Numerical Analysis of Temperature Reduction Effect of Permeable Pavements

: Permeable pavements can effectively reduce the urban road surface temperatures. To study the cooling 10 effect of holding water on the road surface under the comprehensive influence of the external water and heat 11 environment, a numerical model established by a finite element analysis software and an indoor test were used to 12 verify the temperature change behavior of the road surface under different heating temperatures and holding water 13 conditions. The results show that the average error between the numerical model and indoor test is 3.5%, and the 14 model reliability is high. Under the same conditions, the change in thickness of the permeable pavement surface and 15 base course has a negligible effect on the temperature of the road surface. For every 100 J/(kg/°C) increase in the 16 specific heat capacity of the upper surface course and lower surface course, the maximum daily road surface 17 temperature can be reduced by approximately 2.1 °C and 0.4 °C, respectively. The road surface temperature shows a 18 similar pattern when the thermal conductivity increases. Under dry conditions, the maximum daily road surface 19 temperature can be reduced by approximately 3.4 °C and 4.3 °C for surface-permeable and fully permeable 20 pavements, respectively. This study provides reference suggestions for optimizing the selection and design of urban 21 permeable pavement


Introduction 26
With the rapid expansion of the urban scale and urban population, the phenomena of "urban rain island" and 27 "heat island effect" have become increasingly serious (Sun et al. 2019;Zhou et al. 2012). The urban road permeable 28 pavement is an important part of the "sponge city." Compared with the traditional paved road, it has a large porosity 29 and strong permeability, so that the rainwater within the city rapidly infiltrates the road surface, thus reducing the 30 pressure of urban waterlogging (Niu et al. 2016; Roseen et al. 2009). It can store water while using water evaporation 31 to take away heat from the road surface, therefore reducing the temperature of the road pavement and effectively 32 alleviating the "heat island effect" of the city ( the cooling effect of urban permeable pavements in summer and showed that there is a strong relationship between 52 temperature decrease, surface evaporation, and pavement water capacity. Jiang (Fu 2011) used ANSYS to study the 53 cooling effect of a permeable pavement under the combined effect of heat conduction and heat convection, and the 54 results showed a positive linear relationship between its cooling effect and void fraction. Scholars mainly study the 55 cooling effect through outdoor measurements and mathematical models, and the analysis of the factors affecting the 56 cooling effect and its optimization is one of the active areas of research. 57 In summary, there have been numerous analyses on the various properties of permeable pavements, which have 58 laid the foundation for the research on drainage and temperature reduction of permeable pavement structures. 59 However, the existing studies have not addressed the influence of the permeable pavement structure thermal physical 60 parameters, pavement type, and water-holding state on road surface cooling.  (1) Homogeneous and continuous medium for each layer of the permeable pavement structure; 92 (2) The permeable pavement structure is isotropic, and its anisotropic characteristics are not considered; 93 (3) The temperature and heat flow transfer of each structural layer of the permeable pavement is continuous, 94 there is no thermal resistance in the contact between the layers, and the heat transfer interface effect between the 95 layers is not considered. 96 (4) The temperature at the bottom of the subgrade is constant, and the effect of geothermal action on the 97 temperature of the subgrade pavement is not considered. 98 (5) The model is fully insulated at each side boundary, and the heat dissipation effect of the model and heat 99 exchange process with the outside world are not considered in the test. 100 (6) The permeable pavement surface is set to a state of no air flow, which is consistent with the wind-free 101 conditions of the indoor test. 102

3)Model parameter setting 103
The thermal conductivity of a permeable pavement material is less affected by external factors such as water 104 and air, and its comprehensive specific heat capacity should consider the action of air and water in addition to the 105 influence of asphalt and aggregate. The thermal conductivity of the pavement structure can be calculated according 106 to Williamson's formula 24 . Pavement structure in the warming process, the volume and pressure are not changed, 107 can be regarded as equal volume and pressure specific heat capacity, dry and water-holding state of permeable 108 asphalt mixture and other pavement materials integrated specific heat capacity can be calculated according to for 109 where CD (J/(kg/°C) is the integrated specific heat capacity of the structure in the dry state, CM (J/(kg/°C)) is the 113 integrated specific heat capacity of the structure in the water-holding state, M (kg) is the structural mass, and the 114 subscripts a, s, air, and w are asphalt, aggregate, air, and water. 115 The relationship between the porosity VVoid and water holding capacity SR of permeable pavement materials is  The numerical calculation model consists of three layers, and the model parameters include structural and 120 material parameters. The parameter values are listed in Table 1

