This paper examines the existing models for predicting pavement temperatures at a certain depth and formulates a new one using the regression equation to predict the minimum and maximum pavement temperatures at the specified depth depending on the surface pavement temperature and its depth

B. Matić

D. Matić

G. Tepić

P. Ranitović

S. Sremac

Đ. Ćosić

English

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505 METALURGIJA 52 (2013) 4, 505-508B. MATIĆ, D. MATIĆ, Đ. ĆOSIĆ, S. SREMAC, G. TEPIĆ, P. RANITOVIĆA MODEL FOR THE PAVEMENT TEMPERATURE PREDICTION AT SPECIFIED DEPTHReceived – Prispjelo: 2013-01-24Accepted – Prihvaćeno: 2013-04-25Preliminary Note – Prethodno priopćenjeISSN 0543-5846METABK 52(4) 505-508 (2013)UDC – UDK 62.001.57:536.5:625.144=111B. Matić, D. Matić, Đ. Ćosić, S. Sremac, G. Tepić, Faculty of Technical Sciences, University of Novi Sad, SerbiaP. Ranitović, University of Defense, Military Academy, Belgrade, Serbia This paper examines the existing models for predicting pavement temperatures at a certain depth and formulates a new one using the regression equation to predict the minimum and maximum pavement temperatures at the specifi  ed depth depending on the surface pavement temperature and its depth. Key words: model, temperature, pavement, prediction, depthINTRODUCTIONOne of the most important environmental factors that signiﬁ  cantly affect the mechanical properties of as-phalt mixtures is temperature.The structural capacity of the hot mix asphalt con-crete layers depends on many factors including its tem-perature. Moreover, tempe-rature can be a major con-tributor to several types of distresses.Therefore, temperature is a signiﬁ  cant factor that af-fects the performance and life span of a pavement.After the introduction of the Superpave pavement temperature estimation procedures in 1993, many re-searchers expressed concerns regarding the accuracy of the temperature algorithms and the implications of us-ing the estimated values.The objective of this study is to make a valid model for predicting the pavement temperature at a certain depth for characteristic region. Like the modern logistics systems bring us back to the beginning of scientiﬁ  c development [1], accurate prediction of the asphalt pavement temperature at dif-ferent depths based on air temperatures and other sim-ple weather station measurements can help engineers in performing back calculations of asphalt concrete modu-lus and in estimating pavement deﬂ  ections. The temperature distribution of ﬂ  exible pavements is directly affected by the enviro-nmental conditions, to which it is exposed, Figure 1 [2].The main task, then, is to determine physical and mechanical properties of materials in the conditions equivalent to the conditions in the real pavement struc-ture [3].Pavement temperature is very important in evaluat-ing frost action and frost penetration. Modeling pave-ment surface temperature as a function of such weather condition (air temperature, dew point, relative humidity and wind speed) can provide an additional component that is essential for winter maintenance operations [4]. Like heat transfer properties for nanoﬂ  uids [5] and other materials and structures are very important, for pave-ment structures are especially important. STATE OF THE ARTThe purpose of the review is to ﬁ  nd out the strengths and the weaknesses of available models in order to pro-vide the basis for more detailed evaluations, selection and improvement of models. Several pavement performance prediction models have been proposed over the years. Many of these mod-els are developed for application in a particular region or country under speciﬁ  c trafﬁ  c and climatic conditions. Hence, they cannot be directly applied in other coun-tries or conditions.Strategic Highway Research Program (SHRP) formed the Long-Term Pavement Performance (LTTP) program in 1987 as a product of 20-year-long research for better deﬁ  ning the pavement characteristics in situ. 64 (LTTP) locations were selected as a part of the Sea-Figure 1 Energy balance on the surface of the pavement [2]506   METALURGIJA 52 (2013) 4, 505-508B. MATIĆ et al.: A MODEL FOR THE PAVEMENT TEMPERATURE PREDICTION AT SPECIFIED DEPTHsonal Monitoring Program (SMP). The result of the SMP research is the SUPERPAVE (Superior Perform-ing Asphalt Pavement) method for designing asphalt courses [6].Updated versions of the SHRP models for predicting pavement temperatures at depth were developed by Mohseni, 1998 [7].Lukanen et al. (1998) presented their own maximum and minimum pavement temperature prediction models based on an expanded set of SMP data [8].Bosscher et al. (1998) were also interested in deter-mining the pavement temperature as it varied with depth in relationship to the low air temperature [9].Ovik et al. (1999) presented an analysis of tempera-ture data from the MnRoad test site in Minnesota [10].Park et al. (2001) developed a model that could be used to predict pavement temperatures given the sur-face temperature and the time of day for use with FWD analysis [11].Marshall et al. (2001) presented another temperature prediction model for usage with FWD analysis [12].The research of Marshal et al. [12], and Denneman et al. [13] provide an empirical model that enables the user to estimate the temperature proﬁ  le of the pavement structure during any part of the day.EXPERIMENTAL PARTInstrumentationIn total, six sensors for measuring the pavement temperature at speciﬁ  ed depth were set.Data was measured during the experimental research by setting the temperature measuring sensors at the depth of the ﬂ  exible pavement structure, at the univer-sity campus, in the street Dr Ilije Đuričića, Novi Sad, Serbia.To measure the asphalt layer temperature in the pavement structure, the temperature sensors DS18S20 manufactured by Dallas Semiconductor (i.e. Maxim) were selected.DS18S20 measures temperatures in the range be-tween 55 °C and +125 °C, which is a wide enough tem-perature range for the application with asphalt, while their measuring precision is better than 0,5 °C.The realized measuring system comprises 6 temper-ature sensors, micro controller PIC16F877 and a com-puter (PC), Figure 2.On setting the sensors on a Pertinax board, they are insulated with the heat shrink material to ensure their function without physical damage (Figure 3).Data utilized in model formation were gathered in the period December (2011 ÷ 2012).The analysis was performed on a ﬂ  exible pavement structure where there were two bearing courses (15,0 cm Base course - crushed stone 0 ÷ 31 mm and 20,0 cm Subbase course - crushed stone 0 ÷ 63 mm) and two asphalt courses (5,0 cm Wearing course and 9,0 cm Binder course), Figure 4. The overall thickness of as-phalt layers was 14,0 cm.Figure 2  Block diagram for the measuring systemFigure 3    Sensors for pavement temperature measurement at a specifi  ed depth: sensors DS18S20 before being set in asphaltFigure 4 Overview of the analyzed pavement structure507 METALURGIJA 52 (2013) 4, 505-508B. MATIĆ et al.: A MODEL FOR THE PAVEMENT TEMPERATURE PREDICTION AT SPECIFIED DEPTHRESULTS AND DISCUSSIONMethodology and anticipated resultsThe model developed with the objective of predict-ing pavement temperature at depth is based on the re-gression data analysis. Regression equations are formed to predict maximum and minimum pavement tempera-tures at depth, depending on the maximum and mini-mum surface pavement temperature and depth.Regression equations The model predicting maximum pavement tempera-tures at speciﬁ  ed depth can be presented by the follow-ing equation:  ymax = 0,963288xmax – 0,151137xd +  4,452996    (1)     Standard model deviation is 0,83 oC. Corre-lation coefﬁ  cient is 0,973.The model predicting minimum pavement tempera-tures at speciﬁ  ed depth can be presented by the follow-ing equation:   ymin = 1,004801xmax – 0,1992731xd + 0,051532  (2)Standard model deviation is 0,9 oC. Corre-lation co-efﬁ  cient is 0,985.Model validationBased on the formulated model for predicting maxi-mum and minimum pavement temperatures at speciﬁ  ed depth (1, 2), the model validation has been performed by comparing measured and predicted pavement tem-peratures at depth (Figure 5). The mean absolute error (MAE) between measured and