6. Conclusions
An improved two-dimensional finite difference model is presented that is capable of determining the temperatures and thermally induced stresses on an hour-by-hour basis at any arbitrary point in an asphalt pavement. The model considers thermal ambient conditions such as the ambient dry bulb temperature, global solar radiation intensity, detailed pavement geometry and orientation, ambient wind conditions, effects of precipitation and pavement thermal properties. Following conclusions may be drawn from the analyses presented:
- The numerical model presented provides a powerful tool in determining pavement thermal behavior. The model allows for an hour-by-hour calculation of the pavement thermal response in the form of pavement temperatures and stresses using primary weather data for varying asphalt materials. The various lifts of asphalt materials can be entered into the model approximating layer geometry in 25mm grid increments in the direction normal to the asphalt surface through specification of thermal properties of asphalt materials (thermal conductivity, volumetric specific heat capacity and emissivity). This allows for the determination of temperature responses and thermal stresses at different lifts. In addition, the model allows for the specification of different asphalt materials in the horizontal direction. Thus, it is possible to define varying materials in each highway lane as well as in different lifts. This is a significant improvement over Superpave algorithms that were developed using analytical curve fitting techniques based on observed asphalt performance data.
- The numerical model predictions (temperatures and thermal stresses) are strongly dependent on climate data in addition to accurate knowledge of the thermal properties of pavement materials and pavement geometry.
- Pavement tilt angle can have a significant impact on top surface temperature. Depending on the surface azimuth, temperatures on a tilted surface will be seasonally higher or lower than temperatures on a horizontal surface.
- Precipitation and evaporation have a significant cooling effect on the pavement surface temperatures.
- Thermal stresses in asphalt pavements are significantly impacted by the thermal properties of pavement materials, specifically the thermal conductivity of asphalt layers. From the simulation results, it was observed that lower thermal stresses occur in the pavement when higher thermal conductivity layers are placed at the pavement top surface.
For the stress estimation model to be of practical use, stiffness modulii and tensile stresses of the asphalt must be known. These data are highly sample-specific, strongly depending on the bitumen content of the asphalt, and are difficult to obtain. In some cases, it may not be practical to measure these parameters, and therefore the model results are only as good as the estimates of the parameters.
7. Recommendations for Further Work
The following recommendations are made for further research in order to improve numerical model predictions to determine the maximum and minimum asphalt temperatures using local typical meteorological year weather data. Note that a number of the recommendations made in phase I of this project (Yavuzturk and Ksaibati, 2002) are reinforced below:
- Further improvements to the two-dimensional numerical model are of interest through additional field validations using high quality weather and pavement data. This may be accomplished through a specially designed and instrumented pavement segment with a fully dedicated weather station nearby that would reflect the true ambient thermal conditions the pavement is exposed to. A dedicated weather station coupled with a specially designed test segment would allow for a more reliable field validation of pavement temperature and thermal stress predictions.
- The numerical model may be further expanded to apply to pavements on bridge decks where an adiabatic bottom surface cannot be assumed due to convective cooling of the exposed bottom of the bridge deck. This convective cooling is primarily responsible for bridge deck icing during seasons when low ambient air temperatures are encountered along with high wind conditions.
- The two-dimensional finite difference model may be expanded to the third dimension so that temperature changes can be assessed between pavement segments along the length of the pavement. A three-dimensional modeling would also allow for the accurate assessment of pavements including pavement thermal responses at bankments and slopes.
- In cold climates, the effects of snow cover and freezing rain on pavement surfaces as well as freezing inside the asphalt material due to water seepage (varying moisture content of the pavement slab) impact the maximum and minimum asphalt temperatures considerably. The snow cover typically has an insulating effect on the surface reducing the amount of convective heat losses through the pavement. Although a significant step has been taken with this research to assess thermally induced stresses in pavements, the numerical model may be further expanded to include the effects of snow and mushy zones for a more realistic prediction of pavement temperatures allowing for more accurate and reliable pavement designs.
- A graphical user interface that utilizes Windows programming techniques may be of interest for easy use by field engineers so that changes can be entered by the user on-the-fly without reliance on special programming tools.
8. References and Bibliography
- Adkins, D.F. and G.P. Merkley. 1990. Mathematical model of temperature changes in concrete pavements. Journal of Transportation Engineering, 116, 3: 349-358.
