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Federal Highway Administration Research and Technology
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This report is an archived publication and may contain dated technical, contact, and link information |
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Publication Number: FHWA-RD-98-085 |
Sample Data for Bells Equations
Surf. Temp., °C | Time | Depth, mm | Prev. Days Avg. Air Temp., °C |
BELLS2, °C | BELLS3, °C |
---|---|---|---|---|---|
10 | 14:10 | 75 | 23 | 16.5 | 15.6 |
12 | 14:10 | 75 | 23 | 17.8 | 16.8 |
14 | 14:10 | 75 | 23 | 19.1 | 18.1 |
16 | 14:10 | 75 | 23 | 20.4 | 19.3 |
18 | 14:10 | 75 | 23 | 21.7 | 20.6 |
20 | 14:10 | 75 | 23 | 23 | 21.8 |
22 | 14:10 | 75 | 23 | 24.3 | 23 |
24 | 14:10 | 75 | 23 | 25.6 | 24.3 |
26 | 14:10 | 75 | 23 | 26.9 | 25.5 |
28 | 14:10 | 75 | 23 | 28.2 | 26.8 |
30 | 14:10 | 75 | 23 | 29.5 | 28 |
32 | 14:10 | 75 | 23 | 30.8 | 29.3 |
34 | 14:10 | 75 | 23 | 32.1 | 30.5 |
36 | 14:10 | 75 | 23 | 33.4 | 31.7 |
38 | 14:10 | 75 | 23 | 34.7 | 33 |
20 | 8:00 | 75 | 23 | 21.4 | 20.1 |
20 | 9:00 | 75 | 23 | 21.4 | 20.1 |
20 | 10:00 | 75 | 23 | 21.5 | 20.2 |
20 | 11:00 | 75 | 23 | 21.6 | 20.3 |
20 | 12:00 | 75 | 23 | 21.8 | 20.6 |
20 | 13:00 | 75 | 23 | 22.3 | 21.1 |
20 | 14:00 | 75 | 23 | 22.9 | 21.7 |
20 | 15:00 | 75 | 23 | 23.6 | 22.3 |
20 | 16:00 | 75 | 23 | 24.3 | 23 |
20 | 17:00 | 75 | 23 | 24.9 | 23.5 |
20 | 18:00 | 75 | 23 | 25.4 | 23.8 |
20 | 19:00 | 75 | 23 | 25.7 | 24 |
20 | 20:00 | 75 | 23 | 25.7 | 23.9 |
20 | 21:00 | 75 | 23 | 25.4 | 23.6 |
20 | 22:00 | 75 | 23 | 25 | 23.1 |
20 | 23:00 | 75 | 23 | 24.3 | 22.5 |
20 | 0:00 | 75 | 23 | 23.6 | 21.9 |
Tm, °C | Tr, °C | ATAFDefault |
---|---|---|
0 | 21 | 0.362 |
5 | 21 | 0.461 |
10 | 21 | 0.587 |
15 | 21 | 0.748 |
20 | 21 | 0.953 |
25 | 21 | 1.213 |
30 | 21 | 1.545 |
35 | 21 | 1.968 |
40 | 21 | 2.506 |
Tm, °C | Tr, °C | ac | Defl36 | theta | AREA | BAFAREA |
---|---|---|---|---|---|---|
5 | 21 | 75 | 50 | 30 | 20.156 | 0.91 |
5 | 21 | 75 | 50 | 45 | 18.127 | 0.9 |
5 | 21 | 75 | 130 | 30 | 22.044 | 0.918 |
5 | 21 | 75 | 130 | 45 | 19.518 | 0.908 |
5 | 21 | 150 | 50 | 30 | 23.956 | 0.901 |
5 | 21 | 150 | 50 | 45 | 21.926 | 0.892 |
5 | 21 | 150 | 130 | 30 | 26.814 | 0.912 |
5 | 21 | 150 | 130 | 45 | 24.289 | 0.903 |
30 | 21 | 75 | 50 | 30 | 17.336 | 1.059 |
30 | 21 | 75 | 50 | 45 | 15.306 | 1.066 |
30 | 21 | 75 | 130 | 30 | 19.224 | 1.053 |
30 | 21 | 75 | 130 | 45 | 16.698 | 1.061 |
30 | 21 | 150 | 50 | 30 | 20.262 | 1.066 |
30 | 21 | 150 | 50 | 45 | 18.233 | 1.073 |
30 | 21 | 150 | 130 | 30 | 23.121 | 1.058 |
