DEVELOPMENT AND VALIDATION OF A MODEL TO PREDICT PAVEMENT TEMPERATURE PROFILE

Transcription

1 Diefenderfer,Al-Qadi,Reubush,andFreeman DEVELOPMENT AND VALIDATION OF A MODEL TO PREDICT PAVEMENT TEMPERATURE PROFILE Brian K. Diefenderfer Project Manager Concorr, Inc Oakbrook Court, Suite 160 Sterling, VA bdief@concorr.com Phone: Fax: Imad L. Al-Qadi Charles E. Via, Jr. Professor of Civil and Environmental Engineering Via Department of Civil and Environmental Engineering and Virginia Tech Transportation Institute 3500 Transportation Research Plaza Blacksburg, VA alqadi@vt.edu Phone: Fax: Stacey D. Reubush Graduate Research Assistant Via Department of Civil and Environmental Engineering and Virginia Tech Transportation Institute 3500 Transportation Research Plaza Blacksburg, VA doodle@vt.edu Phone: Fax: Thomas E. Freeman Senior Research Scientist Virginia Transportation Research Council, VDOT, 530 Edgemont Road Charlottesville, VA Tom.Freeman@viginiadot.org Phone: Fax: Submission Date: August 1, 2002 Word Count: 3256 words + 10 figures + 1 table

2 Diefenderfer,Al-Qadi,Reubush,andFreeman 1 PREDICTION OF DAILY TEMPERATURE PROFILE IN FLEXIBLE PAVEMENTS AT MULTIPLE LOCATIONS USING LTPP DATA ABSTRACT Flexible pavements comprise a majority of the primary highways in the United States. These primary roads are subjected to heavy loading that can cause significant damage to the hot-mix asphalt (HMA) pavements. As HMA is a viscoelastic material, the structural or load-carrying capacity of the pavement varies with temperature. Thus, to determine in-situ strength characteristics of flexible pavement, it is necessary to predict the temperature distribution within the HMA layers. The majority of previously published research on pavement temperature prediction has consisted of predicting the annual maximum or minimum pavement temperature so as to recommend a suitable asphalt binder performance grade. To determine the pavement temperature profile, the influence of ambient temperature and seasonal changes must be understood such that the effects of heating and cooling trends within the pavement structure can be quantified. Recent investigations have shown that it is possible to model daily pavement maxima and minima temperature by knowing the maximum or minimum ambient temperatures, the depth at which the pavement temperature is desired, and the day of year at a particular location. This paper extends that model to incorporate either the calculated daily solar radiation or latitude such that the model can be applied to any location. The suggested location independent model was successfully validated utilizing data from the Virginia Smart Road and two LTPP-SMP sites.