Model reliability verification 126
The indoor test model for permeable pavement temperature change used a 20 cm in diameter, 80 cm in height, 127 and 2 cm in thickness cylindrical glass test barrel. Model side with height scale, along the vertical direction every 128 5cm set 1cm diameter small hole, for the drainage pipe and temperature sensor to leave the hole channel. Bury the 129 temperature sensor as required. For the test, at the three interfaces, a PT100 RTD temperature sensor was used with 130 display accuracy of 0.1 °C, and a 500 W round plate type cast aluminum electric heating plate was adopted for the 131 upper surface temperature control heating. The indoor test model is shown in Figure 2. The initial conditions inside the model were set to 29 °C. The drying and water holding states were controlled by 137 changing the density, specific heat capacity, and thermal conductivity of each layer. The results of temperature 138 variation at each depth location for the dry and water-holding state permeable pavement models were calculated 139 under 12 h loading, and the inter-model error was calculated using Eq. 4. 140 Abs T -T e = T locations for each loading condition were calculated to be 7.18%, 4.69%, and 4.04%, respectively. At the 40 °C, 153 50 °C, and 60 °C loading conditions, 39% and 61%, 29% and 71%, and 28% and 72% of the total data volume were 154 accounted for by the upper left and lower right data of the contours, respectively. From the 45° contour map and the 155 average error calculation of the depth position of the surface layer, it can be observed that the points where the model 156 calculated value is higher than the measured value are mainly distributed in the higher temperature interval; that is, 157 the model calculated value in the upper depth region is slightly higher than the measured value. This is due to the 158 fact that the thermal boundary conditions of the upper surface of the calculated model do not consider heat loss during 159 the heating process, which produces differences with the actual indoor tests. With increasing depth, the effect of heat 160 loss gradually decreases, and the calculated error between the calculated and measured values gradually decreases. 161 In summary, the error interval between the calculated value of the numerical model and the measured value of 162 the indoor test was 0.1%-15%, with an average error of 3.5%, and the Pearson correlation coefficient was higher 163 process, which provides a basis for the parameter setting of urban road paving models. 167

