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Okay, everyone.
I think we’ll get started.

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Thanks for coming out today.
I have a few announcements.

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So next week, our speaker on
July 31st will be Ross Boulanger.

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He’ll be giving the 2019
EERI Distinguished Lecture.

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And then also a reminder
about AGU abstracts.

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They’re due to the center at the
end of this week on the 28th.

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So now today’s speaker
is Stephanie Taylor.

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She has a B.S. in geosciences from
Pennsylvania State University.

00:00:38.170 --> 00:00:41.440
She recently got her Ph.D. in
Earth science from the University

00:00:41.440 --> 00:00:45.269
of California-Santa Cruz.
And she’s currently a postdoc there

00:00:45.269 --> 00:00:49.140
in the seismology group
as well as a visiting researcher

00:00:49.140 --> 00:00:53.740
at the Naval Postgraduate School
in the Department of Physics.

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And, with that,
I’ll turn it over to her.

00:01:01.520 --> 00:01:04.300
- Thank you so much.
I’m excited to be here.

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Today I’m going to talk about
a set of laboratory experiments that

00:01:09.460 --> 00:01:13.540
I completed on granular material.
So this video is from some of those –

00:01:13.540 --> 00:01:17.500
one of those experiments.
And I’m going to try to talk about

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how we might use this field of granular
physics to think about the rheology of

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geophysical shear zones and granular
systems that we find in nature.

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So I’m interested in granular flow
rheology for a few reasons.

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One of the things that I think
is interesting about them

00:01:38.229 --> 00:01:42.530
is that they really defy
simple characterization.

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So granular materials have different
kind of phase behavior, depending

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on how fast they’re flowing.
And you’ve seen this in your own life.

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If you go to the beach,
and you stand on the sand,

00:01:53.420 --> 00:01:56.189
you’re standing on solid ground.
You don’t sink into it.

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Whereas, if you are jogging on
the beach, all of the sudden,

00:01:59.200 --> 00:02:03.860
it starts splashing around like a fluid.
And, if a really strong wind comes by,

00:02:03.860 --> 00:02:06.980
then suddenly, there’s sand
everywhere, even 6 feet high,

00:02:06.980 --> 00:02:08.760
and it’s in your eye.

00:02:08.760 --> 00:02:14.300
So, in this way, granular materials
can be like a solid or a liquid or a gas,

00:02:14.300 --> 00:02:20.900
even. And the challenge for us as
physicists and geophysicists is

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to establish a constitutive law
describing all of these rheological

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phase regimes in
a complete way.

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And the reason that this is important
for us is that granular materials are

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central to a wide range of Earth
and planetary science processes.

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So, of course, for this group,
you know that earthquake faults

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are filled with ground-up rock.
And fault zones are just full of

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damaged, broken sand, rock,
powder, gouge – you name it.

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But other granular materials
include snow and ice.

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Desert dunes and sand
systems in arid regions.

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Bedload transport
in streams.

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Of course, landslides
and debris flows.

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And even in planetary systems,
such as Mars and on the moon,

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we see a lot of different granular
systems mimicking some of the

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things that we find on Earth
and displaying behaviors

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that we don’t quite
understand yet as well.

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So understanding in what
circumstances these types of materials

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are going to strengthen or weaken,
flow slowly or flow quickly,

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compact or dilate,
is key to all of these processes.

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So that’s why I’m really interested
in trying to establish a better

00:03:50.170 --> 00:03:54.380
understanding of the rheology
of naturalistic granular flows.

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So there are some things
that we do already know.

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So when flowing at a low velocity,
granular behaviors behave almost like

00:04:04.090 --> 00:04:08.120
a solid, as I said. And a good
example of this is an hourglass.

00:04:08.120 --> 00:04:11.799
So why does an hourglass work?
If this were water, then the discharge

00:04:11.799 --> 00:04:17.220
rate would change as the height
of the water in the top part

00:04:17.220 --> 00:04:22.509
of the hourglass changes.
But the sand actually buttresses itself

00:04:22.509 --> 00:04:28.960
against the walls of the hourglass.
So this image on the right here is from

00:04:28.960 --> 00:04:35.280
an experiment in Bob Behringer’s lab
at Duke using photoelastic discs.

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A close-up is shown here.
So, as you squeeze one of these discs,

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and it deforms,
its optical properties change.

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So, the brighter a grain
is in this top image,

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it’s showing that it’s
under more stress.

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So, for an hourglass, the volume of
sand that can mobilize at the bottom

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here actually remains the same
no matter how much sand is overlying

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it because it’s able to buttress itself
against the walls of the hourglass.

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And it’s moving so slowly that it can
re-establish all of these kind of

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force networks that you see
in that top photo as the sand

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discharges through
the hourglass.

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And so this regime is
called quasi-static flow.

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And its defining characteristic is
that the force in the system is

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distributed through many –
networks of many grains.

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At high velocity, these
force chains start to go away.

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Individual grains are much
less connected to their flow,

00:05:40.630 --> 00:05:44.210
and they’re driven by the momentum
of the grains and the grain mass

00:05:44.210 --> 00:05:47.330
bouncing into each other.
And this – so this regime is

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much more inertially dominated,
and we call it the inertial flow regime.

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And we know that, in this regime,
granular materials are shear thickening

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and shear strengthening, so, as velocity
increases, the coefficient of friction –

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or, in other words, the force required
to maintain that flow – increases

00:06:06.470 --> 00:06:10.360
under constant pressure – increases.
And, under constant pressure,

00:06:10.360 --> 00:06:14.020
you’ll see the volume of
the flow increasing as well.

00:06:16.080 --> 00:06:18.960
So, the flow will
dilate with velocity.

00:06:18.960 --> 00:06:23.050
So the inertial flow regime is
dominated by grain-grain collisions

00:06:23.050 --> 00:06:26.580
and momentum transfer,
and it’s dilatational.

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In between these two end members,
granular flow rheology is much

00:06:30.300 --> 00:06:34.039
less well-understood.
In this regime, there are still

00:06:34.039 --> 00:06:38.539
some force chains, but there
tends to be higher rates of turnover

00:06:38.539 --> 00:06:42.610
of those force chains.
Maybe they’re shorter sometimes.

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And this regime is vaguely referred
to as the transitional flow regime.

00:06:48.139 --> 00:06:50.800
There have been some successes
describing this rheology as

00:06:50.800 --> 00:06:59.129
a frictional viscoplastic liquid,
with its closest proxy that

00:06:59.129 --> 00:07:02.380
we would all recognize
being toothpaste.

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It’s kind of like toothpaste,
except it also has a coefficient of

00:07:08.050 --> 00:07:15.270
friction that depends on shear rate.
And this current model of the frictional

00:07:15.270 --> 00:07:18.669
viscoplastic liquid doesn’t quite match
up with either of those other two

00:07:18.669 --> 00:07:20.550
end members that
I just showed you

00:07:20.550 --> 00:07:23.419
and the model that
we use to describe those.

00:07:23.419 --> 00:07:27.830
So this is an imperfect
characterization of the –

00:07:27.830 --> 00:07:32.510
of the liquid, or transitional,
phase regime of granular materials.

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Furthermore, this model was
created based on the behavior of

00:07:37.930 --> 00:07:41.860
pretty idealized grains.
So this image here is showing the

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classical experimental material for
granular experiments, and it’s usually

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spherical glass beads, which is –
which is not what you find in nature.

00:07:54.449 --> 00:07:56.639
And, when you start to
change up this particle type,

00:07:56.639 --> 00:07:58.789
you start to see some
different behaviors.

