Collapsed Shape of Shallow Unlined Tunnels Based on Functional Catastrophe Theory

Table 1

Potential functions used in ECT.

Name	Potential function	State variable	Control variable
Fold
Cusp
Swallowtail
Butterfly
Indian tent
Elliptic umbilic
Hyperbolic umbilic
Parabolic umbilic
Symbolic umbilic
Second hyperbolic umbilic
Second elliptic umbilic