# Influence of Monolith Length on Temperature Field of Concrete Gravity Dams
## 4 Analysis Results
### Verification of the Model
Figure 12 shows the changes in the calculated temperatures in node 2938 that occurred with a monolith length change, and in relation to the temperature values obtained in the thermal analysis for a monolith length of 20.0 m. It can be seen that the most extreme values of temperature changes in node 2938 were as follows: 1.1 \({}^{\circ}\)C for a reduction of 5.0 m, 1.8 \({}^{\circ}\)C for a reduction of 7.50 m, and 2.6 \({}^{\circ}\)C for a reduction of 10.0 m.  
The concrete temperature in node 3016, located above the monolith's central zone, closer to the downstream face, reached the following maximum values, depending on the considered monolith length: 35.1 \({}^{\circ}\)C (L-20), 34.3 \({}^{\circ}\)C (L-15), 33.5 \({}^{\circ}\)C (L-12.5), and 32.3 \({}^{\circ}\)C (L-10). As in the case of node 2938, the maximum values of the concrete temperatures occurred at different times, depending on the considered monolith length: after 83 days (L-20), after 66 days (L-15), after 60 days (L-12.5), and after 56 days (L-10). In the final analysis step, the concrete temperatures had the following values: 19.8 \({}^{\circ}\)C (L-20), 19.7 \({}^{\circ}\)C (L-15), 19.7 \({}^{\circ}\)C (L-12.5), and 19.6 \({}^{\circ}\)C (L-10). Figure 14 shows the changes in the calculated temperatures in node 3016 that occurred with a monolith length change, and in relation to the temperature values obtained in the thermal analysis for the monolith length of 20.0 m. It can be seen that the most extreme values of temperature changes in this node were as follows: 1.5 \({}^{\circ}\)C for a reduction of 5.0 m, 2.4 \({}^{\circ}\)C for a reduction of 7.50 m, and 3.4 \({}^{\circ}\)C for a reduction of 10.0 m.  
The concrete temperatures in node 3184, which was located in the zone of the dam's crest, indicated a significant influence of seasonal changes on the air temperature. It can also be seen that the concrete temperatures in the node were closer to the average annual air temperature. The concrete temperature at node 3184 reached the following maximum values, depending on the considered monolith length: 31.5 \({}^{\circ}\)C (L-20), 31.8 \({}^{\circ}\)C (L-15), 31.8 \({}^{\circ}\)C (L-12.5), and 31.3 \({}^{\circ}\)C (L-10). The maximum values of the concrete temperatures occurred at different times, depending on the considered monolith length: after 32 days (L-20), after 27 days (L-15 and L-12.5), and after 25 days (L-10). In the final analysis step, the concrete temperatures had a value of 14.7 \({}^{\circ}\)C for all the considered monolith lengths. Figure 16 shows the changes in the calculated temperatures of node 3184 that occurred with a change in the monolith length, and in relation to the temperature values obtained in the thermal analysis for a monolith length of 20.0 m. It can be seen that the most extreme values of temperature changes in this node were as follows: 0.5 \({}^{\circ}\)C for a reduction of 5.0 m, 0.9 \({}^{\circ}\)C for a reduction of 7.50 m, and 1.6 \({}^{\circ}\)C for a reduction of 10.0 m.  
Many empirical formulae have been developed to obtain the temperature variations in concrete dams. One such equation, which was developed for thick concrete sections and assumes a sinusoidal representation for the air temperature, is given in [23]. In the control nodes 3016 and 3184, where the influence of the ambient temperature penetration can be seen in the previously shown images, verification of the amplitude of the concrete temperature oscillations was carried out using the aforementioned calculation method proposed in [4; 23], which was suitable for this dam.