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Federal Highway Administration Research and Technology
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Publication Number: FHWA-HRT-05-150
Date: February 2006
Review of The Long-Term Pavement Performance (LTPP) Backcalculation Results
Chapter 4. Initial LTPP Backcalculation Data Screening Results
During the development phase of the project (phase I), the researchers selected 18 LTPP pilot sections to evaluate and verify the forwardcalculation methodology. Although only these pilot test sections (albeit with a wide variety of layer thicknesses and test locations) were screened for comparison purposes, this selection still resulted in a large number of data pairs and, accordingly, an adequate sampling of the large volume of data in the LTPP database. Many data points resulted because each individual FWD test point (each with up to four FWD drop heights using multiple drops) provided independently calculated values using both back- and forwardcalculation techniques. Thus, each of the fifteen 152.4-meter (m) (500-foot (ft)) -long flexible sections contains around 500 comparable pairs of moduli. In addition, each 152.4-m (500-ft) rigid section contains somewhat fewer moduli—around 80 comparable pairs of data for the 3 rigid sections screened.
For the phase I study, the researchers picked representative but diverse test sections from the appropriate data tables. In all, 15 flexible and 3 rigid sections were selected for review and the development of the screening techniques that were eventually used during phase II. The 18 sections all contained backcalculated data for most or all of the FWD test points along each of the test sections, and they were selected based on diverse layer thicknesses, geographic location, and test dates. Both General Pavement Studies (GPS) and Specific Pavement Studies (SPS) sections were used to further ensure a wide range of input values.
The data were imported from the appropriate LTPP data tables into various Microsoft™ Excel spreadsheets for further processing. Parallel columns of data, both backcalculated and forwardcalculated (described below), were arranged for ease of postprocessing and comparisons of related stiffnesses, or moduli.
The following LTPP sections and dates of FWD tests comprised the 18 trial datasets:
For the phase I preliminary analyses, these data were processed and analyzed as described in the following sections.
At the outset of phase I, the scope of work assumed that the level E backcalculated values present in the database, for both rigid and flexible pavements, at a minimum, matched the measured deflection basin, i.e., within a reasonable root mean square (RMS) value. Accordingly, spot checks were made on a few of the deflection basins to see whether the same set of moduli could be obtained using the same backcalculation program (MODCOMP). Even if these results were not exactly the same, another approach was to determine whether the RMS values in the level E database were the same as those that could be derived by using the backcalculated values in the database to forwardcalculate a new RMS value.
Although the RMS value comparisons were within reason, they were not identical. It was also not possible, in all cases, to obtain the same set of backcalculated values by rerunning the FWD data through MODCOMP. Nevertheless, the differences could well be attributed to how the backcalculation program was run (e.g., user-controlled inputs) or to rounding differences that cannot be precisely reproduced.
Based on the LTPP sections checked and a general review of the results, the researchers determined that the data in the existing level E database are acceptable insofar as the backcalculated moduli can be used to recalculate a deflection basin and an RMS value that are within reason. Accordingly, the existing backcalculated database was screened as originally proposed in the original scope of work.
Figure 14 shows a log-log plot of all flexible test points analyzed using forwardcalculation techniques versus the backcalculated values for the same test points and drop heights. This graph shows that the two methods of analysis correlate well for most of the data. However, the overall correlation is not very good (the r-squared value = 0.39). A careful review of Figure 14 reveals that a number of outliers caused the low r-squared value and that these outliers are primarily caused by backcalculated values that do not follow the trend. (Using a log-log scale makes the graph look better than a linear plot and regression analysis would.)
Figure 14. Graph. Back- versus forwardcalculated subgrade moduli for 15 trial LTPP flexible sections.
Another way to view the data is to examine the overall nationwide averages and the variability of each set of values.
Certainly, variability in subgrade moduli is to be expected. Examining at least 15 varying subgrade soils spread across several states and regions with obvious differences causes differences, while spatial variability also exists within any given 152.4-m (500-ft) test section. On the other hand, both the averages and the overall variability for each method should be similar, since they are all based on the same FWD test data, the same sections, and the same test points. Table 3 summarizes the basic statistics for the two analysis methods.
