E*-Master Curves · Web viewDynamic modulus test was conducted for Mix 1 and Mix 2 at different asphalt contents; optimum and ±0.5 AC% from optimum, all these mixes were designed

Appendix CData Analysis: E*, GS, FN and APA (Prepared by: A. Abu Abdo and F. Bayomy)

This appendix describes further analysis of test data that were developed during this quarter. The data includes dynamic modulus (E*), Gyratory Stability (GS), Flow Number (FN) and the Asphalt Pavement Analyzer (APA).

The analysis is performed under Task A5 – Data Analysis

E*-Master CurvesDynamic modulus test data was compiled and analyzed. Master curves were constructed at a reference temperature of 21.1 °C. A sigmoidal curve fitting equation (Eq. 1) was used. The sigmoidal function shape parameters were determined using the minimum square error method. These parameters are listed in Table 1.

log E¿=δ+ α1+exp ⌊ β+γlog ( f shifted ) ⌋ (Eq. 1)

where,

E*: Dynamic Modulus,𝛿: Log minimum value of E*,δ + α: Log maximum value of E*,

β, γ: Shape Parameters of the Sigmoidal Function, and

fshifted: Shifted Frequencies.

QR4_Appendix C: Data Analysis (E*, GS, FN, APA) - Page 1

Table 1 E* Master Curve Fitting Parameters

Mix Conditionlog E* =𝛿+ 𝛼/[1+exp(𝛽 + 𝛾(log(fshifted)))] Shift Factor @𝛿 𝛼 𝛾 𝛽 4.4°C 21.1°C 37.8°C 54.4°C

1 Opt 1.82315 2.37408 -0.8773 -0.5985 120 1 0.0306 0.00351 -0.5% AC 1.96638 2.31606 -0.8783 -0.5979 120 1 0.02 0.00151 +0.5% AC 1.62788 2.57484 -0.8783 -0.5979 110 1 0.03123 0.00251 PG 58-28 1.29003 2.88701 -0.8422 -0.8203 120 1 0.015 0.00111 PG 64-28 1.46992 2.76558 -0.87 -0.9937 120 1 0.01875 0.0011 PG 70-22 1.95472 2.34749 -0.8022 -1.0907 120 1 0.01137 0.000931 PG 70-34 1.60584 2.48665 -0.8773 -0.5985 120 1 0.01606 0.0009

FA Fine Mix 1.6994 2.46575 -0.7798 -0.8923 150 1 0.01307 0.00105CA Coarse Mix 1.51455 2.53525 -0.8241 -0.8981 110 1 0.0152 0.001552 Opt 1.72997 2.26722 -0.7773 -0.9285 150 1 0.0106 0.00062 -0.5% AC 1.8806 2.2083 -0.7773 -0.8985 170 1 0.0106 0.00062 +0.5% AC 1.92063 2.04252 -0.8773 -0.2985 140 1 0.0126 0.0022 PG 58-34 1.29383 2.64414 -0.7773 -0.5985 150 1 0.0176 0.0022 PG 70-34 2.06985 1.96893 -0.7773 -0.9985 150 1 0.0106 0.00062 PG 70-28 1.70219 2.36354 -0.7773 -0.8985 170 1 0.0106 0.00082 PG 64-22 1.63599 2.54099 -0.6277 -0.9985 190 1 0.00998 0.000452 PG 64-28 1.89209 2.22777 -0.5773 -0.8985 170 1 0.0106 0.00041 Field Mix 1.95134 2.32682 -0.6973 -0.8985 180 1 0.0106 0.00052 Field Mix 1.45939 2.49869 -0.8773 -0.5985 150 1 0.0186 0.00123 Field Mix 1.71349 2.34622 -0.6773 -0.7889 150 1 0.01298 0.00084 Field Mix 1.38751 2.60745 -0.8273 -1.0999 200 1 0.01306 0.00065 Field Mix 1.81837 2.26658 -0.7773 -0.9985 150 1 0.01598 0.00086 Field Mix 1.83155 2.26015 -0.7773 -0.9985 200 1 0.01306 0.00057 Field Mix 1.5832 2.36387 -0.8973 -0.9985 130 1 0.01306 0.0004

Data Analysis for E*, FN, and APA

Aggregates Structure EffectsTo study the effect of changes in aggregates structures on the E* prediction model parameters, four different aggregate structures were evaluated; Mix 1 (25mm mix), Mix 2 (19mm mix), very coarse mix (25mm mix), and fine mix (4.75mm mix). To ensure that only the change in aggregate structure is evaluated, these mixes were designed using the same asphalt binder grade (PG 70-28) and content (4.9%). E* Master Curves (Figure 1) for these mixes showed the finer the mix the lower stiffness would be, especially at higher temperature, thus the mix stability is lower, until a point is reached where the lack of fine materials causes the mix to become less stable, due to the decrease of friction between aggregate particles which is necessary for aggregate interlocking. FN and APA results for these mixes (Figure 2 and Figure 3) showed the same trend, where Mix 1 yielded higher FN and lower rut depth results than Mix 2, which lead to the conclusion that Mix 1 shall perform better than Mix 2 under the same loading conditions.


