## 5 Conclusions  
In this paper, a detection model was established to measure the structural strain by combining the structural mechanics model and FBG detection technology. The load range before cracking is determined by the performance test. Then, the gradient cooling experiments were conducted under different stress constraints, further revealing the strain patterns of the annular concrete structure under the dual constraints of stress and temperature. By verifying numerical simulations and field experiments, a comprehensive analysis of the annular concrete structure was conducted. The primary conclusions are as follows. (1) Using the finite element software, the MWC model is selected to establish the thermal coupling model of the annular concrete structure under the constraints of temperature and stress, and the three-dimensional numerical simulation analysis of the annular concrete structure is carried out. The simulation results are analyzed and verified by field experiments, and the established model can effectively predict the test results. (2) An FBG strain sensor was used to measure the strain of the structure under pressure. When the load reached 3108 N, the ring structure first experienced failure at the top and bottom of the inner wall, followed by the outer wall at the waist of the structure, with a failure load of approximately 3200 N, representing an 8.8% error. As the load on the structure increased, the FBG sensor showed a maximum offset at 2500 N with a value of 4.75 \(\mu\varepsilon\) and an error of 4.6%. (3) In the temperature range from 20 \({}^{\circ}\)C to \(-\)40 \({}^{\circ}\)C, the total strain of the concrete structure increases as the temperature decreases. When the temperature is cooled from 20 \({}^{\circ}\)C to \(-\)20 \({}^{\circ}\)C, the change in thermal strain of the stress constrained structure increases. When the temperature is cooled from \(-\)20 \({}^{\circ}\)C to \(-\)40 \({}^{\circ}\)C, the change in thermal strain of the stress-constrained structure decreases. The thermal strain amplitude of the concrete shows a significant turning point under the temperature gradient. (4) under different pressure conditions, the thermal strain sensitivity of concrete increases with the gradual increase of pressure confinement, that is, the greater the pressure, the greater the influence on the cooling process of concrete. This method provides a comprehensive evaluation of the thermodynamic behavior of annular concrete structures under different stress and temperature conditions, that is, with the decrease of temperature, the strain of annular concrete structures gradually increases, and the thermal strain amplitude shows an obvious inflection point. The thermal strain sensitivity of the structure increases with the gradual increase of pressure constraint, and the cooling process is significantly affected by pressure. The findings provide basis and methodological support for the reliability assessment of concrete structures in cold environments. However, there are limitations to the study. The method used in this study is suitable for the analysis of mechanical properties of radially compressed annular concrete structures under low temperature conditions, such as secondary tunnel linings and pipelines. It is not applicable to the case that the structure is subjected to external pressure and internal force compression at the same time, or the stretching or compression perpendicular to the direction of the ring structure. Further studies can focus on more complex loading conditions, including simultaneous external pressures and internal forces, as well as studying the long-term effects of repeated thermal cycling on annular concrete. Conceptualization, C.L. and Y.R. ; methodology, C.L. and Y.R. ; software, Y.R. and J.L. ; validation, Y.R., J.L. and Q.X. ; formal analysis, X.W. ; investigation, J.L. ; resources, C.L. and H.L. ; data curation, Y.R. and H.L. ; writing--original draft preparation, Y.R. ; writing--review and editing, C.L. and X.W. ; visualization, J.L. and Q.X. ; supervision, C.L.