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So we’re going to focus on what
some of those differences are.

00:08:04.390 --> 00:08:09.180
This experiment is looking at
how the thickness on the top here

00:08:09.180 --> 00:08:16.660
and the noise – so recorded acoustic
noise during shear on the bottom –

00:08:16.660 --> 00:08:20.880
changes with shear velocity
on the X axis here.

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So, at these low velocities,
the volume doesn’t change.

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For – I’m sorry – and I’m comparing
the spherical beads in these blue circles

00:08:31.530 --> 00:08:35.120
with angular grains
in black triangles here.

00:08:35.120 --> 00:08:40.040
So, at low velocities, the volume
doesn’t change across kind of

00:08:40.040 --> 00:08:41.640
a range of low velocities.

00:08:41.640 --> 00:08:44.520
That doesn’t seem to affect the volume.
And the noise is pretty low.

00:08:44.520 --> 00:08:48.270
It’s a quiet flow, and it’s not
changing much. It’s pretty stable.

00:08:48.270 --> 00:08:51.820
At high velocities, both the spherical
beads and the angular grains are

00:08:51.820 --> 00:08:55.240
dilating quite a bit,
and they’re making more noise.

00:08:55.250 --> 00:08:59.050
This – I should add – this kind of
taper you see here is just the result

00:08:59.050 --> 00:09:03.700
of the acoustic sensor
maxing out about here.

00:09:03.700 --> 00:09:07.790
So that’s not physical.
But, when you look inside this

00:09:07.790 --> 00:09:12.260
transitional regime, you see major
differences between the spherical beads

00:09:12.260 --> 00:09:15.990
that are typical of granular physics
experiments, and angular grains,

00:09:15.990 --> 00:09:20.340
which is typical of what we
actually find in natural systems.

00:09:20.340 --> 00:09:24.540
So, at these transitional velocities,
these spherical beads kind of

00:09:24.540 --> 00:09:30.640
smoothly go from their stable quasi-
static state into a dilatational state.

00:09:30.640 --> 00:09:34.250
But the angular grains don’t.
They actually show a weakening

00:09:34.250 --> 00:09:40.440
before the dilatational inertial regime.
And this weakening is associated

00:09:40.440 --> 00:09:46.920
with an increase in the noise
produced by the flow in this regime.

00:09:46.920 --> 00:09:51.670
So the angular grains are much
louder than the spherical beads.

00:09:51.670 --> 00:09:56.270
And what’s happening is, this noise
is actually high enough amplitude to

00:09:56.270 --> 00:10:00.170
vibrate the sample and cause it to
compact, or weaken, in this regime.

00:10:00.170 --> 00:10:03.331
And these are controlled pressure
experiments, which I’ll explain

00:10:03.331 --> 00:10:07.750
the method of in a second.
But the important takeaway is that

00:10:07.750 --> 00:10:10.080
we see this major difference
between angular grains and

00:10:10.080 --> 00:10:16.080
spherical beads in this critical
transitional flow regime.

00:10:18.740 --> 00:10:20.140
So …

00:10:25.000 --> 00:10:27.770
So one of our – the first things
to remember is that angular grains

00:10:27.770 --> 00:10:32.000
are more susceptible to the effects
of acoustics in the transitional flow

00:10:32.000 --> 00:10:36.860
regime. And this transitional flow
regime, remember, is one of the most

00:10:36.860 --> 00:10:43.270
important for geophysicists because
this is the regime in which a granular

00:10:43.270 --> 00:10:47.160
system is going to move from
flowing very slowly, or creeping,

00:10:47.160 --> 00:10:50.570
to flowing very quickly,
or having a catastrophic failure.

00:10:50.570 --> 00:10:53.980
So this is the regime that we
especially want to understand.

00:10:56.620 --> 00:10:59.920
And this is just to remind
everyone that these natural systems

00:10:59.920 --> 00:11:03.380
are not made up of
spherical particles.

00:11:03.380 --> 00:11:09.860
So these kinds of differences are
really important to understand.

00:11:09.860 --> 00:11:14.370
The complexities of natural systems
that I’m going to try to incorporate

00:11:14.370 --> 00:11:18.290
into the rheological theory of granular
flows that we can then bring into

00:11:18.290 --> 00:11:24.450
geophysical systems are, what do we
expect in the transitional flow regime?

00:11:24.450 --> 00:11:28.770
What do we expect in flows
with mixed-phase regimes?

00:11:28.770 --> 00:11:31.510
So flows where you will
have some parts moving fast

00:11:31.510 --> 00:11:34.120
and other parts moving slowly.

00:11:34.120 --> 00:11:38.160
And what is the relative influence
of different material properties

00:11:38.160 --> 00:11:41.530
on the overall rheology of the flow?
Not everything is made of glass.

00:11:41.530 --> 00:11:45.660
What happens when you have
materials with different strengths

00:11:45.660 --> 00:11:49.680
or toughnesses or
fracture properties?

00:11:50.880 --> 00:11:56.340
So I’m going to start with
the transitional flow regime.

00:11:59.360 --> 00:12:05.660
And, just to go a little further into the
description of these phase regimes,

00:12:05.670 --> 00:12:08.180
the phase regimes of granular flow
are understood in terms of a

00:12:08.180 --> 00:12:12.790
dimensionless number called the inertial
number shown here, which takes into

00:12:12.790 --> 00:12:19.460
account confining pressure,
density, shear rate, and grain size.

00:12:19.460 --> 00:12:25.880
So it is – so the only thing you really
need to take away is that a low inertial

00:12:25.880 --> 00:12:30.020
number is a slow flow. A high inertial
number is a very fast flow.

00:12:30.020 --> 00:12:34.450
But what it is is a ratio of time scales.
So we have on the top the time for

00:12:34.450 --> 00:12:40.020
a grain to drop into a grain-sized
gap in the layer below it.

00:12:40.020 --> 00:12:42.660
So this is the sort of pressure
component of the flow.

00:12:42.660 --> 00:12:48.120
And, on the bottom, we have
the time for a grain to pass

00:12:48.120 --> 00:12:53.780
a grain in the layer below it.
So this is the inverse of shear rate.

00:12:56.320 --> 00:13:03.860
And a flow is considered solid-like
and slow at inertial numbers

00:13:03.870 --> 00:13:07.510
below 10 to the minus 3.
And it’s considered fast and

00:13:07.510 --> 00:13:11.560
gas-like at inertial numbers
above 10 to the minus 1.

00:13:11.560 --> 00:13:15.580
And then, in between,
it’s considered a transitional flow.

00:13:16.450 --> 00:13:18.700
So sometimes it’s weak.
Sometimes it’s dilatational.

00:13:18.700 --> 00:13:21.500
It’s hard to reach a
stable, steady state.

00:13:21.500 --> 00:13:28.840
And it spans a few orders of magnitude
of pressure and shear rate values.

00:13:30.120 --> 00:13:33.100
So it’s a non-trivial
range of flow conditions.

00:13:33.960 --> 00:13:40.680
So here is a video, or a set of videos,
showing the experiments I’m going to

00:13:40.680 --> 00:13:44.560
be talking about in these
different regimes of flow.

00:13:48.180 --> 00:13:52.700
And, as I said before, the transitional
regime tends to be what we as

00:13:52.710 --> 00:13:57.000
geoscientists care the most about.
So this top purple box is showing

00:13:57.000 --> 00:14:03.390
a set of some common Earth science
processes and the inertial

00:14:03.390 --> 00:14:05.460
numbers associated with them.
And, as you can see, they all

00:14:05.460 --> 00:14:08.640
cross right through the
transitional regime.

