Development and Evaluation of Performance Tests to Enhance Superpave Mix Design and Implementation in Idaho. Quarterly Progress Report QR4

Transcription

1 Development and Evaluation of Performance Tests to Enhance Superpave Mix Design and Implementation in Idaho USDOT Assistance No. DTOS59-06-G (NIATT Project No. KLK479) ITD Project No. RP 181 (NIATT Project No. KLK483) Quarterly Progress Report QR4 For the period April1to June 30, 2008 Submitted to U.S. Department of Transportation Ed Weiner, COTR And Idaho Transportation Department Ned Parrish, Research Manager Michael J. Santi, PE, Assistant Material Engineer UI Research Team Dr. Fouad Bayomy, PI Dr. S. J. Jung, Co-PI Dr. Thomas Weaver, Co-PI Dr. Richard Nielsen, Co-PI Mr. Ahmad Abu Abdo, Graduate Research Assistant Mr. Seung II Baek, Graduate Research Assistant University of Idaho (UI) National Institute for Advanced Transportation Technology (NIATT) Center for Transportation Infrastructure (CTI) July 9, 2008

2 1. Introduction This is the fourth quarter report of the project which summarizes progress during the period April to June The focus during this period addressed several tasks as will be discussed in the report. In previous reports, a description of the project objectives and work plan has been presented. These reports are posted on the designated project reports web page at: This QR4 report focuses on progress during the 4 th quarter of the project. Description of work progress is presented on task by task basis. 2. Progress by Task The chart in Table 1 summarizes the progress as % work completed as of June 30, Phase / Task Table 1 Approximate Level of Work Completed by Task at the end of Quarter 4 Quarter Year 1 Year 2 Year 3 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Calendar Yr 2007 Calendar Yr 2008 Calendar Yr 2009 Month Phase A: Evaluation of Mix Resistance to Deformation Task A1 Review of previous studies and available 10% 10% 2% 0% 2% 6% 0% 10% 10% 20% 70% data Task A2 Analytical Analysis 12% 2% 4% 0% 7% 0% 5% 5% 15% 50% Task A3 Experimental Design, Binder and Agg. 15% 15% 10% 5% 15% 0% 5% 10% 10% 85% Eval. Task A4 Prep and Evaluation of Asphalt Mixtures 5% 5% 10% 15% 20% 15% 15% 0% 0% 85% Task A5 Data Analysis 10% 0% 5% 10% 10% 20% 55% Phase B: Evaluation of Mix Resistance to Fracture and Fatigue Cracking Task B1 Literature Review 10% 15% 5% 5% 5% 5% 0% 5% 0% 50% Task B2 Finite Element Analysis 5% 5% 5% 5% 15% 5% 2% 3% 5% 50% Task B3 Development of the Fracture Test 12% 2% 5% 16% 5% 5% 10% 55% Procedure Task B4 Prep and Evaluation of Asphalt Mixtures 0% 15% 10% 15% 20% 60% Task B5 Data Analysis 0% Task B6 Reliability Analysis 5% 3% 5% 13% Phase C: Implementation of Research Products and Training Task C1 Development of Implementation Plan 0% Task C2 Training Program for ITD Personnel 0% Reporting Tasks A6, B7 and C3 Quarter Reports for USDOT R1 R2 R3 R4 R5 R6 R7 Final 0% Phase D: Final Report Review and Submittal Task D1: External peer review of the final report 0% Task D2: Final report review by ITD 0% Task D3: Final Report Submittal 0% Total % Task Completed Work performed during the report period in the various project tasks is described below: 1

3 Phase A: Evaluation of Mix Resistance to Deformation Task A1 Review of previous studies and available data During this quarter, literature review continued to address the various models of the asphalt pavement permanent deformation, and its interaction with the dynamic modulus of the mix. Method of predicting permanent deformation in the new MEPDG guide is also addressed. A summary of work performed under this task is presented in Appendix A. The work completed in this task is estimated by about 70%. Task A2 Analytical Analysis The focus of this task is on the development of constitutive models that relate the mix properties to the properties of its constituents. Research efforts during this quarter focused on reviewing work related to viscoplastic models. An initial analysis using ABAQUS software is performed to develop a predictive model for the dynamic modulus of the asphalt mixtures. A brief summary of this analysis is presented in Appendix B. The work completed in this task (so far) is estimated by about 50% Task A3 Experimental Design, Binder and Aggregate Evaluation Binder testing: All binder testing is now completed, and has been reported in previous quarter reports. During this quarter, independent binder grade verification is conducted by ITD, and all binders were verified. Aggregate testing: Other than the aggregate gradations that have been identified in QR1 report, no further evaluation on aggregates have been made in this period. Aggregates Imaging System (AIMS) Testing is still pending. The work completed in this task is estimated to be about 85%. Task A4 Preparation and Evaluation of Asphalt Mixtures Work in this task focused on the preparation of lab samples for E* testing. Simultaneously, samples for Jc and triaxial testing are also being prepared for the designated mixes. All required samples for various tests have been prepared except for those tests that are pending as listed below: Gyratory Stability Testing: 100% completed. E-star and Flow number Testing: 100% completed. APA test: Completed at ITD lab in Boise. Image Analysis: pending. MnRoad samples preparation: pending Samples for Jc (Fatigue fracture testing are being prepared under Task B4. Work completed in this task is still estimated by about 85% 2

