Application of the Laplace Transform and Its Numerical Inversion to Temperature Profile of a Two-Layer Pavement under Site Conditions

REFERENCES

• E. J. Yoder and M. W. Witczak , Principles of Pavement Design, , 2nd ed. , pp. 3 – 76 , John Wiley , New York , 1975 .
   Google Scholar
• H. Y. Huang , Pavement Analysis and Design , pp. 6 – 168 , Prentice Hall , Englewood Cliffs , 1993 .
   Google Scholar
• S. Brown , Achievements and Challenges in Asphalt Pavement Engineering, 8th International Conference on Asphalt Pavements, Seattle, USA, vol. 8, Keynote Address, pp. 1–23, Nottingham, 1997.
   Google Scholar
• H. A. Wahhab , M. I. ASI , and R. H. Ramandhan , Modeling Resilient Modulus and temperature Correction for Saudi Roads , J. of Materials in Civil Eng. , vol. 13 , pp. 298 – 305 , 2001 .
   Web of Science ®Google Scholar
• R. K. Wolfe , D. C. Colony , and R. D. Eaton , Microprocessor plus SauĺYev Method Solves Simultaneous Partial Differential Equations of the Diffusion Type with Highly Nonlinear Boundary Conditions, in P. Lykos (ed.), Minicomputers and Large Scale Computations, American Chemical Society Series 57 , Washington D.C. , 1977.
   Google Scholar
• R. K. Wolfe , G. L. Heath , and D. C. Colony , Hand-Held Microprocessor Implementation of heretofore Large Computer Simulation , Comp. and Industrial Eng. , vol. 4 , pp. 1 – 12 , 1980 .
   Google Scholar
• R. K. Wolfe and B. W. Randolph , Temperature Adjustment of Dynamic Deflection Measurements of Asphalt Concrete Pavements, Ohio Department of Transp. Report FHWA/OH-93/010, Columbus, Ohio, 1993.
   Google Scholar
• R. K. Wolfe , W. R. Brian , and D. C. Colony , Standardized Elastic Moduli Pavement Layers for Overlay Design , J. Transp. Eng., ASCE , vol. 121 , pp. 221 – 232 , 1995 .
   Google Scholar
• R. G. Robinson , A Model for Calculating Pavement Temperatures from Meteorological Data, Highways and Structures Department, Transport and Road Research Laboratory, Res. Rep. 44, Pavement Design and Maintenance Division, Crow Thorne, Berkshire, England, 1985.
   Google Scholar
• L. M. G. Motta , Método de Dimensionamento de Pavimentos Flexíveis, Critérios de Confiabilidade e Ensaios de Cargas Repetidas, PhD thesis, The Federal University of Rio de Janeiro, Rio de Janeiro, Brazil, 1991.
   Google Scholar
• R. B. McGennis , R. M. Anderson , T. W. Kennedy , and M. Solaimanian , Background of Superpave Asphalt Mixture Design and Analysis, Report FHWA-SA-95-003, Federal Highway Administration, U.S. Department of Transportation, Washington, 1995.
   Google Scholar
• A. Mohseni , LTPP Seasonal AC Pavement Temperature Models (SATP), FHWA, October 29, 1996.
   Google Scholar
• LTPP-FHWA, LTPP Data Analysis: Improved Low Pavement Temperature Prediction, U.S. Department of Transportation, FHWA RD-97-104, 2003.
   Google Scholar
• P. J. Bosscher , H. U. Bahia , S. Thomas , and J. S. Russell , Relationship between Pavement Temperature and Weather Data: Wisconsin Field Study to Verify Superpave Algorithm , Transp. Res. Record: J. of the Transp. Res. Board , vol. 1609/1998 , pp. 1 – 11 , 2007 .
   Google Scholar
• A. Mohseni and S. Carpenter , Development of Enhanced Algorithm for Superpave High Temperature Performance Grade (PG) Selection and New Software Version, Long-Term Pavement Performance Group, FHWA, 2004.
   Google Scholar
• H. S. Carslaw and J. C. Jaeger , Conduction of Heat in Solids, , 2nd ed. , pp. 319 – 326 , Oxford University Press , London , 1959 .
   Google Scholar
• M. V. Griffith and G. K. Horton , The Transient Flow of Heat through a Two-Layer Wall , Proc. Phys. Soc. 58 , pp. 481 – 487 , 1946 .
   Google Scholar
• W. Chester , R. Bobone , and E. Brocher , Transient Conduction through a Two-Layer Medium , Int. J. Heat Mass Transfer , vol. 27 , pp. 2167 – 2170 , 1984 .
   Google Scholar
• C. W. Tittle , Boundary Value Problems in Composite Media , J. Appl. Phys. , vol. 36 , pp. 1486 – 1488 , 1965 .
   Google Scholar
• G. P. Mulholland and M. M. Cobble , Diffusion through Composite Media , Int. J. Heat Mass Transfer , vol. 15 , pp. 147 – 160 , 1972 .
   Web of Science ®Google Scholar
• H. Salt , Transient Conduction in a Two-Dimensional Slab, I. Theoretical Development of Temperature Modes , Int. J. Heat Mass Transfer , vol. 26 , pp. 1611 – 1616 , 1983 .
   Web of Science ®Google Scholar
• L. Feijo , H. T. Davis , and D. Ramkrishna , Heat Transfer in Composite Solids with Heat Generation , J. Heat Trans. , vol. 101 , pp. 137 – 143 , 1979 .
