USE OF BBR TEST DATA TO ENHANCE THE ACCURACY OF G* -BASED WITCZAK MODEL PREDICTIONS

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1 USE OF BBR TEST DATA TO ENHANCE THE ACCURACY OF G* -BASED WITCZAK MODEL PREDICTIONS Mekdim T. Weldegiorgis * PhD. Candidate, Department of Civil Engineering, University of New Mexico, USA * 1 University Blvd NE, University of New Mexico, Albuquerque, NM 8716, USA. mteshome@unm.edu Hasan M. Faisal PhD. Student, Department of Civil Engineering, University of New Mexico, USA Rafiqul A. Tarefder Associate Professor and Regents' Lecturer, Department of Civil Engineering, University of New Mexico, USA ABSTRACT: The latest model to predict dynamic modulus of asphalt concrete is the G* -based Witczak model. This model utilizes binder shear modulus, G*, and phase angle data to take into account the temperature and frequency dependent nature of asphalt concrete dynamic modulus. However, it is very difficult to determine the G* for temperatures below 4.4 C, which is the major cause of error in the Witczak model predictions. In this study, dynamic modulus testing was performed on three typical mixes from New Mexico at five different temperatures (-1, 4,, 37 and 54 C) and six frequencies (.1,.5, 1, 5, 1, 5 Hz). G* of the binders utilized for mix production was determined at seven temperatures (4.4, 1.8, 1.1, 9.4, 37.8, 46.1 and 54.4 C) using Dynamic Shear Rheometer (DSR) test. To supplement DSR test results for the Witczak model prediction at low temperatures, creep stiffness test was conducted using Binder Beam Rheometer (BBR). BBR testing was conducted for the binders at four temperatures (-1, -15, - and -3 C). Creep stiffness mastercurves are developed and converted to G* mastercurves which are then used as input in the G* -based Witczak model. Dynamic modulus prediction was performed with and without the use of G* data obtained from BBR testing for three types of asphalt mixes and compared with laboratory determined dynamic modulus. The use of low temperature BBR test data produced an enhanced accuracy for the G* -based Witczak model predictions. KEY WORDS: Dynamic, Modulus, Witczak, Binder, Shear, Rheometer 1. INTRODUCTION The G* -based Witczak model used to predict the dynamic modulus, E*, is shown by Equation (1) [1]. The major advantage of this model is the use of binder G* as an input to take into account the temperature and loading frequency dependent nature of binders in asphalt concrete. However, it is impossible to determine the G* of binders at very low temperatures using DSR test equipment. Instead, low temperature G* value is assumed to have a maximum value of 1GPa []. However, assuming the maximum G* to be 1 GPa for all binders contributes to errors in the E* prediction, especially since G* is one of the most sensitive parameters in the G* -based Witczak model [1]. In this research, actual BBR test was conducted at very low temperatures and the results are converted to G* data. Then, G* -based Witczak model was implemented using G* data computed form BBR testing. E* predictions with and without BBR data are compared to investigate the effect of including low temperature G* data from BBR test * *.5 log E G b * V beff v a 1.6 Vbeff Va Copyright 13 IJPC International Journal of Pavements Conference, São Paulo, Brazil Page 1

