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Publication Number: FHWA-HRT-04-079
Date: July 2006

Seasonal Variations in The Moduli of Unbound Pavement Layers

Chapter 3: Data Acquisition and Assessment


As indicated previously, this investigation used data obtained via the LTPP Seasonal Monitoring Program. This chapter provides information regarding the LTPP data that were used, as well as the data manipulation and assessment that were conducted prior to application of the data in model evaluation and development. In addition, information on the variability observed in the data is presented to provide context for evaluating the outcome of the work presented in Chapters 4 through 6.


The locations of the LTPP seasonal monitoring test sections considered here are shown in Figure 2. In the figure, square symbols designate test sections used in the evaluation of the EICM, discussed in Chapter 4. All sections shown in the figure were used in the development of predictive models for backcalculated pavement layer moduli, discussed in Chapter 5.

The layer thickness ranges for these test sections are summarized in Table 18, while the distribution of soil classifications for the test sections is summarized in Table 19. While the more fine-grained subgrade soil classifications are relatively scarce, the test sections represent a reasonably broad array of conditions.

Table 18. Layer thickness ranges for LTPP Seasonal Monitoring Program test sections considered in this investigation
Layer Type Minimum Thickness (m) Maximum Thickness (m)
Asphalt concrete 0.071 0.282
Granular base 0.102 0.655
Treated base 0 0.122
Granular subbase 0 0.668
Total thickness above subgrade 0.206 1.069
Table 19. Distribution of soil classification by pavement layer
Layer Type Number of Test Sections with Layer Classification of:
A-1-a A-1-b A-2-4 A-2-6 A-3 A-4 A-6
Granular Base 16 5 1
GS Granular Subbase 1 3 1
Subgrade Soil 2 3 6 1 3 5 2

The data used in the analyses presented herein are drawn from DataPave 2.0, except as follows: [72]

  • Data tables SMP_TDR_AUTO_MOISTURE and SMP_FROST_PENETRATION, SMP_FREEZE_STATE are from release 10.0 of the LTPP Information Management System.
  • Tables TST_... are from release 10.2 of the LTPP Information Management System.
  • Backcalculated moduli and supporting data used in the analysis are prerelease versions of the data subsequently uploaded to LTPP database tables MON_DEFL_BACKCALCULATION... for the initial release from those tables.
  • In a few instances, input data required for application of the ICM were obtained from the seasonal monitoring installation reports for the test sections. Data from this source are annotated as such in the tables where the data are presented.

The review, manipulation, and processing of these data prior their application are discussed in the remainder of this chapter.


Backcalculated layer modulus is the key dependent variable considered in this investigation. The first subsection of this chapter provides an overview of the process used in the backcalculation of those layer moduli. Subsequent subsections discuss the evaluation of those moduli and findings with regard to the variability in the backcalculated moduli.

Backcalculation of Pavement Layer Moduli

The backcalculated pavement layer moduli used in this investigation were derived through a separate study by Von Quintus and Simpson.[73] The backcalculated layer moduli considered in this investigation were provided to the author prior to detailed review or the application of the quality control checks ordinarily applied prior to the release of data from the LTPP database. The author’s evaluation of the backcalculation results to assess their adequacy for use in this study are discussed below.

Figure 2. Locations of LTPP seasonal monitoring sections considered in this study

The figure is a map of the United States with locations pinpointed throughout it. Test sections used in the evaluation of the enhanced integrated climatic models (EICM) are Arizona, Colorado, Connecticut, Georgia, Maine, Minnesota, New Hampshire, Texas, Utah, Vermont, Manitoba, and Saskatchewan.

Evaluation of Backcalculated Layer Moduli

As noted in Chapter 2, one complicating factor in the backcalculation of pavement layer moduli from deflection data is that there is no closed-form solution to the problem. For any given set of measured load and deflections, layer thicknesses, and Poisson’s ratios (the input to the backcalculation process), there may be several, sets of "matching" layer moduli. It is therefore incumbent upon the engineer to carefully evaluate the output of the backcalculation process to determine whether the moduli determined through that process are in fact plausible for the set of circumstances surrounding the collection of the deflection data. Absolute judgments as to the accuracy of any given set of backcalculated moduli are impossible to make, as the true values are never known. Furthermore, the acceptability of a given set of backcalculated moduli depends to some degree on the intended application.

Prior to being used in subsequent analysis, the backcalculated moduli were evaluated against several criteria. First, the moduli were subjected the following series of objective checks.

  • Error Limits: Backcalculation results with root mean square errors (differences between measured and calculated deflections) greater than 2.0 percent were removed from the working data set. Though somewhat arbitrary, the 2.0 percent error limit is a widely used rule of thumb for assessing the adequacy of backcalculation results. Backcalculation results having higher levels of error may be acceptable for use in some applications, but lack the precision needed for this application.
  • Frost Affected Data: Backcalculation results for test dates on which one or more frozen layers were identified in the pavement cross section were removed from the working data set, in keeping with the scope of this investigation.
  • Range Checks: Sets of backcalculation results (i.e., the values associated with a single input data set) for which one or more of the layer moduli fell outside the applicable range defined in Table 20 were removed from the working data set. The upper and lower bounds used in this screening were based on the values reported by Rada et al.[74] The purpose of this step in the process was to remove values that are clearly not plausible for the materials in question. For a given set of backcalculation results, an out-of-range value for any one layer resulted in deletion (from the working data set) of the moduli for all layers. This is deemed necessary due to compensating error effects that occur in the backcalculation process.
    Table 20. Modulus ranges used in screening of layer moduli (MPa)[74]
    Layer Type Minimum Maximum
    Asphalt concrete 500 21,000
    Granular base 35 1,100
    Treated base 35 28,000
    Granular subbase 35 700
    Treated subgrade 35 28,000
    Subgrade soil No limit 1,100
  • Proximity: Backcalculated moduli for test points more than 3 meters from the instrumentation used to monitor in situ temperature and moisture conditions were excluded. The application of this limit is based on the assumption that the moisture and temperature data are most representative of the materials closest to the monitoring location.

