Seismic Design of Tunnels - Parsons Brinckerhoff

deformations result. Section 2.4 in Chapter 2 includes a detailed discussion on the
strength and ductility requirements for both MDE and ODE loading combinations.
(l) The structure, including its members and the overall configurations, should be
redesigned if:
• The strength and ductility requirements based on step (k) evaluation could not be met,
and/or
• The resulting inelastic deformations from step (k) evaluation exceed the allowables
(which depend on the performance goals of the structure)
In this case, repeat the procedure from step (e) to step (l), using the properties of the
redesigned structure section until all criteria are met.
Verification of the Simplified Frame Model
The simplified frame models according to Equation 5-8 and Figures 38A and 38B
were performed for Cases 1 through 5 (see Table 4) to verify the models’ validity. The
bending moments induced at the exterior joints of the one-barrel rectangular framed
structure (simplified analyses) were compared to those calculated by the dynamic finiteelement
soil/structure interaction analyses (rigorous analyses). The comparisons are
presented, using the concentrated force model, in Figures 39 and 40 for bending
moments at the roof-wall connections and the invert-wall connections, respectively.
Similar comparisons made for the triangular pressure distribution model are shown in
Figures 41 and 42.
As Figures 39 and 40 show, the simplified frame analyses using the concentrated
force model provide a reasonable approximation of the structure response under the
complex effect of the soil/structure interaction. One of the cases, however, indicates an
underestimation of the moment response at the bottom joints (i.e., invert-wall connections)
by about fifteen percent (Figure 40). When the triangular-pressure distribution model is
used, the simplified frame analyses yield satisfactory results in terms of bending moments
at the bottom joints (Figure 42). The triangular-pressure distribution model, however, is not
recommended for evaluation at the roof-wall connections, as it tends to underestimate the
bending moment response at these upper joints (Figure 41).
Through the comparisons made above, and considering the uncertainty and the many
variables involved in the seismological and geological aspects, the proposed simplified
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