Civil Engineering Reference
In-Depth Information
rather stiff in relation to the ground, particularly if it is a wide rectangular
box structure. Therefore, the interaction between the soil and the structure
is likely to make a significant difference to the behavior. Hence, this type
of analysis is not recommended other than to get an initial feeling for the
behavior of the tunnel.
A more suitable method of analysis for the structure is a dynamic analy-
sis using a ground motion input. Numerous pieces of design software exist
in the marketplace to enable such an analysis to be carried out. However,
some care is needed in selecting the best approach in order to get mean-
ingful design load effects and ground deformations. Linear or nonlinear
analysis can be carried out.
The dynamic mass spring model has been the most popular method
of modeling immersed tunnel structures. This takes account of the soil-
structure interaction by defining the connectivity between the structure
and the soils as a series of complex springs. The tunnel structure is linked
through the springs to a series of masses representing the ground. The
ground masses have stiffness parameters defined to model the interac-
tion between them. Motion is introduced to the masses and the structure
response can be seen, based on how the connectivity is defined. This type
of model is often known as a Winkler model. The tunnel structure can
be modeled as a series of elements or segments, each with its own mass
spring. The rotational and compression stiffness characteristics of the
joints between tunnel elements and between tunnel segments can be mod-
eled. The stratigraphy between the bedrock and the tunnel can be modeled
in the soil mass characteristics with springs and dashpots to represent the
variation in ground inertia with depth. This was illustrated by Kiyomiya in
a number of papers and the principle described can be seen in Figure 9.25.
The FE continuum model is now becoming the preferred method of
analysis, where the soil mass can be modeled in three dimensions, the
structure can be modeled in detail, including the joint characteristics, the
ground geometry can be modeled, and the various ground motions applied
either to the soil mass or to the bedrock and nonlinear analyses under-
taken. There are many sophisticated pieces of software that can be used
for this, usually as time step analyses, but they still need much care when
defining critical parameters. With careful definition of the soil and mate-
rial properties and the interface conditions between the soil and the struc-
ture, the mass-spring approach is replicated with much a greater degree
of accuracy and in a continuous manner rather than as a series of discrete
masses. Nonlinear hysteretic soil models can be used to accurately define
the ground characteristics. These can be based on experimental data or
recorded data. This approach is recommended to get the best understand-
ing of the behavior of the structure and the joints under seismic load
conditions.
