1、Designation: D5858 96 (Reapproved 2015)Standard Guide forCalculating In Situ Equivalent Elastic Moduli of PavementMaterials Using Layered Elastic Theory1This standard is issued under the fixed designation D5858; the number immediately following the designation indicates the year oforiginal adoption
2、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 el
3、astic 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 particu
4、lar 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 gener
5、al 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 vari
6、ous 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 desi
7、red, 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 does
8、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 co
9、llection 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 is
10、 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 ha
11、s been approvedthrough the ASTM consensus process.2. Referenced Documents2.1 ASTM Standards:4D653 Terminology Relating to Soil, Rock, and ContainedFluidsD4123 Test Method for Indirect Tension Test for ResilientModulus of Bituminous Mixtures (Withdrawn 2003)5D4602 Guide for Nondestructive Testing of
12、Pavements Us-ing Cyclic-Loading Dynamic Deflection EquipmentD4694 Test Method for Deflections with a Falling-Weight-Type Impulse Load DeviceD4695 Guide for General Pavement Deflection Measure-ments3. Terminology3.1 DefinitionsIn addition to Terminology D653, the fol-lowing definitions are specific t
13、o this standard: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 and Evaluation.Current edition approved May 1, 2015. Published June 2015. Originallyapproved in 1996. Last previous edit
14、ion approved in 2008 as D5858 96 (2008).DOI: 10.1520/D5858-96R15.2The 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 th
15、e 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. M. Stoffels“ Determining Asphalt ConcretePavement Structural Properties by Nondestructive Testing,” NCHRP Report No.327, National Cooperative Highway Research Program, 1
16、990.4For 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.5The last approved version of this historical standard is
17、 referenced onwww.astm.org.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States13.1.1 backcalculationanalytical technique used to deter-mine the equivalent elastic moduli of pavement layers corre-sponding to the measured load and deflectio
18、ns. 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-linear regression equations developedfrom layered elastic analysis output data). The pr
19、imary 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 involves assuming “seed” moduli values fora layered pavement structure, computing the surf
20、ace 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 and measured deflections are withinselected tolerance(s) or the maximum number of iterati
21、ons 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 is found that “closely matches” themeasured deflection basin. When analyzing pavementbe
22、havior, surface deflections and other responses are typicallycalculated (in the “forward” direction) from layered pavementanalysis programs that use layer moduli as input. In“backcalculation,” layer moduli are selected and adjusted toultimately compute surface deflections that best match knownsurfac
23、e deflections.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 minimize angular rotation with respect to itsmeasuring plane at the expected movement. Sensor
24、s 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 the peak measurements of five or more deflection sensors.3.1.4 equivalent elastic modulusthe
25、 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-dures for an assigned layer of known or assumed thickness.The collection of all of these la
26、yer 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 to thatused in backcalculation.3.1.5 pavement materialsthe physical constituents that arec
27、ontained in all of the various layers of the pavement system;these layers consist of various thicknesses of placed or stabi-lized 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 test
28、measurement 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 by the recoverable axial strainthat occurs when a confined or unconfined and axially loade
29、dcylindrical material specimen is loaded and unloaded. Theresilient modulus is a function of load duration, load frequency,and number of cycles:Mr5 d/er(1)where:d= the applied deviator stress, ander= the recoverable (resilient) axial strain.4. Summary of Guide4.1 A necessary requirement of most over
30、lay 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 determine the overall structural effectiveness ofthe existing pavement to carry load repetit
31、ions. 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-tively describe the overall structural capacity of the pavementsystem.4.2 A pavement defle
32、ction basin can be induced by a staticor dynamic surface load. Some pavement materials areviscoelastic, meaning they exhibit elastic behavior at high ratesof loading while viscous flow becomes more significant at veryslow rates of loading. For this reason, layered elastic theory isappropriate for dy
33、namic 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 at each of thedeflection sensors are also dynamic; however, these peakamplitude values do not
34、 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 of “equal”magnitude had been applied statically.4.3 Layered elastic theory is one of the mo
35、re 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 layer moduli in flexible pavements. Variouscomputer programs that use some type of deflection-ma
36、tchingiterative procedure or database searching technique have beendeveloped to estimate 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 and
37、overlay design calculations.6The 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.Army Corps of EngineersWaterways Experiment
38、 Station.See VanCauwelaert, Alexander, Barker, and White,“ A Competent MultilayerSolution and Backcalculation Procedure for Personal Computers,” ASTM STP 1026,November 1989.D5858 96 (2015)24.4 Presently, there are two distinct categories of analysismethods that may be applied to flexible pavements:
39、quasi-staticand 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 finite element methods. As a general principle, theselection of a method for analyzing NDT data to
40、 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 is to be used in analyzing the pavements for rehabili-tation design purposes, the same compu
41、ter 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 design, it also should be used for analyzing NDT pavementdata. In summary, it is important t
42、o 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 layermoduli is that the solution initiates at the outer deflectionsensor location(s) to determine
43、 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”lower layer moduli and the deflections at smaller radial offsetsto calculate the moduli of the
44、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 trans-formed section methods, the sequence may not be the same. Inall approaches, layer thickn
45、esses 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 specificpavement types and specific NDT devices.3Also, some pave-ment analysis models are rest
46、ricted 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 is intended to present the elements of anapproach for estimating layer moduli from deflectio
47、n 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 and used by some overlay designprocedures is the resilient modulus. Deflection analysis pro-
48、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 samples. For many overlaydesign procedures that are based on layered elastic theory, theresi
49、lient 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 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 guid