Modeling of permeable pavement for urban roads 168
To study the factors influencing the cooling of the pavement of a permeable pavement structure of actual urban 169 roads and the difference in road surface temperature changes in different types of urban road pavements under 170 different water holding conditions, and to provide a reference for the design and optimization of permeable pavement 171 structures from the perspective of the road surface cooling behavior, three models of an urban road permeable 172 pavement structure with a width of 700 cm (standard width of two lanes) under actual solar radiation conditions were 173 established, which are non-permeable, surface-permeable, and fully permeable pavement structures. The numerical 174 calculation of the road surface temperature change process and the solar radiation intensity change curve is presented 175 in Figure 4.  surface-permeable asphalt mixture porosity was set to 20%, with water holding rate of 1.58% and dry and water 183 holding state integrated specific heat capacity of 865 J/(kg/°C) and 995 J/(kg/°C). The AC-13 type surface layer 184 porosity was set to 5.5%, with water holding rate of 0.887% and dry and water holding state integrated specific heat capacity of 824 J/(kg/°C) and 853 J/(kg/°C). The ATPB type surface layer porosity was set to 22%, with water holding 186 rate of 1.663% and dry and water holding state integrated specific heat capacity of 860 J/(kg/°C) and 915 J/(kg/°C). 187 The porosity of the base course cement-stabilized gravel mix was set to 5.1%, with water-holding rate of 0.868% and 188 combined specific heat capacity of the dry and water-holding states of 811 J/(kg/°C) and 840 J/(kg/°C). The water-189 holding rate of the base graded gravel mix was 4.27% using the indoor test results, and the combined specific heat  (1) Effect of specific heat capacity parameter of upper surface course 235 The specific heat capacity of the upper surface course of OGFC was set to 800, 900, 1000, 1100, and 1200 236 J/(kg/°C), and the other parameters remained unchanged. 237 (2) Influence of specific heat capacity parameter of the lower surface course 238 The specific heat capacity of the lower surface course of ATPB was set to 800, 900, 1000, 1100, and 1200 239 J/(kg/°C), and the other parameters remained unchanged. 240 (3) Influence of specific heat capacity parameter of the base course 241 The specific heat capacity of the graded gravel base was set to 800, 900, 1000, 1100, and 1200 J/(kg/°C), and 242 the other parameters remained unchanged. 243 Under the above parameters, the numerical calculation of the road surface temperature under actual loading 244 conditions for 12 h was carried out, and the change curve of the road surface temperature with loading time was 245 plotted under the change in specific heat capacity parameters of the different layers of the permeable pavement. The 246 results are shown in Figure 6. which is significantly lower than the upper surface course results. For the base course, the change in specific heat 260 capacity at this location has almost no effect on the road surface temperature. As can be observed from Figure 8 (2) Influence of thermal conductivity parameters of the lower surface course 277 The thermal conductivity of the lower surface course of ATPB was set to 0.6, 0.7, 0.8, 0.9, and 1.0 W/(m/°C), 278 and the other parameters remained unchanged. 279 (3) Influence of thermal conductivity parameters of the base course 280 The thermal conductivity of the graded gravel base was set to 0.9, 1.0, 1.1, 1. course structure on the road surface temperature is relatively low, whereas the change in thermal conductivity of the 296 subgrade has almost no influence on the road surface temperature. It can be observed that the effect of the change in 297 thermal conductivity on the cooling effect of the permeable pavement surface decreases gradually with an increase 298 in the depth of the structure. As can be found from Figure 9(d), the maximum daily road surface temperature decreases 299 with an increase in the thermal conductivity of the upper surface course and the lower surface course, the trend 300 gradually becomes slower, and the influence on the road surface temperature gradually decreases. 301 From the perspective of permeable pavement material parameters, an upper layer with a larger specific heat 302 capacity or thermal conductivity of the material, or the use of modified materials and additives to change the 303 comprehensive specific heat capacity or thermal conductivity of the material, can result in better cooling effect on 304 the road surface. The effect of the thermal parameters of the materials of the following layer, the grassroots level, and 305 other deeper layers on the road surface cooling effect is low. Therefore, to achieve an optimal cooling effect, priority 306 should be given to modification of the material of the permeable pavement upper layer. 307 4 Analysis of cooling effect of the permeable pavement surface 308 Urban road pavement because of high heat absorption rate, low specific heat capacity, a large amount of heat 309 absorption in the short heating time, the surface temperature rises rapidly, and as a heat source of near surface 310 continuous heating, resulting in the road surface near the temperature rise, intensifying the urban "heat island effect". 311 To analyze the differences in the road surface temperature changes of different urban road pavements, the non-312 permeable, surface-permeable, and fully permeable pavement types in the dry state were recorded as Ad, Bd, Cd, and 313 those in the water-holding state were recorded as Aw, Bw, Cw. The road surface temperature changes during 12 h in 314 the dry and water-holding states were calculated to analyze the effects of road pavement types and dry and wet states 315 on the road surface temperature. As can be observed from Figure 8(a), the temperature of the non-permeable road surface during the warming 325 process in the dry state is significantly higher than that of the permeable pavement, and the maximum daily 326 temperature of the road surface of type A is 3.4 °C and 4.3 °C higher than those of types B and C, respectively, and 327 2.6 °C and 3.9 °C higher than those of types B and C at the end of warming. The maximum daily road surface 328 temperature of the surface-permeable pavement is approximately 1.3 °C higher than that of a fully permeable 329 structure. Under dry conditions, the difference in road surface temperature is mainly reflected in the non-permeable 330 and permeable pavements, and the trend of changes in road surface temperature with time is the same for the three 331 pavement structures. 332 As can be observed from Figure 8(b), during the warming process of the non-permeable road pavement in the 333 holding water state, the road surface temperature is significantly higher than that of permeable pavement. The 334 maximum daily road surface temperatures of type A are 5.8 °C and 8.1 °C higher than those of types B and C, 335 respectively, and 5.7 °C and 7.8 °C higher than those of types B and C at the end of warming. The maximum daily 336 road surface temperature of the surface-permeable pavement is approximately 2 °C higher than that of a fully 337 permeable structure, and its temperature can be approximately 1.8 °C higher at the end of the warming and loading 338 process. The three types of permeable pavements produce a difference in road surface temperature between 0-1.9 °C 339 owing to the different water holding ranges, and the difference in road surface temperature between non-permeable 340 and permeable pavements increases slowly under different warming time domains, reaching a temperature peak when 341 the temperature difference reaches a maximum value, and then decreases as the road surface temperature decreases. 342 4.2 Analysis of the effect of water-holding effect of permeable pavement on road surface temperature 343 To analyze the effect of the water-holding effect on the temperature of a permeable pavement road surface, the 344 curves of the change in road surface temperature with loading time in the dry and water-holding states of the B and 345 C permeable pavement structures were plotted, and the results are presented in Figure 9.

