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

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

Appendix G. FWD SN 130, August 25, 1994–September 7, 1994

This previously reported sensor position error was located in the database using an automated version of SLIC which employs a model that was specifically chosen to predict the position of sensor 7 with a close to zero overall bias and the best possible precision (see appendix B). With this method, after regressions are fit to the model 7 prediction based on the data from sensors 3 through 6, two plots for each FWD are created. One is a plot of the sequence of R2 terms, and the other is the predicted position of sensor 7. The first graph shown in this appendix (figure 30) is a plot of all of the R2 values for FWD SN #130, for the regression that best fits each test date using the data from sensors 3 through 6. The period of time was 1994 through the end of 1996, and the data are for lane 1, drop height 4 FWD tests. The second graph in this appendix (see figure 31) uses the same period of time and data to predict the position of sensor 7 for each test date.

In both figures 30 and 31, it can be seen that there is a serious anomaly starting at test sequence 50, which corresponds to August 25, 1994. The average R2 value during the period of time in question was only 0.881, whereas when the FWD sensors used in the regression are correctly placed, the regression fits so well that the values of R2 are generally 0.998 or better. Based on a detailed analysis of the data, for example as shown in the succeeding three figures in this appendix, it is clear that the sensor positions used were 0, 8, 12, 18, 36, 48, and 60 inches. All three section-specific plots depict these sensor positions, with d5 and d6 simply shifted 12 inches into the wrong sensor holders, leaving the 24-inch sensor holder inadvertently empty.

In figures 32, 33, and 34, the gray lines and data points are plots of both actual and erroneous data for d5 and d6 for the particular date. The gray lines that are parallel to the rest of the data are the correct plots, with d5 and d6 set to 61 cm (24 inches) and 91.4 cm (36 inches), respectively.

Because of this information, and the previous information supplied to FHWA, it can be concluded with certainty that d5 and d6 were not positioned correctly, at 61 cm (24 inches) and 91.4 cm (36 inches) respectively; rather, they were positioned at 91.4 cm (36 inches) and 121.9 cm (48 inches) (or very close to these positions) respectively, on FWD SN #130 between August 25, 1994, and September 7, 1994. These dates correspond to the dates when the data generated included lane 1 tests from 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 before August 22, 1994 and on or after September 8, 1994, clearly show that d5 and d6 were correctly positioned at 61 cm (24 inches) and 91.4 cm (36 inches) (as per protocol), respectively.

Figure 30. Graph. R-squared model for D7 prediction, unit 130, 1994 to 1996. The figure is a scatter plot showing, for serial number 130, the R-squared values for the D7 regression fits for 1994 through 1996 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 50, the R-squared values are very close to 1.00. From approximately observation 50 to approximately observation 67, the R-squared values range between 0.84 and 0.92. Beyond approximately observation 67, most of the R-squared values are very close to 1.00. The exceptions are individual observations rather than groups of observations. The most noteworthy exceptions are an R-squared value of approximately 0.94 at approximate observations 78 and 90, a value of approximately 0.98 at approximate observations 100 and 170, and a value of approximately 0.925 at approximate observation 230.

Figure 30. Graph. R2 model for d7 prediction, unit #130, 1994–96.

Figure 31. Graph. Predicted position of D7, unit number 130, 1994 to 1996. The figure is a scatter plot of all serial number 130 D7 sensor position predictions from 1994 through 1996 for 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 predicted position of sensor D7 in inches and ranges from 35 to 80 inches parenthesis 88.9 to 203.2 centimeters end parenthesis. With the exception of a few individual outliers and a grouping beginning at approximately observation 50, the predictions fall between 50 and 68 inches parenthesis 127 and 172.2 centimeters end parenthesis. The grouping between approximate observations 50 and 67 ranges between 40 and 47 inches parenthesis 101.6 and 119.3 centimeters end parenthesis.

Figure 31. Graph. Predicted position of d7, unit #130, 1994–96.

Figure 32. Graph. SLIC plots for section 20–0101 including unit 130 in August 1994. The figure is a line graph showing the SLIC plots for falling weight deflectometer testing on section 20–0101 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 2.0 to 1.0. With the exception of the testing by FWD serial number 130 on August 25, 1994, 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 130 on August 25, 1994, 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 rapidly and finishes by flattening out.

Figure 32. Graph. SLIC plots for section 20–0101 including unit #130, August 1994.

Figure 33. Graph. SLIC plots for section 20–0111, including unit 061 in September 1994. The figure is a line graph showing the SLIC plots for falling weight deflectometer testing on section 20–0111 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 2.0 to 0.5. With the exception of the testing by FWD serial number 130 on August 26, 1994, 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 130 on August 26, 1994, 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 rapidly and finishes by flattening out.

Figure 33. Graph. SLIC plots for section 20–0111 including unit #130, August 1994.

Figure 34. Graph. SLIC plots for section 20–3060 including unit 061 in September 1994. The figure is a line graph showing the SLIC plots for FWD parenthesis falling weight deflectometer end parenthesis testing on section 20–3060 on two different test dates. The X-axis is the natural logarithm of the offset in inches and ranges from 2.0 to 4.5 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 3.5 to 0.0. The plot for a test on 9/18/1989 is generally linear and rises from left to right. The plot for the testing by FWD serial number 061 on 9/7/1994 is divided into two parts. One part, which plots the correct data, is parallel to the 9/18/1989 plot. The other part, which plots the incorrect data, is identical to the first part at its beginning but then rises rapidly and finishes by flattening out.

Figure 34. Graph. SLIC plots for section 20–3060 including unit #061, September 1994.

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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).
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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