Report on the geology of the Henry MountainsGilbert, Grove Karl
Science
Report on the geology of the Henry Mountains
Gilbert, Grove Karl
Geology -- Utah -- Henry Mountains; Intrusions (Geology) -- Utah -- Henry Mountains
I am led by the analogy of allied problems in mechanics to assume that
the resistance of the body of strata varies with some power of its
depth, but I am unable to say _what_ power. So far as I am aware,
neither mathematical analysis nor experimentation has been directed to
the problem in question. According to Rankine “the resistances of
flexure of similar cross-sections [of elastic beams] are as their
breadths and as the _squares_ of their depths” (“Applied Mechanics”,
page 316), and it is possible that the same law applies to the
resistances which continuous strata oppose to the uplifts of domes. But
it appears more probable that the greater complexity of the strains
developed in the formation of domes causes the depth to enter into the
formula with a higher power than the second.
On the other hand, some allowance should be made for the fact that the
elasticity of the resisting strata is imperfect.
If we call the power with which the depth enters the formula a, equation
1 becomes
_r_ = _d^a_ _c_ _C_{lll}_ (4).
and equation 3 becomes
_c_ = _d^a_ (_C_{lll}_/_C_{ll}_) (5).
It is probable that the true value of _a_ is not less than 2, nor more
than 3.
Interpreting these equations in the same manner as those applying to
deformation by faulting, we reach the following conclusions:
1st. At a given depth beneath the surface, lava injected under a given
pressure cannot form a laccolite of less than a certain area. This may
be called its _limital area_.
2d. The pressure of injection remaining constant, the limital area of a
laccolite is a direct function of its depth beneath the surface. The
limital area is greater when the depth is greater, and less when the
depth is less.
3d. A laccolite of small volume will not exceed the limital area, but
will grow by lifting its cover. If however the volume of intruded lava
be great, its own weight becomes a factor in the equilibrium of forces
and modifies the distribution of the pressures. As the rock bubble
rises, the weight of the contained fluid is progressively subtracted
from the pressure against its top, and this proceeds until the upward
and lateral pressures become proportional to the resistances which
severally oppose them. Further expansion is then both upward and
outward.
Public-domain text, read in full here on John Shaqi.
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