A Closed-Form Solution for the Analysis of Antifreeze Disease Fortification Length in a Permafrost Tunnel

Frost damage in permafrost tunnels is very common, and this can have a negative influence on traffic. The most serious frost damage typically occurs at a certain length from the tunnel opening. Thus the antifreeze measures of the lining structure in this area need to be strengthened. In this study, the antifreeze disease fortification length for permafrost tunnels is determined from heat transfer and mathematical physics equations by the theoretical analysis method. The temperature distribution characteristics of the lining along the tunnel axis under the influence of the tunnel depth, the tunnel radius, the wind velocity at the tunnel opening, and the thermal conductivity of the insulation layer are analysed. The results show that the longitudinal temperature characteristics in the tunnel axis are influenced by many factors. The proposed antifreeze disease length of the permafrost tunnel was found to be approximately 31 times of the tunnel diameter, which agrees with the results of the numerical simulation. It verifies the rationality of the theoretical calculation. This value, 31 times of the tunnel diameter, can be used as a reference for the design of the tunnel antifreeze disease fortification length.

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