Page 57 - Fundamentals of Physical Volcanology

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34 CHAPTER 3

The above discussion tacitly assumed that density. However, it is now understood to be an
because the magma in a dike is buoyant the frac- expression of the combination of a number of rock
ture will grow upward. In fact the orientation of properties, including the tensile strength of the
the fracture will be strongly controlled by the state of rock (i.e., its ability to resist its mineral grains being
stress in the rocks that are fracturing. As discussed pulled apart from one another), the typical size of
earlier, the hot rocks in the mantle behave as fluids the mineral grains, and the difference between the
on long time scales. A fluid cannot sustain differ- pressure in the molten rock waiting to enter the
ential stresses – the fluid flows to remove the dif- fracture when it opens and the compressive stress
ferences in stress, and so the force acting within trying to force the fracture shut. The compressive
a body of fluid is the same in all orientations. stress is partly due to the weight of the overlying
However, the cooler rocks in the crust can easily rock in the place where the fracture is about to
resist deformation on short time scales, and so can form and partly due to any other tectonic stresses
support nonzero stress differences. The basic stress that are present, such as those linked to plate tec-
acting on any body of rock is the vertical compres- tonics. The surface tension between the molten
sive force representing the weight of the overlying rock and the mineral grains is also important. We
rocks. The horizontal forces acting may be sig- saw in section 2.4.2 that surface tension prevents
nificantly different from this, since they include liquid rock spreading in an infinitely thin film over
the consequences of horizontal movements within the surfaces of mineral grains so that, when melting
the crust due to, for example, plate tectonics. The first begins, a finite amount of melt is needed before
result is that horizontal stresses in the deep crust an interconnected melt network can exist. In the
are generally found to be about 30% less than the same way, melt cannot enter an extremely narrow
vertical stress. When a fracture opens, the amount crack at all, and so the extreme tip of an opening
of work that it has to do in deforming the surround- fracture will not contain liquid rock.
ing rocks will be minimized if it opens in a plane One might imagine this implying that there must
that is oriented at right angles to the least compres- be a vacuum in the fracture tip, but in practice all
sive stress, and since this is very likely to be hori- molten rocks contain dissolved volatiles. At low
zontal, the plane of the resulting dike will almost pressures, some of these volatiles will be released
certainly be vertical. The situation can be quite dif- from the liquid rock as gases and can enter the frac-
ferent at very shallow depths in the crust, where ture tip, providing a pressure that is greater than
the presence of local layers of rock with low den- zero, but less than the compressive effect of the

sities can cause the least compressive stress to be overlying rocks. The pressure difference, strictly
vertical. In that case, a vertically rising fracture may speaking a stress difference, between the inside
cease to extend upward and may instead spread and outside acts to try to push the tip of the crack
sideways, especially if it finds a weak boundary shut while at the same time the pressure of the
between two rock layers. The approximately hori- underlying molten rock trying to get into the frac-
zontal layer of magma that eventually fills such a ture is exerting a leverage acting to force it open.
fracture is called a sill. It is the competition between these two effects
Much of the study of the propagation of dikes that determines the value of the apparent fracture
is concerned with two critical issues: what condi- toughness of the host rocks. However, because the
tions allow brittle fractures to start forming, and apparent fracture toughness depends on the amount
what conditions cause the resulting dikes to cease of volatiles exsolved, which in turn depends on
propagating. The rock property controlling these both the amount of volatiles originally dissolved in
processes is called the fracture toughness, and it is the magma in its source zone and the exact condi-
a measure of the maximum intensity of the stress tions within the crack tip, it is very hard to antici-
that the mineral grains at the dike tip can withstand pate the exact value of apparent fracture toughness
before failing. For many years scientists treated to be expected in a given situation. The units
fracture toughness as a basic rock property such as in which fracture toughness is measured are stress