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Federal Highway Administration Research and Technology
Coordinating, Developing, and Delivering Highway Transportation Innovations

This report is an archived publication and may contain dated technical, contact, and link information
Publication Number: FHWA-HRT-04-079
Date: July 2006

Seasonal Variations in The Moduli of Unbound Pavement Layers

Chapter 7: Conclusions and Recommendations

This research represents the first application of the data collected via the LTPP Seasonal Monitoring Program to the development of improved methods for estimating seasonal variations in backcalculated moduli for unbound pavement layers exclusive of frost effects. The approach taken was to build upon the foundation of the EICM by: (1) evaluating the moisture predictive capabilities of that model; (2) developing predictive equations for backcalculated pavement layer moduli; and (3) demonstrating how the resulting relationships might be applied in practice.

This investigation provided the impetus for developing EICM Version 2.6 by demonstrating the practical inadequacies of EICM Versions 2.0 and 2.1 when applied to the prediction of in situ moisture content, and then demonstrated that substantial improvement in the moisture predictive capability of the EICM had been achieved in Version 2.6. Second, the research identified fundamental discrepancies between the stress states used in laboratory resilient modulus testing and those computed using linear layered-elastic theory.

Detailed implications of these findings and other conclusions of lesser importance are presented below. The conclusions are followed by recommendations to address needs identified or reaffirmed through this study and to improve upon the results obtained.


The Enhanced Integrated Climatic Model

In the short term, the most important findings from this study are those related to the moisture prediction accuracy of the EICM, by virtue of their contribution to the development of the 2002 Guide for Design of New and Rehabilitated Pavement Structures currently ongoing through NCHRP Project 1-37A. Key conclusions related to the EICM moisture prediction capabilities are as follows:

  1. Application of EICM Version 2.0 with data commonly available to pavement engineers and assumed or model default values for key input parameters (e.g., the Gardener coefficients) yielded predicted moisture content profiles that were markedly different from the monitored data for two LTPP Seasonal Monitoring Program sites, one in Connecticut, the other in Minnesota. Volumetric moisture content differences of 20 percentage points or more were observed for some monitoring depths in the limited evaluation that was conducted. The EICM model revisions embodied in Version 2.1 were the direct result of this finding.
  2. Application of EICM Version 2.1 with data commonly available to pavement engineers may yield poor predictions of in situ moisture contents. For the test sections and data sets considered in the evaluation of EICM Version 2.1, the R2 values for the relationship between monitored and predicted moisture contents for base and subgrade layers were only 0.01 and 0.30, respectively. Numerical differences between monitored and predicted volumetric moisture contents again exceeded 20 percentage points in some cases. The model revisions embodied in EICM Version 2.6 were the direct result of this finding.
  3. Enhancements in EICM Version 2.6 have substantially improved the practical applicability of the model. When applied with data commonly available to pavement engineers, EICM Version 2.6 yielded predicted volumetric moisture contents that were within the estimated 95 percent confidence intervals for the monitored moisture data in most instances. The R2 values for the relationship between monitored and predicted subgrade moisture contents for the base and subgrade layers for applications of EICM Version 2.6 were 0.71 and 0.51, respectively, a substantial improvement in predictive accuracy. Thus, application of EICM Version 2.6 with input data commonly available to pavement engineers can provide reasonable predictions of in situ moisture contents for unbound pavement layers.
  4. Between-user differences in the application of the EICM may yield significant differences in the model output. In the limited evaluation of between-user differences, the observed mean difference in predicted volumetric moisture content for individual pavement layers (reported in Table 31) varied in the range of 0.1 to 11.1 percentage points, depending on the pavement section under consideration and the nature and extent of the between-user differences. The observed differences for 84 percent of the pavement layers considered were statistically significant at the 5 percent level of significance. Thus improved user guidance and other measures to ensure consistent and correct application of the EICM are needed.

