Finite Element Method (FEM) - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 257

Figure 10.28 Simulation of a pre-stressed anchor
Support in advance of a tunnel excavation
In loose rock, steel spiles made of rebars with diameters of 25 - 28 mm, which are
installed over a certain part of the circumference of the excavation profile, can serve as
an advancing support preceding the excavation of a tunnel (Section 20.2.6). Since spiles
do not offer appreciable support, they are normally not simulated in FEM stability
analyses.
Pipe umbrellas consisting of pipes are often constructed for the advancing support of
the workspace at the temporary face of tunnels in weak rock (Section 20.2.6). The outer
diameter of the pipes varies between 76 mm and 200 mm, while the wall thickness of
the pipes ranges from 8 mm to 25 mm. Because of the large dimensions of the pipes
that are grouted with cement-based suspension or mortar, pipe umbrellas are far stiffer
than spiles and extend further in advance of the excavation. The supporting effect of
pipe umbrellas should therefore be simulated by isoparametric elements. The normal
and bending stiffness of the elements modeling a pipe or pipe group must be selected to
be equal to the normal and bending stiffness of the corresponding pipe or pipe group.
In the example of a three-dimensional stability analysis for a tunnel represented in
Fig. 10.29, each pipe is simulated by one row of isoparametric elements. From the ob-
tained stress distribution within the elements simulating the pipes the bending moments
along the pipes can be calculated. Thus, a pipe umbrella can be dimensioned on the
basis of the results of three-dimensional finite element analyses.