Seismic Design of Tunnels - Parsons Brinckerhoff

4.3 Lining Conforming to Free-Field Shear Deformations
When a circular lining is assumed to oval in accordance with the deformations
imposed by the surrounding ground (e.g., shear), the lining’s transverse sectional stiffness
is completely ignored. This assumption is probably reasonable for most circular tunnels in
rock and in stiff soils, because the lining stiffness against distortion is low compared with
that of the surrounding medium. Depending on the definition of “ground deformation of
surrounding medium,” however, a design based on this assumption may be overly
conservative in some cases and non-conservative in others. This will be discussed further
as follows.
Shear distortion of the surrounding ground, for this discussion, can be defined in two
ways. If the non-perforated ground in the free-field is used to derive the shear distortion
surrounding the tunnel lining, the lining is to be designed to conform to the maximum
diameter change, DD , shown in Figure 8. The diametric strain of the lining for this case
can be derived as:
DD
D =±g max
2
(Eq. 4-3)
where
D = the diameter of the tunnel
g max = the maximum free-field shear strain
On the other hand, if the ground deformation is derived by assuming the presence of
a cavity due to tunnel excavation (Figure 9, for perforated ground), then the lining is to be
designed according to the diametric strain expressed as:
DD
D
=±2g max (1 - vm)
(Eq. 4-4)
where
n m = the Poisson’s Ratio of the medium
Equations 4-3 and 4-4 both assume the absence of the lining. In other words, tunnelground
interaction is ignored.
Comparison between Equations 4-3 and 4-4 shows that the perforated ground
deformation would yield a much greater distortion than the non-perforated, free-field
ground deformation. For a typical ground medium, an engineer may encounter solutions
provided by Equations 4-3 and 4-4 that differ by a ratio ranging from 2 to about 3. By
intuition:
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