## 5 Dynamic Mechanical Response Analysis of Asphalt Pavement under the Influence of Groundwater
### Analysis of Asphalt Pavement Deflection Calculation  
Asphalt is a road-binding material with extremely high temperature sensitivity. Therefore, this study fully considers the impact of temperature on the deflection of asphalt pavements, conducting research on the mechanical response variations of asphalt pavements under both ambient (20 \({}^{\circ}\)C) and high-temperature (45 \({}^{\circ}\)C) conditions. The related deflection time history curve calculations and analysis results are shown in Figures 6 and 7.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**Sensor Number** & **D1** & **D2** & **D3** & **D4** & **D5** & **D6** & **D7** & **D8** & **D9** \\ \hline Distance from & 0 & 203 & 305 & 457 & 610 & 914 & 1219 & 1574 & 1829 \\ Load Center (mm) & & & & & & & & & \\ \hline \end{tabular}
\end{table}
Table 2: Arrangement of Dynatest 8000 FWD sensors.  
Figure 4: Finite element model of pavement.  
Figure 5: Mesh partitioning of the model.  
It can be observed that as the time increased, the deflection values at various sensor locations initially increased and then decreased, exhibiting a sinusoidal pattern similar to the applied load. Additionally, the arrival time of the peak deflection values at different sensor locations lagged as the sensor locations moved farther away. This observed lag phenomenon aligns with the real-world scenario, indicating a certain degree of reasonableness in the computed results. At the same time, it was found that temperature has a significant impact on the dynamic deflection changes of asphalt pavements. As the temperature increased, the deflection values of the asphalt pavement continuously grew, with the most noticeable increase in the maximum deflection value at the load center position. However, as the distance from the loading center point increased, the influence of temperature on dynamic deflection gradually diminished.  
To further validate the accuracy of the computed results, a comparison was made between the maximum deflection values obtained using finite element analysis and spectral element analysis, as shown in Table 3 and Figure 8.  
Figure 6: Time history curves of deflection measurements at ambient temperature (20 \({}^{\circ}\)C).  
Figure 7: Time history curves of deflection measurements at high temperature (45\({}^{\circ}\)C).  
From Table 3 and Figure 8, it can be observed that the maximum absolute value of the relative error between the results obtained by the two methods was only 1.85%, and the average absolute value of the relative error was only 0.70%. This demonstrates that the accuracy of the calculation method in this paper meets the engineering requirements. Both methods were computed on the same computer, with the finite element method taking approximately 7 min for the pavement deflection calculation, while the spectral element method took approximately 12 s. It is necessary to note that numerical experiments were conducted on an assembled desktop computer equipped with an Intel Core i7-12700 KF (5.0 GHz,12 cores) (Intel, Santa Clara, CA, USA), 64 GB DDR4 RAM, 1 TB SSD (Lenovo, Beijing, China), and a 2 TB hard disk (DELL, Austin, TX, USA), and the system ran on Windows 10. It can be seen that the spectral element method has significantly improved computational efficiency compared to the finite element method.