30 | 21 | 150 | 130 | 45 | 20.595 | 1.065 |
Sample Data for the F1 Equation
Tm, °C | Tr, °C | ac | Defl36 | theta | LogF1 | F-1 | BAFF-1 |
---|---|---|---|---|---|---|---|
5 | 21 | 75 | 50 | 30 | -0.0422 | 0.9075 | 1.244 |
5 | 21 | 75 | 50 | 45 | 0.0557 | 1.1367 | 1.244 |
5 | 21 | 75 | 130 | 30 | -0.1393 | 0.7256 | 1.244 |
5 | 21 | 75 | 130 | 45 | -0.0176 | 0.9603 | 1.244 |
5 | 21 | 150 | 50 | 30 | -0.2294 | 0.5896 | 1.323 |
5 | 21 | 150 | 50 | 45 | -0.1316 | 0.7386 | 1.323 |
5 | 21 | 150 | 130 | 30 | -0.3743 | 0.4223 | 1.323 |
5 | 21 | 150 | 130 | 45 | -0.2526 | 0.559 | 1.323 |
30 | 21 | 75 | 50 | 30 | 0.1061 | 1.2767 | 0.884 |
30 | 21 | 75 | 50 | 45 | 0.2039 | 1.5993 | 0.884 |
30 | 21 | 75 | 130 | 30 | 0.0089 | 1.0208 | 0.884 |
30 | 21 | 75 | 130 | 45 | 0.1307 | 1.351 | 0.884 |
30 | 21 | 150 | 50 | 30 | -0.0394 | 0.9132 | 0.854 |
30 | 21 | 150 | 50 | 45 | 0.0584 | 1.144 | 0.854 |
30 | 21 | 150 | 130 | 30 | -0.1843 | 0.6541 | 0.854 |
30 | 21 | 150 | 130 | 45 | -0.0626 | 0.8657 | 0.854 |
Sample Data for the Delta Equations
Tm, °C | Tr, °C | ac | Defl36 | theta | LogDelta8 | Delta8 | BAFDelta8 | LogDelta12 | Delta12 | BAFDelta12 | LogDelta18 | Delta18 | BAFDelta18 | LogDelta24 | Delta24 | BAFDelta24 | LogDelta36 | Delta36 | BAFDelta36 | LogDelta60 | Delta60 | BAFDelta60 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
5 | 21 | 75 | 50 | 30 | 1.7288 | 53.6 | 1.326 | 1.9822 | 96 | 1.239 | 2.1482 | 140.7 | 1.187 | 2.15 | 141.3 | 1.323 | 2.2299 | 169.8 | 1.272 | 2.3567 | 227.3 | 1.222 |
5 | 21 | 75 | 50 | 45 | 1.8424 | 69.6 | 1.517 | 2.0881 | 122.5 | 1.434 | 2.2617 | 182.7 | 1.362 | 2.3083 | 203.4 | 1.368 | 2.3841 | 242.1 | 1.309 | 2.3567 | 227.3 | 1.222 |
5 | 21 | 75 | 130 | 30 | 1.8922 | 78 | 1.326 | 2.1685 | 147.4 | 1.239 | 2.3426 | 220.1 | 1.187 | 2.4459 | 279.2 | 1.149 | 2.5229 | 333.4 | 1.14 | 2.6265 | 423.1 | 1.222 |
5 | 21 | 75 | 130 | 45 | 2.0057 | 101.3 | 1.517 | 2.2744 | 188.1 | 1.434 | 2.4793 | 301.5 | 1.362 | 2.6395 | 436 | 1.169 | 2.7121 | 515.3 | 1.158 | 2.6265 | 423.1 | 1.222 |
5 | 21 | 150 | 50 | 30 | 1.3037 | 20.1 | 1.589 | 1.5302 | 33.9 | 1.508 | 1.7162 | 52 | 1.428 | 1.7708 | 59 | 1.517 | 1.9043 | 80.2 | 1.422 | 2.1294 | 134.7 | 1.262 |
5 | 21 | 150 | 50 | 45 | 1.4201 | 26.3 | 1.858 | 1.6393 | 43.6 | 1.787 | 1.8326 | 68 | 1.673 | 1.9313 | 85.4 | 1.595 | 2.0603 | 114.9 | 1.483 | 2.1294 | 134.7 | 1.262 |
5 | 21 | 150 | 130 | 30 | 1.467 | 29.3 | 1.589 | 1.7165 | 52.1 | 1.508 | 1.9106 | 81.4 | 1.428 | 2.0667 | 116.6 | 1.318 | 2.1974 | 157.5 | 1.274 | 2.3992 | 250.7 | 1.262 |
