Seismic Design of Tunnels - Parsons Brinckerhoff

locations of roof and invert are approximately 0.26 inch and 0.17 inch for case I and case
II respectively. When both soil and structure are included in the analysis, the calculated
racking distortions (between the roof and the invert) were only about 13 percent and 32
percent of the free-field deformations for case I and case II, respectively (see Figures 25
and 26).
Conclusions. The results of the analysis lead to the following conclusions:
• It may be very conservative to design a rectangular tunnel structure to accommodate
all the shear deformations in the free-field, particularly when the structure is stiff and
the surrounding ground is soft. This finding coincides with results from several
previous studies (Hwang and Lysmer, 1981; and TARTS, 1989).
• As the relative stiffness between the soil and the structure decreases (e.g., from case
II to case I), the actual structure racking deformation would also decrease, when
expressed as a percentage of the free-field deformation. This suggests that the soilstructure
interaction effect on the racking of a rectangular tunnel should be:
-Similar to that on the ovaling of a circular tunnel (Chapter 4)
-A function of the relative stiffness between the ground and the structure
A series of analyses performed to define this relationship and their results are
presented and discussed next.
5.5 Tunnel-Ground Interaction Analysis
Although closed-form solutions accounting for soil-structure interaction, such as those
presented in Chapter 4, are available for deep circular lined tunnels, they are not available
for rectangular tunnels due primarily to the highly variable geometrical characteristics
typically associated with rectangular tunnels. Conditions become even more complex
because most of the rectangular tunnels are built using the cut-and-cover method at
shallow depths, where seismically induced ground distortions and stresses change
significantly with depth.
It is desirable, therefore, that a simple and practical procedure be developed for use
by design engineers that accounts for the soil-structure interaction effect. To that end, a
series of dynamic soil-structure interaction finite element analyses were performed in this
study. The results from these complex analyses were then transformed so that they could
be adapted easily to simple analytical tools used currently in design practice.
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