- Anderson, D.A., L. Lapalu, M.O. Marasteanu, Y.M. Le Hir, J.P. Planche, and D. Martin. 2001. Low-temperature thermal cracking of asphalt binders as ranked by strength and fracture properties. Transportation Research Record, 1766: 1-6.
- Ali, H.A. and A. Lopez. 1996. Statistical analyses of temperature and moisture effects on pavement structural properties based on seasonal monitoring data. Transportation Research Record, 1540: 48-55.
- ASHRAE, 2001. ASHRAE Handbook, Fundamantals. American Society of Heating, Refrigeration and Air-Conditioning Engineers, Inc., Atlanta, GA.
- van Bijsterveld, W.T., L.J.M. Houben, A. Scarpas, and A.A.A. Molenaar. 2001. Using pavement as solar collector - effect on pavement temperature and structural response. Transportation Research Record, 1778: 140-148.
- Branco, F.A. and P.A. Mendes. 1993. Thermal actions for concrete bridge design. Journal of Structural Engineering, 119, 8: 2313-2331.
- Boutin, G. and C. Lupien, 2000. Thermal Cracking of Asphalt Pavement. Proceedings of the 2nd Eurasphalt & Eurobitume Congress, Barcelona, Book II, pp. 45-59.
- Bouzoubaa, N, M. Lachemi, B.Miao, and P.C. Aitcin. 1997. Thermal damage of mass concrete: experimental and numerical studies on the effect of external temperature variations. Canadian Journal of Civil Engineering, 24: 649-657.
- Bliss, R.W., 1961. Atmospheric Radiation Near the Surface of the Ground. Solar Energy, 5(103).
- Chandra, D., K.M. Chua, and R.L. Lytton. 1989. Effect of temperature on the load response of granular base course material in thin pavements. Transportation Research Record, 1252: 33-41.
- Choubane, B. and M. Tia. 1995. Analysis and verification of thermal-gradient effects on concrete pavement. Journal of Transportation Engineering, 121, 1: 75-81.
- Deacon, J.A., J.S. Coplantz, A.A. Tayebali, and C.L. Monismith. 1994. Temperature considerations in asphalt-aggregate mixture analysis and design. Transportation Research Record, 1454: 97-112.
- Duffie, J.A. and W.A. Beckman, 1991. Solar Engineering of Thermal Processes, 2nd Edition. John Wiley and Sons.
- Harik, I.E., P. Jianping, H. Southgate, and D. Allen. 1994. Temperature effects on rigid pavements. Journal of Transportation Engineering, 120, 1: 127-143.
- Hermansson, A. 2000. Simulation model for calculating pavement temperature including maximum temperature. Transportation Research Record, 1699: 134-141.
- Hermansson, A. 2001. Mathematical model for calculation of pavement temperatures. Transportation Research Record, 1764: 180-188.
- Hills, J.F., 1974. Predicting the fracture of asphalt mixes by thermal stress. Institute of Petroleum.
- Inge, E.H. and Y.R. Kim. 1995. Prediction of effective asphalt layer temperature. Transportation Research Record, 1473: 93-100.
- Irvine, T.F. Jr. and Liley, P.E., 1984, Steam and Gas Tables with Computer Equations, Academic Press, Inc.
- Ioannides, A.M. and L. Khazanovich. 1998. Nonlinear temperature effects on multilayered concrete pavements. Journal of Transportation Engineering, 124, 2: 128-136.
- Jung, D. and T.S. Vinson. 1993. Thermal stress restrained specimen test to evaluate low-temperature cracking of asphalt-aggregate mixtures. Transportation Research Record, 1417.
- Kapila, D., J. Falkowsky, and J.L. Plawsky. 1997. Thermal effects during the curing of concrete pavements. ACI Materials Journal, 94, 2: 119-128.
- Kim, N. R. Roque, and D. Hiltunen. 1994. Effect of moisture on low-temperature asphalt mixture properties and thermal-cracking performance of pavements. Transportation Research Record, 1454: 82-88.
- Kuo, C.M. 1998. Effective temperature differential in concrete pavements. Journal of Transportation Engineering, 124, 2: 112-116.
