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

Table 3

Bolt parameters.

Diameter/mm	Length	Young’s modulus	Shear modulus	Spring stiffness
	lb (mm)	Eb (MPa)	Gb (MPa)	K (kN·m^−1)
27	600	2.06 × 10^5	7.94 × 10^4	Kx	7.6 × 10^4
				Ky	1.9 × 10^5
				Kz	7.6 × 10^4

The rotation of bolt is not considered, so the spring rotation constants K_θx, K_θy, and K_θz can be taken as 1 × 10¹⁰  kN m rad⁻¹ [11].