Institut Henri Poincare,

1
Institut Henri Poincare, Session on Granular
Materials 5 January to 8 April 2005 Thematic
Meeting, 24-25 February Instabilities,
Bifurcations, Localization Large scale
localization Thermal weakening of faults
during seismic slip James R. Rice Department
of Earth and Planetary Sciences and Division of
Engineering and Applied Sciences Harvard
University Lecture 2, 25 February
2005 Downloads Lecture 1 (yesterday)
http//esag.harvard.edu/rice/IHP_granular_Rice_Lec
t1_05.ppt Lecture 2 (today) http//esag.harvard.e
du/rice/IHP_granular_Rice_Lect2_05.ppt
2
Fault Zone Processes during Seismic Slips
Questions How does shear stress (t) vary
with slip (d) during earthquakes? Focus
is on rapid, large slip d -- i.e., d gtgt slips
of order 0.01 mm to 0.1 mm at which events
are thought to nucleate -- according to rate
state concepts. What are the physical
mechanism of weakening during slip?
Suggested here Thermal
pressurization of pore fluid and
Flash heating at highly stressed frictional
contacts are the primary mechanisms. Both
seem to be important. Melting may
occur too for large, deep slips. What fracture
energy (G) is implied by the t vs. d relation?
Important because we can thereby test any
proposed t vs. d against seismic
constraints on G.
3
Relation of fracture energy to slip weakening
properties
peak strength
initial stress
residual strength (may not be well defined)
4
Background for theoretical modeling of stress vs.
slip relation Field observations of exposures
of mature, highly slipped fault zones Slip in
individual events occurs primarily within a thin
shear zone (h lt 1-5 mm), within a finely
granulated (ultracataclastic, possibly clayey)
fault core that is of order 10s to 100s mm
thickness. that despite the existence of
much wider, 1 to 100 m, damage zones (with
granulation, pervasive cracking and/or minor
faulting) Hypotheses Earthquake failure
occurs in a water-saturated fault zone. It has
material properties (permeability, porosity,
poroelastic) like those inferred from lab studies
of fault materials from the Median Tectonic Line
(MTL) and Nojima faults in Japan.
locations for which relatively complete data
exists
5
F. Chester, J. Evans and R. Biegel, J. Geoph.
Res., 98 (B1), 771-786 (1993)
30-100 m
(Damage highly cracked rock. Zone with
macro faults or fractures extends 10x further.)
1-10 m (Sometimes described as foliated
gouge, or for some faults, simply as gouge.)
10s-100s mm
(But principal failure surface is much
thinner, typically lt 1-5 mm!)
6
J.Geophys. Res. (1993)
7
Chester, F. M., and J. S. Chester,
Ultracataclasite structure and friction processes
of the Punchbowl fault, San Andreas system,
California, Tectonophysics, 295 (1-2)
199-221,1998
Prominent slip surface (pss) is located in the
center of the layer and identified by the black
arrows.
8
from J. S. Chester and D. L. Goldsby, SCEC Ann.
Rpt., 2003 Punchbowl Fault prominent slip
surface
mm-thick layer crystal-lattice preferred
orientation (evidence uniform birefringence, brig
ht layer) contains distinct microscopic slip
surfaces.
9
Median Tectonic Line Fault (MTL), Japan
10
Median Tectonic Line Fault, Japan
h 3 mm Wibberley (priv. commun., 2003)
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(Wibberley and Shimamoto, JSG, 2003) permeability
of clay gouge containing the central slip zone,
Median Tectonic Line Fault, Japan
Gas permeability data from the first pressure
cycle p 20 MPa.
