Thermo-hydro-mechanical response of a cylindrical tunnel with strain relaxations based on fractional-order three-phase-lag thermoelasticity

Thermal disturbances induced by explosions or fires can rapidly alter the stress and temperature fields in surrounding rock masses, triggering strongly coupled thermo-hydro-mechanical processes that accelerate rock degradation, weaken structural integrity, and may ultimately threaten tunnel stability, posing a significant risk to long-term operational safety. In this work, the thermo-hydro-mechanical response of a cylindrical tunnel embedded in saturated soil subjected to thermal loading is investigated. Conventional thermoelastic models may not fully capture the finite-speed heat propagation, memory-dependent thermal transport, and delayed deformation behavior of soils under transient thermal shocks. Therefore, a fractional-order three-phase-lag generalized thermoelastic model incorporating strain relaxation effect is proposed to describe the coupled thermo-hydro-mechanical responses of saturated soils. The governing equations are solved using the Laplace transform method to obtain the corresponding solutions. The influence of fractional-order parameter, thermal relaxation time, strain relaxation time, and the magnitude of thermal loading is systematically examined. Results show that fractional-order and relaxation parameters significantly affect the evolution of temperature, pore water pressure, and displacement fields, while thermal loading mainly amplifies their magnitudes near the tunnel wall without changing the overall distribution patterns. The proposed model provides insight into the coupled heat and mass transfer under transient thermal shocks and offers guidance for mitigating stress concentration and improving tunnel stability.