2 .558.3V a Vbeff.713 Vbeff V 1 e a.14 * log G b.884 b.1 Copyright 13 IJPC International Journal of Pavements Conference, São Paulo, Brazil Page is dynamic modulus, psi; phase angle of binder associated with, ;, dynamic shear modulus of binder, psi; is air void content, %; is effective bitumen content, % by volume; is cumulative % retained on the 19-mm (3/4-in.) sieve; is cumulative % retained on the 9.5-mm (3/8-in.) sieve; is cumulative % retained on the 4.76-mm (No. 4) sieve; is % passing the.75-mm (No. ) sieve Hypothesis and Objective This study was based on the hypothesis that the Bending Beam Rheometer (BBR) test data at low temperature can be converted to binder G* data and the results can be used to improve the E* predictions using the G* based Witczak model. The objectives of this study were to: conduct E* test for asphalt mixes typically used by the New Mexico Department of Transportation (NMDOT) conduct G* and BBR test for the two binder types used for producing typical mixes of NMDOT predict test E* data with the G* -based Witczak model using only G* test data and a combination of low temperature BBR data with G*. perform statistical analysis to assess the improvements in G* -based Witczak model predictions gained through use of low temperature BBR data.. EXPERIMENTAL DESIGN For this study, dynamic modulus, bulk specific gravity and aggregate gradation tests are conducted for asphalt mixes and dynamic shear modulus and bending beam rheometer tests are conducted on binders..1. Materials Typical asphalt mixes that were used in this research were collected from an actual road reconstruction project in the state of New Mexico. Asphalt mixes typically used by the New Mexico Department of Transportation (NMDOT) are SP-II, SP-III and SP-IV mixes [3]. The nominal maximum aggregate size and binder PG-grade for SP-II, SP-III and SP-IV mixes are 5 mm with PG 64-, 19 mm with PG 7- and 1.5 mm with PG 7- respectively. All mixtures have recycled asphalt pavement with a proportion of 15% by weight of aggregates [3]. Table 1 provides mix properties useful for application of G* -based Witczak model. Table 1. Superpave mixture data for G* -based Witczak model application Mix Designation SP-II SP-III SP-IV VA (%) (by volume) 5.5±.5 5.5±.5 5.5±.5 Vbeff (%) (by volume) P34 (%) - Cumulative % retained on 3/4 sieve P38 (%) - Cumulative % retained on 3/8 sieve P4 (%) - Cumulative % retained on No.4 sieve P (%) - % passing No sieve Binder grade PG 64- PG 7- PG 7-.. Dynamic Modulus ( E* ) Testing Dynamic modulus samples were prepared by coring out the central part of an oversized sample. Gyratory compaction machine was used to compact the oversized sample with a 15 mm diameter and 17 mm height. Afterwards, using the core drilling machine a 1 mm diameter sample was cored out and using the laboratory 34 (1)

3 diamond edge wet saw the ends were trimmed to a height of 15 mm. Then, the AASHTO TP6-7 [4] requirements for specimen geometry are checked for the perpendicularity, waviness and accuracy of dimensions. Laboratory dynamic modulus test was conducted as per the requirements of AASHTO TP6-7 [4]. During dynamic modulus testing asphalt samples were exposed to a sinusoidal loading and resulting deformation and phase angles were measured. The applied loads are selected depending on the temperature and frequency to insure the specimen remained in the linear viscoelastic rage. Dynamic modulus tests were performed at five different temperatures (-1, 4,, 37 and 54 C) and six frequencies (.1,.5, 1, 5, 1, 5 Hz) under each testing temperature. Three replicates of each mix are tested..3. Dynamic Shear Modulus ( G* ) Test G* test was conducted on the two types of binders, PG 7- and PG 64-. These binders are used to manufacture asphalt mixes for dynamic modulus testing. The AASHTO T 315 [5] test standard was used as a guideline for conducting G* tests. G* test was conducted at seven test temperatures (54.4, 46.1, 37.7, 9.4, 1.1, 1.7, 1 C) and 31 frequencies (.5-5 rad/sec) for each temperature. 5mm diameter samples were tested at 54.4 and 46.1 C. However, torsion force required to maintain a measurable strain level of a 5mm sample at intermediate temperatures exceeded the machine capacity. Therefore, the 8mm diameter sample size was used to conduct DSR testing 37.7, 9.4, 1.1, 1.7 and 1 C. The G* test was conducted in a stain controlled fashion. That is shear stress was measured while applying a preselected strain level. The preselected strain level must be measureable to the Dynamic Shear Rheometer (DSR) compliance while taking in to consideration the maximum stress that can be applied by the machine. Therefore the testing strain level was selected in such a way that it is large enough to be measured by the equipment and small enough so that the stress capacity of the machine is not exceeded. The applied strain level for the 8mm and 5mm samples was 1.%..4. Bending Beam Rheometer (BBR) Test To supplement the binder shear modulus data for the Witczak model prediction at low temperature, creep stiffness test was also conducted using Binder Beam Rheometer (BBR). BBR testing was conducted for the binders at four temperatures (-1, -15, - and -3 C) and creep stiffness calculations are made at 8, 15, 3, 6, 1 and 4 seconds of loading. Both PG 7- and PG 64- are tested for creep stiffness at low temperatures following AASHTO T 313 [7] test standard. 3. E* TEST RESULTS The dynamic modulus of all mixes was found to decrease as the temperature increased and under constant temperature dynamic modulus was observed to increase with increasing loading frequency, which is consistent with literature [4, 7]. Dynamic modulus mastercurves for each mixture tested were developed using the sigmoidal function shown in Equation (1). Individual dynamic modulus mastercurves were developed at a reference temperature of 1 C [7]. All calculations to determine appropriate shift factors and sigmoid function parameters (α, β, γ and δ) of the mastercurve were performed using MS excel spread sheet solver function. Table provides the all mastercurve parameters for each mix type and Figure 1 provides pictorial presentation of mastercurves for all three mixes used in this study. () (1) is the minimum value of E* ; is the maximum value of E* ;, are parameters describing the shape of the sigmoidal function; is reduced frequency of loading at reference temperature Copyright 13 IJPC International Journal of Pavements Conference, São Paulo, Brazil Page 3