3 Diefenderfer,Al-Qadi,Reubush,andFreeman 2 INTRODUCTION Characterization of the in-situ strength performance of roadways constructed using HMA is difficult due to the nature of the material. Hot-mix asphalt is a viscoelastic material; that is, it exhibits the properties of both a viscous and an elastic material. At low temperatures, HMA acts as an elastic solid in which low amounts of applied strain are recoverable; thus, permanent deformation is not likely to occur until this low strain limit is surpassed. However, at high temperatures, HMA acts as a viscous fluid in which the material begins to flow with an applied strain. The temperature within a pavement varies due to several factors including ambient temperature, solar radiation, wind speed, and reflectance of the pavement surface. Thus, to study the difference in strength characteristics of various pavement designs, it is imperative to know the temperature distribution within the pavement cross-section. Testing at the Virginia Smart Road was conducted in an effort to construct models for temperature prediction within the HMA layers of various pavement cross-sections. Virginia Smart Road The Virginia Smart Road, in Blacksburg, Virginia, was constructed as a testing facility for various types of transportation related technologies. Included in this facility are instrumented pavement test sections. The pavement test facility is approximately 2.7km in length, of which 1.3km is flexible pavement. The flexible pavement is divided into 12 sections of approximately 100m each. Each flexible pavement test section is comprised of a multi-layer pavement system and possesses a unique structural configuration. Each layer in each section is instrumented to measure quantitative pavement responses to traffic loading and environmental conditions. In total, more than 500 instruments were installed as the pavement was constructed. Therefore, it is believed that the Virginia Smart Road provides a more realistic representation of the in-situ properties than existing pavements that have been retrofitted with instruments. At the Virginia Smart Road, thermocouples were chosen to monitor the temperature of the pavement sections. The thermocouples were fabricated in-house, and a total of 115 were installed across all 12 sections with depths ranging from to 1.12m from the pavement surface. Additional details of the testing program at the Virginia Smart Road can be found in Al-Qadi et al. (1). Pavement Temperature Prediction Barber (2) was among the first researchers to discuss the calculation of maximum pavement temperatures based on weather reports. However, his model incorporates a total daily radiation factor instead of a more accurate measure such as hourly radiation. Rumney and Jimenez (3) developed nomographs to predict pavement temperatures at the surface and at a depth of 50mm. The collected data included pavement temperature and hourly solar radiation. A simulation model based on the theory of heat transfer and energy balance at the pavement surface was later developed by Dempsey (4). Until the initiation of the Long-Term Pavement Performance (LTPP) program, there was little information present in the general literature on this topic. The Strategic Highway Research Program (SHRP) established the LTPP program in 1987 as a 20-year study to better characterize the in-situ performance of pavements. Approximately 2,500 sites throughout North America were selected to represent a broad range of pavement types and climatic conditions. To specifically deal with the challenges of studying climatic conditions, 61 LTPP sites were selected to become part of the Seasonal Monitoring Program (SMP). The 1994 SMP research was designed to measure and evaluate the effects of temperature and moisture variations on pavement performance; thus making it possible to monitor the appropriateness of the varying Superpave mixture designs (5). From the initial SHRP testing and the more recent SMP data, pavement temperature models were developed to assist with the selection of the proper asphalt binder performance grade for usage in a particular location (6, 7, 8, 9). Solaimanian and Kennedy (10) present an analytical approach to predict pavement temperatures by employing heat and energy transfer theory. Regression based models using other data sets were presented by Bosscher et al. (9), Marshall et al. (11), and Park et al. (12). A computer simulation model that predicts summertime pavement temperatures based on the theoretical heat transfer models given in Solaimanian and Kennedy (10) was recently presented by Hermansson (13, 14).

4 Diefenderfer,Al-Qadi,Reubush,andFreeman 3 Although many researchers have studied temperature distribution within a pavement, most of the previous work has primarily focused on determining yearly maximum and minimum pavement temperatures for the purpose of binder selection; very few studies have discussed daily pavement temperature prediction. Only recently (11, 12, 13, 14) have efforts been presented to predict pavement temperatures on a smaller time scale. A recent study (15), using regression models based on data obtained at the Virginia Smart Road, has shown that daily maximum or minimum pavement temperatures can be predicted given the daily maximum or minimum ambient temperatures, day of year, and depth at which the pavement temperature is desired. These models have also been shown to be independent of the particular asphalt mixtures utilized in the pavement. This paper describes research performed to extend these models for use in other locations by replacing the day of year variable with the received daily solar radiation calculated for any location. PAVEMENT TEMPERATURE MONITORING AT THE VIRGINIA SMART ROAD Daily Temperature Prediction Models Several linear models were developed for predicting daily maximum and minimum temperatures based on data collected at the Virginia Smart Road. Data was used from three depths within the pavement for model development: 0.038, 0.063, and 0.188m below the surface. All three depths were located within HMA layers. Additional description of the development of pavement prediction models based on data collected at the Virginia Smart Road can be found in Diefenderfer et al. (15). The basic form of the temperature prediction model presented within this study is expressed as follows: T p =a+bt m +cy+dp d (1) where T p = predicted pavement temperature ( C); a = intercept coefficient; b = ambient temperature coefficient; T m = measured ambient temperature ( C); c = day of year coefficient; Y = day of year (1 to 183); d = depth coefficient; and P d = depth within the pavement (m). Given the depths of temperature measurement upon which the above model was developed, the maximum depth considered in this study is 0.188m below the pavement surface. The daily ambient temperatures were obtained for the Blacksburg Municipal Airport (BCB) from the National Virtual Climatic Data section within the National Oceanographic and Atmospheric Administration (NOAA) website. The Blacksburg Municipal Airport is a second order weather station, approximately 1.7km from the Virginia Smart Road, and thus only daily (and not hourly) ambient temperatures were available for this station. As there is currently no weather station at the Virginia Smart Road, the National Virtual Climatic Data website was the only known source for this information. The day of year coefficient was introduced as a method to differentiate between seasonal temperature variations. The day of year coefficient increases linearly each day from the first day of the year through day 183 (January 1 to July 2), and decreases linearly from day 182 through the end of the year (July 3 to December 31) depending on which day the daily pavement temperature is desired. One day is added to the range of the values during a leap year. The day of year variable was utilized in the early stages of model development as a substitute for solar radiation.

