Seismic Design of Tunnels - Parsons Brinckerhoff

expressed in terms of internal moments and forces, which can be calculated
according to the lining deformations (distortions) imposed by the surrounding ground.
If the “strength” criteria expressed by Equation 2-1 or 2-2 can be satisfied based on
elastic structural analysis, no further provisions under the MDE are required.
Generally the strength criteria can easily be met when the earthquake loading intensity
is low (i.e., in low seismic risk areas) and/or the ground is very stiff.
• If the flexural strength of the tunnel lining, using elastic analysis and Equation 2-1 or 2-
2, is found to be exceeded (e.g., at certain joints of a cut-and-cover tunnel frame), one
of the following two design procedures should be followed:
(1) Provide sufficient ductility (using proper detailing procedure) at the critical
locations of the lining to accommodate the deformations imposed by the ground
in addition to those caused by other loading effects (see Equations 2-1 and 2-2).
The intent is to ensure that the structural strength does not degrade as a result of
inelastic deformations and the damage can be controlled at an acceptable level.
In general the more ductility is provided, the more reduction in earthquake forces
(the “EQ” term) can be made in evaluating the required strength, U. As a rule of
thumb, the force reduction factor can be assumed equal to the ductility provided.
This reduction factor is similar by definition to the response modification factor
used in bridge design code (AASHTO).
Note, however, that since an inelastic “shear” deformation may result in strength
degradation, it should always be prevented by providing sufficient shear
strengths in structure members, particularly in the cut-and-cover rectangular
frame.
(2) Re-analyze the structure response by assuming the formation of plastic hinges at
the joints that are strained into inelastic action. Based on the plastic-hinge
analysis, a redistribution of moments and internal forces will result.
If new plastic hinges are developed based on the results, the analysis is re-run by
incorporating the new hinges (i.e., an iterative procedure) until all potential plastic
hinges are properly accounted for. Proper detailing at the hinges is then carried
out to provide adequate ductility. The structural design in terms of required
strength (Equations 2-1 and 2-2) can then be based on the results from the
plastic-hinge analysis.
As discussed earlier, the overall stability of tunnel structures during and after the
MDE has to be maintained. Realizing that the structures also must have sufficient
capacity (besides the earthquake effect) to carry static loads (e.g., D, L, E1, E2
and H terms), the potential modes of instability due to the development of plastic
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