00:14:11.520 --> 00:14:16.060
So, across all these velocity regimes,
one of the key unresolved questions

00:14:16.070 --> 00:14:23.080
in granular flow is how instantaneous
variations from the mean velocity

00:14:23.080 --> 00:14:26.180
contribute to rheology.
So these kinds of fluctuations have

00:14:26.180 --> 00:14:33.860
been thought to control the dilation
we see in high-velocity shear flows.

00:14:35.100 --> 00:14:38.560
So, as mean velocity increases,
the grains will collide with each other

00:14:38.560 --> 00:14:42.760
and bounce away from nearby
grains at higher velocity,

00:14:42.760 --> 00:14:45.580
ultimately dilating the flow.

00:14:45.580 --> 00:14:50.240
So, in analogy to molecular gas,
a kinetic theory of granular gas

00:14:50.240 --> 00:14:55.630
relates pressure and volume along
the lines of the ideal gas law using

00:14:55.630 --> 00:15:02.350
granular temperature – this term here –
to represent fluctuation energy

00:15:02.350 --> 00:15:08.550
in the flow. So, for a molecular gas,
the fluctuation of a given characteristic

00:15:08.550 --> 00:15:13.230
and the time scale over which that
variation occurs are orders of

00:15:13.230 --> 00:15:18.860
magnitude smaller than the mean flow.
But, in a granular system, the scale

00:15:18.860 --> 00:15:24.270
of fluctuations is the same scale
as the mean flow. So your velocity

00:15:24.270 --> 00:15:30.100
fluctuations are going to be pretty large
compared to your mean flow field.

00:15:31.840 --> 00:15:40.600
And that leads to one of the enduring
questions in granular gas rheology,

00:15:40.610 --> 00:15:43.970
which is, how do instantaneous
variations from the mean velocity

00:15:43.970 --> 00:15:47.570
contribute to the effective
rheology of a granular material?

00:15:47.570 --> 00:15:51.370
And how does energy transfer between
granular temperature and aspects

00:15:51.370 --> 00:15:54.060
of the mean flow?
So these bottom two images are

00:15:54.060 --> 00:15:58.420
showing how, with the same mean
flow – this purple arrow – you can

00:15:58.420 --> 00:16:03.540
have small instantaneous variations
or quite large ones and still

00:16:03.540 --> 00:16:07.330
have the same mean flow.
So this is all going to be in

00:16:07.330 --> 00:16:11.300
a granular system dominated
by grain-grain collisions.

00:16:12.160 --> 00:16:15.440
Experimentally,
granular temperature presents

00:16:15.440 --> 00:16:18.430
some measurement challenges.
The main method for inferring

00:16:18.430 --> 00:16:21.360
granular temperature is
through image analysis.

00:16:21.360 --> 00:16:27.560
The bottom two images here are from
image analysis studies using a rotating

00:16:27.560 --> 00:16:33.260
drum experiment on the left and a gas-
fluidized bed experiment on the right.

00:16:33.260 --> 00:16:36.760
Which I won’t go into, but the
takeaway is that this type of

00:16:36.760 --> 00:16:40.070
measurement has major limitations
in terms of what kinds of materials

00:16:40.070 --> 00:16:45.100
you can use, what kinds of shear
geometries you can set up,

00:16:45.100 --> 00:16:50.260
and you really need to be using
uniform particles, often in

00:16:50.260 --> 00:16:53.950
a single layer, in order to
image them well.

00:16:53.950 --> 00:16:57.250
And it’s not a great method for
analyzing dense flows or analyzing

00:16:57.250 --> 00:17:02.080
flows with really disparate
grain shapes and sizes.

00:17:02.940 --> 00:17:06.430
So how do we measure granular
temperature in a dense shear flow?

00:17:06.430 --> 00:17:09.220
You can actually do it
using acoustic energy.

00:17:09.220 --> 00:17:12.770
So the sound created by grains
colliding into each other in

00:17:12.770 --> 00:17:17.340
a dense shear flow can get us
to granular temperature.

00:17:21.120 --> 00:17:25.000
To test this idea, I ran experiments
on a torsional rheometer.

00:17:25.000 --> 00:17:30.860
So I have a glass cylinder here
that I fill with granular sample.

00:17:30.860 --> 00:17:35.960
The steel rotor lowers down into
the glass cylinder on top of the

00:17:35.960 --> 00:17:40.740
sample and exerts a constant normal
stress down onto the sample.

00:17:40.741 --> 00:17:42.940
And then I control the
rotor rotation speed.

00:17:42.940 --> 00:17:46.940
So, if the pressure that that sample is
exerting against the rotor changes as

00:17:46.940 --> 00:17:51.260
the rotor speed changes, then the rotor
will raise or lower in order to

00:17:51.260 --> 00:17:57.030
maintain that constant pressure.
So, in maintaining a constant pressure,

00:17:57.030 --> 00:18:00.780
controlling the shear velocity,
and measuring the rotor height,

00:18:00.780 --> 00:18:04.010
as well as noise produced by the
sand during the flow using this

00:18:04.010 --> 00:18:10.900
accelerometer here and here that is
glued to the outside of the shear cell.

00:18:10.900 --> 00:18:15.650
The velocities I’m testing are between
25 and 300 radians per second, which

00:18:15.650 --> 00:18:21.280
is about 25 to 300 centimeters per
second, at the edge of the sample cell.

00:18:23.520 --> 00:18:29.150
So the reason that we can use acoustic
energy to measure granular temperature

00:18:29.150 --> 00:18:33.740
with no flow is because deviations
of instantaneous velocity from

00:18:33.740 --> 00:18:36.750
the mean will depend on the
difference in grain velocity

00:18:36.750 --> 00:18:40.140
before and after
collisions, specifically.

00:18:40.140 --> 00:18:43.430
So the specific acoustic value
I’ll be referring to is average

00:18:43.430 --> 00:18:48.660
acoustic energy produced per grain.
So that’s the accelerometer amplitude

00:18:48.660 --> 00:18:52.910
squared, divided by the number
of grains in the outermost

00:18:52.910 --> 00:18:55.100
radial layer of the flow.

00:18:58.610 --> 00:19:02.340
So here are results from
some of these experiments.

00:19:02.350 --> 00:19:07.860
So here’s the acoustic energy
for four grain sizes of quartz sand.

00:19:07.860 --> 00:19:12.120
So acoustic energy on the Y axis
and inertial number on the X axis.

00:19:12.120 --> 00:19:17.120
So the cooler colors are larger grains,
and the warmer colors are

00:19:17.120 --> 00:19:22.590
smaller grains.
And you can see that the acoustic

00:19:22.590 --> 00:19:28.530
energy scales linearly with inertial
number for all four grain sizes.

00:19:28.530 --> 00:19:33.970
And, if acoustic energy represents
kinetic energy from these collisions,

00:19:33.970 --> 00:19:37.470
then it should scale with grain mass.
Or, in this case, since they’re all quartz

00:19:37.470 --> 00:19:42.340
grains with the same density, it should
scale with grain diameter cubed.

00:19:42.340 --> 00:19:46.980
So acoustic energy divided by inertial
number does scale with grain diameter

00:19:46.980 --> 00:19:51.550
cubed, shown in this top plot.
I have acoustic energy normalized

00:19:51.550 --> 00:19:55.621
by inertial number versus the grain
diameter, and you can see that it

00:19:55.621 --> 00:19:58.530
scales with the diameter cubed.
So it therefore is a measurement of

00:19:58.530 --> 00:20:02.800
the granular temperature of the flow,
which makes this a great tool to use

00:20:02.800 --> 00:20:07.840
to study the granular temperature
or the vibration, really,

00:20:07.840 --> 00:20:10.760
within a dense
granular shear flow.