predicted maximum pavement temperatures at depth is 0,700457, and between measured and predicted minimum pavement temperatures MAE is 0,782117. On comparing measured and predicted pavement temperatures at depth, it can be concluded that the mod-els predict pavement temperatures with adequate accu-racy.CONCLUSIONThe paper formulates new models for predicting minimum and maximum pavement temperatures at speciﬁ  ed depth using the regression equations, in de-pendence on the surface pavement temperature and pavement depth.During the data analysis and the formation of the pavement temperature prediction model for speciﬁ  ed depths, it has been determined that temperatures behave differently depending on the pavement surface tempera-ture, daylight, pavement surface depth, and the part of the day.It can be concluded that temperatures at certain lay-ers become lower in the periods without solar radiation on the pavement surface, and that temperature become higher in the period after the sunrise, and especially during the solar radiation peak between 12:00 and 18:00.Furthermore, it can be concluded that the pavement layer temperature at certain depth is inﬂ  uenced by the pavement temperature from the day before, since tem-peratures in pavement layers alter signiﬁ  cantly slower in relation to the surface pavement temperature, Figure 6.With greater depth, the ratio between surface pave-ment temperature and the temperature at certain depth decreases, i.e. surface pavement temperature varies a greater deal more in relation to the temperatures at a certain depth.Based on the correlation coefﬁ  cient, standard model deviation and mean absolute error (MAE), it can be concluded that these models can be utilized with the ad-equate accuracy for predicting maximal and minimal pavement temperature at depth; yet the model for pre-dicting maximal pavement temperature at certain depth provides a somewhat more accurate result.Also, the model validation has been conducted. Based on the correlation coefﬁ  cient, standard model de-viation and mean absolute error (MAE), it can be con-cluded that the models predict pavement temperatures at depth well and that they can be utilized for calcula-tions in practice.  Mesured max Tk  at 6,0 cm (L) Predicted max Tk  at 6,0 cm (R)210 215 220 225 230 235 240 245Day (July)28303234363840424446485052542830323436384042444648505254 Measured min Tk  at 6,0 cm (L) Predicted min Tk  at 6,0 cm (R)-5 0 5 10 15 20 25 30 35Day (January)-12-10-8-6-4-20246-14-12-10-8-6-4-2024Figure 5   Validation of the model for predicting maximum (a) and minimum (b) pavement temperatures at depth, for characteristic months: July and January (for example, at 6,0 cm)a)b)508   METALURGIJA 52 (2013) 4, 505-508B. MATIĆ et al.: A MODEL FOR THE PAVEMENT TEMPERATURE PREDICTION AT SPECIFIED DEPTHAcknowledgmentThe authors acknowledge the support of research projects TR 36017 and 174019, funded by the Ministry of Science and Technological Development of Serbia. Legend of symbols ymax predicted maximum pavement temperature at depth /°C,xmax daily maximum surface pavement tempera-ture /°C,ymin predicted minimum pavement temperature at depth /°C,xmin daily minimum surface pavement temperature /°C andxd depth from the surface /cm.REFERENCES[1]  J. Tepić, I. Tanackov, G. Stojić, Ancient Logistics – His-torical Timeline and Etimology, Technical Gazette, 18 (2011) 3, 379-384.[2]  W. M. Herb, M. Stefan, G. Heinz, Simulation and Charac-terization of Asphalt Pavement Temperatures, Minnesota Department of Transportation (MNDOT), University of Minnesota, 2006.[3]  B. Matić, J. Tepić, S. Sremac, V. Radonjanin, D. Matić, P. Jovnović, Development and evaluation of the model for the surface payment temperature prediction, Metalurgija 51 (2012) 3, 329-332. [4]  B. Matić, H. A. Salem, D. Matić, Đ. Uzelac, Development and Validation of Model To Predict Pavement Temperature for Winter Maintenance Operations in Serbia, International Conference 8th APTE Conference: Asean Transport Chal-lenge, Thailand, 2012.[5]  P. Ternik, R. Rudolf, Heat Transfer Enhancement for Natu-ral Convection Flow of Water-Based Nanoﬂ   uids in a Square Enclosure, International Journal of Simulation Modelling, 11 (2012) 1, 29-39.