4 Task A5 Data Analysis During this quarter, extensive analysis is conducted of the data developed under E* test and the Gyratory stability (GS) to determine the relationship between the GS and other mix properties including (aggregate structure, asphalt content, and mix density). The data analysis progress is as follows: GS, E*, and FN: 100% completed Model Development: 100% completed MEPDG Runs: In progress APA: In progress MnRoad samples testing: pending The analysis is presented in Appendix C of this report. Work completed in this task is estimated by about 55% Phase B: Evaluation of Mix Resistance to Fracture and Fatigue Cracking Task B1 Literature Review on Fracture The reviewed literature was presented in QR2 and QR. No further review was conducted in this quarter. The work completed in this task is still estimated to be about 50%. Task B2 Finite Element Analysis Work in this task overlaps two phases (Task A2 and Task B2). Use of FE under task A2 focuses on the constitutive modeling under the numerical analysis. The work developed using the ABAQUS software package is reported under task A2 and is presented in Appendix B. Under task B2, the use of FE analysis addresses the simplified fatigue model. In this regard, a DEM model is sought. Details f this analysis is developed along with Task B3 and presented in Appendix D. The effort spent in this task, so far, is estimated by about 50% of the work level in this task. Task B3 Development of the Fracture Test Procedure The focus of this task is on the development of a simple test to predict fatigue cracking from a simple fracture test under static loading condition. The goal is to link a simple static fracture test to a dynamic fracture test, and develop correlations from which the fatigue can be estimated from the simple fracture test. The work completed in this task so far is estimated by about 55%. Task B4 Prep and Evaluation of Asphalt Mixtures During this quarter, more than 90 samples were prepared. Dynamic testing is being performed on these samples. Details of the developed work are presented in Appendix D. 3

5 The work completed in this task so far is estimated by about 60%. Task B6 Reliability Analysis A sufficient number of asphalt samples have been tested to determine the statistical parameters and probability distributions of key parameters for the permanent deformation model, including the gyratory stability GS, the maximum specific gravity G mm, the binder content P b %, and the air voids, AV%, the dynamic modulus, E*, and the dynamic shear modulus, G*. The statistical parameters and probability distributions for the permanent deformation model were used to develop a simulation model for permanent deformations. The simulations compare the permanent deformations from the E* model to the deformations predicted by the Mechanistic- Empirical Design Guide. One hundred thousand simulations were run at various temperature levels to determine the probability that the deformations predicted by the E* model exceed those allowed by the Mechanistic-Empirical Design Guide. Tasks B5 and Phases C and D Work in these tasks and phases did not commence yet. 3. Equipment Development and Troubleshooting During this quarter research team focused on the upgrade of the MTS machine. 1. A new controller has been acquired. Training of the team is conducted and the test set-up has been modeled. Preliminary testing is underway. 2. An in-house system for sample coring, slicing and notching have been developed and used for sample preparation for fracture tests. 3. Work is still in progress on developing a temperature control room for low temperature fracture testing. 4. Summary The main outcomes that have been achieved during this quarter can be summarized as follows: 1. Further review of the permanent deformation models, especially those used in the MEPDG were prepared. 2. Analysis of the E* data and GS data led to a statistical relationship between E* and GS. Dimensional analysis was sued to reach at an E* model that proved to be statistically significant. 3. APA testing of mixes was completed. 4. Binder grades were independently verified at the ITD lab in Boise. 5. MTS testing system controller is now in operation. 6. Coring and notching jigs for preparation Jc samples are complete and operational. 7. Progress in building a cooling system for fracture testing at low temperature. 8. Samples for fatigue fracture testing are being prepared 9. The model of PFC2D (discrete element program) was generated and examined with test condition to compare the specimen test results. 10. Continued literature review 4