00:20:13.770 --> 00:20:16.160
So we can use this to answer,
how does fluctuation energy

00:20:16.160 --> 00:20:20.400
in granular flow affect the overall
rheology, and what relationship does

00:20:20.400 --> 00:20:24.960
volume of the flow have to shear
velocity and granular temperature?

00:20:26.620 --> 00:20:32.950
So now, on the – on the Y axis,
now this is showing the heights

00:20:32.950 --> 00:20:38.000
of the samples normalized by
grain size versus inertial number.

00:20:38.000 --> 00:20:46.180
So you can see that the change
in height scales with inertial number

00:20:46.180 --> 00:20:50.700
to power of 0.7. So this is
interesting because it’s not 1.

00:20:50.700 --> 00:20:56.920
If you think back to that ideal
gas law analogy, PV equals nRT,

00:20:56.920 --> 00:21:01.510
temperature should dictate dilation
in a system with constant pressure.

00:21:01.510 --> 00:21:05.340
So some amount of driving energy
is put into the system, achieving

00:21:05.340 --> 00:21:07.890
a given inertial number.
And I observed that granular

00:21:07.890 --> 00:21:10.930
temperature scales linearly
with inertial number.

00:21:10.930 --> 00:21:19.410
So then, where is that energy going?
Because what we’re seeing is the –

00:21:19.410 --> 00:21:24.120
is not a 1-to-1 scaling as
predicted by this ideal gas law.

00:21:24.120 --> 00:21:27.900
Which, again, of course it doesn’t.
[chuckles] Because we are looking

00:21:27.900 --> 00:21:33.020
at a granular system where the
grains have mass, and it’s not going

00:21:33.020 --> 00:21:36.650
to be the same as a molecular gas.
But we would like to understand

00:21:36.650 --> 00:21:42.000
why and exactly where these different
dissipative processes are found.

00:21:42.000 --> 00:21:45.140
So put in another way,
only some of the fluctuation energy

00:21:45.140 --> 00:21:49.140
is going towards
dilating the sample.

00:21:49.140 --> 00:21:52.740
So dilation scales with granular
temperature to a power of 0.6.

00:21:52.740 --> 00:21:59.070
So here again I have dilation on the Y
axis and acoustic energy on the X axis.

00:21:59.070 --> 00:22:05.100
And this purple line is just showing
what a 1-to-1 scaling would look like.

00:22:07.260 --> 00:22:08.260
So …

00:22:12.960 --> 00:22:18.720
So, once again, some amount of
driving energy put into the system

00:22:18.720 --> 00:22:25.570
to achieve a given inertial number
is being diverted away from

00:22:25.570 --> 00:22:29.240
flow dilation.
So then where is that energy going?

00:22:29.240 --> 00:22:31.600
And that’s going to be
a question I’ll return to.

00:22:31.600 --> 00:22:36.540
So, in terms of the rheology of
naturalistic granular flows, right now,

00:22:36.540 --> 00:22:40.370
we know that angular grains are more
susceptible to the effects of acoustics

00:22:40.370 --> 00:22:43.840
in the transitional flow regime.
And we know that acoustic energy

00:22:43.840 --> 00:22:49.400
measures granular temperature.
And fluctuation energy is partitioned

00:22:49.400 --> 00:22:53.390
between dilation
and other flow properties.

00:22:53.390 --> 00:22:58.630
So now I’m going to talk about mixed
flow regimes, where we might find

00:22:58.630 --> 00:23:04.190
that some of this missing energy
that we were thinking might

00:23:04.190 --> 00:23:07.100
go towards dilation could be
diverted to influencing the

00:23:07.100 --> 00:23:09.960
rheology of other
parts of the flow.

00:23:12.550 --> 00:23:16.780
So a mixed regime flow – in any
system with inherent stress gradients,

00:23:16.790 --> 00:23:19.500
high inertial number gas-like flows
are going to be found directly

00:23:19.500 --> 00:23:23.980
adjacent to lower inertial number
transitional velocity regime flows,

00:23:23.980 --> 00:23:26.330
or even quasi-static flows.

00:23:26.330 --> 00:23:29.950
Sources of such stress gradients
are abundant in natural settings

00:23:29.950 --> 00:23:38.040
that can include wall friction,
irregular geometry shear zones,

00:23:38.040 --> 00:23:40.540
inconsistent forcings.

00:23:40.540 --> 00:23:46.760
Here are some images showing
a earth flow on the left and

00:23:46.760 --> 00:23:50.160
a fault zone on the right.
And, as you can see, these are not

00:23:50.160 --> 00:23:53.620
beautifully consistent shear zones.
So you’re going to find these

00:23:53.620 --> 00:23:58.140
kinds of gradients and mixed
flows in nature all the time.

00:24:00.440 --> 00:24:04.760
So the physics of the different
rheological phases of granular

00:24:04.760 --> 00:24:08.650
materials are quite distinct.
But the velocity profiles across

00:24:08.650 --> 00:24:11.910
them are presumably continuous.
So understanding how these different

00:24:11.910 --> 00:24:16.290
regimes affect each other is going to
be crucial to understanding the

00:24:16.290 --> 00:24:20.990
overall physics of high-velocity
shear flows in natural settings.

00:24:20.990 --> 00:24:24.460
So I used the same rheometer setup
that I just described here except

00:24:24.460 --> 00:24:31.170
I’ve now added video in order to
get the velocity profiles

00:24:31.170 --> 00:24:34.350
in these shear systems.

00:24:34.350 --> 00:24:39.320
So here you can – I sort of divided
the flow to show the fastest part –

00:24:39.320 --> 00:24:44.830
the inertial regime, the transitional
regime, and a quasi-static regime.

00:24:44.830 --> 00:24:47.490
And the mixed flow regime in
my experiments is the result of

00:24:47.490 --> 00:24:50.700
the wall friction with
the sample cylinder.

00:24:54.740 --> 00:24:59.140
So the – so we’re trying to answer the
question, can one regime influence

00:24:59.140 --> 00:25:05.100
or change another regime?
And the way to think about this is,

00:25:05.100 --> 00:25:08.960
if it doesn’t – if one regime is
completely independent of any other

00:25:08.960 --> 00:25:15.360
regime of flow nearby, then you should
be able to have laws that describe these

00:25:15.360 --> 00:25:19.150
distinct regimes that you can sort of
put together like building blocks.

00:25:19.150 --> 00:25:26.070
So it shouldn’t matter if I have a,
in this setup, a fast – my fastest part

00:25:26.070 --> 00:25:31.580
of the flow is an inertial number of 3
or an inertial number of 10 –

00:25:31.580 --> 00:25:34.350
[chuckles] it got cut off there.

00:25:34.350 --> 00:25:38.940
The sections of flow below the
quasi-static layer in blue

00:25:38.940 --> 00:25:44.180
and the transitional layer in purple
should have the same thicknesses

00:25:44.180 --> 00:25:47.970
regardless in these
constant-pressure experiments.

00:25:47.970 --> 00:25:50.860
Because they’re behaving
completely independently.

