Geoscience Reference
In-Depth Information
conduction follows a linear relationship and
consequently, once conductivity is measured,
there are no scaling problems in terms of voltage
(some corrections for the frequency dependence
is needed; see Chapter 5). In plastic properties,
the relationship between stress and strain-rate is
not always linear. When the constitutive relation
is nonlinear, then rather than the proportional
coefficient one needs to determine the functional
relationship between stress and strain-rate.
There is no single-valued viscosity but effective
viscosity (defined as a ratio of stress to strain-rate)
that depends on the strain-rate (or stress). For
instance, if the relationship between stress and
strain-rate follows the power-law behavior, viz.,
·
σ
n
,
ε
(
T
,
P
,
L
,
C
W
)
=
A
(
T
,
P
,
L
,
C
W
)
(4.1)
ε
is strain-rate,
T
is temperature,
P
is pres-
sure,
L
is grain-size,
C
W
is water content and
n
is
a nondimensional parameter, then one needs to
determine both
A
and
n
as a function of various
where
log stress
1/T
(a)
(b)
geological strain-rate
lab strain-rate
log grain-size
log water content
(c)
(d)
Fig. 4.1
Rheological properties (effective viscosities) depend on various parameters. The vertical axis is log
(viscosity) (or log (stress)) to see the
relative
change in viscosity (or strength). (a) stress dependence of viscosity
behavior. Power-law regime in the low stress region and the Peierls mechanism in the high stress region are shown.
If lab experiments are done in the same regime as Earth (lab-I), the results can be extrapolated to Earth, but if lab
experiments are made in the different regime (lab-II), extrapolation cannot be justified. (b) temperature dependence
(low T versus high T mechanisms). Similar to (4.1), lab data can be extrapolated only when experiments are made in
the same regime as in Earth (lab-I). (c) grain-size dependence. A change in the deformation mechanisms with
grain-size occurs at different grain-size between geological deformation and laboratory experiments. To simulate, in
the lab, how grain-size may affect rheological properties, one should use smaller grain-size than grain-size in Earth.
(d) water content dependence. Water content affects the viscosity of a rock, but the manner in which water affects
the viscosity depends on the mechanisms of deformation.