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Figure 1 E* Masters Curve for Four Different Aggregates Structures

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Figure 2 Effect of Aggregate Structure on FN

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Figure 3 Evaluation of Different Aggregates Structures Using APA Test Results


Binder Content EffectsDynamic modulus test was conducted for Mix 1 and Mix 2 at different asphalt contents; optimum and ±0.5 AC% from optimum, all these mixes were designed to achieve four percent air voids. As per Superpave Mix Design, these mixes should perform best at the optimum asphalt content, at which the air voids of the compacted specimen at N-design is four percent. E* Master Curves (Figure 4) showed that E* values for -0.5% asphalt content from optimum is higher than optimum asphalt content and +0.5% asphalt content for the same mix. FN and APA results (Figure 5 and Figure 6) followed similar pattern, where Mix 1 and Mix 2 yielded higher FN and lower rut depth results at a -0.5% asphalt content that at optimum. Therefore, it is expected that for Mix 1 and Mix 2 that with a -0.5% asphalt content from optimum these mixes will perform better than optimum.

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Figure 4 E* Master Curve for Mix 1 and Mix 2 at Different Binder Contents

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Figure 5 E* FN Results for Mix 1 and Mix 2 at Different Binder Contents


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Figure 6 APA Test Results for Mix 1 and Mix 2 at Different Binder Contents

Binder Grade EffectsTo evaluate changes of binder grades on E*, the upper and lower grades of the binder grades were changed. The upper grade represents the highest temperature the binder can operate, and it is mainly considered for permanent deformation. On the other hand, the lower grade represents the lowest temperature, and it is mainly considered for thermal cracking. Therefore, it expected that the stiffness of higher grade should be higher than a lower grade. E* results for Mix 1 and 2, as presented in Figure 7-a, show that at high temperatures the higher binder grade (70, 64, and 58) yielded higher E* values and nearly the same values at low temperatures.

Figure 7-b presents E* results for mixes with low temperature binder grades (-34, -28, and -22). It was speculated that at higher temperatures, E* values would be similar since upper grade is the same, and E* values would vary at low temperatures. At lower binder grade (e.g PG 64-34) it is expected to have low stiffness (lower E* values) than a binder with a higher binder grade (e.g PG 64-22) to resist thermal cracking. Results showed that both mixes did not follow that trend at high temperatures, but followed the trend at lower temperatures.


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a) Changes in Upper Binder Grade b) Changes in Lower Binder Grade

Figure 7 E* Master Curve for Mix 1 and Mix 2 with Different Binder Grades

Quality Control MeasurementsTo evaluate the possibility of utilizing Gyratory Stability (GS) as a quality control tool in the field,

GS, FN, and rut depth measured by APA were determined for seven field mixes. As shown in Figure 8 and Figure 9 GS results correlated well with FN and APA results. The higher GS is the higher FN and the lower rut depth will be. In addition, a trend has been observed, the lower the asphalt content the higher the GS values (Figure 10), due to the increase of friction and interlocking between aggregate particles.


Mix 4 Mix 7 Mix 6 Mix 2 Mix 3 Mix 5 Mix 10

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Figure 8 Relation between GS vs. FN for All Field Mixes

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Figure 9 Relation between GS vs. FN for Field Mixes

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Figure 10 GS vs. AC% for Field Mixes


Dynamic Modulus (E*) Proposed ModelUsing the Dimensional analysis (Bridgman 1963, Buckingham 1914 & Curtis et al. 1982),

E* was found to be a function of binder dynamic shear modulus (G*), Gyratory Stability (GS), percent maximum specific gravity (%Gmm), and binder content (Pb). Where the binder effects are measured by G*, %Gmm, and Pb, aggregates effects are measured by GS, %Gmm, and (1-Pb), and finally air voids are measured by %Gmm. Further, it was found that the model consists of two sets of parameters; (G*/Pb) and (GS.%Gmm/(1- Pb)). To determined the relation between these parameters and E*, the sensitivity of E* versus (G*/Pb) and (GS.%Gmm/(1- Pb)) were investigated and a model was developed as shown in Eq. 2.

E*=10 .462(G∗.GS .%GmmPb (1−Pb ) )

0 .568

(Eq. 2)

where,

E*: Dynamic Modulus for Asphalt Mix, MPa,

G*: Dynamic Shear Modulus for RTFO Aged Binder, MPa,

Pb: Binder Content,

GS: Gyratory Stability, kN.m,

%Gmm = Gmb/Gmm = Gmm (1-AV%),

Gmb: Bulk Specific gravity of Mix,

Gmm: Maximum Specific gravity of Mix, and

AV%: Air Voids.

