Seismic Design of Tunnels - Parsons Brinckerhoff

5.3 Dynamic Earth Pressure Methods
Mononobe-Okabe Method
Dynamic earth pressure methods have been suggested for the evaluation of
underground box structures by some engineers. The most popular theory for determining
the increase in lateral earth pressure due to seismic effect is the Mononobe-Okabe theory
described, for example, by Seed and Whitman (1970), recognized by Japanese Society of
Civil Engineers for earthquake resistant design of submerged tunnels (1975), and
recommended in several other documents (Converse Consultants, 1983; EBMUD, 1973).
Using this method, the dynamic earth pressure is assumed to be caused by the inertial
force of the surrounding soils and is calculated by relating the dynamic pressure to a
determined seismic coefficient and the soil properties.
Originally developed for aboveground earth retaining walls, the Mononobe-Okabe
method assumes that the wall structure would move and/or tilt sufficiently so that a yielding
active earth wedge could form behind the wall. For a buried rectangular structural frame,
the ground and the structure would move together, making it unlikely that a yielding active
wedge could form. Therefore, its applicability in the seismic design of underground
structures has been the subject of controversy.
The obvious applicable situation is limited to the typical “boat section” (i.e., U-section)
type of underground construction, where the structure configuration resembles that of
conventional retaining walls. Another situation where the use of the Mononobe-Okabe
method may also be adequate is when the structure is located at a very shallow depth.
Experience from PB’s recent underground transportation projects has indicated that the
Mononobe-Okabe earth pressure, when considered as an unbalanced load, may cause a
rectangular tunnel structure to rack at an amount that is greater than the deformation of the
surrounding ground. This unrealistic result tends to be amplified as the depth of burial
increases. This amplification is primarily due to the inertial force of the thick soil cover,
which acts as a surcharge and, according to the Mononobe-Okabe method, has to be
considered. In spite of this drawback, the method has been shown to serve as a
reasonable safety measure against dynamic earth thrust for tunnels buried at shallow
depths (e.g., in the Los Angeles Metro Project).
Wood Method
Another theoretical form of dynamic earth pressure was derived by Wood (1973). By
assuming infinite rigidity of the wall and the foundation, Wood derived a total dynamic
87