# Prediction of Thermal Cracking During Construction of Massive Monolithic Structures
## 3 Results and Discussion  
### Verification of the Calculation Methodology  
At the first stage, to verify the developed program, a calculation was performed with a constant modulus of elasticity of fresh concrete \(E=10^{4}\) MPa over time, followed by a comparison with the solution in the ANSYS 2021R1 software package (Figure 5). The material model in ANSYS was adopted as a linear elastic one without time dependence of the elastic modulus. The old concrete had a compressive strength class B45 with a corresponding modulus of elasticity \(E\) = 3.7 \(\times\) 10\({}^{4}\) MPa. The size of the finite element mesh was taken to be 0.2 m, which ensured an optimal balance between the speed and accuracy of the results. The time step was taken to be 0.5 h. The remaining data used in the calculation are given in Table 1.  
Table 2 presents a comparison of maximum temperatures at different points in time obtained as a result of calculation in the authors' program and in the ANSYS software package. The discrepancy between the results is insignificant. The maximum temperature was 41.3 \({}^{\circ}\)C, which is consistent with the data of field temperature measurements using thermocouples installed inside the structure (\(T_{max}^{experiment}\) = 41 \({}^{\circ}\)C). The thermocouple that recorded the maximum temperature was installed inside the structure at a distance of 1.1 m from the upper surface and 1.4 m from the left edge in the middle of the block (Figure 1). Figure 6 shows graphs of the change in time of maximum normal stresses \(\sigma_{z}\) obtained in the authors' program and in ANSYS with a constant modulus of elasticity of fresh concrete. The maximum discrepancy between the results is 2.5%. \begin{table}
\begin{tabular}{c c c} \hline
**Quantity** & **Unit of Measurement** & **Value** \\ \hline Linear thermal expansion coefficient of old and new concrete & 1/\({}^{\circ}\)C & 10\({}^{-5}\) \\ Thermal conductivity coefficient of old and new concrete & W/(m\({}^{\circ}\)C) & 2.67 \\ Density of old and new concrete & kg/m\({}^{3}\) & 2500 \\ Specific heat capacity of old and new concrete & J/(kg\({}^{\circ}\)C) & 1000 \\ Heat transfer coefficient on the upper surface & W/(m\({}^{2.\circ}\)C) & 25 \\ Heat transfer coefficient on side surfaces covered by formwork & W/(m\({}^{2.\circ}\)C) & 10 \\ Initial temperature of the base made of old concrete & \({}^{\circ}\)C & 10 \\ \hline \end{tabular}
\end{table} 
Table 1: Initial data used in the calculation. Figure 5: Finite element model in the ANSYS software package. Results of Stress-Strain State Calculation of the Dock Wall with Time-Varying Concrete Elastic Modulus  
The calculation with time-dependent elastic modulus of concrete was performed for five options:  
1. Concrete cubic compressive strength \(R\) was calculated as a function of its maturity degree \(DM\) using Formula (17). The elastic modulus was calculated as a function of the prismatic compressive strength \(R_{b}\) according to Formula (12). 2. The elastic modulus was determined as a function of concrete equivalent age \(t_{eq}\) with the use of Formula (11). 3. The cubic compressive strength \(R\) was calculated by the equivalent age with the use of Equation (15). The elastic modulus was determined by the prismatic strength \(R_{b}\) according to Formula (12). 4. The value of \(R\) was calculated by the value \(DM\) using Formula (17). The elastic modulus was determined by the \(R\) value using Formula (14). 5. The value of \(R\) was determined by the equivalent age according to Formula (15). The elastic modulus was calculated by the \(R\) value using Formula (14). \begin{table}
\begin{tabular}{c c c} \hline \hline \(t\), \(h\) & \(T_{\text{max}}\)\({}^{\circ}\)C (ANSYS) & \(T_{\text{max}}\)\({}^{\circ}\)C (Authors) \\ \hline
10 & 22.717 & 22.721 \\
20 & 34.470 & 34.498 \\
30 & 39.173 & 39.259 \\
40 & 40.898 & 41.020 \\
50 & 41.136 & 41.254 \\
60 & 40.525 & 40.615 \\
70 & 39.410 & 39.471 \\ \hline \hline \end{tabular}
\end{table}