6 Appendices Appendix A: Prediction of HMA Permanent Deformation (Task A1) Appendix B: Viscoplastic Analyses of Asphalt Pavements (Task A2) Appendix C: Data Analysis (EStar, GS, FN, APA) (Task A5) Appendix D: Simplification of Fatigue Test (Tasks B3 and B4) 5

7 Appendix A Prediction of HMA Permanent Deformation (Prepared by: A. Abu Abdo and F. Bayomy) This appendix describes further literature review of permanent deformation models for asphalt pavements, which is performed under Task A1 Review of previous studies and available data. Prediction of HMA Permanent Deformation Permanent deformation or rutting is one of the major stresses in flexible pavements, which is caused by the densification and movement of materials under repeated loads, and also might results from lateral plastic flow under the wheel track (NCAT 2000). When the new Superpave binder grade system was developed under SHRP (Strategic Highway Research Program), it was suggested that choosing the right upper binder grade could extend the life of flexible pavements with regards to permanent deformation; unfortunately that is not the case. Many approaches have been used to predict permanent deformation in HMA. Most of the widely used approaches are based on the classic power relationship between the permanent strain and number of load cycles as shown in Eq. 1. (Eq. 1) where, ε p : Accumulated Permanent Strain at N cycle, N: Number of Load Repetitions, and a,b: Non linear Regression Coefficients. This classic power equation is derived from the secondary stage in a typical behavior of HMA tested sample under repetitive loads as shown in Figure 1, where a is the intercept at N = 1 cycle and b is the slope of the line. The widely used approaches to predict permanent deformation in flexible pavements includes; Layered Vertical Permanent Strain Approach, Plastic Elastic Vertical Strain Ratio Approach, Permanent Strain Rate Approach, and Rutting Rate Approach. QR4_Appendix A: Prediction of HMA Permanent Deformation - Page 1

8 Figure 1 Typical Permanent Deformation Behavior for HMA under Repetitive Loading (After NCHRP 1 37A) Layered Vertical Permanent Strain Approach Layered Vertical Permanent Strain Approach is based on determining the permanent strain in each layer as a function of repeated load applications. Then the total deformation is computed by summing up permanent deformation in each layer. Two famous models used this approach; Allen and Dean Models (Allen and Dean 1986) and Asphalt Institute Model (May and Witczak 1992). Allen and Dean Models were developed for all pavement layers. These models are incorporated in software called PAVRUT. In addition to permanent deformation models, traffic and temperatures models were added to the software (Allen and Dean 1986). This software can be used to estimate the permanent deformation for any flexible pavement. The permanent deformation model for HMA is as follow, (Eq. 2) where, ε p : Permanent Axial Strain, N: Number of Stress or Wheel Load Repetitions, C o = T T ( T).Log (σ 1 ), σ 1 : Deviator Stress, psi, T: Temperature, F, C 1 = , C 2 = , and C 3 = QR4_Appendix A: Prediction of HMA Permanent Deformation - Page 2

9 Based on triaxial tests on 251 samples, the Asphalt Institute has developed a model that determines the permanent deformation of HMA by including the effects of mix design properties. Thus, Eq. 3 was developed. Users need to take into consideration that this model cannot be used for mixes with less than 3% air voids or for deviator stresses larger than 90 psi (May and Witczak 1992) log (Eq. 3) where, ε p : Permanent Axial Strain, N: Number of load repetitions to failure, T: Temperature, F, S d : Deviator Stress, psi, V: Viscosity at 70 F, Ps x10 6, P eff : Percent by volume of effective asphalt content, and V v : Percent by volume of air voids. Plastic Elastic Vertical Strain Ratio Approach Plastic Elastic Vertical Strain Ratio Approach was based on the constitutive relationship developed from the statistical analysis of repeated load permanent deformation lab tests. This model is in a form of the classical power model, but determines the ratio of the permanent strain to the elastic (resilient) strain as in Eq. 4, (Eq. 4) where, ε p : Accumulated Permanent Strain at N cycle, ε r : Resilient Strain as a function of asphalt mixes properties, N: Number of load repetitions, a, b: Non linear regression coefficients, and r : Field adjustment factor. Many studies have been conducted to determine the regression factors by relating these factors to different mixes properties. Leahy (1989) argued that temperature was the most important factor. Leahy s model was less sensitive to loading condition and mix properties as seen in Eq log (Eq. 5) where, QR4_Appendix A: Prediction of HMA Permanent Deformation - Page 3

