1、Designation: E 1486 98 (Reapproved 2004)Standard Test Method forDetermining Floor Tolerances Using Waviness, Wheel Pathand Levelness Criteria1This standard is issued under the fixed designation E 1486; the number immediately following the designation indicates the year oforiginal adoption or, in the
2、 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 test method covers data collection and analysisprocedures to determine surface fl
3、atness and levelness bycalculating waviness indices for survey lines and surfaces,elevation differences of defined wheel paths, and levelnessindices using the inch-pound system of units.NOTE 1This test method is the companion to SI Test MethodE 1486M; therefore, no SI equivalents are shown in this t
4、est method.NOTE 2This test method was not developed for, and does not applyto, clay or concrete paver units.1.1.1 The purpose of this test method is to provide the userwith floor tolerance estimates as follows:1.1.1.1 Local survey line waviness and overall surfacewaviness indices for floors based on
5、 deviations from themidpoints of imaginary chords as they are moved along a floorelevation profile survey line. End points of the chords arealways in contact with the surface. The imaginary chords cutthrough any points in the concrete surface higher than thechords.1.1.1.2 Defined wheel path criteria
6、 based on transverse andlongitudinal elevation differences, change in elevation differ-ence, and root mean square (RMS) elevation difference.1.1.1.3 Levelness criteria for surfaces characterized by ei-ther of the following methods: the conformance of elevationdata to the test section elevation data
7、mean or the conformanceof the RMS slope of each survey line to a specified slope foreach survey line.1.1.2 The averages used throughout these calculations areRMS (that is, the quadratic means). This test method givesequal importance to humps and dips, measured up (+) anddown (), respectively, from t
8、he imaginary chords.1.1.3 Appendix X1 is a commentary on this test method.Appendix X2 provides a computer program for waviness indexcalculations based on this test method.1.2 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility
9、 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.2. Referenced Document2.1 ASTM Standards:2E 1486M Test Method for Determining Floor TolerancesUsing Waviness, Wheel Path, and Levelness Criteria
10、 (Met-ric)3. Terminology3.1 Descriptions of Terms Specific to This Standard:3.1.1 defined wheel path traffctraffic on surfaces, orspecifically identifiable portions thereof, intended for definedlinear traffic by vehicles with two primary axles and fourprimary load wheel contact points on the floor a
11、nd withcorresponding front and rear primary wheels in approximatelythe same wheel paths.3.1.2 levelnessdescribed in two ways: the conformance ofsurface elevation data to the mean elevation of a test section(elevation conformance), and as the conformance of surveyline slope to a specified slope (RMS
12、levelness).3.1.2.1 elevation conformancethe percentage of surfaceelevation data, hi, that lie within the tolerance specified fromthe mean elevation of a test section. The absolute value of thedistance of all points, hi, from the test section data mean istested against the specification, dmax. Passin
13、g values arecounted, and that total is divided by the aggregate quantity ofelevation data points for the test section and percent passing isreported.3.1.2.2 RMS levelnessdirectionally dependent calculationof the RMS of the slopes of the least squares fit line throughsuccessive 15-ft long sections of
14、 a survey line, L. The RMSLVLis compared with the specified surface slope and specifiedmaximum deviation to determine compliance.3.1.3 Waviness Index Terms:3.1.3.1 chord lengththe length of an imaginary straight-edge (chord) joining the two end points at j and j + 2k. Thislength is equal to 2 ks (se
15、e Fig. 1) where the survey spacing s1This test method is under the jurisdiction of ASTM Committee E06 onPerformance of Buildings and is the direct responsibility of Subcommittee E06.21on Serviceability.Current edition approved April 1, 2004. Published April 2004. Originallyapproved in 1994. Last pre
16、vious edition approved in 1998 as E 1486 98.2For 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.1Copyright ASTM I
17、nternational, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.is equal to 1 ft and k is equal to 1, 2, 3, 4, and 5 to define chordlengths of 2, 4, 6, 8, and 10 ft, respectively, unless values fors and k are otherwise stated.3.1.3.2 deviation (Dkj)the vertical dist
18、ance between thesurface and the mid-point, j + ks, of a chord of length 2kswhose end points are in contact with the surface.3.1.3.3 length adjusted RMS deviation (LADk)calculatedfor a reference length Lrof 10 ft, unless otherwise stated, inorder to obtain deviations that are independent of the vario
