Environmental Engineering Reference
In-Depth Information
as explained below, the modulus of deforma-
tion value that results in output data that most
accurately match the convergences values is the
following:
analysis at each stage. it shows a good correlation
between the two values.
The greatest difference was obtained at stage 6,
excavation of ditches. When these were filled up,
the deformation was not yet stabilized, thus it
is higly likely that overall value is greater than
measured, matching the analysis value.
e = 1700 MPa
4.3.3
Shotcrete
The analysis input parameters are:
4.4.2
Crown-wall convergences
The proportion between convergences crown-wall
and wall-wall in the analysis is 28%, which matches
the measured values. This percentage is linked to
the location of the basalt-pyroclastics interface
on the section as well as to the value of k
0
. This
confirms the adopted assumptions.
γ = 2.3 t/m
3
e = 27,300 MPa
µ = 0,20
The
repié
or overwidth of the shotcrete layer at
the base of the sidewalls, has been modeled as a
soil material with the concrete geotechnical param-
eters. This is more realistic than modeling it as
beam elements, as it allows for rotational stiffness
effect at the wall base.
4.4.3
Strength of support
internal forces of the support shell have been
checked against its capacity for all shotcrete layers.
This derived the following:
• shotcrete capacity is clearly exceeded at the end
of stage 2 (installation of plain shotcrete layer)
• Reinforced layer capacity is close to its limit at
the end of stage 4 (removal of
repiés
)
• capacity of whole support (with all layers) is
clearly enough at stage 6 (excavation of ditches)
This fits with the cracking and loosening
observed in the plain shotcrete layer and with the
subsequent behaviour of the reinforced shotcrete.
in the analysis, a thickness of the plastic zone
at the tunnel boundary of about 3 to 4 m was
obtained.
4.3.4
Other analysis parameters
in addition to ground and support geotechnical
and geometric parameters, described above, the
following parameters need to be considered in the
analysis:
• lateral earth pressure coeicient k
0
: a value of
1.0 has been adopted, for both soil types, basalts
and pyroclastics.
• coninement loss, λ (Panet, 1995): at each stage
a fictitious stress applied to the walls has been
considered in the calculation. This was defined
as (1-λ)σ
0
, where σ
0
is the natural stress. The
following assumptions have been adopted:
Phase 1. excavation of the tunnel. λ = 0.30
Phase 2. Plain shotcrete layer (3 cm). λ = 0.89
Phase 3: First reinforcement shotcrete layer
(10 cm of shotcrete reinforced with steel
fibers). λ = 1.0
Following phases: λ = 1.0
in phase two, the value of λ is lower than one,
although installation of the reinforced shotcrete
layer was over a month after the excavation and
the working face was over 100 m away. This is
due to the rheological behavior of the ground,
which results in deformations taking place over a
significant lapse of time. This is shown in Figures 8
and 9, where it can be seen that, after placing the
reinforced layer, deformation continued for several
months. The value of λ only reaches 1.0 after a
period of four months.
4.4.4
Possible variations in the adopted analysis
parameters
The validity of the ground parameters assumed
in the analysis is largely conditioned by the great
number of variables that take part in the calculation,
which compels us to adopt a great number of
initial hypotheses. The different variables involved
are analyzed below:
• The values of c
M
and Φ
M
of basalts do not have
any effect on the calculation. This is due to its high
values, that prevent soil failure. Therefore, the
accuracy of the calculation value of both param-
eters does not affect the calculation validity.
• The values of e and µ of the basalt have little
effect on the deformations of the tunnel.
This is based on the reasonable assumption
that its modulus of deformation is clearly
greater than the pyroclastics´. This results in
an insignificant deformation of the section
due to basalts. Therefore, the accuracy of the
calculation value of both parameters does not
affect, or affects very little, the validity of the
calculation.
4.4
Calculation results
4.4.1
Horizontal convergences
The table below compares measured horizontal
convergences with values obtained from the
