Page 207 - Numerical Analysis and Modelling in Geomechanics

188 ANNAMARIA CIVIDINI AND GIANCARLO GIODA
Figure 6.12 shows the plastic zone at the end of excavation, by means of the
contour lines of the square root of the second invariant of deviatoric plastic
strains. In the same figure, zone G denotes the grouted zone that represents the
modified foundation of the upper arch.
It can be observed that the modified construction procedure involves a marked
reduction of the extension of the plastic zone with respect to that characterising
the original procedure. This, in turn, leads to a decrease of the surface
settlements, as shown in Figure 6.13 by comparison of the vertical displacements
calculated for the two excavation procedures.
As previously observed, the accuracy of the elasto-plastic model could be
improved, since its parameters were not calibrated on the basis of a back
analysis. In spite of this, some useful information is obtained by the numerical
analysis, concerning in particular the surface settlements which are reduced by a
factor of about 2 to 2.5 with respect to those calculated for the original
excavation procedure.
This information can be used, together with that related to the increment of the
cost of excavation, to predict the effects of the reduced (but still non-negligible)
settlements on buildings in the construction area, etc. as one of the parameters
for evaluating the effectiveness of the modified technique.

Back analysis of a tunnel in a ‘viscous’ rock mass

Tunnel characteristics
A second application concerns the back analysis of the displacements measured
in situ during the excavation of the Frejus motorway tunnel. This tunnel,
excavated between 1975 and 1979, crosses the Alps and joins the towns of
Modane (France) and Bardonecchia (Italy). Its total length is approximately 13
km.
The main portion of the tunnel on the Italian side is excavated in a schistose
rock, with a depth of cover ranging from 700 m to about 1700 m. The rock mass
is characterised by three major joint sets that intersecting the schistosities could
lead to the formation of unstable wedges at the excavation crown.
The tunnel has a horseshoe-shaped section, with a height of 9 m and a vertical
radius of 6 m. The construction was based on conventional methods, using
mainly rock bolts and shotcrete as a primary support. The rock bolts have a
diameter of 24 mm, their length varies from 3 to 5 m and their “density” is about
2
1 bolt every 1.4 m . The shotcrete is approximately 10 cm thick.
Steel ribs were also used in the zones where the rock quality was particularly
poor. The permanent concrete lining, 80 cm thick, was installed 300 to 400 m
behind the excavation face.
Comprehensive geomechanical studies were carried out during construction
[24, 25]. They included plate load and flat jack tests, for the evaluation of the