Seismic Design of Tunnels - Parsons Brinckerhoff

• 254 ft/sec for case I
• 415 ft/sec for case II
These shear wave velocities are assumed to be compatible with the shear strains the
soil experiences during the design earthquake. Assuming a unit weight of 115 pcf for the
silty clay, the corresponding shear moduli are:
• G = 230 ksf for case I
• G = 615 ksf for case II
Figure 23 shows the shear wave velocity profiles used in the analysis.
Structure Properties. A reinforced one-barrel concrete box structure with the following
properties is assumed:
Structure Elastic* Moment of Thickness Length
Member Modulus(ksi) Inertia(ft 4 /ft) (ft) (ft)
Side Wall 3640 42.7 8.0 26
Base Slab 3640 51.2 8.5 90
Roof Slab 3640 51.2 8.5 90
* Plane Strain Elastic Modulus
The structure members are modeled as rigid continuous beam elements under a twodimensional
plane strain condition.
Analytical Model. Earthquake excitation is represented by a vertically propagating shear
wave accelerogram originated from the rigid bedrock. The relative geometric relationship
between the soil and the tunnel structure is described in Figure 22.
To assess the effect of soil-structure interaction the analysis is conducted using the
dynamic finite element program FLUSH (1975). Under horizontal earthquake excitation
the seismic loading condition is anti-symmetrical. Therefore, only one half of the soilstructure
system need be analyzed, by imposing horizontal rollers along the vertical axis of
anti-symmetry (see Figure 21). A more detailed description of the time-history finite
element analysis including the input ground motions and the structural modeling will be
given in Section 5.5.
Results. Figure 24 shows results based on free-field analysis, ignoring the presence of
structure and the opening. The free-field differential deformations between the projected
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