## 4 Thermal Strain Performance Analysis of Annular Concrete Under Pressure Confinement
When the pressure load reaches the limit the structure can withstand, due to the brittleness of the concrete material, the stress concentration areas crack under tensile stress, and the sensor fails [24]. By inserting the pertinent parameters of the structure into Equation (2) reveals that the ultimate pressure the structure can withstand is 3509 N, and the theoretical value(CV)-strain curve of the structure is shown in the figure below. The simulated load-strain curve of the structure shows that when the load reaches 3598 N, the strain values at the top and bottom of the inner wall undergo a sudden change, with an error of 2.54%. The measured load-strain curve indicates that a sudden change in strain values at the top and bottom of the inner wall occurs when the load reaches 3108 N; additionally, at a load of 3140 N, the strain values at the 90\({}^{\circ}\) outer wall also show a sudden change. The results indicate that under external load, the annular structure first fails at the inner wall of the top and bottom, with a failure load of approximately 3200 N and an 8.8% error, which is within an acceptable range considering the actual test conditions. As the load on the annular structure increases, the FBG sensor has a maximum offset at 2500 N with a value of 4.75 \(\mu\epsilon\) and an error of 4.6%. According to the ultimate bearing capacity of the actual test of the annular concrete member is 3108 N, three different pressure conditions of 0 N, 1500 N, 2000 N and 3000 N are selected for cooling experiment, and 0N is used as the control group. Figure 8: Load-strain curve of the annular concrete structure measured by FBG sensors. Figure 7: Fracture pattern of the annular concrete structure. The cooling experimental setup is composed of FBG strain measuring system, displacement loading device and low temperature test chamber, as shown in Figure 9. The FBG strain sensors are arranged in the inner wall of the arch and the arch bottom, that is, the stress concentration zone of the pressure-constrained annular concrete structure. The loading device is assembled by combining the load sensor with the reaction device, as shown in Figure 9a. The pressure load is applied using a screw, which is first transmitted to the load sensor, then to the steel plate and finally to the structure. The load sensor displays the pressure load in real time. Due to the mismatch in thermal expansion coefficient between steel and concrete during gradient cooling, it is necessary to adjust the pressure to keep its value constant. In this case, since the amount of change is small, the applied stress strain in the loading test is taken as the strain generated by the pressure during the cooling experiments. The measurement range of the load sensor is 0 to 5000 N, which is suitable for the experimental temperature, and the accuracy meets the measurement requirements. Figure 9b shows the FBG strain measurement system. As shown in Figure 9c, the low temperature test chamber can create 160\(\sim\)-60 \({}^{\circ}\)C temperature environment, with an error of \(\pm\)2 \({}^{\circ}\)C. It can perform gradient cooling on the structure, meeting the basic experimental requirements. After the radial load is applied, the annular concrete structure is gradually cooled in the low temperature test chamber, and the strain changes of the FBG sensor attached to the structure were recorded and analyzed. The design temperature range of the experiment is 20 \({}^{\circ}\)C to \(-\)40 \({}^{\circ}\)C. The temperature started from 20 \({}^{\circ}\)C and the gradient cooling amplitude is 10 \({}^{\circ}\)C. To cool the concrete completely, it is necessary to stay at each temperature gradient for a period of time, and the recorded FBG wavelength is considered to be valid when it becomes stable at each temperature gradient [25]. By substituting the wavelength offset value into Equation (5), the total strain at the test point of the structure can be obtained. Set the tensile strain to positive.