Propagation Mechanism Modeling in the Near-Region of Arbitrary Cross-Sectional Tunnels

Table 2

Simplification of the dividing point model in certain specific situations.

Situation	Condition	Tunnel	Type	Dividing point 𝑧𝑟
	(𝑥𝑡=𝑥𝑟=𝑋,	Rectangular	—	Min4(𝑎−𝑌)^2𝜆,4(𝑏±𝑋)^2𝜆,4(𝑐+𝑌)^2𝜆
One	𝑦𝑡=𝑦𝑟=𝑌)	Circular	—	4𝑅−𝑋^2+𝑌^22𝜆
		Arched	Type I	Min4𝑅−𝑋^2+𝑌^22𝜆,4(𝑏±𝑋)^2𝜆,4(𝑐+𝑌)^2𝜆
		Arched	Type II	Min4𝑅−𝑋^2+𝑌^22𝜆,4(𝑐+𝑌)^2𝜆
	(𝑥𝑡=𝑥𝑟=𝐿,	Rectangular	—	Min4(𝑎−𝐿)^2𝜆,4(𝑏±𝐿)^2𝜆,4(𝑐+𝐿)^2𝜆
Two	𝑦𝑡=𝑦𝑟=𝐿)	Circular	—	4𝑅−√2𝐿^2𝜆
		Arched	Type I	Min4𝑅−√2𝐿^2𝜆,4(𝑏±𝐿)^2𝜆,4(𝑐+𝐿)^2𝜆
		Arched	Type II	Min4𝑅−√2𝐿^2𝜆,4(𝑐+𝐿)^2𝜆
	(𝑥𝑡=𝑥𝑟=0,	Rectangular	—	Min4(𝑎−𝑌)^2𝜆,4𝑏^2𝜆,4(𝑐+𝑌)^2𝜆
Three	𝑦𝑡=𝑦𝑟=𝑌)	Circular	—	4(𝑅−𝑌)^2𝜆
		Arched	Type I	Min4(𝑅−𝑌)^2𝜆,4𝑏^2𝜆,4(𝑐+𝑌)^2𝜆
		Arched	Type II	Min4(𝑅−𝑌)^2𝜆,4(𝑐+𝑌)^2𝜆
	(𝑥𝑡=𝑥𝑟=𝑋,	Rectangular	—	Min4𝑎^2𝜆,4(𝑏±𝑋)^2𝜆,4𝑐^2𝜆
Four	𝑦𝑡=𝑦𝑟=0)	Circular	—	4(𝑅−𝑋)^2𝜆
		Arched	Type I	Min4(𝑅−𝑋)^2𝜆,4(𝑏±𝑋)^2𝜆,4𝑐^2𝜆
		Arched	Type II	Min4(𝑅−𝑋)^2𝜆,4𝑐^2𝜆
	(𝑥𝑡=𝑥𝑟=0,	Rectangular	—	Min4𝑎^2𝜆,4𝑏^2𝜆,4𝑐^2𝜆
Five	𝑦𝑡=𝑦𝑟=0)	Circular	—	4𝑅^2𝜆
		Arched	Type I	Min4𝑅^2𝜆,4𝑏^2𝜆,4𝑐^2𝜆
		Arched	Type II	Min4𝑅^2𝜆,4𝑐^2𝜆