Permeability, k ( m2 )
12
Lockner, Naka, Tanaka, Ito and Ikeda,
Permeability and strength of core samples from
the Nojima fault of the 1995 Kobe earthquake,
USGS Open File Rpt. 00-129, 2000
1017 m2
1019 m2
1017 m2
1019 m2
1017 m2
1019 m2
13
Lockner et al., USGS (2000)
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Governing equations, 1-space-dimension shearing
field, constant normal stress sn
heat flux
fluid mass flux
pore pressure
velocity
temperature
15
Form of fluid mass conservation equation, in
terms of p and T
storage factor
thermal pressurization factor
inelastic dilatancy rate
Origin, poro-thermo-elastic calculations to
express dm/dt
inelastic dilatancy rate

(Should evaluate bn and ln for condition
fault-normal stress sn const., and
fault-parallel strains e 0, using
poro-thermoelastic theory.)
storage factor
thermal pressurization factor
16
Two simple models, shear zone of fixed
thickness h (including case h 0)
Building on Sibson (1973), Lachenbruch
(1980), Mase Smith (1985, 1987), Rudnicki
Chen (1988), Segall Rice (1995), Sleep
(1995), Andrews (2002), Vardoulakis
(2002), Garagash Rudnicki (2003)
heat flux
fluid mass flux
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Pore pressure on fault plane
Temperature on fault plane
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Note multi-scale nature of the slip-weakening no
well-defined Dc
22
(Plot thanks to Alan Rempel)
23
Take V 1 m/s , ath 1 mm2/s , bf 7 x
1010 /Pa , hf 104 Pa-s Low end of
poromechanical parameter range lab exp's on
undisturbed, confined MTL samples k 1020 m2,
n 0.04, bn/bf 1 ( gt ahy 1.8 mm2/s
, Tmax Tamb 2.9 (sn po ) ºC / MPa )
L 4 mm if f 0.25 (flash heating) High
end of poromechanical parameter range k, bn
increased due to stressing and damage at tip of
propagating rupture (Poliakov et al., 2002 Rice
et al., 2004 k 1019 m2, n 0.04, bn/bf
2 ( gt ahy 12 mm2/s , Tmax Tamb 8.4
(sn po ) ºC / MPa ) L 30 mm if f
0.25 (flash heating)
24
Rice et al. (to BSSA,2003), building on Poliakov
et al. (JGR, 2002)
For R/L 0.1, and tr / tp 0.2 (nearly complete
strength loss)
YELLOW shear failure RED tensile failure
Poroelastic effects included Skempton B 0.6
Dp B D(s11 s22 s33 )/3
Scale length in plots (Ro)avg 20-30
m, Ro 1-70 m, fitting model to
Heaton (1990) earthquake set, assuming fp 0.6
and hydrostatic initial pore pressure.
25
Comparison, Model 2 (Slip on a plane)
Predictions of G and seismic estimates
Common parameters for all predictions shown
cth 1 mm2/s , bf 7 x 1010 /Pa , hf
104 Pa-s , sn po 126 MPa (7 km depth) , f
0.25 (flash heating) , V 1 m/s Low-end
poromechanical parameters k 1020 m2, n
0.04, bn/bf 1, ahy 1.8 mm2/s L 4
mm High-end poromechanical parameters k 1019
m2, n 0.04, bn/bf 2, ahy 12 mm2/s
L 30 mm

26
Aside on frictional weakening by flash heating
Rice, EOS, Trans. AGU, 1999 Beeler
Tullis, manuscript, 2003
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Melting does not necessarily weaken!
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Weakening of friction coefficient f at high slip
rates Results here for Arkansas novaculite (100
quartzite), determined in rotating annular
specimens
Prakash (2004), 2 to 4 m/s
Tullis and Goldsby (2003a,b), up to 0.36 m/s
Slip rates V up to 0.36 m/s imposed in Instron
testing frame for 45 mm slip, after 1.2 mm
pre-slip at 10 mm/s. At low V, friction
coefficient f 0.65, whereas at V gt 0.3 m/s, f
0.3. Comparable rate-weakening was found
for granite, Tanco albite (100 feldspar),
and gabbro, but ambiguous results for calcite.
Pre-twisted torsional Kolsky bar (split
Hopkinson bar) imposes slip at V 3-4 m/s,
resulting in f slightly less than 0.2.
Experiment becomes uninterpretable after
small slip (marked) due to cracking in wall of
specimen.
