Collapsed Shape of Shallow Unlined Tunnels Based on Functional Catastrophe Theory

Table 2

Comparison of ECT and FCT.

	ECT	FCT
Fundamental theories	① Implicit function theorem
	② Morse lemma
	③ Thorn splitting lemma
Research content	The non-Morse critical point (or singular) of the potential function
Potential function	Elementary function (polynomial functions)	Functional
State variables
Non-Morse critical points
Control variables
Catastrophic conditions