5 | 21 | 150 | 130 | 45 | 1.5835 | 38.3 | 1.858 | 1.8256 | 66.9 | 1.787 | 2.0503 | 112.3 | 1.673 | 2.2625 | 183 | 1.363 | 2.3883 | 244.5 | 1.311 | 2.3992 | 250.7 | 1.262 |
30 | 21 | 75 | 50 | 30 | 1.9202 | 83.2 | 0.853 | 2.1274 | 134.1 | 0.887 | 2.2648 | 184 | 0.908 | 2.3398 | 218.7 | 0.854 | 2.3933 | 247.3 | 0.873 | 2.4928 | 311 | 0.893 |
30 | 21 | 75 | 50 | 45 | 2.1251 | 133.4 | 0.791 | 2.3325 | 215 | 0.817 | 2.4711 | 295.9 | 0.841 | 2.5207 | 331.7 | 0.839 | 2.567 | 369 | 0.859 | 2.4928 | 311 | 0.893 |
30 | 21 | 75 | 130 | 30 | 2.0835 | 121.2 | 0.853 | 2.3137 | 205.9 | 0.887 | 2.4592 | 287.9 | 0.908 | 2.5404 | 347 | 0.925 | 2.6117 | 409 | 0.929 | 2.7625 | 578.8 | 0.893 |
30 | 21 | 75 | 130 | 45 | 2.2885 | 194.3 | 0.791 | 2.5189 | 330.3 | 0.817 | 2.6888 | 488.4 | 0.841 | 2.7452 | 556.1 | 0.916 | 2.8114 | 647.8 | 0.921 | 2.7625 | 578.8 | 0.893 |
30 | 21 | 150 | 50 | 30 | 1.618 | 41.5 | 0.771 | 1.809 | 64.4 | 0.794 | 1.9578 | 90.7 | 0.818 | 2.0537 | 113.2 | 0.791 | 2.1431 | 139 | 0.82 | 2.2873 | 193.8 | 0.877 |
30 | 21 | 150 | 50 | 45 | 1.8406 | 69.3 | 0.706 | 2.0333 | 108 | 0.721 | 2.182 | 152.1 | 0.749 | 2.248 | 177 | 0.769 | 2.3276 | 212.6 | 0.801 | 2.2873 | 193.8 | 0.877 |
30 | 21 | 150 | 130 | 30 | 1.7814 | 60.5 | 0.771 | 1.9954 | 98.9 | 0.794 | 2.1523 | 142 | 0.818 | 2.2543 | 179.6 | 0.856 | 2.3615 | 229.9 | 0.873 | 2.5571 | 360.7 | 0.877 |
30 | 21 | 150 | 130 | 45 | 2.004 | 100.9 | 0.706 | 2.2196 | 165.8 | 0.721 | 2.3997 | 251 | 0.749 | 2.4724 | 296.8 | 0.84 | 2.572 | 373.2 | 0.859 | 2.5571 | 360.7 | 0.877 |
Sample Data for the Ratio Equation
Tm, °C | Tr, °C | ac | Defl36 | theta | LogRatio8 | Ratio8 | BAFRatio8 | LogRatio12 | Ratio12 | BAFRatio12 | LogRatio18 | Ratio18 | BAFRatio18 | LogRatio24 | Ratio24 | BAFRatio24 | LogRatio36 | Ratio36 | BAFRatio36 | LogRatio60 | Ratio60 | BAFRatio60 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
5 | 21 | 75 | 50 | 30 | 0.0872 | 1.222 | 1.106 | 0.1628 | 1.455 | 1.159 | 0.3241 | 2.109 | 1.157 | 0.4432 | 2.774 | 1.194 | 0.6172 | 4.142 | 1.229 | 0.8812 | 7.607 | 1.185 |
5 | 21 | 75 | 50 | 45 | 0.0995 | 1.257 | 1.106 | 0.1979 | 1.577 | 1.136 | 0.3817 | 2.408 | 1.157 | 0.5279 | 3.372 | 1.194 | 0.7388 | 5.48 | 1.229 | 1.0348 | 10.834 | 1.185 |
5 | 21 | 75 | 130 | 30 | 0.0878 | 1.224 | 1.037 | 0.1433 | 1.391 | 1.112 | 0.254 | 1.795 | 1.157 | 0.3562 | 2.271 | 1.194 | 0.5342 | 3.421 | 1.229 | 0.7585 | 5.735 | 1.185 |
5 | 21 | 75 | 130 | 45 | 0.1 | 1.259 | 1.037 | 0.1869 | 1.538 | 1.085 | 0.3116 | 2.049 | 1.157 | 0.4409 | 2.76 | 1.194 | 0.6558 | 4.527 | 1.229 | 0.9121 | 8.167 | 1.185 |
5 | 21 | 150 | 50 | 30 | 0.0531 | 1.13 | 1.106 | 0.1028 | 1.267 | 1.159 | 0.1918 | 1.555 | 1.185 | 0.2704 | 1.864 | 1.229 | 0.4338 | 2.715 | 1.27 | 0.7131 | 5.165 | 1.218 |