31
from T. E. Tullis and D. L. Goldsby, SCEC Ann.
Rpt., 2003
rotary shear, 1.2 mm slow pre-slip (10 mm/s),
then 45 mm of fast slip
Arkansas Novaculite (Quartzite)
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from T. E. Tullis and D. L. Goldsby, SCEC Ann.
Rpt., 2003
Also seen in Granite, Tanco Feldspar Gabbro,
but just weakly/ambiguously in Calcite.
Westerly Granite
Gabbro (of Tsutsumi Shimamoto)
33
from Vikas Prakash, SCEC Ann. Mtg.,
2004 Schematic illustration of the torsional
Kolsky bar apparatus
34
Seismic estimates of fracture energy (G) Method
A (Rice, Sammis and Parsons, BSSA, in press
2004-05), Use of seismic
slip inversion results from Heaton (PEPI, 1990)
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Elastodynamic stress and displacement field
solution used to estimate G Rice, Sammis
Parsons (BSSA, in press 2004-05) generalization
of Broberg (GJRAS, 1978), Freund (JGR, 1979),
Heaton (EPSL, 1990), Poliakov, Dmowska Rice
(JGR, 2002)
denotes parameter estimated from seismic slip
inversion, Heaton (1990) -- L, d and vr
F1(R/L) varies by a factor of two as R / L varies
from 0 to 1.
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Fracture energies G and slips ?, large
earthquakes (arranged in order of slip
magnitude) Mo l
w ? G Event 1018 Nm km km m MJ/m2 Mich
oacan 1985 (M8.1) 1,500
150 120 2.8 6.6 Heaton Rice, Sammis
Parsons Landers 1992 (M7.1) 56
60 14 2.2 5.0 Peyrat, Olsen Madariaga San
Fernando 1971 (M6.5) 7
12 14 1.4 6.9 Heaton Rice, Sammis
Parsons Borah Peak 1983 (M7.3) 23
40 20 0.96 2.9 Heaton Rice, Sammis
Parsons Kobe 1995 (M6.9) 22
48 20 0.78 1.5 Guaterri, Spudich
Beroza Imperial Valley 1979 (M6.5) 5
30 10 0.56 1.3 Heaton Rice, Sammis
Parsons Imperial Valley 1979 0.81 Favreau
Archuleta Morgan Hill 1984 (M6.2)
2.1 20 8 0.44 2.0 Heaton Rice, Sammis
Parsons Morgan Hill 1984 2.0 Beroza
Spudich N. Palm Springs 1986 (M6.0) 1.8
18 10 0.33 0.15 Heaton Rice, Sammis
Parsons Coyote Lake 1979 (M5.9) 0.35
6 6 0.32 0.57 Heaton Rice, Sammis
Parsons For Rice, Sammis Parsons events, the
G values are averages of their Gmin and Gmax ( 2
Gmin) i.e., G 1.5 Gmin.
39
Seismically inferred fracture energies G vs.
slips d, large earthquake data set. Compared to
theoretical predictions, Model 2 (slip on a
plane), based on high-end (L 30 mm) and
low-end (L 4 mm) parameter values, and on f
0.25 and sn po 126 MPa.
Large earthquake data set (symbols) RSP
results, shown as Gavg here, for Heaton (1990)
event set, with separate estimates for Morgan
Hill 1984 and Imperial Valley 1979 of that set,
and for Kobe 1995 and Landers 1992.
