.Other analysis procedures, such as finite element modeling,may be used, but modifications to the procedure are required.NOTE 1If other analysis methods are d
7、esired, the report listed inFootnote 3 can provide some guidance.1.3 The values stated in inch-pound units are to be regardedas the standard. The SI units given in parentheses are forinformation only.1.4 This standard does not purport to address all of thesafety concerns, if any, associated with its
8、 use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.31.5 This guide offers an organized collection of informationor a series of options and does not recommend a specif
9、iccourse of action. This document cannot replace education orexperience and should be used in conjunction with professionaljudgment. Not all aspects of this guide may be applicable in allcircumstances. This ASTM standard is not intended to repre-sent or replace the standard of care by which the adeq
10、uacy ofa given professional service must be judged, nor should thisdocument be applied without consideration of a projects manyunique aspects. The word “Standard” in the title of thisdocument means only that the document has been approvedthrough the ASTM consensus process.2. Referenced Documents2.1
11、ASTM Standards:4D 653 Terminology Relating to Soil, Rock, and ContainedFluidsD 4123 Test Method for Indirect Tension Test for ResilientModulus of Bituminous MixturesD 4602 Guide for Nondestructive Testing of PavementsUsing Cyclic-Loading Dynamic Deflection EquipmentD 4694 Test Method for Deflections
12、 with a Falling-Weight-Type Impulse Load DeviceD 4695 Guide for General Pavement Deflection Measure-ments3. Terminology3.1 DefinitionsIn addition to Terminology D 653, thefollowing definitions are specific to this standard:1This guide is under the jurisdiction of ASTM Committee E17 on Vehicle-Paveme
13、nt Systems and is the direct responsibility of Subcommittee E17.41 onPavement Management.Current edition approved Dec. 1, 2003. Published December 2003. Originallyapproved in 1996. Last previous edition approved in 1996 as D 5858 96e1.2The concepts of elastic layer theory are discussed in Chapter 2
14、of Principles ofPavement Design, by E. J. Yoder and M. W. Witczak, published by John Wiley andSons, Inc., 1975.3Corrections or adjustments and a complete discussion of the use of each ofthese analysis methods with different NDT devices may be found in: Lytton, R. L.,F. P. Germann, Y. J. Chou, and S.
15、 M. Stoffels“ Determining Asphalt ConcretePavement Structural Properties by Nondestructive Testing,” NCHRP Report No.327, National Cooperative Highway Research Program, 1990.4For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For
16、Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.3.1.1 backcalculationanalytical technique used to deter-mine the equival
17、ent elastic moduli of pavement layers corre-sponding to the measured load and deflections. The analysismay be performed by any of the following methods: iteration,database-searching, closed-form solutions (currently availableonly for two layer pavement systems), and simultaneousequations (using non-
18、linear regression equations developedfrom layered elastic analysis output data). The primary empha-sis of this guide will be concerned with the first method;however, many of the ideas pertaining to the use of the iterativeconcept also apply to the other approaches. An iterativeanalysis procedure inv
19、olves assuming “seed” moduli values fora layered pavement structure, computing the surface deflectionat several radial distances from the load, comparing thecomputed and measured deflections, and repeating the process,changing the layer moduli each time, until the differencebetween the calculated an
20、d measured deflections are withinselected tolerance(s) or the maximum number of iterations hasbeen reached. Alternatively, the analysis procedure may in-volve searching through a data base of precalculated deflectionbasins computed from a factorial of known layer moduli andthicknesses until a basin
21、is found that “closely matches” themeasured deflection basin. When analyzing pavement behav-ior, surface deflections and other responses are typicallycalculated (in the “forward” direction) from layered pavementanalysis programs that use layer moduli as input. In “backcal-culation,” layer moduli are
22、 selected and adjusted to ultimatelycompute surface deflections that best match known surfacedeflections.3.1.2 deflection sensorthe term that shall be used in thisguide to refer to the electronic device(s) capable of measuringthe vertical movement of the pavement and mounted in such amanner as to mi
23、nimize angular rotation with respect to itsmeasuring plane at the expected movement. Sensors may be ofseveral types, such as seismometers, velocity transducers, oraccelerometers.3.1.3 deflection basinthe idealized shape of the deformedpavement surface due to a cyclic or impact load as depictedfrom t
24、he peak measurements of five or more deflection sensors.3.1.4 equivalent elastic modulusthe effective in situmodulus of a material, which characterizes the relationship ofstress to strain, specific to the conditions that existed at the timeof NDT testing, that is determined by backcalculation proce-
25、dures for an assigned layer of known or assumed thickness.The collection of all of these layer moduli will produce, withinreasonable limits, the same surface deflections as measured atvarious distances from the center of the load when entered intoa layered elastic pavement simulation model analogous
26、 to thatused in backcalculation.3.1.5 pavement materialsthe physical constituents thatare contained in all of the various layers of the pavementsystem; these layers consist of various thicknesses of placed orstabilized in-place materials for supporting traffic as well as thenative subgrade or embank
27、ment material being protected.3.1.6 resilient modulus of elasticity (Mr)a laboratory testmeasurement of the behavior of a material sample (either anintact core or a recompacted specimen) used to approximatethe in situ response. Specifically as shown below, the appliedcyclic deviator stress divided b
28、y the recoverable axial strainthat occurs when a confined or unconfined and axially loadedcylindrical material specimen is loaded and unloaded. Theresilient modulus is a function of load duration, load frequency,and number of cycles:Mr5sd/er(1)where:sd= the applied deviator stress, ander= the recove
