# ASTM D7228-06a (Reapproved 2015)

Designation: D7228 − 06a (Reapproved 2015)Standard Test Method forPrediction of Asphalt-Bound Pavement Layer Temperatures1This standard is issued under the fixed designation D7228; the number immediately following the designation indicates the year oforiginal adoption 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 test method covers a means of predicting tempera-tures within the asphalt-bound layer(s) of a flexible pavementsection.1.2 Deflection testing commonly involves the measurementof pavement surface temperatures. This standard is based ontemperature relationships developed as part of the FederalHighway Administration (FHWA) Long Term Pavement Per-formance (LTPP) Seasonal Monitoring Program.2. Referenced Documents2.1 ASTM Standards:2D4694 Test Method for Deflections with a Falling-Weight-Type Impulse Load DeviceD4695 Guide for General Pavement Deflection Measure-mentsD4602 Guide for Nondestructive Testing of Pavements Us-ing Cyclic-Loading Dynamic Deflection EquipmentD5858 Guide for Calculating In Situ Equivalent ElasticModuli of Pavement Materials Using Layered ElasticTheory2.2 AASHTO Standards:3T256-00 Standard Method of Test for Pavement DeflectionMeasurementsT317-02 Standard Method of Test for Prediction of Asphalt-Bound Pavement Layer Temperatures2.3 Federal Highway Administration:4FHWA-RD-98-085, Temperature Predictions and Adjust-ment Factors for Asphalt Pavements, June 2000LTPP Guide to Asphalt Temperature Prediction and Correc-tion, Online Temperature Prediction and CorrectionGuide—TOC, November 20023. Terminology3.1 Definitions of Terms Specific to This Standard:3.1.1 BELLS —an acronym based on the initials of the fourdevelopers of the method: Baltzer, Ertman-Larsen, Lukanen,and Stubstad.3.1.2 depth—the distance below the surface of the top layerof asphalt.3.1.3 1-day air temperature—the average of the minimumand maximum air temperatures at the location of testing duringthe previous complete 24-hour day.4. Summary of Test Method4.1 Input Data Elements:4.1.1 IR Temperature—The exposed surface temperature ofan asphalt pavement is measured, preferably with an infrared(IR) temperature sensing device that is properly calibrated.4.1.2 Time of Day—The time of day the temperature mea-surement takes place is recorded.4.1.3 1-Day Temperature—The average 1-day air tempera-ture of the previous complete 24-hour day is determined andrecorded.4.1.4 Pavement Depth—The depth at which an estimate ofthe asphalt layer temperature is required is specified.4.2 The input data elements are entered into a regressionformula that predicts the temperature within the asphalt pave-ment at depth.5. Significance and Use5.1 Analysis of deflection data from asphalt pavementsalmost always requires that the raw deflections or the analysisresults from the load-deflection data be adjusted for the effectsof pavement surface course temperature. Measuring the tem-perature at-depth normally requires that a hole be drilled intothe pavement, partially filled with fluid, and the temperaturemeasured with a hand-held device.Alternatively, thermistors orother temperature instrumentation may be permanently in-stalled at various locations.5.2 Current deflection testing equipment is often equippedwith surface temperature sensing devices, for example an1This test method 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 Sept. 1, 2015. Published December 2015. Originallyapproved in 2006. Last previous edition approved in 2011 as D7228 – 06A(2011).DOI: 10.1520/D7228-06AR15.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at service@astm.org. For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.3Available from American Association of State Highway and TransportationOfficials (AASHTO), 444 N. Capitol St., NW, Suite 249, Washington, DC 20001.4Available from Federal Highway Administration (FHWA) 400 Seventh Street,SW Washington, DC 20590.