DEVELOPMENT OF APPROACH TO ESTIMATE VOLUME FRACTION OF MULTIPHASE MATERIAL USING DIELECTRICS A Dissertation by SANG ICK LEE Submitted to the Office of Graduate Studies of Texas A&M University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY May 2010 Major Subject: Civil Engineering DEVELOPMENT OF APPROACH TO ESTIMATE VOLUME FRACTION OF MULTIPHASE MATERIAL USING DIELECTRICS A Dissertation by SANG ICK LEE Submitted to the Office of Graduate Studies of Texas A&M University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Approved by: Chair of Committee, Dan G. Zollinger Committee Members, Robert L. Lytton Dallas N. Little Mohammed E. Haque Head of Department, John Niedzwecki May 2010 Major Subject: Civil Engineering iii ABSTRACT Development of Approach to Estimate Volume Fraction of Multiphase Material Using Dielectrics. (May 2010) Sang Ick Lee, B.S., Chung-Ang University, Korea; M.S., Chung-Ang University, Korea Chair of Advisory Committee: Dr. Dan G. Zollinger Most engineering as well as pavement materials are composites composed of two or more components to obtain a variety of solid properties to support internal and external loading. The composite materials rely on physical or chemical properties and volume fraction of each component. While the properties can be identified easily, the volume fraction is hard to be estimated due to the volumetric variation during the performance in the field. Various test procedures have been developed to measure the volume fractions; however, they depend on subjective determination and judgment. As an alternative, electromagnetic technique using dielectric constant was developed to estimate the volume fraction. Empirical and mechanistic approaches were used to relate the dielectric constant and volume fraction. While the empirical models are not very accurate in all cases, the mechanistic models require assumptions of constituent dielectric constants. For those reasons, the existing approaches might produce less accurate estimate of volume fraction. In this study, a mechanistic-based approach using the self consistent scheme was developed to be applied to multiphase materials. The new approach was based on calibrated dielectric constant of components to improve results without any assumptions. Also, the system identification was used iteratively to solve for dielectric parameters and volume fraction at each step. As the validation performed to verify the viability of the new approach using soil mixture and portland cement concrete, it was found that the approach has produced a significant improvement in the accuracy of the estimated volume fraction. iv DEDICATION To my mother and father for their deepest love and unconditional support, and to my wife, Su Jin Park, for her endless love and help v ACKNOWLEDGEMENTS My sincere appreciation and thanks go to my committee chair, Dr. Dan G. Zollinger for his great advice and constant support throughout my Ph.D. program. And, I must express my sincere appreciation to Dr. Robert L. Lytton for his noble academic advice and support throughout the course of this research. I also would like to thank Dr. Dallas N. Little and Dr. Mohammed E. Haque for serving on my committee and providing me with comments on my dissertation. I want to extend my gratitude to all TDR project participants who share their good knowledge with me and to Mr. Praveen Rai for helping me develop the computational program. I will never forget precious and pleasant memories with my friends and colleagues at Texas A&M University. Last, but definitely not the least, I would like to express my deepest gratitude to my mother and father for their continuous support and love and to my wife for her true love. vi TABLE OF CONTENTS Page ABSTRACT..................................................................................................................... iii DEDICATION ..................................................................................................................iv ACKNOWLEDGEMENTS ...............................................................................................v TABLE OF CONTENTS..................................................................................................vi LIST OF FIGURES............................................................................................................x LIST OF TABLES ......................................................................................................... xiii CHAPTER I INTRODUCTION ................................................................................................1 Background...................................................................................................1 Objective and Scope of Research .................................................................4 II LITERATURE REVIEW .....................................................................................7 Composite Materials.....................................................................................7 Fundamental Assumptions for Composite Materials ............................9 Composite Pavement Materials...........................................................10 Soil Mixture..................................................................................10 Portland Cement Concrete ...........................................................11 Hot Mix Asphalt Concrete ...........................................................12 Test Methods to Measure Volume Fraction ...............................................14 Thermogravimetric Methods...............................................................14 Nuclear Methods .................................................................................18 Overview of Dielectric Constant ................................................................21 Complex Permittivity ..........................................................................21 Relative Complex Permittivity (Dielectric Constant) .........................24 Measurement of Dielectric Constant ..........................................................26 Time Domain Reflectometry...............................................................27 TDR Measurement in LTPP SMP................................................27 Interpretation of TDR Trace..................................................30 Computation of Dielectric Constant......................................31 Percometer...........................................................................................34 Ground Penetrating Radar ...................................................................35 Mathematical Dielectric Constant Models .................................................37 Empirical Approach.............................................................................37 Polynomial and Square Root Models...........................................38 Klemunes Model ..........................................................................40 vii CHAPTER Page Empirical Model Used in LTPP SMP ..........................................42 Mechanistic Approach.........................................................................45 Classical Binary Mixture Models.................................................47 Complex Refractive Index Model ................................................48 Three-Phase Mixture.............................................................50 Four-Phase Mixture...............................................................52 Maxwell-DeLoor Mixing Model..................................................56 III DEVELOPMENT OF NEW APPROACH.........................................................58 Self Consistent Approach and Bounds of Dielectric Constant...................58 Self Consistent Approach....................................................................58 Bounds of Dielectric Constant.............................................................59 Application of Self Consistent Model for Multiphase Material..........60 Procedure of New Approach ......................................................................62 Determination of Composite Dielectric Constant (Step 1)..................63 Calibration of Component Properties (Step 2) ....................................63 Forward Calculation of Volume Fraction (Step 3)..............................66 System Identification as Solution Methodology.........................................67 Overview of System Identification......................................................67 Parameter Adjustment Algorithm........................................................69 IV APPLICATIONS OF NEW APPROACH.........................................................72 Soil Mixture................................................................................................72 Volumetric Relationship of Soil Mixture Components......................72 Data Collection....................................................................................75 Determination Process for Water Content in Soil Mixture .................76 Determination of the Composite Dielectric Constant (Step 1).....77 Transmission Line Equation .................................................78 Use of SID for Dielectric Constant Determination...............81 Calibration of Soil Component Dielectrics (Step 2) ....................83 Forward Computation of Water Content and Dry Density (Step 3) .........................................................................................86