## 3 Components of the Predictive Formula  
### Effect of Cooling Pipes  
Owing to the point-thermometers located in the middle of the two layers of cooling pipes, the cooling effects of the upper and lower cooling pipes at the measuring point of the thermometer were reflected by related data. Therefore, the data at a later age were suitable for this study, with the rate of hydration being very slow during this period and the temperature decreases inside the concrete almost definitely caused by the cooling pipes. According to practical experience, when the difference between the temperatures of the concrete and the water is large, the cooling effect is more obvious; the same is true for the water flow rate. However, when the flow rate increases to a certain point, the increasing rate of the cooling effect slows down as the flow rate increases [26].  
The factors that affect cooling also include the material, section size, length, and spacing of the cooling pipes [26; 27; 28; 29; 30]. Because the specifications of the cooling pipes were determined and the length of the cooling pipes in the Baihetan and Wudongde dams were required to be as similar as possible, the impacts mentioned above are not considered in this study for simplification reasons. According to the analysis above, Equation (1) was established to reflect the cooling effect of the upper or lower cooling pipe on the thermometer located in the middle of the two layers of pipes, and the least square fitting method was used to calculate the parameters based on the field data.  
\[\Delta\mathrm{T_{w}}=\mathrm{P_{1}}\times(\mathrm{T_{c}}-\mathrm{T_{w}})\times \frac{q}{\mathrm{P_{2}}+q}\times\Delta t, \tag{1}\]  
Figure 2: Arrangement of the thermometer string: (**a**) spacing of thermometers (cm); (**b**) concrete column.  
where \(\Delta\mathrm{T_{w}}\) is the temperature falling caused by cooling pipe during the time of \(\Delta\mathrm{t}\) (\({}^{\circ}\)C); \(\mathrm{T_{c}}\) is the concrete temperature at the beginning of the time period \(\Delta\mathrm{t}\) (\({}^{\circ}\)C); \(\mathrm{T_{w}}\) is the average temperature of the cooling water at the inlet of the cooling pipe during the time period \(\Delta\mathrm{t}\) (\({}^{\circ}\)C), which was measured by the thermometer located inside the cooling pipe; \(\mathrm{q}\) is the average flow rate of the cooling water during the time period \(\Delta\mathrm{t}\) (L/min); and \(\mathrm{p_{1}}\) and \(\mathrm{p_{2}}\) are parameters to be determined. The time represented by \(\Delta\mathrm{t}\) is either one or two days herein. The data of each branch pipe were unable to be obtained; therefore, for the point-thermometers located in the same pouring layer and between the same main pipes, the average values of these thermometer readings were used to fit the data. The superposition of the cooling effect of the upper and lower cooling pipes was taken into account in the fitting procedure.  
The parameter values are listed in Table 3, which were obtained by fitting according to the data of the two dams. The fitted results and measured values are depicted in Figure 3. From the comparison, the fitting results of the formula were in good agreement with the measured values. In addition to the systematic error, some results with relatively large differences from the actual values may have resulted from uneven distribution of flow from the main pipes to the branch pipes. Further, the cooling effect of the Baihetan dam was relatively weaker than that of the Wudongde dam according to Equation (1) and the parameter values of the two dams, as listed in Table 3, owing to the Baihetan dam being thicker than the Wudongde dam.