Environmental Engineering Reference
In-Depth Information
of Bieniawski, Grimstad and Barton, bolts and
shotcrete are used to approach homogeneity.
We assume then a beam with a simply supported
beam with span of 10 m (very conservative hypoth-
esis as its free span is really shorter due to the shape
of the dome and also it might be considered at least
some elastic embeddings at the ends).
The area of the parable of charge within 10 m
of the alleged beam span is:
5
⋅
∫
y dx = 28358 kg
2
Figure 2.
Parable of loads on the tunnel.
0
representing a uniform overload of less than
28.940 kg/m. This load is increased by 60% (Pro-
todiakonov recommended 50%).The maximum
bending moment is found to be:
have to use stronger supporting methods: trusses,
mesh, greater thicknesses of shotcrete and even
rigid protective umbrella in advance.
1.6 ⋅ 28.94 ⋅ 10
2
/8 = 5,788,000 mn
4.2
Bag of pyroclasts more or less welded and
other non-competent materials
in our opinion, the problem of supporting and
bearing capacities according to soil mechanics
classical hypothesis (Terzaghi, Protodiakonov and
others) should be approached here. Unfortunately,
geomechanics classifications are not applicable
nowadays.
if objective data is available, and if the whole
tunnel is dug through this homogeneous section,
not only the application of computer calcula-
tions (finite elements, etc) but also the formulae
of authors such as Protodiakonov may be valid to
establish the bearing hypothesis. This applies not
only to calculate the support (usually rigid) of the
entire section of the tunnel, but also to calculate
the stability of a slab on grade formed by the last
basaltic lava flow over the crown, from where this
homogeneous ground starts.
here we consider both cases: that of the last lava
flow, which we will find in the transition from lava
flows to pyroclasts and the support to build inside
pyroclasts.
in both cases the load to bear will be obtained
from Protodiakonov method, which we consider
very appropriate for this case.
The parable of charge on the tunnel, having an
influence on the walls, with a pyroclastic density of
1.60 kg/cm
3
and a friction angle of 30º is:
The average resistance to compression of the
basalt is, according to tests made, 1 MPa. it is very
likely to present a series of faults and joints which
will confer an anisotropy, although this aspect of
understanding the negative effects of these discon-
tinuities, if it is not true fractures or cracks of con-
siderable size, are not as fearsome as if we spoke of
flexotraction or pure traction. Moreover, systematic
bolting, which is designed following the indications
of Bieniawski and Barton, tends to homogenize the
rock mass. Given all this, we apply a load decrease
coefficient of the resistance of 0.50, quite conserva-
tive, while also estimating the edge of the lava flow
to prevent from appearing thrusts:
c = [(12 ⋅ 578.80)/5000]
½
= 1.18 m
The borehole shows that this lava flow is approx-
imately 1.60 m thick, though this number is not so
reliable until checked.
The parameters that do offer actual margins of
safety are:
Free span (10 m) of the lintel
• Double-supported beam hypothesis
• Density 1.60 to pyroclasts
• Friction angle 30°
• 1.60 load increase coeicient
• 2.0 load decrease coeicient (50%) of the
uniaxial compressive strength.
We also have the added thickness of shotcrete
which we define according to geomechanics clas-
sifications and which is is capable of absorbing
substantial effort.
in this case of alternate lava flows the horizon-
tal stress on the walls is much lower because the
basaltic lava flows prevent vertical loads directly
influence the horizontal thrusts.
y = -0.2765 x
2
+ 31.24
4.2.1
The case of the final lava flow as a carrier
for these loads
From the data obtained, strength index and joint-
ing, we get the calculation of the final lava flow,
(derived from rock drilling #2, depth 102.80 to
104.60, from transition of lava flows to pyro-
clasts). Based on these and the recommendations