[6]  T. Kennedy, G. Huber, E. Harrigan, R. Cominsky, C. Hughes, H. V. Quintus, J. Moulthrop, Superior Performing Asphalt Pavements (Superpave): The product of the SHRP Asphalt Research Program, National Research Council, Washington, DC, 1994.[7]  A. Mohseni, M. Symons, Effect of Improved LTPP AC Pavement Temperature Models on SuperPave Performance Grades, Proceedings of 77th Annual Meeting, Transporta-tion Research Board, Washington, DC, 1998b.[8]  E. O. Lukanen, H. Chunhua, E. L. Skok, Probabilistic Method of Asphalt Binder Selection Based on Pavement Temperature, Transportation Research Record, Transpor-tation Research Board, 1609 (1998), 12-20.[9]  P. J. Bosscher, H.U Bahia, S. Thomas, J. S. Russel, Relation-ship Between Pavement Temperature and Weather Data: Wisconsin Field Study to Verify SuperPave Algorithm, Transportation Research Record, 1609 (1998),  1-11.  [10]  J. Ovik, B. Birgisson, D.E. Newcomb, Characterizing Sea-sonal Variations in Flexible Pavement Material Properties, Transportation Research Record, 1684 (1999), 1-7.[11]  D. Park, N. Buch, C. Karim,  Effective Layer Temperature Prediction Model and Temperature Correction via FWD Deﬂ  ections, Transportation Research Record, 1764 (2001), 97-111.[12]  C. Marshall, R. Meier, M. Welch, Seasonal Temperature Effects on Flexible Pavements in Tennessee, Transporta-tion Research Record, 1764 (2001), 89-96.[13]  E. Denneman, The application of locally developed pave-ment temperature prediction Algorithms in Performance Grade (PG) Binder Selection, The Challenges of Imple-menting policy-SATC 2007: The 26th Annual Southern African Transport Conference and Exhibition, Pretoria, South Africa, 9-12 July, 2007, p.10.Note:   The responsible translator to the English language is V. Bogdanović, Faculty of Technical Sciences, Novi Sad, Serbia  -15,0 -12,0 -9,0 -6,0 -3,0 Tk- 2 0 2 4 6 8 1 01 21 41 61 82 02 22 42 6Hour / h182022242628303234363840424446  -15,0 -12,0 -9,0 -6,0 -3,0 Tk-2 0 2 4 6 8 10 12 14 16 18 20 22 24 26Hour / h121416182022242628Figure 6   Temperature overview of the pavement structure layer for two consecutive days

A model for the pavement temperature prediction at specified depth

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505METALURGIJA 52 (2013) 4, 505-508B. MATIĆ, D. MATIĆ, Đ. ĆOSIĆ, S. SREMAC, G. TEPIĆ, P. RANITOVIĆA MODEL FOR THE PAVEMENT TEMPERATURE PREDICTION AT SPECIFIED DEPTHReceived – Prispjelo: 2013-01-24Accepted – Prihvaćeno: 2013-04-25Preliminary Note – Prethodno priopćenjeISSN 0543-5846METABK 52(4) 505-508 (2013)UDC – UDK 62.001.57:536.5:625.144=111B. Matić, D. Matić, Đ. Ćosić, S. Sremac, G. Tepić, Faculty of Technical Sciences, University of Novi Sad, SerbiaP. Ranitović, University of Defense, Military Academy, Belgrade, Serbia This paper examines the existing models for predicting pavement temperatures at a certain depth and formulates a new one using the regression equation to predict the minimum and maximum pavement temperatures at the specifi ed depth depending on the surface pavement temperature and its depth. Key words: model, temperature, pavement, prediction, depthINTRODUCTIONOne of the most important environmental factors that signiﬁ cantly affect the mechanical properties of as-phalt mixtures is temperature.The structural capacity of the hot mix asphalt con-crete layers depends on many factors including its tem-perature. Moreover, tempe-rature can be a major con-tributor to several types of distresses.Therefore, temperature is a signiﬁ cant factor that af-fects the performance and life span of a pavement.After the introduction of the Superpave pavement temperature estimation procedures in 1993, many re-searchers expressed concerns regarding the accuracy of the temperature algorithms and the implications of us-ing the estimated values.The objective of this study is to make a valid model for predicting the pavement temperature at a certain depth for characteristic region. Like the modern logistics systems bring us back to the beginning of scientiﬁ c development [1], accurate prediction of the asphalt