1、Designation: D 5858 96 (Reapproved 2008)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 () 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 parti
4、cular 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 gen
5、eral 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 va
6、rious 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 de
7、sired, the report listed inFootnote 3 can provide some guidance.1.3 The values stated in inch-pound units are to be regardedas standard. The values given in parentheses are mathematicalconversions to SI units that are provided for information onlyand are not considered standard.1.4 This standard doe
8、s 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-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.31.5 This guide offers an organized
9、collection of informationor a series of options and does not recommend a specificcourse 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
10、is not intended to repre-sent or replace the standard of care by which the adequacy 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
11、has been approvedthrough the ASTM consensus process.2. Referenced Documents2.1 ASTM Standards:4D 653 Terminology Relating to Soil, Rock, and ContainedFluidsD 4123 Test Method for Indirect Tension Test for ResilientModulus of Bituminous Mixtures5D 4602 Guide for Nondestructive Testing of PavementsUsi
12、ng Cyclic-Loading Dynamic Deflection EquipmentD 4694 Test Method for Deflections 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 standa
13、rd:1This guide is under the jurisdiction of ASTM Committee E17 on Vehicle -Pavement Systems and is the direct responsibility of Subcommittee E17.41 onPavement Testing, Evaluation, and Management Methods.Current edition approved June 1, 2008. Published July 2008. Originally approvedin 1996. Last prev
14、ious edition approved in 2003 as D 5858 96 (2003).2The concepts of elastic layer theory are discussed in Chapter 2 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 o
15、fthese analysis methods with different NDT devices may be found in: Lytton, R. L.,F. P. Germann, Y. J. Chou, and S. M. Stoffels“ Determining Asphalt ConcretePavement Structural Properties by Nondestructive Testing,” NCHRP Report No.327, National Cooperative Highway Research Program, 1990.4For refere
16、nced 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.5Withdrawn.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box
17、C700, West Conshohocken, PA 19428-2959, United States.3.1.1 backcalculationanalytical technique used to deter-mine the equivalent 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-se
18、arching, closed-form solutions (currently availableonly for two layer pavement systems), and simultaneousequations (using non-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
19、the ideas pertaining to the use of the iterativeconcept also apply to the other approaches. An iterativeanalysis procedure involves assuming “seed” moduli values fora layered pavement structure, computing the surface deflectionat several radial distances from the load, comparing thecomputed and meas
20、ured deflections, and repeating the process,changing the layer moduli each time, until the differencebetween the calculated and measured deflections are withinselected tolerance(s) or the maximum number of iterations hasbeen reached. Alternatively, the analysis procedure may in-volve searching throu
21、gh a data base of precalculated deflectionbasins computed from a factorial of known layer moduli andthicknesses until a basin is found that “closely matches” themeasured deflection basin. When analyzing pavement behav-ior, surface deflections and other responses are typicallycalculated (in the “forw
22、ard” direction) from layered pavementanalysis programs that use layer moduli as input. In “backcal-culation,” layer moduli are 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 re
23、fer to the electronic device(s) capable of measuringthe vertical movement of the pavement and mounted in such amanner as to minimize angular rotation with respect to itsmeasuring plane at the expected movement. Sensors may be ofseveral types, such as seismometers, velocity transducers, oracceleromet
24、ers.3.1.3 deflection basinthe idealized shape of the deformedpavement surface due to a cyclic or impact load as depictedfrom the peak measurements of five or more deflection sensors.3.1.4 equivalent elastic modulusthe effective in situmodulus of a material, which characterizes the relationship ofstr
25、ess to strain, specific to the conditions that existed at the timeof NDT testing, that is determined by backcalculation proce-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 m
26、easured atvarious distances from the center of the load when entered intoa layered elastic pavement simulation model analogous 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 o
27、f various thicknesses of placed orstabilized in-place materials for supporting traffic as well as thenative subgrade or embankment 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 recompact
