Seismic Design of Tunnels - Parsons Brinckerhoff

First, try the simplified equation as used in Design Example 1. The combined
maximum axial strain and curvature strain is calculated as:
emax = ±
Vs
± AsR
2C cos 3 q=± 3.2 . 0.6x32.2x10
± cos
Cs 2 s
2x350 3 45 o
( 350) 2
=±0.0046 ± 0.0006 =±0.0052
The calculated maximum compression strain exceeds the allowable compression
strain of concrete (i.e., e max > e allow = 0.003).
Now use the tunnel-ground interaction procedure.
1. Estimate the predominant natural period of the soil deposit (Dobry, et al, 1976).
T = 4H C s
= 4x100'
350
= 1.14 sec.
2. Estimate the idealized wavelength (Equation 3-5):
L = TxC s = 4H
= 400 ft
3. Estimate the shear modulus of soil:
G m =rC s
2
= 0.110kcf
32.2
x350 2 = 418.5ksf
4. Derive the equivalent spring coefficients of the soil (Equation 3-6):
K = K = 16pG m (1 -n m ) d
a t
(3- 4n m ) L
16px418.5 (1 - 0.5)
=
(3 - 4 x0.5)
= 526 kips/ft
x 20
400
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