Seismic Design of Tunnels - Parsons Brinckerhoff

thrust that is approximately 1.5 to 2.0 times the thrust calculated by the Mononobe-Okabe
method. Model experiments by Yong (1985) confirmed these theoretical results. This
method is possibly adequate for a volume structure (e.g., a basement) resting on a very
stiff/hard medium (such as rock) and rigidly braced across (e.g., by transverse shear wall
diaphragms). A possible application of this method in a cut-and-cover tunnel construction
is at the end walls of a subway station, where the end walls act as rigid shear wall
diaphragms and prevent the structure from making sideways movements during
earthquakes. For regular rectangular cross-sections under plane strain condition, the
Wood theory, like the Mononobe-Okabe method, would lead to unrealistic results and is
not recommended for use in typical tunnel sections with significant soil cover thickness.
Implications for Design
It is logical to postulate that the presence of a rectangular frame structure in the
ground will induce dynamic earth pressures acting upon the structure. This earth pressure
loading, however, is in a form of complex distributions of shear stresses as well as normal
pressures along the exterior surfaces of the roof, the walls and the invert. To quantify
these external earth loads accurately requires a rigorous dynamic soil-structure analysis.
Realizing that the overall effect of this complex external earth loading is to cause the
structure to rack, engineers find it more realistic to approach the problem by specifying
the loading in terms of deformations. The structure design goal, therefore, is to ensure that
the structure can adequately absorb the imposed racking deformation (i.e., the
deformation method), rather than using a criterion of resisting a specified dynamic earth
pressure (i.e., the force method). The focus of the remaining sections of this chapter,
therefore, is on the method based on seismic racking deformations.
5.4 Free-Field Racking Deformation Method
Conventionally, a rectangular tunnel structure is designed by assuming that the
amount of racking imposed on the structure is equal to the free-field shear distortions of
the surrounding medium. The racking stiffness of the structure is ignored with this
assumption. In Section 4.2 (Chapter 4), the commonly used approach to estimating the
free-field shear distortions of the medium was discussed. Using the free-field racking
deformation method, Figure 20 shows a typical free-field soil deformation profile and the
resulting differential distortion to be used for the design of a buried rectangular structure.
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