Geology Reference
In-Depth Information
11.3
Strain and Strain Partitioning
Strain can play a significant role in structural balancing. Presented here are the practical
strain measurements that can be applied to field examples at the map and cross-section
scale. The most readily quantifiable macroscopic measures of strain are bed length and
bed thickness (Fig. 11.10). Separate equations are given for the strain parallel and per-
pendicular to bedding, even though the forms are identical, in order to better emphasize
the origins of the interpretations that will appear in subsequent sections.
Bed length change can be quantified as
L = L 1 - L 0 ,
(11.1)
e L =( L 1 - L 0 )/ L 0 , or
(11.2)
e L =( L 1 / L 0 ) - 1 ,
(11.3)
where
L = change in bed length, e L = the infinitesimal normal strain parallel to bed-
ding, L 0 = the bed length before deformation, L 1 = the bed length after deformation.
Exactly equivalent equations can be written for bed thickness change:
t = t 1 - t 0 ,
(11.4)
e t =( t 1 - t 0 )/ t 0 , or
(11.5)
e t =( t 1 / t 0 ) - 1 ,
(11.6)
where
t = change in bed thickness, e t = the infinitesimal normal strain perpendicular to
bedding, t 0 = the bed thickness before deformation, t 1 = the bed thickness after deforma-
tion. With the equations in the forms given, extension is positive and contraction is nega-
tive. The value of e is a fraction but is commonly given as a percent by multiplying by 100.
The strain can be also be measured with the stretch,
β
, (McKenzie 1978):
β L =( L 1 / L 0 ) ,
(11.7)
β t =( t 1 / t 0 ) ,
(11.8)
where
β t = layer-normal stretch. The stretch is always
positive, greater than 1 for extension and less than 1 for contraction. For a constant
area rectangle the stretch has the convenient property that
β L = layer-parallel stretch and
β L =1/
β t .
(11.9)
From Eqs. 11.7, 11.8 and 11.9, the stretches can also be given as
β L = t 0 / t 1 ,
(11.10)
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