## 4 Thermal Strain Performance Analysis of Annular Concrete Under Pressure Confinement  
Conduct loading experiments on the annular concrete structure. The inner diameter, outer diameter and length of the test components are 300, 380 and 100 mm, respectively. The specific indices and parameters of the concrete structure are detailed in Table 2.  
The selected detection system is composed of FBG strain demodulator and computer. The FBG strain measurement system is composed of ASE broadband light source, strain sensor, fiber grating demodulation instrument and host system, which can be used to collect wavelength information of fiber grating sensor in multiple channels. The computer can detect and analyze the dynamic strain signal synchronously. Figure 5 shows the collection process of the detection system. Figure 4: Contour plot of maximum principal stress in the annular concrete structures. Figure 5: The collection process of the detection system. \begin{table}
\begin{tabular}{l l l l l l} \hline \hline \(\mathbf{E}\) (MPa) & \(\mathbf{v}\) & \(\mathbf{\rho}\) & \(\mathbf{\sigma_{c}}\) (MPa) & \(\mathbf{\sigma_{t}}\) (MPa) & \(\mathbf{\alpha}\) (\(\mathbf{10^{-6}}\)\(\mathbf{C^{-1}}\)) \\ \hline
12,000 & 0.2 & 2300 & 19.1 & 1.83 & 11.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Performance parameters of annular concrete structures. Before formal loading, the FBG strain sensor calibration experiment is carried out. Different loads are applied to the sensor to verify that \(S_{\varepsilon}\approx 1.21\times 10^{-6}\)\(\mu\varepsilon^{-1}\) and \(S_{\mathrm{T}}\approx 10.3\times 10^{-6}\) C\({}^{-1}\). Since it is necessary to keep the structure undamaged when detecting the strain change under different pressure conditions in the process of gradient cooling, the performance test of the concrete must be carried out in the room temperature environment first to determine the stress range that the concrete structure can bear before cracking. Considering the symmetry of structural loads,the FBG sensors are placed between 0\({}^{\circ}\) and 180\({}^{\circ}\) of the annular concrete structure, arranged semi-circularly as shown in the Figure (a)a. FBG1 and FBG2 are positioned at 0\({}^{\circ}\) and 180\({}^{\circ}\) on the inner wall, while FBG3, FBG4, and FBG5 are positioned at 90\({}^{\circ}\), 45\({}^{\circ}\), and 135\({}^{\circ}\) on the outer wall, respectively. The universal pressure testing machine, shown in Figure (b)b, is used for the experimental performance test. The load is applied along the vertical and radial direction of the concrete pipe, and the axis of the specimen is parallel to the upper and lower clamping surface. Loading is carried out in force control mode, with a step size of 250 N. The loading continues from the start until the structure fails and fractures. At each interval of 250 N load, the loading is stopped, and the FBG wavelength data is monitored for 2 min. When the structure fails in the process of load increase, The failure load of the structure is determined by calculating the average load value between the current and previous states. Through observation, it can be seen that when the maximum pressure that concrete can bear is exceeded, the structure suddenly breaks from the top and bottom. As the annular concrete structure continued to be squeezed by external pressure loads, due to the failure of the top and bottom, the stress on the structure along the 90\({}^{\circ}\) direction rapidly increased until fracture occurred. The failure state is shown in Figure 7.  
Figure 6: Overall diagram of loading test. The structural strains at 0\({}^{\circ}\)and 180\({}^{\circ}\) on the inner wall and 90\({}^{\circ}\), 45\({}^{\circ}\) and 135\({}^{\circ}\) on the outer wall were extracted by FBG sensor, and the load-strain curve is plotted, as shown in Figure 8. From the figure, it can be seen that with the gradual increase of pressure load, the strain measured at each measuring point has a linear relationship with the applied load.