An Exploratory Study on Functionally Graded Materials with Applications to Multilayered Pavement Design Ernie Pan, Wael Alkasawneh, and Ewan Chen Prepared in cooperation with The Ohio Department of Transportation and the U.S. Department of Transportation, Federal Highway Administration State Job Number 134256 August 2007 1. Report No. 2. Government Accession No. 3. Recipient’s Catalog No. FHWA/OH-2007/12 4. Title and subtitle 5. Report Date An Exploratory Study on Functionally Graded Materials with August 2007 Applications to Multilayered Pavement Design 6. Performing Organization Code 7. Author(s) 8. Performing Organization Report No. Ernie Pan, Wael Alkasawneh, Ewan Chen 10. Work Unit No. (TRAIS) 9. Performing Organization Name and Address 11. Contract or Grant No. 134256 Department of Civil Engineering The University of Akron 13. Type of Report and Period Akron, OH 44325-3905 Covered Final Report 12. Sponsoring Agency Name and Address 14. Sponsoring Agency Code Ohio Department of Transportation 1980 West Broad Street Columbus, OH 43223 15. Supplementary Notes 16. Abstract The response of flexible pavement is largely influenced by the resilient modulus of the pavement profile. Different methods/approaches have been adopted in order to estimate or measure the resilient modulus of each layer assuming an average modulus within the layer. In order to account for the variation in the modulus of elasticity with depth within a layer in elastic pavement analysis, which is due to temperature or moisture variation with depth, the layer should be divided into several sublayers and the modulus should be gradually varied between the layers. A powerful and innovative computer program has been developed for elastic pavement analysis that overcomes the limitations of the existing pavement analysis programs. The new program can predict accurately and efficiently the response of the pavement consisted of any number of layers/sublayers and any number of loads. The complexity of the tire-pavement loading configuration can be modeled easily as well. Practical pavement engineering problems have been analyzed and discussed taking into consideration the modulus variation with depth as well as the complex tire-pavement loading configuration utilizing our newly developed MultiSmart3D program. The analyzed problems illustrated that powerful analytical tools, such as MultiSmart3D, are needed to study and predict the pavement response in practical and fast manners. For example, the predicted life time of the pavement can be increased or decreased by a factor more than two if the modulus of elasticity variation with depth is taken into consideration. 17. Key Words 18. Distribution Statement Multilayered elastic analysis, Pavement, Temperature, No restrictions. This document is available to Resilient modulus, Tire contact pressure, Tire footprint, the public through the National Technical Stress/strain discontinuity, Fatigue/rutting life prediction Information Service, Springfield, Virginia 22161 19. Security Classif. (of this report) 20. Security Classif. (of this page) 21. No. of Pages 22. Price Unclassified Unclassified 135 Form DOT F 1700.7 (8-72) Reproduction of completed pages authorized ii An Exploratory Study on Functionally Graded Materials with Application to Multilayered Pavement Design Prepared by Ernian Pan, PhD (Principal Investigator) Wael Alkasawneh, P.E. (Graduate Student) Ewan Chen (Graduate Student) Department of Civil Engineering The University of Akron Akron, OH 44325-3905 iii Final Report August 2007 Disclaimer Statement: The contents of this report reflect the views of the authors who are responsible for the facts and accuracy of the data presented herein. The contents do not necessarily reflect the official views of the Ohio Department of Transportation or the Federal Highway Administration. This report does not constitute a standard, specification or regulation. iv An Exploratory Study on Functionally Graded Materials with Application to Multilayered Pavement Design TABLE OF CONTENTS Page Disclaimer…………………………………………………………………………………….......iv Table of Contents. ……………………………………………………………………………. ..v List of Figures..………………………………………………………………………………. viii List of Tables .………………………………………………………………………………….xii Chapter 1- Introduction .............................................................................................................1 1.0 Introduction.............................................................................................................1 1.1 Pavement Loading Response ..................................................................................2 1.2 Elasticity Theory.....................................................................................................2 1.2.1 Hook’s Law....................................................................................................2 1.2.2 Boussinesq’s Equation...................................................................................2 1.2.3 Charts Method................................................................................................6 1.3 Method of Equivalent Thickness (MET) ...............................................................7 1.4 Finite Element Method ..........................................................................................8 1.5 Discrete Element Method ......................................................................................9 1.6 Viscoelasticity Method ..........................................................................................9 1.6.1 Maxwell Model ...........................................................................................10 1.6.2 Kelvin-Voigt Model ....................................................................................11 1.6.3 Burgers Model ............................................................................................11 1.6.4 Creep Testing .............................................................................................11 1.7 Layered Systems ..................................................................................................11 1.7.1 Elastic Multilayer Theory ...........................................................................12 1.7.2 Factors Affecting Elasticity ........................................................................13 1.7.2.1 Anisotropy ......................................................................................13 1.7.2.2 Shear Sensitivity ............................................................................14 Chapter 2 Resilient Modulus Variation Studies ………………………………….…...15 2.0 Introduction...........................................................................................................15 2.1 Mechanistic-Empirical Pavement Design Guide..................................................16 2.1.1 Seasonal Variation of Resilient Modulus ....................................................19 2.1.2 Seasonal Variation of Poisson’s Ratio.........................................................23 2.2 Temperature Variation .........................................................................................25 2.2.1 Pavement Temperature Variation ...............................................................25 2.2.2 Pavement Modulus Variation .....................................................................29 2.3 Pavement Response to Temperature ....................................................................30 2.4 Temperature Variation in Ohio ............................................................................31 2.4.1 Pavement Material Equations .....................................................................31 2.4.1.1 Asphalt Concrete .............................................................................31 2.4.1.2 Base/Subbase ...................................................................................33 2.4.1.3 Permeable Asphalt-Treated Base/Subbase (PATB) .......................34 v Page 2.4.2 Resilient Modulus vs. Temperature.............................................................34 2.4.3 Poisson’s Ratio vs. Temperature..................................................................35 2.5 Daily Temperature Variation ................................................................................37 2.6 Resilient Modulus Variation Example..................................................................38 2.6.1 Pavement Damage Prediction......................................................................49 2.7 Conclusions...........................................................................................................52 Chapter 3 Effective Modulus Variation with Depth........................................................54 3.0 Introduction...........................................................................................................54 3.1 Stress/Strain Discontinuity....................................................................................54 3.2 Flexible Pavement Application.............................................................................58 3.2.1 Effect of Sublayer Number ..........................................................................63 3.2.2 Burmister Solution.......................................................................................65 3.3 Discussions and Conclusions ...............................................................................66 Chapter 4 Pavement Response Verification .....................................................................67