19、uschord lengths, 2ks.3.1.3.4 wavinessthe relative degree to which a survey linedeviates from a straight line.3.1.4 Symbols:A = area of test section, ft2.d = point i, of the (15/s + 1) point subset of i =1to imax, where d is a point within the(15/s + 1) point subset, used to evaluateRMS levelness.dhL
20、= number of elevation data points of surveyline, L, which lie within the maximumallowable deviation from the test sectionelevation data mean, dmax.Dkj= deviation from chord midpoint, j+k,to thesurvey line, in.dmax = specified maximum allowable deviationfrom the test section elevation data mean.EC =
21、the percentage of elevation data within a testsection complying to a specified maximumdeviation, dmax, from the mean of all eleva-tion data points within a test section.ECL= the percentage compliance of each surveyline to a specified maximum deviation,dmax, from the mean of all elevation datapoints
22、within a test section.hi= elevation of the points along the survey line,in.hai= elevation of the points along the survey lineof the left wheel path of defined wheel pathtraffic, in.hbi= elevation of the points along the survey lineof the right wheel path of defined wheel pathtraffic, in.i = designat
23、ion of the location of survey pointsalong a survey line (i = 1, 2, 3 . . . imaxL).imaxL= total number of survey points along a surveyline.imaxLx= total number of survey points along one ofthe pair of survey lines, Lx, representing thewheel paths of defined wheel path traffic.j = designation of the l
24、ocation of the surveypoint which is the initial point for a devia-tion calculation (j = 1, 2, 3 . . . jmaxk).jmaxk= total number of deviation calculations with achord length 2ks along a survey line.k = number of spaces of length s between thesurvey points used for deviation calcula-tions.kmaxL= maxi
25、mum number (rounded down to aninteger) of spaces of length s that can beused for deviation calculations for imaxLsurvey points (kmaxL=5unless otherwisespecified).L = designation of survey lines (L = 1, 2, 3 . . .Lmax).LADk= length-adjusted RMS deviation based onpoints spaced at ks and a reference le
26、ngth ofLr.Lg = total number of survey spaces between pri-mary axles of a vehicle used as the basis forlongitudinal analysis of each pair of surveylines representing the wheel paths of definedwheel path traffic. Lg equals the integerresult of the primary axle spacing, ft, dividedby s.Lmax = the numbe
27、r of survey lines on the testsurface.Lr= a reference length of 120 in., the length towhich the RMS deviations, RMS Dk, fromchord lengths other than 120 in. are adjusted.LDi= longitudinal elevation difference betweencorresponding pairs of points separated byLg of defined wheel paths, mm (i = 1, 2, 3.
28、 . . (imaxL Lg).LDCi= incremental change in longitudinal elevationdifference, LDi, along defined wheel pathtraffic wheel paths, in./ft (i = 1, 2, 3 .(imaxLLg1).Lx = designation of the pair of survey lines usedfor defined wheel path traffic analysis.mhd= mean elevation of each 15-ft section ofsurvey
29、line, L, mm (d = 1, 2, 3 . . .(imaxL 15/s).msd= mean slope of the least squares fit line ofeach 15-ft section of survey line, L, in./ft(d = 1, 2, 3 . . . (imaxL 15/s).nL= total number of calculated deviations forsurvey line L (equal to the sum of the valuesof jmaxkfor all values of k that are used).
30、The symbol nLis a weighting factor used incalculating both the waviness and surfacewaviness indices.FIG. 1 Explanation of SymbolsE 1486 98 (2004)2RMS Dk= root mean square of chord midpoint offsetdeviations, Dkj, based on points spaced at ks.RMS LDLx= root mean square of longitudinal elevationdiffere
31、nces, LDi, on paired wheel path sur-vey lines for defined wheel path traffic, withprimary axles separated by Lg, in.RMS TDLx= root mean square of transverse elevationdifferences, TDi, on paired wheel path sur-vey lines for defined wheel path traffic, in.RMS LVL= RMS levelness, calculated as the root
32、 meansquare slope of each survey line, L, in./ft.s = spacing between adjacent survey pointsalong a survey line (1 ft unless a smallervalue is stated), ft.SWI = surface waviness index determined by com-bining the waviness indices of all the surveylines on the test surface, in.TDi= transverse elevatio
33、n difference between cor-responding points of defined wheel pathtraffic wheel paths, in.(i = 1, 2, 3 .imaxLx).TDCi= incremental change in transverse elevationdifference, TDialong defined wheel pathtraffic wheel paths, in./ft (i = 1, 2, 3 .(imaxLx 1).WIL= waviness index for survey line L with chordle
34、ngth range from 2.0 to 10 ft unless adifferent range is stated, in.3.2 Sign ConventionUp is the positive direction; conse-quently, the higher the survey point, the larger its hivalue.4. Summary of Test Method4.1 EquationsEquations are provided to determine thefollowing characteristics:4.1.1 Waviness
