The Distribution Characteristics of Frost Heaving Forces on Tunnels in Cold Regions Based on Thermo-Mechanical Coupling

To address the freezing damage to tunnel lining caused by frost heaving of the surrounding rock in water-rich tunnels in cold regions, a numerical thermo-mechanical coupling model for tunnel-surrounding rock that considers the anisotropy of frost heave deformation was established by examining overall frost heaves in a freeze–thaw cycle. Using a COMSOL Multiphysics 6.0 platform and the sequential coupling method, the temperature field evolution of tunnel-surrounding rock, freezing cycle development, and distribution characteristics of the frost heaving force of a tunnel lining under different minimum temperatures, numbers of negative temperature days, frost heave ratios, and anisotropy coefficients of frost heave deformation were systematically simulated. The results revealed that the response of the temperature field of tunnel-surrounding rock to the external temperature varies spatially with time lags, the shallow surface temperatures and the area around the lining fluctuate with the climate, and the temperature of the deep surrounding rock is dominated by the geothermal gradient. The extent of the freezing cycle and the frost heaving force increase significantly when lowering the minimum temperature. The maximum frost heaving force usually occurs in the region of the side wall and the spring line, and tensile stress is prone to be generated at the spring line; the influence of slight fluctuations in the minimum temperature or the short shift in the coldest day on the frost heaving force is limited. A substantial increase in frost heaving force is observed with higher frost heave ratios; for example, an increase from 0.25% to 2.0% results in a 116% rise at the sidewall. Although the increase in the anisotropy coefficient of frost heave deformation does not change the overall distribution pattern of frost heaving force, it can exacerbate the directional concentration of frost heave strain, which can increase the frost heaving force at the periphery of the top arch of the lining. This study revealed the distribution pattern and key influencing factors of the freezing cycle and frost heaving force for tunnels, providing a theoretical basis and data reference for the frost resistance design of tunnels in cold regions.