Seismic Design of Tunnels - Parsons Brinckerhoff

- In the JSCE (Japanese Society of Civil Engineers) Specifications for Earthquake
Resistant Design of Submerged Tunnels, the values of wavelength that will
maximize Equations 3-1, 3-3 and 3-4 are determined and substituted back into
each respective equation to yield the maximum sectional forces.
- St. John and Zahran (1987) suggested a maximization scheme that is similar to
the Japanese approach except that the spring coefficients (K a or K t ) are assumed
to be functions of wavelength, L, in the maximization process.
Both of these approaches assume that the free-field ground displacement response
amplitude, D, is independent of the wavelength. This assumption sometimes may
lead to very conservative results, as the ground displacement response amplitude
generally decreases with the wavelength. It is, therefore, the author’s view that
Equations 3-1 through 3-4 presented in this section will provide a practical and
adequate assessment, provided that the values (or the ranges of the values) of L, D,
and K t (or K a ) can be reasonably estimated.
A reasonable estimate of the wavelength can be obtained by
L = T C s
(Eq. 3-5)
where T is the predominant natural period of the shear wave traveling in the soil
deposit in which the tunnel is built, and C s is the shear wave propagation velocity
within the soil deposit.
Often, T can also be represented by the natural period of the site. Dobry, Oweis and
Urzua (1976) presented some procedures for estimating the natural period of a linear
or equivalent linear model of a soil site.
• The ground displacement response amplitude, D, should be derived based on sitespecific
subsurface conditions by earthquake engineers. The displacement
amplitude represents the spatial variations of ground motions along a horizontal
alignment. Generally, the displacement amplitude increases as the wavelength, L,
increases. For example, the displacement spectrum chart prepared by Housner
(SFBARTD, 1960) for the SF BART project was expressed by D = 4.9 x 10 -6 L 1.4 ,
where the units of D and L are in feet. This spectrum is intended for tunnel tubes in
soft San Francisco Bay muds and was derived for a magnitude 8.2 earthquake on the
San Andreas fault. The equation shows clearly that:
- The displacement amplitude increases with the wavelength.
- For any reasonably given wavelength, the corresponding ground displacement
41