Seismic Design of Tunnels - Parsons Brinckerhoff

R = radius of the tunnel lining
t = thickness of the tunnel lining
I = moment of inertia of the tunnel lining (per unit width)
Of these two ratios, it is often suggested that the flexibility ratio is the more important
because it is related to the ability of the lining to resist distortion imposed by the ground.
As will be discussed later in this chapter, the compressibility ratio also has an effect on the
lining thrust response.
The following examples on the seismic design for several tunnel-ground
configurations are presented to investigate the adequacy of the simplified design
approach presented in the previous section.
Example 1
The first illustrative example is a tunnel cross-section from the LA Metro project. The
ground involved is an old alluvium deposit with an effective shear wave propagation
velocity, C s , equal to 1000 ft/sec. The peak shear wave particle velocity, V s , according to
the design criteria, is 3.4 ft/sec.
Using Equation 4-1, the maximum free-field shear strain, g max , is calculated to be
0.0034. The reinforced cast-in-place concrete lining properties and the soil properties are
assumed and listed in the following table.
Lining Properties
Soil Properties
R = 9.5 feet
E m = 7200 ksf
t = 8.0 inches n m = 0.333
E l /(1- n l
2) = 662400 ksf
I = 0.0247 ft 4 /ft
Flexibility Ratio, F = 47
Compressibility Ratio, C = 0.35
Note that uncertainties exist in the estimates of many of the geological and structural
parameters. For instance:
• The effective shear wave propagation velocity in the old alluvium may have an
uncertainty of at least 20 percent.
• Uncertainty up to 40 percent may also be applied to the estimates of E m .
61