*1 megapascal (MPa) = 145 pounds per square inch (psi)
Based on the overall results shown in Table 3, it is apparent that the Hogg forwardcalculation model indicates a smaller variability in subgrade stiffness (coefficient of variation (COV) = 46%) compared to the backcalculation method (COV = 154%). Some of the subgrade layers used during backcalculation (when more than one layer was classified as a subgrade material) were not included in this pilot analysis. The subgrade layers that were not included were the ones with the poorest relationship to forwardcalculation and with the highest variability (see also Figure 20 in chapter 4). Also the median value is probably more indicative of a true average than the averages (arithmetic means), which are increased by the high and implausible modulus values in the backcalculated database.
It appears that the nationwide variability of subgrade materials, expressed as COV, should be in the 40 to 60 percent range. The nationwide standard deviation for backcalculation was even larger than the average value found, which is not feasible and confirms again that some backcalculated values were implausibly high.
By comparison, the average P46 laboratory moduli reported for LTPP’s fine-grained soils was 71 MPa (around 55% of the forwardcalculated median). Meanwhile, the COV in moduli for the same nationwide soil samples was 45 percent—see, for example, LTPP Data Analysis: Variations in Pavement Design Inputs (10). This NCHRP research indicates that the distribution of forwardcalculated subgrade moduli is similar to the distribution of the LTPP P46 laboratory test moduli.
The 45 percent COV for subgrade materials found through an independent means therefore adds credence to the Hogg model COV of 46 percent found during Phase I of this study. The difference between the forwardcalculated Hogg modulus and the laboratory-associated P46 modulus is probably because the subgrade, when tested in situ by the FWD, is covered and well-confined by a pavement system, while the laboratory P46 tests are conducted directly on elements of the subgrade, whether disturbed or not, with or without soil suction, etc.
One level of identifying suspect backcalculated subgrade moduli using the forwardcalculated values could be to limit the divergence of the two approaches to a factor of two. Using this factor of two as an example, if the subgrade modulus from forwardcalculation = 80 MPa (11,600 psi), then the acceptable (unflagged) range of the backcalculated values would be 40–160 MPa (5,800–23,200 psi). Out of the 15 flexible section set of trial data, some 30% of the backcalculated values were not within this acceptable range.
For the concrete sections, all 132 backcalculated subgrade moduli were within a factor of 1.5 below or above the minimum and maximum of the forwardcalculated values. Figure 15 shows that the values were always above so for PCC sections, none of the phase I backcalculated subgrade moduli appear to be candidates for flagging. Figure 15 also shows that the Hogg model produces lower subgrade modulus values, probably because these values represent the apparent (estimated) subgrade modulus under the load, with an effective depth to a rigid layer, whereas the backcalculation approach did not use such an assumption.
Since the spread in back- and forwardcalculated subgrade moduli under concrete pavements was smaller than in the case of the other values compared in the phase I pilot study, these values were plotted in arithmetic form in Figure 15—which still resulted in a surprisingly good r-squared value of 0.84.
Figure 15. Graph. Back- versus forwardcalculated subgrade moduli for three trial LTPP rigid sections.
Figure 16 shows a log-log plot of all flexible layer test points analyzed using forwardcalculation techniques introduced in chapter 3 versus the backcalculated values for the same test points and drop heights. This graph shows that the overall values track quite well; the correlation is good, with an r-squared of 0.67 for the back- versus forwardcalculated moduli.
Although there is a reasonable correlation between the back- versus forwardcalculated AC moduli, as shown in Figure 16, this graph (and others that follow) reveals two or more simultaneous trends. In this instance, out of the 15 asphaltic test sections, most of the points north of the best-fit regression line were from two Florida sites while most of the points south of the line were from two Nebraska sites. Table 4 (Florida) and Table 5 (Nebraska) show the average moduli (all layers) for these four sites using the two methods of analysis.
Figure 16. Graph. Back- versus forwardcalculated asphalt layer moduli for 15 trial LTPP flexible sections.
