# Study on Temperature Correction of Asphalt Pavement Deflection Based on the Deflection Change Rate
## 5 Deflection Temperature Modelling
### Temperature Correction Model for the Deflection Basin
#### 5.2.3 Temperature Correction Based on the Deflection Change Rate at a Radial Distance of 20 cm  
This method first selects a certain distance from 0 to 90 cm at each radial distance as the basis and then corrects other deflections in the deflection basin. The selection principle of this radial distance is that the fitting result between the deflection ratios before and after temperature correction and the temperature is the best. The temperature correction results for deflections at each radial distance were obtained by fitting the deflections from 0 to 90 cm to the temperature. The fitting result at the load center is shown in Figure 7, and the fitting results at other radial distances are shown in Figure 10.  
The correlation coefficients of the fitting results at each radial distance are shown in Table 4.  
As seen in the above table, the best fitting result was obtained for the point at a radial distance of 20 cm, with \(R^{2}\) reaching 0.964. Therefore, this method looks for the relationship between the change rate before and after the temperature correction of deflections at other radial distances and the deflection change rate at a radial distance of 20 cm to correct the deflection basin. The deflection change rate at the load center and radial distance of 30-90 cm and the deflection change rate at the radial distance of 20 cm are fitted to obtain the ratio of the deflection change rate at each radial distance to the radial distance of 20 cm, and the results are shown in Figure 11. Adjustment coefficients for deflections are shown in Table 5. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Radial** & **0** & **20** & **30** & **45** & **60** & **90** \\
**Distances** & **0** & **20** & **30** & **45** & **60** & **90** \\ \hline \(R^{2}\) & 0.874 & 0.964 & 0.938 & 0.883 & 0.831 & 0.741 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Fitting results at each radial distance. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Radial** & **0** & **30** & **45** & **60** & **90** \\
**Distance/cm** & **0** & **30** & **45** & **60** & **90** \\ \hline \(k\) & 1.6994 & 0.8276 & 0.7382 & 0.6793 & 0.5623 \\ \(R^{2}\) & 0.9033 & 0.9831 & 0.9499 & 0.9024 & 0.8095 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Adjustment coefficients for deflections at each radial distance. In the above graphs, the fitting degree of this method is better than that of the correction based on the load center deflection, and the obtained results are more accurate. The fitted images at radial distances from 30 to 90 cm are \"comet\" shaped, with the comet head at the (0, 0) coordinate and the comet tail at the third quadrant away from the (0, 0) point. The tail's divergence becomes higher as the distance from the measurement point increases. In contrast, the fitted image at the load center is not \"comet-like\" and appears to be more diffuse. According to [PERSON]'s principle, this is due to the stress concentration at the load center. The load center is affected by the drop weight, and the configuration of the pavement has a great influence on the stress distribution generated by the drop weight, resulting in large fluctuations in the deflection at the load center due to the nearby stress distribution, while points farther away from the drop are hardly affected by this. Figure 10: Deflection fitting results at other radial distances: (**a**) 20 cm; (**b**) 30 cm; (**c**) 45 cm; (**d**) 60 cm; (**e**) 90 cm. Then, a more suitable deflection temperature correction model at different radial distances in the temperature-affected range is obtained, as shown in Equation (10):  
\[\left\{