Fault rock heterogeneity
can
produce fault weakness and
reduce fault stability
:
Supple
mentary
material
John D. Bedford
1
*
, Daniel R. Faulkner
1
& Nadia Lapusta
2,3
1
Rock Deformation Laboratory, Department of Earth, Ocean and Ecological Sciences,
University of
Liverpool
2
Department of
Mechanical and Civil Engineering, Division of Engineering and Applied Science,
California Institute of Technology
3
Seismological Laboratory, Division of Geological and Planetary Sciences, California Institute of
Techn
ology
*Corresponding author: jbedford@liverpool.ac.uk
Supple
mentary
Figure 1| Schematic diagram of the direct shear arrangement used in the
experiments.
The gouge layer is comprised of either heterogeneous patches of quartz and clay (as shown
in this
figure) or as a homogeneous quartz
-
clay mixture.
The diameter of the platens is 20 mm
and the
length of the fault gouge layer is 50 mm
.
Supple
mentary
Figure 2| Pore volume and layer thickness data for the endmember quartz and clay
gouges during shearing
. a,
P
ore volume reduction and
b,
layer thickness evolution of the gouge layers as
they compact during an experiment. At the end of the experiment, the layer thicknesses were measured
using a micrometer
to be almost identical
. The thickness evolution durin
g the experiment was then back
-
calculated using the pore volume data, assuming the sliding area remains constant and that all volumetric
strain is accommodated by a change in layer thickness
1
(see Methods
in main article
)
. The compaction
evolution can be s
eparated into
two
regimes. Stage (I): Loading of the gouge layers. Stage (II): Frictional
shearing of the gouge layers, where the quartz gouge experiences a greater amount of shear enhanced
compaction than the clay. While the endmember layer thicknesses do
not differ much in the post
-
yield
frictional shear regime, there is a difference of about 20
μm
there. This difference can account for a
significant fraction of the progressive weakening observed in the friction data of the heterogeneous faults
(Fig. 1
c
)
as discussed in
Supple
mentary
Note 1
below
. Note that the reason the gouges do not have the
same layer thicknesses at the start of the experiment is because the clay gouge compacts more than the
quartz during initial pressurization to the
starting conditions, as has been shown in previous work on clay
-
quartz gouges
2
.
Supple
mentary
Figure 3| Evolution of the coefficient of friction (
μ
) with displacement for
heterogeneous faults consisting of central clay patch bound by two quartz patches.
This data is from
heterogeneous faults with opposite symmetry gouge layers to th
ose
presented in Fig. 1
c
of the main article
.
These heterogeneous faults exhibit similar weakening to those in Fig. 1
c
, showing that the arrangement of
the different gouge pat
ches in the layer does not dictate the overall frictional response and that progressive
weakening is ubiquitous for all heterogeneous faults.
Although similar weakening is observed, we note that
some of
the
(
a
-
b
) values
from the reversed symmetry faults
are slightly higher than for the heterogeneous
faults comprised of a central quartz patch (
Supple
mentary Table 1). We have no explanation for this
difference; although it could be due to
(
a
-
b
)
data from friction experiments generally
being quite
scattered
,
when compared to coefficient of friction data, and thus caution should be taken when directly comparing
individual velocity steps.
Supple
mentary Figure 4|
Predicted (
a
-
b
)
evolution
with
displacement from clay smearing in the
heterogeneous faults
.
Also shown are the
obtained
(
a
-
b
) values
from
both heterogeneous and
homogeneous fault
experiments
for
clay fractions of
a.
40%,
b.
50%,
c.
60% and
d.
70%.
The predicted
(
a
-
b
)
evolution
is calculated
using the arithmetic mean of
the
(
a
-
b
)
values for the endmember
quartz and
clay gouges (from 1.5 mm displacement in
Supple
mentary Table 1) and by assuming the length of the clay
patch increases by the amount of displacement on the
fault as the clay is smeared along localized Y
-
shear
planes
–
as was done for coefficient of friction in Fig. 2
c
of the main
article
.
