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Publication Number: FHWA-RD-03-093
Date: August 2006

Study of Long-Term Pavement Performance (LTPP): Pavement Deflections

Appendix F. FWD SN 061, February 26, 1989– September 8, 1989

These previously reported sensor position errors were located in the database and also identified and analyzed using an automated screening version of SLIC for the two regions in which they occurred (Regions 2 and 4). The SLIC screening versions used were tailored for predicting the positions of both sensors 2 and 7. Since several of the sensors were positioned somewhat differently from protocol, it was necessary to use the overall SLIC regression fits to verify the positioning errors found. The first graph shown in this appendix (see figure 23) is a plot of all the SN #061 values of R2 for the d2 regression fits during all of 1989 and the first half of 1990, for lane 1, drop height 4 FWD tests. The second graph (figure 24) is the same plot of all the values of R2 for the d7 regression fits over the same period of time.

In figures 23 and 24, it can be clearly seen that the average R2 values during the period of time in question were generally between 0.980 and 0.990 (actual arithmetic average = 0.987). Generally, when the FWD sensors used in the regression are correctly placed, the regression produces a value of R2 of 0.998 or better, on average. Clearly the R2 values differed significantly during the period in question. Individual plots, such as those reproduced in figures 25 to 29 in this appendix, corroborate that the reported sensor configuration was nonprotocol.

It should be noted that other forensic work previously conducted revealed the following probable (metric) sensor positions: 0, 200, 300, 600, 750, 1200, and 1800 mm. Based on detailed analyses of the data, as shown in figures 25 to 29 in this appendix, it is just as likely that the sensor positions used were 0, 8, 12, 24, 30.5, 48, and 72 inches. In fact, all five section-specific plots depict these sensor positions. However, both possible sets of sensor positions plot almost equally well; thus, either set can be used with a high degree of confidence—and very little difference in terms of backcalculation results, since both are roughly the same (proportionally) in the two different units of measurement.

In figures 25 through 29, the results shown graphically utilize gray lines and data points for the dates that include the erroneous data, which were taken between February and September 1989. The gray lines and points show the plots for all sensors in both the sensors’ actual (U.S. customary in these cases) and incorrect (protocol) offset positions. The portions of the gray lines that are parallel to the other data plots are the correct plots, with sensors d2 through d7 set to 0, 8, 12, 24, 30.5, 48, and 72 inches, respectively.

Because of this information, and the previous information supplied to FHWA, it can be concluded with certainty that the reported (protocol) sensor configuration was incorrect; rather, the correct configuration was either 0, 200, 300, 600, 750, 1200, and 1800 mm or 0, 8, 12, 24, 30.5, 48, and 72 inches on FWD SN #061 between February 26, 1989 and September 8, 1989. These dates correspond to the dates when lane 1 tests were conducted at drop height 4. This period of time may need to be extended slightly, if other tests were conducted along different lanes or at different drop heights. In any case, FWD tests conducted on or after September 11, 1989, indicate protocol sensor positions. FWD SN #061 was delivered to SHRP and driven to the Western Region sometime prior to February 26, 1989; all tests from the time of delivery through the beginning of September 1989 were conducted using the SLIC-determined sensor positions in lieu of the reported (protocol) positions.

Figure 23. Graph. R-squared model for D2 prediction, unit number 061, 1989 to 1990. The figure is a scatter plot showing, for serial number 061, the R-squared values for the D2 regression fits for all of 1989 and the first half of 1990 for the falling weight deflectometer tests for lane one, drop height four. The X-axis is the number of the observation from one to approximately 250. The Y-axis is the R-squared value and ranges from 0.80 to 1.00. From observation one to approximately observation 85, the R-squared values are between 0.98 and 1.00. From approximately observation 85 to approximately observation 100, the R-squared values include a number of readings between 0.96 and 0.98. Beyond approximately observation 100, most of the R-squared values are very close to 1.00.

Figure 23. Graph. R2 model for d2 prediction, unit #061, 1989–90.

Figure 24. Graph. R-squared model for D7 prediction, unit number 061, 1989 to 1990. The figure is a scatter plot showing, for serial number 061, the R-squared values for the D7 regression fits for all of 1989 and the first half of 1990 for the falling weight deflectometer tests for lane one, drop height four. The figure is almost identical to figure 23. The X-axis is the number of the observation from one to approximately 250. The Y-axis is the R-squared value and ranges from 0.80 to 1.00. From observation one to approximately observation 85, the R-squared values are almost all between 0.98 and 1.00. From approximately observation 85 to approximately observation 100, the R-squared values include a number of readings between 0.96 and 0.98. Beyond approximately observation 100, most of the R-squared values are very close to 1.00.

Figure 24. Graph. R2 model for d7 prediction, unit #061, 1989–90.

