# Simulation of the Cooling Effect of Porous Asphalt
## 1 Introduction  
Summer has the strongest solar radiation in the year, and the surface temperature of pavement in this season is usually 15-30 degrees higher than the air. Asphalt concrete is a temperature-sensitive material, and high temperature is an extremely unfavorable condition for asphalt concrete. Various properties of the concrete will change in such a circumstance [1; 2]. Under high-temperature conditions, the rutting resistance of the pavement will be weakened, which greatly increases the possibility of rutting on the asphalt pavement surface and affects the safety performance of the pavement [3]. Porous asphalt pavements are often referred to as cool pavements. The application of porous pavement can reduce the temperature peak inside the pavement so as to achieve cooling performance. The cooling performance of porous asphalt pavement is greatly affected by the air voids, and the related theory is not yet mature [4; 5]. Therefore, it is necessary to study the influence of the air voids on the pavement temperature field and determine the cooling performance. Mathematical methods have often been used to predict the internal temperature distribution of pavements by forming a specific database for predicting the regional temperature field distribution by monitoring the internal temperature of the pavement for a long time [6; 7; 8; 9]. However, the object of the method is rather special and not suitable for wide applications. Therefore, numerical analysis methodswhich mostly use the zone discretization method to calculate the temperature of each node have been developed and utilized. Based on the heat conduction equation, [PERSON] [6] used the finite difference approximation method to establish a simulation model of an asphalt pavement temperature field. [PERSON] et al. [7] used discrete elements to discretize the pavement structure into several nodes and obtained the temperature values of each node by iteration. [PERSON] [8] utilized a method proposed by [PERSON] [9] to establish a model for the internal temperature simulation of pavement and verified it using LTPP data. Different from the statistical and numerical analysis methods, analytical methods can comprehensively consider the influence of solar radiation, atmospheric temperature, pavement surface radiation, and environmental factors on the pavement temperature field during the pavement heat conduction process and thereby obtain a more rigorous and accurate solution. The advantage of this type of method is that there is no need to consider time steps or numerical stability and convergence conditions. [PERSON] [10] used an isotropic surface layer, and the heat transfer problem under cyclic thermal force was solved through the analysis of the temperature field of the multilayer system. [PERSON] and [PERSON] [11] proposed a theoretical solution for three-layer pavement based on the Fourier-Biot heat conduction equation. [PERSON] and [PERSON] [12] proposed an analytical solution for one-dimensional pavement heat conduction by Laplace transform. On the premise that the pavement surface temperature is uniform, [PERSON] [13] obtained the analytical solution of the one-dimensional road temperature field of the pavement surface temperature. On the basis of the Laplace transform method, [PERSON] et al. [14] proposed a method for determining the pavement surface temperature under dynamic conditions such as geographical location, temperature, cloud cover, sunshine duration, and material properties. Although domestic and international scholars have been deeply involved in various aspects of asphalt pavement research, there are relatively few studies on porous asphalt pavement, and the related technology is not yet mature. The internal temperature of asphalt pavement affects the service level and safety level of the pavement. The higher the temperature, the more prone to rutting, slippage, and deflection is the pavement, resulting in failure of the pavement and instability [15; 16; 17; 18].