The
(
a
-
b
)
data
are more
scattered than the friction data in Fig. 2
c
, so caution should be taken when interpreting the r
esults; however,
the data show that clay smearing generally underpredicts the
(
a
-
b
)
values for the heterogeneous faults.
The actual
(
a
-
b
)
values from the heterogeneous experiments are higher than predicted
,
suggesting that the
frictional properties of the
clay patches
contribute more to the average
(
a
-
b
)
values, as would be consistent
with
higher normal stresses
in the clay patches
than
i
n
the quartz patch
due to differential compaction
which
could
also
potentially explain
some of
the progressive weakening trends in our experiments
(see
Supple
mentary
Note 1
below for full discussion of this effect). Note, however, that even though the
experi
mental
(
a
-
b
)
values
are higher than predicted for the heterogeneous faults, they are still consistently
lower than
(
a
-
b
)
values
from the equivalent
homogeneous faults. Also note
that
only
(
a
-
b
)
values
from
up
-
steps in the sliding velocity
(from
0.3 to 3 μm·s
-
1
)
are shown
in the figure
as there is asymmetry in the
frictional response between velocity up
-
steps and down
-
steps (from
3 to
0.
3 μm·s
-
1
), something that has
been
reported
in previous studies on
the
ra
te
-
dependent frictional behaviour of fault gouge
s
3
–
5
.
Supple
mentary
Table 1| Processed values of the rate
-
and
-
state parameters
a
,
b
and
Dc
from all the
velocity steps in this study.
Data are shown for both heterogeneous and homogeneous faults with varying
clay
-
quartz compositions (displayed as % clay fraction). There are a total of seven velocity steps for each
experiment (every 1 mm of displacement, starting at a displacement of 1.5
mm). Note that for displacements
>1.5 mm, the rate
-
and
-
state parameters could not be calculated for the endmember quartz fault (i.e. 0% clay
fraction) or the heterogeneous fault with a 20% clay fraction, as stick
-
slip instabilities were triggered by
the ve
locity steps; these values have therefore been left blank.
Also shown are the processed
a
,
b
and
Dc
values from the heterogeneous fault experiments with a reversed symmetry
, where a central clay patch is
bound by two quartz patches (
Supple
mentary Fig. 3).
Supple
mentary
Note 1
Estimating the potential effect of differential compaction
on interface weakening
The normal stress applied to the sample by the confining pressure (
푃
푐
)
and the
pore fluid pressure
(
푃
푓
)
within the gouge
are
held constant during all tests in this study, resulting in the constant average
effective normal stress
휎
푛
̅
̅
̅
=
푃
푐
−
푃
푓
. So there should be no evolving elastic compaction during the tests,
and any inferred compaction is inelastic. Both the quartz and clay g
ouge layers have the same thickness at
each moment of time in the experiment, constrained by the steel assembly that is effectively rigid compared
to the elastic properties of the gouge. Assuming that the total normal stress is the sum of the elastic and
i
nelastic parts, any differential inelastic compression between the quartz and clay gouge would result in
different elastic fault
-
normal strain in the two gouges and hence potentially different normal stresses,
causing redistribution of normal stress. For t
his redistribution to result in a progressive weakening of shear
resistance, the normal stress has to increase on the weaker, clay phase, which would require that clay
compacts less (and quartz compacts more). This is indeed the case (
Supple
mentary
Fig. 2)
.
To compensate for the larger compression of the quartz gouge during the loading phase, extra
thickness of the quartz gouge material was initially applied. This procedure worked, since the peak value
of the friction coefficient at the end of the loading
phase, where the friction curve turns the corner into
frictional sliding, for all heterogeneous fault experiments is consistent with both clay and gouge layers
being at the same applied effective normal stress. For example, for the heterogeneous interface
with the
clay fraction
푓
푐푙
of 0.4 (or
40% of the interface filled with clay gouge), the peak friction coefficient is about
0.5, which is quite similar to the sum of the contributions from both quartz and clay layers at the same
normal stress,
휇
푐푙
푓
푐
푙
+
휇
푞푢
(
1
−
푓
푐푙
)
=
0
.
27
∙
0
.