Results in Table 4 and Table 5 above show two primary factors involved in these discrepancies. The first was that the two Florida sections shown in Table 4 had a very thin layer of asphalt concrete (64 mm (2.5 inches) or less), which is not well suited for backcalculation. In contrast, the forwardcalculation results for these two sections appear reasonable.
The second and probably the most important overall factor that caused the relatively large discrepancies between back- and forwardcalculated values for these four sections was the so-called compensating layer effect that often results from an iterative backcalculation routine. The compensating layer effect is a result of backcalculating the modulus of successive layers from the subgrade up, which has a tendency to compensate for even relatively small errors in the layer or layers below by alternately over- and underestimating the modulus of each successive layer in the pavement system. The compensating layer effect is especially pronounced for Florida section 12-9054, where the subbase layer (actually a compacted fine-grained soil) results in an unrealistically high modulus (14,000 MPa (2,000,000 psi)), followed upwards by a base layer (well-compacted limerock) with an unrealistically low modulus of 80 MPa (11,600 psi). This layer, in turn, is followed by an unrealistically high modulus (at that test site) for the hot mixed asphalt surface course of some 12,500 MPa (1,800,000 psi). Meanwhile, forwardcalculation results in a subgrade modulus of approximately upper 3 m (10 ft) of material of 120 MPa (17,000 psi), followed by a combined base and subbase layer of 300 MPa (42,000 psi). Finally, forwardcalculation indicates a modulus for the asphalt layer of around 6,000 MPa (880,000 psi), resulting in asphalt moduli points north of the best-fit line for all sections shown in Figure 16.
The materials used in Florida section 12-1370 were identical (see modulus comparison in Table 4, although the compensating layer effect is different, with too high a subgrade modulus for the upper 3 m (10 ft) of subgrade from backcalculation.
The opposite effect in the asphaltic surface course is evident for the Nebraska sections shown in Table 5, although to a lesser degree, with seemingly reasonable backcalculated subgrade and subbase moduli, but very high base course moduli, especially for section 31-0121. Because of the compensating layer effect, lower surface course moduli result from backcalculation than from forwardcalculation (see values in Table 5). In both of these sections, the subbase was a crushed stone, the base was a permeable asphalt treated base, and the surface course was dense graded asphalt concrete.
As was shown with the subgrade moduli screening results in chapter 4, another way to examine these data is to consider the overall nationwide averages and the variability associated with each set of values. With the asphalt layer, the averages and variability associated with the same set of test sections and the time of FWD test should be similar.
Table 6 summarizes the basic statistics for both the backcalculated and forwardcalculated (AREA12) analysis methods.
*1 megapascal (MPa) = 145 pounds per square inch (psi)
Based on the overall results shown in Table 6, both methods produce essentially the same average AC modulus, approximately 7,500 MPa (1,100,000 psi). While these modulus levels appear higher than normal for asphalt concrete, in fact these results are reasonable medians and averages, since the data included both high, medium, and low AC mat temperatures from FWD tests conducted at all seasons except when the subgrade was frozen. Furthermore, the coefficient of variation associated with each analysis procedure appears plausible (56 and 79 percent for forward- and backcalculation, respectively), although once again the forwardcalculation method appears somewhat more stable. The 15-section nationwide forwardcalculated COV is greater for AC than for subgrade materials, probably because of the temperature-sensitive, viscoelastic properties of asphalt-bound materials as opposed to unbound subgrade materials, which are generally not viscoelastic.
One of the 15 flexible sections analyzed had two surface course layers that were used in backcalculation. The extra or second-layer plots are described in the extra layer results section. Since these were not indicative of the overall trend, they are not included in Figure 16 or the statistics shown above.
In screening the backcalculated results, if a criterion of a factor of two (times or divided by) were used, then some 15 percent of the backcalculated asphalt concrete moduli would be flagged as out-of-range; if the factor is changed to 1.5, then 24 percent would be out-of-range, and so on. The use of several levels of flagging was eventually adopted and recommended for the LTPP backcalculated database (see chapter 5).
