## 4 Thermal Stress Analysis and Optimization of Contraction Joint Distance
### Results of Stress Field Analysis  
Results of SF analysis are shown in the chosen distinctive time sections in the figures that follow. Each of the figures shows the SF for two monolith lengths under consideration (20.0 m and 15.0 m). The results are shown in the mid-plane of the monolith, as the \(\sigma_{z}\) (SZ) stresses in this plane are the greatest. It can be noticed from the obtained results that all blocks of the dam undergo similar stress fields during construction. Instantly upon concreting one of the blocks, heating and expansion occur, as a result of the released hydration heat, which, arising from limited deformation caused by the interaction with neighboring blocks, causes compressive stresses in the block and its narrow zone (freshly cast blocks in the upper parts of the monolith in Figures 19-21). The heating of one block can be additionally facilitated by the extreme air temperatures over a longer period (as described in Figure 15). Subsequently, the concrete cooling process can be abrupt (resulting from a sudden change in the seasonal temperature)  
Figure 18: Temperature field for day 1804 (25 th of September of the sixth year) with horizontal cross-section at 170.50 msl; maximum: node 2899, minimum: node 4143. Observing the results of TF for the 84 th and 512 th day (Figures 14 and 16), which are under the influence of winter air temperatures, it can be concluded that the maximum TTS (Figures 19 and 21) is a consequence of a sudden cooling of the concrete in the surface region. Precisely, the process of sudden cooling is responsible for the occurrence of the maximum TTS in the entire analysis period (day 512, crest zone--Figure 21). Extreme values of TTS also appear in the blocks between the vertical joints which progressed faster compared to concreting of the remaining parts of the structure (Figures 8 and 20-23, orange-yellow zones), which caused the heat released in the cement hydration process to become trapped inside the concrete as a result of the faster progress. TTS emerges when the heat is emitted, and the blocks start to cool. Figures 24 and 25 show the extreme values of \(\sigma_{z}\) for different monolith lengths as a function of the time period after the completion of construction, and the difference in these values during the same period, respectively. The oscillations of the \(\sigma_{z}\) stresses coincide with the annual ambient temperature changes, represented as \(T_{a}\) in these Figures. Figure 26 shows the extreme \(\sigma_{z}\) value as a function of the ambient temperatures \(T_{a}\). Figure 23: Stresses \(\sigma_{z}\) in the mid-plane of the monolith 20 m long (**left**) and 15 m long (**right**) for the 1804 th day (25 th of September of the sixth year); extremums: nodes 301,351 and 27,434. Figure 22: Stresses \(\sigma_{z}\) in the mid-plane of the monolith 20 m long (**left**) and 15 m long (**right**) for the 1080 th day (2 nd of October of the fourth year); extremums: nodes 301,351 and 27,434. Figure 24: Extreme values of \(\sigma_{z}\) [MPa] as a function of the time period after the completion of construction (blue—monolith length 20.0 m; orange—monolith length 15.0 m; yellow—ambient temperature \(T_{a}\) [\({}^{\circ}\)C]). Figure 25: The difference between extreme values of \(\sigma_{z}\) [MPa] between two monolith lengths as a function of the time period after the completion of construction (grey) and ambient temperature \(T_{a}\) [\({}^{\circ}\)C] (yellow). The reservoir filling contributes to the cooling process of the entire cross-section of the dam (as described in Figures 17 and 18); however, locally, in the zone of the interface of the upstream face of the structure with water of a constant temperature of 9.0 \({}^{\circ}\)C, the concrete tensile resistance is not exceeded.