4
+
0
.
7
∙
0
.
6
=
0
.
52
,
where
휇
푐푙
=
0
.
27
and
휇
푞푢
=
0
.
7
are the near
-
constant friction coefficients of the clay and quartz gouges, respectively, from the
homogeneous interface tests. Hence it appears that the quartz and clay gouge laye
rs are at about the same
effective normal stress at the end of the loading phase, as intended.
However, there is much smaller but continuing differential compaction between quartz and clay in
the frictional sliding regime (Stage II of
Supple
mentary
Fig.
2 which starts at about 1 mm of displacement),
of about 20
m more compaction in quartz, based on the homogenous interface tests. This corresponds to
normal strain of about 0.02 for the (rounded) layer thickness of 1 mm. The following highly simplified
ca
lculation allows us to estimate the potential impact of such differential compaction on the average friction
coefficient. The additional fault
-
normal compressive elastic strain
휖
푎푑푑
of 0.02 in the clay layer (which
would arise due to the same thickness
of both quartz and clay layers) would correspond to the additional
fault normal compressive stress of
휎
푎푑푑
=
(
퐾
+
4
퐺
3
)
휖
푎푑푑
, where
K
and
G
are the bulk and shear modulus
of the clay layer
,
respectively
. Assuming
(
퐾
+
4
퐺
3
)
of 2 to 4 GPa
(
ref.
6
)
, we get
휎
푎푑푑
in the clay gouge
of 40 to 80 MPa, which implies significant redistribution of normal stress. Since the normal stresses in the
clay and quartz gouges have to balance the externally applied normal stress, we can find the normal stresses
휎
푞푢
and
휎
푐푙
=
휎
푞푢
+
휎
푎푑푑
in the quartz and clay gouges, respectively, from
휎
푐푙
푓
푐푙
+
휎
푞푢
(
1
−
푓
푐푙
)
=
푃
푐
.
For example, for the clay fraction
푓
푐푙
=
0
.
4
,
푃
푐
= 60 MPa, and
휎
푎푑푑
=
40
MPa, one gets
휎
푞푢
=
44
MPa
and
휎
푐푙
=
휎
푞푢
+
휎
푎푑푑
=
84
MPa, a substantial difference between the normal stress in the two layers.
Since the weaker clay gouge would support more of the normal load, the interface would become weaker
than for the spatially uniform normal stress. The combined friction coefficient
휇
푐표푚푏
of the two layers with
such normal stress redistribution due to differential compaction would then be given by
휇
푐표푚푏
=
[
(
휎
푐푙
−
푃
푓
)
휇
푐푙
푓
푐푙
+
(
휎
푞푢
−
푃
푓
)
휇
푞푢
(
1
−
푓
푐푙
)
]
/
(
푃
푐
−
푃
푓
)
=
0
.
43
for
푓
푐푙
=
0
.
4
and
푃
푓
= 20 MPa.
The resulting
ave
rage interface friction coefficient of
휇
푐표푚푏
=
0.43 is substantially weaker than the peak one of 0.5,
accounting for about half of the observed friction reduction from 0.5 to 0.35 for the 40% clay case of Fig.
1
c
. If this calculation is redone with th
e (higher) additional compressive stress of 80 MPa (corresponding
to higher elastic moduli of clay gouge), one gets
휇
푐표푚푏
=
0.32, even slightly more than the observed
reduction.
We conclude that the differential compaction between the quartz and cla
y gouges during shear
-
and the associated normal stress redistribution
-
may account for a significant portion of the observed
interface weakening, with some caveats that would require additional study. For example, the compaction
data of
Supple
mentary
Fi
g.
2
is obtained under the constant effective normal stress, whereas the
redistribution of normal stress due to differential compaction in heterogeneous samples would result in
varying normal stress for both quartz and clay layers, potentially resulting in
different evolution of
compaction. Furthermore, the elastic properties of the gouge layers are not precisely known and may evolve
with compaction and changing normal stress. At the same time, such differential compaction may be
important during shear of h
eterogeneous natural faults and requires further experimental and theoretical
study.
Supple
mentary
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