## 4 Results and Discussion
### Establishment of Moisture Damage Model of Aggregate-Bitumen Interface Shear Strength
The control equations and constitutive relations used in the calculation are as follows. (1) Control equation  
The calculation of the percolation diffusion issue obeys the mass conservation law of the diffusion phase. \[\int\limits_{V}\frac{dc}{dt}dV+\int\limits_{S}n\cdot JdS=0,\]  
Figure 11: Aggregate-bitumen interface shear strength of BA and NHSSMA at different immersion times. where \(c\) is mass concentration of diffusion material, \(V\) is any volume, \(S\) is surface of \(V\), \(n\) is the out-of-plane normal direction of \(S\), \(J\) is the diffusion flux of the diffusion phase, and \(t\) is the time. Apply the divergence theorem to get the following formula. \[\int\limits_{V}\!\!\!\left(\frac{dc}{dt}+\frac{\partial}{\partial x}\cdot J \right)dV=0.\]  
Due to the arbitrariness of the volume, the following formula can be obtained. \[\int\limits_{V}\delta\phi\!\!\left(\frac{dc}{dt}+\frac{\partial}{\partial x} \cdot J\right)dV=0,\]  
where \(\delta\phi\) is an arbitrary continuous scalar field. The above formula can be extended to the following formula. \[\int\limits_{V}\!\!\!\left[\delta\phi\!\!\left(\frac{dc}{dt}\right)+\frac{ \partial}{\partial x}\cdot(\delta\phi I)-J\cdot\frac{\partial\delta\phi}{ \partial x}\right]dV=0,\]  
where \(\phi\) is the standard concentration, \(\varphi=c/s,s\) is the solubility of the diffusion material in the base material. The following formula is obtained by applying the divergence theorem again. \[\int\limits_{V}\!\!\!\left[\delta\phi\!\!\left(\frac{dc}{dt}\right)-\frac{ \partial\delta\phi}{\partial x}\cdot J\right]dV+\int\limits_{S}\delta\phi n \cdot JdS=0.\]  
(2) Constitutive relationship  
Diffusion is assumed to chemical potential gradient drive, and the basic constitutive relationship is as shown in the following equation. \[J=-\mathrm{sD}\left[\frac{\partial\phi}{\partial x}+k_{s}\frac{\partial}{ \partial x}(ln(\theta-\theta^{z}))+k_{p}\frac{\partial p}{\partial x}\right],\]  
where, \(\mathrm{D}(c,\theta,f)\) is the diffusion coefficient; \(s(\theta,f)\) is solubility; \(k_{s}(c,\theta,f)\) is the [PERSON] effect factor, related to the temperature gradient and affects the diffusion; \(\theta\) is the temperature; \(\theta^{z}\) is all zero degrees; \(k_{p}(c,\theta,f)\) is the compressive stress factor and is related to the equivalent compressive stress gradient \(p\), which affects the diffusion; \(f\) is any predefined field variable. The size of simulated model is consistent with the size of the actual shear specimen, which is composed of two \(40\times 40\times 10\) mm cubic granite stones. The main parameter is the moisture diffusion coefficient of the rock material (\(\mathrm{D}_{\mathrm{rock}}\)), and \(\mathrm{D}_{\mathrm{rock}}\) is 0.6 mm\({}^{2}\)/h according to the granite stone. The boundary condition is that the water immersion is half of the height of the lower block, so the water concentration of all surfaces below the 1/2 height of the block is 1. The collected data is the interfacial moisture content at different immersion times in the calculation, and the total immersion time is 144 h. All conditions of the calculation are consistent with the actual situation. The interfacial moisture content is calculated as follows. \[\phi=\frac{C_{m}}{C_{m}^{max}},\]  
where \(\phi\) is the interfacial moisture content, \(C_{m}\) is the interfacial moisture concentration, \(C_{m}^{max}\) is the extreme limit of interfacial moisture concentration. If \(\phi=1\), it means that the moisture at the interface has reached a state of saturation. Figure 12 shows the moisture content of shear specimen at 4 h of immersion. Figure 13 shows fitting curve of interfacial moisture content with immersion time. It can be seen from Figure 13 that interfacial moisture content increases rapidly at the early stage of immersion, and can reach 60% of the extreme limit of interfacial moisture concentration after 50 h of immersion. After 100 h of immersion, the interfacial moisture content tends to be saturated, and the growth rate is obviously slowed down.