5 Diefenderfer,Al-Qadi,Reubush,andFreeman 4 Following the form of Equation 1, separate models were developed to express the linear relationship between maximum and minimum ambient and pavement temperatures based on data collected at the Virginia Smart Road from February 2000 through May The model developed to predict maximum daily pavement temperatures, T pmax,isasfollows: T pmax = T max Y P d (2) The RMSE for this model is 3.54 and the adjusted R 2 value is 91.36%. The model developed to predict minimum daily pavement temperatures, T pmin,isasfollows: T pmin = T min Y P d (3) The RMSE for this model is 2.79 and the adjusted R 2 was found to be 91.41%. These values indicate that the model for predicting the minimum daily pavement temperature is slightly more accurate than the model for predicting the maximum daily pavement temperature. The models presented in Equations 2 and 3 were evaluated using temperature data from the Virginia Smart Road for the dates of July 1, 2001 through December 31, This time period offers temperature data that is outside the original data set used to create the models in Equations 2 and 3. The evaluation RMSE and adjusted R 2 values were calculated as 3.76 and 90.25%, respectively, for the maximum daily pavement temperature model. The evaluation RMSE and adjusted R 2 values for the minimum daily pavement temperature model were calculated as 3.15 and 89.95%, respectively. Figure 1 presents the actual maximum daily pavement temperature and the predicted maximum daily pavement temperature at a depth of 0.038m for this model validation time period. Figure 2 presents the actual minimum daily pavement temperature and the predicted minimum daily pavement temperature at a depth of 0.038m for this model validation time period. The RMSE and correlation coefficient values show that Equations 2 and 3 can accurately predict the pavement temperature at the Virginia Smart Road using data outside the original dataset. Daily Temperature Prediction Models Incorporating Calculated Solar Radiation While the models presented in Equations 2 and 3 can accurately predict the maximum and minimum daily pavement temperatures at the Virginia Smart Road, these models cannot accurately predict pavement temperatures at other locations. This is because the incoming solar radiation, expressed in Equations 2 and 3 through the day of year variable, varies with location (i.e., with respect to latitude) and affects the resulting pavement temperature. One reason for this variation is that as the earth traverses its orbit around the sun, different locations on the planet receive varying amounts of solar radiation due to the tilt of the North/South Axis with respect to the orbital plane. This tilt is termed the solar declination. The declination is given as a positive value when the sun is in the northern latitudes and as a negative value when the sun is in the southern latitudes (16). At the vernal and autumnal equinoxes, the declination is zero. In addition, there are seasonal variations on the incoming solar radiation since the earth s orbit follows an elliptical path. The changing distance between the sun and the earth causes a daily variation in the solar radiation received at the earth s surface. An eccentricity factor expresses this variation in distance in terms of one astronomical unit (AU). One AU is equal to the mean distance between the earth and sun (1.496x10 8 km). In order to model the pavement temperature at other locations (designated by their respective latitude), these parameters must be calculated. The daily amount of solar radiation at any location on the earth can be determined using the latitude and day of the year. From these variables, the solar declination and eccentricity factor can be calculated and then used to determine the daily solar radiation (17). The eccentricity factor is given as: E 0 = cosΓ sin Γ cos2Γ sin 2Γ (4)

