Numerical Analysis on the Behavior of Existing Tunnels Subjected to the Undercrossed Shield Tunneling at a Small Proximity

Table 4

The longitudinal equivalent stiffness models.

Longitudinal equivalent models	Location of the neutral axis φ (%)	Influence coefficient of circular seam λ	Effective ratio of longitudinal bending stiffness η
Model 0	—	—	1.00
Model 1 [11]	48.7	—	0.11
Model 2 [12]	Change with λ	—	0.2–0.14
Model 3 [13]	64.2	0.5	0.22
Model 4 (modified model)	39.2	0.5	0.35