00:25:53.460 --> 00:25:58.080
So, when I go in and look at the
velocity profiles of these regimes,

00:25:58.080 --> 00:26:03.400
I find that that’s not the case.
And, in fact, as I increase the fastest

00:26:03.400 --> 00:26:07.600
velocity in the flow –
the driving velocity, I see changes

00:26:07.600 --> 00:26:12.310
in the other regimes of flow.
So what I observe, that I’m going to

00:26:12.310 --> 00:26:18.560
show you, is that the quasi-static
regime actually – so this is basically

00:26:18.560 --> 00:26:23.150
the thickness between two identical
inertial numbers within the

00:26:23.150 --> 00:26:28.950
quasi-static regime actually thickens.
So this is not due to a dilation

00:26:28.950 --> 00:26:32.430
of that part of the flow.
It’s due to an increase in creep.

00:26:32.430 --> 00:26:36.000
So you’re pulling more grains at the
bottom more easily into the flow.

00:26:36.000 --> 00:26:40.370
And then the
transitional regime thins.

00:26:40.370 --> 00:26:43.980
So it could be compaction.
It could be a thinning.

00:26:45.640 --> 00:26:49.000
So here I’m going to prove it.

00:26:49.960 --> 00:26:54.860
This is a plot showing depth in the
flow below the rotor on the Y axis.

00:26:54.860 --> 00:26:58.600
And then the local inertial
number on the X axis.

00:26:58.600 --> 00:27:02.680
So this is going to be based on the
local shear rate, not the total shear rate.

00:27:02.680 --> 00:27:08.780
And then, at the top, I have the
driving inertial number, essentially.

00:27:08.780 --> 00:27:13.500
So the – based on the top shear zone.
And the colors here are

00:27:13.500 --> 00:27:17.260
showing the driving velocity.
So blue is the slowest velocity.

00:27:17.260 --> 00:27:22.530
I tested it at 50 radians per second.
Red is the fastest at 300 radians

00:27:22.530 --> 00:27:25.580
per second, and then
everything else in between.

00:27:25.580 --> 00:27:28.840
So you’re going to have the fastest
part of the flow – the inertial regime –

00:27:28.850 --> 00:27:31.460
up here. And then
the transitional regime.

00:27:31.460 --> 00:27:33.790
And then, at the bottom,
quasi-static regime.

00:27:33.790 --> 00:27:40.610
So I think these colors aren’t quite
working, but, on the left here, you can

00:27:40.610 --> 00:27:45.230
see – well, I divided the whole plot
into the different regimes of flow.

00:27:45.230 --> 00:27:50.980
So here you can see all of the driving
velocities in the quasi-static regime.

00:27:50.980 --> 00:27:53.830
All of the velocities
in the transitional regime.

00:27:53.830 --> 00:27:58.990
And then my camera was
not fast enough to capture

00:27:58.990 --> 00:28:02.260
the fastest-fastest
part of the flow.

00:28:02.260 --> 00:28:05.930
But the driving inertial numbers
are in the inertial regime.

00:28:05.930 --> 00:28:11.560
So I’m going to remove all of the
in-between velocities and just

00:28:11.560 --> 00:28:13.400
talk about the
end member velocities –

00:28:13.400 --> 00:28:17.260
the 50 radians per second
and 300 radians per second.

00:28:18.160 --> 00:28:22.620
And explain how I analyzed these
different regimes of flow and

00:28:22.630 --> 00:28:27.730
how the rheology changes
depending on the driving velocity.

00:28:27.730 --> 00:28:31.740
So we’re going to start just
looking at the quasi-static layer.

00:28:31.740 --> 00:28:41.080
And what I did was just compare
the thickness between two inertial

00:28:41.080 --> 00:28:45.160
numbers within the quasi-static layer –
compare the thickness of the

00:28:45.170 --> 00:28:50.710
different – of the different
driving velocity flows.

00:28:50.710 --> 00:28:54.679
So, for the 50 radians
per second flow, the thickness

00:28:54.679 --> 00:28:59.050
between 10 to the minus 3
inertial number and, like,

00:28:59.050 --> 00:29:04.560
3 times 10 to the minus 5 inertial
number is this blue line here.

00:29:04.560 --> 00:29:10.240
And then I do the same thing for
the 300 radians per second flow.

00:29:10.250 --> 00:29:16.570
And I find that the thickness of
the quasi-static layer is increasing

00:29:16.570 --> 00:29:20.670
with driving velocity.
In other words, a larger zone of creep.

00:29:20.670 --> 00:29:26.190
So I do the same exercise for every
velocity in the quasi-static regime

00:29:26.190 --> 00:29:31.980
and also in the – or, transitional regime
and then compare the different layer

00:29:31.980 --> 00:29:35.760
thicknesses across
driving velocities.

00:29:35.760 --> 00:29:40.890
So here I’m showing the driving
inertial numbers on the X axis.

00:29:40.890 --> 00:29:45.390
And then the quasi-static
layer thickness here in blue.

00:29:45.390 --> 00:29:48.820
And the transitional layer
thickness here in purple.

00:29:48.820 --> 00:29:52.390
So what we see is that the
quasi-static regime layer thickens

00:29:52.390 --> 00:29:56.730
with increasing driving velocity.
And the way to think about this is

00:29:56.730 --> 00:30:03.920
that we see a larger zone of creep
with increasing driving velocity.

00:30:03.920 --> 00:30:08.280
And, in the transitional regime, there’s
actually a thinning or a compaction.

00:30:08.290 --> 00:30:10.910
So there’s some sort of
weakening here.

00:30:10.910 --> 00:30:13.240
Another way to think of this could be –
it could be a compaction.

00:30:13.240 --> 00:30:16.820
It could be a changing of
the nature of the transitional regime

00:30:16.820 --> 00:30:19.820
as we increase
driving velocity.

00:30:21.780 --> 00:30:26.720
But I’m going to go into the
mechanisms for some of this now.

00:30:29.040 --> 00:30:33.260
[Silence]

00:30:33.740 --> 00:30:35.460
Yes. Okay.

00:30:35.460 --> 00:30:40.090
So, in thinking about that larger zone
of creep that we see in the quasi-static

00:30:40.090 --> 00:30:46.031
regime, I did a set of experiments
shearing the granular sample

00:30:46.040 --> 00:30:52.940
very slowly and then applying external
vibrations – like, sustained external

00:30:52.940 --> 00:30:58.360
vibrations with a transducer and
observing the change in sample

00:30:58.360 --> 00:31:04.000
thickness as well as the change in
coefficient of friction of the flow.

00:31:04.000 --> 00:31:09.990
So here is kind of the procedure.
The X axis in both of these is just time.

00:31:09.990 --> 00:31:14.180
And then here I’ve got gap – or, sample
height, and here I’ve got acoustic

00:31:14.180 --> 00:31:20.290
energy. So you can see the green are
sections where the vibration is on.

00:31:20.290 --> 00:31:24.530
And so all the noise in these
flows is externally applied.

00:31:24.530 --> 00:31:32.340
And what I see in these quasi-static
experiments is that the friction –

00:31:32.340 --> 00:31:37.860
frictional weakening increases
with increasing vibrational energy.

00:31:37.860 --> 00:31:43.710
So here, again, the X axis,
I have acoustic energy per grain.

00:31:43.710 --> 00:31:50.610
And the Y axis is coefficient of
friction over coefficient of friction

00:31:50.610 --> 00:31:55.510
without vibration. So this is
showing the change in friction.

00:31:55.510 --> 00:32:00.640
And you can see that the friction
changes with acoustic energy

00:32:00.640 --> 00:32:09.570
to a power of about minus 0.2.
And it’s pretty consistent.

