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EARTH, ATMOSPHERIC,
AND PLANETARY SCIENCES
Dynamic rupture initiation and propagation in a
fluid-injection laboratory setup with diagnostics
across multiple temporal scales
Marcello Gori
a,1
, Vito Rubino
b
,AresJ.Rosakis
b
, and Nadia Lapusta
c,d
a
Planetary Sample Acquisition and Handling, NASA Jet Propulsion Laboratory, Pasadena, CA 91109;
b
Graduate Aerospace Laboratory, California Institute
of Technology, Pasadena, CA 91125;
c
Mechanical and Civil Engineering, California Institute of Technology, Pasadena, CA 91125; and
d
Seismological
Laboratory, Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA 91125
Edited by Paul Segall, Department of Geophysics, Stanford University, Stanford, CA; received November 20, 2020; accepted November 3, 2021
Fluids are known to trigger a broad range of slip events, from
slow, creeping transients to dynamic earthquake ruptures. Yet, the
detailed mechanics underlying these processes and the conditions
leading to different rupture behaviors are not well understood.
Here, we use a laboratory earthquake setup, capable of injecting
pressurized fluids, to compare the rupture behavior for different
rates of fluid injection, slow (megapascals per hour) versus fast
(megapascals per second). We find that for the fast injection
rates, dynamic ruptures are triggered at lower pressure levels and
over spatial scales much smaller than the quasistatic theoretical
estimates of nucleation sizes, suggesting that such fast injection
rates constitute dynamic loading. In contrast, the relatively slow
injection rates result in gradual nucleation processes, with the
fluid spreading along the interface and causing stress changes
consistent with gradually accelerating slow slip. The resulting
dynamic ruptures propagating over wetted interfaces exhibit dy-
namic stress drops almost twice as large as those over the dry
interfaces. These results suggest the need to take into account the
rate of the pore-pressure increase when considering nucleation
processes and motivate further investigation on how friction
properties depend on the presence of fluids.
laboratory earthquakes | fluid-induced seismicity | earthquake source
physics | fluid pore-pressure rate | nucleation length
T
he close connection between fluids and faulting has been
revealed by a large number of observations, both in tectonic
settings and during human activities, such as wastewater disposal
associated with oil and gas extraction, geothermal energy pro-
duction, and CO
2
sequestration (1–11). On and around tectonic
faults, fluids also naturally exist and are added at depths due to
rock-dehydration reactions (12–15) Fluid-induced slip behavior
can range from earthquakes to slow, creeping motion. It has
long been thought that creeping and seismogenic fault zones
have little to no spatial overlap. Nonetheless, growing evidence
suggests that the same fault areas can exhibit both slow and
dynamic slip (16–19). The existence of large-scale slow slip in
potentially seismogenic areas has been revealed by the pres-
ence of transient slow-slip events in subduction zones (16, 18)
and proposed by studies investigating the physics of foreshocks
(20–22).
Numerical and laboratory modeling has shown that such com-
plex fault behavior can result from the interaction of fluid-related
effects with the rate-and-state frictional properties (9, 14, 19, 23,
24); other proposed rheological explanations for complexities in
fault stability include combinations of brittle and viscous rhe-
ology (25) and friction-to-flow transitions (26). The interaction
of frictional sliding and fluids results in a number of coupled
and competing mechanisms. The fault shear resistance
τ
res
is
typically described by a friction model that linearly relates it to
the effective normal stress
ˆ
σ
n
via a friction coefficient
f:
τ
res
=
f
ˆ
σ
n
=
f
(
σ
n
p
),
[1]
where
σ
n
is the normal stress acting across the fault and
p
is the
pore pressure. Clearly, increasing pore pressure
p
would reduce
the fault frictional resistance, promoting the insurgence of slip.
