Analytical Modeling of Heat Transfer and Deformation Around a Circular Cavity in Elastic Ground

The subsurface is increasingly exploited to host energy, utilities, and infrastructure systems that interact with surrounding soils and rocks through their thermal and functional operation. Prominent examples are provided by energy geostructures, district heating networks, buried power cables, steam and water pipes, and underground nuclear waste repositories. Many of these systems incorporate cylindrical cavities and operate under varying thermal conditions, thereby influencing the thermo-mechanical state of the surrounding ground. While advanced numerical simulations have significantly improved understanding of these processes, their complexity and computational cost restrict their use in engineering practice. By contrast, analytical models offer computational efficiency and theoretical rigor, but limited analytical solutions are currently available to address the analysis of cavity-type systems involving non-isothermal conditions and interconnected mechanical interactions with the ground. To address this gap, this study introduces an analytical model that extends the classical cavity expansion theory to non-isothermal conditions. The formulation integrates thermo-elastic effects under both steady-state and transient regimes, enabling the prediction of stress, strain, and displacement distributions induced by temperature variations around a cylindrical cavity. Validation against finite element simulations confirms the reliability of the proposed analytical approach across a range of subsurface conditions. The analytical model provides a practical and theoretically robust tool that overcomes the daunting resources required by multiphysical numerical modeling approaches.