Structural design verifications, structural analysis of tunnels - Tunnel Engineering: Basics and Additional Services for Design and Construction - page 103

3.4 Analytical processes and their modelling

There is a basic difference between tunnels in loose ground and those in solid rock regard-
ing loading assumptions and modelling. For tunnels in loose ground, shallow and deep
tunnels are also differentiated, with a tunnel being considered deep when the overburden
is at least twice the diameter, or the equivalent diameter of non-circular sections (Fig. 3-6).
The difference between these three groups of tunnels is significant above all in analyti-
cal calculations. With the increased use of numerical calculation methods - above all the
Finite Element Method (FEM) - this categorisation has become ever less important. Ana-
lytic processes are now briefly discussed.
Two-dimensional models, which are the most commonly used at the moment, are pre-
sented for the three groups. Recently, however, three-dimensional models have been used
increasingly as these are becoming ever more practical for daily use with the development
of computers and programmes.

3.4.1 Modelling of shallow tunnels in loose ground
Shallow tunnels in loose ground are normally calculated using a model of a pipe covered
by loose material. It is assumed that the rock mass or soil cannot form a load-bearing ring
and that the tunnel support has to resist the entire load. Tunnels of this type with over-
burdens of up to one diameter are often driven in an open trench, since the soil cannot be
assumed to have sufficient stand-up time until the support is sufficiently load-bearing.

Figure 3-6 Approaches
for the contribution of the
ground to load-bearing.

3.4.2 Modelling deep tunnels in loose ground
For deep tunnels, the assumption is made in accordance with Terzaghi's silo theory [238,
242] that the actual ground pressure is nearly independent of the actual overburden and
is determined by the ground properties. The model assumes that a vault forms at a certain
height due to the internal friction of the material and this resists loading from above. The
formation of this vault depends on a deformation of the ground or the soil, which results
from the relaxation of the sides of the tunnel as the section is excavated. A similar effect
can be observed in a silo, when the material “hangs” at the side walls of the silo due to
friction between the material in the silo and the wall surface and the material does not flow
out although the silo is full.