The Andbjerg Plough Radio-carbon dated at year 1520 (± 100 years)

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1 The Andbjerg Plough Radio-carbon dated at year 1520 (± 100 years) The Andbjerg Plough is an example of an early aggregate wear testing device. The landside of the plough is studded with granite pebbles to prevent wear on the wood. The hole in front is for the insertion of the share (1). 1

2 Surface Amplitude Roughness and Correlation with Pavement Friction Measurements ABSTRACT Average Roughness, (R a ) a widely used measurement of surface amplitude roughness is used as a parameter to correlate pavement surface texture with field and laboratory friction measurements. INTRODUCTION Thirty different pavement sites were selected for this study. Construction data, traffic levels, and field friction measurements, (FN) were known for all of the sites. A maximum of four and minimum of two cores, (200 mm in diameter) were taken from the wheel paths at each site, and profiles were collected from the pavement wear surfaces with an Optical Gaging Products, Incorporated, (OGP) COBRA Laser Profile Scanner. Subsequently, two laboratory measurements of friction were taken from the core surfaces: MDOT Laboratory Friction Tester values (LBF), and British Pendulum Numbers (BPN). R a measurements were correlated with the friction measurements to develop a Roughness Index that may be used to characterize surface roughness. EXPERIMENTAL Data Collection From each pavement surface sample, two sets of profiles were recorded. The first set of macro measurements consisted of twelve mm long traverse lines oriented parallel to the traffic direction, and evenly distributed across the sample. Each mm long traverse consisted of 1,024 points spaced at mm. Figure 1 shows the traverse pattern on the core surface. The macro measurements were made using the OPG Digital Range Sensor System DRS The second set of micro measurements consisted of ten mm long traverse lines oriented parallel to the traffic direction, and were recorded solely from exposed aggregate surfaces. Each mm long traverse consisted of 1,024 points spaced at mm. To collect the second set of measurements, a 7 x 7 grid of 3 mm x 3 mm windows was placed over the sample. In 2

3 some cases, an exposed aggregate would appear in the window. If the area of the aggregate revealed in the window was sufficient, a traverse was recorded. The first ten aggregate surfaces encountered in this manner were recorded. Figure 2 shows the grid pattern on the core surface. The micro measurements were made using the OPG Digital Range Sensor System DRS-500. Figure 1: Layout of traverse lines for macro profiles. Figure 2: Layout of grid used to collect micro profiles. 3

4 Average Roughness The general example of a surface profile shown in Figure 3 can be represented by the function y=f(x). The amplitude and wavelength of a profile are two obvious choices for parameters to quantify surface roughness. Average roughness (R a ) is the most widely used measurement of surface amplitude roughness (2,3). R a is defined as: L 1 R a = zdx L (Equation 1) Where: R a L z x 0 = Average Roughness = Sampling Length = the difference in elevation between the profile and the mean line = abscissa Figure 3: An example of a surface profile To collect a distribution of R a measurements, a best fit least squares reference line of length L was stepped over the profile traverse, and a value for R a was computed for each step. Reference lines consisting of 2 2, 2 3, 2 4, 2 5, 2 6, 2 7, and 2 8 consecutive elevation points were used. Figures 4 and 5 show examples of R a distributions from two different cores. Figure 6 shows a cumulative percentage plot for the R a distributions shown in Figures 4 and 5. 4

5 Figure 4: Distribution of R a measurements for a core with a relatively smooth surface. Figure 5: Distribution of R a measurements for a core with a relatively rough surface. 5

6 Figure 6: Cumulative percentile plot for distributions shown in Figures 4 and 5. RESULTS Correlation with Friction To determine the reference line length L to best characterize the surface roughness, correlations were computed between the R a distribution cumulative percentage values from all of the cores and the corresponding friction measurements. Figures 7 through 13 plot the correlation values between the friction measurements and the cumulative percentiles with increasing reference line lengths for the macro traverse data. Figures 14 through 20 plot the correlation values between the friction measurements and the cumulative percentiles with increasing reference line lengths for the micro traverse data. As shown in Figure 9, for the macro traverse data, the best correlation with the friction measurements occurred with an L of mm (2 4 points). As shown in Figure 20, for the micro traverse data, the best correlation with the friction measurements occurred with an L of mm (2 8 points). The maximum R 2 values occurred at different cumulative percentile values for the different friction measurements. Table 1 summarizes the maximum R 2 values and the corresponding cumulative percentile values for the macro traverse data. Table 2 summarizes the maximum R 2 values and the corresponding cumulative percentile values for the micro traverse data. 6

7 Figure 7: R 2 values for macro traverse data to show correlation between R a cumulative percentile levels and friction measurements, reference line length L = mm (2 2 points). Figure 8: R 2 values for macro traverse data to show correlation between R a cumulative percentile levels and friction measurements, reference line length L = mm (2 3 points). 7

