Seismic Design of Tunnels - Parsons Brinckerhoff

Other assumptions and parameters used in this example are:
• Design Earthquake Parameters: Peak Ground Acceleration,
A s = 0.6 (Maximum Design Earthquake, MDE)
• Peak Ground Velocity, V s = 3.2 ft/sec
• Soil surrounding Tunnel: Fernando Formation
• Effective Shear Wave Velocity: C s = 1360 ft/sec (in Fernando Formation under MDE)
• Tunnel Structure: Cast-in-place circular segmented reinforced lining,
with Radius R =10 feet
From Table 1, the combined maximum axial strain and curvature strain would be:
e max =± Vs
± As R
2C s C cos 2 3 q
s
=± 3.2
2x1360 ± 0.6x32.2x10
1360
( ) 2 cos 3 45
=±0.00118 ± 0.000037
=±0.00122
As the results of calculations indicate, the curvature (bending) component (0.000037)
is, in general, relatively insignificant for tunnel structures under seismic loads. According
to the LA Metro criteria, the maximum usable compression strain (under MDE) in the
concrete lining is e allow =0.002, since the strain is almost purely axial. With e max < e allow ,
the lining is considered adequate in compression under the Maximum Design Earthquake
(MDE).
The calculated maximum axial strain (=0.00122) is cyclic in nature. When tension is in
question, a plain concrete lining would obviously crack. The assumed lining is reinforced,
however, and the opening of these cracks is transient due to the cyclic nature of seismic
waves. As long as no permanent ground deformation results, these cracks will be closed
by the reinforcing steel at the end of the shaking. Even in the unreinforced concrete lining
cases, the lining generally is considered adequate as long as:
• The crack openings are small and uniformly distributed
• The resulting tension cracks do not adversely affect the intended performance goals
of the lining
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