29、rable (resilient) axial strain.4. Summary of Guide4.1 A necessary requirement of most overlay or rehabilita-tion design procedures is some measure of the in situ or“effective” structural value of the existing pavement. For years,center-of-load (or maximum) deflection measurements havebeen used to de
30、termine the overall structural effectiveness ofthe existing pavement to carry load repetitions. The analysis ofindividual surface deflection values and the deflection shape or“basin” represents a technique that can be used to determineseparate estimates of the effective layer properties that collec-
31、tively describe the overall structural capacity of the pavementsystem.4.2 A pavement deflection basin can be induced by a staticor dynamic surface load. Some pavement materials are vis-coelastic, meaning they exhibit elastic behavior at high rates ofloading while viscous flow becomes more significan
32、t at veryslow rates of loading. For this reason, layered elastic theory isappropriate for dynamic loading; however, it is difficult toverify whether these magnitudes of deflection equate to thosemeasured under static loading. When dynamic loadings areapplied, the resulting displacements registered a
33、t each of thedeflection sensors are also dynamic; however, these peakamplitude values do not all occur at the same time. In a staticanalysis, such as layered elastic theory, these peak dynamicdeflections are analyzed as if they are equivalent in magnitudeto the deflections that would occur if a load
34、 of “equal”magnitude had been applied statically.4.3 Layered elastic theory is one of the more commonanalysis methods being used in the design of flexible pave-ments and, to a lesser degree, rigid pavements. This guide isprimarily concerned with the use of layered elastic theory tocalculate the laye
35、r moduli in flexible pavements. Variouscomputer programs that use some type of deflection-matchingiterative procedure or database searching technique have beendeveloped to estimate the pavement material moduli.5Thisguide discusses the various elements of procedures for calcu-lating and reporting in
36、situ layer moduli of the pavementcross-section that could then be used in rehabilitation andoverlay design calculations.4.4 Presently, there are two distinct categories of analysismethods that may be applied to flexible pavements: quasi-static5The following is a list of some of the backcalculation c
37、omputer programs thathave been developed: MODULUS, ELMOD, ISSEM4, MODCOMP, FPEDD1,EVERCALC, WESDEF, and BOUSDEF. One of the procedures, WESDEF, isavailable through the U.S.Army Corps of EngineersWaterways Experiment Station.See VanCauwelaert, Alexander, Barker, and White,“ A Competent MultilayerSolu
38、tion and Backcalculation Procedure for Personal Computers,” ASTM STP 1026,November 1989.D 5858 96 (2003)2and dynamic. The quasi-static elastic approaches referred to inthis guide, include the Boussinesq-Odemark transformed sec-tion methods, the numerical integration layered subroutines,and the finit
39、e element methods. As a general principle, theselection of a method for analyzing NDT data to determinelayer moduli should be compatible with the analysis procedurethat will eventually be used for designing the flexible pavementrehabilitation. That is, if a particular layered elastic computerprogram
40、 is to be used in analyzing the pavements for rehabili-tation design purposes, the same computer program (or itsequivalent) should be used as the basis for determining thematerial properties from nondestructive testing of pavements.Similarly, if a finite element procedure is to be used as a basisfor
41、 design, it also should be used for analyzing NDT pavementdata. In summary, it is important to consistently use the sameanalysis method in both backcalculation and design applica-tions.4.5 The fundamental approach employed in most iterativebackcalculation analysis methods estimating the in situ laye
42、rmoduli is that the solution initiates at the outer deflectionsensor location(s) to determine the moduli of the lowestsubgrade layer above the apparent stiff layer, that usually hasan assigned modulus (see Fig. 1). The calculation sequenceprogresses toward the center of the basin using the “known”lo
43、wer layer moduli and the deflections at smaller radial offsetsto calculate the moduli of the higher layers. This sequence isrepeated in an iterative cycle until a solution is obtained thatnearly matches the calculated and measured deflections. Whenusing the database-searching or Boussinesq-Odemark t
44、rans-formed section methods, the sequence may not be the same. Inall approaches, layer thicknesses and Poissons ratios musteither be known or assumed. Although the principles of theseapproaches are applicable to all pavement types (flexible andrigid), some analysis methods are more appropriate for s
45、pecificpavement types and specific NDT devices.3Also, some pave-ment analysis models are restricted to pavement structureswhere the strength of layers decreases with depth (for example,cement-aggregate mixtures could not be modeled below agranular base material).5. Significance and Use5.1 This guide
46、 is intended to present the elements of anapproach for estimating layer moduli from deflection measure-ments that may then be used for pavement evaluation oroverlay design. To characterize the materials in the layers of apavement structure, one fundamental input parameter mea-sured in the laboratory
47、 and used by some overlay designprocedures is the resilient modulus. Deflection analysis pro-vides a technique that may be used to estimate the in situequivalent layer elastic moduli of a pavement structure asopposed to measuring the resilient moduli in the laboratory ofsmall and sometimes disturbed
48、 samples. For many overlaydesign procedures that are based on layered elastic theory, theresilient modulus is approximated by this equivalent layerelastic modulus, because the equivalent modulus is determinedas an average value for the total layer at the in situ stressconditions of an actual pavemen
49、t.5.2 It should be emphasized that layer moduli calculatedwith this procedure are for a specific loading condition and forthe environmental conditions at the time of testing. For thesemoduli to be used in pavement evaluations and overlay design,adjustments to a reference temperature, season, and design loadmay be required. These adjustments are not a part of this guide.5.3 The underlying assumption used in the solution is that arepresentative set of layer moduli exists for the particularloading condition (magnitude and area) and temperature con-dition, such that the theoret
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