Geoscience Reference
In-Depth Information
BOX 2.2
In Situ Stress State
The full characterization of the state of stress at a point of the subsurface requires in principle six independent
quantities, illustrated through the following example.
Imagine that a small cube of rock centered on the point of interest is cut from its surrounding. To leave the
material inside the cube undisturbed by the cutting, forces have to be applied on each face of the cube to mimic
the action of the surrounding medium onto the cut material, noting also that forces acting on opposed faces are
equal and opposite in direction. However, in considering in situ stress state, using the term “stress,” which is
equivalent to the force exerted over a defined area, is more appropriate than discussing “force” alone; in this
way, stress is not dependent on the size of the cube.
If the cube is rotated in space, the stresses acting on its faces change in magnitude and direction. However,
a certain orientation of the cube exists for which each face is only loaded by a stress normal to the face (Figure
1). The three independent normal stresses are referred to as principal stresses, and their corresponding orienta-
tions in space as principal directions. On two faces of the cube oriented according to the principal directions,
the normal stress is maximum and minimum and for any other orientation of the cube, the normal stress on any
face is in between these two limiting values. The principal stress acting on the face parallel to the minimum and
maximum principal stresses is called intermediate.
A set of six quantities, the three principal stresses and their directions, thus represents the state of stress.
Fortunately, vertical can often be considered as one of the principal directions, with the consequence that the
vertical stress
σ
v
at depth
h
is then simply given by the weight of the overlying rock (i.e.,
σ
v
=pgh
, where
p
is
the average density of the overlying rock and
g
is gravity). Determination of the state of stress is then reduced
to identifying three quantities, the minimum and maximum horizontal stresses, respectively
σ
h
and
σ
H
, and the
azimuth of
σ
H
(or equivalently of
σ
h
).
Stress data compiled by Brown and Hoek (1978) confirm that, despite some scattering, the vertical stress is
proportional to depth in a manner consistent with an average rock density
p =
2,700 kg/m
3
(~170 lb/ft
3
) (Fig-
Figure 1
State of stress in the subsurface, with one of the principal stress directions being vertical. By conven-
tion,
σ
H
>
σ
h
.
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