6 Diefenderfer,Al-Qadi,Reubush,andFreeman 5 where E 0= eccentricity factor; and Γ =dayangle(rad). The day angle is expressed as the following: Γ = ( d ) 2 1 π n 365 (5) where d n is the day number of the year ranging from 1 to 365. The final term used to calculate the daily solar radiation at a particular location is the sunrise hour angle. The hour angle is the angle between the sun s highest point each day (where the hour angle is zero) and the location of the sun at sunrise or sunset. At sunrise the hour angle is positive and at sunset the hour angle is negative. The sunrise hour angle is given as the following: ω = cos 1 tan s ( φ tanδ ) (6) where ω s = sunrise hour angle (degrees); φ = latitude (degrees); and δ = solar declination (degrees), and can be calculated as follows: cosΓ sin Γ cos2Γ δ = sin 2Γ cos3Γ sin 3Γ 180 π (7) From Equations 4 through 7, the daily solar radiation on a horizontal surface can be given as the following: 24 ω s π H 0 = I sc E0 sin( φ ) sin( δ ) tan( ω s ) (8) π 180 where H 0 = daily solar radiation on a horizontal surface (kj/m 2 day); and I SC = solar constant = 4871 kj/m 2 h. Table 1 gives an example of the difference in solar radiation values for four locations in the eastern United States at different times of the year. A second set of models was developed from the same dataset collected at the Virginia Smart Road that was used to develop Equations 2 and 3. The model to predict the maximum daily pavement temperature, utilizing the calculated daily solar radiation in place of the day of year, is given as follows: T psmax = T max x10-4 R s P d (9) where T psmax = predicted pavement temperature ( C); T max = maximum daily ambient temperature ( C);

7 Diefenderfer,Al-Qadi,Reubush,andFreeman 6 R s = calculated daily solar radiation (kj/m 2 day); and P d = depth from the surface (m). The RMSE and adjusted R 2 for this model were calculated to be 5.76 and 77.07%, respectively. The model to calculate the minimum daily pavement temperature, utilizing the calculated daily solar radiation in place of the day of year, is given as follows. T psmin = T min x10-4 R s P d (10) where T psmin = predicted pavement temperature ( C); T min = minimum daily ambient temperature ( C); R s = calculated daily solar radiation (kj/m 2 day); and P d = depth from the surface (m). The RMSE and adjusted R 2 for this model were calculated to be 4.28 and 79.79%, respectively. The models presented in Equations 9 and 10 were evaluated using an independent data set: pavement temperature data from the Virginia Smart Road from July 1, 2001 through December 31, This is the same data set used to evaluate Equations 2 and 3; the only difference being that the calculated solar radiation was included in place of the day of year variable. The evaluation RMSE and adjusted R 2 values were calculated as 4.15 and 87.14%, respectively, for the maximum daily pavement temperature model. The evaluation of the maximum pavement temperature model (Equation 9) and the actual pavement temperature at a depth of 0.038m are presented in Figure 3. The evaluation RMSE and adjusted R 2 values for the minimum daily pavement temperature model were calculated as 4.61 and 72.46%, respectively. The evaluation of the minimum temperature model (Equation 10) and the actual pavement temperature at a depth of 0.038m are presented in Figure 4. Validation of Daily Pavement Temperature Prediction Models Using LTPP-SMP Data Daily pavement and ambient temperature data for LTPP sites included in the SMP testing is readily available for numerous test sites in the United States and portions of Canada. To validate the daily pavement temperature models presented in Equations 9 and 10, two LTPP-SMP sites were randomly selected for inclusion in this study. The two selected LTPP-SMP test locations are test sites and LTPP test site is located in New London, CT at latitude N. The pavement is comprised of a 0.079m thick HMA surface layer, a 0.109m thick HMA base layer, and a third layer of compacted gravel. LTPP test site is located in Hall, TX at latitude N. The pavement is comprised of a 0.037m thick HMA surface layer, a 0.040m thick HMA base layer, and a layer of crushed stone. The models presented in Equations 9 and 10 were evaluated using the data from these LTPP test sites in an effort to validate the applicability of these models to multiple locations. The latitude of the LTPP test site, date, and maximum/minimum daily ambient temperatures were used in Equations 9 and 10 to predict the maximum/minimum daily pavement temperatures. The predicted maximum and minimum daily pavement temperatures were then compared to the measured maximum or minimum daily pavement temperatures for each site, respectively. Instrumentation to measure the pavement temperature at LTPP site in Connecticut was placed at depths of 0.025, 0.089, and 0.153m below the surface of the pavement. These three depths are located within the HMA layers of the pavement structure. The input data covered the period of January 21, 1994 through June 21, Analysis of the maximum daily pavement temperatures at LTPP site using Equation 9 yielded an adjusted R 2 and a RMSE of 82.39% and 5.25, respectively. Analysis of the minimum daily pavement temperatures at LTPP site using Equation 10 yielded an adjusted R 2 of 89.28% and a RMSE of 3.04, respectively. The actual pavement temperature at a depth of 0.025m

