Seismic Design of Tunnels - Parsons Brinckerhoff

The most widely used approach is to simplify the site geology into a horizontally
layered system and to derive a solution using one-dimensional wave propagation theory
(Schnabel, Lysmer, and Seed, 1972). The resulting free-field shear distortion of the
ground from this type of analysis can be expressed as a shear strain distribution or shear
deformation profile versus depth. An example of the resulting free-field shear distortion for
a soil site using the computer code SHAKE is presented in Figure 7.
Simplified Equation for Shear Deformations
For a deep tunnel located in relatively homogeneous soil or rock, the simplified
procedure by Newmark (presented in Table 1) may also provide a reasonable estimate.
Here, the maximum free-field shear strain, g max , can be expressed as:
g max = V s
C s
(Eq. 4-1)
where
V s = peak particle velocity
C s = effective shear wave propagation velocity
The values of C s can be estimated from in-situ and laboratory tests. An equation
relating the effective propagation velocity of shear waves to effective shear modulus, G m ,
is expressed as:
C s =
G m
r
(Eq. 4-2)
where
r = mass density of the ground
It is worth noting that both the simplified procedure and the more refined SHAKE
analysis require the parameters C s or G m as input. The propagation velocity and the shear
modulus to be used should be compatible with the level of shear strains that may develop
in the ground under design earthquake loading. This is particularly critical for soil sites
due to the highly non-linear behavior of soils. The following data are available:
• Seed and Idriss (1970) provide an often used set of laboratory data for soils giving the
effective shear wave velocity and effective shear modulus as a function of shear
strain.
• Grant and Brown (1981) further supplemented the data sets with results from a series
of field geophysical measurements and laboratory testing conducted for six soil sites.
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