Figure 17 shows a log-log plot of all rigid test points analyzed using the checking for errors or anomalies screening method versus the backcalculated values for the same test points and drop heights. Two backcalculated values are shown because two methods were used in the backcalculation process: slab-on-dense-liquid (DL) foundation and slab-on-elastic-solid (ES) foundation. In both cases, the r-squared values are somewhat poorer than with asphalt concrete (r-squared = 0.61 and 0.70 for the ES and DL cases, respectively). However, this result is to be expected, since the range of values encountered for AC is greater than for PCC because of the viscoelastic nature of asphalt-bound materials.
Using screening criteria, for example, where the backcalculated values should be within a factor of 1.5 times, or divided by 1.5, the corresponding forwardcalculated values, only 18 out of 124 PCC moduli (or 14.5 percent of the total) would be considered out-of-range (reduced to 8 out of 124, or 6.5 percent, if a flagging factor of 2 is used).
Figure 17. Graph. Back- versus
forwardcalculated concrete layer moduli
Table 7 summarizes the basic statistics for both the backcalculated and forwardcalculated (AREA36) rigid pavement analysis methods.
*1 megapascal (MPa) = 145 pounds per square inch (psi)
The averages are very similar between the forwardcalculated model and the backcalculated DL model, while the backcalculated ES model is somewhat lower.
The coefficients of variation were 16, 19, and 46 percent for the backcalculated DL model, ES model, and forwardcalculated AREA36 model, respectively. The forwardcalculation model results in a COV that appears too high when compared to both backcalculation models in the LTPP computed parameter database. Yet it is still possible that the forwardcalculation model used in this study is better able to reveal significant differences between low- and high-strength concrete mixes than either backcalculation model. This trend was discovered during an NCHRP project.(3)
As stated in chapter 3, backcalculation of the intermediate layer, or layers, between a subgrade and a bound surface course is the most tenuous and uncertain of all. This situation is true whether the analyst starts with both of the upper and lower layers as through forwardcalculation or with the subgrade alone, as is generally done through backcalculation. To reiterate this point, any errors in the process leading up to the base course calculation of stiffness or modulus, however slight they may be, will lead to much larger and offsetting errors in the base layer(s) if a closed-loop solution is sought. (A closed-loop solution is one where the sum of the vertical strains under the FWD test load in all underlying pavement layers is equal to the load from the measured center deflection.) In backcalculation, this phenomenon is known as the compensating layer effect, which will influence the pseudobackcalculation routine developed for the intermediate layer after forwardcalculation of the upper and lower layers, even if to a lesser degree. If the Dorman and Metcalf equation is used, this drawback will not apply since the intermediate layer is simply calculated as a ratio of the subgrade modulus (as a function of the thickness of this layer).
Figure 18 shows a log-log plot of all flexible test points analyzed using the pseudo-backcalculation screening approach versus the backcalculated values for the same test points and drop heights.
Figure 18. Graph. Back- versus
forward-based base layer moduli
Figure 18 shows virtually no relationship between the two sets of values. The backcalculation routine chosen to create the computed parameter data tables has evidently fixed the minimum possible base course modulus at 5 or 6 MPa (~750 psi), while the pseudobackcalculation/ forwardcalculation-based approaches used a maximum possible base course modulus of some 2,500 MPa (360,000 psi). Obviously, both of these values are outside of typical ranges for granular or unbound base courses. As Figure 18 shows, the correlation between the forwardcalculation-based method and backcalculation only yields an r-squared value of 0.15. Meanwhile, both approaches suffer from excessive variability, with the pseudobackcalculation approach having a COV of 66 percent and backcalculation having a COV of 272 percent (see Table 8). This anomaly presents a problem because COV levels should be similar to those found for unbound (and generally even more inconsistent) subgrade materials.
*1 megapascal (MPa) = 145 pounds per square inch (psi)
As Table 8 shows, the average and median intermediate layer moduli derived through either approach appear reasonable, with the possible exception of the median backcalculated value (approximately 150 MPa (~20,000 psi)), which is too low.
Of the 15 flexible sections analyzed, 4 had 2 base course layers that were used in backcalculation. The extra, or second-value, plots are discussed below.