pavement temperature at dif-ferent depths based on air temperatures and other sim-ple weather station measurements can help engineers in performing back calculations of asphalt concrete modu-lus and in estimating pavement deﬂ ections. The temperature distribution of ﬂ exible pavements is directly affected by the enviro-nmental conditions, to which it is exposed, Figure 1 [2].The main task, then, is to determine physical and mechanical properties of materials in the conditions equivalent to the conditions in the real pavement struc-ture [3].Pavement temperature is very important in evaluat-ing frost action and frost penetration. Modeling pave-ment surface temperature as a function of such weather condition (air temperature, dew point, relative humidity and wind speed) can provide an additional component that is essential for winter maintenance operations [4]. Like heat transfer properties for nanoﬂ uids [5] and other materials and structures are very important, for pave-ment structures are especially important. STATE OF THE ARTThe purpose of the review is to ﬁ nd out the strengths and the weaknesses of available models in order to pro-vide the basis for more detailed evaluations, selection and improvement of models. Several pavement performance prediction models have been proposed over the years. Many of these mod-els are developed for application in a particular region or country under speciﬁ c trafﬁ c and climatic conditions. Hence, they cannot be directly applied in other coun-tries or conditions.Strategic Highway Research Program (SHRP) formed the Long-Term Pavement Performance (LTTP) program in 1987 as a product of 20-year-long research for better deﬁ ning the pavement characteristics in situ. 64 (LTTP) locations were selected as a part of the Sea-Figure 1 Energy balance on the surface of the pavement [2]506  METALURGIJA 52 (2013) 4, 505-508B. MATIĆ et al.: A MODEL FOR THE PAVEMENT TEMPERATURE PREDICTION AT SPECIFIED DEPTHsonal Monitoring Program (SMP). The result of the SMP research is the SUPERPAVE (Superior Perform-ing Asphalt Pavement) method for designing asphalt courses [6].Updated versions of the SHRP models for predicting pavement temperatures at depth were developed by Mohseni, 1998 [7].Lukanen et al. (1998) presented their own maximum and minimum pavement temperature prediction models based on an expanded set of SMP data [8].Bosscher et al. (1998) were also interested in deter-mining the pavement temperature as it varied with depth in relationship to the low air temperature [9].Ovik et al. (1999) presented an analysis of tempera-ture data from the MnRoad test site in Minnesota [10].Park et al. (2001) developed a model that could be used to predict pavement temperatures given the sur-face temperature and the time of day for use with FWD analysis [11].Marshall et al. (2001) presented another temperature prediction model for usage with FWD analysis [12].The research of Marshal et al. [12], and Denneman et al. [13] provide an empirical model that enables the user to estimate the temperature proﬁ le of the pavement structure during any part of the day.EXPERIMENTAL PARTInstrumentationIn total, six sensors for measuring the pavement temperature at speciﬁ ed depth were set.Data was measured during the experimental research by setting the temperature measuring sensors at the depth of the ﬂ exible pavement structure, at the univer-sity campus, in the street Dr Ilije Đuričića, Novi Sad, Serbia.To measure the asphalt layer temperature in the pavement structure, the temperature sensors DS18S20 manufactured by Dallas Semiconductor (i.e. Maxim) were selected.DS18S20 measures temperatures in the range be-tween 55 °C and +125 °C, which is a wide enough tem-perature range for the application with asphalt, while their measuring precision is better than 0,5 °C.The realized measuring system comprises 6 temper-ature sensors, micro controller PIC16F877 and a com-puter (PC), Figure 2.On setting the sensors on a Pertinax board, they are insulated with the heat shrink material to ensure their function without physical damage (Figure 3).Data utilized in model formation were gathered in