Environmental Engineering Reference
In-Depth Information
there are any overloads due to volcanic erup-
tions, the safety factor is not very altered, and
it is equally close to 1,1. The presence of seismic
movement is very important, since it makes the
factor of safety lover than 1 (around 0.6), what
indicates that the sliding of an important slope
mass could be imminent. For all the cases above,
the fault surfaces are very close to the foot of
the volcanic edifice, between the surfaces ia and
ii-iii, indicating that the mechanical character-
istics of these two layers are the ones that deter-
mined the threat of sliding for this flank.
- stability of the oriental lank: The results are
shown on Fig 3b and Table 7. The critical fault
surfaces do not match for all the load states. The
lowest safety factors are given for the stability
analysis of the cone with relatively small fault
surfaces, meanwhile, for the global stabilization,
the fault surfaces are very extensive but shallow,
which shows that the mechanical properties of
the first layers are the ones that determine the
risk of sliding for this volcanic cone.
in all cases, the factor of safety is above 1, this is
why the risk of sliding for this flank is low compare
to the factor of safety of the occidental flank. The
lowest factor is 1.3, so we have to be careful, but
the sliding is not imminent, unless the geotechnical
conditions change (for example tectonism, exces-
sive load due to the growth of cone c, vibrations
due to the explosions).
a 150 m thickness would be 3625 kPa and
2014 kPa for the horizontal stress.
- case of the arenal cone: We can assume a sim-
plified geometrical shape as a vertical struc-
ture of 1100 m (height), and where γ is the
volumetric weight of the lava (25 kn/m
3
) for an
overload of 27 500 kPa. it is clear that a bidi-
mensional shape of triangular section or a three-
dimensional shape of conic section would be
closer to reality. The overweight that transmits
the cone under its peak, and considering the
relations presented by hoek & Brown (22), to
its foundation may vary between 8000 and 29
700 kPa (maximum value) and horizontally
between 3127 and 55 350 kPa. however, gener-
ally these values are over estimated (particularly
the vertical component of the stress), which
can be even 5 times inferior, specially at depths
between 500 and 1500 m, since the equation
used is only the best fit curve. if we use a finite
element method (siGMa/W Program), we may
observe that the vertical stresses under the cone
'
s
peak are around 19 875 kPa and the horizontal
stresses are 10 426 kPa. at 5100 m of depth from
the base, they would be >5000 and 1250 kPa,
respectively. These increases are caused by the
effect of the cone, without considering the weight
of the foundation. in conclusion, the most real-
istic results of the stresses generated by the cone
in contact with the foundation may be around
20 000 kPa for the vertical σ and 10 000 kPa for
the horizontal σ.
The shear stress caused by a body with an ideal
triangular section on the foundation, has a maxi-
mum value around the depth h (equal to a quarter
of the width of the base, i.e. 2 km), whose shear
stress (∆τ) is close to 0.3p, where p represents the
maximum pressure under the cone
'
s peak (1,1 km
height) by the unit weight (
Fig 7
). Thus, we may
conclude that the shear stress τo, at depth h under
the cone
'
s axis, that under the foundation acts by
symmetry to 45° from the base, is very close to the
maximum value (41), p. 68), that is to say:
5
analYsis oF sTRess
anD DeFoRMaTion
5.1
Stress Calculation
There are many methods to calculate geostatic
stresses through the theory of elasticity (36).
stamotopoulos & kotzias (41) clarify that even
though the elastic solution provide an acceptable
method to calculate the changes in the vertical
stress, they are based on suppositions that simplify
the work, thus the results are only reasonable esti-
mations. Different cases that could be presented
in the arenal Volcano are shown in the following
information.
- case of an individual lava low: For a low that
reaches the pyroclastic deposits at the foot of the
volcano, with a 60 m front and a 16 m thick-
ness, we can calculate the vertical stress at 14 m
of depth. The result is 390 kPa. a lava flow of
10 m of thickness transmits a load of 250 kPa,
while the admissible load for the arenal soils are
between 50 and 250 kPa (see (44), p. 507).
- case of a lava ield: The maximum vertical
stresses generated at the arenal lava field under
τo = 0.25 γh + 0.3p
(2)
where γ is the volumetric weight of the lava, with
an average value of 25 kn/m
3
and a humid weight
of the foundation of 22 kn/m
3
.
in the case of study,
τo = 0.25 (22 kn/m
3
) × 2000 m + 0.3 (25 kn/m
3
)
× 1100 m = 19 250 kPa
if τo is less than the shear resistance, the soil
stresses would be values close to ones determined
by the elastic solutions, and the soil won
'
t yield.