10 ε p : Accumulated Permanent Strain at N cycle, ε r : Resilient Strain as a function of asphalt mixes properties, N: Number of load repetitions, T: Temperature, F, σ d : Deviator stress, psi, η: Viscosity at 70 F, 10 6 poise, V beff : Percent by volume of effective asphalt content, and V a : Air voids, percent. Similar to Leahy s approach, Kaloush and Witczak (1999) developed two models that have fewer parameters, but with approximately the same accuracy. These models are, (Eq. 6) and, (Eq. 7) where, ε p : Accumulated Permanent Strain at N cycle, ε r : Resilient Strain as a function of asphalt mixes properties, N: Number of load repetitions, and T: Temperature, F, These models tend to under predict the ε p /ε r ratio at higher number of load repetitions, mainly due to determination of the regression coefficients from steady state zone of creep or repeated load tests. To obtain better results, Kaloush and Witczak (1999) presented another model that predict the number of cycle at failure based on the asphalt mix volumetric properties, binder viscosity, temperature and stress level. The model is expressed as follow, where, N f : Number of load repetitions to failure, T: Temperature, F, S: Deviator stress, psi, η: Viscosity at 70 F, 10 6 poise, V beff : Percent by volume of effective asphalt content, and V a : Air voids, percent... (Eq. 8) QR4_Appendix A: Prediction of HMA Permanent Deformation - Page 4

11 Permanent Strain Rate Approach Permanent Strain Rate Approach is based on modifying the classical power model (Eq. 1) and determining the rate of permanent strain with changes per cycle as shown in Eq. 9, (Eq. 9) Divide by the resilient strain (ε r ), (Eq. 10) By letting, and 1. The final model form is similar to the classic power form as shown in Eq. 11. (Eq. 11) The term μ is the permanent deformation parameter representing the constant proportionality between ε p and ε r. The term is the permanent deformation parameter that indicates the decrease in permanent deformation as the number of cycles increases. Rutting Rate Approach The most famous model under Rutting Rate Approach is the Ohio State University Model (Majidzadeh et al. 1981); the model describes the progression of rutting in all pavement layers. The permanent strain in any layer is determined as follows, (Eq. 12) where, ε p: Permanent Strain, N: Number of allowable load applications, and A, m: Experimental constants. It was found (Barenberg and Thompson 1990) that values of m does not vary significantly ( ). However, A varies widely (12.4x x10 4 ) as per the material type, the stress level and the environment. Role of E* in the Prediction of Permanent Deformation in the 2002 AASHTO MEPDG (NCHRP 1 37A) MEPDG utilizes the Layered Vertical Permanent Strain Approach to determine the permanent deformation for HMA layers. Where the general form is, (Eq. 13) where, ε p : Accumulated Permanent Strain at N cycle, QR4_Appendix A: Prediction of HMA Permanent Deformation - Page 5

12 ε r : Resilient Strain as a function of asphalt mixes properties, N: Number of load repetitions, T: Temperature, F, and a i : Non linear regression coefficients. While this relation provides adequate results, field shift factors ( ri ) were introduced to provide more accurate predictions of this model, as shown in Eq. 14, (Eq. 14) Based on 88 Long Term Pavement Performance (LTPP) sites loca ted in 28 states, Eq was calibrated and modified using 387 observations to obtain better predictions than the original model. Later, a depth parameter k 1 was introduced based on MnRoad test site (Stroup Gardiner and Newcomb 1997), to increase the accuracy of this model as follows, (Eq. 15) where, , depth: Depth to computational point, in, , , and h ac : Total Asphalt Layer thickness, in. The resilient (elastic) strain is determined using the general Hooke s Law (Eq. 16), where the asphalt dynamic modulus is incorporated. There fore, the determined resilient modulus is a function of materials properties, temperature and load frequency. (Eq. 16) where, ε rz : Resilient Strain in the vertical direction, E*: Dynamic Modulus of HMA, σ z, σ x, and σ y : Stresses in the z, x, and y directions, and ν: Poison s Ratio of HMA. Finally, the determined permanent strain in any layer is used to determine the permanent deformation by, where,.δ (Eq. 17) QR4_Appendix A: Prediction of HMA Permanent Deformation - Page 6

