Development and Evaluation of Performance Tests to Enhance Superpave Mix Design and its Implementation in Idaho

Transcription

1 Development and Evaluation of Performance Tests to Enhance Superpave Mix Design and its Implementation in Idaho USDOT Assistance No. DTOS59-06-G (NIATT Project No. KLK479) ITD Project No. RP 8 (NIATT Project No. KLK483) Final Report Part 2 Phase B: Evaluation of Mix Resistance to Fracture and Fatigue Cracking Submitted to U.S. Department of Transportation Mr. Peter Belenky, Contracting Officer Technical Representative (COTR) and Idaho Transportation Department Mr. Michael J. Santi, PE, Assistant Materials Engineer Mr. Ned Parrish, Research Program Manager UI Research Team Dr. Fouad Bayomy, Principal Investigator Dr. S. J. Jung, Co- Principal Investigator Dr. Thomas Weaver, Co- Principal Investigator Dr. Richard Nielsen, Co- Principal Investigator Dr. Ahmad Abu Abdo, Postdoctoral Mr. Seung Il Baek, Graduate Research Assistant Mr. Prashant Darveshi, Graduate Research Assistant University of Idaho National Institute for Advanced Transportation Technology Center for Transportation Infrastructure January 200

2 This document is disseminated under the sponsorship of the Idaho Transportation Department and the United States Department of Transportation in the interest of information exchange. The State of Idaho and the United States Government assume no liability for its contents or use thereof. The contents of this report reflect the views of the author(s), who are responsible for the facts and accuracy of the data presented herein. The contents do not necessarily reflect the official policies of the Idaho Transportation Department or the United States Department of Transportation. The State of Idaho and the United States Government do not endorse products or manufacturers. Trademarks or manufacturers names appear herein only because they are considered essential to the object of this document. This report does not constitute a standard, specification or regulation. ii

3 . Report No. 2. Government Accession No. 3. Recipient's Catalog No. 4. Title and Subtitle Development and Evaluation of Performance Tests to Enhance Superpave Mix Design and its Implementation in Idaho Phase B: Evaluation of Mix Resistance to Fracture and Fatigue Cracking 7. Author(s) Jung, S.J., Baek, S., Bayomy, F., Abu Abdo, A., Weaver, T., Nielsen, R., and Darveshi, P. 9. Performing Organization Name and Address National Institute for Advanced Transportation Technology ( University of Idaho PO Box 44090; 5 Engineering Physics Building; Moscow, ID Sponsoring Agency Name and Address Idaho Transportation Department 33 West State Street Boise, ID Report Date January Performing Organization Code KLK483 / KLK Performing Organization Report N09-0B 0. Work Unit No. (TRAIS). Contract or Grant No. USDOT No. DTOS59-06-G and ITD Project No. RP 8 3. Type of Report and Period Covered Final Report July 2007 Jan Sponsoring Agency Code 5. Supplementary Notes 6. Abstract This project addresses the development and evaluation of simplified test procedures to augment the Superpave mix for its implementation in Idaho. The project has two phases. Phase A, which focused on the deformation characteristics and Phase B, which focused on the fatigue/fracture properties of the mix. Hence the final report is developed in two parts. Part addresses Phase A and Part 2 for Phase B. In phase B, a two stage study was initiated to improve the evaluation of hot mix asphalt (HMA) fracture and fatigue resistance. The study focused on using semi-circular notched sample to overcome the difficulty of preparation of HMA beam samples for fatigue testing,. The first stage was to investigate and compare the stress intensity factor (KIC) determined by two test setups; the semi-circular notched bending fracture (SCNBF) and the single-edge notched beam (SENB) tests. In Stage 2, the potential of correlating a simple monotonic (static) test to a cyclic (dynamic) SCNBF test was investigated. Two additional Superpave mixes were modified to obtain 4 different mixes which were evaluated. Overall, the results of KIC determined by monotonic and cyclic SCNBF followed the same trend. Further, several models that predict fatigue parameters using monotonic SCNBF results were developed to simplify the estimation of fatigue life of an asphalt mix. Overall, results in both stages suggested that the SCNBF test was beneficial in characterizing the fracture and fatigue resistance of asphalt mixes. The SCNBF test is simple and repeatable; it can be used as a screening tool at the mix design stage to assess the fracture resistance of mixes, and help to eliminate weak mixes before conducting more sophisticated and time consuming tests. 7. Key Word Superpave, HMA, Dynamic Modulus, Fatigue Fracture, Semi Circular Notched Fracture 8. Distribution Statement Unrestricted. This document is available to the public at: and 9. Security Classif. (of this report) Unrestricted 20. Security Classif. (of this page) Unrestricted 2. No. of Pages Price iii

4 iv

5 Executive Summary This project addresses the development and evaluation of simplified test procedures to augment the Superpave mix for its implementation in Idaho. The project has two phases. Phase A, which focused on the deformation characteristics and Phase B, which focused on the fatigue/fracture properties of the mix. Hence the final report is developed in two parts. Part addresses Phase A and Part 2 for Phase B. In Phase B, the fatigue evaluation of hot mix asphalt (HMA) was conducted. To improve asphalt mix fracture and fatigue resistance evaluation and to overcome the difficulty of preparation of HMA beam samples for fatigue testing, a two stage study was initiated. The first stage was to investigate and compare the stress intensity factor (K IC ) determined by 2 test setups; the semi-circular notched bending fracture (SCNBF) and the single-edge notched beam (SENB) tests. Two Superpave mixes were used for experimental verification. The asphalt binder content and grade were modified to obtain eight different mixes. It was observed that there was no significant difference between K IC values determined by SCNBF and SENB tests within the statistical margin of error. In addition, results of K IC determined by SCNBF at different temperature ranges illustrated a similar pattern for all tested mixes. Hence, the SCNBF was adopted. In Stage 2, the potential of correlating a simple monotonic (static) test to a cyclic (dynamic) SCNBF test was investigated. Two additional Superpave mixes were modified to obtain 4 different mixes which were evaluated. Overall, the results of K IC determined by monotonic and cyclic SCNBF followed the same trend. Further, several models that v

6 predict fatigue parameters using monotonic SCNBF results were developed to simplify the estimation of fatigue life of an asphalt mix. Overall, results in both stages suggested that the SCNBF test was beneficial in characterizing the fracture and fatigue resistance of asphalt mixes. The SCNBF test is simple and repeatable; it can be used as a screening tool at the mix design stage to assess the fracture resistance of mixes, and help to eliminate weak mixes before conducting more sophisticated and time consuming tests. vi