35、 Index Equations:4.1.1.1 RMS Dk= RMS deviation (see Eq 4).4.1.1.2 LADk= length-adjusted deviation (see Eq 5).4.1.1.3 WIL= waviness index (see Eq 6 and 7).4.1.1.4 SWI = surface waviness index (see Eq 8).4.1.1.5 |Dkj| = absolute value of the length adjusted devia-tion (see Eq 24).4.1.2 Defined Wheel P
36、ath Traffc Equations:4.1.2.1 TDi= transverse elevation difference between thewheel paths of defined wheel path traffic (see Eq 9).4.1.2.2 TDCi= transverse change in elevation differencebetween wheel paths of defined wheel path traffic (see Eq 10).4.1.2.3 RMS TDLx= RMS transverse elevation difference
37、between wheel paths of defined wheel path traffic (see Eq 11).4.1.2.4 LDi= longitudinal elevation difference betweenfront and rear axles on wheel paths of defined wheel path traffic(see Eq 12).4.1.2.5 LDCi= Longitudinal change in elevation differencebetween front and rear axles on wheel paths of def
38、ined wheelpath traffic (see Eq 13).4.1.2.6 RMS LDLx= RMS longitudinal elevation differencebetween axles on wheel paths of defined wheel path traffic (seeEq 14).4.1.3 Levelness Equations:4.1.3.1 mhL= mean elevation of survey line, L, calculatedfor use only in calculating mhTS(see Eq 15).4.1.3.2 mhTS=
39、 mean elevation of a test section, calculatedfor use only in calculating dhL(see Eq 16).4.1.3.3 dhL= number of elevation data points of survey line,L, passing the specification, dmax, used for calculating both ECL and EC (see Eq 17 and 18).4.1.3.4 ECL= percentage of elevation data points on surveyli
40、ne, L, that comply with dmax (see Eq 19).4.1.3.5 EC = percentage of elevation data points within atest section complying with dmax (see Eq 20).4.1.3.6 mhd= mean elevation of each 15-ft section of surveyline, L, calculated for use only in calculating RMS LVL(see Eq21).4.1.3.7 msd= mean slope of the l
41、east squares fit line of each15-ft section of survey line, L, calculated for use only incalculating RMS LVL(see Eq 22).4.1.3.8 RMS LVL= RMS of least squares fit 15-ft slopes(see Eq 23).4.2 Waviness IndexChord Length Range:4.2.1 Unless a different range is specified, the wavinessindex, WIL, shall be
42、calculated for a 2-, 4-, 6-, 8-, and 10-ftchord length range.4.2.2 The chord length, 2ks, is limited by the total number ofsurvey points along a survey line. To ensure that the elevationof every survey point is included in the deviation calculationthat uses the largest value of k, the maximum value
43、of k, calledkmaxL, is determined by:kmaxL5 imaxL/3 rounded down to an integer! (1)4.2.3 Reduce the maximum chord length so that 2(kmaxL)sis approximately equal to the maximum length that is ofconcern to the user.NOTE 3For longer survey lines, kmaxL, which is determined using Eq1, permits the use of
44、chord lengths, 2ks, longer than those of interest orconcern to the floor user.4.2.4 The maximum chord length for suspended floor slabsshall be 4 ft, unless the slab has been placed without camberand the shoring remains in place.4.3 Waviness IndexMaximum Number of Deviation Mea-surements per Chord Le
45、ngth:4.3.1 As the values of k are increased from 1 to kmaxL, thenumber of deviation calculations decreases.jmaxk5 imaxL2 2k (2)4.4 Waviness IndexDeviation:4.4.1 As shown in Fig. 1, the deviation, Dkj, isDkj5 hj 1 k212hj1 hj 1 2k! in. (3)4.5 Waviness IndexRMS Deviation:4.5.1 RMS Dkis calculated for e
46、ach chord length using allpoints along the survey line.RMS Dk5(i51jmaxkDkj2jmaxkin. (4)4.6 Waviness IndexLength-Adjusted Deviations: LADkiscalculated for a reference length, Lr, using Eq 5.E 1486 98 (2004)3LADk5 !Lr2ksF(i51jmaxkDkj2Gjmaxkin. (5)4.7 Waviness IndexThe values of LADkobtained for eachva
47、lue of k shall be combined with other LAD values for eachline L by weighing the values in proportion to jmaxkto obtainthe waviness index, WIL.WIL5(k51kmaxLjmaxkLADk2!nLin. (6)wherenL5(k51kmaxLjmaxk(7)4.8 Surface Waviness IndexThe individual values ofwaviness index, WIL, obtained for each survey line
48、 shall becombined to give a surface waviness index, SWI, by combin-ing them in proportion to nL.SWI 5!(L51LmaxnLWIL2(L51LmaxnLin. (8)4.9 Defined Wheel Path Calculations:4.9.1 Transverse Elevation DifferenceTDiis calculated fora pair of wheel path survey lines, using Eq 9 (i=1,2,3.imaxLx).TDi5 hbi2 h
49、ai! in. (9)where TDiis positive when the right wheel path is higher thanthe left and negative when the right wheel path is lower thanthe left.4.9.2 Transverse Change in Elevation DifferenceTDCiiscalculated for each pair of wheel path survey lines using Eq 10(i = 1, 2, 3 . . . (imaxLx 1).TDCi5 TDi 112 TDi!/s in./ft (10)where TDCiis positive when the vehicle tilted left from itsprevious position and negative when it is tilted right from itsprevious position (i = 1, 2, 3 . . . imaxLx).4.9.3 Transverse RMS Elevation DifferenceRMS TDLxiscalc
