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

Table 1

Frost damage characteristics in permafrost tunnels [1].

Tunnel name	Icy pavement	Frozen drainage ditches	Lining cracking	Ice hanging on arch	Tunnel opening cracking	Spalling of lining	Water leakage
Tiziling	✓		✓
Qidaoliang	✓	✓	✓
Dabanshan	✓		✓	✓			✓
Lingding	✓	✓	✓	✓		√	✓
Kuixian						√
Xinganling	✓
Yuximole	✓		✓	✓
Beiweizi	✓
Baikaer			✓	✓		✓
No. 2 Xiluoqi			✓	✓		✓
Yaling					✓
Nenlin	✓		✓	✓		✓
No. 2 Cuiling	✓		✓	✓		✓
Kunlunshan		✓		✓		✓	✓
Nanshan		✓					✓
Qingshanli		✓					✓
No. 1 Songyue		✓					✓
Aolaling
Mijiang	✓		✓	✓			✓
Guanjiao			✓	✓			✓
Habutegai			✓
No. 2 Hujiriyan			✓
Yongan				✓
Fenshuiling			✓	✓			✓
No. 2 Tianshan	✓			✓