   Google Scholar
• S. C. Huang and Y. P. Chang , Heat Conduction in Unsteady, Periodic and Steady States in Laminated Composites , J. Heat Trans. , vol. 102 , pp. 742 – 748 , 1980 .
   Google Scholar
• C. Yavyzturk and K. Ksaibati , Assessment of Temperature Fluctuations in Asphalt Pavements due to Thermal Environmental Conditions Using a Two-Dimensional Transient Finite Difference Approach, MPC Report No. 02-136, October, 2002 .
   Google Scholar
• A. K. Schindler , J. M. Ruiz , R. O. Rasmussen , G. K. Chang , and L. G. Wathne , Concrete Pavement Temperature Prediction and Case Studies with the FHWA HIPERPAV Models, Cement and Concrete Composites , vol. 26, pp. 463–471, 2004.
   Web of Science ®Google Scholar
• R. E. Beckett and S. C. Chu , Finite Element Method Applied to Heat Conduction in Solids with Nonlinear Boundary Conditions , J. Heat Trans. , vol. 95 , pp. 126 – 129 , 1973 .
   Web of Science ®Google Scholar
• S. Sugiyama , M. Nishimura , and H. Watanabe , Transient Temperature Response of Composite Solids , Int. J. Heat Mass Transfer , vol. 17 , pp. 875 – 883 , 1974 .
   Google Scholar
• B. S. Reddy , The Transient Heat Transfer Analysis of Solids with Radiative Boundary Condition Using the Finite Element Analysis , Int. Commun. Heat Mass Trans. , vol. 12 , pp. 169 – 178 , 1985 .
   Google Scholar
• L. Yuanming , Z. Shujuan , and M. Long , Effect of Climatic Warming on the Temperature Fields of Embankments in Cold Regions and a Countermeasure , Numeri. Heat Transfer A , vol. 45 , pp. 191 – 210 , 2004 .
   Web of Science ®Google Scholar
• R. L. Lytton , D. E. Pufahl , H. S. Michalak , H. S. Liang , and B. J. Dempsey , An Integrated Model of the Climatic Effects on Pavements, Texas Transp. Inst., College Station, Report No. FHWA-RD-90-033, Mclean, 1990.
   Google Scholar
• G. Larson and B. Dempsey , ICM Software. Enhanced Integrated Climatic Model Version 2.0 (ICM), The University of Illinois, Urbana, Illinois, 1997.
   Google Scholar
• H. T. Chen , T. M. Chen , and C. K. Chen , Hybrid Laplace Transform/Finite Element Method for One Dimensional Transient Heat Conduction Problems , Comput. Meth. Appl. Mech. Eng. , vol. 63 , pp. 83 – 95 , 1986 .
   Google Scholar
• H. T. Chen and C. K. Chen , Hybrid Laplace Transform/Finite Element Method for Two-Dimensional Transient Heat Conduction , J. Thermophys. Heat Trans. , vol. 2 , pp. 31 – 36 , 1988 .
   Google Scholar
• H. T. Chen and J. Y. Lin , Application of the Hybrid Method to Transient Heat Conduction in One-Dimensional Composite Layers , Comp. & Structures , vol. 39 , pp. 451 – 458 , 1991 .
   Google Scholar
• L. C. Wroble and C. A. Brebbia , A Formulation of the Boundary Element Method for Asisymmetric Transient Heat Conduction , Int. J. Heat Mass Transfer , vol. 24 , pp. 843 – 850 , 1981 .
   Google Scholar
• M. Heydarian , N. Mullineux , and J. Reed , Solution of Parabolic Partial Differential Equations , Appl. Math. Model. , vol. 5 , pp. 448 – 449 , 1981 .
   Google Scholar
• P. O. Beyer , H. A. Vielmo , and M. T. Vilhena , Estudo Comparativo entre Soluç[otilde]es para a Transferência de Calor em Paredes Multicompostas, XIII Congresso Brasileiro e II Congresso Ibero – Americano de Engenharia Mecânica, Belo Horizonte, Brazil, 1995.
   Google Scholar
• I. B. Aseka , M. T. Vilhena , and P. O. Beyer , Solução da Equação de Condução do Calor Bidimensional, Não-Estacionária, em um Meio Constituído de Quatro Camadas, 10th Brazilian Congress of Thermal Sciences and Engineering – ENCIT, Rio de Janeiro, Brazil, Braz. Soc. Mechanical Sciences and Engineering, ABCM, 2004.
   Google Scholar
• M. B. Couto , Introdução à Radiação Solar, PROMEC, The Federal University of Rio Grande do Sul, Porto Alegre, Brazil, 1995.
   Google Scholar
• J. L. Threlkeld , Thermal Enviromental Engineering, , 2nd ed. , Prentice-Hall Inc. , Englewood Cliffs , New Jersey , 1970 .
   Google Scholar
• R. K. Wolfe , G. L. Heath , and D. C. Colony , Cooling Curve Prediction of Asphaltic Concrete , J. Transp. Eng., ASCE , vol. 109 , pp. 137 – 147 , 1983 .
   Google Scholar
• L. Hellmann , Determination of Thermal Properties of Pavement Materials, Master Paper, The Northwest Regional University of South Rio Grande State, Ijui, Rio Grande do Sul, Brazil, 2008.
   Google Scholar