Page 594 - Petrophysics

ROCK DEFORMATION 56 1

WAX
__1
,A +X
-

6Pz
A' -.Ax
A2 6X

B' AOB' Is the final position and
configuration of the original
right angle AOB
Shear Strain 'Yxz--Ol-O,
'I
z
Figure 9.5. Shear strain [7].

The maximum shear stress occurs on a plane inclined at 45" to the
principal plane, and is given by:

(9.16)

The normal strain, E~, and shear strain, 'ye, in a plane inclined at 01 to the
x axis, as shown in Figure 9.50>) are:

Yxz
Ex - EZ
Ex + E2 +- cos 20 + -sin 20
2 2 2
Eo = ~ (9.17)
yo = yxzcos 20 - (Ex - EZ) sin 20 (9.18)
It is obvious from these equations that in order to completely describe
strain, it is necessary to specify not only its magnitude, direction and
sense, but also the plane upon which it acts.
ROCK DEFORMATION

The relationship between stress and strain for reservoir rocks is
influenced by a large number of factors. Some of these factors are: the
composition and lithology of rocks, their degrees of cementation and
alteration, type of cementing material, amount and type of fluids in the
porous space, compressibility of the rock matrix and fluids, porosity
and permeability, and reservoir pressure and temperature. Many of these
factors are interdependent, and their separate and combined effect on
the stress-strain relationship can be measured only in the laboratory,
using an actual rock sample from the reservoir and controlling the testing