- Liang, R.Y. and Y.Z. Niu. 1998. Temperature and curling stress in concrete pavements: analytical solutions. Journal of Transportation Engineering, 124, 1: 91-100.
- Liao, C.J. and T.D. Hogue. 1996. Thermal stress predictions for geothermally heated bridge decks. Oklahoma State University; prepared for State of Oklahoma, Department of Transportation, 44 p.
- Marrero, T.R. and E.A.Mason, 1972. Gaseous Diffusion Coefficients. Journal of Physical and Chemical Reference Data. 1: 3-118.
- Marshall, C., R. Meier, M. Welch. 2001. Seasonal temperature effects on flexible pavements in Tennessee. Transportation Research Record, 1764: 89-96.
- Masad, E., R. Taha, and B. Muhunthan. 1996. Finite-element analysis of temperature effects on plain-jointed concrete pavements. Journal of Transportation Engineering, 122, 5: 388-398.
- Mills, A.F., 1995. Basic Heat and Mass Transfer. Prentice Hall.
- Nishizawa, T, S. Shimeno, A. Komatsubara, and M. Koyanagawa. 1998. Study on thermal stresses in continuously reinforced concrete pavement. Transportation Research Record, 1629: 99-107.
- Pane, I., W. Hansen, and A.R. Mohamed. 1998. Three-dimensional finite element study on effects of nonlinear temperature gradients in concrete pavements. Transportation Research Record, 1629: 58-66.
- Park, D.Y., N. Buch, and K. Chatti. 2001. Effective layer temperature prediction model and temperature correction via falling weight deflectometer deflections. Transportation Research Record, 1764: 97-111.
- Raad, L., S. Saboundjian, P. Sebaaly, and J. Epps. 1998. Thermal cracking models for AC and modified mixes in Alaska. Transportation Research Record, 1629: 117-126.
- Rao, D.S.P. 1986. Temperature distributions and stresses in concrete bridges. ACI Journal, 83, 4: 588-596.
- Rees, S.J., J.D. Spitler, and X. Xiao. 2002. Transient analysis of snow-melting system performance. ASHRAE Transactions, 108, 2: 406-423.
- Roeder, C.W. and Moorty, S. 1991. Thermal movements in bridges. Transportation Research Record, 1290: 135-143.
- Schindler, A.K. and B. McCullough. 2002. Importance of concrete temperature control during concrete pavement construction in hot weather conditions. Transportation Research Record, 1813: 3-10.
- Shalaby, A., A.O. Abd El Halim, and S.M. Easa. 1996. Low-temperature stresses and fracture analysis of asphalt overlays. Transportation Research Record, 1539: 132-139.
- Shen, W and D.J. Kirkner, 2001. Thermal Cracking of Viscoelastic Asphalt-Concrete Pavement. Journal of Engineering Mechanics, Vol. 127, No. 7, pp. 700-709.
- Solaimanian, M. and T.W. Kennedy. 1993. Predicting maximum pavement surface temperature using maximum air temperature and hourly solar radiation. Transportation Research Record, 1417: 1-11.
- Spencer, J.W., 1971. Fourier Series Representation of the Position of the Sun. Search, 2(5).
- Stoffels, S.M., W.R. Lauritzen, and R. Roque. 1993. Temperature estimation for low-temperature cracking of asphalt concrete. Transportation Research Record, 1417: 158-167.
- Tart, R.G. 2000. Pavement distress and roadway damage caused by subsurface moisture and freezing temperatures - case histories from Alaska. Transportation Research Record, 1709: 91-97.
- Tinker, J.A. and J.G. Cabrera. 1992. Modeling the thermal conductivity of concrete based on its measured density and porosity. In Thermal Performance of the Exterior Envelopes of Buildings V; Proceedings of the ASHRAE/DOE/BTECC Conference, Clearwater Beach, FL: 91-95.
- Yoder, E.J. and M.W. Witczak, 1975. Principles of Pavement Design, 2nd Edition. John Wiley and Sons.
- Yu, H.T., L. Khazanovich, M.I. Darter, and A. Ardani. 1998. Analysis of concrete pavement responses to temperature and wheel loads measured from instrumented slabs. Transportation Research Record, 1639: 94-101.
- Zuk, W. 1965. Thermal behavior of composite bridges - insulated and uninsulated. Highway Research Record, 76: 231-.