points on the two surfaces. The stress, as indicated
by the values associated with each contour, is positive (tensile) in the first and third quadrants and
negative (compressive) in the second and fourth
quadrants. Furthermore there is a stress concentration at the terminations of the model fault: the
values associated with the contours increase
toward the fault tip and the spacing between contours decreases. In fact the stress becomes so great
very near the model fault tips that the contours
merge into a pattern that is no longer distinguishable at the scale of this figure. Thus we have omitted
the contouring in a small region around each tip.
Figure 1.15 is an example of a plot prepared
using MATLAB®, the computational and graphics
engine that we employ throughout this textbook.
The m-file used to compute the values of the stress
component at the grid points and to prepare the
contour plot is available at the textbook website.
There, a color version of the contour plot is viewable along with contour plots of other stress components. This procedure is followed throughout
the textbook where grayscale figures are used to
reduce printing costs and color versions are available at the website.
To relate the veins and solution surfaces at the
Les Matelles outcrop to the left-lateral faults we
have to recognize that the veins and solution surfaces are secondary structures and the faults are the
primary structures. In other words, the veins and
solution surfaces formed in response to the stress
changes in the rock mass as slip developed on the
faults. We can correlate the symmetry of these secondary structures with the symmetry of the stress
field about the model fault (Fig. 1.15). The veins are
cracks that are pulled open by tensile stresses and
therefore are associated with the field of tensile
stress in quadrants 1 and 3. Conversely, the solution surfaces form in response to elevated compressive stresses and therefore are associated with
the field of compressive stress in quadrants 2 and 4.
The correlation between the model and the
exposure observations is supported by the fact
that the veins and solution surfaces do not cross
the fault surfaces where the model indicates a
discontinuity (change in sign) of the stress.
Furthermore, the model provides an explanation
for the initiation of these secondary structures
near the terminations of the faults. This is the
region of greatest stress concentration, and therefore is the locality where secondary structures are
most likely to form. Finally, the stress distribution
offers an explanation for the limited extent of the
secondary structures. The stress decreases away
from the fault tips toward much lower values at a
distance that scales with the length of the fault.
This decrease in stress is consistent with the termination of the veins and solution surfaces at
modest distances from the fault tips. Although
this two-dimensional model provides important
insights, additional understanding of the faulting
process may be achieved using three-dimensional
models (Willemse et al., 1996; Willemse, 1997;
Martel and Boger, 1998).
The authors became intrigued by the structures at Les Matelles over twenty years ago and, in
the course of investigating models for their formation, conceived of the concept of anticracks. At
that time we had no practical applications for this
concept in mind. Nor, to our knowledge, did the
exposure at Les Matelles figure significantly in the
solution of any problem relevant to society. For us
this was an academic exercise, motivated by a
strong (and inexplicable) urge to understand these
structures, and nothing more. However, explanations for certain features of very deep and largemagnitude earthquakes now utilize the concept of
anticracks (Green and Burnley, 1989). Also, the evolution of fault zones in limestone through a
complex sequence of vein development, solution
surface development, and slip on solution surfaces
has been documented and interpreted using the
anticrack concept (Willemse et al., 1996). In addition, the development of compaction bands in
porous sandstone has been explained using the
anticrack concept (Mollema and Antonellini,
1996). These tabular zones of localized compaction
appear to propagate as anticracks in response to
elevated compression, and they also have a
significant effect on the permeability of reservoirs
and aquifers in porous sandstone (Sternlof et al.,
2004). Perhaps the time and the taxpayers’ dollars
spent working on the seemingly arcane concept of
anticracks at the Earthquake Studies Branch of the
US Geological Survey can be justified in light of
these applications.
1.4 ANTICRACKS IN SOUTHERN FRANCE
19
by the values associated with each contour, is positive (tensile) in the first and third quadrants and
negative (compressive) in the second and fourth
quadrants. Furthermore there is a stress concentration at the terminations of the model fault: the
values associated with the contours increase
toward the fault tip and the spacing between contours decreases. In fact the stress becomes so great
very near the model fault tips that the contours
merge into a pattern that is no longer distinguishable at the scale of this figure. Thus we have omitted
the contouring in a small region around each tip.
Figure 1.15 is an example of a plot prepared
using MATLAB®, the computational and graphics
engine that we employ throughout this textbook.
The m-file used to compute the values of the stress
component at the grid points and to prepare the
contour plot is available at the textbook website.
There, a color version of the contour plot is viewable along with contour plots of other stress components. This procedure is followed throughout
the textbook where grayscale figures are used to
reduce printing costs and color versions are available at the website.
To relate the veins and solution surfaces at the
Les Matelles outcrop to the left-lateral faults we
have to recognize that the veins and solution surfaces are secondary structures and the faults are the
primary structures. In other words, the veins and
solution surfaces formed in response to the stress
changes in the rock mass as slip developed on the
faults. We can correlate the symmetry of these secondary structures with the symmetry of the stress
field about the model fault (Fig. 1.15). The veins are
cracks that are pulled open by tensile stresses and
therefore are associated with the field of tensile
stress in quadrants 1 and 3. Conversely, the solution surfaces form in response to elevated compressive stresses and therefore are associated with
the field of compressive stress in quadrants 2 and 4.
The correlation between the model and the
exposure observations is supported by the fact
that the veins and solution surfaces do not cross
the fault surfaces where the model indicates a
discontinuity (change in sign) of the stress.
Furthermore, the model provides an explanation
for the initiation of these secondary structures
near the terminations of the faults. This is the
region of greatest stress concentration, and therefore is the locality where secondary structures are
most likely to form. Finally, the stress distribution
offers an explanation for the limited extent of the
secondary structures. The stress decreases away
from the fault tips toward much lower values at a
distance that scales with the length of the fault.
This decrease in stress is consistent with the termination of the veins and solution surfaces at
modest distances from the fault tips. Although
this two-dimensional model provides important
insights, additional understanding of the faulting
process may be achieved using three-dimensional
models (Willemse et al., 1996; Willemse, 1997;
Martel and Boger, 1998).
The authors became intrigued by the structures at Les Matelles over twenty years ago and, in
the course of investigating models for their formation, conceived of the concept of anticracks. At
that time we had no practical applications for this
concept in mind. Nor, to our knowledge, did the
exposure at Les Matelles figure significantly in the
solution of any problem relevant to society. For us
this was an academic exercise, motivated by a
strong (and inexplicable) urge to understand these
structures, and nothing more. However, explanations for certain features of very deep and largemagnitude earthquakes now utilize the concept of
anticracks (Green and Burnley, 1989). Also, the evolution of fault zones in limestone through a
complex sequence of vein development, solution
surface development, and slip on solution surfaces
has been documented and interpreted using the
anticrack concept (Willemse et al., 1996). In addition, the development of compaction bands in
porous sandstone has been explained using the
anticrack concept (Mollema and Antonellini,
1996). These tabular zones of localized compaction
appear to propagate as anticracks in response to
elevated compression, and they also have a
significant effect on the permeability of reservoirs
and aquifers in porous sandstone (Sternlof et al.,
2004). Perhaps the time and the taxpayers’ dollars
spent working on the seemingly arcane concept of
anticracks at the Earthquake Studies Branch of the
US Geological Survey can be justified in light of
these applications.
1.4 ANTICRACKS IN SOUTHERN FRANCE
19