Using the two tail statistical t-Test with α equal to 0.01 (99% reliability), it was found that there was no significant difference between the actual and predicted E* mean values. As shown in Figure 11-a, it was found that the developed model had a correlation of R-square of 0.962 and an upper and lower bounds of 12%. To verify the ability of the model to predict E* for mixes other than the ones used in the model development, the predicted E* with actual E* data for other tested mixes (field mixes) were compared. It was found as shown in Figure 11-b that the proposed model could predict E* for these different mixes with correlation of R-square of 0.9469. When using the two tail statistical t-Test with α equal to 0.01 (99% reliability), it was found that there was also no significant difference between the actual and predicted E* mean values.

The next step in the model validation process was to compare the proposed model prediction for all mixes with other models. Actual E* values were compared to predicted values by Witczak model (Witczak and Fonesca 1996) that was incorporated in the 2002 AASHTO MEPDG. Further, E* values were compared to the newly revised model by Witczak (Bari and


Witczak 2006); it has been the suggested that Witczak new model has better prediction when compared to the earlier model.

Results from both Witczak models did not predict the actual E* values as well when compared to the proposed model as presented in Figure 11-c & Figure 11-d. It was observed that the second Witczak model results were less scattered than the first model and unlike the proposed model, both Witczak models seemed to over predict E* values.

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Figure 11. Results of Predicted E* Using Proposed and Witczak Models

To verify if predicted E* by the proposed model can be used in the MEPDG instead of actual E* test data, reliability and probabilistic analysis has been carried out to determine how


reliable the proposed model was in predicting permanent deformation determined by MEPDG (NCHRP 1-37A) when compared to actual E* test results.

The analysis is based on simulation techniques, where some phenomena are numerically simulated and then determine the number of times some events happen such as failure. Utilizing variables probability distributions, random variables are generated and then used in the analysis. Thus, making sure that the wide range of inputs and variables that might occur is taken into account in the design. One of the widely used simulations is the Latin Hypercube Sampling Method. The main advantage of this method is the lower number of random variables needed to obtain good results. The range of random variables is divided into sections and a value from each section is used only once in the simulation. This prevents any variable clusters and selection from one section (Nowak and Collins 2000).

The first step of any reliability and probabilistic analysis is to determine the probability distributions of variables. The distributions of the variables used in this study were determined; Pb, %Gmm, and GS were found to be normal random variables since their probability distributions were normally distributed. On the other hand, G* and E* were considered as a lognormal random variables.

Using Latin Hypercube Sampling, 100,000 random variables have been generated. These variables were used to determine permanent deformation exerted by standard axle load over a 200mm HMA layer, stresses were determined using KENPAVE software (Huang 2004). The overall reliability of the proposed model was found to be 95% for all cases, which is better than the recommended reliability used in MEPDG of 90%. Reliability results for different temperatures are summarized in Table 2.

Table 2. Reliability Analysis Results for Proposed Model

Temperature (°C) Reliability

4.4 99%

21.1 96%

37.8 93%

54.4 92%

Overall 95%

Summary and Conclusions

Based on the test results and data analysis presented in this study, the following conclusions and observations are made:


E* was found to be a function of binder grade and content, and aggregates properties and structures.

Dimensional analysis was used effectively in determining the dynamic modulus (E*) model parameters. It was found that E* is a function of binder dynamic shear modulus (G*), Gyratory Stability (GS), Percent of maximum specific gravity of the mix (%Gmm) and binder content (Pb).

Based on Dimensional Analysis and by using a regression analysis an E* prediction model has been developed, with an R-square of 0.962. When using a two tail t-Test, it was found there is no significant difference between the means of the actual and predicted E* values with a reliability of 99%.

Using seven field mixes, the model was validated by using a two tail t-Test, it was found there is also no significant difference between the means of the actual and predicted E* values with a reliability of 99% and an R-square of 0.9469.

The proposed model results were compared to the two recent Witczak’s models (1996 and 2006); it was found that the proposed model has better predictions.

Using the reliability and probabilistic analysis, the overall reliability of the developed model was found to be 95%, when used to determine the permanent deformation using the 2002 AASHTO Mechanistic Empirical Pavement Design Guise (MEPDG) prediction models versus using actual E* test results.

ReferencesBari J. and M.W. Witczak. Development of a New Revised Version of the Witczak E* Predictive

Model of Hot Mix Asphalt Mixtures. Journal of the Association of Asphalt Paving Technologist, Volume 75, 2006.

Bridgman, P.W.. Dimensional Analysis. Yale University Press, 1963.Buckingham, E.. On Physically Similar Systems; Illustrations of the Use of Dimensional

Equations. Physical Review 4, 1914. Curtis, W.D., J.D. Logan and W.A. Parker. Dimensional Analysis and Pi Theorem. Linear Algebra

And Its Applications 47, 1982.Witczak, M.W. and O.A. Fonseca. Revised Predictive Model for Dynamic (Complex) Modulus of

Asphalt Mixtures, Transportation Research Record 1540, Washington D.C., 1996.Nowak, A.S. and K.R. Collins. Reliability of Structures. Mc Graw Hill Higher Education, Boston,

2000.


Documents

E*-Master Curves · Web viewDynamic modulus test was conducted for Mix 1 and Mix 2 at different asphalt contents; optimum and ±0.5 AC% from optimum, all these mixes were designed