8 Figure 9: R 2 values for macro traverse data to show correlation between R a distribution cumulative percentile levels and friction measurements, reference line length L = mm (2 4 points). Figure 10: R 2 values for macro traverse data to show correlation between R a distribution cumulative percentile levels and friction measurements, reference line length L = mm (2 5 points). 8

9 Figure 11: R 2 values for macro traverse data to show correlation between R a distribution cumulative percentile levels and friction measurements, reference line length L = mm (2 6 points). Figure 12: R 2 values for macro traverse data to show correlation between R a distribution cumulative percentile levels and friction measurements, reference line length L = mm (2 7 points). 9

10 Figure 13: R 2 values for macro traverse data to show correlation between R a distribution cumulative percentile levels and friction measurements, reference line length L = mm (2 8 points). Figure 14: R 2 values for micro traverse data to show correlation between R a distribution cumulative percentile levels and friction measurements, reference line length L = mm (2 2 points). 10

11 Figure 15: R 2 values for micro traverse data to show correlation between R a distribution cumulative percentile levels and friction measurements, reference line length L = mm (2 3 points). Figure 16: R 2 values for micro traverse data to show correlation between R a distribution cumulative percentile levels and friction measurements, reference line length L = mm (2 4 points). 11

12 Figure 17: R 2 values for micro traverse data to show correlation between R a distribution cumulative percentile levels and friction measurements, reference line length L = mm (2 5 points). Figure 18: R 2 values for micro traverse data to show correlation between R a distribution cumulative percentile levels and friction measurements, reference line length L = mm (2 6 points). 12

13 Figure 19: R 2 values for micro traverse data to show correlation between R a distribution cumulative percentile levels and friction measurements, reference line length L = mm (2 7 points). Figure 20: R 2 values for micro traverse data to show correlation between R a cumulative percentile levels and friction measurements, reference line length L = mm (2 8 points). 13

14 Table 1: Cumulative percentile levels that yield maximum R 2 values for macro traverse data when L = mm (2 4 points). Friction measurement method cumulative percentile of R a distribution R 2 FN BPN LBF Table 2: Cumulative percentile levels that yield maximum R 2 values for micro traverse data when L = mm (2 8 points). friction measurement method cumulative percentile of R a distribution R 2 FN BPN LBF Roughness Index The division of the surface profile data collection into macro and micro traverses was made in an effort to determine at what scale surface texture most influences friction. A comparison of the R 2 values from Table 1 and 2 shows that the macro traverse data correlates better with the friction measurements than does the micro traverse data. An arithmetic combination of the macro and micro data can yield an even better correlation with the friction measurements. The simple addition of the R a values for the macro and micro traverses at the cumulative percentile levels shown in Tables 1 and 2, along with a multiplier can yield a Roughness Index (RI) with a better correlation to friction measurements. The general formula for the Roughness Index is as follows: 14

15 R a1 + x(r a2 ) = RI (Equation 2) Where: R a1 R a2 x RI = R a value at chosen cumulative percentile level for macro traverse data = R a value at chosen cumulative percentile level for micro traverse data = multiplier = Roughness Index After R a distribution cumulative percentile levels are selected from the macro and micro traverse data, a multiplier x was found to maximize the correlation with friction using the Microsoft Excel Solver Add-In. However, the choice of cumulative percentile levels depends on which method of friction measurement is selected. Tables 3, 4, and 5 list the different multipliers and cumulative percentile levels that optimize the correlation between the RI and the selected friction measurement method. Table 3: Roughness Index parameters required to optimize the correlation with FN friction measurements. Roughness Index parameters R a1 = R a2 = 62 nd percentile 6 th percentile x = 10.3 friction measurement method R 2 FN 0.59 BPN 0.63 LBF

16 Table 4: Roughness Index parameters required to optimize the correlation with BPN friction measurements. Roughness Index parameters R a1 = R a2 = 24 th percentile 31 st percentile x = 1.8 friction measurement method R 2 FN 0.51 BPN 0.64 LBF 0.74 Table 5: Roughness Index parameters required to optimize the correlation with LBF friction measurements. Roughness Index parameters R a1 = R a2 = 21 st percentile 31 st percentile x = 1.6 friction measurement method R 2 FN 0.51 BPN 0.63 LBF 0.74 Rather than have three separate Roughness Indices, RI FN, RI BPN, and RI LBF, it is desirable to choose one Roughness Index that will work for all three friction measurement methods. For the sake of simplicity, the 25 th percentile of the R a distribution for the macro traverse data and the 25 th percentile of the R a distribution for the micro traverse data were selected as the inputs for the final RI formula as shown in Equation 3. The additional multiplier of 3,500 was added to force the RI values into a range of zero to one hundred: 16