However, such slip need not be fast enough to radiate seismic
waves, as would be characteristic of an earthquake, but can be
slow and aseismic. In fact, the critical spatial scale
h
for the
slipping zone to reach in order to initiate an unstable, dynamic
event is inversely proportional to the effective normal stress (27,
28) and hence increases with increasing pore pressure, promoting
stable slip. This stabilizing effect of increasing fluid pressure
holds for both linear slip-weakening and rate-and-state friction;
it occurs because lower effective normal stress results in lower
fault weakening during slip for the same friction properties. For
example, the general form for two-dimensional (2D) theoretical
estimates of this so-called nucleation size,
h
, on rate-and-state
faults with steady-state, velocity-weakening friction is given by:
h
=(
μ
D
RS
)
/
[
F
(
a
,
b
)(
σ
n
p
)],
[2]
where
μ
=
μ/
(1
ν
)
for modes I and II, and
μ
=
μ
for mode
III (29);
D
RS
is the characteristic slip distance; and
F
(
a
,
b
)
is a function of the rate-and-state friction parameters
a
and
b
. The function
F
(
a
,
b
)
depends on the specific assumptions
made to obtain the estimate:
F
RR
(
a
,
b
)=4(
b
a
)
(ref. 27,
equation 40) for a linearized stability analysis of steady sliding,
Significance
Fluids present in the Earth’s crust promote earthquakes, as well
as a variety of aseismic slip events, both in natural tectonic
settings and potentially due to industrial activities, such as
wastewater disposal, geothermal energy production, and CO
2
storage. To study the physical processes linking fluids and slip
motion, we have devised a laboratory earthquake setup capa-
ble of injecting fluid onto a simulated fault and monitoring the
resulting slip on a wide range of temporal and spatial scales.
Our findings indicate that faster injection rates result in lower
fluid pressure at rupture initiation, highlighting the role of
fluid injection rate in inducing seismic or aseismic slip events.
We also find that the presence of fluids significantly affects the
dynamic rupture propagation.
Author contributions: M.G., V.R., A.J.R., and N.L. designed research; M.G. performed
research; M.G. analyzed data; and M.G., V.R., and N.L. wrote the paper.
The authors declare no competing interest.
This article is a PNAS Direct Submission.
Published under the
PNAS license
.
1
To whom correspondence may be addressed. Email: marcello.gori00@gmail.com.
This article contains supporting information online at
https://www.pnas.org/lookup/
suppl/doi:10.1073/pnas.2023433118/-/DCSupplemental
.
Published December 16, 2021.
PNAS
2021 Vol. 118 No. 51 e2023433118
https://doi.org/10.1073/pnas.2023433118
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or
F
RA
(
a
,
b
)=
[
π
(
b
a
)
2
]
/
2
b
, with
a
/
b
>
1
/
2
for quasistatic
crack-like expansion of the nucleation zone (ref. 30, equation 42).
Hence, an increase in pore pressure induces a reduction in the
effective normal stress, which both promotes slip due to lower
frictional resistance and increases the critical length scale
h
,
potentially resulting in slow, stable fault slip instead of fast, dy-
namic rupture. Indeed, recent field and laboratory observations
suggest that fluid injection triggers slow slip first (4, 9, 11, 31).
Numerical modeling based on these effects, either by themselves
or with an additional stabilizing effect of shear-layer dilatancy
and the associated drop in fluid pressure, have been successful
in capturing a number of properties of slow-slip events observed
on natural faults and in field fluid-injection experiments (14, 24,
32–34). However, understanding the dependence of the fault re-
sponse on the specifics of pore-pressure increase remains elusive.
Several studies suggest that the nucleation size can depend on
the loading rate (35–38), which would imply that the nucleation
size should also depend on the rate of friction strength change
and hence on the rate of change of the pore fluid pressure.
The dependence of the nucleation size on evolving pore fluid
pressure has also been theoretically investigated (39). However,
the commonly used estimates of the nucleation size (Eq.
2
)have
been developed for faults under spatially and temporally uniform
effective stress, which is clearly not the case for fluid-injection
scenarios. In addition, the friction properties themselves may
change in the presence of fluids (40–42). The interaction between
shear and fluid effects can be further affected by fault-gauge
dilation/compaction (40, 43–45) and thermal pressurization of
pore fluids (42, 46–48).
Recent laboratory investigations have been quite instrumental
in uncovering the fundamentals of the fluid-faulting interac-
tions (31, 45, 49–57). Several studies have indicated that fluid-
pressurization rate, rather than injection volume, controls slip,
slip rate, and stress drop (31, 49, 57). Rapid fluid injection may
produce pressure heterogeneities, influencing the onset of slip.
The degree of heterogeneity depends on the balance between the
hydraulic diffusion rate and the fluid-injection rate, with higher
injection rates promoting the transition from drained to locally
undrained conditions (31). Fluid pressurization can also interact
with friction properties and produce dynamic slip along rate-
strengthening faults (50, 51).