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1infrared thermometer that measures the surface temperature atevery test location. To adequately adjust the deflection ordeflection results for the effects of temperature, the temperatureat some depth must be known.5.3 This test method provides a means of estimating thetemperature at-depth from the pavement surface temperature,the time of day, the previous day’s high and low airtemperatures, and the desired depth where the temperature is tobe estimated. Utilization of this method results in a significantsavings in time over the conventional practice of manuallydrilling holes into the pavement, and it results in a significantincrease in the volume of temperature data (one pavementtemperature for each test point) and the ability to recordtemperature variations between test points.6. Apparatus6.1 Surface Temperature Measurement Device—The surfacetemperature measurement device can be an infrared (IR)thermometer mounted on a deflection device, a hand-held IRthermometer, or a surface contact thermometer. The tempera-ture measurement device should be calibrated according to themanufacturer’s recommendations.7. Calculation7.1 BELLS Method—The BELLS method for productiontesting (called BELLS3 in other publications) has been derivedbased on temperature measurements taken on pavement sur-faces that have been shaded for a short period (less than oneminute) of time. The following equation is valid for approxi-mately 30 seconds of shading:Td5 0.9510.892*IR1$log~d! 2 1.25% $20.448*IR10.621*~1 2 day!11.83* sin ~hr182 15.5!%10.042*IR* sin ~hr182 13.5! (1)where:Td= pavement temperature at depth d, °C,IR = infrared surface temperature, °C,log = base 10 logarithm,d = depth at which asphalt temperature is to bepredicted, mm,1-day = average of the minimum and maximum airtemperatures, °C, for the previous complete 24-hourday before testing,sin = sin function in 18-hour clock system, with 2πradians equal to one 18-hour cycle, andhr18= time of day, in 24-hour system, but calculated usingan 18-hour temperature rise and fall cycle, asindicated in 7.1.1 and 7.1.2.7.1.1 When using the sin (hr18– 15.5) decimal timefunction, only use times from 11:00 to 05:00 hrs. If the actualtime is not within this time range, then calculate the sin as if thetime is 11:00 hrs (where the sin = –1). If the time is betweenmidnight and 05:00 hrs, add 24 to the actual decimal time.Then calculate as follows: If the time is 13:15, then in decimalform, 13.25 – 15.50 = –2.25; –2.25/18 = –0.125; –0.125 × 2π= –0.785 radians; sin (–0.785) = –0.707. In this case an 18 hoursin function is assumed, with a flat (= –1) sin segment between05:00 and 11:00 hours.7.1.2 When using the sin (hr18– 13.5) decimal function,only use times from 09:00 to 03:00 hrs. If the actual time is notwithin this time range, then calculate the sin as if the time is09:00 hrs (where the sin = –1). If the time is between midnightand 03:00 hrs, add 24 to the actual (decimal) time. Thencalculate as follows: If the time is 15:08, then in decimal form,15.13 – 13.50 = 1.63; 1.63/18 = 0.091; 0.091 × 2π = 0.569radians; sin (0.569) = 0.539. In this case an 18 hour sinfunction is assumed, with a flat (= –1) sin segment between03:00 and 09:00 hours.NOTE 1—BELLS has been verified using the LTPPdatabase at both middepth and third depth temperature points.The regressions derived from thedata at either depth were virtually identical; therefore, they were combinedin deriving the BELLS equations. The asphalt layer thicknesses covered inthe database were primarily between 50 mm and 300 mm; thereforetemperature prediction depths within the AC layer should be limited tobetween 25 mm and 150 mm beneath the surface. Although this testmethod may be used for at-depth temperatures greater than 150 mmthrough extrapolation, the results have not been verified or calibrated todate. Since the equation’s boundary condition at depth=0isinconsistentwith the input IR temperature value, the determination of an at-depthpayment temperature less than 25 mm is not recommended.NOTE 2—The database used to derive the BELLS equations consistsprimarily of data gathered during daylight hours between approximately06:00 hrs and 18:00 hrs.Although the test method may be used outside ofthis time frame through extrapolation of the 18-hour sinusoidalrelationships, the results have not been verified or calibrated to date.8. Report8.1 The type of temperature measuring