# ASTM E1486-14

Designation: E1486 − 14Standard Test Method forDetermining Floor Tolerances Using Waviness, Wheel Pathand Levelness Criteria1This standard is issued under the fixed designation E1486; 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 data collection and analysisprocedures to determine surface flatness 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 1—This test method is the companion to SI Test MethodE1486M; therefore, no SI equivalents are shown in this test method.NOTE 2—This test method was not developed for, and does not apply to,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 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 based on transverse andlongitudinal elevation differences, change in elevationdifference, 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 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 the 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 The values stated in inch-pound units are to be regardedas standard. No other units of measurement are included in thisstandard.1.3 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 establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Document2.1 ASTM Standards:2E1486M Test Method for Determining Floor TolerancesUsing Waviness, Wheel Path and Levelness Criteria (Met-ric)3. Terminology3.1 Definitions of Terms Specific to This Standard:3.1.1 defined wheel path traffıc—traffic 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 in approximatelythe same wheel paths.3.1.2 levelness—described 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 levelness).3.1.2.1 elevation conformance—the 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. Passing 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 levelness—directionally dependent calculationof the RMS of the slopes of the least squares fit line through1This 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, 2014. Published May 2014. Originallyapproved in 1994. Last previous edition approved in 2010 as E1486 – 98 (2010).DOI: 10.1520/E1486-14.2For 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.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1successive 15-ft long sections of 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 length—the length of an imaginary 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 sis 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 distance 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 variouschord lengths, 2ks.3.1.3.4 waviness—the 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 =1toimax, where d is a point within the (15/s +1)point subset, used to evaluate RMS levelness.dhL= number of elevation data points of survey line,L, which lie within the maximum allowabledeviation from the test section elevation datamean, dmax.Dkj= deviation from chord midpoint, j+k,to thesurvey line, in.dmax = specified maximum allowable deviation fromthe test section elevation data mean.EC = the percentage of elevation data within a testsection complying to a specified maximumdeviation, dmax, from the mean of all elevationdata points within a test section.ECL= the percentage compliance of each survey lineto a specified maximum deviation, dmax, fromthe mean of all elevation data points within atest section.hi= elevation of the points along the survey line, in.hai= elevation of the points along the survey line ofthe left wheel path of defined wheel pathtraffic, in.hbi= elevation of the points along the survey line ofthe right wheel path of defined wheel pathtraffic, in.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 of thepair of survey lines, Lx, representing the wheelpaths of defined wheel path traffic.j = designation of the location of the survey pointwhich is the initial point for a deviation calcu-lation (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 calculations.kmaxL= maximum number (rounded down to an inte-ger) of spaces of length s that can be used fordeviation calculations for imaxLsurvey points(kmaxL=5unless otherwise specified).L = designation of survey lines (L = 1, 2, 3 . . .Lmax).LADk= length-adjusted RMS deviation based on pointsspaced at ks and a reference length of Lr.Lg = total number of survey spaces between primaryaxles of a vehicle used as the basis for longi-tudinal analysis of each pair of survey linesrepresenting the wheel paths of defined wheelpath traffic. Lg equals the integer result of theprimary axle spacing, ft, divided by s.Lmax = the number of survey lines on the test surface.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 between cor-responding pairs of points separated by Lg ofdefined wheel paths, mm (i = 1, 2, 3 .