1、Designation: E1486M 98 (Reapproved 2010)Standard Test Method forDetermining Floor Tolerances Using Waviness, Wheel Pathand Levelness Criteria (Metric)1This standard is issued under the fixed designation E1486M; the number immediately following the designation indicates the year oforiginal adoption o
2、r, 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 data collection and analysisprocedures to determine su
3、rface flatness and levelness bycalculating waviness indices for survey lines and surfaces,elevation differences of defined wheel paths, and levelnessindices using SI units.NOTE 1This test method is the companion to inch-pound Test MethodE1486.NOTE 2This test method was not developed for, and does no
4、t apply toclay 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 deviations from themidpoints of imaginary chords as they are moved a
5、long 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 based on transverse andlongitudinal elevation differences, change in
6、 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 mean; or by theconformance of the RMS slope of each survey line to as
7、pecified slope for each survey line.1.1.2 The averages used throughout these calculations arethe root mean squares, RMS (that is, the quadratic means). Thistest method gives equal importance to humps and dips,measured up (+) and down (), respectively, from the imagi-nary chords.1.1.3 Appendix X1 is
8、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 of the user of this standard to establis
9、h appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Document2.1 ASTM Standards:2E1486 Test Method for Determining Floor Tolerances Us-ing Waviness, Wheel Path and Levelness Criteria3. Terminology3.1 Descriptions of Terms Sp
10、ecific 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 and withcorresponding front and rear primary wheels i
11、n 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 survey lineslope to a specified slope, RMS levelness.3.1.2.1 elevation conformancethe percentage
12、 of surfaceelevation data, hi, that lie within the tolerance specified fromthe mean elevation of a test section from the mean elevation ofall data within a test section. The absolute value of the distanceof all points, hi, from the test section data mean is tested againstthe specification, dmax. Pas
13、sing values are counted, and thattotal is divided by the aggregate quantity of elevation datapoints for the test section, and percent passing is reported.3.1.2.2 RMS levelnessdirectionally dependent calculationof the RMS of the slopes of the least squares fit line throughsuccessive 4.5-m long sectio
14、ns of a survey line, L. The RMSLVLis compared to the specified surface slope and specifiedmaximum deviation to determine compliance.3.1.3 Waviness Index Terms:1This test method is under the jurisdiction of ASTM Committee E06 onPerformance of Buildings and is the direct responsibility of Subcommittee
15、 E06.21on Serviceability.Current edition approved Oct. 1, 2010. Published November 2010. Originallyapproved in 1994. Last previous edition approved in 2004 as E1486M 98 (2004).DOI: 10.1520/E1486M-98R10.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Serv
16、ice at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.3.1.3.1 chord lengththe length of an imagina
17、ry straight-edge (chord) joining the two end points at j and j + 2k. Thislength is equal to 2ks (see Fig. 1) where the survey spacing, s,is equal to 0.3 m, and where k is equal to 1, 2, 3, 4, and 5 todefine chord lengths of 0.6, 1.2, 1.8, 2.4, and 3.0 m, respec-tively, unless values for s and for k
18、are otherwise stated.3.1.3.2 deviation (Dkj)the vertical distance between thesurface and the midpoint, j + ks, of a chord of length 2ks whoseend points are in contact with the surface.3.1.3.3 length adjusted RMS deviation (LADk)calculatedfor a reference length Lrof 3 m, unless otherwise stated, inor
19、der to obtain deviations that are independent of the variouschord lengths, 2ks.3.1.3.4 wavinessthe relative degree to which a survey linedeviates from a straight line.3.2 Symbols:A = area of test section, square metres.d = point i, of the (4.5/s + 1) point subset of i =1to imax, where d is a point w
20、ithin the(4.5/s + 1) point subset, used to evaluateRMS levelness.dhL= 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, mm.dmax = specified maximu
21、m allowable deviationfrom the test section elevation data mean.EC = 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= percentage compliance of each survey lineto a specified maximu
22、m deviation, dmax,from the mean of all elevation data pointswithin a test section.hi= elevation of the points along the survey line,mm.hai= elevation of the points along the survey lineof the left wheel path of defined wheel pathtraffic, mm.hbi= elevation of the points along the survey lineof the ri
23、ght wheel path of defined wheel pathtraffic, mm.i = designation 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
24、paths of defined wheel path traffic.j = designation of the location 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 t
25、hesurvey points used for deviation calcula-tions.kmaxL= maximum 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