    The final step in the evaluation process was a graphical evaluation, in which the backcalculated moduli remaining in the working data set were plotted as a function of time and (for the AC layers) temperature to facilitate identification of observations warranting further scrutiny. Tabular presentations of the data were reviewed to draw final conclusions as to whether individual sets of backcalculated moduli were or were not plausible. The factors considered in this evaluation were:

  • Temperature trends in the AC layers.
  • Time trends (both within day and month-to-month).
  • The plausibility of the backcalculated moduli in relation to those for adjacent layers (taking into consideration the materials in question).
  • Trends with respect to load level.

As with the range checks, all layer moduli associated with a given set of deflection data were treated as a set. Sets of moduli judged to be implausible were flagged as such, so that they could be excluded from analysis sets, but were not deleted from the database. Data reflecting consistent behavior that differed from expectations (e.g., consistent load-softening in a material classified as granular) were not flagged unless there was some other reason to consider them suspect.

Variation in Moduli Under Nonfrozen Conditions

Following the evaluation discussed in the previous section, an exploratory analysis of the backcalculated moduli and their inherent variation was undertaken. The purpose of this analysis was twofold:

  1. To provide information on the amplitude of seasonal and load-associated variations in the backcalculated moduli.
  2. To provide context (in terms of information on the expected within-day variation) for evaluating the outcome of subsequent parts of this study.

The findings of that work are discussed in the next few sections.

Variation with FWD Load

The extent to which the backcalculated moduli vary with FWD load level is characterized in Table 21. This table presents the mean layer moduli for the nominal 40-kN and 71-kN FWD loads, and the mean difference between them, for each AASHTO soil class represented in the data set. The statistics in this table indicate that the A-1-a, A-1-b, and A-2-4 soils tend to be load hardening, whereas the A-2-6, A-3, A-4, and A-6 soils tend to be load softening. The observed trends for the A-1-a, A-1-b, A-4, and A-6 soils are consistent with expectations, and the load softening of the A-2-6 is not unexpected, in light of the clay component in these materials. However, the load softening of the A-3 soils is not consistent with expectations. Rather, one would expect these granular materials to be load hardening. Statistics for the individual pavement layers considered in the computation of the A-3 soil class statistics in Table 21 are presented in Table 22. Possible explanations for the unexpected trends are offered in the next paragraphs.

The variation in the A-3 subgrade soils at sections 251002 and 271018 is very small, and is therefore attributed to errors in the backcalculated moduli, rather than true load-softening behavior. At sections 271018 and 276251, the moduli for the upper portion of the A-3 subgrade exhibit the expected load hardening behavior, whereas those for the lower portion exhibit a lesser degree of load softening. It is likely that this is attributable, at least in part, to compensating error effects.

Table 21. Variation in moduli with applied FWD load by soil class
Soil Class Mean Layer Modulus Difference (E71-E40)
40-kN FWD Load (MPa) 71-kN FWD Load (MPa) Mean (MPa) Range (MPa) Standard Deviation (MPa) As Percent of E40 Number of Obs.
A-1-a 222 247 25 -249 to 225 58 12% 718
A-1-b 228 261 33 -112 to 310 71 12% 315
A-2-4 254 300 47 -115 to 406 94 19% 171
A-2-6 159 147 -12 -25 to -1 8 -7% 19
A-3 287 267 -21 -106 to 40 25 -6% 145
A-4 204 193 -11 -60 to47 15 -5% 366
A-6 108 106 -2 -25 to 38 10 -1% 114

The load-softening behavior of the subgrade (layer 3 and 4) soil at section 351112 is attributed to the presence of fine-grained soils in the deeper subgrade strata. The soils, characterized in the boring log for the section as sandy clay, silty clay, and clayey silt, are below the depth at which samples were obtained for the laboratory characterization.

Table 22. Variation in moduli with load for individual A-3 layers
Section Layer Soil Class Percent Passing 200 Mean Layer Modulus Mean Difference (E70-E40)
40-kN FWD Load (MPa) 71-kN FWD Load (MPa) MPa As percent of E4) Number of Obs.
251002 4 A-3 7.1 235 231 -4 -2% 1
271018 3 A-3 5.2 173 190 17 10% 8
271018 4 A-3 5.2 46 44 -3 -5% 8
276251 3 A-3 7.7 199 224 25 13% 1
276251 4 A-3 7.7 71 70 -1 -1% 1
351112 3 A-3 3.6 292 260 -32 -10% 63
351112 4 A-3 3.6 334 316 -18 -5% 63

Within-Day Variations

For a given nominal test location and FWD load level, within-day variations in backcalculated moduli for unbound pavement layers may occur as a result of both true within-day changes in the in situ moduli (arising from stress-state changes induced by temperature-related changes in the stiffness of an overlying AC layer, for example), or as a result of variations (errors) in the deflection testing and backcalculation process. The latter would include variations due to 4 5deflection and load-measurement errors, variations in placement of the FWD relative to the nominal test point, variations in FWD load from the nominal values, and backcalculation errors.

