Seismic Design of Tunnels - Parsons Brinckerhoff

4.0 OVALING EFFECT ON CIRCULAR TUNNELS
The primary purpose of this chapter is to provide methods for quantifying the seismic
ovaling effect on circular tunnel linings. The conventionally used simplified free-field
deformation method, discussed first, ignores the soil-structure interaction effects.
Therefore its use, as demonstrated by two examples, is limited to certain conditions.
A refined method is then presented that is equally simple but capable of eliminating the
drawbacks associated with the free-field deformation method. This refined method — built
from a theory that is familiar to most mining/underground engineers — considers the soilstructure
interaction effects. Based on this method, a series of design charts are developed
to facilitate the design process. The results are further validated through numerical analyses.
4.1 Ovaling Effect
As defined in Chapter 3, ovaling of a circular tunnel lining is primarily caused by
seismic waves propagating in planes perpendicular to the tunnel axis (see Figure 2).
Usually, it is the vertically propagating shear waves that produce the most critical ovaling
distortion of the lining. The results are cycles of additional stress concentrations with
alternating compressive and tensile stresses in the tunnel lining. These dynamic stresses
are superimposed on the existing static state of stress in the lining. Several critical modes
may result (Owen and Scholl, 1981):
• Compressive dynamic stresses added to the compressive static stresses may exceed
the compressive capacity of the lining locally.
• Tensile dynamic stresses subtracted from the compressive static stresses reduce the
lining’s moment capacity, and sometimes the resulting stresses may be tensile.
4.2 Free-Field Shear Deformations
As discussed in Chapter 3, the shear distortion of ground caused by vertically
propagating shear waves is probably the most critical and predominant mode of seismic
motions in many cases. It causes a circular tunnel to oval and a rectangular underground
structure to rack (sideways motion), as shown in Figure 3. Analytical procedures by
numerical methods are often required to arrive at a reasonable estimate of the free-field
shear distortion, particularly for a soil site with variable stratigraphy. Many computer
codes with variable degree of sophistication are available (e.g., SHAKE, 1972; FLUSH,
1975; and LINOS, 1991).
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