of 8
1
Supplementary Information for
2
Dynamic rupture initiation and propagation in a fluid-injection laboratory setup with
3
diagnostics across multiple temporal scales
4
Marcello Gori
a
,
1
, Vito Rubino
b
, Ares J. Rosakis
b
, Nadia Lapusta
c
,
d
5
1
Corresponding Author: Marcello Gori.
6
E-mail: marcello.gori00@gmail.com
7
This PDF file includes:
8
Supplementary text
9
Figs. S1 to S4
10
Table S1
11
SI References
12
Gori et al.,
Proc. Natl. Acad. Sci.
, 2021
PNAS |
November 16, 2021
| vol. XXX | no. XX |
1–8
Supporting Information Text
13
On the full set of stress measurements obtained with the strain gauges.
The stress tensor components are reported in Figures S2
14
and S3 for the case of rapid and slow pressure ramp up, respectively, and they are obtained as detailed in Strain Acquisition
15
System. The shear
σ
12
(yellow), fault-normal
σ
22
(green) and fault-parallel
σ
11
(cyan) stresses are plotted over three temporal
16
scales, ranging from minutes on the left (a, d, and g), to milliseconds in the center (b, e, and h) and microseconds on the right
17
(c, f, and i). The solid, brighter lines correspond to the strain gauge positioned in proximity of the injection site just below the
18
interface (denoted SG-0 in Figs. 2 and S1); and the dashed, darker lines correspond to the strain gauge positioned
20
mm away
19
from SG-0 in the positive
x
1
-direction (SG-20 in Figs. 2 and S1).
20
As before,
t
= 0
denotes the initiation of the dynamic rupture. The vertical far-field load (Fig. 2, yellow arrows) is applied
21
quasi-statically in displacement-control mode at a constant rate of strain of
6
.
7
×
10
5
s
1
. Upon reaching the final level of
22
15
MPa, the system switches to load-control mode, keeps the load constant, and the strain rates drastically diminish. At
23
this point, the strain acquisition system is zeroed and the strain variations with respect to this initial condition are recorded.
24
Thus, all strain (and stress) readings represent changes with respect to this initial condition. Significantly, under constant
25
strain, the polymeric material undergoes slow viscoelastic relaxation. As a consequence, to keep the applied load constant,
26
the loading frame adds small compressive displacement increments, which are recorded by the strain gauges as compressive
27
vertical strains and, due to the Poisson’s effect, tensile strains in the horizontal direction. The strain gauges measure these
28
strains in a reference system aligned with the fault, in the
x
1
,
x
2
-direction. Hence, the accumulation of the strain signals over
29
several minutes prior to the initiation of the dynamic rupture embeds the contribution of the viscoelastic relaxation of the
30
polymer, and as a result the increase in stress is a potential artifact (Fig. 7a and c; Figs. S2 and S3, a, d, and g). During
31
the quasi-static loading phase, we focus on stress changes from the viscous-flow-induced trend, and on relative variations
32
between different locations. When the signals of the two measurements stations deviate from each other, their difference is
33
proportional to the different amount of slip those locations experience. Over shorter timescales, during the dynamic phase,
34
the viscoelastic material behavior mainly results in increasing in the effective elastic moduli (
1
3
), which we account for, as
35
explained in Materials and Methods. The stress behavior at the locations SG-0 and SG-20 is influenced by the 2D nature of
36
the interface (Fig. S1b). In particular, as the pressurized fluid is delivered to the interface, heterogeneous pore pressure and
37
slip profiles arise, where patches at higher pore-pressure tend to accumulate more slip. The shear stress released at a patch
38
through slipping is redistributed to the surrounding patches, which, in turn, experience more or less slip, depending on their
39
local frictional strength. Locked patches, close to the slipping ones, experience shear and normal stress accumulation, while
40
weaker patches slip more easily and accumulate less (or release) shear stress.