The magnitude of the observed within-day variations in the backcalculated moduli is characterized in Table 23. The statistics presented in this table are pooled values, computed in accordance with American Society for Testing and Materials (ASTM) standard E122. The pertinent equations are Equations 23 and 24:

Pooled within-day variation is equal to the square root of (open bracket) the summation from J equal to 1 to K of (open first parenthesis) N sub J minus 1 (close first parenthesis) times S sub J squared divided by the summation from J equal to 1 to K of (open second parenthesis) N sub J minus 1 (close second parenthesis) (close bracket).3 (23)


Pooled coefficient of variation is equal to the square root of open bracket open first parenthesis the summation from J equal to 1 to K of open second parenthesis N sub J minus 1 close second parenthesis times the coefficient of variation sub J squared close first parenthesis divided by open first parenthesis the summation from J equal to 1 to K open second parenthesis N sub J minus 1 close second parenthesis close first parenthesis close bracket. (24)

In computing these statistics, the individual sj values represent the within-day standard deviation for a particular section, test point, nominal FWD load level, and layer, and nj is the number of individual observations associated with that value. The values presented in Table 23 are pooled over all test points, sections, layers, and nominal FWD load levels for the soil class or layer type indicated. Thus, in this table k is the number of combinations of date, test section, test point, layer, and FWD load level for a given soil class or layer type.

In most cases, the variation in variability statistics with nominal FWD load level is small in comparison to the variation between the different layers. For example, the COV for section 091803), layer 2 varies in the range of 18 to 20 percent, whereas that for layer 3 varies in the range of 5 to 7 percent. Also, for the many of the pavement sections (e.g., 040113, 041024, 091803, 131005, 251002, 271018, 351112, 481077, 491001, 561007, and 871622), the base layer (layer 2) is more variable than either the subbase/upper subgrade (layer 3) or the subgrade/lower subgrade (layer 4), independent of the measure (standard deviation or coefficient of variation) considered. This may occur as an artifact of the testing and backcalculation process, or it may come about as a result of within-day variations in the stress state within the pavement structure arising from variations in the temperature (and therefore stiffness) of the AC surface layer. The author believes that both factors contribute to the observed variation.

Table 23. Pooled single-point within-day variation in moduli by soil class and layer type
Soil Class or Layer Type Standard Deviation (MPa) Coefficient of Variation (%) k
A-1-a 44 18 1031
A-1-b 34 13 537
A-2-4 63 20 320
A-2-6 4 3 17
A-3 18 7 268
A-4 13 7 481
A-6 12 7 154
Base 55 19 951
Subbase 13 14 176
Subgrade 25 11 1685

Section 501002 is one pavement for which the variability of the upper subgrade is greater than that of the base whether one considers the standard deviation or the COV. Both the base and subgrade at this section are classified as A-1-a soils, such that the true in situ moduli may be very similar. If this is, in fact, the case, the similarity will be reflected in the measured deflections, and it will be difficult to distinguish between the two in the backcalculation process. Thus, the fact that the upper subgrade at this section appears to be more variable than the base may be attributable to the similarity of the materials—i.e., a spurious result.

The magnitude of variation for the more coarse-grained soils (A-1-a, A-1-b, and A-2-4) is consistently greater than that for the more fine-grained soils. However, the author believes that this occurrence is primarily attributable to the predominant use of the coarse-grained soils as base material, whereas the more fine-grained materials are generally seen only in the subgrade. That is, the extent of variability in the backcalculated moduli is driven more by the location of the soil in the pavement structure than by the grain-size distribution of the soil. This interpretation is supported by the data presented in Table 24, which presents within-day statistices pertaining to individual A-1-b pavement layers. The variation in the A-1-b base soils is generally (but not always) greater than that for the A-1-b subbase/subgrade soils.

Table 24. Within-day variation in moduli of A-1-b pavement layers
Section Layer Number Pooled Standard Deviation (MPa) Pooled Coefficient of Variation
27-kN 40-kN 53-kN 71-kN 27-kN 40-kN 53-kN 71-kN
131031 2 61 53 87 83 11 12 18 17
271018 2 42 39 38 44 21 18 19 22
276251 2 - - - 30 - - - 9
491001 2 45 52 61 62 25 27 30 27
871622 2 35 56 59 63 13 18 14 15
040113 3 5 4 4 5 6 4 5 5
231026 3 21 17 15 16 11 11 10 11
251002 3 - 4 4 1 - 5 5 2
271028 3 14 10 13 10 7 5 5 4
331001 3 19 16 18 14 23 19 22 18
871622 3 7 8 8 8 5 5 5 5
906405 3 - - 13 10 - - 7 6
040113 4 4 6 5 4 3 4 4 2
231026 4 51 39 33 41 11 8 7 9
271028 4 6 5 3 3 3 2 2 2
906405 4 - - 2 2 - - 1 1

Seasonal Variations

The extent of seasonal variation in the moduli backcalculated for nonfrozen conditions is characterized in Table 25 and Table 26. Pavement layers for which the backcalculated moduli in the data set spanned less than 6 months were excluded in the computation of the statistics presented. For this reason, the means, minima, and maxima presented in Table 25 differ somewhat from those presented in Table 21, which considers all available pairs of data for the 40- and 71-kN load levels. The maxima and minima presented herein do not reflect the true maxima and minima occurring in all pavements because the data set has been restricted to frost-free conditions.

