Environmental Engineering Reference
In-Depth Information
stability). Therefore, the base of the crater wall
that supports these fluids should equilibrate the
overturning moment caused by the lava thrust:
the horizontal hydrostatic force from the lava
pool was bigger than the gravitational force
contained in the lava wall. The sum of moments
in point a ( Fig. 4c ) , indicates that the width of
the theoretical base to cause pivoting, would be
around 120 m. as a matter of fact, based on
field observations and oblique photographs, we
can estimate that the crater wall in 1993 had a
thickness of at least 60 m, so it was unstable due
to its relatively thin thickness.
4.1.2 General stability analysis (cone and
foundation)
non-dimensional parameters according to the
Buckingham Π Theorem
Merle & Borgia (31) and van Wyk de Vries &
Matela (49) made experiments in the laboratory to
study the spreading during the building phase of
volcanoes. alvarado (1, 2, 5) applied this method
to the arenal Volcano. The experiments deter-
mined multiple non-dimensional relations named
Π which predict if the spreading (material dis-
placement at its base) may or may not take place,
therefore, there are a series of referred variables to
Π relations ( Table 4 ) and at least three dimensional
data (gravitational, inertial and viscous force),
whose relations are needed to maintain the same
value in nature and the experiments.
Therefore, the main geometrical variables are:
height of the volcano (h), radius of the volcanic
cone (R), the slope angle (α), the volcano's stratifi-
cation thickness (e), the brittle of the substratum
(D) and the thickness of the ductile susbstrate (i),
the depth of the sectorial collapse (Da), the layer
thickness and the displacement of the fault (F).
Within the variable properties of the materials we
have the density of the volcano (ρv) and the sub-
strate (ρs), the time spam for deformation (T), the
plastic substrate viscosity (µ), the angle of internal
friction (Φ), the cohesion (cv) and the unit density
(γ). The gravity acceleration (g) is the responsible
force of the destabilization process. Therefore, a
mode of analysis, based on laboratory information
and its comparison with real cases is the one that
considers the non dimensional values shown in
Table 4. of particular importance, we can find the
relation between the thickness of the brittle layer
(foundation) and the height of the volcano (Π 2 ), as
well as the ratio between the thickness of the brit-
tle layer and the thickness of the weak substrate
3 ). Π 2 must be big enough to cause the substrate
failure before the dispersion occurs. Meanwhile,
Π 3 controls the deformation style. if Π 3 >>1, the
volcano will not deform, however it twists with the
basement; if Π 3 = 1-2, one single concentric ridge
Figure 4. simplified model of slope stability analysis of
the c cone and its lava pool.
considered. For these parameters, the factor of
safety is 1.3. From the stability analysis of the
model, it was determined that with only an increase
in the slope of the fault plane of 1.5° (upgrading
Ψp), the block fails (factor of safety = 0.99). This
may be due to gases or intrusion (dike or crypto-
dome). it is interesting to note that 1.5° is trans-
lated to distance B, right in the internal lava lake
with the wall, with an opening of 4.5 m near the
crater that would need only 6000 kPa to cause the
crater wall collapse.
in addition to the parameters exposed here,
we have to contemplate the force generated by
the daily lava discharge (21 600-43 200 m 3 /day)
and its associated pressure on the sides (lava and
gas pressure), combined with the explosive erup-
tions (that in the case of the la soufriére Volcano
had pressures between 3000 and 15 000 kPa; (19))
that weaken the structure, decreasing its cohesion
gradually.
- Dam (i.e. crater wall) under the weight of a luid
by the reservoir (lava pool): once again, we can
model that one of the crater walls (the slid one)
behaved as a retaining wall or dam holding the
fluid in the reservoir (in our case a lava pool).
The volume of slid material during the eruption
of 1993 was 2.3 ± 0.8 × 10 6 m 3 (3). assuming
that the depth of the lava pool was 80 m, for
γlv = 25 kn/m 3 and a lava wall of 22-25 kn/m 3
(due to the porosity between blocks). The equiva-
lent volume of dense rock was 1.35 ± 0.4 × 10 6 m 3
( = Vlv), therefore, we can calculate the weight
of the lava pool and wall or slid wedge that had
a volume of 0.55 × 10 6 m 3 . To keep the lava pool
stable, it must be contained between the walls
with a determined or minimum thickness (and
 
Search WWH ::




Custom Search