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

<div>Variation of longitudinal direction temperature function with different tunnel radii: (a) the average air temperature function, <i>H</i>(<i>z</i>), under tunnel length; (b) the air temperature amplitude function, <i>K</i>(<i>z</i>), under tunnel length.</div>

Advances in Civil Engineering

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Figure 5

Figure 5: A Closed-Form Solution for the Analysis of Antifreeze Disease Fortification Length in a Permafrost Tunnel 