The amplitude of the observed variation varies with the nominal FWD load level. For 67 percent of the individual layers considered, the amplitude of the observed variation decreases between the minimum and maximum FWD loads. However, the variation from one load level to the next is not always monotonic. Some differences may be attributable to differences in the time span considered. The interaction of stress and moisture may also be a factor in the observed differences. The lower subgrade for section 131031 is somewhat exceptional in that the amplitude of variation varies by only 1 MPa between load levels.

The amplitude of the observed variation tends to be higher for the granular materials than it is for the more fine-grained materials. For example, in Table 25 it may be observed that the amplitude of variation for the A-1-a soil class varies in the range of 72 to 96 percent (depending on load level), whereas that for the A-4 soil class varies in the range of 53 to 63 percent. Similarly, in Table 26 it may be observed that the amplitude of variation decreases with increasing depth in the pavement, with the base layers being most variable on an absolute basis (152–168 MPa, compared with 57 to 76 MPa for subbase layers, and 8 to 88 MPa for subgrade layers). This observation is consistent with the findings of Newcomb et al. and Uhlmeyer et al.[62, 63] However, the subbase layers are more variable on a percentage basis (95 to 123 percent, compared with 90 to 101 percent for the base layers and 6 to 67 percent for the subgrade layers). It is hypothesized that the amplitude of variation (in absolute terms)tends to decrease with increasing depth because the observed seasonal variations are caused, in part, by changes in stress state arising from temperature-induced changes in the modulus of the overlying AC layer, and this effect is more pronounced for the layers closer to the pavement surface.

Table 25. Extent of variation in backcalculated moduli by soil class
AASHTO Soil Class Statistic Nominal FWD Load
27-kN 40-kN 53-kN 71-kN
A-1-a Mean 223 221 234 247
  Min 157 164 181 183
  Max 294 288 295 320
  Amplitude of variation 138 124 114 136
  Variation (% of min) 96 75 72 75
  Number of layers 14 15 15 15
A-1-b Mean 250 225 232 250
  Min 197 171 188 206
  Max 318 290 286 298
  Amplitude of variation 121 119 98 93
  Variation (% of min) 87 80 62 51
  Number of layers 11 12 12 13
A-2-4 Mean 180 183 182 186
  Min 133 134 127 124
  Max 223 242 241 228
  Amplitude of variation 100 109 114 104
  Variation (% of min) 66 81 101 88
  Number of layers 8 8 8 8
A-3 Mean 182 209 208 190
  Min 149 172 174 168
  Max 230 268 276 232
  Amplitude of variation 81 96 103 64
  Variation (% of min) 54 57 59 38
  Number of layers 6 4 4 6
A-4 Mean 204 201 191 186
  Min 168 167 160 155
  Max 245 248 228 217
  Amplitude of variation 77 81 68 62
  Variation (% of min) 57 63 58 53
  Number of layers 9 9 9 9
A-6 Mean 140 139 138 138
  Min 128 118 128 125
  Max 154 158 149 149
  Amplitude of variation 27 40 21 25
  Variation (% of min) 18 31 17 20
  Number of layers 4 4 4 4
Table 26. Extent of variation in backcalculated moduli by pavement layer
AASHTO Soil Class Statistic Nominal FWD Load
27-kN 40-kN 53-kN 71-kN
Base Mean 258 258 276 302
Min 187 181 202 214
Max 339 354 355 383
Amplitude of variation 152 173 153 168
Variation (% of min) 95 101 101 90
Number of layers 16 16 16 17
Subbase Mean 117 117 122 127
Min 84 85 94 100
Max 160 159 160 157
Amplitude of variation 76 74 66 57
Variation (% of min) 121 123 114 95
Number of layers 4 4 4 4
Subgrade (Layer 3) Mean 158 151 148 155
Min 118 116 118 128
Max 197 189 190 196
Amplitude of variation 80 74 72 67
Variation (% of min) 67 62 58 55
Number of layers 14 14 14 15
Subgrade (Layer 4) Mean 226 226 219 205
Min 189 192 191 178
Max 277 269 259 234
Amplitude of variation 88 77 69 56
Variation (% of min) 46 38 33 29
Number of layers 17 17 17 18
Subgrade (Layer 5) Mean 140 141 144 143
Min 133 134 141 139
Max 147 155 149 150
Amplitude of variation 14 21 8 11
Variation (% of min) 10 15 6 8
Number of layers 1 1 1 1

In the time variation in the backcalculated layer moduli at selected sections is illustrated in Figure 3 through figure 7. The moduli shown in these plots are daily average values for the nominal 53-kN FWD load, and the error limits shown in the plots are within-day standard deviations. In Figure 3, the observed variation with time for section 040113 (sited in Arizona) is negligible for the lower portion of the subgrade, and very modest for the upper portion of the subgrade and the base layer. Also, it may be noted that the magnitude of the seasonal variation is not much greater than the within-day variation illustrated by the error limits on the individual data points. Greater variability in all pavement layers is seen in Figure 4 through Figure 8. The subgrade data for sections 131005 (Georgia, Figure 5) and 481077 (Texas, Figure 7) follow a more-or-less sinusoidal trend. The variations for sections 091803 (Connecticut, Figure 4), 271018 (Minnesota, Figure 6) and 501002 (Vermont, Figure 8) are more difficult to characterize. The relationship between these variations and potential explanatory variables will be explored in Chapter 5.