the period December (2011 ÷ 2012).The analysis was performed on a ﬂ exible pavement structure where there were two bearing courses (15,0 cm Base course - crushed stone 0 ÷ 31 mm and 20,0 cm Subbase course - crushed stone 0 ÷ 63 mm) and two asphalt courses (5,0 cm Wearing course and 9,0 cm Binder course), Figure 4. The overall thickness of as-phalt layers was 14,0 cm.Figure 2  Block diagram for the measuring systemFigure 3   Sensors for pavement temperature measurement at a specifi ed depth: sensors DS18S20 before being set in asphaltFigure 4 Overview of the analyzed pavement structure507METALURGIJA 52 (2013) 4, 505-508B. MATIĆ et al.: A MODEL FOR THE PAVEMENT TEMPERATURE PREDICTION AT SPECIFIED DEPTHRESULTS AND DISCUSSIONMethodology and anticipated resultsThe model developed with the objective of predict-ing pavement temperature at depth is based on the re-gression data analysis. Regression equations are formed to predict maximum and minimum pavement tempera-tures at depth, depending on the maximum and mini-mum surface pavement temperature and depth.Regression equations The model predicting maximum pavement tempera-tures at speciﬁ ed depth can be presented by the follow-ing equation: ymax = 0,963288xmax – 0,151137xd + 4,452996  (1) Standard model deviation is 0,83 oC. Corre-lation coefﬁ cient is 0,973.The model predicting minimum pavement tempera-tures at speciﬁ ed depth can be presented by the follow-ing equation:  ymin = 1,004801xmax – 0,1992731xd + 0,051532  (2)Standard model deviation is 0,9 oC. Corre-lation co-efﬁ cient is 0,985.Model validationBased on the formulated model for predicting maxi-mum and minimum pavement temperatures at speciﬁ ed depth (1, 2), the model validation has been performed by comparing measured and predicted pavement tem-peratures at depth (Figure 5). The mean absolute error (MAE) between measured and predicted maximum pavement temperatures at depth is 0,700457, and between measured and predicted minimum pavement temperatures MAE is 0,782117. On comparing measured and predicted pavement temperatures at depth, it can be concluded that the mod-els predict pavement temperatures with adequate accu-racy.CONCLUSIONThe paper formulates new models for predicting minimum and maximum pavement temperatures at speciﬁ ed depth using the regression equations, in de-pendence on the surface pavement temperature and pavement depth.During the data analysis and the formation of the pavement temperature prediction model for speciﬁ ed depths, it has been determined that temperatures behave differently depending on the pavement surface tempera-ture, daylight, pavement surface depth, and the part of the day.It can be concluded that temperatures at certain lay-ers become lower in the periods without solar radiation on the pavement surface, and that temperature become higher in the period after the sunrise, and especially during the solar radiation peak between 12:00 and 18:00.Furthermore, it can be concluded that the pavement layer temperature at certain depth is inﬂ uenced by the pavement temperature from the day before, since tem-peratures in pavement layers alter signiﬁ cantly slower in relation to the surface pavement temperature, Figure 6.With greater depth, the ratio between surface pave-ment temperature and the temperature at certain depth decreases, i.e. surface pavement temperature varies a greater deal more in relation to the temperatures at a certain depth.Based on the correlation coefﬁ cient, standard model deviation and mean absolute error (MAE), it can be concluded that these models can be utilized with the ad-equate accuracy for predicting maximal and minimal pavement temperature at depth; yet the model for pre-dicting maximal pavement temperature at certain depth provides a somewhat more accurate result.Also, the model validation has been conducted. Based on the correlation coefﬁ cient, standard model de-viation and mean absolute error (MAE), it can be con-cluded that the models predict pavement temperatures at depth well and that they can be utilized for calcula-tions in practice.  