41
For the rapid pore-pressure ramp-up scenario, in the accelerated-slip phase few hundreds of milliseconds prior to the
42
triggering of the dynamic rupture (Fig. S2b, e, and h), the shear stress
σ
12
at SG-0 (Fig. S2b, bright yellow line) and the
43
fault-normal stress
σ
22
(Fig. S2e, bright green line) clearly evolve, both testifying that the patch around SG-0 is undergoing
44
slip. The positive fault-parallel stress variation
σ
11
(Fig. S2h, bright cyan line) indicates that the accelerated slip is inducing a
45
tensile lobe through SG-0 (
4
,
5
). This suggests that the accelerated slip is nucleating somewhere in the positive
x
1
-direction
46
with respect to SG-0, and its leftward tip (Fig. 2a) swipes across the SG-0 station as it propagates in the negative
x
1
-direction.
47
The rightward tip during the slip-accelerated phase does not reach the SG-20 location, which does not measure any stress
48
signal.
49
After the dynamic rupture initiates (Fig. S2c, f, and i), the anti-symmetric rupture pattern (
4
,
5
) results in nearly constant
50
levels of normal stress
σ
22
(Fig. S2f, bright green line.) The fault-parallel stress
σ
11
is characterized by a small positive signal
51
at SG-0 and a more pronounced negative signal at SG-20 (Fig. S2i), corresponding to tensional and compressional lobes in the
52
fault-parallel direction, associated with with the rupture initiating in the positive
x
1
-direction.
53
The slow pore-pressure ramp-up scenario exhibits a substantially different behavior compared to the rapid ramp-up one
54
discussed above. During the accelerated-slip phase few tens of milliseconds prior to the triggering of the dynamic rupture
55
(Fig. S3b, e, and h), the shear stress increase
σ
12
at SG-0 (Fig. S3b, bright yellow line) more pronounced than at SG-20, and
56
the fault-normal stress
σ
22
(Fig. S3e, bright green line) is accumulated, rather than released. This different stress behavior
57
indicates that the patch around SG-0 is undergoing slip, yet in minor amount than the surrounding patches, whose additional
58
release of normal stress is accumulated short distances away by frictionally stronger patches (i.e., SG-0), which undergo less
59
accelerated slip. The negative fault-parallel stress variation
σ
11
(Fig. S3h, bright cyan line) indicates that the accelerated
60
slip is inducing a compressive lobe through SG-0 (
4
,
5
). This suggests that the accelerated slip is nucleating somewhere in
61
the negative
x
1
-direction with respect to SG-0, and its rightward tip (view of Fig. 2a) swipes across the SG-0 station as it
62
propagates in the positive
x
1
-direction. This ‘tip’ does not reach the SG-20 location, which does not measure any stress signal.
63
After the dynamic rupture initiates (Fig. S3c, f, and i), the anti-symmetric rupture pattern results in nearly constant,
64
mildly compressive, fault-normal stress
σ
22
(after initial tensile and compressive peaks around
10
μ
s
, Fig. S3f, dark green line).
65
The fault-parallel stress
σ
11
experiences a fault-parallel compressive lobe
σ
11
at the SG-20 station (Fig. S3i, dark cyan line),
66
consistent with the rupture propagating rightward (view of Fig. 2a). Note that the variations in the fault-parallel stress tend to
67
leave a more persistent change in this case, while in the rapid pressure ramp-up case the fault-parallel stress changes have a
68
more transient nature.
69
Materials and Methods
70
Specimen Configuration and Fluid-Injection Setup.
In order to investigate the effects of fluids on the frictional faulting, a new
71
hydraulic setup has been developed to inject pressurized water onto the interface of a Poly(Methyl Meth-Acrylate) (PMMA)
72
2 of 8
| www.pnas.org/cgi/doi/10.1073/pnas.XXXXXXXXXX
Gori et al.,
Proc. Natl. Acad. Sci.
, 2021
Table S1. Results from repeated fluid-injection experiments. Slow and fast nucleation have been performed on the same specimens under
analogous nominal conditions. The first two tests are the ones presented in the manuscript. Couples of tests grouped between horizontal lines
are conducted on the same specimen using the two fluid injection procedures – slow and fast, respectively – for direct comparison. To ensure
consistent surface conditions, the interface is prepared before each test using the same procedures, including the polishing and bead-blasting
procedure described in Materials and Methods. The “pressure” column gives the injected pore fluid pressure at the initiation of dynamic slip.