In summary, the single-point within-day variation in backcalculated moduli for unbound pavement layers, expressed in terms of the coefficient of variation, was found to vary in the range of 1 to 38 percent. Pooled values of 19, 14, and 11 percent were computed for the base, subbase, and subgrade layers, respectively. The amplitude of the observed seasonal variation (exclusive of frost effects) was found to vary in the range of 6 to 123 percent of the observed minimum value, corresponding to amplitudes of 8 to 173 MPa. In absolute terms, the largest variations were observed for the base layers, and the smallest variations were observed for the deeper subgrade layers. On a percentage basis, the subbase layers were more variable than the base layers, and both base and subbase layers were more variable than the deep subgrade layers.

Figure 3. Seasonal variation in daily average moduli, section 040113 (Arizona)

Graphs. Seasonal variation in daily average moduli, section 040113 (Arizona). The figure has two graphs. Both graphs have the date graphed on the horizontal axis from August 1995 to March 1997. The modulus is graphed on the vertical axis from 0 to 200 megapascals. The top graph has the A-1 lowercase A base plotted from 1996 between 100 to 160 megapascals. The bottom graph has the A-1 lowercase A upper and lower subgrade graphed. The lower subgrade ranges at 150 mega Pascal in 1996. The upper subgrade begins at 80 megapascals and increases to 120 throughout 1996. The variation is negligible for the lower portion of the subgrade and very modest for the upper portion of the subgrade and the base layer.

Figure 4. Seasonal variations in daily average moduli, section 091803 (Connecticut)

Graphs. Seasonal variations in daily average moduli, section 091803 (Connecticut). There are two graphs. The date is graphed on the horizontal axis from August 1993 to March 1995. The modulus is graphed on the vertical axis up to 350 megapascals. The first graph has the A-1 lowercase A base beginning at 260 megapascals in 1993, and then it decreases in 1994 to 150 megapascals. The base continues to increase and decrease between 240 to 300 megapascals. The second graph has A-1 lowercase A upper subgrade and A-4 lower subgrade. The A-4 lower subgrade ranges between 250 to 340 megapascalss throughout the graph. The upper subgrade ranges from 125 to 200 megapascalss. Figure 4 has higher variability in all pavements.

Figure 5. Seasonal variations in daily average moduli, section 131005 (Georgia)

Graph. Seasonal variations in daily average moduli, section 131005 (Georgia). The graph has the date graphed on the horizontal axis from August 1994 to March 1996. The modulus is graphed on the vertical axis up to 450 megapascals. There are three pavements tested: A-1 lowercase A base, the A-4 upper subgrade, and A-4 lower subgrade. All three pavements increase from spring to summer before decreasing drastically in winter. Figure 5 has higher variability in all pavements.

Figure 6. Seasonal variations in daily average moduli, section 271018 (Minnesota)

Seasonal variations in daily average moduli, section 271018 (Minnesota). There are two graphs situated vertically. The date is graphed on the horizontal axis from August 1993 to March 1995. The modulus is graphed on the vertical axis up to 300 megapascals. The top graph has the A-1 lowercase B base starting at 240 megapascals in 1993 and remaining at that modulus until spring of 1994. The base then continues the zigzag up and down in 1994. The second graph has two subgrades: A-3 upper subgrade and A-3 lower subgrade. Both subgrades remain at an even level in 1993, increase in spring and summer of 1994, and fall in autumn of 1994. The upper subgrade has a higher modulus than lower subgrade.

Figure 7. Seasonal variations in daily average layer moduli, section 481077 (Texas)

Graph. Seasonal variations in daily average layer moduli, section 481077 (Texas). The date is graphed on the horizontal axis from October 1993 to May 1995. The modulus is graphed on the vertical axis up to 500 megapascals. Two lines are shown: A-1 lowercase A base and A-4 subgrade. The base has a higher modulus, starting at 380 megapascals and increasing and decreasing in a zigzag pattern. The subgrade begins at 200 megapascals and increases and decrease at a wavy pattern. There is great variability between the two lines.

Figure 8. Seasonal variation in moduli, section 501002 (Vermont)

Graphs. Seasonal variation in moduli, section 501002 (Vermont). There are three different graphs situated vertically. All three graphs have the date graphed on the horizontal axis from September 1993 to April 1995. The elastic modulus is graphed on the vertical axis from 0 to 400 megapascals. The first graph has the A-1 lowercase A base graphed on the figure and varies between 225-350 megapascals. The second graph measures A-1 lowercase A upper subgrade and averages between 125-250 megapascals. The third graph measures A-1 lowercase A lower subgrade and is between 150-260 megapascals. There is no visible pattern in the lines and there is great variability between the graphs.


Stress parameters considered in the development of predictive models for backcalculated moduli discussed in Chapter 5 were the bulk stress (? = s1 + s2 + s3), and the octahedral shear stress (toct = 1/3[(s1-s2 )2 + [(s2-s3 )2 (s3-s1 )2]½). Selection of the bulk and octahedral shear stresses was based on their prior use in the constitutive models discussed in Chapter 2.

