## 2 Numerical Simulation  
### Theoretical Foundation  
Asphalt mixture is a type of porous medium material. Based on the porous medium theory, a porous structure with liquid filled inside its pores can be regarded as a plate containing a circular pore according to elastic mechanics [8; 16]. As shown in Figure 1, the radii of the pore and the plate are \(r\) and \(R\), respectively; the pressure distribution inside the pore is \(q\); and the distribution of tangential stress \(\sigma_{\theta}\) at the edge of the pore can be expressed in the polar coordinate system as Equation (1), where \(\rho\) is the density of liquid inside the pore. Therefore, tensile stress will always be produced at the edge of the pore due to its internal pressure distribution, which will induce the raveling and stripping of asphalt mixture particles and eventually develop into moisture damage. Tensile stress at the edge of the pore is closely related to the porosity of the porous medium material and the increased rate of external stress. \[\sigma_{\theta}=\frac{\frac{R^{2}}{p^{2}}-1}{\frac{R^{2}}{r^{2}}-1}\times q\infty \tag{1}\]  
Biot consolidation theory in soil mechanics is referred to in order to interpret the coupling effect between pore water pressure and the solid skeleton of porous medium inside the internal structure of asphalt pavement [17; 18; 19; 20]. The theory assumes that the studied object is composed of an ideal elastic material, which is homogeneous and thoroughly saturated; the structural deformation is extremely small; both the material particle and its internal pore water are incompressible; and the pore water obeys [PERSON]'s law with a constant permeability coefficient. Based on Biot consolidation theory, the dynamic equilibrium equation of elastic porous medium is expressed as Equation (2) [21]. \(\overrightarrow{u}\), \(\overrightarrow{v_{s}}\), and \(\overrightarrow{v_{f}}\) are displacement vector, velocity vector for porous medium, and velocity vector for fluid, respectively. \(G\) is porous medium shear modulus, and \(\
u\) is its Poisson's ratio. \(p\) and \(n\) are pore pressure and porosity, respectively, while \(\rho_{s}\) is porous medium density and \(\rho_{f}\) is fluid density. Further, the seepage continuous differential equation is shown as Equation (3), in which \(k\) is the permeability coefficient, and both \(\beta_{f}\) and \(\gamma_{f}\) are the fluid compressibility coefficient and bulk density, respectively. \[G\
abla^{2}\overrightarrow{u}+\frac{G}{1-2\
u}\
abla div\overrightarrow{u }=\
abla p+(1-n)\rho_{s}\frac{\partial\overrightarrow{v_{s}}}{\partial t}+n \rho_{f}\frac{\partial\overrightarrow{v_{f}}}{\partial t} \tag{2}\]  
\[\frac{k}{\gamma_{f}}\
abla^{2}p=n\beta_{f}\frac{\partial p}{\partial t}+ \frac{\partial\Big{(}div\overrightarrow{u}\Big{)}}{\partial t} \tag{3}\]  
The fluid-solid coupling effect inside the asphalt mixture is the interaction between water flow and solid medium. During the process of water seepage, internal pore water pressure will be changed under a vehicle load, which results in the change of effective stress and strain fields on the porous medium skeleton of the asphalt mixture and makes the pavement structure exist in a more severe environment. Moreover, these changes will further inversely affect water seepage and pore water pressure distribution inside asphalt pavement; for example, the compressed pore channel structure will accelerate the water flow. In fact, aggregate particles with different sizes randomly distribute inside the asphalt mixture, which makes the asphalt mixture exhibit physical and mechanical properties with anisotropy. Meanwhile, pore distribution inside the asphalt mixture is also not uniform. This study mainly investigates the influence of pore water pressure on  
Figure 1: Internal pressure distribution of the circular pore in a plate [16]. structural dynamic responses of asphalt pavement at full-scale, which focuses on their variation trends presented by the entire asphalt pavement structure.