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Frost damage is a frequent occurrence in cold regions and can threaten the normal use and structural stability of tunnel engineering projects. To accurately determine the frost heaving force and effectively evaluate the frost damage in cold-region tunnels, an analytical solution for the frost heaving force considering the freeze-thaw (F-T) damage and transversely isotropic characteristics of surrounding rock is presented based on complex variable theory and the power series method. The calculation results indicate that the frost heaving force acts on the lining considering that the transversely isotropic characteristics of surrounding rock are significantly greater than those when assuming the surrounding rock is homogeneous isotropic media. This demonstrates that the transversely isotropic characteristics of surrounding rock have a considerable impact on the frost heaving force and should be considered. The frost heaving force continuously increases as the bedding angle increases from 0° to 90°, and the maximum frost heaving force in the Guanjiao tunnel (the rock mass bedding angle is 30°) of the Xining-Geermu Railway in China is approximately 1.04 MPa. In addition, the influence of F-T cycles on the frost heaving force in cold-region tunnels is investigated based on the analytical solution of the frost heaving force proposed in this paper. The frost heaving force acting on the lining decreases with an increasing number of F-T cycles due to the deterioration of the mechanical parameters of the surrounding rock.

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An Analytical Solution for the Frost Heaving Force considering the Freeze-Thaw Damage and Transversely Isotropic Characteristics of the Surrounding Rock in Cold-Region Tunnels