Finite Element Method (FEM) - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 259

10.5.5 Representation of Results
The results of FEM stability analyses for rock engineering structures, particularly those
of three-dimensional analyses, due to their complexity are often diffi cult to understand
and thus to account for along with the design. The representation of the results is there-
fore of considerable importance and requires special diligence and effort.

Tunnels
Figure 10.30 shows a three-dimensional representation of the calculated principal
normal stresses (left) and displacements due to excavation (right) in the vicinity of
the temporary face of a tunnel after excavation of the vault. The rock mass exhibits
two vertical joint sets J1 and J2 and a horizontal set B of bedding-parallel discon-
tinuities. In the represented stage of construction a supporting core is left in the
middle of the temporary face.
In the area around the vault the strength of the horizontal and vertical discontinuities
is exceeded, resulting in a plastic zone represented in Fig. 10.30 (left). The three-dimen-
sional load-bearing behavior of the rock mass is clearly visible from the stress trajecto-
ries running in front of the temporary face and adjacent to the sidewalls of the vault.
The displacements due to excavation reach up to the ground surface and approximately
one vault's diameter behind of the temporary face (Fig. 10.30, right).

A global representation of analysis results like that in Fig. 10.30 is only suitable for
understanding the overall load-bearing behavior of the rock mass. It has to be supple-
mented and supported by more detailed representations of the analysis results.
Figures 10.31 - 10.33, for example, show results of a three-dimensional stability anal-
ysis for a tunnel driven by a shielded TBM (Wittke et al. 2006). The required jacking
force F J to overcome the skin friction can be determined from the calculated radial
loading

σ r acting on the shield as follows (Fig. 10.31):

(10.15)

where A s is the skin surface of the shield and is the friction coeffi cient between the

shield and the rock mass. The calculated radial displacements represented in Fig. 10.32
(right) lead to stress resultants shown in Fig. 10.33.
Figure 10.34 shows the stresses in the segmental lining of a machine driven tunnel. In
the area of the longitudinal joints at the internal side of the segments, high compressive
stresses occur normal to the longitudinal joints while transverse tension arises parallel
to the joints that must be covered by a corresponding reinforcement.

μ