349
(c) Comparison of temperature difference between wet and dry road surfaces by pavement type 350 Figure 9 Comparison of road surface temperature of permeable pavement in dry and water-holding condition 351 From Figure 9, it can be observed that the trend of temperature change of permeable pavement types B and C 352 under dry and water-holding conditions is basically the same. The class B surface-permeable pavement has a 353 maximum daily road surface temperature difference of 3.5 °C between the dry and wet conditions and 3.4 °C after 354 12 h. The class C fully permeable pavement has a maximum daily road surface temperature difference of 4.9 °C 355 between the dry and wet conditions and 3.9 °C after loading is completed. Because of the different levels of permeable 356 layers, the effect of water retention on the cooling effect of each type of permeable pavement is slightly different, 357 and the effect of water retention of the surface layer permeable pavement on the road surface cooling is relatively 358 weaker than that of the fully permeable type of pavement. From the perspective of permeable pavement structure 359 type, a fully permeable pavement structure has an excellent road surface cooling effect. 360

Conclusion 361
This paper provides reference suggestions for the optimization of permeable pavement surface cooling from 362 three perspectives: design, material parameters, and structure type, with the following main conclusions: 363 (1) Under the same environmental conditions, it is difficult to influence the road surface temperature of a 364 permeable pavement by changing the thickness of each structural layer, and the structural layer thickness parameter 365 does not have a significant effect on the cooling effect of the road surface. 366 (2) The change in the specific heat capacity of the upper surface course of a permeable pavement has a more 367 significant effect on the temperature of the permeable pavement surface, and the degree of influence gradually 368 decreases with increasing depth. For every 100 J /(kg/°C) increase in specific heat capacity of the upper and lower 369 surface courses, the maximum daily road surface temperature can be reduced by approximately 2.1 °C and 0.4 °C, 370 respectively, under the same warming environment. 371 (3) The effect of change in thermal conductivity on the cooling effect of a permeable pavement surface 372 gradually decreases with an increase in the depth of the structure, and the change in thermal conductivity of the upper 373 surface course of the structure near the surface of the road has a relatively high degree of influence on the cooling 374 effect of the road surface. For every 0.1 W/(m/°C) increase in thermal conductivity of the upper and lower layers, the 375 maximum daily road surface temperature can be reduced by approximately 0.9 °C and 0.2 °C, respectively. 376 (4) Under the same warming environment, the maximum daily road surface temperature of the surface-377 permeable and fully permeable pavements in the dry state can be reduced by approximately 3.4 ℃ and 4.3 ℃ 378 compared to non-permeable pavement, and can be reduced by approximately 5.8 ℃ and 8.1 ℃, respectively, in the 379 water-holding state. The maximum daily road surface temperatures in the dry and water-holding states of the fully 380 permeable pavement can be reduced by approximately 1.3 °C and 1.8 °C, respectively, compared with those of the 381 surface-permeable pavement, and the cooling effect is better than that of the surface-permeable pavement.  Effect of thickness on the temperature of the permeable pavement surface Figure 6 Effect of speci c heat capacity on the temperature of permeable pavement surface Effect of thermal conductivity on the temperature of permeable pavement surface Comparison of road surface temperature of permeable pavement in dry and water-holding condition