4 Log( E* ) (Mpa) Table : Mastercurve parameters for dynamic modulus test (ref. Temp = 1 ºC) Asphalt mix Master curve parameters SP-II SP-III SP-IV G* TEST RESULTS 5 4,5 4 3,5 3,5 SP-II SP-IV SP-III Log(frquency) (Hz) Figure 1. Mastercurves for SP-II, SP-III and SP-IV mixes Mastercurves for G* test results were also developed using the time temperature superposition principle. For G* data the modified sigmoidal model was found to be the best function for fitting the shifted data into mastercurve [8]. The modified sigmoidal function used for G* mastercurve development is given in Equation (). Mastercurves for phase angle are also developed using the parameters determined for G* mastercurves. Equation (3) provides the mathematical relationship used for fitting phase angle mastercurves [9]. Table 3 provided the fitted model parameters for each binder type. G* mastercurves developed for binders grades PG 64- and PG 7- are presented in Figure and Figure 3 respectively. While, phase angle mastercurves are presented in Figure 4 and Figure 5 for binders grades PG 64- and PG 7- respectively. () () ( ) (3) where G* = dynamic modulus; = the minimum value of E* ; max= the maximum value of which is taken as 1.Gpa; are parameters that describe the shape of the sigmoidal function, is reduced frequency of loading at a reference temperature. Table 3. Mastercurve parameters for dynamic shear modulus test (ref. Temp = 1 ºC) Binder Grade Master curve parameters = PG PG Copyright 13 IJPC International Journal of Pavements Conference, São Paulo, Brazil Page 4

5 Phase angle (Deg) G* (pa) G* (Pa) 1,E+8 1,E+7 1,E+6 1,E+5 1,E+4 1,E mc 1,E+,1,1, ,E+8 1,E+7 1,E+6 1,E+5 Figure. G* mastercurve for binder grade PG #REF! mc 1,E+4 1,E+3 1,E+,1,1,1 1 1 Figure 3. G* mastercurve for binder grade PG mc,1,1,1 1 1 Figure 4. Phase angle mastercurve for binder grade PG 64- Copyright 13 IJPC International Journal of Pavements Conference, São Paulo, Brazil Page 5