Mesured max Tk  at 6,0 cm (L) Predicted max Tk  at 6,0 cm (R)210 215 220 225 230 235 240 245Day (July)28303234363840424446485052542830323436384042444648505254 Measured min Tk  at 6,0 cm (L) Predicted min Tk  at 6,0 cm (R)-5 0 5 10 15 20 25 30 35Day (January)-12-10-8-6-4-20246-14-12-10-8-6-4-2024Figure 5  Validation of the model for predicting maximum (a) and minimum (b) pavement temperatures at depth, for characteristic months: July and January (for example, at 6,0 cm)a)b)508  METALURGIJA 52 (2013) 4, 505-508B. MATIĆ et al.: A MODEL FOR THE PAVEMENT TEMPERATURE PREDICTION AT SPECIFIED DEPTHAcknowledgmentThe authors acknowledge the support of research projects TR 36017 and 174019, funded by the Ministry of Science and Technological Development of Serbia. Legend of symbols ymax predicted maximum pavement temperature at depth /°C,xmax daily maximum surface pavement tempera-ture /°C,ymin predicted minimum pavement temperature at depth /°C,xmin daily minimum surface pavement temperature /°C andxd depth from the surface /cm.REFERENCES[1] J. Tepić, I. Tanackov, G. Stojić, Ancient Logistics – His-torical Timeline and Etimology, Technical Gazette, 18 (2011) 3, 379-384.[2] W. M. Herb, M. Stefan, G. Heinz, Simulation and Charac-terization of Asphalt Pavement Temperatures, Minnesota Department of Transportation (MNDOT), University of Minnesota, 2006.[3] B. Matić, J. Tepić, S. Sremac, V. Radonjanin, D. Matić, P. Jovnović, Development and evaluation of the model for the surface payment temperature prediction, Metalurgija 51 (2012) 3, 329-332. [4] B. Matić, H. A. Salem, D. Matić, Đ. Uzelac, Development and Validation of Model To Predict Pavement Temperature for Winter Maintenance Operations in Serbia, International Conference 8th APTE Conference: Asean Transport Chal-lenge, Thailand, 2012.[5] P. Ternik, R. Rudolf, Heat Transfer Enhancement for Natu-ral Convection Flow of Water-Based Nanoﬂ uids in a Square Enclosure, International Journal of Simulation Modelling, 11 (2012) 1, 29-39.[6] T. Kennedy, G. Huber, E. Harrigan, R. Cominsky, C. Hughes, H. V. Quintus, J. Moulthrop, Superior Performing Asphalt Pavements (Superpave): The product of the SHRP Asphalt Research Program, National Research Council, Washington, DC, 1994.[7] A. Mohseni, M. Symons, Effect of Improved LTPP AC Pavement Temperature Models on SuperPave Performance Grades, Proceedings of 77th Annual Meeting, Transporta-tion Research Board, Washington, DC, 1998b.[8] E. O. Lukanen, H. Chunhua, E. L. Skok, Probabilistic Method of Asphalt Binder Selection Based on Pavement Temperature, Transportation Research Record, Transpor-tation Research Board, 1609 (1998), 12-20.[9] P. J. Bosscher, H.U Bahia, S. Thomas, J. S. Russel, Relation-ship Between Pavement Temperature and Weather Data: Wisconsin Field Study to Verify SuperPave Algorithm, Transportation Research Record, 1609 (1998),  1-11.  [10] J. Ovik, B. Birgisson, D.E. Newcomb, Characterizing Sea-sonal Variations in Flexible Pavement Material Properties, Transportation Research Record, 1684 (1999), 1-7.[11] D. Park, N. Buch, C. Karim,  Effective Layer Temperature Prediction Model and Temperature Correction via FWD Deﬂ ections, Transportation Research Record, 1764 (2001), 97-111.[12] C. Marshall, R. Meier, M. Welch, Seasonal Temperature Effects on Flexible Pavements in Tennessee, Transporta-tion Research Record, 1764 (2001), 89-96.[13] E. Denneman, The application of locally developed pave-ment temperature prediction Algorithms in Performance Grade (PG) Binder Selection, The Challenges of Imple-menting policy-SATC 2007: The 26th Annual Southern African Transport Conference and Exhibition, Pretoria, South Africa, 9-12 July, 2007, p.10.Note:  The responsible translator to the English language is V. Bogdanović, Faculty of Technical Sciences, Novi Sad, Serbia  -15,0 -12,0 -9,0 -6,0 -3,0 Tk-2 0 2 4 6 8 10 12 14 16 18 20 22 24 26Hour / h182022242628303234363840424446  -15,0 -12,0 -9,0 -6,0 -3,0 Tk-2 0 2 4 6 8 10 12 14 16 18 20 22 24 26Hour / h121416182022242628Figure 6  Temperature overview of the pavement structure layer for two consecutive days

A model for the pavement temperature prediction at specified depth

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