7 Acknowledgments This project was co-funded by the US Department of Transportation (USDOT), and the Idaho Transportation Department (ITD). Their support and the help provided by their personnel are greatly appreciated. Special thanks are due to Mike Santi (ITD) for his tireless effort to help the research team succeeds in all tasks. In addition, many individuals from ITD have contributed to the work in this project directly and indirectly, including Jeff Miles, Muhammad Zubery, Mark Wheeler, Monte Tish, and Chad Clawson. ITD provided all the needed mixes and graded aggregates for making the lab mixes. Thanks are due to Monte Tish and ITD lab personnel for their great efforts in grading more than 2,500 lbs of aggregate for this project. We also would like to acknowledge the cooperation of Ben Worel and John Siekmeier of MnDOT for providing MnRoad samples and performance data for the E* model verification. The binder testing in Dynamic Shear Rheometer was performed at the Idaho Asphalt Supply in Boise. The lab work at the University of Idaho could not be completed without the great support and dedication of Donald Parks, of the Department of Civil Engineering who kept the equipment in good operating condition and worked tirelessly to solve equipment problem when they occurred. Thanks are also due to NIATT personnel, Judy LaLonde and Debbie Foster, for their dedicated efforts in facilitating project administration. Dr. Gary Hicks, Project Manager of the California Pavement Preservation Center, graciously served as the external reviewer of this report. Dr. Robert Eddy of Washington State University served as the technical editor. Their services are greatly appreciated. vii

8 Blank Page

9 Table of Contents Cover Page.... i Executive Summary...v Acknowledgments.. vii Table of Contents....viii List of Figures... xi List of Tables....xiii.0 Introduction.... Background....2 Research Objectives....3 Project Tasks Phase B Report Organization Review of Fatigue Evaluation of Hot Mix Asphalt Introduction Theories and Prediction Models Monotonic Testing to Assess Fatigue Fracture Parameter Stress Intensity Factor, K IC Sample Geometry Effect on Fracture Toughness Summary Experimental Program and Data Analysis Introduction Materials Material for Stage Tests Material for Stage 2 Tests Sample Preparation Test Setup viii

10 3.4. Semi-Circular Notched Bending Fracture (SCNBF) Test (Stage ) Stage 2 Monotonic Semi-Circular Notched Bending Fracture Tests Stage 2 Cyclic Semi-Circular Notched Bending Fracture Tests Preliminary Fatigue Testing Fatigue Failure and Strain Energy Monotonic Loading Rate and Fatigue Displacement Range Results and Data Analysis Stage : Geometry and Temperature Effects Test Geometry Effect Temperature Effect Stage 2: Monotonic versus Cyclic Loading Evaluation Binder Content Effect Binder Grade Effects Fatigue Models Model I: Cyclic Stress Intensity Factor Model II: Cyclic Strain Energy (U * /t) Model III: Number of Cycles to Failure (N f ) Model IV: Strain Energy in Monotonic (U s ) Summary Guideline for Practical application of the Fracture test Sample Preparation and Tests Setup Semi-Circular Notched Bending Fracture Test Monotonic Fracture Testing Procedure Calculation of Testing Parameter Stress Intensity Factor, K IC Strain Energy Dynamic Young s Modulus ix

11 4.4 Calculation and Estimate Fatigue Life Potential Summary Summary, Conclusions, and Recommendations Summary Conclusions Recommendations References Appendix A HMA Mixes Details Appendix B Experimental Data x

12 List of Figures Figure 2. Constant-Amplitude Stress Time Pattern... 6 Figure 2.2 A Simplified Relationship between Log S m and Log t... 8 Figure 2.3 Schematic Diagram of Pseudostrain Energy Density Functions (after Lee et al. 2002)... 3 Figure 2.4 Flowchart for Proposed Test Procedure (Daniel and Kim 2002)... 2 Figure 2.5 Flowchart for Proposed Test Procedure Analysis (Daniel and Kim 2002) Figure 2.6 Line Contour Surrounding Crack Tip Figure 2.7 Three Point Loading Test Setup Figure 2.8 Finite Element Analysis Results for three Point Loading Test Setup Figure 2.9 Three-Point Load Testing Set-up on the MTS Machine Figure 2.0 Semi-Circular Notched Model for PFC2D (0.5 in.) Figure 2. Semi-Circular Notched Model with Fracture Pattern (PFC2D) Figure 3. Transition from Elastic to Plastic Displacements During Fatigue Test Figure 3.2 Transition Zone Between Elastic and Plastic of Fatigue Test... 4 Figure 3.3 Uneven Displacement Intervals at Transition Zone... 4 Figure 3.4 Number of Equivalent 8,000 lb Single Axle Load (ESAL) Applications at. 42 Figure 3.5 Load Cycles vs Pavement Depth for All Cyclic Load Ranges Figure 3.6 Load Cycles vs. Pavement Depth at a Load Range of Percent of the Maximum Static Load Capacity Figure 3.7 Illustration of Strain Energy of Monotonic and Cyclic Test Figure 3.8 Cyclic Loading at Hz and 0. Hz Figure 3.9 K IC versus J c at Room Temperature xi

13 Figure 3.0 K IC for SCNBF and SENB Tests Results Figure 3. Fracture Energy versus Stress Intensity Factor (K IC ) Figure 3.2 Stress Intensity Factor K IC at Different Temperature Figure 3.3 Binder Content Effects... 5 Figure 3.4 Changes in Upper Binder Grade Effects Figure 3.5 Changes in Lower Binder Grade Effects Figure 3.6 Measured K * * IC versus Predicted K IC (Model I) Figure 3.7 Measured U * /t versus Predicted U * /t (Model II) Figure 3.8 Measured N f versus Predicted N f (Model III) Figure 3.9 Measured vs. Predicted Number of Cycle xii

14 List of Tables Table 3. Mixes Matrix Stage Table 3.2 Mixes Matrix Stage Table 3.3 Fatigue Test Parameters Table 3.4 Fatigue Load range and number of cycle at failure Table 3.5 Preliminary Test Results for Mix Group Table A. Stage : Properties of Asphalt Mixes Table A.2 Stage 2: Properties of Asphalt Mixes Table B. Stage : SCNBF Test Results Table B.2 Stage : SENB Test Results Table B.3 Stage : SENBF Test Results at Different Temperatures Table B.4 Stage 2: Tests Results xiii

15 .0 Introduction. Background The Superpave mix design method has been used by pavement engineers for more than a decade. Superpave is supposed to ensure low rutting and cracking pavement design mixes using Performance Grade (PG) binders. However, there are no reliable design criteria and/or test methods that ensure that the designed mix will not crack. Cyclic testing has generally been used to assess the fatigue life of asphalt pavements. Test procedures for cyclic testing are time consuming and costly in comparison with monotonic testing. There is a need for the development and evaluation of a simple test method and design criteria to ensure Superpave mixes are resistant to fracture and cracking. Research efforts since the release of Superpave in 992 have continued to address this issue. With the full implementation of Superpave mix design in the state of Idaho, researchers at the University of Idaho, in cooperation with ITD, have been investigating a three point bending fracture test setup which utilizes standard gyratory compactor samples (Bayomy et al. 2007). The work done by Bayomy et. al was based on static fracture testing. The purpose of this study is to evaluate the 3 point loading test in dynamic mode (fatigue) and determine whether the static 3 point loading test can reflect the dynamic fatigue resistance of the mix..2 Research Objectives The main objective of this study was to evaluate the potential of a correlation between simple monotonic (static) and more complex cyclic (dynamic) fracture tests to simplify the evaluation of the fatigue resistance of pavements. To accomplish this main objective, this research included:

16 Evaluation of using a semi-circular notched bending fracture (SCNBF) test setup instead of the single edge notched beam (SENB) test setup; Investigating whether a correlation exists between monotonic and cyclic fracture tests; Developing a model that predicts fatigue life of asphalt mixes from a simple fracture test..3 Project Tasks Phase B The following set of tasks was performed to achieve the stated objectives within the scope of the project. Task B: Review of Previous Studies and Available Data: A literature review was completed on earlier fatigue test procedures and models that were developed to predict fatigue life in asphalt pavements. In addition, work in this task focused on a review of the published work in the area of fracture mechanics with special attention to the use of the semi circular samples in the fracture analysis for the asphalt mixes. Task B2: Finite Element Analysis (FEA): Finite Element Analysis simulations were conducted to compare different monotonic test setups; semi-circle and rectangular beam notched test setups. Task B3: Development of the Fracture Test Procedure: The focus of this task was on the development of a simple test to predict fatigue cracking from a simple fracture test under a monotonic loading condition. Task B4: Preparation and Evaluation of Asphalt Mixtures: Testing and experimental work was carried out in two stages. In Stage, fracture test geometry and 2

17 changes in testing temperature were investigated. Stage 2, the goal was to link a simple monotonic fracture test to a dynamic fracture test, and develop correlations from which the fatigue can be estimated from the simple fracture test. Task B5: Data Analysis: Tests results in both stages were analyzed to determine if the objectives of the study were achieved..4 Report Organization This report is Part 2 of the final report of the project. It is focused on Phase B. It is divided into five chapters, a list of references and two appendices. Following is a brief description of each: Chapter provides background about the study topic. It describes the research problem statement, overall project objectives, and the research approach and organization of the report. Chapter 2 presents a literature review that focuses on fatigue and fracture of asphalt mixes and the earlier developed models that predicted fatigue life. Chapter 3 presents the experimental program and data analysis of tests results. Chapter 4 presents guideline for conducting monotonic fracture tests and use of a simple model to assess the fatigue life potential of asphalt pavement mixes. Chapter 5 summarizes the study outcomes and presents conclusions. 3

18 Blank Page

19 2.0 Review of Fatigue Evaluation of Hot Mix Asphalt 2. Introduction Modern engineering evaluation and design practices should be based on dynamic loading conditions. However, most engineering designs are based on experimental and field data in monotonic or quasi-monotonic loading conditions due to test simplicity or unavailability of materials behavior under dynamic conditions. Cyclic loads result in cracking caused by fatigue. Fatigue may be characterized as a progressive failure phenomenon that begins by the initiation and subsequent propagation of cracks to an unstable condition. Although we have understood for some time that fatigue failure is the cause of most engineering failures in asphalt pavements, there is no complete agreement on the microscopic details of the initiation and propagation of cracks. To improve asphalt pavement design, simple and dependable tests and validated procedures are needed to enhance the mix design process to prolong asphalt pavement life, especially in fatigue. Currently, the fatigue test that is used to estimate asphalt pavement life is considered expensive and time-consuming. Thus, fatigue testing may not be feasible for each project. Therefore, it is very important to develop effective and simple methods or predictive models to evaluate the fatigue resistance of asphalt pavements. The following sections in this chapter present theoretical and prediction models for estimating fatigue life of pavements, background on the use of monotonic testing in assessing the fatigue potential of asphalt pavement, background on the stress intensity factor (the theory utilized in this study in assessing both monotonic and cyclic test results), and preliminary results from numerical analyses on the effect the asphalt sample geometry on pavement fracture toughness. 4

20 2.2 Theories and Prediction Models When studying fatigue cracking, some basic concepts should be understood. These simplified concepts are presented below, followed by various theories and models for predicting pavement fatigue life by using parameters including strength, material characteristic, strain energy concept, statistical approach, etc. Stress spectra are required to assess fatigue life. The simplest fatigue stress spectrum is a zeromean sinusoidal stress-time pattern of constant amplitude and fixed frequency, applied for a specified number of cycles. Such a stress-time pattern is illustrated in Figure 2., and several useful terms and symbols can be defined: σ max = Maximum stress in the cycle; σ m = Mean stress = (σ max + σ min )/2; σ min = Minimum stress in the cycle; σ a = Alternating stress amplitude = (σ max - σ min )/2; σ a = Range of stress = σ max - σ min; R = stress ratio = σ min /σ max ; A = amplitude ratio = σ a /σ m = (-R)/(+R). 5

21 Figure 2. Constant-Amplitude Stress Time Pattern Fracture occurs in asphalt pavement mainly due to concentration of tensile stresses in the bottom of the asphalt mix layer resulting from traffic loads. Many existing fatigue models were developed using regression analysis of experimental data. Wöhler developed a relation that utilized tensile strains resulting from a cyclic load, change in temperature, and other conditions, to investigate pavement fracture as follows (Medani and Molenaar 2000), N f = k ε n k N f = k ε (Eq. 2.) 2 or ( 0 ) where, N f = number of load applications to failure, εo= tensile strain at the bottom of the asphalt layer, k, k 2, and n= factors, depending on the composition and properties of the asphalt mix. da = A K ). dn k 2 is the same as the parameter n of Paris s Law, ( ( ) n 6

22 Based on Eq. 2., the values of n have been estimated using regression analysis. The value of n was determined to be 5 (SPDM 978 and Bonnaure et al. 980) and (Tayebali et al. 994). Eq. 2. was modified to include properties of the asphalt mix as follows, SPDM (978), N f 5 = (0.856V b +.08) ( Sm.0 ) 6.8 ( ) ε 5 (Eq. 2.2) Bonnaure et al. (980), N f = (4.402PI 0.205PI. Vb 2.707) ( Sm.0 ) ( ) (Eq. 2.3) SHRP (Tayebali et al. 994), ε VFB N f = 2.738*0 exp ε ( Sm sinδ ) (Eq. 2.4) where, N f = number of load applications to failure, V b = asphalt binder content, S m = modulus of asphalt mix, δ = phase angle. Medani and Molenaar (2000) simplified the estimation of fatigue characteristics of asphalt mixes. Their method is based on the mix properties and stiffness modulus master curve(s) which is the relationship between the loading time and the stiffness of asphalt mix. The parameter n can be found using a master curve of the log of the mix modulus versus log of the loading time from a simple dynamic indirect tensile test. First, the slope of the master curve is determined as shown in Figure

23 Figure 2.2 A Simplified Relationship between Log S m and Log t d(log S m ) m = (Eq. 2.5) d(logt) The relationship between n and m for a strain-controlled condition is, 2 n mas = (Eq. 2.6) m A correction factor is needed to correct the difference between n mas and n. nmas n = (Eq. 2.7) CF CF = n mas V a (Eq. 2.8) where, m = slope of a master curve, nmas= n-value determined from the master curve, S m = asphalt mix modulus (MPa), t = loading time, CF= correction factor, 8