6 Creep Stiffness (MPa) Creep Stiffness (MPa) Phase angle (Deg) mc 1,1,1, BBR TEST RESULTS Figure 5. Phase angle mastercurve for binder grade PG 7-. Creep stiffness test results show increasing trend with decreasing temperature and decreasing trend with increasing loading time as shown in Figure 6 (a) and Figure 6 (b) for PG 7- and PG 64- binder grades respectively. In order to confirm the applicability of time temperature superposition on the stiffness data, mastercurves are developed at the reference temperature of -1 ºC. The results, as shown in Figure 6 (a) and Figure 6 (b), indicate that the mastercurves follow a simple power function perfectly. This confirms that the BBR tests at different temperature are conducted with in the linear viscoelastic region and time temperature superposition is applicable. 1,E+3 1,E+ S(t) = 69.6(t) R² = S(t) = 96.8(t) -.85 R² = ,E S(t)* MC@ -1C Potência (S(t)* MC@ -1C) 1,E+,1,1 1 1 Time (Sec) ,1,1,1 1 1 Time (Sec) (a) Creep stiffness for binder grade PG 7- (b) Creep stiffness for binder grade PG 64- Figure 6. BBR test results Creep stiffness data was converted into G* data and G* mastercurves at -1 ºC are utilized to supplement the G* test data at low temperatures. The process of converting creep stiffness data from BBR test to G* involves converting the flexural creep stiffness to relaxation modulus in the time-domain converting time-domain, relaxation modulus into storage and loss moduli in frequency-domain, calculating the magnitude of relaxation complex modulus in frequency domain and converting it in to shear complex modulus. These calculations are performed using the following relationships given below: Kim et.al [9] provided the relationship between flexural creep stiffness and uniaxial relaxation modulus for converting as shown in Equation (4). (4) Copyright 13 IJPC International Journal of Pavements Conference, São Paulo, Brazil Page 6

7 : is relaxation modulus, is flexural creep stiffness, is local log-log slope of the flexural creep stiffness represented analytically by, is time Then, using the relationship provided by Kim [11], the storage modulus, loss modulus and relaxation modulus in the frequency domain can be computed from as follows: Storage modulus ( ) and loss modulus ( ) are determined by relationships given in Equation (5) and Equation (6) and the magnitude of relaxation complex modulus in frequency domain () is determined by Equation (7). (5) (6) (7) and are adjustment factors defined as (8) (9) analytically by is gamma function and. is local log-log slope of the storage modulus that can be represented Finally, dynamic shear modulus of the binder can be determined form the relaxation complex modulus in frequency domain using Equation (1). The Poisson ratio in Equation (1) was assumed to be.5 and the phase angle associated with the dynamic shear modulus can be determined using Equation (11). (1) is Poisson ratio. (11) is phase angle. Figure 8 (a) and (b) present the converted G* data for PG 7- and PG 64- respectively. It can be observed from the figures that the converted G* values are increasing with decreasing temperature and increasing load frequency. The maximum converted G* values were found to be.6 GPa and 1.9 GPa at.3 loading frequencies for binder grades PG 7- and PG 64- respectively. G* mastercurves are also developed at a reference temperature of -1 ºC for both binders and the results indicate a very good fit to power function for both binder types. G* mastercurves developed by including the converted G* data form BBR test are provided in Figure 8 and Figure 9 for PG 7- and PG 64- binder grades respectively. It can be observed from Figure 8 and 9 that the converted G* data for low temperatures is considerably higher than test G* data collected through DSR testing, which indicated that converted data was reasonable. Mastercurves developed using the converted data were also found to fit very well with the sigmoidal function, which indicated that the time temperature superposition principle is valid for the data. Sigmoidal function parameters for mastercurves developed by including converted G* data are provided in Table 4. Copyright 13 IJPC International Journal of Pavements Conference, São Paulo, Brazil Page 7

8 G* (Pa) G* from BBR (Pa) G* from BBR (Pa) Figure 1 and Figure 11 present mastercurves developed for phase angles of PG 7- and PG 64- binders respectively. It can be observed form Figure 1 and Figure 11 that phase angles obtained computationally from BBR data are lower that the phase angles found form DSR testing. This indicates the more elastic behavior of both binders at lower temperatures. Phase angle mastercurves developed using the converted data are found to fit very well with the relationship presented in Equation (11). 1,E+9 1,E+8 1,E G* MC@ -1C Potência (G* MC@ -1C) G* = 6E+7(f).344 R² =.996 1,E+6,1,1, ,E+1 1,E+9 1,E+8 1,E G* MC@ -1C Potência (G* MC@ -1C) G* = E+8(f).3947 R² = ,E+6,1,1, (a) Converted G* for binder PG 7- (b) Converted G* for binder grade PG 64- Figure 7. BBR to G* conversion results Table 4: Mastercurve parameters for dynamic shear modulus test (ref. Temp = 1 ºC) Binder Grade Master curve parameters PG PG ,E+9 1,E+8 1,E+7 1,E+6 mc 1 1,E ,E ,E ,E+,1,1, Figure 8. G* mastercurve for binder grade PG 7- (including converted BBR data) Copyright 13 IJPC International Journal of Pavements Conference, São Paulo, Brazil Page 8