8 Diefenderfer,Al-Qadi,Reubush,andFreeman 7 versus the predicted temperature is shown in Figures 5 and 6 for maximum and minimum temperatures, respectively. Instrumentation to measure the pavement temperature at LTPP site in Texas was placed at depths of 0.025, 0.065, 0.105, and 0.182m below the pavement surface; all four levels were located within the HMA layers. The input data for this test section covered a period of January 1, 1994 through June 27, Analysis of the maximum daily pavement temperatures using Equation 9 yielded an adjusted R 2 and a RMSE of 90.41% and 4.12, respectively. Analysis of the minimum daily pavement temperatures using Equation 10 yielded an adjusted R 2 and a RMSE of 92.96% and 2.94, respectively. The actual pavement temperature at a depth of 0.025m versus the predicted temperature is shown in Figures 7 and 8 for maximum and minimum temperatures, respectively. Daily Pavement Temperature Prediction at Multiple Locations By incorporating data from the Virginia Smart Road and the two LTPP-SMP test locations, Equations 9 and 10 were rewritten to include the day of year (1-365) and the latitude in the model, as these are easily obtainable quantities. Including the day of year and the latitude in place of the solar radiation calculations will provide a simplified means of predicting the maximum or minimum daily pavement temperature. The model developed to predict the maximum daily pavement temperature including the day of year and latitude is given as follows: T plmax = T max Y d L P d (11) where T plmax = predicted pavement temperature ( C); T max = maximum daily ambient temperature ( C); Y d = day of year (1 to 365); L = latitude (degrees); and P d = depth from surface (m). The RMSE and adjusted R 2 for this model were calculated to be 5.88 and 79.36%, respectively. Figure 9 presents the actual pavement temperature at a 0.038m depth from the Virginia Smart Road and the predicted temperature from Equation 11. The model developed to predict the minimum daily pavement temperature including the day of year and latitude is given as follows: T plmin = T min Y d L P d (12) where T plmin = predicted pavement temperature ( C); T min = minimum daily ambient temperature ( C); Y d = day of year (1 to 365); L = latitude (degrees); and P d = depth from surface (m). The RMSE and adjusted R 2 for this model were calculated to be 3.59 and 86.63%, respectively. Figure 10 presents the actual pavement temperature at a 0.038m depth from the Virginia Smart Road and the predicted temperature from Equation 12. CONCLUSIONS Accurate models for predicting the maximum and minimum daily pavement temperatures were developed and validated using data from the Virginia Smart Road and two LTPP-SMP test sites. Two sets of models were developed: the first incorporates the depth within the pavement, calculated daily solar radiation, and maximum or minimum daily ambient temperature:

9 Diefenderfer,Al-Qadi,Reubush,andFreeman 8 T psmax = T max x10-4 R s P d T psmin = T min x10-4 R s P d (maximum temperature) (minimum temperature) A second set of more practical models was developed to include the depth within the pavement, latitude of the location in question, day of the year, and the maximum or minimum daily ambient temperature. This model is expressed as follows: T plmax = T max Y d L P d T plmin = T min Y d L P d (maximum temperature) (minimum temperature) ACKNOWLEDGEMENTS This research is part of the Virginia Smart Road Pavement Research Project sponsored by the Virginia Transportation Research Council and the Virginia Department of Transportation. The assistance of Amara Loulizi, Samer Lahouar, and the Virginia Department of Transportation personnel is greatly appreciated. REFERENCES 1) Al-Qadi, I. L., W. M. Nassar, A. Loulizi, G. W. Flintsch, and T. Freeman. Flexible Pavement Instrumentation at the Virginia Smart Road. Presented at 79 th Transportation Research Board Annual Meeting, Washington, DC, January ) Barber, E. S. Calculation of Maximum Pavement Temperatures from Weather Reports. Bulletin 168, Highway Research Board, National Research Council, 1957, pp ) Rumney, T. N. and R. A. Jimenez. Pavement Temperatures in the Southwest. Highway Research Record No. 361, National Research Council, 1969, pp ) Dempsey, B. J. A Heat Transfer Model for Evaluating Frost Action and Temperature Related Effects in Multilayered Pavement Systems. Highway Research Record No. 342, National Research Council, 1970, pp ) Ali, H. and A. Lopez. Statistical Analysis of Temperature and Moisture Effects on Pavement Structural Properties Based on Seasonal Monitoring Data. Transportation Research Record 1540, TRB, National Research Council, Washington, DC, 1996, pp ) Mohseni, A. and M. Symons. Improved AC Pavement Temperature Models from LTPP Seasonal Data. Presented at Transportation Research Board 77 th Annual Meeting, Washington, DC, January ) Mohseni, A. and M. Symons. Effect of Improved LTPP AC Pavement Temperature Models on SuperPave Performance Grades. Presented at Transportation Research Board 77 th Annual Meeting, Washington, DC, January ) Lukanen, E. O., C. Han, and E. L. Skok, Jr. Probabilistic Method of Asphalt Binder Selection Based on Pavement Temperature. Transportation Research Record 1609, TRB, National Research Council, Washington, DC, 1998, pp ) Bosscher, P. J., H. U. Bahia, S. Thomas, and J. S. Russell. Relationship Between Pavement Temperature and Weather Data: Wisconsin Field Study to Verify SuperPave Algorithm. Transportation Research Record 1609, TRB, National Research Council, Washington, DC, 1998, pp ) Solaimanian, M. and T. W. Kennedy. Predicting Maximum Pavement Surface Temperature Using Maximum Air Temperature and Hourly Solar Radiation. Transportation Research Record 1417, TRB, National Research Council, Washington, DC, 1993, pp ) Marshall, C., R. W. Meier, and M. Welsh. Seasonal Temperature Effects on Flexible Pavements in Tennessee. Presented at Transportation Research Board 80 th Annual Meeting, Washington, DC, January 2001.

10 Diefenderfer,Al-Qadi,Reubush,andFreeman 9 12) Park, D., N. Buch, and K. Chatti. Development of Effective Layer Temperature Prediction Model and Temperature Correction Using FWD Deflections. Presented at Transportation Research Board 80 th Annual Meeting, Washington, DC, January ) Hermansson, A. Simulation Model for Calculating Pavement Temperatures, Including Maximum Temperature. Transportation Research Record 1699, TRB, National Research Council, Washington, DC, 2000, pp ) Hermansson, A. A Mathematical Model for Calculating Pavement Temperatures, Comparisons Between Calculated and Measured Temperatures. Presented at Transportation Research Board 80 th Annual Meeting, Washington, DC, January ) Diefenderfer, B. K., I. L. Al-Qadi, and S. D. Reubush. Prediction of Daily Temperature Profile in Flexible Pavements. Presented at Transportation Research Board 81 st Annual Meeting, Washington, DC, January ) Anderson, E. E. Fundamentals of Solar Energy Conversion. Addison-Wesley Publishing Co., Reading, MA, ) Iqbal, M. An Introduction to Solar Radiation. Academic Press, New York, NY, 1983.

11 Diefenderfer,Al-Qadi,Reubush,andFreeman 10 LIST OF FIGURES FIGURE 1. Maximum Daily Pavement Temperature Utilizing Day of Year at 0.038m Depth Showing Actual Versus Predicted for Virginia Smart Road. FIGURE 2. Minimum Daily Pavement Temperature Utilizing Day of Year at 0.038m Depth Showing Actual Versus Predicted for Virginia Smart Road. FIGURE 3. Maximum Daily Pavement Temperature Utilizing Solar Radiation at 0.038m Depth Showing Actual Versus Predicted for Virginia Smart Road. FIGURE 4. Minimum Daily Pavement Temperature Utilizing Solar Radiation at 0.038m Depth Showing Actual Versus Predicted for Virginia Smart Road. FIGURE 5. Maximum Daily Pavement Temperature at 0.025m Depth Showing Actual Versus Predicted for LTPP Site (CT). FIGURE 6. Minimum Daily Pavement Temperature at 0.025m Depth Showing Actual Versus Predicted for LTPP Site (CT). FIGURE 7. Maximum Daily Pavement Temperature at 0.025m Depth Showing Actual Versus Predicted for LTPP Site (TX). FIGURE 8. Minimum Daily Pavement Temperature at 0.025m Depth Showing Actual Versus Predicted for LTPP Site (TX). FIGURE 9. Maximum Daily Pavement Temperature Utilizing Latitude and Day of Year at 0.038m Depth Showing Actual Versus Predicted for Virginia Smart Road. FIGURE 10. Minimum Daily Pavement Temperature Utilizing Latitude and Day of Year at 0.038m Depth Showing Actual Versus Predicted for Virginia Smart Road. LIST OF TABLES TABLE 1. Daily solar radiation values for four locations in the eastern United States.