Stress parameters were computed for each individual set of backcalculated layer moduli considered in the analysis (where a"set" is defined by test section, date, time, test point, and FWD load). Stresses were computed for a single radial location, that being the center of the loaded area. The depths at which the stresses were computed corresponded to the quarterpoints for each finite layer, and 0.1, 0.2, and 0.3 m below the layer interface for semi-infinite subgrade layers.

In calculating the stress parameters, both load-induced and overburden stresses were considered. The load-induced stresses were computed through application of the CHEVLAY 2 layered–elastic analysis program to the backcalculated layer moduli.[26] To ensure consistency, the layer thicknesses and Poisson’ s ratios used in the stress calculations were those reported with the backcalculated moduli.

The calculation of overburden stresses took into consideration variations in total (wet) soil density with time due to fluctuations in moisture content, as well as variations in the depth of the water table. Effective stresses were used for soils below the water table, while total stresses were used for soils above the water table. Several different values of K0 were considered in the overburden computations, as will be discussed in Chapter 5.


At each LTPP Seasonal Monitoring Program test section, moisture content is monitored through the use of Time Domain Reflectometry (TDR) probes placed at approximately 10 depths in the unbound base, subbase (if present), and subgrade layers. The number of monitoring depths within a given layer at a particular section varies from one to five, depending on the layer thicknesses at that particular section. The number of observations for a given probe on a given test date varies from one to three.

TDR is an indirect method of monitoring moisture. The raw data collected with the TDR instrumentation are interpreted to determine the dielectric constants (Ka) for the soil. The volumetric moisture content is then computed using regression equations relating the dielectric constant (and possibly other soil parameters) to moisture content. Knowledge of the soil dry density allows computation of the gravimetric moisture content. The specifics of the methodology as applied to the LTPP Seasonal Monitoring Program sections are presented elsewhere.[75,76,77] Both volumetric and gravimetric moisture contents are provided in the LTPP database. The work reported herein utilized the volumetric moisture contents.

Four different regression models were used in determining the moisture contents for the LTPP seasonal monitoring sections. The models are presented in Table 27. The conditions of application for each of the four models, as well as the minimum and maximum estimated errors (for 95 percent confidence limits) in the TDR moisture contents are summarized inTable 28. Note that the magnitude of the estimated error varies with the dielectric constant, and, thus, with the moisture content.

The vast majority of the data considered in this investigation were derived using the Coarse Ka Model (TDR Model 1). TDR Model 2 was used only for the deeper (subgrade soil) probes at sections 308129, 481068 and 871622. TDR Model 3 was used for many observations in the subgrade soil at section 501002, and for some data sets at other sections. TDR Model 4 wasused only at sections 481077, 481068, 241634, and 081053.

The volumetric moisture data were reviewed through plots of the mean moisture content as a function of time, analysis of the within–day variation reflected in the data, and comparison of day–of–installation TDR moisture contents with laboratory values for samples collected fromthe backfill material as the probes were installed.

Table 27. Volumetric moisture models used in determining moisture content from LTPP TDR data (as reported by Jiang and Tayabji[76])
Model Name Equation
1 Coarse Ka Vw= –5.7875 – 3.41763Ka –0.13117Ka2+0.00231Ka3
2 FineKa Vw=0.4756 + 2.75634Ka – 0.061667Ka2 + 0.000476Ka3
3 All soil Ka Vw=–0.8120+2.38682Ka - 0.04427Ka2 + 0.000292Ka3
4 Fine gradation Vw=1761.78 + 2.9145Ka –0.07674Ka2 + 0.000722Ka3
–19.6649P1.5+4.3667P0.5 +5.516P#4 + 2.7737P#10
+ 0.06057P#200 – 0.2057PL+0.10231LL
Vw = volumetric moisture content P#4=% passing No.4 sieve
Ka = bulk dielectric constant P#10 = % passing No.10 sieve
P1.5=% passing 38 mm (1.5") sieve P#200=% passing No.200 sieve
P0.5 = % passing 13 mm (½") sieve PL = plastic limit; LL=liquid limit
Table 28. Minimum and maximum estimated errors (95 percent confidence interval) for TDR moisture content prediction models (adapted from Jiang and Tayabji[76])
Moisture Prediction Model Minimum Error Maximum Error Applicable to:
Limit % Vol.Moisture Content % Limit % Vol.Moisture Content %
1 Coarse Ka 5.1 0.0 5.4 33.8 Coarse–grained soils with 1.5< Ka<24.8
2 Fine Ka 8.2 12.2 13.5 46.2 Fine-grained soils with 3<Ka<58.4 and gradation and/or Atterberg limits either not available, or outside inference spacefor Model 4
3 All soil Ka 2.7 9.8 9.9 43.4 Coarse–grained soils with Ka>24.8 or fine–grained soils where neither model 2 nor model 4 can be applied
4 Fine gradation 7.1 8.7 8.3 50.8 Fine-grained soils with 3< Ka <58.8 and required gradation and Atterberg limits available and within inference space of model

The within–day variation for the TDR moisture data is characterized in Table 55 of Appendix A. The values shown are pooled values, computed in accordance with ASTM standard E122. The pertinent equation is:

equation25 (25)

For each combination of test section and TDR probe, n is the number of moisture observations in a given day, and k is the number of days for which moisture data are available for that probe. The number of test dates considered in the computation of the within day variation statistics is presented in Table 56 (Appendix A), while the average number of observations per day is presented in Table 57 (Appendix A). The pooled standard deviation and coefficient of variation computed over all moisture observations (i.e., k = number of combinations of monitoring date test, section, and TDR probe) are 1.18 and 8.8 percent, respectively.