00:32:09.570 --> 00:32:15.450
So if you look back, again, at that
quasi-static layer thickness plot,

00:32:15.450 --> 00:32:20.299
here I have the quasi-static layer
thickness is increasing with

00:32:20.299 --> 00:32:26.960
driving inertial number raised
to a power of about 0.3. So remember

00:32:26.960 --> 00:32:32.680
that the acoustic energy varies linearly
with the driving inertial number.

00:32:32.680 --> 00:32:38.580
And this suggests that the frictional
weakening by vibration explains the

00:32:38.580 --> 00:32:43.920
increase in creeping mass observed as
the driving inertial number increases.

00:32:43.920 --> 00:32:47.720
So, depending on how fast your
driving the top, you’re creating

00:32:47.720 --> 00:32:51.260
all this new vibrational energy
that’s feeding back into the quasi-static

00:32:51.260 --> 00:32:55.720
layer and changing its frictional
properties, inducing some creep.

00:32:57.640 --> 00:33:01.030
And then compaction from vibration,
which may be occurring in the

00:33:01.030 --> 00:33:06.620
transitional regime, this plot is
showing compaction – so change

00:33:06.620 --> 00:33:15.280
in sample height, versus a normalized
vibration strength for a few different

00:33:15.280 --> 00:33:20.470
data sets as sort of a sanity check.
So the bottom here is showing

00:33:20.470 --> 00:33:26.610
compaction caused by internal flow
noise at transitional driving velocities.

00:33:26.610 --> 00:33:31.160
So these would be driving velocities
slower than the ones I tested,

00:33:31.160 --> 00:33:33.559
where you’re in
the transitional regime,

00:33:33.560 --> 00:33:37.840
and the grain pack is only
just starting to produce noise.

00:33:37.840 --> 00:33:40.660
You’ll see some
compaction from that noise.

00:33:40.660 --> 00:33:45.820
And then on the top here is compaction
caused by external vibration in the

00:33:45.820 --> 00:33:49.540
experiments that I just showed you.
And then the magenta points here

00:33:49.549 --> 00:33:57.070
are the purple – are the approximate
compaction that we observed

00:33:57.070 --> 00:34:06.380
in these experiments if
you consider – one second.

00:34:06.380 --> 00:34:08.731
If you consider the change in
transitional layer thickness

00:34:08.740 --> 00:34:13.560
as a compaction,
which it very well could be.

00:34:14.480 --> 00:34:18.080
So what we see is that,
in a mixed-flow regime,

00:34:18.090 --> 00:34:21.830
the vibration, or the granular
temperature, couples the inertial,

00:34:21.830 --> 00:34:24.960
transitional, and
quasi-static flow regimes.

00:34:25.889 --> 00:34:31.080
And then finally, I’m going to talk
about the – a quick exploration of

00:34:31.080 --> 00:34:37.860
material properties and their relative
influence on granular flow rheology.

00:34:37.860 --> 00:34:41.580
So, for this, I had to
do some more experiments.

00:34:41.580 --> 00:34:45.180
As a place to start in comparing
different mineralogies of sand,

00:34:45.180 --> 00:34:49.320
I looked at the Mohs Hardness Scale,
eliminating anything that would just

00:34:49.320 --> 00:34:55.040
pulverize in the machine instantly,
as well as expensive semi-precious

00:34:55.040 --> 00:35:01.020
gemstones, precious ones. [laughs]
And I end up with fluorite, apatite,

00:35:01.020 --> 00:35:04.160
feldspar, quartz,
and corundum.

00:35:04.160 --> 00:35:07.450
So these are the grains that I tested.
And here are some images of them

00:35:07.450 --> 00:35:11.970
so you can kind of
compare their angularities.

00:35:11.970 --> 00:35:15.560
And what I did was the same set of
experiments that I just showed you,

00:35:15.560 --> 00:35:19.450
and I looked at how coupled
the different flow regimes were

00:35:19.450 --> 00:35:24.470
between these different minerals.
So I’ll explain what that looks like.

00:35:24.470 --> 00:35:29.490
So the X axis here is inertial number.
It’s the driving velocity.

00:35:29.490 --> 00:35:35.290
And the Y axis here is the change
in volume between velocity steps

00:35:35.290 --> 00:35:40.780
divided by the change in granular
temperature between velocity steps.

00:35:40.780 --> 00:35:44.880
So the more coupled the different
regimes of flow are, the more

00:35:44.880 --> 00:35:51.070
negative this power law is going to be.
And it looks a mess, but I’m going to

00:35:51.070 --> 00:35:55.970
break it down a little more. [laughs]
So here are the – that same plot

00:35:55.970 --> 00:36:00.369
divided up for the different minerals.
So you can see that the amount

00:36:00.369 --> 00:36:05.021
of coupling that we see for the
different minerals changes quite a bit.

00:36:05.021 --> 00:36:10.790
And it’s not systematic with Mohs
hardness, at least, or yield strength.

00:36:10.790 --> 00:36:14.470
And, even if you start looking at the
different grain characteristics,

00:36:14.470 --> 00:36:17.609
they’re not – I would say fluorite
and corundum have the most

00:36:17.609 --> 00:36:22.119
similar shapes – and maybe
quartz and orthoclase.

00:36:22.119 --> 00:36:29.220
But their coupling exponents
represented – so X is the exponential

00:36:29.220 --> 00:36:33.510
fit of these plots. And I’m going
to call that the coupling exponent.

00:36:33.510 --> 00:36:36.160
So their coupling exponents
are quite different.

00:36:36.160 --> 00:36:39.190
And it doesn’t seem to vary
particularly with shape or

00:36:39.190 --> 00:36:43.680
particularly with yield strength.
So …

00:36:45.960 --> 00:36:47.800
Let’s look at some
other material properties.

00:36:47.800 --> 00:36:52.040
So the primary deformation regimes
are plastic, elastic, and fracture.

00:36:52.040 --> 00:36:55.150
So I start – I chose to look at
hardness, fracture toughness,

00:36:55.150 --> 00:37:00.720
and elastic modulus as representative
parameters to compare.

00:37:00.720 --> 00:37:05.380
And I’m just going to skip to the
results. [laughs] So this, again, looks

00:37:05.380 --> 00:37:08.890
a little bit of a mess, but I’m going to
clarify what we’re looking at here.

00:37:08.890 --> 00:37:15.300
So this is the coupling exponent – is
the – is the Y axis in all of these plots.

00:37:15.300 --> 00:37:21.590
And the X axis is hardness,
Young’s modulus, fracture toughness,

00:37:21.590 --> 00:37:25.119
and then these are – the bottom row
are different combinations

00:37:25.119 --> 00:37:30.030
of these parameters.
So I have the brittleness index here.

00:37:30.030 --> 00:37:38.090
The fracture energy release rate here.
And then a parameter called

00:37:38.090 --> 00:37:43.920
plastic displacement length here,
which I’ll explain.

00:37:43.920 --> 00:37:49.950
And the takeaway from this – so,
again, the Y axis coupling, the more

00:37:49.950 --> 00:37:55.490
negative that the coupling exponent is,
the more coupled the flow is.

00:37:55.490 --> 00:37:59.720
So that’s what we’re looking at here.
So the best fit – you’ll see, for most of

00:37:59.720 --> 00:38:04.160
these parameters, there really is no fit.
There’s no systematic variation of

00:38:04.160 --> 00:38:07.220
the coupling exponent
with a lot of these parameters.