12 Diefenderfer,Al-Qadi,Reubush,andFreeman predict temperature ( C) /28/01 7/28/01 8/27/01 9/26/01 10/26/01 11/25/01 12/25/01 date FIGURE 1. Maximum Daily Pavement Temperature Utilizing Day of Year at 0.038m Depth Showing Actual Versus Predicted for Virginia Smart Road.

13 Diefenderfer,Al-Qadi,Reubush,andFreeman predict temperature ( C) /28/01 7/28/01 8/27/01 9/26/01 10/26/01 11/25/01 12/25/01 date FIGURE 2. Minimum Daily Pavement Temperature Utilizing Day of Year at 0.038m Depth Showing Actual Versus Predicted for Virginia Smart Road.

14 Diefenderfer,Al-Qadi,Reubush,andFreeman solar predict temperature ( C) /28/01 7/28/01 8/27/01 9/26/01 10/26/01 11/25/01 12/25/01 date FIGURE 3. Maximum Daily Pavement Temperature Utilizing Solar Radiation at 0.038m Depth Showing Actual Versus Predicted for Virginia Smart Road.

15 Diefenderfer,Al-Qadi,Reubush,andFreeman solar predict temperature ( C) /28/01 7/28/01 8/27/01 9/26/01 10/26/01 11/25/01 12/25/01 date FIGURE 4. Minimum Daily Pavement Temperature Utilizing Solar Radiation at 0.038m Depth Showing Actual Versus Predicted for Virginia Smart Road.

16 Diefenderfer,Al-Qadi,Reubush,andFreeman predict 40 temperature ( C) /17/93 3/17/94 6/15/94 9/13/94 12/12/94 3/12/95 6/10/95 date FIGURE 5. Maximum Daily Pavement Temperature at 0.025m Depth Showing Actual Versus Predicted for LTPP Site (CT).

17 Diefenderfer,Al-Qadi,Reubush,andFreeman predict 40 temperature ( C) /17/93 3/17/94 6/15/94 9/13/94 12/12/94 3/12/95 6/10/95 date FIGURE 6. Minimum Daily Pavement Temperature at 0.025m Depth Showing Actual Versus Predicted for LTPP Site (CT).

18 Diefenderfer,Al-Qadi,Reubush,andFreeman predict 50 temperature ( C) /22/93 1/16/94 2/10/94 3/7/94 4/1/94 4/26/94 5/21/94 6/15/94 7/10/94 date FIGURE 7. Maximum Daily Pavement Temperature at 0.025m Depth Showing Actual Versus Predicted for LTPP Site (TX).

19 Diefenderfer,Al-Qadi,Reubush,andFreeman predict 50 temperature ( C) /22/93 1/16/94 2/10/94 3/7/94 4/1/94 4/26/94 5/21/94 6/15/94 7/10/94 date FIGURE 8. Minimum Daily Pavement Temperature at 0.025m Depth Showing Actual Versus Predicted for LTPP Site (TX).

20 Diefenderfer,Al-Qadi,Reubush,andFreeman lat temperature ( C) /28/01 7/28/01 8/27/01 9/26/01 10/26/01 11/25/01 12/25/01 date FIGURE 9. Maximum Daily Pavement Temperature Utilizing Latitude and Day of Year at 0.038m Depth Showing Actual Versus Predicted for Virginia Smart Road.

21 Diefenderfer,Al-Qadi,Reubush,andFreeman lat temperature ( C) /28/01 7/28/01 8/27/01 9/26/01 10/26/01 11/25/01 12/25/01 date FIGURE 10. Minimum Daily Pavement Temperature Utilizing Latitude and Day of Year at 0.038m Depth Showing Actual Versus Predicted for Virginia Smart Road.

22 Diefenderfer,Al-Qadi,Reubush,andFreeman 21 TABLE 1. Daily Solar Radiation Values for Four Locations in the Eastern United States. Location Latitude, N H 0, kj/m 2 day January 1 May 1 September 1 Caribou, ME Washington, DC Blacksburg, VA Tampa, FL