Models for Prediction of Backcalculated Pavement Layer Moduli

  1. Predictive models that are rational when evaluated in the context of laboratory resilient modulus test experience cannot be derived using layer moduli backcalculated using linear layered elastic theory and computed stress states. Factors that contribute to the observed inconsistencies include:
    1. The use of stress states computed for a single "representative" point for the entire layer when the location of a truly representative point is difficult to define. A single representative point is required in linear layered-elastic theory because each layer is assumed to be homogeneous, when the reality for a nonlinear unbound layer is that stresses, and thus stiffness, vary both vertically and horizontally through the layer.
    2. The fact that the computed radial stresses may increase or decrease as the applied FWD load increases, depending on the location of the point for which the stresses are computed.
    3. The fact that the assumptions on which linear layered-elastic theory is based may yield negative (tensile) radial load stresses.

    The net effect of these factors is that both the sign and the relative importance of the bulk and octahedral stress terms in the constitutive model E/Pa=k1?/Pak2(t/Pa+1)k3 often contradict those observed in the laboratory.

  2. The preceding conclusion has several important implications for considering stress dependency in pavement modeling. First, application of laboratory-derived constitutive model coefficients in combination with stress parameters computed using linear layered-elastic theory may yield inaccurate stress-dependent modulus values by virtue of the discrepancies between the laboratory stress states and those computed using linear layered-elastic theory. Second, meaningful advances in the state of the art for backcalculation of pavement layer moduli cannot be achieved without addressing the limitations inherent in the use of linear layered-elastic theory to model structures composed of materials that are stress-dependent. Models that allow more realistic consideration of the stress-dependent nature of these materials are needed.
  3. In many instances, variations in moisture content are not the most important driver of seasonal variations in backcalculated layer moduli for unbound, nonfrozen pavement layers. Evidence for this may be found in:
    1. The fact that the backcalculated layer moduli for all base layers, 82 percent of the subbase/upper subgrade (layer 3) layers, and 80 percent of the subgrade/lower subgrade (layer 4) layers were less strongly correlated with moisture than they were with one or more of the stress parameters considered.
    2. For some pavement layers (base and subgrade for section 481077 (Texas), base for section 131005 (Georgia), and base and subgrade for section 091803 (Connecticut) the observed correlation between mean layer moisture and backcalculated modulus is close to zero, indicating that there is little or no linear relationship between modulus and moisture for the unbound pavement layers represented. In contrast, relatively strong relationships between modulus and moisture are observed for other layers, such as the subgrade at section 131005 (Georgia), where the R2 values varied in the range of 0.30 to 0.78, depending on layer (upper or lower subgrade) and FWD load level.
    3. The high degree of variability in the ratio ?E/?Vw, as summarized in Table 37 (Chapter 3), suggests that other factors such as stress state and random errors in the backcalculated moduli confound the modulus-moisture relationship.
  4. Given the current state of the art, the combined effects of stress and moisture on backcalculated pavement layer moduli may be modeled for practical purposes using the constitutive model form previously presented as Equation 31:

    Elastic modulus divided by atmospheric pressure is equal to regression coefficient times 10 to the (open first parenthesis) regression coefficient C sub 1 times volumetric moisture content divided by 100 plus (open second parenthesis) regression coefficient C sub 2 plus log of regression coefficient C sub 2 times volumetric moisture content divided by 100 (close second parenthesis) times bulk stress divided by atmospheric pressure (close first parenthesis) times (open third parenthesis)shear stress divided by atmospheric pressure plus 1 (close third parenthesis) to the (open fourth parenthesis) regression coefficient C sub 3 plus log of regression coefficient C sub 3 times volumetric moistures content divided by 100 (close fourth parenthesis). (43)

    This conclusion applies only to moduli backcalculated using linear layered-elastic theory. Model coefficients derived using backcalculated layer moduli are not applicable to laboratory resilient modulus data. The applicability of the constitutive model form to laboratory resilient modulus test data has not been established. Soil class models based on Model 2B are presented in Table 43 (Chapter 5).

Variations in Backcalculated Moduli for Unbound Pavement Layers

Information about the extent of variation in backcalculated moduli exclusive of frost effects was presented in Table 21 through Table 26 of Chapter 3. Summary conclusions derived from this information are as follows.