13 RD: Total Permanent Deformation, i: Layer number, n: Total number of layers, ε pi : Permanent Strain in layer i, and h i : Thickness of layer i. References Allen, D.L. and R.C. Deen. A Computerized Analysis of Rutting Behavior of Flexible Pavement. Transportation Research Record 1095, Washington D.C., ARA, Inc., ERES Consultants Division. Guide for Mechanistic Empirical Design of New and Rehabilitated Pavement Structures. NCHRP Final Report 1 37A, Illinois. Barenb erg, E.J. and M. R. Thompson. Calibrated Mechanistic Structural Analysis Procedures for Pavements, Phase 2 of NCHRP Project National Cooperative Highway Research Program. TRB. Washington, DC., Kaloush, K., and Witczak, M.W.. Development of Permanent to Elastic Strain Ratio Model for Asphalt Mixtures. Development of the 2002 Guide for the Design of New and Rehabilitated Pavement Structure, University of Maryland, College Park, Maryland, Leahy, R.B.. Permanent Deformation Characteristics of Asphalt Concrete. PhD Dissertation, University of Maryland, College Park, Maryland, Majidza deh, K., et al. Implementation of a Pavement Design System Volumes 1 and 2. Final Report, Research Project EES 579, Ohio State University May, R.W. and M.W. Witczak. An Automated Asphalt Concrete Mix Analysis System. Proceeding of the Association of Asphalt Paving Technologists, Volume 61. South Carolina, NCAT. Hot Mix Asphalt Materials, Mixture Design and Construction. National Center for Asphalt Technology. NAPA Research and Education Foundation, 2 nd Edition, Maryland, Stroup Gardiner, M. and D. Newcomb. Investigation of Hot Mix Asphalt Mixtures at Mn/Road. Minnesota Department of Transportation, Office of Research Administration, Final Report, Minnesota, QR4_Appendix A: Prediction of HMA Permanent Deformation - Page 7

14 Appendix B Viscoplastic Analyses of Asphalt Pavements (Prepared by: Thomas Weaver) 1 Numerical Analyses In previous reports, we have presented background information on constitutive models that can be used to predict the stress-strain response of asphalt pavements under physical and environmental loads. After reviewing the literature, we identified two simple constitutive models which may be used for numerical modeling of asphalt pavement response. These constitutive models are available for use in the finite element analysis software ABAQUS (2003). Over the past quarter, we have learned how to use the viscoplastic model in ABAQUS and we have begun to model E* tests from the current project. Results from an analysis of an E* test are presented below. 1.1 Viscoplastic Analyses The constitutive relationship used in our viscoplastic analyses is presented in Equation 1. 1 n vp m + 1 ( Aq [( m +1 ) ε ] ) vp m ε& = (Eq. 1) The viscoplastic strain rate ( ) is a function of deviatoric stress (q), viscoplastic strain ( ), and three constants (A, m, and n). To use this model, the three constants must be specified. In addition to the three model constants the material Young s modulus (E) and Poisson s ratio (ν) must be specified. Analyses have been performed to determine the model parameters for a test designated as 1EC2_21 _25Hz. This was a sample prepared in the laboratory using a course aggregate. The E* test temperature was 21 C, and the cyclic stress was applied at a rate of 25 Hz. The values for the model constants that produced a reasonable match between the analysis and measured test results are provided in Table 1. The stress applied to the asphalt sample in the E* test is shown in Figure 1. This same stress time history was applied to the asphalt sample in the numerical analysis. The strain as a function of time resulting from the applied stress is shown in Figure 2. The strain vs. time from the E* test and analysis compare well. However, the comparison of measured and computed stress vs. strain as shown in Figure 3 do not compare as well. A closer look at the strain vs. time results show that the measured and computed strain data are not perfectly in phase. This difference in phase is likely the cause of the difference in the stress-strain loops. Additional analyses will be performed to improve the comparison between the measured and computed stress-strain loops. We are also in the process of modeling additional E* test results in an effort to determine the model input values for samples with differing properties. Table 1 Viscoplastic Model Input Values for Finite Element Analysis of E* Test 1EC2_21 _25Hz Young s Modulus, E Poisson s Ratio, n A m n 4000 MPa QR4_Appendix B: Viscoplastic Analyses of Asphalt Pavements - Page 1

15 Stress (kpa) Time (sec) Figure 1 Stress vs Time for E* Test 1EC2_21 _25Hz 2.5E E 04 Strain 1.5E E E E Time (sec) Measured Analysis Figure 2 Strain vs Time for E* Test 1EC2_21 _25Hz QR4_Appendix B: Viscoplastic Analyses of Asphalt Pavements - Page 2