In this study, we investigate the relation between the rate of
pressure increase on the fault and spontaneous rupture nucle-
ation due to fluid injection by laboratory experiments in a setup
that builds on and significantly develops the previous genera-
tions of laboratory earthquake setup of Rosakis and coworkers
(58, 59). The previous versions of the setup have been used to
study key features of dynamic ruptures, including sub-Rayleigh
to supershear transition (60); rupture directionality and limiting
speeds due to bimaterial effects (61); pulse-like versus crack-
like behavior (62); opening of thrust faults (63); and friction
evolution (64). A recent innovation in the diagnostics, featuring
ultrahigh-speed photography in conjunction with digital image
correlation (DIC) (65), has enabled the quantification of the
full-field behavior of dynamic ruptures (66–68), as well as the
characterization of the local evolution of dynamic friction (64,
69). In these prior studies, earthquake ruptures were triggered
by the local pressure release due to an electrical discharge. This
nucleation procedure produced only dynamic ruptures, due to
the nearly instantaneous normal stress reduction.
To study fault slip triggered by fluid injection, we have devel-
oped a laboratory setup featuring a hydraulic circuit capable of
injecting pressurized fluid onto the fault plane of a specimen
and a set of experimental diagnostics that enables us to detect
both slow and fast fault slip and stress changes. The range of
fluid-pressure time histories produced by this setup results in
both quasistatic and dynamic rupture nucleation; the diagnostics
allows us to capture the nucleation processes, as well as the
resulting dynamic rupture propagation. In particular, here, we
explore two injection techniques: procedure 1, a gradual, and
procedure 2, a sharp fluid-pressure ramp-up. An array of strain
gauges, placed on the specimen’s surface along the fault, can
capture the strain (translated into stress) time histories over a
wide range of temporal scales, spanning from microseconds to
tens of minutes. Once dynamic ruptures nucleate, an ultrahigh-
speed camera records images of the propagating ruptures, which
are turned into maps of full-field displacements, velocities, and
stresses by a tailored DIC) analysis. One advantage of using a
specimen made of an analog material, such as poly(methyl meth-
acrylate) (PMMA) used in this study, is its transparency, which
allows us to look at the interface through the bulk and observe
fluid diffusion over the interface. Another important advantage
of using PMMA is that its much lower shear modulus results in
much smaller nucleation sizes
h
than those for rocks, allowing
the experiments to produce both slow and fast slip in samples of
manageable sizes.
We start by describing the laboratory setup and the diagnostics
monitoring the pressure evolution and the slip behavior. We
then present and discuss the different slip responses measured
as a result of slow versus fast fluid injection and interpret our
measurements by using the rate-and-state friction framework
and a pressure-diffusion model.
Materials and Methods
Specimen Configuration.
In order to investigate the effects of fluids on the
frictional faulting, we have developed a hydraulic setup capable of injecting
pressurized fluid onto the interface of a quadrilateral PMMA specimen
through a 1-mm-diameter duct (Figs. 1 and 2). The specimen is 200
×
250
×
12.5 mm
3
and is separated into two identical halves by an oblique cut at
an angle
α
(see
SI Appendix
for details). A uniform, vertical-load
P
(yellow
arrows) produces resolved shear and normal prestress components acting on
the frictional interface, given by
τ
0
=
P
sin
(
α
)
cos
(
α
)
and
σ
n
=
P
cos
2
(
α
)
,
respectively. Throughout this work, we choose the notation
τ
or
σ
12
to
indicate the shear stress,
σ
n
or
σ
22
for the fault-normal stress, and
σ
11
for
the fault-parallel stress.
Fluid Injection and Measurements.
The delivery of fluid onto the specimen’s
interface is controlled by two separate valves, depending on the desired
Water tank
Water tank
Water filter
Water filter
Pump
P
High-pressure
regulator
Pressure
Pressure
transducers
transducers
e
Flow-rate
regulator
regulator
t
Low-pressure
Low-pressure
regulator
regulator
Instron
Instron
Hydraulic press
High-speed
High-speed
camera
cam
Laser velocimeters
Laser velocimeters
sensor heads
controllers
controllers
ir
a
ir
a
i
r
air
air
air
Fl
water
water
(high press)
(high
press)
water
water
water
wat
e
r
(amb
press
)
water
water
(amb press)
(amb press)
Solenoid
valve
valve
Sl
P
P
Fig. 1.
Laboratory setup with a fluid-injection circuit and extensive diag-
nostics tailored to capturing both slow slip and fast dynamic ruptures. The
fault is created by cutting the specimen into two identical halves and joining
them together to form an interface that mimics a crustal fault prestressed
in compression and shear. The fluid-injection circuit is designed to deliver
pressurized fluid to the fault over a wide range of fluid pressures and
injection rates. The diagnostics consists of an array of strain gauges, capable
of recording the strain signals over a broad spectrum of time scales, laser
velocimeters tracking well-resolved particle-velocity histories, a low-speed
camera (in the hertz framing rate) monitoring fluid diffusion during slow
injection, and a high-speed camera (in the megahertz framing rate) used
in combination with DIC to provide full-field maps of particle velocity and
shear stress.