24 V a = volume percentage of air in the mix. In addition, Medani and Molenaar (2000) utilized the results of 08 controlled deformation fatigue tests, which were either 3-point or 4-point bending tests, to derive the following equations to determine k, log k 3209 b = n logvb PI S mix Va V T R& B (Eq. 2.9) logk V 446 b = n V bpi logVb Vb + Va Sm (Eq. 2.0) where, S m = asphalt mix stiffness modulus (MPa), V b = volume percentage of binder in the mix, V a = volume percentage of air in the mix, PI = penetration index, T R&B = ring and ball temperature ( C). T R& B These relationships were developed using a wide range of loading conditions (large loads versus small loads) and different rates of loading. However, Medani and Molenaar s (2000) equations were based only on testing at a temperature of 25 C. Since asphalt mixes are characterized as a viscoelastic material, the material behavior is a function of temperature. Therefore, these equations should be also modified to include the effects of temperature change. Other researchers have developed general relationships between tensile strain (ε t ) and other factors which effect fatigue as follow, 9

25 Pell and Cooper (975), 4.39 logvb logtrb 40.7 log N logε t = (Eq. 2.) 5.3logV logT 5.8 where, V B = volume percentage of asphalt, T RB = ring and ball softening point, ε t = tensile strain. Shell (987), B RB = (0.856 V +.08) S N ε t B (Eq. 2.2) mix Asphalt Institute (98), [ ( ) ( S ) ] N f = 8.4C ε t mix (Eq. 2.3) M C = 0 (Eq. 2.4) V B M = ( + ) (Eq. 2.5) Vv VB where, C = correction factor V V = volume percentage of air in the mix. Other researchers (Lee et al. 2000, Daniel and Kim 200, and Chehab 2002) used a continuum damage model applied to asphalt concrete under monotonic loading and cyclic loading based on the work potential theory developed by Schapery (990). The work potential theory was used to model the mechanical behavior of linear and nonlinear elastic media with changing structure and growing damage. The theory can be applied to describe the effects of 0

26 viscoelasticity. The work potential theory when applied to viscoelastic media has the following components: Pseudostrain energy density function, W R = W R R ( ε ij, Sm ) (Eq. 2.6) Stress-strain relationship, σ ij R ij R W = (Eq. 2.7) ε Damage evolution law, α R m W S & m = Am S m (Eq. 2.8) Where σ ij and ε R ij are stress and pseudostrain tensors. S m = the internal state variables that accounts for the affects of damage, S & m = the damage evolution rate, W R = the pseudostrain energy density function, and α m = a positive constant. A m is a function of the corresponding internal state variables. The specific functional form of Am was assumed.0, since A m is a constant for isothermal and non-aging systems. R Further, Pseudostrain εij is defined as, t R ε ij ε ij = E( t τ ) dτ (Eq. 2.9) E 0 τ where, R E(t τ) = relaxation modulus,

27 E R = constant reference modulus. Based on Figure 2.3, the pseudostrain energy density function energy density function R WN may be defined as follows: R W and the peak pseudostrain W W R R N R R 2 2 C P ( ) ( R N ε ε s = C PN ε ) = (Eq. 2.20) 2 2 R R 2 2 C ( ε ) ( R N ε s = C ε N ) = (Eq. 2.2) 2 2 C R R ( S ) ( σ N σ s ) /( ε N ε s ) = σ N / R N = ε (Eq. 2.22) R ε N = peak pseudostrain value at the N th cycle, R ε s = smallest pseudostrain value at the N th cycle, σ N R = physical stress corresponding to ε N, σ s = physical stress corresponding to R ε s, R W N = pseudostrain energy density function when R R ε = ε N, S = the first internal state variable that represents the stiffness reduction due to fatigue damage, P N = time-dependence of C over the N th cycle. 2

28 Figure 2.3 Schematic Diagram of Pseudostrain Energy Density Functions (after Lee et al. 2002) Using the above equations, the constitutive relationship can be expressed as, W R = C PN ε (Eq. 2.23) ε R σ = R From equation (Eq. 2.9), (Eq. 2.20), and (Eq. 2.2) W R = P W is assumed. ' N R N where, R ' P ε N = P R ε N 2 N (Eq. 2.24) P N R N ε σ = (Eq. 2.25) R ε σ N ε ε = 0 + sin( ωt π ) 2 2 (Eq. 2.26) where, ε 0 is the strain amplitude and ω is the angular frequency. 3

29 R ε 0 * π V ε = E( t) + E sin( ωt + φ ) 2 (Eq. 2.27) 2 where E * is an absolute value of the complex modulus (i.e., the dynamic modulus) and ε ε R R N V π = + sin( ωt + φ ) 2 2 (Eq. 2.28) σ = π V + sin( ωt + φ + φ D ) σ 2 N 2 (Eq. 2.29) P N π V D + sin( ωt + φ + φ ) = 2 (Eq. 2.30) π V + sin( ωt + φ ) 2 Where, Φ D = the phase angle due to damage incurred in the specimen Φ V = the phase angle due to the time-dependence of the material. For a linear viscoelastic material without damage, Φ D = 0; thus P N =. Thus, P ' N π V π V D = sin( ω t + φ ) + sin( ωt + φ + φ ) (Eq. 2.3) 2 2 Lee et al. (2000) presented a prediction model of asphalt mix fatigue life by using viscoelastic properties only. They found that the fatigue behavior of asphalt mixes is affected by both the viscoelastic properties and fatigue characteristics. Lee et al. (2000) derived mathematically a function in the following form, 2 ' (4 ft 2) P N = e (Eq. 2.32) where, 4

30 f = the loading frequency t = time function. The values of at the initial stage of loading and near failure almost overlap each other, signifying that the fatigue damage dependence of is not as significant as that of P N. Thus, dismissing the loading cycle dependence of, the function of C N is obtained from Equations 2.20 and 2.32, π C N = (Eq. 2.33) 4 f α Lee et al. (2000) also found that the pseudostiffness C decreases as the number of cycles increases due to fatigue damage in various asphalt mixes and obeys a power law in the first internal state variable S. The form of C (S ) is found in his work as follows: C C C2 = ( S ) (Eq. 2.34) where C and C2 are damage evolution characteristics of the material that can be obtained from a regression analysis of fatigue data. 2α α C ( 2 ) α * 2α S ds = (0.5CC2 ) C N E ( ε 0 ) dn (Eq. 2.35) Integrating Equation 2.35 from N= to N f (S becomes S f ) yields: α * 2α 2α N f = 4B f E ( ε 0 ) (Eq. 2.36) π where, p ( S f ) B =, α p(0.5c C ) 2 p = + α ( ), C 2 5

