## 3 Results and Discussion
### Reinforcement Mechanisms
#### 3.4.1 Reinforcement Mechanism of Nano-CaCO\({}_{3}\)-Modified Asphalt Binder  
The nano-CaCO\({}_{3}\) particles are about 10-100 nm in diameter, and they are dispersed into base asphalt by the heating and stirring method to prepare a modified asphalt. The nano-CaCO\({}_{3}\) particles dispersed in the modified asphalt can effectively increase the strength of material that can be explained by the Orowan mechanism and the Hall-Petch reinforcement mechanism. The original idea is to use these small but hard nano-CaCO\({}_{3}\) particles to hinder the asphalt binder movement, thereby increasing the modulus of material without significantly affecting the stiffness of the material [33].  
The Orowan mechanism theory can be expressed by Equation (1):  
\[\tau=\upmu\mathrm{b}/\mathrm{L} \tag{1}\]  
where, \(\tau\) is the yield stress of composite, \(\upmu\) is the shear modulus of matrix, \(\mathrm{b}\) is Burgers vector of matrix, and \(\mathrm{L}\) is the average distance between the particles.  
In this study, according to the Orowan theory, the external load is mainly borne by the asphalt, and nano-CaCO\({}_{3}\) particles hinder the dislocation motion of the asphalt, thereby enhancing the properties of the modified asphalt. The smaller the particle size, the smaller the average distance between the particles, and the greater the yield stress of the modified asphalt.  
According to the Hall-Petch reinforcement mechanism, the atomic arrangement is irregular at the interface between the nano-CaCO\({}_{3}\) particles and asphalt, and the phase interface hinders the plastic deformation of the modified asphalt.  
Figure 8: SEM result of CaCO\({}_{3}\) whiskers-modified asphalt (magnification: 6500\(\times\)).  
Figure 9: SEM result of aramid fiber-modified asphalt (**a**) magnification: 50\(\times\), (**b**) magnification: 92\(\times\).  
The Hall-Petch reinforcement mechanism can be expressed by Equation (2):  
\[\sigma=\sigma_{0}+\mathrm{K}\cdot\delta^{-1/2} \tag{2}\]  
where, \(\sigma\) is the yield strength of the material, which is proportional to the \(-\)1/2 power of the average diameter of the particles. In the case where the particle volume fraction is constant, the smaller the particle size, the more the phase interface, so that the greater the ability to block dislocation motion, and the better the material is strengthened.  
In fact, nano-CaCO\({}_{3}\) enhances the high-temperature performance of asphalt by diffusion enhancement, which may be the result of the above two mechanisms.  
The process of nano-CaCO\({}_{3}\)-modified asphalt is a physical miscibility process. Due to the extremely small particle size of nano-CaCO\({}_{3}\), the miscible system is uniform and stable, and it is suitable for production applications. In this study, nano-CaCO\({}_{3}\) (10-100 nm) was dispersed into the asphalt by heating and stirring. Due to the sufficient thermal stability of nano-CaCO\({}_{3}\) under the use temperature conditions, no chemical reaction occurred between the reinforcement and the matrix. Therefore, it does not dissolve in the asphalt and can last for a long time to enhance the effect.