Page 208 - Numerical Analysis and Modelling in Geomechanics

BACK ANALYSIS OF GEOTECHNICAL PROBLEMS 189

Figure 6.14 Rheological model.
elastic modulus of the rock mass, and laboratory shear tests, for determining the
peak and residual values of the friction angle along the schistosities.
The elastic modulus for the rock mass ranged between 6000 and 14,700 MN/
2
m . The shear tests provided average values of peak and residual friction angles
of about 60° and 34°, respectively. The relatively large value of the peak friction
angle depends on the appreciable influence of its “geometrical” portion.
In addition to the above investigation, the following measurements were also
carried out during excavation to monitor the overall stability of the opening:

1) Size of the relaxed zone around the tunnel using multiple point
extensometers to a depth of 6 to 10m.
2) Convergence of the opening contour.
3) Axial force in the rock bolts.
4) Seismic wave velocity by geophysical survey.

Model for the analysis
The mentioned in situ measurements showed an appreciable time-dependent
deformation of the opening. This suggested to base the back analyses on the
rheological material model depicted in Figure 6.14. It consists of a linear spring
(governing the instantaneous response of the rock mass), a friction block (with
limit resistance governed by the Mohr-Coulomb criterion) and a linear dashpot
(that accounts for the observed time-dependent behaviour).
The rock mass surrounding the tunnel did not exhibit an appreciable volume
increase (or swelling) during time. This allows the disregarding of the volumetric
part of the viscous behaviour, i.e. the one related to the spherical component of
the state of stress, and to consider only one deviatoric viscosity coefficient η for
the rheological model.
The shear strength c, φ and viscosity η parameters of the rock mass represent
the free variables of the back analysis. The values of the elastic constants were
chosen on the basis of in situ investigations. As suggested in [24], the average
2
value of the elastic modulus from the plate load tests (E=10,000 MN/m ) was
adopted, and Poisson’s ratio was estimated equal to 0.3.