The prediction error limits presented in Table 28 provide a frame of reference for evaluating the magnitude of the within-day variations in TDR monitored moisture, as characterized by the pooled standard deviation. In Table 58 (Appendix A), the pooled standard deviation for each probe is expressed as a decimal fraction of the maximum estimated error for TDR Model 1 from Table 28 – that is, 5.4. A single value was used for all TDR probes for simplicity. The value for TDR Model 1 was selected because it was used in the computation of the vast majority of the moisture data, and because it is conservative in comparison to the maximum values for the other TDR moisture models.

The TDR moisture error estimates presented in Table 28 are computed as twice the standard error of the prediction. Thus, Table 58 (Appendix A) values greater than 0.5 indicate that the within-day standard deviation is greater than the estimated standard error of the prediction. Ratios greater than 0.5 are denoted in the table by gray shading. They occur for most of the probes for section 481068 and one probe each for sections 040113, 161010, and 308129. The data in Table 58 (Appendix A) are summarized in the form of a frequency histogram in Figure 9. Values in the range of 0.1 to 0.3 occur with the greatest frequency, indicating that in most cases, the within-day standard deviation is small in comparison to the estimated model error.

Individual observations for the within-day standard were evaluated by comparing them to the overall pooled within-day standard deviation of 1.18. In cases where the within-day standard deviation for a given date and probe depth exceeded three times the pooled within-day standard deviation computed over all sections, the individual observations for that probe and test date were reviewed in an attempt to ascertain whether the high variance could be attributed to anything other than random error in the measurement process. The data sets identified for examination are listed in Table 59. They include observations associated with the high pooled within-day standard deviation values denoted by shading in Table 58. The findings of the review of these data were as follows.

Figure 9. Frequency histogram for ratio of within-day standard deviation/ maximum TDR Model 1 error

Graph. Frequency histogram for ratio of within-day standard deviation/maximum time domain reflectometry (TDR) model 1 error. The histogram has the within-day standard deviation/prediction error graphed on the horizontal axis from 0 to 0.6 or more. The frequency is graphed on the vertical axis from 0 to 140. The within-day error of 0.1 has the highest frequency at 120. As the within-day standard deviation/prediction error increases, the frequency decreases.

Within-Day Standard Deviation/Prediction Error

  • Section 091803, February 17, 1994, TDR Probe Numbers 3 and 4: At these monitoring depths, the observed moisture contents increased substantially (from approximately 9 percent to approximately 19 percent) over a 4-hour period in the morning. This increase, coupled with the time of year, suggested that the change might be attributable to thawing in the pavement. The temperature-depth data for this date are consistent with this hypothesis–i.e., the temperatures near the probes in question are close to 0° C. Therefore, the large increase in moisture content observed for section 091803 on February 17, 1994, was attributed to thawing of the materials surrounding the TDR probes, and the data were therefore excluded from the data set used in subsequent analysis, as this investigation is concerned with nonfrozen materials.
  • For section 161010, TDR Probe Number 10, TDR Model 1 was used to derive some of the moisture contents for the test dates in question, and TDR model 3 was used to derive other values. The greater variability observed may be related to this fact. Removal of any or all of the data points does not appear to be justified.
  • Section 481068 August 21, 1997, TDR Probe Numbers 2, 3, 5, 6, 7, and 10: The monitored moisture contents for these probes decreased by more than a factor of 10 over a 4-hour period from mid-morning to early afternoon. It is implausible that a change of this magnitude could occur within 4 hours. A review of the available data yielded no plausible explanation for a change in moisture of this magnitude. It is, however, noted in the comments table that the piezometer pipe at the section was dry on this date, a fact that seems inconsistent with the higher moisture contents that were observed. Overall, it was noted that moisture data for this section were extremely scarce. For 8 of the 10 monitoring depths at this section, the only available moisture content data (as of Information Management System Release 10.0) were for the August 1997 monitoring date. This paucity of data, combined with the inconsistency of the data for the one date for which data are (relatively) plentiful led to the exclusion of this section from subsequent analysis.

In the remaining instances where the within-day standard deviation for a given section and test date exceeded three times the overall pooled within-day standard deviation, no plausible explanation for the observed variation was identified. That is, there was neither a clear indication that the data were erroneous, nor any indication of conditions likely to cause a within-day moisture content change of the magnitude reflected in the data. It was therefore assumed that the observed variance was attributable to random variation in the measurement processes, and that exclusion of these data from the analysis was not justified.

The observed within-day variation in moisture content reflects both true within-day changes in moisture content and variability arising from measurement errors. Because the observed values are, in most cases, small in comparison to the estimated error associated with the measurement technology used, as characterized in Table 28, it is reasonable to assume that within-day variation in the true moisture content of the soil surrounding a given TDR probe is small in comparison to the measurement error associated with the moisture content data. Therefore, the best available estimate of the in situ moisture content at a given time is the daily mean value for the test date in question. For this reason, and because a one-to-one correspondence between the time of TDR moisture observations and the time of FWD deflection tests does not exist, the analyses reported herein use the mean daily moisture content for a given test date, rather than the individual observations.