31 S f = value of S at failure. N f = a function of the damage evolution characteristics of the material (C and C 2 ), viscoelastic material properties (m and E * ), fatigue test conditions (f and ε 0 ), and a failure criterion (S f ). Further, Lee et al. (2000) used the work of others to simplify their equations, as follows, B = 4 k α / π f E * 2α ( ε ) 2α 0 k 2 (Eq. 2.37) The value of k 2 can be found by using the stiffness of an asphalt mix and a reference k. Rauhut and Kennedy (982) developed the following form: k 2 = log k (Eq. 2.38) Schapery (984) proposed that α = (+/m) or α = /m, depending on the characteristics of the failure process zone at the crack tip. k 2 = n = 2α (Eq. 2.39) Because the k 2 values are between the 2+2/m and 2/m lines, the best fit of the measurement data occurs when k 2 = +2/m, α = (0.5+/m) is used in the analysis. Since B is strain amplitude dependent, the values of B are calculated at three strain amplitudes of , , and 0.00 for each mix. Lee (2000) found a relationship between B and α as follow: B = a α ) ( b (Eq. 2.40) 6

32 Since B changes with strain amplitude, a and b are functions of strain amplitude. Therefore, an analysis was conducted to obtain a and b values at different strain amplitudes, and the following relationship was established: a a2 = a ( ε 0 ) (Eq. 2.4) where, a = and a 2 = b b2 = b ( ε 0 ) estimated value from Lee et al. (2000) (Eq. 2.42) where, b = 2.30 and b 2 = k 4 f (0.5+ b) * 2α = a( α) E π (Eq. 2.43) k = α = 2 / m N 4 f 2α a( α ) ( ε ) α = E π (0.5+ b) * 2 f 0 (Eq. 2.44) where, f = loading frequency E* = dynamic modulus a i, b i = regression constants Comparing equations Eq and Eq. 2.44, the coefficients of parameter B in Equation 2.36 should be characterized for each individual mix, whereas, the model coefficients a and b in Eq are applicable to different types of mixes. Therefore, using Eq. 2.44, the fatigue life of individual mixes could be evaluated by creep or dynamic modulus tests after the regression 7

33 coefficients a, a 2, b, and b 2 are determined. Using Eq is a more simple process than using the cyclic fatigue testing of individual mixes. Lee et al. (2000) recommended that the dynamic modulus values of the asphalt mixes should be measured at the same frequency as those of the fatigue tests to minimize error. Eq is a simplification to characterize model coefficients and is able to predict the fatigue life of various types of mixes using viscoelastic properties only, without changing the model coefficients. Daniel (2002) presented a methodology based on a single testing condition that can be used to predict material response under different uniaxial tension test conditions. Utilizing the work potential theory and the continuum damage theory, a constitutive model for asphalt concrete was developed. Daniel (2002) suggested that if α was defined in accordance with α = (+/m), the C (S ) curve would exhibit the same characteristic regardless of the applied loading conditions (cyclic versus monotonic, amplitude/rate, frequency) at any temperature below 20 C. Schapery (984) suggested that stresses and strains are not necessarily physical quantities in the viscoelastic body, instead he used pseudo variables in the form of convolution integrals. According to Schapery, the uniaxial pseudo strain (ε R ) is defined as: ε R = E R t dε E( t τ ) dτ dτ 0 (Eq. 2.45) where, ε = uniaxial strain, E R = reference modulus that is an arbitrary constant, 8

34 E(t τ) = uniaxial relaxation modulus, t = elapsed time from specimen fabrication and the time of interest, τ = time when loading began. Using the definition of pseudo strain the equation can be found below, R σ = ERε (Eq. 2.46) For a controlled-strain testing mode, the constitutive equations using Schapery s work potential theory and correspondence principle become, W R m = I C 2 R 2 ( S)( ε m ) (Eq. 2.47) σ = IC S ) ε (Eq. 2.48) m ( R m where R W m is the pseudo strain energy density function when C = S R /I, and S in an internal state variable and I is initial pseudo stiffness. S α N I (+ α ) R 2 (+ α ) ( t) ( mi ) ( Ci Ci ) ( ti ti ) i= 2 R R ε = ε m, C is defined as in ε (Eq. 2.49) α = + (Eq. 2.50) m C ( S) = C0 C( S) C 2 (Eq. 2.5) where C x are a series of regression coefficients. In the case of cyclic loading, damage can be accumulated only during the loading portion of each cycle. Hence, only the time associated with the tensile loading portion (approximately one quarter of the whole cycle time) can be included in the calculation of S. 9

35 20 α α α ε + + = = 2 4 ) ( ) ( 2 ) ( i i N i i i R t t C C I t S (Eq. 2.52) In the case of the time-temperature superposition principle time, t, is replaced by the reduced time ξ as follow, ( ) α α α ξ ξ ε + + = = 2 ) ( ) ( 2 i i N i i i R C C I S (Eq. 2.53) α α α ξ ξ ε + + = = 2 4 ) ( ) ( 2 i i N i i i R C C I S (Eq. 2.54) Daniel (200) found that a half of a cycle or a quarter of a cycle could be used for an approximation case; in this case a quarter of a cycle was used. From the pseudo strain and functional form of the characteristic curve, the stress response may be predicted: ) ( ) ( ) ( t S C t R ε σ = (Eq. 2.55) 2 ) ( ) ( C S C S C = (Eq. 2.56) Flowcharts and associated analysis for the procedure recommended by Daniel are shown in Figures 2.4 and 2.5. Lundstrom and Isacsson (2003) further investigated the work of Daniel and Kim (2002) to determine whether the monotonic test was able to predict fatigue characteristics of asphalt concrete mixtures. The work potential theory was a relatively simple approach for modeling material experiencing damage growth. The results of the study showed that generally monotonic tests cannot be used for the characterization of fatigue behavior. The explanation for the difference between monotonic and cyclic tests was that the cyclic test samples undergo short fatigue lives (i.e. low number of cycles is needed to failure). Another possibility was that

36 the loading level was not enough to cause significant damage growth. In addition, when viscoelastic material was subjected to multiple load cycles, some of the work was converted to heat. Therefore, more effort is needed to predict fatigue characteristic of asphalt concrete mixtures using monotonic tests. Figure 2.4 Flowchart for Proposed Test Procedure (Daniel and Kim 2002) 2

37 Figure 2.5 Flowchart for Proposed Test Procedure Analysis (Daniel and Kim 2002) Liu and Ross (996) suggested that the failure of a viscoelastic material could be described by the value of the intrinsic free energy of the material. The energy can be expressed as: w c t = f 0 ( w & ) & D dt R (Eq. 2.57) 22

