# Study on Temperature Correction of Asphalt Pavement Deflection Based on the Deflection Change Rate
## 4 Effective Influence Distance of Temperature on the Deflection Basin
### Analysis and Results  
The deflection basins before and after correction under different temperatures at a measurement point were used as an example for analysis which were shown in Figure 4.  
According to the above comparison chart, the influence of temperature on deflection decreases with the increasing radial distance. The deflection difference between the calculated and measured deflections when the radial distance is less than 90 cm is obvious and increases with the increasing temperature difference. However, the deflection differences when the radial distances are farther than 90 cm are not obvious. Then, the difference between the measured and calculated deflection of each measuring point is calculated, and the absolute value of the difference is averaged. The results are shown in Figure 5.  
Figure 3: Modulus–temperature model (at middle depth).  
From the graph of the mean value of the absolute difference between the measured and calculated deflection, the deviation first decreased and then increased and reached a minimum value near the radial distance of 90 cm.  
To further verify this conclusion, this paper adopts a method for selecting the effective influence distance based on the minimum mean square error criterion. For the deflection at the same radial distance of a certain measuring point, first calculate the average value of the measured deflections at different test temperatures. Next, calculate the mean value of the measured deflections at different test temperatures with other radial distances. Then, the root mean squared error (RMSE) is calculated by summing the squared differences between the measured deflection and the mean value at different radial distances. The  
Figure 4: Comparison of deflection basins at different temperatures: (**a**) 16.1 \({}^{\circ}\)C; (**b**) 25.1 \({}^{\circ}\)C; (**c**) 35.2 \({}^{\circ}\)C; (**d**) 41.6 \({}^{\circ}\)C.  
Figure 5: The mean of the absolute value of the deflection difference.  
distance between the load center and the point with the smallest RMSE value is the effective influence distance of the structure. The calculation formula of the RMSE is as follows:  
\[\left\{\begin{array}{l}\text{RMSE}=\sqrt{\frac{1}{n}\sum\limits_{i=1}^{n} \left(\frac{def_{i}-\overline{def}}{def}\right)^{2}}\times 100\%\\ \overline{def}=\frac{1}{n}\sum\limits_{i=1}^{n}def_{i}\end{array}\right. \tag{5}\]  
where \(n\) is the number of different test temperatures selected, \(def_{i}\) is the deflection of the \(i\)th test temperature, and \(\overline{def}\) is the average value of the different test temperatures from a certain measurement point.  
Figure 6 shows that the overall trend of the RMSE first decreases and then increases and reaches the minimum value at 90 cm.  
In summary, it can be determined that the effective radial distance of the temperature on the influence of the deflection basin is 90 cm. The deflections from the load center to the radial distance of 90 cm must be corrected for temperature. The deflection at further radial distances does not require correction.