  1. The single point, within-day coefficient of variation for backcalculated moduli for unbound pavement layers may approach 40 percent, with values in the range of 5 to 20 percent being typical. Furthermore, the "conventional wisdom" that backcalculated moduli for deeper layers are less variable than those for the upper layers is supported by these findings. The pooled single-point within-day coefficient of variation for the base layers was 19 percent, while that for the subgrade layers was 11 percent.
  2. The amplitude of seasonal variations in backcalculated layer moduli, exclusive of frost effects, ranges from less than 10 percent (typically for deeper subgrade layers) to more than 200 percent (typically for base layers). The amplitude of the variations (whether expressed on a percentage basis or absolute magnitude) is typically greatest for the base layers and least for the deepest layers.

Application of Research Results To Predict Moduli Backcalculated for Unbound Pavement Layers Using Linear Layered-Elastic Theory

In light of the low overall rate of success in predicting backcalculated layer moduli in the trial applications discussed in Chapter 6, particularly when using either limited data set or soil class models, the only well-founded conclusion that can be drawn is that further research is needed to develop: (1) procedures for backcalculation that rely on more accurate models of the pavement structure and material response; (2) better, broadly applicable predictive models; and (3) improved procedures for their application. Specific recommendations in this regard are provided in the next section.


This study has shed light on a number of issues warranting further investigation. While many are in no sense new, the findings presented earlier reinforce the need for further work. Specific recommendations are as follows.

The Enhanced Integrated Climatic Model

  1. As noted in Chapter 4, the evaluation of the EICM conducted for this study was imperfect because the available data set did not include complete, section-specific values for all input parameters required by the EICM. Another limitation of the evaluation was the consideration of only one test section representing an arid climate. Further evaluation of the EICM moisture predictive capabilities is needed to: (1) more fully establish the sensitivity of the model to the input parameters; (2) confirm or refute the hypothesis that the poor results achieved for section 041024 (Arizona, see Figure 17) are attributable to incompatibility between the theory on which the EICM is based and the true mechanisms of soil moisture movement in arid climates. If possible, this work should be pursued using data sets that include all required input parameters for the test sections under consideration
  2. Further enhancement to the EICM user interface is recommended to improve ease of use and reduce the potential for error arising from the need for manual manipulation of data to create input data sets. Automated entry (and interpolation) of initial temperature profiles would be particularly helpful.
  3. The development of improved user documentation (relative to that available to the author when this work was initiated) is recommended. It is imperative that very specific guidance for the application of the model be provided to minimize the potential for incorrect application of the model and between-user differences. Issues that must be clearly addressed include the ramifications of using or not using input data that are recommended but not required, the selection of the initial conditions used in the moisture prediction (such as the need to avoid simulation starting dates that reflect frozen pavement conditions), and information on the required precision of the input parameters–e.g., how accurate does the depth to ground water need to be, and how does the answer vary with climatic conditions?

The State of the Art of Backcalculation of Pavement Layer Moduli

The stress-sensitive nature and lack of tensile strength in unbound pavement materials has long been recognized. The findings of this study reaffirm the importance of considering the stress sensitivity of unbound materials when analyzing pavement structures. It is therefore recommended that improved methods of backcalculation be developed that provide for more correct consideration of stress sensitivity of pavement layer materials.

Consideration of Stress Dependency in Pavement Modeling

Despite its inadequacies, it is likely that practicing pavement engineers will continue to use linear layered elastic theory in pavement analysis for some time to come. For this reason, the applicability of laboratory-derived resilient modulus nonlinear constitutive model coefficients to pavement analysis based on linear layered-elastic theory should be studied further to fully assess the magnitude and implications of the observed discrepancies between the computed stress states and those used in current laboratory test protocols (see Figure 39 through Figure 41 in Chapter 5).

LTPP Data Used in This Investigation

  1. Supplementary data collection at all LTPP seasonal monitoring test sections should be undertaken to provide an expanded data set for verification of the TDR-based moisture data and to meet other data needs. (This work is in progress via NCHRP 9-23.) The collected data should be incorporated into the LTPP database.
  2. A comprehensive review of all LTPP backcalculation results should be undertaken to: (1) identify those data sets for which the backcalculation conducted to date needs to be revisited, such that the data stored in and disseminated from the LTPP database are of the highest possible quality; and (2) provide the basis to advance the state of the art relative to the evaluation of backcalculation results in general. Use of Model 3 (E/Pa = k110k2?/Pa(t/Pa+1)k3))as the basis for additional objective evaluation criteria should be considered.
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