## 2 Experimental Setup
### Experimental Strategy  
An electrical high-temperature furnace with a capacity of heating up to 1000 \({}^{\circ}\)C is used to supply thermal cycles on the concrete specimens. Thermal cycles are carried out at temperatures in the range of ambient temperature (25 \({}^{\circ}\)C) to the maximal value (400 \({}^{\circ}\)C, 500 \({}^{\circ}\)C, and 600 \({}^{\circ}\)C). Five cycles are considered, and the tests are denoted by 400-25-5, 500-25-5, and 600-25-5, respectively. In order to consider the high-temperature operation condition of the thermal energy storage, the lower temperature during the thermal cycles is selected as 300 \({}^{\circ}\)C instead of the ambient temperature. Two cases--one performing 5 cycles and the other 10 cycles--are taken into account. We denote 400-300-5, 500-300-5, and 600-300-5 for the 5-cycle tests; and 400-300-10, 500-300-10, and 600-300-10 for the 10-cycle tests. In addition, non-cycling tests, exposure of specimens to high temperatures of 200, 300, 400, 500, and 600 \({}^{\circ}\)C is considered to examine the effect of thermal cycling. Each test case uses three concrete specimens. The test cases are listed in Table 2.  
A sufficiently long heating time is necessary to ensure the internal temperature of concrete specimens reaches the expected maximal temperature during the heating process. A finite element (FE) method based heat transfer analysis is carried out to determine a reasonable heating time. Two concrete specimens, in which temperature sensors are buried, are heated to approximate 400 \({}^{\circ}\)C in the furnace. The temperatures of the surface and internal of the concrete specimens are measured, and the variation curves are shown in Figure 2. \begin{table}
\begin{tabular}{c c c c} \hline
**Test Cases** & **Maximal Temperature (\({}^{\circ}\)C)** & **Lower Temperature (\({}^{\circ}\)C)** & **Thermal Cycles** \\ \hline
400-300-5 1 & 400 & 300 & 5 \\
500-300-5 & 500 & 300 & 5 \\
600-300-5 & 600 & 300 & 5 \\
400-300-10 & 400 & 300 & 10 \\
500-300-10 & 500 & 300 & 10 \\
600-300-10 & 600 & 300 & 10 \\
400-25-5 & 400 & 25 & 5 \\
500-25-5 & 500 & 25 & 5 \\
600-25-5 & 600 & 25 & 5 \\
200 \({}^{\circ}\)C & 200 & 25 & - \\
300 \({}^{\circ}\)C & 300 & 25 & - \\
400 \({}^{\circ}\)C & 400 & 25 & - \\
500 \({}^{\circ}\)C & 500 & 25 & - \\
600 \({}^{\circ}\)C & 600 & 25 & - \\ \hline \end{tabular} \({}^{1}\) 400 and 300 denote the maximal and lower temperatures, respectively, in the thermal cycling test. 5 is the cycle number.  
\end{table} 
Table 2: Test cases and heating scheme. Figure 2: Temperature variation curves of the surface and internal of the specimens. A two-dimensional FE model is used to simulate the heat transfer process. The concrete specimen is discretized into 3 \(\times\) 3 mm\({}^{2}\) quadrilateral FE mesh. The measured surface temperature is applied as boundary condition in the simulation. Inverse analysis is carried out according to the temperature curves of specimen 1 to determine the thermal parameters, i.e., the thermal conductivity of concrete and the heat transfer coefficient (HTC) between concrete and air. Figure 3 shows the results of the inverse analysis. It can be found that the calculated internal temperatures gradually approach the measured curve when increasing HTCs from 0.5 to 10 W/m\({}^{2.}\)\({}^{\circ}\)C. Therefore, the thermal conductivity of concrete and HTC are taken as 1.94 and 10 W/m\({}^{2.}\)\({}^{\circ}\)C. The internal temperature of specimen 2 is reproduced using the FE model with the determined thermal parameters. The numerical result shown in Figure 4 is in good agreement with the measured curve, indicating the FE model has sufficient accuracy for heat transfer analysis of the test concrete. In the numerical modeling, the first heating experiment is considered. The water in the concrete is ignored, which has important influence on heat transfer during subsequent heating of concrete thermal storage structures.