device, the measure-ment shading conditions, the time of measurement, the date ofmeasurement, and the depth at which the temperature wascalculated should be identified.9. Precision and Bias9.1 A precision and bias statement for this standard has notbeen developed at this time. Therefore, this standard should notbe used for acceptance or rejection of a material for purchasingpurposes.NOTE 3—The BELLS equation for production testing (BELLS3) wasderived using the LTPP database (10 304 observations; R-squared =0.975). The regression’s standard estimate of error was 61.9°C based onan adjustment using the LTPP database for 30 seconds of shading. Usingthe regression approach on this database, by definition there was no bias.10. Keywords10.1 asphalt temperature; backcalculation; Benkelmanbeam; dynaflect; falling weight deflectometer; FWD; layermoduli; pavement temperature correction; road raterD7228 − 06a (2015)2APPENDIX(Nonmandatory Information)X1. EXAMPLE SOURCE CODE FOR CALCULATING THE PREDICTED ASPHALT TEMPERATUREBY THE BELLS METHODX1.1 ExplanationX1.1.1 Purpose—The source code is presented to illustrateapplication of the temperature prediction equations, particu-larly the application of the 18-hour sin functions.X1.1.2 Language—The source code is written in BASICand can be run on a number of basic interpreters or compilers,or easily converted to other computer languages.X1.2 Example Source Code Listing X1.2’Program to illustrate the implementation of the BELLS3 equation‘for routine testing with approximately 30 seconds of surface shade.’****************************************************************CLSINPUT 9Input Surface Temperature 9;irINPUT 9Input Hour of test 9;hrINPUT 9Input Minutes past the hour 9;minINPUT 9Input the depth for predicting the asphalt temperature 9;dINPUT 9Input average air temperature for the day before the testdate 9;airdecimal.hrs = hr + min / 60IF decimal.hrs 11 OR decimal.hrs 9ORdecimal.hrs 3 THENIF decimal.hrs 3 THEN decimal.hrs = decimal.hrs + 24sine13.5 = SIN(2 * pi * (decimal.hrs -13.5) / 18)ELSEsine13.5 = -1END IFtd=0.95+0.892*irlogdepth = LOG (d) / LOG (10) – 1.25firstbracket = –0.448 * ir + 0.621 * air + 1.83 * sine15.5last.term = 0.042 * ir * sine13.5td = td + logdepth * firstbracket + last.termX1.3 Example Temperature CalculationX1.3.1 The following link, LTPP Guide to Asphalt Tem-perature Prediction and Correction, courtesy of FHWA, pro-vides a spreadsheet macro to calculate any at-depth pavementtemperature: http://www.tfhrc.gov/pavement/ltpp/fwdcd/index.htm. When using this link, refer to the “BELLS3”calculation cells for routine pavement testing methods.IR temperature = 12.5°CTime of day = 08:10 hrsMid-depth of pavement surface course = 75 mmPrevious 1-day average air temperature = 23°CT75 mm5 0.9510.892*12.51$log~75! 2 1.25% 3 $20.448*12.510.621*~23!11.83* sin ~2 π 3 ~11.00 2 15.5! /18%10.042*12.5* sin ~2 π 3 ~08.17 2 13.5! / 18 (X1.1)T75 mm5 0.9510.892*12.51$1.875 2 1.25% 3 $20.448*12.510.621*~23!11.83*21%10,042*12.5*20.958 (X1.2)T75 mm5 0.95111.1510.625 3 $25.6114.28 2 1.83% 2 0.50 5 15.9°C(X1.3)ASTM International takes no position respecting the validity of any patent rights asserted in connection with any item mentionedin this standard. Users of this standard are expressly advised that determination of the validity of any such patent rights, and the riskof infringement of such rights, are entirely their own responsibility.This standard is subject to revision at any time by the responsible technical committee and must be reviewed every five years andif not revised, either reapproved or withdrawn. Your comments are invited either for revision of this standard or for additional standardsand should be addressed to ASTM International Headquarters. Your comments will receive careful consideration at a meeting of theresponsible technical committee, which you may attend. If you feel that your comments have not received a fair hearing you shouldmake your views known to the ASTM Committee on Standards, at the address shown below.This standard is copyrighted by ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959,United States. 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