Page 157 - Fundamentals of Physical Volcanology

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134 CHAPTER 9

(a)
Cooled crust
Hot unsheared plug
Hot Fig. 9.14 Models of the internal
zone of shearing structures of lava flow lobes. (a) The
structure expected if all of the lava
Levée Chilled basal layer Levée behaves as a Bingham plastic: the
parabolic levée profile extends all
the way to the centre of the central
(b) Cooled crust channel. (b) The structure expected
when the hot lava in the central
Hot Newtonian core channel is nearly Newtonian, and so
has a very different rheology from
Levée Chilled basal layer Levée the levées.

(Fig. 9.13a), the lava can move only if its depth d is The earliest treatments of lava flows as Bingham
great enough that the shearing stress at the base of plastics assumed that each flow consisted entirely
the flow exceeds the yield strength of the lava, S . of material with the same rheological properties.
y
The shearing stress S is given by One consequence was that the parabolic shapes of
the levées were expected to extend right into the
S = ρ gd sin α (9.2) middle of the central channel (see Fig. 9.14a), with
an upper layer of lava that, like the levées, does not
where α is the slope of the ground over which the suffer enough shearing stress to make it deform. So
flow is moving, ρ is the bulk density of the lava flow although it is still hot enough to be molten, this
and, as usual, g is the acceleration due to gravity. So upper layer rides as an apparently rigid “plug” on
the minimum lava depth that can move, which top of the lower layer of lava that is stressed enough
defines the maximum thickness of the levée at its to make it flow. These conditions make it possible
boundary with the central channel, is found from to derive expressions for the width and center-line
eqn 9.2 to be depth of the channel in terms of the yield strength
of the lava. A second consequence of assuming
d = S /(ρ g sin α) (9.3) a Bingham rheology was that the plastic viscosity
b y
of the lava could be linked to the yield strength
At right angles to the downslope direction, it is (because lavas with high crystal or bubble contents
the change in stress at the base of the levée due would be expected to have large values for both
to its curved upper surface that controls the levée of these properties) and both properties could
shape, and it can be shown that the shape is a be linked to the composition of the lava (on the
parabolic curve (see Fig. 9.13b). The width w of grounds, again reasonable, that lavas with a given
b
each levée is given by composition tend to erupt at similar temperatures
and with similar crystal and bubble contents). Some
2
w = S /(2 ρ g sin α) (9.4) flows of high-silica content lavas – rhyolites and
b y
dacites – do sometimes have cross-sectional shapes
Combining the last two equations it can be seen similar to that shown in Fig. 9.14a. Indeed, many
that such flows move only a little further downslope
from the vent than they spread sideways, and there
d /w = 2 sin α (9.5) is so much resistance to flow from the high visco-
b b
sity that some lava is forced uphill from the vent,
which shows that on shallower slopes we expect so that a bulbous feature called a lava dome, only
levées to be relatively thin and wide. slightly elongated in the downslope direction, is