## 4 Thermal Stress Analysis and Optimization of Contraction Joint Distance
### Boundary Conditions and Actions  
In the analysis of the temperature field (TF), the following boundary conditions are taken into account: (I) at the interface between the blocks and the rock mass, (II) at the interface between the old and newly poured blocks, (III) at the surfaces of blocks that are in contact with air and water, as well as (IV) temperature levels of the surrounding rock mass and the fresh concrete mix. In every phase of the analysis, the ambient temperatures during construction and service life are applied on the surface of the blocks that are in contact with air [44], ranging from \(-2.0\) to 33.0 \({}^{\circ}\)C (Table 1). The ambient temperatures were measured by the meteorological station that was built immediately upstream of the dam construction site. The boundary condition concerning the air temperature on the blocks' side surfaces is applied taking into consideration the sequence of pouring of the blocks of the neighboring monolith in space and time (Figure 5). In this case, proper cooling of a freshly cast block of the monolith considered is enabled from all sides. Figure 4: Concrete blocks in the gravity dam (numbers coincide with the sequence of pouring). of 9.0 \({}^{\circ}\)C is applied [44]. Water temperature does not vary with depth as a result of the assumption of water flow resulting from the operation of the power plant intake near the upstream face of the dam. This assumption leads to the fact that the model of temperature variation through depth [45], typical for deep reservoirs, is not applied in this analysis. On the downstream side, the non-overflowing monolith is not in contact with the tailwater, and therefore the impact of the tailwater's temperature on the structure is excluded. The temperature of the surrounding rock mass is adopted as the constant mean multiannual value of 13.0 \({}^{\circ}\)C.  
The temperature of the fresh concrete mixture ranges from 9.50 to 13.10 \({}^{\circ}\)C [44], depending on the season in which the mixing and transport are taking place (Table 3). In the analysis of the stress field (SF), the displacement boundary condition is applied along the bottom, upstream, and downstream boundaries of the rock mass. In these areas, the nodal displacements (\(u\)) are restrained in all directions (Figure 6). \[u_{x}=u_{y}=u_{z}=0 \tag{11}\]  
This way, a more realistic simulation of the rock mass behavior is enabled, as well as the self-weight-induced deformation when compared to the traditionally used fully clamped models of concrete dams without surrounding rock mass. The specified boundary conditions take into account all the relevant thermal processes (including the impact of the reservoir water temperature on the structure) and self-weight of the structure, but disregards other actions which would disturb the realistic TTS field (hydrostatic pressure and the uplift forces). At the beginning of each phase of the analysis, an active part of the model is defined, because the concrete blocks are being born successively one after another at the exactly defined time intervals (\"birth and death element\"). Thereby, a history of deformations from the preceding phases is taken into account. The dam's self-weight and the weight of the surrounding rock mass are taken as an initial action on the model, which serves as a basis for defining the initial SF. Derivation of stresses and deformations resulting from the self-weight is performed in the first step of each of the analysis phases. The temperature field (TF) for the corresponding SF analysis step is taken from the previously conducted thermal analysis, by using semi-coupled TSA (in which deformations are impacted by temperature, but not vice versa). Hydrostatic pressure and uplift actions are not considered in the analysis, because including these actions in the analysis would conceal the actual impact of the thermal factors on the SF in the dam's body.