38 where w c, strain, describes the recoverable part of deformation, the over-dot ( ) denotes the derivative with respect to time t, is the rate of stress-work done on the material, is rate of dissipation of nonelastic energy, and R is a material constant, which sometimes is defined as the resilience of the material. Eq may be called the failure condition. If all the energy applied to the material was assumed to only be stored and dissipated energy (no developed heat), the failure cycle can be found using, W t = W e + W d (Eq. 2.58) where W t is the total work, W e is elastic energy and W d is dissipated energy. The total energy can be measured using a simple test. The dissipated energy in a linear viscoelastic material for a flexural fatigue test was determined using the following equation, W di = π i σ i ε i sinφ i (Eq. 2.59) where W di is the dissipated energy in cycle i, σ i is the stress amplitude at cycle i, ε i is the strain amplitude at cycle i, and Φ i is the phase difference between the stress and strain-wave signals at the same cycle i. (Ghuzlan and Carpenter 2006). By summing up W di at each cycle, the total dissipated energy W t was determined, n W t = W i i= (Eq. 2.60) Van Dijk et al. (972) were among the first researchers to do an extended study on fatigue of bitumen and asphalt aggregate mixtures based on the dissipated energy concepts. The following relationship was obtained: z W fat = AN f (Eq. 2.6) 23

39 where N f is the number of load cycles to failure and A and z are mixture constants equal to 0 9 and.6, respectively. 2.3 Monotonic Testing to Assess Fatigue Early work in the 960 s and 970 s guided researchers to the use of notched beam specimens statically loaded in a 3-point loading configuration to assess fatigue and fracture properties of asphalt pavements. This test is well known as the single-edge notched beam (SENB) test (ASTM E399). Dongre et al. (989) evaluated fracture resistance of asphalt mixes at low temperatures using SENB test by determining the J-Integral (J c ). Lee and Hesp (994) and Lee et al. (995) used the same test setup to evaluate the fracture toughness of modified asphalt binders at low temperature. Bhurke et al. (997) studied polymer modified asphalt concrete using the J c fracture resistance approach employing the same test setup. They used AC-5 asphalt as a base and polymers such as styrene-butadiene-styrene, and styrene-butadiene rubber as modifiers. All studies concluded that a three-point bending beam test was repeatable, and test results were sensitive to material differences. Although the use of beams were convenient to test-set up, it was not readily convenient to produce homogenous samples that represent the mix conditions. When the Superpave mix design method was introduced in the 990 s, the pavement industry looked more favorably to the use of samples that are produced by the Superpave Gyratory Compactor (SGC) so that consistency of samples would be dependable. In addition, extracting field cores is much easier than cutting beams from pavement slabs when testing field samples. Several studies have investigated the use of gyratory compacted samples to determine fracture by creating a semi-circular specimen to conduct a fracture test in bending. Ven et al. (997), 24

40 Molennar et al. (2002), and Li and Marasteanu (2004) adopted the semi-circular bending (SCB) test setup. Using samples compacted by SGC, models were developed to determine the tensile strength of asphalt mixtures in an effort to replace the indirect tension (IDT) test. Unfortunately, un-notched samples were used and their studies were not focused on fracture resistance parameters. Lim et al. (994) used a semi-circular notched specimen in a bending test to evaluate fracture properties of natural rocks by determining the stress intensity factor (K IC ). Mull et al. (2002) built on Lim s results, and adopted the SCNBF test to measure fracture resistance properties of asphalt mixtures. They evaluated the fracture resistance of chemical crumb rubber asphalt (CMCRA) mixes as measured by J c. Huang et al. (2004) used the SCNBF test to study fracture properties of various reclaimed asphalt pavement (RAP) mixes. Mohammad et al. (2004) extended the concept of SCNBF test to study fatigue crack propagation of asphalt mixes. They have found that the geometry of SCNBF test was more suitable for fatigue crack propagation analysis of asphalt mixes. Results of the fatigue study on the crumb rubber modified mixtures have confirmed the monotonic results generated earlier by Mull et al. (2002). Both studies found the SCNBF test to be a reliable test for asphalt mixtures evaluation. Bayomy et al. (2007) conducted an extensive study on various asphalt mixes to determine fracture toughness (J c ) of Idaho asphalt mixes using the SCNBF test. They concluded that SCNBF test was simple, repeatable and was sensitive to asphalt mix properties. In addition, studies have shown that a relationship between K IC and J c exists in metals. Landes et al. (984) related K IC to J c using the following equation, 2. = J E K IC (Eq. 2.62) C ν 2 where E is elastic modulus, and ν is poison ratio. 25

41 McCabe et al. (2005) used a modified equation to determine an equivalent stress intensity factor defined as K JC (Eq. 2.63). It has been demonstrated that to determine K JC, specimens can be /40 th the size required for K IC as required by ASTM E 399 and still maintain sufficient control of loading conditions. K = E Jc (Eq. 2.63) JC. The aforementioned literature studies reveal that J c can be determined by various methods and used as an indicator of the asphalt material s fracture resistance to cracking Fracture Parameter The fracture parameter, J c, used in this study is based on the study conducted by Rice (968). J c is defined as a path independent integration of strain energy density, traction, and displacement along an arbitrary contour path around the crack as shown in Figure 2.6 and can be quantified using the following equation: J c u = Wdy T ds (Eq. 2.64) Γ Γ x where Γ is any path surrounding the crack tip, x,y are rectangular coordinates normal to the crack front, ds is the increment along contour Γ, T is the stress vector acting on the contour, u is a displacement vector, and W is the strain energy density = σ ijd ε ij. 26

42 Y crack I O X ds n Figure 2.6 Line Contour Surrounding Crack Tip Rice (968) also presented an alternative and equivalent definition for J c based on the pseudopotential energy difference between two identically loaded bodies possessing slightly different crack lengths. A simplified form of Eq is given below: U J c = (Eq. 2.65) a t where U is the strain energy to failure, which is the area underneath the load-deformation curve up to the peak load, t is the specimen thickness, and a is the notch depth. 2.4 Stress Intensity Factor, K IC A simple and widely used approach to determine fracture toughness in materials, especially polymers, is the linear elastic fracture mechanics (LEFM) theory. The main assumption of this approach is that the material behaves as a linear elastic solid. It was found (Osswald et al. 2003) that this approach works well even when inelastic behavior is observed near the region at the tip of a crack. For viscoelastic materials such as HMA, this approach can be assumed valid if the size of the plastic zone at the tip of the crack is small compared to the initial crack. In addition, the LEFM approach is only applicable for short-term tests, not long tests such as creep tests (Osswald et al. 2003). 27

43 Fracture toughness is represented by the stress intensity factor (K C ). Depending on the type of loading, different numerical solutions have been developed to determine K C. Traditionally; 3 possible loading modes (Mode I, II, and III) have been considered with regard to crack propagation. Where Mode I (K IC ) represents a pure tension mode, Mode II (K IIC ) represents an in-plane shear mode and Mode III (K IIIC ) represents tearing or an out of plane shear mode (Stephens et al. 200). It has been widely observed that fracture occurs in asphalt pavements mainly due to concentration of tensile stresses due to loads and/or temperature variations. Thus, the stress intensity factor in Mode I (K IC ) has been widely used to evaluate fracture toughness of asphalt mixes. K IC is generally determined by, K IC = EG = Yσ πa (Eq. 2.66) c c where, K IC = critical stress intensity factor (Mode I), E =: elastic modulus, G c = critical strain energy release, Y = numerical modification factor to account for crack geometry, loading conditions and edge effects, σ c = applied critical stress, P = applied vertical load, a = notch depth. 28

