# Optimization Method for Improving Efficiency of Thermal Field Reconstruction in Concrete Dam
## 3 Optimization Method for Thermal Field Reconstruction
### Interpolation Algorithm Evaluation and Selection
#### 3.1.1 Interpolation Algorithm Comparison
\[f(y)=\sum_{i=1}^{m}\beta_{i}f(p_{i}). \tag{7}\]  
\[\beta_{i}=\frac{d_{i}^{-1}}{\sum\limits_{i=1}^{m}d_{i}^{-1}}. \tag{8}\]  
where \(f(p_{i})\) is the measured value of the monitoring points; \(d_{i}\) is the distance between the monitoring points and the point to be interpolated; \(m\) is the total number of monitoring points. 3.1.2 Evaluation of Thermal Field Reconstruction Effectiveness  
Surfer (version 14) was employed to perform the three interpolation algorithms, which is professional interpolation software Surfer (version 14) [45]. The data analyzed were collected from the 7#-44 dam block in the WDD dam during its construction, and the optical fiber layout scheme is \"Z\" type [24], as shown in Figure 5. The low-heat Portland cement was utilized, with a slump of 30-40 mm. The concrete incorporates 35% fly ash and 0.6% water-reducing admixture. Based on the field measurements, the ambient temperature was 19.6 \({}^{\circ}\)C on the upstream side and 20.3 \({}^{\circ}\)C on the downstream side when 7#-44 was poured. The reconstructed thermal field in this study is based on actual temperature measurements from the optical fibers, meaning that factors such as cooling water, ambient temperature, and pouring temperature are inherently considered. Thermal field reconstruction results are illustrated in Figures 6-8, respectively. Figure 5: The locations of digital thermometers, optical fiber measurement points, and concrete block 7#-44 of the WDD dam. “#”: This symbol is used to represent the numbering of concrete block. “V”: This symbol indicates the elevation level, which is a standard representation in engineering and geological diagrams. Red “7#”: The red color is used to highlight the selected concrete block, which corresponds to dam section 7#. Kriging  
When the concrete was initially poured, it was affected by the ambient temperature, with the downstream and upstream sides showing higher temperature than the middle. At the age of 1 d, the middle concrete temperature is lower because of the low pouring temperature (about 16 \({}^{\circ}\)C) and less heat of cement hydration. At the age of 3 d, due to the cement hydration, the overall temperature rose sharply, and the maximum temperature rise was 15 \({}^{\circ}\)C. Compared with the age of 3 d, the concrete temperature shows a slight decrease at 5 d and 7 d due to water cooling. The selected concrete block 7#-44 is located at the dam corbel, where secondary aggregate grading concrete was poured. This type of concrete contains a higher amount of cement and emits more hydration heat. To control the downstream concrete temperature, the amount and duration of cooling water were increased, and more cooling water pipes were arranged at the downstream side of the concrete block 7#-44. Therefore, the extra heat at the downstream side was dissipated, resulting in a uniform temperature distribution throughout the structure. As shown in Figure 4:0  
Figure 4:1 Thermal field based on Kriging interpolation algorithm. (**a**) Day 1, (**b**) Day 3, (**c**) Day 5, (**d**) Day 7, (**e**) Day 14, and (**f**) Day 28.