Deformation, stress and strain - Introducing Tectonics, Rock Structures and Mountain Belts - page 22

easily demonstrated by placing a weight
on a large piece of floating wood, say,
which stays afloat, and comparing it
with the effect of the same weight on
a smaller piece of wood, which sinks
under the weight (Figure 4.1B). Thus the
same size of force will produce different
sizes of stress depending on the surface
area of the body on which the force acts,
since stress equals force divided by area .
Rocks at depth are subject to very
great pressure due to the effect of
gravity, i.e. the weight of the rocks

above. These gravitationally derived
stresses are equal in every direction
and do not just act downwards, in the
same way as water pressure acts at great
depth in the sea; this state of stress is
termed the lithostatic pressure (or
just 'the pressure') (Figure 4.2A). In
solid rock, this lithostatic pressure is
usually added to by directional stresses
caused by tectonic forces, which can
be either positive ( compressional )
or negative ( extensional ), so that a
rock at depth subjected to directional

stresses would have two components;
the lithostatic component , equal to
the mean stress , plus a directional
component (equal to the difference
between the maximum and minimum
stress) which is the element of the
stress field potentially capable of pro-
ducing deformation (Figure 4.2B).

Normal stress and shear stress
Figures 4.1 and 4.2 show forces, and
therefore stresses, acting at right angles
to a surface. However, in the general
case, a force will act obliquely to a
surface (Figure 4.3A). When this force is
opposed by an equal and opposite force,
the resulting stress can be imagined as
being composed of two components:
one acting at right angles to the surface,
the normal stress , and the other acting
parallel to the surface, the shear stress
(Figure 4.3B) . The effect of the normal
stress is to act across the surface; the
effect of the shear stress is to attempt
to make the two sides of the surface
move in opposite directions. Shear
stress is important in understanding the
behaviour of faults and shear zones, as
we shall see in the following chapters.
If we consider the effect of an oblique
stress acting across a surface separating
two blocks of rock, the size of the shear
stress component will influence how
readily movement takes place along the
surface between the blocks, whereas
the normal stress component will either
inhibit movement (if compressive) or
assist movement (if extensional).

P1

P1

P3

P3

P2

P2

P2

P3 P2

P3

P1

P1

B

A

P1=P2=P3

P1>P2>P3

Figure 4.2 Pressure. A. in lithostatic pressure, the stresses exerted on a body in every direction are
equal; this can be represented by three mutually perpendicular stress axes P1, P2 and P3, where
P1=P2=P3. B. A variable stress field can be represented by three mutually perpendicular stress axes
such that P1 is the maximum stress, P3 the minimum and P2 the intermediate, i.e. P1>P2>P3. The
shape of the box illustrates diagrammatically the strain of an initial cube subjected to a stress field of
this type. Note that P3, the minimum stress here, is negative, i.e. an extension.

normal
stress oblique

force

shear
stress

shear
stress

oblique
force

normal
stress

A B

Strain
As explained above, strain is defined as
the change in shape and/or volume of a
body. A change in volume only, termed
a dilation (Figure 4.4A), which may be

Figure 4.3 Normal stress and shear stress. An oblique force opposed by an equal and opposite
force acting on a thin slab ( A ) can be represented by a normal stress acting at right angles to the
slab and a shear stress acting parallel to the slab ( B ) and tending to move the top of the slab to the
left and the bottom to the right; this is sometimes referred to as a rotational stress; in this case the
material inside the slab will tend to rotate in an anticlockwise sense, i.e. the strain will be rotational
(see Figures 4.4, 4.5).