Angle
Load
Injection
Pressure
(
)
(MPa)
Rate
(MPa)
29
15
.
0
Slow
8
.
7
29
15
.
0
Fast
4
.
9
29
15
.
0
Slow
13
.
3
29
15
.
0
Fast
5
.
0
29
15
.
0
Slow
8
.
7
29
15
.
0
Fast
4
.
3
26
15
.
0
Slow
12
.
2
26
15
.
0
Fast
5
.
3
specimen (Figs. 1, 2, and S1). The specimen is a
200
×
250
×
12
.
5
mm
3
PMMA prism divided into two identical halves by an
73
oblique cut at an angle
α
with respect to the
200
-mm dimension (Fig. 2). The juxtaposition of these two halves creates an
74
interface (green-shaded area), whose surfaces have been polished and bead-blasted to obtain desired and repeatable tribological
75
conditions (
4
). The micro-bead blasting procedure is performed via abrasive glass spherical particles between
104
and
211
μ
m
76
in diameter. A thin duct is manufactured on the lower half of the specimen to allow the injection of pressurized fluid on the
77
interface. Its diameter varies for machining purposes and equals
1
mm in the final 2.5-cm-long portion towards the interface
78
(Figs. 2 and S1b, blue channel). The specimen assembly is compressed by a static pre-load
P
. In the experiments presented
79
here we consider the specimen configuration with
P
= 15
MPa and
α
= 29
. Upon the application of the external load
P
, the
80
interface experiences a resolved normal and shear stress of
σ
n
=
P
cos
2
(
α
)
11
.
5
MPa and
τ
0
=
P
sin
(
α
)
cos
(
α
)
6
.
4
MPa,
81
respectively. Note that the load
P
is kept constant by setting the loading frame to switch to load-control mode after load has
82
reached
15
MPa.
83
Under these constant-load conditions, the fluid is introduced onto the interface through the
1
-mm-diameter duct by
84
pressurizing it (Figs. 2 and S1a, blue channel), following either Procedure (1) or Procedure (2). As described in the main text,
85
these procedures are characterized by a slow (
5
.
3
×
10
3
MPa/s) or a fast (
3
.
1
×
10
1
MPa/s) pressure increase, respectively.
86
The same specimen where Procedure (1) followed is subsequently used to conduct a test with Procedure (2). Yet, to guarantee
87
consistent surface roughness, before each test the interface is prepared using the polishing and bead-blasting procedure described
88
above. A list of four sets of tests – featuring slow and fast injection – is presented in Table S1. A new specimen is used for each
89
pair of tests shown in the table.
90
A Buna-N rubber o-ring, placed at the bottom of the specimen, guarantees the seal from water spills; however, it adds
91
a small thickness that is reduced as the specimen is compressed by the loading frame. This reduction in volume tends to
92
squeeze a small quantity of fluid out onto the interface. For this reason, a
1
-cm-long layer of (compressible) air, approximately
93
corresponding to
3
.
1
×
10
8
m
3
, is left on top of the fluid meniscus prior to starting the loading phase. After the desired
94
far-field load is reached and the absence of liquid on the interface is confirmed, the fluid pressurization phase can begin.
95
The fluid-injection setup features an air-driven hydraulic pump connected to the specimen via a
2
-m-long stainless-steel
96
pipe (Figs. 1 and S1a), where a series of components are installed in order to achieve a wide range of water peak pressure
97
(from
p
amb
0
.
1
MPa to
p
max
17
MPa), pressure rise-time (from
10
2
to
10
1
MPa/s), and duration of pressure plateau.