16 Stress (kpa) E E E E E E 04 Strain Analysis Measured Figure 3 Stress vs Strain for E* Test 1EC2_21 _25Hz 2 References ABAQUS/Theory Manual (2003). Version 6.4, Hibbit, Karlson & Soren Pirabarooban, S., Zaman, M., and Tarefder, R.A. (2003). Evaluation of rutting potential in asphalt mixes using finite element modeling, 2003 Annual Conference of the Transportation Association of Canada, 16p. QR4_Appendix B: Viscoplastic Analyses of Asphalt Pavements - Page 3

17 Appendix C Data 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 Curves Dynamic 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. (Eq. 1) where, E*: Dynamic Modulus, : Log minimum value of E*, δ α: Log maximum value of E*, β, γ: Shape Parameters of the Sigmoidal Function, and f shifted : Shifted Frequencies. QR4_Appendix C: Data Analysis (E*, GS, FN, APA) - Page 1

18 Table 1 E* Master Curve Fitting Parameters log E* = + / [1+exp( + (log(f shifted )))] Shift Mix Condition 4.4 C 21.1 C 37.8 C 54.4 C 1 Opt % AC % AC PG PG PG PG FA Fine Mix CA Coarse Mix Opt % AC % AC PG PG PG PG PG Field Mix Field Mix Field Mix Field Mix Field Mix Field Mix Field Mix Data Analysis for E*, FN, and APA Aggregates Structure Effects To 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. QR4_Appendix C: Data Analysis (E*, GS, FN, APA) - Page 2

19 E*, MPa Frequency, Hz Coarse Mix Mix 1 (Opt) Mix 2 (Opt) Fine Mix Figure 1 E* Masters Curve for Four Different Aggregates Structures FN, cycle Fine Mix Mix 2 Mix 1 Coarse Mix Lab Mixes Figure 2 Effect of Aggregate Structure on FN 3 Rut Depth,mm Fine Mix Mix 2 Mix 1 Coarse Mix Lab Mixes Figure 3 Evaluation of Different Aggregates Structures Using APA Test Results QR4_Appendix C: Data Analysis (E*, GS, FN, APA) - Page 3

20 Binder Content Effects Dynamic 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 E*, MPa 1000 E*, MPa 1000 Mix 1 (Opt) 100 Mix 1 ( 0.5% AC) Mix 1 (+0.5% AC) Frequency, Hz Mix 2 (PG Opt) 100 Mix 2 ( 0.5% AC) Mix 2 (+0.5% AC) Frequency, Hz Figure 4 E* Master Curve for Mix 1 and Mix 2 at Different Binder Contents Mix 1 Mix 2 FN, cycle % Opt +0.5% Asphalt Content Figure 5 E* FN Results for Mix 1 and Mix 2 at Different Binder Contents QR4_Appendix C: Data Analysis (E*, GS, FN, APA) - Page 4

21 3 3 Mix 1 Mix 2 Rut Depth, mm % Opt +0.5% Asphalt Content Figure 6 APA Test Results for Mix 1 and Mix 2 at Different Binder Contents Binder Grade Effects To 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. QR4_Appendix C: Data Analysis (E*, GS, FN, APA) - Page 5

22 E*, MPa 1000 E*, MPa Mix 1 (PG 70 28) Mix 1 (PG 64 28) 100 Mix 1 (PG 70 28) Mix 1 (PG 70 34) Mix 1 (PG 58 28) Frequency, Hz Mix 1 (PG 70 22) Frequency, Hz E*, MPa E*, MPa Mix 2 (PG 64 34) Mix 2 (PG 70 34) 100 Mix 2 (PG 64 34) Mix 2 (PG 64 28) 10 Mix 2 (PG 58 34) 10 Mix 2 (PG 64 22) Frequency, Hz Frequency, Hz 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 Measurements To 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. QR4_Appendix C: Data Analysis (E*, GS, FN, APA) - Page 6

23 GS, kn.m GS, kn.m FN, cycle Mix 4 Mix 7 Mix 6 Mix 2 Mix 3 Mix 5 Mix FN, cycle Figure 8 Relation between GS vs. FN for All Field Mixes GS, kn.m GS, kn.m Rut Depth, mm Rut Depth, mm 0 0 Mix 1 Mix 3 Mix 5 Mix 6 Mix 7 Figure 9 Relation between GS vs. FN for Field Mixes GS, kn.m GS, kn.m AC% Mix 1 Mix 2 Mix 3 Mix 4 Mix 5 Mix 6 Mix 7 7% 6% 5% 4% 3% 2% 1% 0% AC% Figure 10 GS vs. AC% for Field Mixes QR4_Appendix C: Data Analysis (E*, GS, FN, APA) - Page 7