26、RMS deviation based onpoints spaced at ks and a reference length 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 o
27、f the primary axle spacing, in metresdivided by s.Lmax = number of survey lines on the test surface.Lr= reference length of 3 m, the length to whichthe RMS deviations, RMS Dk, from chordlengths other than 3 m are adjusted.LDi= longitudinal elevation difference betweencorresponding pairs of points se
28、parated byLg of defined wheel paths, mm (i = 1, 2, 3. . . (imaxL Lg).LDCi= incremental change in longitudinal elevationdifference, LDialong defined wheel pathtraffic wheel paths, mm/m (i = 1, 2, 3 .(imaxLLg1).Lx = designation of the pair of survey lines usedfor defined wheel path traffic analysis.mh
29、d= mean elevation of each 4.5-m section ofsurvey line, L, mm (d = 1, 2, 3 . . .(imaxL 4.5/s).FIG. 1 Explanation of SymbolsE1486M 98 (2010)2msd= mean slope of the least squares fit line ofeach 4.5-m section of survey line, L, mm/m(d = 1, 2, 3 . . . (imaxL 4.5/s).nL= total number of calculated deviati
30、ons forsurvey line L (equal to the sum of the valuesof jmaxkfor all values of k that are used).naLis a weighting factor used in calculat-ing both the waviness and surface wavinessindices.RMS Dk= root mean square of chord midpoint offsetdeviations, Dkj, based on points spaced at ks.RMS LDLx= root mea
31、n square of longitudinal elevationdifferences, LDi, on paired wheel path sur-vey lines for defined wheel path traffic, withprimary axles separated by Lg, mm.RMS TDLx= root mean square of transverse elevationdifferences, TDi, on paired wheel path sur-vey lines for defined wheel path traffic, mm.RMS L
32、VL= RMS levelness, calculated as the root meansquare slope of each survey line, L, mm/m.s = spacing between adjacent survey pointsalong a survey line (0.3 m unless a smallervalue is stated), m.SWI = surface waviness index determined by com-bining the waviness indices of all the surveylines on the te
33、st surface, mm.TDi= transverse elevation difference between cor-responding points of defined wheel pathtraffic wheel paths, mm (i = 1, 2, 3 .imaxLx).TDCi= incremental change in transverse elevationdifference, TDialong defined wheel pathtraffic wheel paths, mm/m (i = 1, 2, 3 .(imaxLx 1).WIL= waviness
34、 index for survey line L with chordlength range from 0.6 to 3.0 m unless adifferent range is stated, mm.3.3 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 thefol
35、lowing characteristics:4.1.1 Waviness 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 Eqs 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-
36、tion (see Eq 24).4.1.2 Defined Wheel Path 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 TDL
37、x= RMS transverse elevation differencebetween 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 fron
38、t and rear axles on wheel paths of defined 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, calculatedonly for use in cal
39、culating mhTS(see Eq 15).4.1.3.2 mhTS= mean elevation of a test section, calculatedonly for use 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 Eq 18).4.1.3.4 ECL= percen
40、tage of elevation data points on surveyline, L, which 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 4.5-m section ofsurvey line, L, calculated only for use in calculating RMS LVL(
41、see Eq 21).4.1.3.7 msd= mean slope of the least squares fit line of each4.5-m section of survey line, L, calculated only for use incalculating RMS LVL(see Eq 22).4.1.3.8 RMS LVL= RMS of least squares fit 4.5-m slopes(see Eq 23).4.2 Waviness IndexChord Length Range:4.2.1 Unless a different range is s
42、pecified, the wavinessindex, WIL, shall be calculated for a 0.6, 1.2, 1.8, 2.4, and3.0-m chord 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
43、uses the largest value of k, the maximum value 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, det
44、ermined using Eq 1,permits the use of 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 1.2 m, unless the slab has been placed without camberand the shoring remains in place.4.3 Waviness IndexMaximum Number of
45、 Deviation Mea-surements per Chord Length: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! mm (3)E1486M 98 (2010)34.5 Wavine
46、ss IndexRMS Deviation:4.5.1 RMS Dkis calculated for each chord length using allpoints along the survey line.RMS Dk5(j51jmaxkDkj2jmaxkmm (4)4.6 Waviness IndexLength-Adjusted Deviations: LADkiscalculated for a reference length, Lr, using Eq 5.LADk5 !Lr2ksF(j51jmaxkDkj2Gjmaxkmm (5)4.7 Waviness Index Th
47、e values of LADkobtained for eachvalue 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!nLmm (6)where:nL5(k51kmaxLjmaxk(7)4.8 Surface Waviness IndexThe individual values ofwaviness index,
48、 WILobtained for each survey line shall becombined to give a surface waviness index, SWI, by combin-ing them in proportion to nL:SWI 5!(L51LmaxnLWIL2(L51LmaxnLmm (8)4.9 Defined Wheel Path Calculations:4.9.1 Transverse Elevation DifferenceTDiis calculatedfor a pair of wheel path survey lines, using E
49、q 9 (i = 1, 2, 3 .imaxLx).TDi5 hbi2 hai! mm (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 1 12 TDi!/s mm/m (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