98
After being pressurized by the pump, the water pressure is modulated by a manual regulator (Figs. 1 and S1a). The pressure
99
regulator allows a wide range of rising times, spanning from few MPa per hour (Fig. 3a) to few MPa per second. A solenoid
100
valve, characterized by a rapid opening time, is employed to produce sharper rising times of the order of few MPa per
101
tens of milliseconds (Fig. 3b), which would otherwise be impossible to replicate with the manual pressure regulator. In a
102
zero-time-to-open approximation, the valve mimics a theoretical diaphragm separating a fluid at different pressure levels on
103
either side. The sudden disappearance (opening) of such diaphragm gives rise to a Riemann problem (
6
,
7
) in which a shock
104
wave travels downstream of the pipe followed by a (slower) contact discontinuity, while an expansion fan travels upstream. The
105
solenoid valve, which is actuated via a small electrical circuit, allows the creation of much sharper pressure ramp-up signals
106
to be delivered to the specimen’s interface (Figs. 2b and S1a). Two pressure transducers are located on either side of the
107
solenoid valve in order to simultaneously measure the pressure upstream and downstream of it, regardless of the open or close
108
configuration of the valve. These transducers are characterized by a cut-off frequency of
5
Hz and
3
kHz, respectively. For the
109
sake of clarity, the same color scheme associated with each of the two pressure transducers in Figure S1a will be consistently
110
adopted in the plots throughout the manuscript: purple refers to the pressure measured upstream of the solenoid valve and
111
blue to the pressure downstream of it. The pressure value measured downstream of the valve is delivered to the specimen’s
112
interface (Fig. S1a). At ambient pressure and temperature, the speed of sound in water is approximately
1
.
5
km/s. In order to
113
achieve pressure equilibrium over a
2
-meter-long pipe,
5
ms are needed for 3 to 4 wave reverberations to occur. Considering
114
that the shortest time scale in the injection circuit is that of the opening of the solenoid valve, which is in the order of tens
115
Gori et al.,
Proc. Natl. Acad. Sci.
, 2021
PNAS |
November 16, 2021
| vol. XXX | no. XX |
3–8
of milliseconds, assuming pressure equilibrium between the pressure transducer downstream of the valve and the injection
116
location on the specimen’s interface is an acceptable approximation.
117
Local Pressure Measurements with the Tactile Sensor Film.
The pressure transducers offer a high-resolved measurement of the
118
pressure temporal evolution in the duct; however, they cannot quantify the pressure at other locations on the interface as the
119
pressure diffuses away from the duct. For this reason, a separate experiment is conducted, where an array of holes of
0
.
5
mm in
120
both diameter and depth is drilled over the bottom half interface of a specimen with an horizontal interface (
α
= 0
) (Fig. 4a).
121
Upon the juxtaposition of the two halves of the specimen, in correspondence to each hole, there is no surface contact and a
122
small volume of air at ambient pressure (
p
amb
0
.
1
MPa) is trapped there.
123
A
0
.
5
-mm-thick tactile pressure-indicating sensor film characterized by a measurement range between
2
.
4
and
9
.
7
MPa (Fujifilm
124
Prescale
®
) is inserted onto this interface before the two halves of the specimen are juxtaposed and loaded. The horizontal angle
125
prevents slip during fluid-injection and preserves the integrity of the pressure film. The specimen is loaded at the same level
126
of far-field normal stress experienced by a specimen with
α
= 29
and
P
= 15
MPa, i.e.,
P
|
α
=0
= 15
cos
2
(29
) = 11
.
5
MPa.
127
When the final far-field load is applied to the specimen, the film experiences the resolved normal stress everywhere but in
128
correspondence to the drilled holes, where no stress variation is recorded. The film locally and irreversibly changes color in
129
proportion to the amount of pressure it experiences, with a spatial resolution is of
15
μ
m
and an accuracy of
±
2%
(data
130
provided by the manufacturer – Sensor Products Inc.)
131
Under these conditions, pressurized fluid is injected over the interface following a pressure profile equivalent to that of a
132
slow pressure ramp-up scenario (Fig. 3a). As the fluid diffuses over the interface and fills the holes, the film coloration
within
133
each hole permanently changes whenever
2
.
4
MPa of pressure are exceeded (in Fig. 4c, the measured values of pressure smaller
134
than
2
.
4
MPa have been manually set to the ambient pressure
p
amb
).