24 Dynamic Modulus (E*) Proposed Model Using 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 (%G mm ), and binder content (P b ). Where the binder effects are measured by G*, %G mm, and P b, aggregates effects are measured by GS, %G mm, and (1 P b ), and finally air voids are measured by %G mm. Further, it was found that the model consists of two sets of parameters; (G*/P b ) and (GS.%G mm /(1 P b )). To determined the relation between these parameters and E*, the sensitivity of E* versus (G*/P b ) and (GS.%G mm /(1 P b )) were investigated and a model was developed as shown in Eq. 2. G *. GS.% G mm E* =. 462 ( 1 ) (Eq. 2) Pb Pb where, E*: Dynamic Modulus for Asphalt Mix, MPa, G * : Dynamic Shear Modulus for RTFO Aged Binder, MPa, P b : Binder Content, GS: Gyratory Stability, kn.m, %G mm = G mb /G mm = G mm (1 AV%), G mb : Bulk Specific gravity of Mix, G mm : 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 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 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 QR4_Appendix C: Data Analysis (E*, GS, FN, APA) - Page 8

25 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 E*, MPa E*, MPa Equality Line 10 Equality Line E* Est, MPa E* Est, MPa a) Developed Model (Lab Mixes) b) Developed Model (Field Mixes) E*, MPa E*, MPa Equality Line 10 Equality Line E* Est, MPa E* Est, MPa c) Witczak Model (1996) d) Witczak Revised Model (2006) 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 QR4_Appendix C: Data Analysis (E*, GS, FN, APA) - Page 9

26 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; P b, %G mm, 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 % % % % Overall 95% Summary and Conclusions Based on the test results and data analysis presented in this study, the following conclusions and observations are made: QR4_Appendix C: Data Analysis (E*, GS, FN, APA) - Page 10

27 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 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 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. References Bari 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, Bridgman, P.W.. Dimensional Analysis. Yale University Press, Buckingham, E.. On Physically Similar Systems; Illustrations of the Use of Dimensional Equations. Physical Review 4, Curtis, W.D., J.D. Logan and W.A. Parker. Dimensional Analysis and Pi Theorem. Linear Algebra And Its Applications 47, Witczak, M.W. and O.A. Fonseca. Revised Predictive Model for Dynamic (Complex) Modulus of Asphalt Mixtures, Transportation Research Record 1540, Washington D.C., Nowak, A.S. and K.R. Collins. Reliability of Structures. Mc Graw Hill Higher Education, Boston, QR4_Appendix C: Data Analysis (E*, GS, FN, APA) - Page 11

28 Appendix D Simplification of Fatigue Test (Prepared by: S. Jung and Seung Baek) The proposed experimental study is focused on developing a procedure of simplification of Fatigue Test by using a semi circular notched sample (hereafter SCNS). SCNS has been proven[1] that it is easy to prepare and simple to test. Total 92 semi circular samples for preliminary experimental test were prepared from 23 cylindrical samples with field mixes. Preliminary mix (first group) was used to verify the study parameters including frequency, temperature, and strain rate. Table 1 illustrated the study parameters, which were used by other researchers, to improve the understanding of fatigue behavior under different study parameters. Sample testing was conducted with upgraded MTS control system to verify between input control and output result. Based on the previously studied parameter by other researcher, sample tests based on parameters in table 1 were also conducted with the following conditions: displacement rate of 100*10-6, 500*10-6, and 1000*10-6 in/sec and cyclic loading at 0.1, 0.5 and 1 Hz, with MTS system. The cyclic test was controlled with force ranges (10-30%, 10-50%, 30-50% and 30-70% of maximum stress) to understand the correlation between static and fatigue test. Based on the outcome of preliminary test, the second group of test samples will be conducted with different combination of several PG grade and asphalt contents (Table 2). Four SCNS, which were prepared from one cylindrical sample, were tested with one static test and three fatigue tests. To determine the test procedure, simple displacement control for loading rate was used including 100*10-6, 500*10-6 and 1000*10-6 in/sec (Table 3). Table 3 illustrated maximum displacements at the failure and higher loading rate illustrated higher strain energy. Displacement with different rates indicates that level of max. displacement during the failure tends to be smaller displacement (Table 3). It means that sample does not have enough time to deform against faster loading rate. The static test was conducted with displacement control on different samples to compare result of strain energy data between static test results and cyclic test. The strain energy for static test was determined at the area under the curve (Figure 1). The fatigue test was QR4_Appendix D: Simplified Fatigue Test Page 1