44 Therefore, 2 major factors affect the evaluation of the K IC for HMA ; the geometry factor and the variation of elastic modulus of the mix under various conditions, especially temperature. These two factors are addressed in further detail below. Certain restrictions apply to the use of K IC to avoid significant violation of LEFM. These restriction pertain to the size of the plastic zone (2r y ) at the tip of the crack; r y a/8, r y t/8, and (w-a)/8, where t is sample thickness, and (w-a) is the uncracked length along the plane of the crack. The plastic zone was determined for monotonic loading using von Mises or maximum shear stress yield criterion. For plane stress conditions it was found that 2r y was three times larger than for plane strain conditions. For plane strain fracture toughness, K IC is considered a true material property because it is independent of thickness. The plastic region for plane strain conditions in the plane of the crack can be expressed using Eq In order to consider the plane strain fracture toughness valid, the sample thickness should be smaller than the ratio between K IC and the yield stress (S y ) as shown in Eq (Stephens et al. 200). For HMA the yield stress (S y ) was assumed to be the stress at which the material starts to behave non-linearly. 2r y = 3π K S y 2 (Eq. 2.67) K t (Eq. 2.68) S y When investigating the geometry effects on K IC, Lim et al. (993) developed equations for the Y factor for a semi-circular sample under 3-point bending (Figure 2.7) for different span ratios and different crack angles. Lim s solutions were verified by Li and Marasteanu (2004) by using 29

45 finite element and LEFM analysis. For a span ratio (s/r) of 0.8, the factor Y can be determined using the following equation, Y S0 = YI + B (Eq. 2.69) r where, Y I = the normalized stress intensity factor, a a Y I = exp , r r S 0 /r = deviation from actual span ratio of s/r = 0.8, B = ( a / r) ( a / r) ( a / r),0.003 a / r 0.8 r = sample radius., Thus, for a SCNBF test K IC can be determined as, K IC = Yσ c πa = Y I S 0 + B σ c πa (Eq. 2.70) r P P a r a W 2s 2r t S B a) SCNBF Test b) SENB Test Figure 2.7 Three Point Loading Test Setup For the single edge notched beam test setup (Figure 2.7), other numerical solutions were developed (Hertzberg 989). To determine K IC the following equation can be used, 30

46 Pc S K IC = 3/ 2 BW f ( a / W ) (Eq. 2.7) where, P c = applied critical vertical load, S = loading span, B = sample thickness, W = sample width, 2 [.99 ( a / W )( a / W 2.7( a / ) ] / 2 3( a / W ) f ( a / W ) = + W 3 / 2 2( + 2a / W )( a / W ) (Eq. 2.72) 2.5 Sample Geometry Effect on Fracture Toughness Prior to conducting experimental tests to study the effect of geometry on fracture toughness, a FEA was carried out using ALGOR Software (Algor Inc, 2007). A simple 2-D analysis was conducted for both geometries. Using the same material properties, loading and boundaries conditions, tensile stress at the tip of the notch was simulated. When loaded, both test setups yielded approximately the same tensile stress at the tip of the notch. The stress at the tip of notch for the SCNBF test setup was 640 kpa (92.83psi) and 597 kpa (86.63 psi) for the SENB test setup as shown in Figure 2.8. The difference was less than7 percent of the maximum tensile stress which might be caused by shape, size, and distribution of elements in the FEA model. Furthermore, K IC measured from the SCNBF and SENB yielded 0.72 MPa.m 0.5 and 0.69 MPa.m 0.5, respectively. The difference was less than 4.2 percent due to the difference between shape factors of f(a/w) (Eq. 2.72) and Y (Eq. 2.69) in the fracture toughness solution. Thus, with ideal conditions, there may be no significant difference in K IC by using either test setup. 3

47 a) SCNBF Test b) SENB Test Figure 2.8 Finite Element Analysis Results for three Point Loading Test Setup To further understand the behavior of fracture patterns and to verify the outcome of experimental tests, the Distinct Element Method (DEM) was also used to observe crack propagation based on time-stepping analysis. With the DEM simulation, numerical analyses can be utilized for the validation of the testing procedure. PFC2D software was used to conduct a DEM simulation. This simulation improved the understanding of the characteristics and mechanisms of fatigue fracture since the fracture pattern could be visualized. In this study, a notched semi-circular sample was modeled in 2-D. The model utilized an applied force to test the particles movement and deformation in a numerical simulation. The models developed in PFC2D are based on configuration of Figure 2.9. The PFC2D test setup and results are illustrated in Figure 2.0 and Figure

48 Figure 2.9 Three-Point Load Testing Set-up on the MTS Machine The outcome of PFC2D simulation proved that fracture patterns are due to tensile stresses. Also, testing setup of the proposed study was adequate since shear failure did not develop under loading in the numerical simulation. During the fatigue experiment, fracture patterns should all be in tension. If the fracture pattern illustrated other than tensile patterns, unusual failure pattern may be caused by geometry, aggregates, voids, binder, human factor, etc. Figure 2.0 Semi-Circular Notched Model for PFC2D (0.5 in.) 33

49 Figure 2. Semi-Circular Notched Model with Fracture Pattern (PFC2D) 2.6 Summary Fatigue failure in asphalt pavement is a critical problem in the transportation industry. Pavement failure occurs mainly due to accumulation of damage due to repeated loads. Many models and relations to assess fatigue failure have been developed. These models generally require results from cyclic testing for implementation. After reviewing the available models, we decided to focus our efforts on the stress intensity factor in comparing monotonic and cyclic test results. The stress intensity factor was chosen because it is a reasonable and simple measure of the fracture toughness of asphalt pavement. Prior to moving forward with our experimental program to investigate the relationship between static and cyclic tests, we completed some preliminary numerical analyses to provide confidence that semi-circular notched samples can be used to reliably quantify the fracture and fatigue properties of pavements. These numerical analyses indicated that semi-circular notched specimens can be used. Additional testing, as presented in the next chapter, was performed to provide additional data to validate these numerical results. 34

50 Blank Page

51 3.0 Experimental Program and Data Analysis 3. Introduction The experimental program consisted of two stages of testing. The purpose of the first stage of testing was to verify that the semi-circular notched beam fracture test meets the criteria associated with use of the stress intensity factor for fatigue characterization and that this semicircular sample can replace beam shaped samples. The purpose of the second stage of testing was to develop a data set that could be used to show that monotonic test results can be used to assess the fatigue behavior of asphalt pavements. To accomplish the objective of this study associated with the second stage testing (i.e. to evaluate the potential of a correlation between simple monotonic and cyclic fracture tests to simplify evaluation of the fatigue resistance of pavements), many cyclic and monotonic load tests were performed on semi-circular notched beam specimens. The following sections describe the materials used for testing, the asphalt material testing procedures, test results, and an analysis of the test results. 3.2 Materials Commonly used mixes in the State of Idaho were selected for both stages of testing. Both stages utilized 2 aggregate gradations (Mix and Mix 2). Details on the gradations are provided in Appendix A. In addition to using two aggregate gradations, various binders and binder contents were used. The specific binders and binder contents for each stage of testing are provided in this section. 35