135
As the pore-pressure is increased, the water diffuses away from the injection location, driven by the pressure gradient, it fills the
136
holes and it increases the pressure level inside them. This pressure increase induces
local
coloration in the film in proportion to
137
the local-hole pressure level inside the holes. After the experiment is completed and the pressure film has assumed its final
138
coloration, the chromatic levels are digitized by a digital camera and each pixel reading is then converted into a pressure level
139
by using a calibration chart provided by the manufacturer (Sensor Products Inc.) and a map of pressure distribution along the
140
interface is produced (Fig. 4b and c). Due to the pixel-to-pixel chromatic variation, for each hole, the pressure is computed as
141
the average of the five smallest values therein: the less colored portions of each hole are typically located to its center and
142
behold a more accurate pressure reading, as they are minimally affected by small irregularities associated with the interaction
143
of the pressure film with the circular border of the hole.
144
In summary, the pressure measured by the film in correspondence to the population of holes is representative of the spatial
145
distribution of pressure over the interface just prior the onset of the dynamic rupture (Fig. 4c).
146
Strain Acquisition System.
On the back side of the specimen (Fig. 2b), two strain gauges are placed just below the interface
147
(Fig. S1b): one in proximity to the injection location (namely SG-0) and the other
20
mm away from it (namely SG-20) in the
148
positive
x
1
-direction. The strain gauges are connected to a digital acquisition system (Dewetron, Inc. DEWE-30-32) capable of
149
collecting data over several minutes (at a reduced sampling rate) – during the nucleation phase (Fig. 7a and c; Figs. S2 and S3,
150
a-b, d-e, g-h) – and also resolving the microsecond time scale once a triggering signal is received – for the dynamic rupture
151
(Fig. 7b and d; Figs. S2 and S3, c, f, i). Using this technique, strain signals are acquired at temporal scales spanning over nine
152
orders of magnitude (from
10
6
to
10
3
s).
153
At the strain gauges locations, the stresses are computed from the measured strains by invoking linear-elastic constitutive
154
properties in the plane-stress approximation (
σ
33
= 0
). Since PMMA displays strain-rate dependent behavior (
1
,
8
,
9
) and our
155
ruptures produce high strain rates (in excess of
10
3
s
1
in correspondence to the rupture tip (
1
)), we have employed dynamic
156
elastic modulus
E
d
= 5
.
9
GPa (using the HSR wave speed values from Gori et al. (
1
)) to compute stress changes during the
157
dynamic rupture, and the quasi-static elastic modulus
E
qs
= 2
.
4
GPa (using the LSR wave speed values from Gori et al. (1))
158
for the nucleation phase, prior to the dynamic rupture (
2
,
3
). Adjacent to the SG-0 station and across the interface from it, a
159
retro-reflective tape is used to mirror the laser beam from a Polytec fiber-optic laser interferometer (model OFV-551) and
160
provide the triggering signal for the 10-MHz sampling acquisition rate for the strain gauges as soon as the initiation of the
161
dynamic event is detected.
162
Full-field Imaging with Digital Image Correlation.
On the front side of the specimen (Fig. 2a) we employ the ultrahigh-speed
163
digital image correlation (DIC) technique (
10
12
). A thin layer of white paint is deposited over the specimen lateral face
164
and a
18
×
11
mm
2
random speckle pattern of optimally-sized black dots is added on top of it, centered at about
120
mm
165
away from the injection location so that well-developed dynamic ruptures are captured as they swipe through it (
1
,
10
,
11
)
166
(Fig. 2a). Digital images are acquired via a
400
×
250
pixel
2
Shumadzu HPV-X at
2
million frames per second, with the long
167
dimension of the camera frame aligned with the inclined interface, in the
x
1
and
x
2
-directions (Fig. 2a). The images are
168
subsequently analyzed with the correlation software VIC-2D (Correlated Solutions Inc.) to produce full-field displacement
169
evolution maps. In analogy with the strain acquisition system, the triggering signal is delivered by a laser velocimeter pointed
170
at a retro-reflective tape placed just above the injection epicenter (Fig. S1b). The displacement fields are then filtered using a
171
non-local (NL) de-noising algorithms (
13
,
14
) and numerically differentiated with respect to time in order to obtain velocity
172
fields and with respect to space to obtain strain fields. Stress maps are obtained from the strain ones by using linear-elastic
173
constitutive properties of PMMA and, in particular, the dynamic value of the elastic modulus
E
d
= 5
.
