1、Designation: D7228 06a (Reapproved 2011)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
2、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 pa
3、vementsection.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 Do
4、cuments2.1 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 PavementsUsing Cyclic-Loading Dynamic Deflection EquipmentD5858 Guide for Calculating In Situ
5、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 ofAsphalt-Bound Pavement Layer Temperatures2.3 Federal Highway Administration:4FHWA-RD-98-
6、085, Temperature Predictions and Adjust-ment Factors for Asphalt Pavements, June 2000LTPP Guide to Asphalt Temperature Prediction and Correc-tion, Online Temperature Prediction and CorrectionGuideTOC, November 20023. Terminology3.1 Definitions of Terms Specific to This Standard:3.1.1 BELLS an acrony
7、m based on the initials of the fourdevelopers of the method: Baltzer, Ertman-Larsen, Lukanen,and Stubstad.3.1.2 depththe distance below the surface of the top layerof asphalt.3.1.3 1-day air temperaturethe average of the minimumand maximum air temperatures at the location of testing duringthe previo
8、us complete 24-hour day.4. Summary of Test Method4.1 Input Data Elements:4.1.1 IR TemperatureThe 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 DayThe time of day the temperature mea-
9、surement takes place is recorded.4.1.3 1-Day TemperatureThe average 1-day air tempera-ture of the previous complete 24-hour day is determined andrecorded.4.1.4 Pavement DepthThe depth at which an estimate ofthe asphalt layer temperature is required is specified.4.2 The input data elements are entere
10、d 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 effects
11、of 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
12、-stalled at various locations.5.2 Current deflection testing equipment is often equippedwith surface temperature sensing devices, for example aninfrared thermometer that measures the surface temperature atevery test location. To adequately adjust the deflection or1This test method is under the juris
13、diction 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, 2011. Published September 2011. Originallyapproved in 2006. Last previous edition approved in 2006 as D7228 06A. DOI:
14、10.1520/D7228-06AR11.2For 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.3Available from American Association of
15、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 20590.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-
16、2959, United States.deflection 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 days high and low air tempera-tures, and t
17、he desired depth where the temperature is to beestimated. 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
18、for each test point) and the ability to recordtemperature variations between test points.6. Apparatus6.1 Surface Temperature Measurement DeviceThe sur-face temperature measurement device can be an infrared (IR)thermometer mounted on a deflection device, a hand-held IRthermometer, or a surface contac
19、t thermometer. The tempera-ture measurement device should be calibrated according to themanufacturers recommendations.7. Calculation7.1 BELLS MethodThe BELLS method for productiontesting (called BELLS3 in other publications) has been derivedbased on temperature measurements taken on pavement sur-fac
20、es 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 0.95 1 0.892 * IR 1 $log d! 1.25%$0.448 * IR1 0.621 * 1day! 1 1.83 * sin hr18 15.5!%1 0.042 * IR * sin hr18 13.5! (1)where:Td= pavement temperature
21、at depth d, C,IR = infrared surface temperature, C,log = base 10 logarithm,d = depth at which asphalt temperature is to be pre-dicted, mm,1-day = average of the minimum and maximum air tem-peratures, C, for the previous complete 24-hourday before testing,sin = sin function in 18-hour clock system, w
22、ith 2pradians equal to one 18-hour cycle, andhr18= time of day, in 24-hour system, but calculatedusing an 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 time func-tion, only use times from 11:00 to 05:00 hrs. If the actual timeis
23、not within this time range, then calculate the sin as if the timeis 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 3 2p= 0.
24、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 t
25、he 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 3 2p = 0.569radians; sin (0.569) = 0.539. In this
26、case an 18 hour sinfunction is assumed, with a flat (= 1) sin segment between03:00 and 09:00 hours.NOTE 1BELLS 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
27、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 use
28、d for at-depth temperatures greater than 150 mmthrough extrapolation, the results have not been verified or calibrated todate. Since the equations boundary condition at depth=0isinconsistentwith the input IR temperature value, the determination of an at-depthpayment temperature less than 25 mm is no
29、t recommended.NOTE 2The 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 sinusoidal relation-ships, th
30、e 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 pre
31、cision 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 3The BELLS equation for production testing (BELLS3) wasderived using the LTPP database (10 304 observations
32、; R-squared =0.975). The regressions standard estimate of error was 61.9C 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; dyna
33、flect; falling weight deflectometer; FWD; layermoduli; pavement temperature correction; road raterD7228 06a (2011)2APPENDIX(Nonmandatory Information)X1. EXAMPLE SOURCE CODE FOR CALCULATING THE PREDICTED ASPHALT TEMPERATUREBY THE BELLS METHODX1.1 ExplanationX1.1.1 PurposeThe source code is presented
34、to illustrateapplication of the temperature prediction equations, particu-larly the application of the 18-hour sin functions.X1.1.2 LanguageThe 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 So
35、urce Code ListingProgram to illustrate the implementation of the BELLS3 equationfor 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
36、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
37、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
38、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 = 12.5CTime of day = 08:10 hr
39、sMid-depth of pavement surface course = 75 mmPrevious 1-day average air temperature = 23CT75 mm5 0.95 1 0.892 * 12.5 1 $log 75! 1.25% 3 $20.448 * 12.51 0.621 * 23! 1 1.83 * sin 2p311.00 15.5!/18%1 0.042 * 12.5 * sin 2p308.17 13.5!/18 (X1.1)T75 mm5 0.95 1 0.892 * 12.5 1 $1.875 1.25% 3 $20.448 * 12.51
40、 0.621 * 23! 1 1.83 * 21% 10,042 * 12.5 * 20.958(X1.2)T75 mm5 0.95 1 11.15 1 0.625 3 $25.6 1 14.28 1.83% 0.505 15.9C (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 expr
41、essly 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 revise
42、d, 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
43、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 State
44、s. Individual reprints (single or multiple copies) of this standard may be obtained by contacting ASTM at the aboveaddress or at 610-832-9585 (phone), 610-832-9555 (fax), or serviceastm.org (e-mail); or through the ASTM website(www.astm.org). Permission rights to photocopy the standard may also be secured from the ASTM website (www.astm.org/COPYRIGHT/).D7228 06a (2011)3
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