5 | 21 | 150 | 50 | 45 | 0.0653 | 1.162 | 1.106 | 0.1379 | 1.374 | 1.136 | 0.2494 | 1.776 | 1.185 | 0.3551 | 2.265 | 1.229 | 0.5555 | 3.593 | 1.27 | 0.8666 | 7.356 | 1.218 |
5 | 21 | 150 | 130 | 30 | 0.0551 | 1.135 | 1.037 | 0.0687 | 1.171 | 1.112 | 0.1217 | 1.323 | 1.185 | 0.1834 | 1.525 | 1.229 | 0.305 | 2.018 | 1.27 | 0.5484 | 3.535 | 1.218 |
5 | 21 | 150 | 130 | 45 | 0.0674 | 1.168 | 1.037 | 0.1122 | 1.295 | 1.085 | 0.1793 | 1.511 | 1.185 | 0.2681 | 1.854 | 1.229 | 0.4266 | 2.67 | 1.27 | 0.702 | 5.035 | 1.218 |
30 | 21 | 75 | 50 | 30 | 0.1553 | 1.43 | 0.945 | 0.2631 | 1.833 | 0.92 | 0.4233 | 2.65 | 0.921 | 0.5635 | 3.66 | 0.905 | 0.757 | 5.715 | 0.891 | 0.9963 | 9.915 | 0.909 |
30 | 21 | 75 | 50 | 45 | 0.1675 | 1.471 | 0.945 | 0.2844 | 1.925 | 0.931 | 0.4809 | 3.026 | 0.921 | 0.6483 | 4.449 | 0.905 | 0.8787 | 7.562 | 0.891 | 1.1499 | 14.121 | 0.909 |
30 | 21 | 75 | 130 | 30 | 0.1127 | 1.296 | 0.98 | 0.2155 | 1.642 | 0.942 | 0.3532 | 2.255 | 0.921 | 0.4765 | 2.996 | 0.905 | 0.674 | 4.721 | 0.891 | 0.8736 | 7.475 | 0.909 |
30 | 21 | 75 | 130 | 45 | 0.1249 | 1.333 | 0.98 | 0.242 | 1.746 | 0.955 | 0.4108 | 2.575 | 0.921 | 0.5613 | 3.641 | 0.905 | 0.7957 | 6.247 | 0.891 | 1.0271 | 10.645 | 0.909 |
30 | 21 | 150 | 50 | 30 | 0.1212 | 1.322 | 0.945 | 0.2031 | 1.596 | 0.92 | 0.3069 | 2.027 | 0.909 | 0.4101 | 2.571 | 0.891 | 0.5962 | 3.946 | 0.874 | 0.8467 | 7.025 | 0.895 |
30 | 21 | 150 | 50 | 45 | 0.1334 | 1.36 | 0.945 | 0.2244 | 1.677 | 0.931 | 0.3645 | 2.315 | 0.909 | 0.4948 | 3.125 | 0.891 | 0.7178 | 5.221 | 0.874 | 1.0002 | 10.005 | 0.895 |
30 | 21 | 150 | 130 | 30 | 0.08 | 1.202 | 0.98 | 0.1408 | 1.383 | 0.942 | 0.2368 | 1.725 | 0.909 | 0.3231 | 2.104 | 0.891 | 0.4673 | 2.933 | 0.874 | 0.682 | 4.808 | 0.895 |
30 | 21 | 150 | 130 | 45 | 0.0923 | 1.237 | 0.98 | 0.1674 | 1.47 | 0.955 | 0.2944 | 1.97 | 0.909 | 0.4078 | 2.558 | 0.891 | 0.5889 | 3.881 | 0.874 | 0.8355 | 6.847 | 0.895 |
Sample Data for the Defl0 Equation
Tm, °C | Tr, °C | ac | Defl36 | theta | TAFDefl0 |
---|---|---|---|---|---|
21 | 5 | 75 | 50 | 30 | 1.21 |
21 | 5 | 75 | 50 | 45 | 1.256 |
21 | 5 | 75 | 130 | 30 | 1.101 |
21 | 5 | 75 | 130 | 45 | 1.126 |
21 | 5 | 150 | 50 | 30 | 1.26 |
21 | 5 | 150 | 50 | 45 | 1.336 |
21 | 5 | 150 | 130 | 30 | 1.15 |
21 | 5 | 150 | 130 | 45 | 1.203 |
21 | 30 | 75 | 50 | 30 | 0.895 |
21 | 30 | 75 | 50 | 45 | 0.876 |
21 | 30 | 75 | 130 | 30 | 0.946 |
21 | 30 | 75 | 130 | 45 | 0.934 |
21 | 30 | 150 | 50 | 30 | 0.868 |
21 | 30 | 150 | 50 | 45 | 0.839 |
21 | 30 | 150 | 130 | 30 | 0.919 |
21 | 30 | 150 | 130 | 45 | 0.895 |