Seismic Design of Tunnels - Parsons Brinckerhoff

3.4 Design Conforming to Free-Field Axial and Curvature
Deformations
Background and Assumptions
The free-field ground strain equations, originally developed by Newmark (Table 1),
have been widely used in the seismic design of underground pipelines. This method has
also been used successfully for seismic design of long, linear tunnel structures in several
major transportation projects (Monsees, 1991; Kuesel, 1969).
When these equations are used, it is assumed that the structures experience the
same strains as the ground in the free-field. The presence of the structures and the
disturbance due to the excavation are ignored. This simplified approach usually provides
an upper-bound estimate of the strains that may be induced in the structures by the
traveling waves. The greatest advantage of this approach is that it requires the least
amount of input.
Underground pipelines, for which this method of analysis was originally developed,
are flexible because of their small diameters (i.e., small bending rigidity), making the freefield
deformation method a simple and reasonable design tool. For large underground
structures such as tunnels, the importance of structure stiffness sometimes cannot be
overlooked. Some field data indicated that stiff tunnels in soft soils rarely experience
strains that are equal to the soil strains (Nakamura, Katayama, and Kubo, 1981). A
method to consider tunnel stiffness will be presented and discussed later in Section 3.5.
Design Example 1: The Los Angeles Metro
For the purpose of illustration, a design example modified from the seismic design
criteria for the LA Metro project (SCRTD, 1984) is presented here. In this project, it was
determined that a shear wave propagating at 45 degree (angle of incidence) to the tunnel
axis would create the most critical axial strain within the tunnel structure. Although a P-
wave (compressional wave) traveling along the tunnel axis might also produce a similar
effect, it was not considered because:
• Measurement of P-wave velocity can be highly misleading, particularly when a soil
deposit is saturated with water (Monsees, 1991).
• The magnitudes of soil strains produced by a nearly horizontally propagating P-wave
are generally small and about the same as those produced in the underlying rock
and, therefore, not as critical as the shear-wave generated axial strains (SFBART,
1960). This phenomenon was discussed previously in Section 3.3.
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