9 Phase angle (Deg) Phase angle (Deg) G* (Pa) 1,E+1 1,E+8 mc 1 1,E ,E ,E+,1,1, Figure 9. G* mastercurve for binder grade PG 64- (including converted BBR data) mc ,1,1, Figure 1. Phase angle mastercurve for binder grade PG 7- (including converted BBR data) mc ,1,1, Figure 11. Phase angle mastercurve for binder grade PG 64- (including converted BBR data) 6. APPLICATION OF G* BASED WITCZAK MODEL G* -based Witczak model was utilized to predict E* mastercurves developed for SP-II, SP-III and SP-IV mixes. To evaluate the effect of utilizing converted G* data on E* prediction, the G* -based Witczak model was applied first with DSR test G* data only and next utilizing the G* data form DSR test and converted G* data form BBR testing. Figure 1, Figure 13 and Figure 14 present the dynamic modulus predictions for SP-II, SP-III and SP-IV mixes. In all cases the G* based Witczak model was found to under predict the test dynamic modulus. The mastercurve predictions using BBR converted G* data was also found to be overlapping with predicted mastercurves using only DSR tested G* data. To compensate for the underprediction the difference Copyright 13 IJPC International Journal of Pavements Conference, São Paulo, Brazil Page 9

10 Log( E* ) (Mpa) Log( E* ) (Mpa) Log( E* ) (Mpa) between the prediction and test data was determined and the average was used as a shift factor. For all mixes the G* -based Witczak model was found to under predict the test dynamic modulus by approximately 7%. Applying a shift factor of.54 for SPIV mix,.93 for SP-III mix and.8 for SP-II mix on the logarithm of Witczak predicted results produced significant improvement Witczak (With BBR) Witczak (G* only) Laboratory Log(frequency) (Hz) Figure 1. SP-II mix new Witczak prediction Witczak (With BBR) Witczak (G* only) Laboratory Log(frequency) (Hz) Figure 13. SP-III mix new Witczak prediction Witczak (With BBR) Witczak (G* only) Laboratory Log(frequency) (Hz) Figure 14. SP-IV mix new Witczak prediction Statistical analysis on the prediction performance of G* -based Witczak model using the two sets of G* data was performed using discrepancy ratio, Mean Normalized Error (MNE) and Average Geometric Deviation (AGD). These statistical analysis tools are presented by Wu et al. [1] and Yusoff et al [8] as follows: Discrepancy Ratio : Copyright 13 IJPC International Journal of Pavements Conference, São Paulo, Brazil Page 1

11 is measured dynamic modulus, is mean of measured dynamic modulus, dynamic modulus, subscript denotes data set number and for prefect fit. (1) is predicted Mean Normalized Error (MNE): is the total number of set of data and for prefect fit. Average Geometric Deviation (AGD): (13) ( ) { } (14) is the total number of set of data and for prefect fit. Table 5 presents the statistical analysis results using, and. The and AGD statistics were found to be closer to the perfect fit indicator value, which is 1., when G* data converted from BBR test was used. Similarly, MNE results were also found to be closer to the ideal value of zero, when converted G* data was utilized. These results indicate the enhanced accuracy for the G* -based Witczak model predictions when low temperature BBR test data was utilized. Table 4: Prediction performance analysis for including converted G* from BBR test Statistical Parameter SP-II Mix SP-III Mix SP-IV Mix -mean G* test only G* and BBR test G* test only G* and BBR test G* test only G* and BBR test CONCLUSION In this study, dynamic modulus and DSR tests are conducted to investigate the accuracy of G* -based Witczak model. Moreover, in addition to DSR test BBR test results are utilized to generate low temperature G* data, with the aim of improving the G* -based Witczak model prediction. Based on this study the following conclusions can be drawn: Consistent with literature, the sigmoidal function was found to be very suitable for developing E* and G* mastercurves. BBR test results at different temperatures can be used to generate creep stiffness mastercurves and simple power function was found to be very suitable for developing creep stiffness mastercurves. Creep stiffness results from BBR test can be converted in to G* data using linear viscoelastic interconversion methods. Copyright 13 IJPC International Journal of Pavements Conference, São Paulo, Brazil Page 11