00:38:07.220 --> 00:38:11.690
And the two that it sort of matches
best with are brittleness index

00:38:11.690 --> 00:38:14.000
or plastic displacement length.

00:38:14.000 --> 00:38:18.560
So I’m going to explain the
plastic displacement length here.

00:38:19.600 --> 00:38:25.590
So this – I chose to look at this
parameter to take into account energy

00:38:25.590 --> 00:38:33.000
dissipation in the form of plastic work.
So this is based off of the cohesion

00:38:33.000 --> 00:38:38.010
zone model of fracture put forth by
Barenblatt in the ’60s suggesting that

00:38:38.010 --> 00:38:44.720
a small zone of plastic deformation
near the crack tip can be quantified

00:38:44.720 --> 00:38:49.420
as this plastic
displacement link, delta.

00:38:51.020 --> 00:38:54.040
So you can think of this delta
as the amount of displacement that

00:38:54.050 --> 00:39:00.790
will occur on a crack before the
crack will propagate through.

00:39:00.790 --> 00:39:03.750
You can also think of it as the
amount of plastic displacement,

00:39:03.750 --> 00:39:07.900
or plastic deformation, that
accompanies any crack formation.

00:39:07.900 --> 00:39:10.280
So any crack that forms
will also be accompanied

00:39:10.280 --> 00:39:12.720
by an amount
of plastic work.

00:39:13.880 --> 00:39:24.500
And so, combined with the average
contact forces between grains,

00:39:24.510 --> 00:39:28.450
delta could efficiently represent
the amount of energy dissipated

00:39:28.450 --> 00:39:31.780
in the form of plastic work
in the whole granular system.

00:39:31.780 --> 00:39:37.020
So what we’re seeing here is that,
where delta is high, the grains

00:39:37.020 --> 00:39:41.280
will dissipate more energy in
the form of plastic deformation.

00:39:41.280 --> 00:39:48.270
And where delta is low, the grains
are more prone to forming cracks or

00:39:48.270 --> 00:39:52.540
fractures and will thus dissipate less
energy in the form of plastic damage

00:39:52.540 --> 00:39:59.340
and maybe pass on more energy
to these nearby regimes of flow.

00:39:59.340 --> 00:40:03.720
So when you have a larger plastic
displacement length, you’re passing

00:40:03.720 --> 00:40:09.410
on less of this fluctuation energy
from the fastest part of your flow.

00:40:09.410 --> 00:40:12.359
And you’re passing on less of
this acoustic noise to the

00:40:12.360 --> 00:40:16.460
lower layers of the flow.
So that was the takeaway.

00:40:18.260 --> 00:40:24.520
So finally, we’ve seen that the angular
grains are more susceptible to the

00:40:24.520 --> 00:40:28.360
effects of acoustics in the transitional
flow regime than spherical grains.

00:40:28.360 --> 00:40:32.520
Acoustic energy measures granular
temperature, and fluctuation energy

00:40:32.520 --> 00:40:36.730
is partitioned between dilation
and other flow properties.

00:40:36.730 --> 00:40:39.380
These other flow properties can
be thought of as coupling

00:40:39.380 --> 00:40:44.099
between different regimes of
flow in mixed-regime flows.

00:40:44.099 --> 00:40:49.250
And, when we’re thinking about
granular systems with different

00:40:49.250 --> 00:40:54.700
materials, a plastic displacement length
or consideration of the amount

00:40:54.700 --> 00:40:58.290
of energy dissipation in the form
of plastic work can determine

00:40:58.290 --> 00:41:03.320
the degree of coupling between
regimes of naturalistic flows.

00:41:03.320 --> 00:41:09.920
And, in terms of applying some of
this to real systems, I just wanted to

00:41:09.920 --> 00:41:13.300
put up some of these images from
the Ridgecrest earthquake recently.

00:41:13.300 --> 00:41:16.270
I actually went on
a little field trip down there.

00:41:16.270 --> 00:41:19.440
We couldn’t get onto the base.
I think only you guys can get there.

00:41:19.440 --> 00:41:22.832
[laughs] But we sort of
skirted around the edges.

00:41:22.832 --> 00:41:28.220
And so this picture here is showing
the kinds of materials that

00:41:28.220 --> 00:41:32.320
we’re seeing in fault zones.
And you can see that these are not

00:41:32.320 --> 00:41:35.930
spherical beads, which is obvious.
But it’s a worthwhile reminder

00:41:35.930 --> 00:41:41.430
that there’s a really complex set of
materials involved in these processes.

00:41:41.430 --> 00:41:44.880
And we can learn a lot from these
idealized models, but we know that

00:41:44.880 --> 00:41:49.270
the complications introduced by weird
shapes and weird materials are going

00:41:49.270 --> 00:41:53.870
to change some of these rheological
rules that we – that we think we have.

00:41:53.870 --> 00:41:56.600
And so it’s really important
to take those into account.

00:41:56.600 --> 00:42:03.310
I also wanted to show – here,
I observed a bunch of these sort of,

00:42:03.310 --> 00:42:11.070
like, 5-kilomgram rock sliding –
rockslides on really shallow slopes.

00:42:11.070 --> 00:42:15.440
So something like 10 degrees,
where a rock shouldn’t be sliding.

00:42:15.440 --> 00:42:18.910
And this, I think, is showing –
you know, it’s a small observation

00:42:18.910 --> 00:42:23.420
[laughs], but it’s showing the kinds of
things that a granular system

00:42:23.420 --> 00:42:28.099
under vibration can produce.
So these are effects that we’re

00:42:28.099 --> 00:42:34.520
seeing in geophysical shear zones.
And then finally, as you all know,

00:42:34.520 --> 00:42:40.540
this is a pretty funny fault – conjugate
fault system to see the angles between

00:42:40.540 --> 00:42:43.900
these are implying a really
low coefficient of friction

00:42:43.900 --> 00:42:47.540
along these faults. And that’s
something that we’re seeing in a few

00:42:47.540 --> 00:42:54.520
kinds of earthquake ruptures recently.
So trying to take into account the fact

00:42:54.520 --> 00:43:02.680
that these are all dominated by granular
materials along their rupture planes

00:43:02.680 --> 00:43:05.980
could be something to start, or
continue, really, taking into account

00:43:05.980 --> 00:43:10.340
when trying to understand the
frictional properties of fault zones.

00:43:10.340 --> 00:43:14.700
So, with that, I can take some
questions, and thank you again.

00:43:14.700 --> 00:43:20.000
[Applause]

00:43:22.320 --> 00:43:24.980
- Thank you.
Are there any questions?

00:43:26.660 --> 00:43:30.500
- I got really excited that
you did the last slide.

00:43:30.500 --> 00:43:32.570
Because we actually observed
those rocks – rock like that

00:43:32.570 --> 00:43:36.050
in Hector Mine also.
And some people were wondering if

00:43:36.050 --> 00:43:40.860
they were evidence of 1g acceleration.
But actually, if the rocks actually

00:43:40.860 --> 00:43:43.200
left the ground –
because we tried it back then.

00:43:43.200 --> 00:43:45.760
You drop them from more than a few
centimeters, you see the impacts.

00:43:45.760 --> 00:43:48.921
- Yeah.
- So they didn’t impact the ground.

00:43:48.921 --> 00:43:52.080
They also didn’t get dragged
just along the ground.

00:43:52.080 --> 00:43:55.350
Because there’s no furrows
for those rocks.

00:43:55.350 --> 00:43:57.220
And so actually, there’s a really
interesting question about what those

00:43:57.220 --> 00:44:00.420
rocks mean for ground motion,
which would then actually, then,

00:44:00.420 --> 00:44:02.820
let us go in and map
them more uniformly.