17 3,500[R α + 2(R β )] = RI (Equation 3) Where: R α R β RI = R a value at 25 th cumulative percentile level for macro traverse data = R a value at 25 th cumulative percentile level for micro traverse data = Roughness Index Figures 21, 22, and 23 plot the R α values for all of the cores versus the three different friction measurement methods. Figures 24, 25, and 26 plot the R β values for all of the cores versus the three different friction measurement methods. It should be noted that while BPN and LBF measurements were made on each core, FN values were available only for the entire core site. Therefore, cores taken from the same site have the same FN number, which explains the vertical stacking of the data points in Figures 21 and 24. Figures 27, 28, and 29 plot the RI values for all of the cores versus the three different friction measurement methods. Figures 30, 31, and 32 plot the site average RI values versus the three different friction measurement methods. Table 6 contains a summary of the RI values and friction measurements for all of the sites, along with mix type and cumulative traffic information. Figure 33 is basically the same as Figure 32, except that the site numbers are listed on the plot in place of the dots used to show the site averages. Figures 34 through 41 plot the RI values versus the LBF values in terms of mix type. Figure 42 plots the RI average site values versus cumulative traffic. CONCLUSIONS There is a moderate correlation between the Roughness Index and the friction measurements. As shown in Figures 30, 31, and 32, the R 2 values are 0.53, 0.69, and 0.79 for the correlation between the site average RI values and the site average FN, BPN and LBF values respectively. The relationship between RI and FN, however, may not be linear, so a polynomial best fit line is included in Figure 30 with an R 2 value of To further demonstrate the relationship between the RI and friction, Figure 42 is included to show the general trend that pavements that have experienced more traffic generally have a lower RI value. The Roughness Index is based on R a measurement distributions. R a is only a measurement of surface amplitude roughness, and does not account for surface 17

18 wavelength roughness. Perhaps in combination with surface wavelength roughness measurements, a better correlation with friction measurements could be obtained. Figure 21: R a value at 25 th cumulative percentile level for macro traverse data versus FN. Figure 22: R a value at 25 th cumulative percentile level for macro traverse data versus BPN. 18

19 Figure 23: R a value at 25 th cumulative percentile level for macro traverse data versus LBF. Figure 24: R a value at 25 th cumulative percentile level for micro traverse data versus FN. 19

20 Figure 25: R a value at 25 th cumulative percentile level for micro traverse data versus BPN. Figure 26: R a value at 25 th cumulative percentile level for micro traverse data versus LBF. 20

21 Figure 27: RI versus FN for all of the wheel path cores. Figure 28: RI versus BPN for all of the wheel path cores. 21

22 Figure 29: RI versus LBF for all of the wheel path cores. Figure 30: RI versus FN, average values for site. 22

23 Figure 31: RI versus BPN, average values for site. Figure 32: RI versus LBF, average values for site. 23

24 Table 6: Summary of site information. Site # avg. RI avg. BPN avg. LBF FN mix type cumulative wheel passes (in millions) A A A A SMA-C SMA-C SMA-C SMA-C B B RP RP B B B-RP/SLAG B-RP/SLAG B A FA MICRO FA MICRO B-RP/SLAG B-RP/SLAG E10-RP E10-RP T-L-RP/SLAG T-L-RP/SLAG T-L-RP/SLAG T-L-RP/SLAG B FA MICRO FA MICRO

25 Figure 33: RI versus LBF, average values for sites with site labels. Figure 34: RI versus LBF emphasizing cores with 13A mix design. 25

26 Figure 35: RI versus LBF emphasizing cores with SMA-C mix design. Figure 36: RI versus LBF emphasizing cores with 4B mix design. 26

27 Figure 37: RI versus LBF emphasizing cores with 13-RP mix design. Figure 38: RI versus LBF emphasizing cores with 1500T-L-RP/SLAG mix design. 27

28 Figure 39: RI versus LBF emphasizing cores with 4B-RP/SLAG mix design. Figure 40: RI versus LBF emphasizing cores with 2FA MICRO mix design. 28

29 Figure 41: RI versus LBF emphasizing cores with 4E10-RP mix design. Figure 42: Site average RI versus cumulative traffic. 29

30 REFERENCES 1) Dowson, D. History of Tribology 2 nd Edition, Professional Engineering Publishing Limited, London, 1998, 768 pages. 2) Thomas, T. R. Rough Surfaces, Longman Group Limited, New York, 1982, 261 pages. 3) Whitehouse, D. J. Handbook of Surface Metrology, Institute Of Physics Publishing Limited, Philadelphia, 1994, 988 pages. 30