## 5 Finite Element Simulation of Void Structure
### Construction of the Finite Element Model  
Sound absorption in porous asphalt pavements is a common acoustic-solid coupling problem that is influenced by a variety of factors, such as air temperature, humidity and vehicle loading, in real-world situations. The majority of existing research has focused on the fields of pressure acoustics or fluctuating acoustics using air as the analysis medium [35; 36; 37]. The damping of pavement structures also has an impact on sound absorption. The sound pressure acts on the structure, causing structural vibrations. At the same time, the structural vibrations cause the surrounding air to vibrate, causing sound waves to radiate outward. The mass coupling matrix and the stiffness coupling matrix are used in Equation (16) to represent this pair of interactions. Numerical solutions were obtained by using the finite element method in this paper. COMSOL Multiphysics is a finite element simulation program that can handle a coupled multi-physics field. This software was used in this study to couple pressure acoustics and solid mechanics to obtain an acoustic-structural boundary. In the simulated results, including the calculated sound pressure and sound pressure level distribution, the noise reduction effect of PAC was analyzed under different void contents, which explains the noise reduction mechanism of PAC from a microscopic perspective. The void structure of PAC is complicated and the distribution of void locations is extremely random. To obtain an accurate void structure, the processed CT images of the PAC samples were used as the import model. For each sample, as the image processing and void identification operations described in Chapter 3.1, the bitmap images were obtained. The bitmap images in this paper were programmed to be converted into vector images in AutoCAD format, which were used as the import models by the COMSOL CAD interface. The result is shown in Figure 9.  
The media involved in the simulation are air and PAC. Based on existing studies [38; 39; 40], the required material parameters are summarized, as shown in Table 7.  
Because material parameters change with external temperature, humidity and other factors, the following assumptions were made to clarify the study's scope and accurately describe the noise absorption of PAC. 1. The acoustic calculations in this paper are solved under linear acoustic conditions. The acoustic pressure is very small compared to the atmospheric pressure because it  
Figure 9: Image import: (**a**) Cross-sectional view; (**b**) Model establishment. is the residual pressure after the atmospheric pressure perturbation. Therefore, in this paper, a compressional wave under a small acoustic perturbation is considered. 2. All the air particles conduct simple harmonic vibration at the acoustic equilibrium position. In this paper, it is assumed that no air flow occurs in the air flow field, i.e., no wind condition. Therefore, the N-S equation can be simplified to a linear N-S equation. 3. The void wall surface is completely filled with air. In the model, the air is in continuous and complete contact with the void structure. 4. The adiabatic condition is applied to the air model boundary. The thermal energy generated by friction between the air and the void wall raises the temperature of the PAC but it does not exchange heat with the air. Only the sound absorption effect at 293.15 K is taken into account. 5. The incident direction of the sound source is selected as the Z direction. The type and size of the sound source have no effect on the final calculation results because the material's SAC is its own property. In this paper, the incident source is a plane wave perpendicular to the surface of the sample model with a pressure amplitude of 1 Pa.