(imaxL− Lg)).LDCi= incremental change in longitudinal elevationdifference, LDi, along defined wheel pathtraffic wheel paths, in./ft (i = 1, 2, 3 .(imaxL−Lg− 1)).Lx = designation of the pair of survey lines used fordefined wheel path traffic analysis.mhd= mean elevation of each 15-ft section of surveyline, L, mm (d = 1, 2, 3 . . . (imaxL−15⁄s)).msd= mean slope of the least squares fit line of each15-ft section of survey line, L, in./ft (d = 1, 2,3 . . . (imaxL− 15/s)).nL= total number of calculated deviations for sur-vey line L (equal to the sum of the values ofjmaxkfor all values of k that are used). Thesymbol nLis a weighting factor used in calcu-lating both the waviness and surface wavinessindices.RMS Dk= root mean square of chord midpoint offsetdeviations, Dkj, based on points spaced at ks.FIG. 1 Explanation of SymbolsE1486 − 142RMS LDLx= root mean square of longitudinal elevationdifferences, LDi, on paired wheel path surveylines for defined wheel path traffic, with pri-mary axles separated by Lg, in.RMS TDLx= root mean square of transverse elevationdifferences, TDi, on paired wheel path surveylines for defined wheel path traffic, in.RMS LVL= RMS levelness, calculated as the root meansquare slope of each survey line, L, in./ft.s = spacing between adjacent survey points along asurvey line (1 ft unless a smaller value isstated), ft.SWI = surface waviness index determined by combin-ing the waviness indices of all the survey lineson the test surface, in.TDi= transverse elevation difference between corre-sponding points of defined wheel path trafficwheel paths, in.(i = 1, 2, 3 . . . imaxLx).TDCi= incremental change in transverse elevationdifference, TDialong defined wheel path trafficwheel paths, in./ft (i = 1, 2, 3 . . . (im-axLx− 1)).WIL= waviness index for survey line L with chordlength range from 2.0 to 10 ft unless a differentrange is stated, in.3.2 Sign Convention—Up is the positive direction;consequently, the higher the survey point, the larger its hivalue.4. Summary of Test Method4.1 Equations—Equations are provided to determine thefollowing 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 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 Path Traffıc 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 differencebetween wheel paths of defined wheel path traffic (see Eq 11).4.1.2.4 LDi= longitudinal elevation difference between frontand rear axles on wheel paths of defined wheel path traffic (seeEq 12).4.1.2.5 LDCi= Longitudinal change in elevation differencebetween front 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, calculatedfor use only in calculating mhTS(see Eq 15).4.1.3.2 mhTS= 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 bothECLand EC (see Eq 17 and 18).4.1.3.4 ECL= percentage of elevation data points on surveyline, 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 least 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 (seeEq 23).4.2 Waviness Index—Chord Length Range:4.2.1 Unless a different range is specified, the wavinessindex, WIL, shall be 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 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 3—For longer survey lines, kmaxL, which is determined using Eq1, 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 4 ft, unless the slab has been placed without camberand the shoring remains in place.4.3 Waviness Index—Maximum Number of 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 Index—Deviation:4.4.1 As shown in Fig. 1, the deviation, Dkj, isDkj5 hj1k212~hj1hj12k! in. (3)4.5 Waviness Index—RMS Deviation:4.5.1 RMS Dkis calculated for each chord length using allpoints along the survey line.RMSDk5!(i51jmaxkDkj2jmaxkin. (4)E1486 − 1434.6 Waviness Index—Length-Adjusted Deviations: LADkiscalculated for a reference length, Lr, using Eq 5.LADk5!Lr2ksF(i51jmaxkDkj2Gjmaxkin. (5)4.7 Waviness Index—The 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!(k51kmaxL~jmaxkLADk2!nLin. (6)where:nL5(k51kmaxLjmaxk(7)4.8 Surface Waviness Index—The individual values of wavi-ness index, WIL, obtained for each survey line 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 Difference—TDiis calculated fora pair of wheel path survey lines, using Eq 9 (i=1,2,3.imaxLx).TDi5 ~hbi2 hai! in. (9)where TDiis positive when the right wheel path is higherthan the left and negative when the right wheel path is lowerthan the left.4.9.2 Transverse Change in Elevation Difference—TDCiiscalculated for each pair of wheel path survey lines using Eq 10(i = 1, 2, 3 . . . (imaxLx− 1)).TDCi5 ~TDi112 TDi!/s in./ft (10)where TDCiis positive when the vehicle tilted left from itsprevious position and negative when it is tilt