Application of the EICM requires assembly of a data set characterizing the pavement crosssection, materials, and external environment. The broad categories of input data required by the EICM are as follows.

  • Initialization data define the analysis period, the geographic location of the section under consideration, and the time increments to be used in the simulation and reporting of the results.
  • Climatic boundary conditions, including temperature, precipitation, windspeed, percent sunshine, and water table depth data. Climatic data provided with the program may be used where section-specific weather data are not available.
  • Thermal properties, which characterize the tendency of the pavement surface to absorb and emit heat, as well as the temperature range over which freezing and thawing occur.
  • Infiltration and drainage inputs, which characterize both the extent of cracking in the surface, and the drainage characteristics of the base material and geometry.
  • Asphalt material inputs, including layer thickness, mix design information, data defining the modulus-temperature relationship, and thermal characteristics.
  • Material properties, including layer thickness, density, saturated permeability, and other data characterizing the base, subbase, and subgrade layers.
  • Initial profiles, which characterize the temperature and (for Version 2.0 and 2.1 of the EICM only) moisture conditions of the pavement on the first day of the simulation period.

In applying the EICM, the author used section-specific data where they were available and pertinent to moisture prediction. However, some required data elements are not among the data assembled for the LTPP test sections. Default or assumed values were used for these parameters. Default or assumed values were also used for a few parameters (e.g., AC mix design information) not pertinent to moisture prediction as a matter of convenience. The following paragraphs provide an overview of the data that were used in applying the EICM. The data themselves (including assumed or default values) are presented in Appendix B. Details that varied from one version of the EICM to another are discussed in the pertinent sections of Chapter 4.

Climatic Boundary Conditions

Daily temperature and rainfall data (including the times at which the daily maximum and minimum temperature occurred), and (nominally) monthly depth to ground water data collected at each section for the time period of the simulation were used in the models. Windspeed and percent sunshine data used were those provided with the EICM for the weather stations identified in Table 60 to Table 64 of Appendix B, as these data are not collected at the seasonal monitoring sections. The recommended default values were used for the remaining variables. Missing observations were filled in through use of the "generate" function of the EICM, except as discussed in the next two paragraphs.

In a few instances, missing water table depth observations were accompanied by comments to the effect that the monitoring well was dry. Where this occurred, a depth to water table slightly greater than the depth of the bottom of the monitoring well was entered. This estimate is deemed more accurate than allowing the program to generate a value by interpolating between known values, which would yield an estimate inconsistent with the observed (dry) state of the monitoring well.

In one case, section 041024, the monitoring well was reported to be dry on all monitoring dates. For this section, a constant water table depth of 152 m (500 ft) was assumed.

Infiltration and Drainage

The EICM requires entry of the linear length of cracks and joints for use in computation of the amount of water infiltrating the pavement. The values used in the simulation were estimated from the yearly mean distress quantities for the year considered in the simulation, distress surveys having been conducted on a quarterly basis. Because several distresses observed at the test sections considered are recorded in terms of the affected pavement area, as opposed to the crack length, it was necessary to convert the distress areas recorded in the LTPP database to equivalent crack lengths. Assumptions made to estimate the equivalent crack length for distresses measured in units of area are summarized in Table 29.

Table 29. Assumed crack lengths for distresses quantified in terms of area
Distress Crack Length (m) per Square Meter of Distress
Low severity alligator cracking 2
Moderate severity alligator cracking 5
High severity alligator cracking 12
Low severity block cracking 1.3
Moderate severity block cracking 4
High severity block cracking 5

Asphalt Material Properties

Program default values were used for the asphalt materials, as it was assumed that these variables would have no impact on the predicted moisture contents for the unbound layers.

Material Properties

For sections where multiple observations for a particular parameter were available, the ones used were those for sample locations closest to the location of the subsurface instrumentation. Default values were used for the saturated permeability, dry thermal conductivity, dry heat capacity, volume compressibility, and Gardner model parameters (Version 2.0 of the EICM only), as these parameters are not among the data available for the LTPP test sections. Assumed values were used for the frozen and unfrozen resilient modulus, Poisson’s ratio, and the length of the recovery period, as these parameters have no bearing on moisture predictions.

Initial Temperature and Pore Pressure Profile

The initial temperature profiles used in the EICM models were derived from section-specific data obtained with thermistor probes installed in the pavement. Linear interpolation was used to estimate the soil temperature at each node from the temperatures at the two closest monitoring depths. The pavement surface temperatures were extrapolated from the available data (measurements having been taken at mid-layer, and approximately 0.025 m below the surface, and 0.025 m above the lower boundary of the layer). Temperatures for the deepest model nodes were estimated. Daily average values were used in all cases.

The initial pore pressure profiles used in applying Version 2.0 of the EICM were computed from the water table depth per the guidance provided in the EICM documentation.[66] Version 2.1 and subsequent versions of the EICM do not utilize an initial pore pressure profile.


The data required for this investigation include backcalculated pavement layer moduli (the key dependent variable), in situ moisture data, pavement cross-section and materials data, and climatic data. These data were acquired from the LTPP database, and (in some cases) off-line files, reviewed and manipulated to create the database and EICM input files necessary for the pursuit of the project objectives. The application of these data to evaluate the moisturepredictive capabilities of the EICM and develop predictive models for backcalculated pavement layer moduli will be discussed in the next two chapters.

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