Seismic Design of Tunnels - Parsons Brinckerhoff

Lining Stiffness, I. The results presented above are based on the assumption that the
lining is a monolithic and continuous circular ring with intact, elastic properties. Many
circular tunnels are constructed with bolted or unbolted segmental lining. Besides, a
concrete lining subjected to bending and thrust often cracks and behaves in a nonlinear
fashion. Therefore, in applying the results presented herewith, the effective (or, equivalent)
stiffness of the lining will have to be estimated first. Some simple and approximate
methods accounting for the effect of joints on lining stiffness can be found in the literature:
• Monsees and Hansmire (1992) suggested the use of an effective lining stiffness that is
one-half of the stiffness for the full lining section.
• Analytical studies by Paul, et al., (1983) suggested that the effective stiffness be from
30 to 95 percent of the intact, full-section lining.
• Muir Wood (1975) and Lyons (1978) examined the effects of joints and showed that
for a lining with n segments, the effective stiffness of the ring was:
Ê
I e = I j + 4 Ë ˆ¯
2
I
n
(Eq. 4-14)
where I e < I and n > 4
I =lining stiffness of the intact, full-section
I j = effective stiffness of lining at joint
I e = effective stiffness of lining
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