29 conducted with different cyclic loading at 0.1, 0.5, 1 Hz and force rages of 30% to 50% and 30% to70% on different sample group for preliminary mix (Figure 2). Based on the displacement and time relationship for cyclic test, the failure point can be determined by changing the slope between elastic and plastic region (Figure 3). Figure 4 shows one of results for static and cyclic test to determine the strain energy. Stain energy was determined for static and cyclic with 0.1 Hz and 1 Hz (Table 4 to 5) from the test results with preliminary mix group 1 and group 3. Based on the preliminary test results, the condition of testing for the second group with different combination of several PG grade and asphalt contents is currently investing for valid test results. The following methods are considered to simplify fatigue test; 1. The amount of energy put into the material is the same as the strain energy which is the area under a stress-strain curve.[2] 2. The work potential theory and a continuum damage theory are used to making a uniaxial constitutive model for asphalt concrete.[3] Table 1 Test conditions Temperature ( C) Strain rate Frequency Monotonic Cyclic (10-6 units/s) (Hz) Daniel [3] 5, 20 5, 12, 20 10, 30, 500, , 10 Lundstrom [4] 0,10,20 100, 200, 400, Medani [5] 5, 15, 20, 25, 30 for n H. J. Lee [6] 25 5 QR4_Appendix D: Simplified Fatigue Test Page 2

30 Table 2 PG Grade and Asphalt Content of samples Mix PG AC% Coarse Mix Fine Mix Figure 1 The stress response to preliminary mix group 3 (100*10-6 in/sec) QR4_Appendix D: Simplified Fatigue Test Page 3

31 Figure 2 Cyclic test (0.1 Hz) with 30-70% of maximum stress Figure 3 Failure of cyclic test QR4_Appendix D: Simplified Fatigue Test Page 4

32 Figure 4 Comparison of strain energy for static and cyclic test result Table 3 Static test results with different rate Rate Displacement Max. load Strain energy Sample # 10-6 in/sec in lb lb-in F5S F5S F5S F5S F5S F5S F5S F5S F5S F5S F5S F5S #: sample number from the same cylinder QR4_Appendix D: Simplified Fatigue Test Page 5

33 Table 4 Test results for preliminary mix group 1 Sample Test condition Sample # Strain energy Displacement Failure (lb-in) (in) (cycle) F5S Static 100*10-6 in/sec F5S F5S F5S Cyclic 30-50% of max. F5S (0.1 Hz) stress F5S F5S Cyclic 30-70% of max. F5S (0.1 Hz) stress F5S Table 5 Test results for preliminary mix group 3 Sample Test condition Sample # Strain energy Displacement Failure (lb-in) (in) (cycle) F5S Static 100*10-6 in/sec F5S F5S F5S Cyclic 30-50% of max. F5S (1 Hz) stress F5S F5S Cyclic 30-70% of max. F5S (1 Hz) stress F5S The model of PFC2D (discrete element program) was generated and examined with test condition to compare the specimen test results (Figure 5) and the model is kept modifying. QR4_Appendix D: Simplified Fatigue Test Page 6

34 Figure 5 Semi-circular notched model for PFC2D (0.5-inch) QR4_Appendix D: Simplified Fatigue Test Page 7

35 Reference: 1. Mull M.A., S.K., Yehia A., Fracture resistance characterization of chemically modified crumb rubber asphalt pavement Journal of Materials Science, Vol. 37: p. pp Daniel, J.S., W. Bisirri, and Y.R. Kim, Fatigue Evaluation of Asphalt Mixtures Using Dissipated Energy and Viscoelastic Continuum Damage Approaches. Journal of Association of Asphalt Paving Technologists, Daniel, J.S., and Y.R. Kim, Development of a Simplified Fatigue Test and Analysis Procedure using a Viscoelastic Continuum Damage Model. Journal of the Association of Asphalt Pavement Technologists, Vol. 71: p. pp R. Lundstrom, a.u.i., Characterization of Asphalt Concrete Deterioration Using Monotonic and Cyclic Tests. International Journal of Pavement Engineering, Volume 4(Issue 3): p T.O. Medani, A.A.A.M., Estimation of fatigue characteristics of asphaltic mixes using simple tests. Heron, Vol. 45(No. 3): p. pp H. J. Lee, Y.R.K., and S. W. Lee, Fatigue Life Prediction of Asphalt Mixes Using Viscoelastic Material Properties. J. of Transportation Research Board, QR4_Appendix D: Simplified Fatigue Test Page 8