Figure 25. Graph. SLIC plots for section 04–1017 including unit 061, April 1998. The figure is a line graph showing the SLIC plots for falling weight deflectometer testing on section 04–1017 on nine different test dates. The X-axis is the natural logarithm of the offset in inches and ranges from 2.0 to 4.5 inches parenthesis 5.2 to 11.4 centimeters end parenthesis. The Y-axis is the natural logarithm, positive or negative, of the normalized deflection, and ranges from minus 2.5 to 1.0. With the exception of the testing by FWD serial number 061 on April 4, 1989, the plots are generally linear, almost parallel to each other, and rise from left to right. The plot for the testing by FWD serial number 061 on April 4, 1989, is divided into two parts. One part, which plots the correct data, is parallel to the other plots. The other part, which plots the incorrect data, is identical to the first part at its beginning but then rises; its latter portion is roughly parallel to the other plots but above the plot of the correct data for April 4, 1989.

Figure 25. Graph. SLIC plots for section 04–1017 including unit #061, April 1989.

Figure 26. Graph. SLIC plots for section 08–9020 including unit 061 in June 1989. The figure is a line graph showing the SLIC plots for falling weight deflectometer testing on section 08–9020 on three different test dates. The X-axis is the natural logarithm of the offset in inches and ranges from 2.0 to 4.5 inches parenthesis 5.2 to 11.4 centimeters end parenthesis. The Y-axis is the natural logarithm, positive or negative, of the normalized deflection, and ranges from minus 3.0 to 0.5. With the exception of the testing by FWD serial number 061 on June 27, 1989, and a small, inverted hump-shaped deviation on a portion of the August 24, 1998, plot, the plots are generally linear, almost parallel to each other, and rise from left to right. The plot for the testing by FWD serial number 061 on June 27, 1989, is divided into two parts. One part, which plots the correct data, is parallel to the other plots. The other part, which plots the incorrect data, is identical to the first part at its beginning but then rises; its latter portion is roughly parallel to the other plots but above the plot of the correct data for June 27, 1989.

Figure 26. Graph. SLIC plots for section 08–9020 including unit #061, June 1989.

Figure 27. Graph. SLIC plots for section 32–1031, including unit 061 in February 1989. The figure is a line graph showing the SLIC plots for falling weight deflectometer testing on section 32–1030 on four different test dates. The X-axis is the natural logarithm of the offset in inches and ranges from 2.0 to 4.5 inches parenthesis 5.2 to 11.4 centimeters end parenthesis. The Y-axis is the natural logarithm, positive or negative, of the normalized deflection, and ranges from minus 2.5 to 1. With the exception of the testing by FWD serial number 061 on February 26, 1989, the plots are generally linear, almost parallel to each other, and rise from left to right. The plot for the testing by FWD serial number 061 on February 26, 1989, is divided into two parts. One part, which plots the correct data, is parallel to the other plots. The other part, which plots the incorrect data, is identical to the first part at its beginning but then rises; its latter portion is roughly parallel to the other plots but above the plot of the correct data for February 26, 1989.

Figure 27. Graph. SLIC plots for section 32–1030 including unit #061, February 1989.

Figure 28. Graph. SLIC plots for section 49–1071 including unit 061 in April 1989. The figure is a line graph showing the SLIC plots for falling weight deflectometer testing on section 49–1017 on four different test dates. The X-axis is the natural logarithm of the offset in inches and ranges from 2.0 to 4.5 inches parenthesis 5.2 to 11.4 centimeters end parenthesis. The Y-axis is the natural logarithm, positive or negative, of the normalized deflection, and ranges from minus 1.5 to 1.0. With the exception of the testing by FWD serial number 061 on April 17, 1989, the plots are generally logarithmic, almost parallel to each other, and rise from left to right. The plot for the testing by FWD serial number 061 on April 17, 1989, is divided into two parts. One part, which plots the correct data, is parallel to the other plots. The other part, which plots the incorrect data, is identical to the first part at its beginning but then rises; its latter portion is roughly parallel to the other plots but above the plot of the correct data for April 17, 1989.

Figure 28. Graph. SLIC plots for section 49–1017 including unit #061, April 1989.

Figure 29. Graph. SLIC plots for section 56–7773 including unit 061 in June 1989. The figure is a line graph showing the SLIC plots for falling weight deflectometer testing on section 56–7773 on three different test dates. The X-axis is the natural logarithm of the offset in inches and ranges from 2.0 to 4.5 inches parenthesis 5.2 to 11.4 centimeters end parenthesis. The Y-axis is the natural logarithm, positive or negative, of the normalized deflection, and ranges from minus 2.0 to 0.5. With the exception of the testing by FWD serial number 061 on June 19, 1989, the plots are generally linear, almost parallel to each other, and rise from left to right. The plot for the testing by FWD serial number 061 on June 19, 1989, is divided into two parts. One part, which plots the correct data, is parallel to the other plots. The other part, which plots the incorrect data, is identical to the first part at its beginning but then rises; its latter portion is roughly parallel to the other plots but above the plot of the correct data for June 19, 1989.

Figure 29. Graph. SLIC plots for section 56–7773 including unit #061, June 1989.

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The Federal Highway Administration (FHWA) is a part of the U.S. Department of Transportation and is headquartered in Washington, D.C., with field offices across the United States. is a major agency of the U.S. Department of Transportation (DOT). Provide leadership and technology for the delivery of long life pavements that meet our customers needs and are safe, cost effective, and can be effectively maintained. Federal Highway Administration's (FHWA) R&T Web site portal, which provides access to or information about the Agency’s R&T program, projects, partnerships, publications, and results.
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