00:44:02.820 --> 00:44:07.460
We were looking for other things
in 1999 as a marker, possibly of

00:44:07.460 --> 00:44:10.030
ground motion variability.
Because you didn’t see them

00:44:10.030 --> 00:44:11.320
everywhere, right? They’re …
- Yeah.

00:44:11.320 --> 00:44:14.619
- So, if they didn’t happen everywhere,
and there was rocks like that all over

00:44:14.619 --> 00:44:19.670
the place, then it’s some sort of
evidence for small-scope ground

00:44:19.670 --> 00:44:21.349
motion variability.
So, actually, I think we actually –

00:44:21.349 --> 00:44:24.250
and then, recently Kate Scharer and
I and a few other people were

00:44:24.250 --> 00:44:26.869
discussing these rocks because
people were noticing them.

00:44:26.869 --> 00:44:30.080
So actually understanding what that
means for the ground motions that got

00:44:30.080 --> 00:44:34.980
those rocks moving in a way that didn’t
create furrows, didn’t create impacts,

00:44:34.980 --> 00:44:38.840
is, I think, a really interesting question
that actually has some applications.

00:44:38.859 --> 00:44:40.780
- Cool.
- So I’d definitely like to

00:44:40.780 --> 00:44:43.560
talk to you more about that.
- Yeah. That would be great.

00:44:43.560 --> 00:44:45.670
- The question I have on the rest of
the talk is, what would happen

00:44:45.670 --> 00:44:49.960
if you start putting fluids
into these granular materials?

00:44:49.960 --> 00:44:55.820
- So we’ve done that a little bit.
And much of what we observe

00:44:55.820 --> 00:45:02.630
is the same – with water, at least.
So, if you have a drained or saturated,

00:45:02.630 --> 00:45:05.820
but not pressurized, system,
that’s what we’ve tested in

00:45:05.820 --> 00:45:08.060
these experiments, at least.

00:45:08.060 --> 00:45:13.280
We still see a pretty high
noise production in the flow.

00:45:13.280 --> 00:45:18.320
And the creep effect is
still pretty observable.

00:45:18.320 --> 00:45:22.400
And even stronger because you have
kind of a kick from the fluid as well.

00:45:22.400 --> 00:45:26.900
But the transitional behavior – that
compaction – I’m not as sure that we’re

00:45:26.900 --> 00:45:30.060
seeing that when
fluids are involved.

00:45:30.060 --> 00:45:31.860
- Okay, thanks.
- Yeah.

00:45:33.300 --> 00:45:42.340
[Silence]

00:45:42.340 --> 00:45:44.940
- Thanks for an interesting talk.

00:45:44.940 --> 00:45:48.860
Correct me if I’m wrong, but I think,
for most of your tests, you’re at

00:45:48.869 --> 00:45:52.670
a very low normal stress.
So there’s grain rolling and bouncing,

00:45:52.670 --> 00:45:56.240
but there is no grain crushing going
on to any substantial degree.

00:45:56.240 --> 00:46:01.990
But, at depth in fault zones,
fracture and crushing could

00:46:01.990 --> 00:46:06.440
dominate the rheology.
So what’s your comment on that?

00:46:06.440 --> 00:46:10.850
- Yeah. This is a very common
question [laughs] for me.

00:46:10.850 --> 00:46:13.640
The normal stresses are really
low in these experiments.

00:46:13.640 --> 00:46:17.590
They’re 3 to 4 kilopascals.

00:46:17.590 --> 00:46:20.230
So we’re not seeing much
grain breakage at all.

00:46:20.230 --> 00:46:25.849
And I think that there – I guess
I would have two comments.

00:46:25.849 --> 00:46:32.260
So one is that the dimensionless
number will work regardless,

00:46:32.260 --> 00:46:36.240
as long as you’re not
talking about grain breakage.

00:46:36.240 --> 00:46:42.160
And, at fault zones, I would think
there is at least a fair amount of

00:46:42.160 --> 00:46:45.530
grains broken to their limit,
so you have such fine grains

00:46:45.530 --> 00:46:49.830
that you’re not seeing
maybe more fracture.

00:46:49.830 --> 00:46:55.540
But the longer answer is, I haven’t
taken into account grain breakage –

00:46:55.540 --> 00:47:00.700
like, true pulverization of grains yet.
But there are some studies that have

00:47:00.700 --> 00:47:07.290
started looking at that recently.
A guy named Ryan Hurley out of

00:47:07.290 --> 00:47:12.849
Johns Hopkins has started doing
some more systematic granular

00:47:12.849 --> 00:47:17.010
physics kind of studies, but trying to
take into account grain breakage.

00:47:17.010 --> 00:47:21.620
And, yeah, it’s an
important question.

00:47:26.060 --> 00:47:28.040
- [coughs]
Excuse me.

00:47:29.020 --> 00:47:36.140
Yeah. In a place where we spend an
awful lot of time with elastic wave

00:47:36.140 --> 00:47:41.200
equations, this is a very interesting
talk. And thanks for giving it.

00:47:41.210 --> 00:47:47.510
The first thing that comes to mind
as I look at this slide is,

00:47:47.510 --> 00:47:52.130
how much does size matter?
I mean, if you were to make half of

00:47:52.130 --> 00:48:00.400
this one size – you know, what,
3 millimeters, and the other

00:48:00.400 --> 00:48:05.319
6 millimeters or 2 millimeters,
what would happen?

00:48:05.319 --> 00:48:10.730
- So I’ve tested that a little bit,
and what I’ve seen is that the flow

00:48:10.730 --> 00:48:16.359
below inertial regime levels is –
the rheology that we can expect is

00:48:16.359 --> 00:48:20.980
what we would expect of the
smaller grain size component.

00:48:20.980 --> 00:48:25.010
And then, in the dilatational phase,
the inertial flow regime, it’s going to

00:48:25.010 --> 00:48:27.849
be dominated by the behavior
we would expect from the larger

00:48:27.849 --> 00:48:32.020
grain size component.
So that’s the short answer.

00:48:32.020 --> 00:48:34.160
But I haven’t played a ton
with different ratios.

00:48:34.160 --> 00:48:40.300
If you just have a little bit versus,
you know, an 8-to-2 ratio.

00:48:41.440 --> 00:48:43.660
- Okay. Thank you.
- Thank you.

00:48:43.660 --> 00:48:45.490
- Any additional questions?

00:48:48.260 --> 00:48:51.119
Okay. Let’s thank
our speaker again.

00:48:51.120 --> 00:48:54.200
[Applause]

00:48:54.200 --> 00:48:57.000
We’ll be taking Stephanie out to
the lunch at the café, so if you’d

00:48:57.000 --> 00:49:01.859
like to join, please do so.
And she’ll be sticking around after that

00:49:01.860 --> 00:49:04.660
to have some meetings, and there’s still
some time available in her schedule.

00:49:04.720 --> 00:49:09.840
So if you want to sign up, the
schedule is up at the front. Thanks.

00:49:19.000 --> 00:49:20.600
- I just thought of a question
now that we’re over.

00:49:20.600 --> 00:49:21.500
- Yeah.
- So you were at the

00:49:21.500 --> 00:49:24.380
Postgraduate School.
How is the Navy interested in this?

00:49:24.380 --> 00:49:29.080
Or you had an army logo …
- Yeah. Neither of them …

00:49:29.080 --> 00:49:39.440
[Silence]