“lock-in” by a mechanism as yet not identified to
exist before decay sets in. Potential instability
exists in combined foliation-parallel extension
and shear, but the strength of instability in the
present case is weak. Continued amplification
with shear takes place in a basic-state flow with
ϽϪ0.6, and aggregate amplification will outweigh
later decay for any value
Ͻ 0.
By integrating the relations (11.120) through a
finite deformation, we may determine the amplitude and orientation history of a component. If an
initial set of perturbations with random initial
slope, A, and phase, and chosen at equal intervals
in orientation to foliation  are followed, the final
form of foliation planes may be computed as a
summation. An example is shown in Fig. 11.25 for
foliation-normal shortening. The initial shape of
the rock element was square. Fold axial planes are
not perfectly normal to the direction of shortening and they are finite in extent, even as seen in
this finite segment of the medium. They are
nearly normal to the direction of shortening, as
expected from the rate of shortening maximum
there (Fig. 11.24).
At present, little quantitative interpretation
of structures in foliated and multi-layer rocks has
been carried out, and this field of study remains
open. Figure 11.24 suggests that the continuity
of axial planes and the distribution in their
d xx
d xx
orientation for a given bulk shortening might
afford some indication of the strength of
anisotropy as described by the parameter m the
basic-state deformation, and the character of the
initial perturbation.
11.6 Concluding remarks
This chapter has introduced a few of the factors
which might be treated in more realistic models
of rock deformation: (i) rheological non-linearity;
(ii) dilatation at a macroscopic scale mediated by
diffusional transport; (iii) bulk properties of a
composite material; and (iv) instability in the
deformation of an anisotropic material. The
models formulated and analyzed are relatively
simple and to a substantial degree build on material presented in earlier chapters. The first two
topics were studied in application to the initiation of pinch-and-swell structures in extension, as
well as to folds and mullions, to suggest the possibility of the study of a wide range of behavior in
structures such as folds or boudinage. Overall,
though, the presentation is one of brief sketches
of restricted subject matter and methods. While
these sketches often supply means of carrying out
the modeling of naturally deformed rock, they
also provide a means of gaining physical insight.
11.6 CONCLUDING REMARKS
455
exist before decay sets in. Potential instability
exists in combined foliation-parallel extension
and shear, but the strength of instability in the
present case is weak. Continued amplification
with shear takes place in a basic-state flow with
ϽϪ0.6, and aggregate amplification will outweigh
later decay for any value
Ͻ 0.
By integrating the relations (11.120) through a
finite deformation, we may determine the amplitude and orientation history of a component. If an
initial set of perturbations with random initial
slope, A, and phase, and chosen at equal intervals
in orientation to foliation  are followed, the final
form of foliation planes may be computed as a
summation. An example is shown in Fig. 11.25 for
foliation-normal shortening. The initial shape of
the rock element was square. Fold axial planes are
not perfectly normal to the direction of shortening and they are finite in extent, even as seen in
this finite segment of the medium. They are
nearly normal to the direction of shortening, as
expected from the rate of shortening maximum
there (Fig. 11.24).
At present, little quantitative interpretation
of structures in foliated and multi-layer rocks has
been carried out, and this field of study remains
open. Figure 11.24 suggests that the continuity
of axial planes and the distribution in their
d xx
d xx
orientation for a given bulk shortening might
afford some indication of the strength of
anisotropy as described by the parameter m the
basic-state deformation, and the character of the
initial perturbation.
11.6 Concluding remarks
This chapter has introduced a few of the factors
which might be treated in more realistic models
of rock deformation: (i) rheological non-linearity;
(ii) dilatation at a macroscopic scale mediated by
diffusional transport; (iii) bulk properties of a
composite material; and (iv) instability in the
deformation of an anisotropic material. The
models formulated and analyzed are relatively
simple and to a substantial degree build on material presented in earlier chapters. The first two
topics were studied in application to the initiation of pinch-and-swell structures in extension, as
well as to folds and mullions, to suggest the possibility of the study of a wide range of behavior in
structures such as folds or boudinage. Overall,
though, the presentation is one of brief sketches
of restricted subject matter and methods. While
these sketches often supply means of carrying out
the modeling of naturally deformed rock, they
also provide a means of gaining physical insight.
11.6 CONCLUDING REMARKS
455