Page 197 - Numerical Analysis and Modelling in Geomechanics

178 ANNAMARIA CIVIDINI AND GIANCARLO GIODA
Back analysis of a tunnel in a granular deposit

Tunnel characteristics

The back analysis problem discussed here concerns the construction of a new
tunnel of the Gotthard railroad connecting Italy to Switzerland. This two-track
tunnel has an internal radius of 5 m, a length of 7.2 km and a portion of it (750 m
in length) crosses an alluvial deposit, consisting mainly of fine sand, at a depth
of about 35m. The water table is located below the invert arch level.
To limit the difficulties of driving a tunnel in a cohesionless soil, jet grouted
columns were adopted for consolidating the sand ahead of the excavation and to
stabilise the tunnel face. The construction steps, illustrated in detail in [16], are
summarised in Figure 6.1. First, the top part of the tunnel was excavated for a
considerable length. Subsequently the bottom excavation was carried out and the
permanent lining was set in place.
During excavation, the surface settlements and the vertical displacements
within the sand deposit were measured at two sections of the tunnel through
topographic survey and sliding micrometers [17]. Figures 6.2 and 6.3 show,
respectively, the soil profile for one of these sections and the location of the
measurement points. The surface settlements measured during the advancing of
the excavation are shown in Figure 6.4. The maximum settlement measured at
the end of the top excavation was about 3 cm. It increased to about 6 cm after the
completion of the opening.
After construction, a back analysis of the in situ measurements performed at
Section 2 (cf. Figure 6.4) was attempted [18]. This had two main purposes: (a)
to identify the “mechanism” that governs the development of the displacements
around the opening, and (b) to evaluate the effectiveness of possible
improvements of the construction procedure in reducing the surface settlements.
Among various back analysis techniques applicable to tunnelling problems [3, 19 ,
20], the previously described direct approach was used, in a deterministic
context, for this application.

Elastic back analysis

A first back analysis was carried out, assuming a linear elastic material
behaviour, in order to determine the equivalent elastic parameters of the sand
deposit. To this purpose the deposit was subdivided into six layers, the secant
elastic moduli of which represent the free variables of the problem. The mesh
adopted in the plane strain calculations is shown in Figure 6.5. The meaning of
the dark zone in this figure will be discussed subsequently.