52 3.2. Material for Stage Tests These mixes used for the Stage tests are shown in Table 3.. Asphalt content and binder grade were varied to study the effect of these changes on test results. The objective of this stage was to determine if the semi-circle sample can be used instead of the traditional beam sample to estimate fatigue resistance and to verify that the semi-circle notch beamed sample met the criteria for evaluation using the stress intensify factor. Table 3. Mixes Matrix Stage Mix PG AC% -.0% -0.5% Optimum +0.5% +% % % Material for Stage 2 Tests A wide range of commonly used mixes in the State of Idaho were selected to construct a mix matrix consisting of two different aggregate structures (Mix and Mix 2). In addition, 3 binder contents (optimum asphalt content and ± 0.5 percent from optimum content) and 8 binder grades were used for a total of 5 mixes as shown in Table 3.2. Seven field mixes were also obtained for additional testing and evaluation. Details of all mixes can be found in Appendix A. 36

53 Table 3.2 Mixes Matrix Stage 2 Asphalt Content -0.5 Opt Opt Opt 0.5 Binder Grade PG PG PG Mix 4.90% Mix 2 Mix PG PG PG Mix % PG PG Mix Mix Sample Preparation All specimens were mixed and compacted under controlled lab conditions. Specimens were compacted using the Servopac Gyratory Compactor to a number of gyrations to produce specimens with 4 ± percent air voids. 3.4 Test Setup Asphalt pavement testing consisted of monotonic semi-circular notched beam fracture tests (SCNBF), single-edge notched beam test (SENB), dynamic modulus tests, and cyclic fatigue tests on semi-circular notched beam samples. The test procedure associated with each experimental stage is described below Semi-Circular Notched Bending Fracture (SCNBF) Test (Stage ) Compacted cylindrical specimens were sliced into 4 semi-circular specimens. Each sample will be about 53.3 mm in thickness. One specimen was left un-notched as a control specimen, and 37

54 the other 3 specimens were notched with 2.7, 25.4 and 3.8 mm notch depths. All specimens had the standard Superpave Gyratory diameter (50 mm). Spacing between the 2 roller supports was 20 mm. A ramp load with a constant vertical deformation rate of 0.5 mm/minute was applied until fracture occurred. Testing was conducted at temperatures of 4.4, 24 and 54.4 C for mixes shown in Table 3.. Single Edge Notched Beam (SENB) Test (Stage ) Semi-circular specimens were sawn into beam specimens with dimensions of 00 mm wide and 50 mm high. Beams were notched with a 2.7 mm notch depth. Spacing between the two roller supports was 80 mm. A ramp load with a constant vertical deformation rate of 0.5 mm/minute was applied until fracture occurred. Testing was conducted at a room temperature of 24 C Stage 2 Monotonic Semi-Circular Notched Bending Fracture Tests Compacted cylindrical specimens for mixes shown in Table 3.2 were sliced into 4 semicircular specimens. Samples were notched with 2.7, 25.4 and 3.8 mm notch depths. Spacing between the 2 roller supports was 20 mm. A MTS 80 machine and Flex Test SE Version 5.0 C 2299 system were used for applying loads to the specimen. A ramp load with a constant vertical deformation rate of 0.075mm/minute was used Stage 2 Cyclic Semi-Circular Notched Bending Fracture Tests Fatigue testing for assessing relationships between cyclic and monotonic tests consisted of cyclic loading at a loading frequency of Hz. The applied load ranged from approximately 30 to 60 percent of the monotonic maximum strength. Based on results from preliminary tests the actual applied cyclic load ranged from 265 N to 530 N for all fatigue tests. Details on why 38

55 this fatigue testing protocol was implemented are provided below. Tests were conducted at room temperature (2 C) Preliminary Fatigue Testing To determine parameters for the fatigue test, a literature review was conducted. In addition, a total of 92 semi-circular samples were prepared from 23 cylindrical gyratory samples from field mixes. These samples were used to understand the function of different test parameters including frequency, temperature, and strain rate. Although, there is no established fatigue testing procedure for asphalt pavements, a survey of published monotonic and fatigue tests indicated the temperature ranges, strain rates, and cyclic frequencies that have been used by previous authors (Table 3.3). Table 3.3 Fatigue Test Parameters Temperature ( C) Monotonic Cyclic Strain rate (0-6 units/s) Frequency (Hz) Daniel [200] 5, 20 5, 2, 20 0, 30, 500, 500, 0 Lundstrom [2003] 0, 0, 20 00, 200, 400, Medani [2000] 5, 5, 20, 25, 30 for n 0-50 H. J. Lee [994] 25 5 Based on this survey, a testing protocol was established for monotonic and fatigue testing of semi-circular notched samples. The followings parameters were reviewed carefully including: notch depth, strain rate, loading frequency and the resulting strain range. The preliminary results illustrate that each parameter affects the pavement fatigue life. Using our MTS system, samples were tested using a combination of recommended parameters (Table 3.3). These combinations were: displacement rate of 50x0-6, 00x0-6, 500x0-6, and 39

56 000x0-6 in./sec for monotonic tests and cyclic loading at 0., 0.5 and Hz for cyclic tests. In this study, most of the experiments were conducted at room temperature to minimize the effect of temperature Fatigue Failure and Strain Energy When conducting cyclic fatigue testing, the following parameters can be varied: loading frequency, loading range, and pavement temperature. The impact of loading range is described below. Before the fatigue testing parameters could be assessed, it was necessary to define a failure condition under dynamic loading. A theoretical failure was defined by examining the spacing between peak cyclic displacements at the transition zone between the elastic and plastic region as shown in Figure 3.. Figure 3. Transition from Elastic to Plastic Displacements During Fatigue Test Figure 3.2 and Figure 3.3 illustrate the transition from elastic to plastic behavior of a specimen loaded at a frequency of Hz. 40

57 Figure 3.2 Transition Zone Between Elastic and Plastic of Fatigue Test Figure 3.3 Uneven Displacement Intervals at Transition Zone Figure 3.3 illustrates uneven displacement intervals for cycles at the transition zone which could be defined as failure. When the cyclic displacement interval increases at the transition zone, fracture has initiated at the tip of notch. The loading frequencies and strain ranges used by other researchers and presented in Table 3.3 were provided without explanation as to the basis for choosing these parameters. To estimate/verify the range of appropriate strain rates and loading frequencies for this study, the research team examined the Asphalt Institute (AI), California, and AASHTO procedures for estimating the life of asphalt pavement based on its thickness. Figure 3.4 illustrates the number of applications of an 8,000 lb equivalent single axle loads (ESALs) to cause failure vs. the depth of the asphalt pavement. 4