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maximum apparent horizontal slip. The authors
demonstrated that the displacement along the zones of
bands is proportional to the number of single bands
present. Along the faults, by contrast, when
displacement reaches 20-30 cm, a continuous discrete
slip surface is recognizable and the number of bands
does not increase for larger amount of displacement
(Tondi et al., 2012).
Figure 3: Cumulative frequency distributions for
(a) thickness, (b) displacement, and (c) length
computed for single compactive shear bands (in
blue), zone of compactive shear bands (in red)
and faults (in green). From Tondi et al. (2012).
The author used a cumulative frequency distribution and zones of bands, and ii) faults (Fig. 3a and b; Tondi
technique to determine the distribution of length,
thickness and displacement properties of the fault
network. In Fig. 3, the cumulative frequency
distributions of the three aforementioned dimensional
parameters are best fitted by negative power-law
(Mandelbrot, 1983):
N( = aS-D (1)
where N is the number of features having a size
greater than or equal to S (e.g. the fault length), a is a
measurement of the sample size, and the power-law
exponent D represents the slope of the best fit line,
which some authors interpreted as the fractal dimension
(Childs et al., 1990; Scholz and Cowie, 1990).
The plots show that there are breaks in the thickness
and displacement distributions between: i) single bands
et al., 2012). With regards to zones of bands vs. faults,
the switch from one power law distribution to another
occurs at about 10 cm of thickness, 10 cm of
displacement and 8 m of length. However, it should be
noted that the lengths distribution contains a lack of
data between 5 and 8 m. The authors interpreted those
as the threshold values for the transition from banding
to slip surfaces and cataclasis and, consequently, the
fault development.
Fluid flow within deformed porous
carbonates
Carbonates are economically important because
about 50% of natural geo-fluids (i.e. mineral and
hydrothermal waters, geothermal fluids, hydrocarbons)
are hosted in these rocks (Schlumberger Market
Analysis, 2007). Carbonate rocks consist of a great
variety of lithotypes, based upon the nature and
organization/shape of the constituting elements (i.e.
grains, pores, cement, clay minerals), and are
characterized by a wide range of porosity and
permeability (Lucia, 1999).
Many scientific papers thoroughly investigated the
formation and development of faults and fractures in
dilatant (tight) carbonates. In contrast, little attention
has been paid so far on the nucleation and development
of localized deformation in compactant (porous)
carbonates.
Because of the micro-mechanisms responsible for
deformation band formation, the effect of shear bands
on porosity and permeability of high-porosity rocks is
opposite to the effect of fractures in low-porosity rocks.
Indeed since deformation bands tend to have a lower
permeability with respect to their host rocks (e.g.
Antonellini & Aydin, 1994; Antonellini et al., 1999;
Tondi, 2007; Rath et al., 2011; Rustichelli et al., 2012),
they may act as barrier for fluid flow. In order to mimic
the compartmentalization effects caused by deformation
bands in a porous rocks, many paper have been
published in the last few decades (Antonellini & Aydin,
Stanford Rock Fracture Project Vol. 24, 2013 E-4