Seismic Design of Tunnels - Parsons Brinckerhoff

As Figures 28A and 28B show, earthquake motions of these two types have very
different frequency characteristics, with the “N.E. EQ” motions displaying significantly
increased high frequency components. The purpose of using two sets of design response
spectra instead of one was to evaluate the effect of ground motion characteristics on
soil/structure interaction.
Note that these design spectra were developed for motions expected at rock outcrop
(ground surface). For motions to be used as rigid base input in the FLUSH analysis, a
suitable modification of ground motion characteristics should be made. This was achieved
in this study by using the one-dimensional site response analysis program SHAKE based on
wave propagation theory. Details of this de-convolution process can be found in Schnabel,
et al.(1972).
Flexibility Ratio for Rectangular Tunnels
Figure 30 shows the five different types of structure configurations that were analyzed.
Note that although the configurations were limited to five types, the racking stiffness of each
structure type was varied further (for parametric studies) by varying the properties of the
structure members (e.g., EI and EA values). Similarly, the stiffness of the surrounding soil,
as represented by shear modulus, was also varied in such a manner that the resulting
relative stiffness between the soil medium and the structure covered a range that was of
interest. This relative stiffness, as represented by the Flexibility Ratio, F, will be defined in
detail in the following paragraphs.
The flexibility ratio for a rectangular tunnel, just as for a circular tunnel, is a measure of
the flexural stiffness of the medium relative to that of the tunnel structure. Under a seismic
simple shear condition, this relative stiffness may be translated into the shear stiffness of the
medium relative to the lateral racking stiffness of the rectangular frame structure.
General Cases. Consider a rectangular soil element in a soil column under simple shear
condition (see Figure 31). Assume the soil element has a width, L, and a height, H, that are
equal to the corresponding dimensions of the rectangular tunnel. When subjected to the
simple shear stress, t, the shear strain (or angular distortion, g) of the soil element is given
by:
g= D H = t G
(Eq. 5-1)
102
where
G = shear modulus of soil
D = shear deflection over tunnel height, H