9
GPa.
174
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| www.pnas.org/cgi/doi/10.1073/pnas.XXXXXXXXXX
Gori et al.,
Proc. Natl. Acad. Sci.
, 2021
Note that ultrahigh-speed DIC and strain gauges cannot be employed simultaneously in our experiments, as the high-power
175
flash illumination required for the ultrahigh-speed image acquisition (
15
), releases a strong electro-magnetic pulse that interferes
176
with the strain gauges compromising their ability to measure physical strains. The data has been acquired on nominally
177
identical experiments.
178
1 mm
20 mm
12 mm
Laser Vibrometer
Į
SG-0
SG-20
to specimen
pressure
transducer
high-press
regulator
pressure
transducer
Solenoid
valve
water
≤ 16
MPa
to digitizer
to switch
water
pump
b
a
Fig. S1. (a)
Schematic of the fluid-injection setup. A pump pressurizes water from ambient pressure (
p
amb
0
.
1
MPa) up to
17
MPa. Downstream of the pump, the
pressurized water flows through a series of components: (
i
) a high-pressure regulator for manual pressure modulation (from few MPa/min to few MPa/s); (
ii
) a pressure
transducer with a 5 Hz bandwidth; (
iii
) a solenoid valve, allowing sharp pressure ramp-up profiles (in the order of few tens of MPa/s); and (
iv
) a pressure transducers with
bandwidth of 3 kHz measuring the fluid pressure just upstream of the specimen. Note that the two pressure transducers are placed on either side of the solenoid valve.
(b)
Close-up view of the frictional interface of the specimen around the injection location. The two strain gauges are glued on the back side (Fig. 2b). The laser vibrometer
signal is used to detect sudden motion in the
x
1
-direction associated with the dynamic rupture event and trigger the acquisition of the strain signals at high-bandwidth (
1
MHz).
-3
-2
-1
0
-0.06
-0.03
0
0.03
0.06
12
(MPa)
Quasi Static
-400
-200
0
200
400
-0.06
-0.03
0
0.03
0.06
Intermediate
12
@ 0 mm
12
@ 20 mm
-40
-20
02
04
06
0
-3
-2
-1
0
1
Dynamic Rupture
-3
-2
-1
0
-0.06
-0.03
0
0.03
0.06
22
(MPa)
-400
-200
0
200
400
-0.06
-0.03
0
0.03
0.06
22
@ 0 mm
22
@ 20 mm
-40
-20
02
04
06
0
-3
-2
-1
0
1
-3
-2
-1
0
time (min)
-0.06
-0.03
0
0.03
0.06
11
(MPa)
-400
-200
0
200
400
time (ms)
-0.06
-0.03
0
0.03
0.06
11
@ 0 mm
11
@ 20 mm
-40
-20
02
04
06
0
time (
s)
-3
-2
-1
0
1
a
b
c
d
e
f
g
h
i
SG-0
SG-20
SG-0
SG-20
SG-0
SG-20
time (
μ
s)
Fig. S2
.
Temporal evolution of the
shear
(a-c)
, fault-normal
(d-f)
and
fault-parallel
(g-i)
stresses recorded
by the two strain-gauge stations
(Figs. 2b and S1b) during the rapid
pressure ramp-up over three time
scales: minutes
(a)
,
(d)
and
(g)
, mil-
liseconds
(b)
,
(e)
and
(h)
, and mi-
croseconds
(c)
,
(f)
and
(i)
. Time
t
= 0
indicates rupture initiation.
Prior to the valve opening
(a)
,
(d)
and
(g)
, no fluid has been delivered
to the interface yet, and stresses
accumulate as a consequence of
the viscoelastic relaxation of the
bulk polymer under constant exter-
nal load. After the valve opening,
in the few hundred of milliseconds
prior to the rupture initiation, the
stress minimally redistributes due to
the limited accelerated slip precur-
soring the incipient dynamic event.
After the rupture is triggered
(c)
,
(f)
and
(i)
, a (left-lateral) dynamic slip
event is recorded.
