# Dynamic Response Analysis of Asphalt Pavement under Pavement-Unevenness Excitation
## 4 Numerical Results
### Effects of Transverse Isotropy  
In this section, six kinds of Young's modulus \(E_{v}\) in different vertical directions are selected, and the Young's modulus \(E_{h}\) in horizontal direction remains unchanged (as shown in Figure 14). In addition, parameter \(\zeta=E_{v}/E_{h}\) is defined, and parameter \(\zeta\) equal to 1 represents isotropy, while parameter \(\zeta\) is not 1 represents transverse isotropy. A speed of 20 m/s and a pavement grade of B are selected to calculate the mechanical response of the pavement with different \(\zeta\) values. The results are shown in Figure 15.  
Figure 13: Influence of interface coefficient on mechanical response at bottom of surface layer. (**a**) Bottom of the surface layer \(\sigma_{zz}\); (**b**) bottom of the surface layer \(\sigma_{xx}\); (**c**) bottom of the surface layer \(\varepsilon_{xx}\); (**d**) bottom of the surface layer \(\varepsilon_{zz}\).  
Figure 15 shows the variation of \(\sigma_{zz}\), \(\sigma_{xx}\), \(\epsilon_{xx}\), and \(\epsilon_{zz}\) with the modulus ratio of \(\zeta\) at the bottom of the surface layer. It can be seen from the figure that there are significant differences between the response at the bottom of the surface layer and the change of displacement stress on the surface. In Figure 15a, the mean value and peak value of \(\sigma_{zz}\) increase with the increase of modulus ratio. Contrary to the change law of surface displacement, when the modulus ratio \(\zeta\) increases from 0.5 to 3, its peak value increases from 0.0364 MPa to 0.0487 MPa, an increase of 33.8%. In Figure 15b, the mean value and peak value of \(\sigma_{xx}\) show a tendency to decrease sharply with the modulus ratio. At the same  
Figure 14: Schematic diagram of isotropic base and base in transverse view.  
Figure 15: Influence of transverse isotropy on mechanical response of surface bottom. (**a**) Bottom of the surface layer \(\sigma_{zz}\); (**b**) bottom of the surface layer \(\sigma_{xx}\); (**c**) bottom of the surface layer \(\epsilon_{xx}\); (**d**) bottom of the surface layer \(\epsilon_{zz}\).  
time, the degree of dispersion also decreases sharply, and the probability of high horizontal stress at a high modulus ratio is greatly reduced. It can be seen from Figure 15c,d that both the mean and peak values of \(\varepsilon_{xx}\) and \(\varepsilon_{zz}\) decrease with the increase of the modulus compared with \(\zeta\). The peak value of \(\varepsilon_{xx}\) decreases from 0.0158 to 0.00817, decreasing by 48.3%, while the peak value of \(\varepsilon_{zz}\) decreases from 0.0271 to 0.0251, decreasing by only 7.8%. The reduction of horizontal strain is much greater than that of vertical strain. At the same time, the horizontal strain \(\varepsilon_{xx}\) distribution in the range of 25%-75% and 1%-99% will decrease with the increase of the modulus ratio, and the degree of dispersion gradually becomes smaller, reducing the probability of high horizontal strain at the bottom of the surface layer, which indicates that too low of a modulus ratio will increase the probability of fatigue failure of the pavement. Therefore, suitable base and bottom base materials should be selected in pavement design to avoid this situation.