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This report is an archived publication and may contain dated technical, contact, and link information
Publication Number:  FHWA-HRT-10-035    Date:  September 2011
Publication Number: FHWA-HRT-10-035
Date: September 2011


LTPP Computed Parameter: Dynamic Modulus


Existing predictive equations, including the original Witczak equation (see equation 1), the modified Witczak equation (NCHRP 1-40D), the Hirsch model, and the law of mixtures parallel model were evaluated for accuracy and potential bias. (See references 2, 5, 6, and 7.)  For fairness to each model, a database consisting of hundreds of mixtures and binders and thousands of single data points from projects across the United States was compiled and used in the evaluation. This effort showed that although each model has certain benefits, no single model is capable of highly accurate predictions over the complete range of necessary conditions. Furthermore, none of these predictive models could predict the |E*| values when only the MRwas available. This final criterion is crucial because more layers had available MR values than the information needed for the existing predictive models. Multiple models are necessary because the layers in the LTPP database are not uniform in their population of material properties. As a result, the research team developed ANN models that, through a pilot study, were shown to yield reasonable and accurate predictions for the complete range of conditions needed. This hierarchical approach thus allows a more complete population of |E*| values.

In the end, three ANN models were developed. Each model differed in the required input parameters. The most accurate ANN model was found to utilize MR as its primary input parameter. The other two models use mixture volumetric properties as well as a binder property as input variables. The VV ANN model uses the binder viscosity and input frequency, whereas the GV ANN model uses the binder |G*| property. These models were extended to include conditions where perfect input values were not available, such as when |G*| had been measured at warm temperatures for the RTFO-aged binder and measured at intermediate temperatures for the PAV binder or when only the binder grade was available. Statistical analysis and engineering judgment were utilized to rank the predictive models, with the MR ANN model being the best, the VV ANN model being the second best, and the GV ANN model being the third best. Imperfect input conditions were also ranked below these three models.

The individual ANN models developed for this project have practical implications beyond the current study. The most direct use of these ANN models is the prediction of |E*| values for MEPDG or other structural/performance analysis of AC pavements. They may be used in the same way that existing closed-form solutions are used. The advantage of using ANN models for this purpose is their improved accuracy when compared to existing closed-form solutions. The MRANN model developed in this project is the only available method for predicting |E*| over the range of temperatures and frequencies needed for complete analysis. Agencies that have managed to compile large databases of MR values may find such a tool useful in local calibration efforts.

The LTPP database was populated with |E*| values at five temperatures and six frequencies by using the prioritized ANN models. This database contains information for a total of 1,806 layers. These layers have binder data available at a combination of different aging conditions, including unaged or original-, RTFO-, PAV-, or field-aged. In the field-aged data, 2,223 records are available because, for some layers, properties may have been measured at different dates. The total resulting number of records is 7,641. Using the combined ANN models and requisite QC checks, modulus values were predicted for 363 records/layers in the original-aged level, 469 records/layers in the RTFO-aged level, 1 record/layer in the PAV level, and 503 records in the field-aged level. These numbers translate to predictions for 17.5 percent of the total number of records available. However, these records are distributed in such a way that a higher percentage of the layers have some sort of valid prediction. Of the 1,806 layers in the database, 1,010, or 56 percent, have a modulus prediction at some aging condition. Of these 1,010 layers, 615, or 34 percent of the total 1,806 layers, have completely reasonable predictions (i.e., an “A” grade), and 89, or 4.9 percent of the total 1,806 layers, have unreasonable predictions (i.e., an “F” grade). The remaining 306 layers, 17 percent of the 1,806 layers, have questionable predictions (i.e., a “C” grade). Thus, the total percentage of layers with a completely valid or questionable prediction is 51 percent.

These populated values will allow users to develop a mastercurve for independent analysis or directly into MEPDG. In addition, mastercurve sigmoidal parameters and temperature shift factors were also computed and included in the population effort. The computed parameters are included in the computed parameter data submitted to FHWA.

The following tasks constitute suggested future research efforts:


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