12 G* -based Witczak model was found to underpredict laboratory dynamic modulus test data conducted on SP-II, SP-III and SP-IV mixes by an average value of 1%. In this research BBR test data was converted in to G* data to enhance the accuracy of G* -based Witczak model prediction. Statistical analysis of G* -based Witczak model performance indicated that the use of low temperature BBR test data indeed provides an enhanced accuracy for the latest G* based Witczak model. ACKNOWLEDGMENTS: The authors would like to express their gratitude to New Mexico State Department of Transportation for supporting this study. Special thanks go to Jeff Mann (Head of Pavement Design, NMDOT), Virgil Valdez (Research Bureau, NMDOT), Robert McCoy (Head of Pavement Exploration, NMDOT), Parveez Anwar (State Asphalt Engineer, NMDOT) and Bob Meyers (Geotechnical Section Manager, NMDOT). REFERENCE: [1] Bari, J., M. W. Witczak. Development of a New Revised Version of the Witczak E* Predictive Model for Hot Mix Asphalt Mixtures. Journal of the Association of Asphalt Paving Technologists, Association of Asphalt Paving Technologists, 6, Volume: 75, pp [] Bonaquist, R., D. W. Christensen. Practical Procedure for Developing Dynamic Modulus Master Curves for Pavement Structural Design. Transportation Research Record: Journal of the Transportation Research Board, 5, Volume 199, pp [3] NMDOT. Standard Specifications for Highway and Bridge Construction. New Mexico Department of Transportation, 7. [4] AASHTO Standard TP 6-7. Standard Method of Test for Determining Dynamic Modulus of Hot Mix Asphalt (HMA). AASHTO Guide, Washington, D.C., 9. [5] AASHTO Standard T 315. Determining the Rheological Properties of Asphalt Binder Using a Dynamic Shear Rheometer (DSR). AASHTO Guide, Washington, D.C., 9. [6] AASHTO Standard T 313. Determining the Flexural Creep Stiffness of Asphalt Binder Using the Bending Beam Rheometer (BBR). AASHTO Guide, Washington, D.C., 9. [7] MEPDG Design Guide for New & Rehabilitated Pavements (Final Report). Part - Design Inputs, Chapter Material Characterization,.. Input Characterization for the Asphalt Material Group. NCHRP Project 1-37A. 4. [8] Yusoff, N., I. Md., G.D. Airey, and M.R. Hainin. Predictability of Complex Modulus Using Rheological Models. Asian Journal of Scientific Research, 1, Volume 3, pp [9] Chailleux, E., G. Ramond, C. D. L. Roche. A mathematical-based master-curve construction method applied to complex modulus of bituminous materials. Road Materials and Pavement Design, EATA 6, pp [1] Y. R. Kim, B. Underwood, M. Sakhaei Far, N. Jackson, and J. Puccinelli. LTPP Computed Parameter: Dynamic Modulus (Final Report). FHWA-HRT-1-3, September 11, Federal Highway Administration, 63 Georgetown Pike, McLean, VA, USA. [11] Kim, Y. R. Modeling of asphalt concrete. McGraw-Hill, New York, 9. [1] Wu, B., D.S. Maren, L.I. Lingyun. Predictability of sediment transport in the Yellow River using selected transport formulas. International Journal of Sediment Research, 8, Volume 3, Issue 4, Pages Copyright 13 IJPC International Journal of Pavements Conference, São Paulo, Brazil Page 1