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Dynamic rupture initiation and propagation in a fluid-injection laboratory setup
with diagnostics across multiple temporal scales
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EARTH, ATMOSPHERIC,
AND PLANETARY SCIENCES
B
20 mm
Back face of the Specimen
Injection Duct
<
1 m
m
Interface
P
P
t
cuD noitc
ejnI
Front face of the Specimen
Field of View
for Dynamic DIC
18 mm
12.5 mm
250 mm
P
P
A
Interface
x
2
x
1
x
1
x
2
x
3
x
3
SG-20
SG-0
Fig. 2.
Front- and back-side views of the specimen. A 250
×
200
×
12.5-mm
3
PMMA sample is separated into two halves by an oblique interface (green-
shaded area) at an angle
α
=
29
to the horizontal. The sample is preloaded by a vertical compression
P
=
15 MPa (yellow arrows). A duct of 1-mm
diameter enables the injection of pressurized fluid directly onto the interface. (
A
) Front side with a pattern of random black dots painted over a flat white
background to allow dynamic DIC measurements. (
B
) Back side with two strain rosettes glued just below the interface 20 mm away from each other. Each
rosette is capable of measuring three strain components, 45
apart from each other. These components can be converted into the strain components along
the fault
ε
11
, normal to it
ε
22
, and the shear one
ε
12
. Note that the strain gauges see a right-lateral fault, while the DIC sees a left-lateral one.
rate of injection, namely, a high-pressure regulator and a solenoid valve
(Figs. 1 and 3
A
and
SI Appendix
). The high-pressure regulator allows manual
adjustment of the fluid pressure, and it is used to produce gradual pressure
ramp-ups (Fig. 3
A
), with valve-opening times ranging from seconds to tens
of minutes. The solenoid valve can achieve opening times in the order of
tens of milliseconds, and it is used to produce rapid pressure ramp-ups
(Fig. 3
B
). The pressure evolution during the injection is measured by two
pressure transducers, each placed immediately downstream of either of the
two valves (Figs. 1 and 3
A
).
While these measurements capture the time evolution of the fluid pres-
sure prior to reaching the interface (Fig. 3), they do not provide information
about the spatial distribution of the pressure over the interface. To gain
insight into the pressure diffusion, we place a pressure-sensitive film onto
the interface for selected and dedicated tests (Fig. 4 and
SI Appendix
). Note
that this pressure transducer can only provide the maximum pressure level
it experiences rather than a time evolution and can only be used with a
horizontal interface (
α
=
0
) to preserve its integrity. Nonetheless, it pro-
vides invaluable measurements that foster our understanding of pressure
diffusion over the fault.
To track the extent of fluid diffusion on the (initially dry) frictional
interface, a sequence of digital pictures is acquired during the fluid injection
(Fig. 5). The camera axis is oriented to look directly at the oblique interface
through the bulk of the specimen. The transparency of PMMA offers an
advantage over natural rocks for this kind of measurement.
Simultaneously, the slip behavior is monitored at two strain-gauge sta-
tions placed on the specimen outer surface within 1 mm from the interface,
one directly corresponding to the injection location and the other 20
mm away along the fault. These measurement stations are denoted as
“SG-0” and “SG-20,” respectively (Fig. 2
B
and
SI Appendix
, Fig. S1
B
). The
main advantage of our strain-gauge system is that it can capture both the
long-term deformation, before the occurrence of the dynamic rupture, and
the rapidly evolving fault behavior during the rupture propagation. This
system’s temporal resolution enables measurements of the strain tensor
over nine orders of magnitude in time, from 10
6
to 10
3
s. From the
knowledge of the strain components along three directions at each station,
the stress tensor can be reconstructed at these two locations via the linear-
elastic constitutive properties (
SI Appendix
, Fig. S1
B
). To complement these
temporally highly resolved, yet spatially coarse, measurements and obtain
the full-field spatial variations of dynamic ruptures, we employ the DIC
method coupled with ultrahigh-speed photography (65).
