Seismic Design of Tunnels - Parsons Brinckerhoff

Generally, the solutions to these interface problems are to provide either of the following:
• A movable joint, such as the one used at the connection between the Trans-Bay Tube
and the ventilation building (Warshaw, 1968)
• A rigid connection with adequate strength and ductility
At these critical interfaces, structures are subjected to potential differential movements
due to the difference in stiffness of two adjoining structures or geological media.
Estimates of these differential movements generally require a dynamic analysis taking into
account the soil-structure interaction effect (e.g., SFBARTD, 1991). There are cases
where, with some assumptions, a simple free-field site response analysis will suffice. The
calculated differential movements provide necessary data for further evaluations to
determine whether special seismic joints are needed.
Once the differential movements are given, there are some simple procedures that
may provide approximate solutions to this problem. For example, a linear tunnel entering
a large station may experience a transverse differential deflection between the junction
and the far field due to the large shear rigidity provided by the end wall of the station
structure. If a conventional design using a rigid connection at the interface is proposed,
additional bending and shearing stresses will develop near the interface. These stress
concentrations can be evaluated by assuming a semi-infinite beam supported on an
elastic foundation, with a fixed end at the connection. According to Yeh (1974) and
Hetenyi (1976), the induced moment, M(x), and shear, V(x), due to the differential
transverse deflection, d, can be estimated as:
M(x) = Kt
2l 2 de -lx (sinlx - coslx)
(Eq. 3-7)
V(x) = K t
l de
Ê Kt
l=
ˆ
Ë4E c I c
¯
-lx cos
1
4
lx
(Eq. 3-8)
where x
I c
= distance from the connection
= moment of inertia of the tunnel cross section
E c = Young’s modulus of the tunnel lining
K t
= transverse spring coefficient of ground (in force per unit deformation per
unit length of tunnel)
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