Finite Element Method (FEM) - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 235

10.4 Computation Section

Since tunnels are linear structures the stability analysis for a tunnel in many cases can
be carried out using a vertical rock disk as the computation section. Further examples
where linear structures can be analyzed using vertical disks as the computation section
are slopes and gravity dams.
The computation section has to be selected large enough so that for a stress-strain anal-
ysis, stress changes and deformations due to excavation do not reach the boundaries
of the computation section. Also, for seepage flow analysis, changes of the piezometric
heads due to any construction activity should not reach the boundaries of the compu-
tation section.
When defining the dimensions of the computation section, various influences must
be considered that will be subsequently shown by means of the example of a two-di-
mensional stability analysis for a tunnel. The dimensions and the shape of the tunnel's
cross-section as well as the in-situ stress state are decisive for the required size of the
computation section.
For a tunnel in elastic rock mass with primary stress state {

σ p } due to gravity the com-
putation section should extend three to four tunnel diameters above and adjacent to
the tunnel and two to three tunnel diameters underneath the tunnel (Fig. 10.9). If the
ground conditions and the geometry of such a tunnel are symmetrical with respect to
the vertical plane through the tunnel axis the computation section can be reduced as
illustrated in Fig. 10.9, including only one half of the tunnel's cross-section.
If the rock mass is loaded due to gravity only, the extent of the rock mass areas above
and below the tunnel which are unloaded due to excavation is larger than the loaded
areas of the rock mass adjacent to the tunnel (Fig. 10.10, left).
If the horizontal component of the primary stress is higher than the vertical component
the situation is reversed. As a consequence, the width of the computation section must
be increased and the height may be reduced (Fig. 10.10, right).

For anisotropic stress-strain behavior of the rock mass the stresses and displacements
after excavation may be asymmetric with respect to the vertical plane through the tun-
nel axis. In this case the computation section must include the entire cross-section of the
tunnel, and the distance between the tunnel's walls and the boundaries of the computa-
tion section has to be selected sufficiently large on both sides of the tunnel. So the extent
of the plastic zone around the tunnel needs to be accounted for. A plastic zone has the
same static effect as a correspondingly larger cross-section of the tunnel because stress
redistribution via this zone is not possible or at least is limited. Thus, a greater width
of the computation section is required corresponding to three to four diameters of the
plastic zone above and adjacent to the tunnel and two to three diameters of the plastic
zone underneath the tunnel (Fig. 10.11).