Two initiation protocols are investigated: procedure 1, a gradual pres-
sure buildup until a dynamic rupture spontaneously occurs (Fig. 3
A
); and
procedure 2, an abrupt pressure buildup, where a sharp pressure profile
is induced by the sudden opening of the solenoid valve (Fig. 3
B
). In the
pressure profiles of Fig. 3, the time is set to zero at the initiation of dynamic
rupture to emphasize the substantially different times leading up to rupture
nucleation in the two cases. Thus, time prior to triggering of the dynamic
rupture is indicated by negative values. The gradual pressure buildup is
achieved by the slow opening of the manual regulator, with the solenoid
valve being in the open configuration throughout (
SI Appendix
, Fig. S1).
The abrupt pressure buildup is obtained by a two-stage process: First, fluid
pressure in the circuit is increased upstream of the solenoid valve, using
the manual regulator, to the same level at which rupture occurs during
the slow pressure ramp-up protocol; at this point, the pipes downstream of
the solenoid are still at ambient pressure. Second, fluid pressure is rapidly
increased downstream by abruptly opening the solenoid valve. The first
step guarantees having the same pressure level upstream of the solenoid
valve in both procedures. Typically, the same specimen employed to produce
a rupture with procedure 1 is subsequently used to perform a test with
procedure 2. To ensure consistency of the frictional interface, the interface
is prepared by polishing and bead-blasting it before running a test on a
specimen using either of the two procedures, as described in
SI Appendix
.
PMMA versus Natural Rock.
One important advantage of using PMMA as
the analog material in our laboratory earthquake setup is its reduced shear
modulus (
μ
PMMA
1 GPa) compared to that of rocks (
μ
rock
30 GPa). Since
characteristic rupture length scales, such as the critical sizes in Eq.
1
, are pro-
portional to the shear modulus of the host material, ruptures propagating
within the bulk of the specimen have characteristic rupture length scales
smaller than rocks by a factor of
μ
rock
PMMA
30, under the assumption
of similar frictional properties. Indeed, the critical crack size falls in the
range of few centimeters for the set of experimental conditions that we
explore, allowing the flexibility to nucleate dynamic ruptures and letting
them spontaneously develop within the 200-mm sample size (70). For this
Gori et al.
Dynamic rupture initiation and propagation in a fluid-injection laboratory setup
with diagnostics across multiple temporal scales
PNAS
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-30
-20
-10
0
Time [min]
0
5
10
15
Pressure [MPa]
Slow Pressure Ramp-up
-50 -25 0 25 50
[ms]
7.5
8
8.5
9
Nucleation of the
Dynamic Rupture
8.7 MPa
8.7 MPa
Resolved Normal
Stress 11.5 MPa
-400
-200
0
200
400
Time [ms]
0
5
10
15
Pressure [MPa]
Sharp Pressure Ramp-up
4.9 MPa
Resolved Normal Stress
11.5 MPa
Nucleation of the
Dynamic Rupture
8.7 MPa
AB
Fig. 3.
Two significantly different pressure ramp-up profiles result in qualitatively different slip responses. Two protocols are employed to deliver pressurized
fluid onto the frictional interface of the sample: slow pressure ramp-up starting at
t
≈−
27 min (
A
) (the
Inset
shows the pressure profile in the few tens of
milliseconds prior to and after the rupture initiation); and rapid one, over a few hundred milliseconds, achieved via the quick opening of a solenoid valve
(
B
). The red star indicates the triggering of the dynamic rupture (
t
=
0) recorded by the laser velocimeter (
SI Appendix
, Fig. S1
B
). The color code for the
pressure data mimics that of the labels of the pressure transducers in
SI Appendix
, Fig. S1
A
: purple for measurements upstream of the solenoid valve and
blue for downstream. The green dashed line represents the resolved normal stress
σ
n
in competition with the fluid pressure.
reason, our laboratory experiments with PMMA offer a unique opportunity
to study rupture features that would otherwise be impossible to reproduce
and observe on manageable samples made of natural rock materials (71, 72).
Another advantage of PMMA is its transparency, which allows tracking the
extent of fluid diffusion over the interface, as already discussed.
Results and Discussion
Pressure Measurements: Slow versus Fast Injection.
Let us consider
two typical experiments where the fluid is injected onto a spec-
imen’s interface with substantially different injection rates. The
specimen is vertically loaded at
P
=15
MPa, and the interface
inclination angle is
α
=29
(Fig. 2), resulting in a resolved
normal and shear stresses of 11.5 and 6.4 MPa, respectively. In
procedure 1 (Fig. 3
A
), the pressure is gradually increased from
the ambient level (about 0.1 MPa)—measured at the duct by
the pressure transducers—until the insurgence of the dynamic
rupture (red star) at 8.7 MPa (76% of the resolved normal stress).
