Thermal-Mechanical Coupling Response Analysis of Three-layer Circular and Horseshoe Shaped Chambers Based on Complex Elastic Mechanics (Contemporary Mathematics, 2025)
Compressed Air Energy Storage (CAES) in abandoned coal mines offers a cost-effective and sustainable solution for large-scale energy storage. This study presents a comprehensive analytical framework to evaluate the thermo-mechanical behavior and long-term structural stability of three-layer underground chambers with circular and horseshoe-shaped cross-sections. Based on the theory of complex elasticity and conformal mapping, analytical solutions for stress and displacement are derived under steady-state thermal conditions. The framework incorporates both mechanical loads-such as in-situ stress and internal gas pressure-and temperature-induced thermal stresses, which are often overlooked in traditional models. Using the Cao Zhuang Coal Mine in Shandong Province as a case study, the analytical results are validated against finite element simulations performed in COMSOL 6.2. The validation demonstrates strong agreement in both temperature and stress distributions across different burial depths. Comparative results reveal that while circular chambers maintain relatively uniform stress profiles, horseshoe-shaped chambers are prone to localized stress concentrations, especially near the lower arch and corner regions. This makes them more vulnerable to structural failure under thermal cycling conditions. The findings underscore the importance of incorporating thermal effects in underground energy storage system design. The developed methodology offers a computationally efficient alternative to fully numerical simulations, enabling rapid scenario assessment and structural optimization. This work provides theoretical and practical insights into the safe reuse of abandoned mine tunnels for energy storage, contributing to the long-term feasibility of compressed air energy storage systems and the advancement of clean energy infrastructure.
Keywords: Compressed Air Energy Storage (CAES); circular chamber; horseshoe shaped chamber; thermal-mechanical coupling; analytical solution