These high variability trends were indicative of the two methods throughout the entire FWD load-deflection database and the backcalculated tables. Therefore, the researchers felt it more realistic to use the ratio published by Dorman and Metcalf to estimate the intermediate layer modulus.(9) This approach assumes that a well-constructed unbound subbase or base course will realize an increase in modulus over and above that of the subgrade by a factor that is only dependent on the thickness of the intermediate layer or layers. This ratio is considered valid for intermediate layer thicknesses between 50 and 600 mm (2 and 24 inches), resulting in ratios from 1.16 for a 50-mm (2-inch) layer and 3.56 for a 600-mm (24-inch) layer.
Using the same 15 flexible section dataset, and considering the fact that 6 of these 15 sections had intermediate layers that were classified in the LTPP database basically as “improved subgrade,” Table 9 shows the remaining 9 section statistics.
*1 megapascal (MPa) = 145 pounds per square inch (psi)
The researchers concluded that the median and average base or subbase moduli from Dorman and Metcalf’s relationship were far more realistic (310–360 MPa (45,000–50,000 psi)) as screening values, as was the reasonable nationwide COV of 39 percent (see Table 9). By contrast, the COV using the pseudobackcalculation procedure was 66 percent (see Table 8). The median base course modulus from backcalculation (250 MPa (35,000 psi)) also appears reasonable, but certainly not the backcalculated average of 921 MPa (135,000 psi) or the COV of 216 percent gained using this method (see Table 9).
Accordingly, the Dorman and Metcalf relationship was used for phase II to screen the entire database. For PCC sections, only two back- or forwardcalculated values were derived, one for the subgrade and one for the rigid upper layer or layers.
This section shows the extra layers used in backcalculation for the phase I trial database, over and above the two or three layers calculated through forwardcalculation. These situations occurred when the MODCOMP backcalculation program used more than three layers (plus any assumed rigid bottom) when generating the computed parameter file of backcalculated values.
y (the y axis—the backcalculated
modulus) = 6 times 10 to the 7th power (6E+07) times x
Figure 19. Graph. Back- versus
forwardcalculated asphalt layer moduli
R2 = the coefficient of determination
Figure 20. Graph. Back- versus
forwardcalculated subgrade moduli for five trial
y (the y axis—the backcalculated
modulus) = 2 times 10 to the 15th power (2E+15) times
Figure 21. Graph. Back- versus
forwardcalculated base course moduli
In the three figures above, two of the three exhibit correlations that regress in the wrong direction. The r-squared values indicate an extremely poor fit, whatever the direction of the best-fit line. Accordingly, it would appear that backcalculation, or any other available method, is not very good at deriving stiffnesses or moduli for more than three unknown structural layers (plus a rigid layer at-depth, if any).
Based on the analyses carried out during phase I, the following screening limits were developed. Table 10 shows these limits with a generic description of each.
In the selection of a fairly broad range of values that are acceptable as far as the backcalculated LTPP computed parameter tables are concerned, researchers found that neither back- nor forwardcalculation offers any certain or unequivocal ground truth of in situ moduli. Both methods, using distinctly different assumptions and theory, arrive at approximations (at best) of in situ modulus values in a layered elastic system consisting of two or more layers. Therefore, it is certainly acceptable if these two different approaches produced moduli within a factor of 1.5 times or divided by each other, for the same layer and test point. In such cases, it is impossible to claim that one is correct while the other is incorrect, because no known ground truth exists. The only valid conclusion is that each value, within an acceptable range of each other, is therefore reasonable or acceptable, provided as well that each lies within a reasonable range for the materials it represents (see also chapter 5 and Table 14).
The same logic was used to arrive at the generic terms marginal, questionable, and unacceptable, as outlined in Table 10. For example, it was unacceptable if records occurred from the two dissimilar methods of analysis, although using exactly the same FWD input data, resulted in a layer modulus more than a factor of three times or divided by each other. In such cases, either one of the two values is reasonable or both are unreasonable. The key screening steps in chapter 5 discuss in more detail how these and the other cases of back- versus forwardcalculation discrepancies delineated in Table 10 were handled.