With an average rate of
5.3
×
10
3
MPa/s, it takes
27 min
to reach the conditions for rupture initiation. In procedure 2
(Fig. 3
B
), the water pressure upstream of the valve and prior to its
opening is manually set to the same level of 8.7 MPa, at which the
rupture spontaneously nucleates when a slow pressure ramp-up
protocol is adopted (Fig. 3
A
). Upon the sudden opening of the
valve, the pressure measured in the duct by the second transducer
(
SI Appendix
,Fig.S1
A
) shows an average rate of about
3.1
×
10
1
MPa/s over a few hundreds of milliseconds (Fig. 3
B
). Under these
conditions, the dynamic rupture initiation occurs at 4.9 MPa, or
42% of the resolved normal stress, much smaller than the 8.7
MPa reached by adopting the slow pressure ramp-up protocol.
We have observed similar outcomes by performing several tests
using these two injection procedures and under the same loading
conditions (
SI Appendix
, Table S1). These results demonstrate
that the rate of injection plays a major role in promoting the
nucleation of dynamic ruptures by considerably reducing both
the pressure and the volume of fluid required for the dynamic
rupture to initiate.
Pressure Measurements with the Tactile Sensor Film.
To measure
the pressure distribution along the interface in the case of the
slow pressure ramp-up scenario (Fig. 3
A
), the pressure protocol
is replicated in an experiment with the pressure film sensor and
a flat interface (
α
=0
) to prevent sliding that would destroy the
film (Fig. 4). The pressure-sensitive film locally and irreversibly
changes color depending on the pressure level. In order for it
to track the fluid pressure and not the normal stress level, an
array of holes is drilled along the specimen’s interface (Fig. 4).
The measurements show that the pore pressure rapidly decays
away from the injection location, with values below the lowest
measurable level (2.4 MPa) for the tactile pressure film just
several millimeters away from the injection site. Whenever the
pore pressure drops below this limit, a value equal to the ambient
pressure (
p
amb
0.1
MPa) has been plotted in Fig. 4. Note that
the pressure film provides the maximum pressure level recorded
during a test. The pressure distribution along the interface at
incipient rupture initiation, associated with the rapid injection-
rate protocol, cannot be captured by using this technique, as the
pressure keeps increasing after the instance at which the rupture
would initiate (Fig. 3
B
).
Imaging and Simulation of Pore-Pressure Diffusion.
To track the
fluid profile as it diffuses over the interface, a series of snapshots
of the interface are taken through the transparent back side of the
specimen (Figs. 2
B
and 5). In the slow pressure ramp-up scenario,
the rupture nucleates when the wetted portion of the interface
reaches an average length of 74 mm, spreading from the 1-mm
injection site.
To record the rupture initiation in the rapid pressure ramp-up
scenario, in analogy to the result shown in Fig. 5, a Shimadzu
HPV-X high-speed camera, capable of resolving the millisec-
ond time scale, is employed. The presence of water on the
interface becomes visible about 1 ms after the initiation. It is
difficult to estimate a characteristic length for the fluid extension
over the interface at rupture initiation. However, it is clear that
the quantity of fluid delivered to the interface is much smaller
compared to the slow nucleation procedure. The experimental
evidence suggests that, if the rate of injection is sufficiently fast,
dynamic events can be triggered at much lower fluid pressures
and smaller volumes of injected fluid. Note that during gradual
procedure 1, droplets of water leak out of the fault before rupture
nucleation, whereas no water is detected leaking out prior to
the nucleation of dynamic rupture during procedure 2. This
is due to the different pressure distribution on the interface
at slip onset developing during the two injection procedures
and the diffusion time scale compared to the nucleation ones.
The fluid leakage from the fault does not significantly affect
the outcome of the presented experiments since pore pressure
rapidly decays away from the injection site, as illustrated by
the numerical model discussed next. However, the droplets do
prevent us from conducting quasistatic DIC next to the fluid-
injection site, which otherwise could enable us to measure the
slow slip that should be associated with the slow fluid injection.
We present indirect evidence for such slip in our strain-gauge
measurements.
4of12
PNAS
https://doi.org/10.1073/pnas.2023433118
Gori et al.
Dynamic rupture initiation and propagation in a fluid-injection laboratory setup
with diagnostics across multiple temporal scales
Downloaded at California Institute of Technology on December 17, 2021