Gori et al.,
Proc. Natl. Acad. Sci.
, 2021
PNAS |
November 16, 2021
| vol. XXX | no. XX |
5–8
-30
-20
-10
0
-0.6
-0.4
-0.2
0
0.2
12
(MPa)
Quasi Static
-40
-20
02
04
0
-0.6
-0.4
-0.2
0
0.2
Intermediate
12
@ 0 mm
12
@ 20 mm
-40
-20
02
04
06
0
-6
-4
-2
0
2
Dynamic Rupture
-30
-20
-10
0
-0.6
-0.4
-0.2
0
0.2
22
(MPa)
-40
-20
02
04
0
-0.6
-0.4
-0.2
0
0.2
22
@ 0 mm
22
@ 20 mm
-40
-20
02
04
06
0
-6
-4
-2
0
2
-30
-20
-10
0
time (min)
-0.6
-0.4
-0.2
0
0.2
11
(MPa)
-40
-20
02
04
0
time (ms)
-0.6
-0.4
-0.2
0
0.2
11
@ 0 mm
11
@ 20 mm
-40
-20
02
04
06
0
time (
s)
-6
-4
-2
0
2
a
b
c
d
e
f
g
h
i
SG-0
SG-20
SG-0
SG-20
SG-0
SG-20
time (
μ
s)
Fig. S3
.
Temporal evolution of the
shear
(a-c)
, fault-normal
(d-f)
and
fault-parallel
(g-i)
stresses recorded
by the two strain-gauge stations
(Figs. 2b and S1b) during the grad-
ual pressure ramp-up over three
time scales: minutes
(a)
,
(d)
and
(g)
,
milliseconds
(b)
,
(e)
and
(h)
, and
microseconds
(c)
,
(f)
and
(i)
. Time
t
= 0
indicates rupture initiation.
The delivery of pressurized fluid be-
gins approximately
27
minutes prior
to the rupture initiation
(a)
,
(d)
and
(g)
(water droplet symbol), promot-
ing slow slip. Note that stresses par-
tially accumulate as a consequence
of the viscoelastic relaxation of the
bulk polymer under constant exter-
nal load. In the few tens of millisec-
onds loading to the rupture initiation,
the stress redistributes due to the lo-
cal accelerated slip at SG-0 precur-
soring the incipient dynamic event.
After the rupture is triggered
(c)
,
(f)
and
(i)
, the fault-parallel and shear-
stress drops are about twice as
large as the rapid-ramp up counter-
parts (Fig. S2).
6 of 8
| www.pnas.org/cgi/doi/10.1073/pnas.XXXXXXXXXX
Gori et al.,
Proc. Natl. Acad. Sci.
, 2021
0
2
4
6
8
10
12
14
Slip Rate [m/s]
0
0.2
0.4
0.6
0.8
1
Coefficient of Friction
Dry Interface
Wet Interface
0
20
40
60
80
100
120
140
160
Slip [μm]
0
2
4
6
8
10
12
14
16
Slip Rate [m/s]
Slip Rate vs. Slip
Dry Interface
Wet Interface
Fig. S4.
Evolution of friction with slip rate (
left
) and evolution of slip rate with slip (
right
) along a dry (red) and pre-wetted (blue) interface. Friction is obtained as the ratio of
shear to normal stress. Stresses, slip and slip rate are measured using the ultrahigh-speed digital image correlation method over a field of view of size
18
×
11
mm
2
. The
curves are obtained for a point at the center of the field of view, with other locations showing similar behavior. The two tests are conducted under the same nominal loading
conditions of
P
= 15
MPa and
α
= 29
. In these tests, ruptures are initiated using a different procedure, not involving fluid-injection (as described in the text), so as to better
characterize the role of pre-existing fluids on the interface.
Gori et al.,
Proc. Natl. Acad. Sci.
, 2021
PNAS |
November 16, 2021
| vol. XXX | no. XX |
7–8
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| www.pnas.org/cgi/doi/10.1073/pnas.XXXXXXXXXX
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Proc. Natl. Acad. Sci.
, 2021