28、ed specimen) used to approximatethe in situ response. Specifically as shown below, the appliedcyclic deviator stress divided by the recoverable axial strainthat occurs when a confined or unconfined and axially loadedcylindrical material specimen is loaded and unloaded. Theresilient modulus is a func
29、tion of load duration, load frequency,and number of cycles:Mr5sd/er(1)where:sd= the applied deviator stress, ander= the recoverable (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
30、” structural value of the existing pavement. For years,center-of-load (or maximum) deflection measurements havebeen used to determine the overall structural effectiveness ofthe existing pavement to carry load repetitions. The analysis ofindividual surface deflection values and the deflection shape o
31、r“basin” represents a technique that can be used to determineseparate estimates of the effective layer properties that collec-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 materia
32、ls are vis-coelastic, meaning they exhibit elastic behavior at high rates ofloading while viscous flow becomes more significant at veryslow rates of loading. For this reason, layered elastic theory isappropriate for dynamic loading; however, it is difficult toverify whether these magnitudes of defle
33、ction equate to thosemeasured under static loading. When dynamic loadings areapplied, the resulting displacements registered at 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,
34、these peak dynamicdeflections are analyzed as if they are equivalent in magnitudeto the deflections that would occur if a load 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
35、a lesser degree, rigid pavements. This guide isprimarily concerned with the use of layered elastic theory tocalculate the layer moduli in flexible pavements. Variouscomputer programs that use some type of deflection-matchingiterative procedure or database searching technique have beendeveloped to es
36、timate the pavement material moduli.6Thisguide discusses the various elements of procedures for calcu-lating and reporting in 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 an
37、alysismethods that may be applied to flexible pavements: quasi-static6The following is a list of some of the backcalculation computer programs thathave been developed: MODULUS, ELMOD, ISSEM4, MODCOMP, FPEDD1,EVERCALC, WESDEF, and BOUSDEF. One of the procedures, WESDEF, isavailable through the U.S.Ar
38、my Corps of EngineersWaterways Experiment Station.See VanCauwelaert, Alexander, Barker, and White,“ A Competent MultilayerSolution and Backcalculation Procedure for Personal Computers,” ASTM STP 1026,November 1989.D 5858 96 (2008)2and dynamic. The quasi-static elastic approaches referred to inthis g
39、uide, include the Boussinesq-Odemark transformed sec-tion methods, the numerical integration layered subroutines,and the finite 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
40、eventually be used for designing the flexible pavementrehabilitation. That is, if a particular layered elastic computerprogram 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 themat
41、erial properties from nondestructive testing of pavements.Similarly, if a finite element procedure is to be used as a basisfor 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 app
42、lica-tions.4.5 The fundamental approach employed in most iterativebackcalculation analysis methods estimating the in situ layermoduli 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 usua
43、lly hasan assigned modulus (see Fig. 1). The calculation sequenceprogresses toward the center of the basin using the “known”lower 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
44、 obtained thatnearly matches the calculated and measured deflections. Whenusing the database-searching or Boussinesq-Odemark trans-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
45、 of theseapproaches are applicable to all pavement types (flexible andrigid), some analysis methods are more appropriate for specificpavement types and specific NDT devices.3Also, some pave-ment analysis models are restricted to pavement structureswhere the strength of layers decreases with depth (f
46、or example,cement-aggregate mixtures could not be modeled below agranular base material).5. Significance and Use5.1 This guide 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. T
47、o characterize the materials in the layers of apavement structure, one fundamental input parameter mea-sured in the laboratory 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 elasti
48、c moduli of a pavement structure asopposed to measuring the resilient moduli in the laboratory ofsmall and sometimes disturbed samples. For many overlaydesign procedures that are based on layered elastic theory, theresilient modulus is approximated by this equivalent layerelastic modulus, because th
49、e equivalent modulus is determinedas an average value for the total layer at the in situ stressconditions of an actual pavement.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