40
Method B (Abercrombie and Rice, GJI, in press
2004-05), Use of radiated
energy, moment, stress drop and slip
41
Abercrombie (JGR, 1995) events, including
Hauksson (JGR, 2000) focal mechanisms figure
from Abercrombie and Rice (GJI, in press,
2004-05)
42
Abercrombie and Rice (GJI, in press 2004-05)
43
Composite data Abercrombie Rice (2004), and
Rice, Sammis Parsons (2004) (ovals) based on
Heaton (1990) event set
44
Comparison, Model 2 (Slip on a plane)
Predictions of G and seismic estimates
Common parameters for all predictions shown
cth 1 mm2/s , bf 7 x 1010 /Pa , hf
104 Pa-s , sn po 126 MPa (7 km depth) , f
0.25 (flash heating) , V 1 m/s Low-end
poromechanical parameters k 1020 m2, n
0.04, bn/bf 1, ahy 1.8 mm2/s L 4
mm High-end poromechanical parameters k 1019
m2, n 0.04, bn/bf 2, ahy 12 mm2/s
L 30 mm

45
Conclusions Crustal faults are likely to
weaken during seismic slip by - shear
heating and thermal pressurization of pore
fluid and by - flash heating at
frictional micro-asperity contacts. The
mechanisms are consistent with geological fault
zone studies and with laboratory determinations
of properties of fault-related materials. They
predict fracture energies (G) in the broad range
inferred seismically. Predictions have what
seems to be an approximately correct scaling
with earthquake slip over the entire range from
a few mm to a few m. The mechanisms explain
why melting does not generally occur at
shallow to moderate depths, or may at least be
delayed until unusually large slips.
46

• Major questions
• - What sets the thickness (h) of the zone of
  highly localized shear?
• - What amount of dilatancy (Dnpl)?
• - What is the pore expansivity (bn) and
  permeability (k) for shearing gouge?
• - What predictions to be made when such
  constitutive laws as derived here are
• used in dynamic rupture simulations?
• - What rheology of the liquefied gouge
  resulting when p sn? Is t 0?
• - What rheology if melting does begin?
• - What role for off-fault inelasticity? Are we
  misinterpreting seismically inferred G?

47
The melting range -- some pictures
(Work in progress by A. W. Rempel, L. M. Jacques
and J. R. Rice, on Fault zone drainage, heating
and melting during earthquake slip)
48
Otsuki, Monzawa Nagase, J. Geophys. Res. (2003)
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Otsuki, Monzawa Nagase, Fluidization and
melting of fault gouge, J. Geophys. Res.
(2003) 9 pseudotachylyte-generating events
No or minimal overlap of shear zones P1, ,
P9. All 9 shear zones fit within a 20 mm
width. Individual zones have h lt 2 mm, often lt
1 mm.
50
Various degrees of melting
high melting
low melting
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Following in case needed
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suction from small-slip dilatancy
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Comparison of Model 1 (adiabatic undrained)
predictions of G to seismic estimates
(flash heating)
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(Prakash, SCEC Ann. Mtg., 2004 Arkansas
novaculite)
60
(Plots thanks to Alan Rempel)
61
With Kobe 1995 and Landers 1992 included, and
separate estimates for Morgan Hill 1984 and
Imperial Valley 1979 (RSP results shown as Gavg
here)
2 points
62
(Rice Rudnicki, in progress, 2004)
Configurational stability of spatially uniform,
adiabatic, undrained, shear (Motivation Why do
zones of localized slip have the thickness that
they do?) Governing equations for shearing
velocity V(y, t), shear stress t(y, t),
pore pressure p(y, t), and temperature T(y,
t)
Simple rate-strengthening friction model
approximately valid only in stable regions
in which rupture cannot nucleate, but may
propagate through (or in unstable regions that
have shear-heated to a frictionally stable T
range). (Fuller rate-state description, with
localization limiter, must be used in regions of
unstable, rate-weakening, friction.)
The spatially uniform solution (Model 1,
revisited)
63
Linearized perturbation about time-dependent
spatially uniform solution
Nature of solution with spatial dependence
exp(2piy/l)
s s(l) satisfies
Typically of order 20-60, in results of low
shear-rate experiments.
64
Note High-end here taken as k 1019 m2, n
0.06, bn/bf 4, ahy 4.8 mm2/s
65
Low end poromechanical parameters
High end poromechanical parameters (see
note, previous page)
Implications Even with velocity
strengthening with f/(b a) large, e.g., of
order gt 20, we must expect large shear strain
to be confined to a thin zone, less
than diffusion penetration distances of heat and
fluid in moderate and larger events.
Justifies use of Model 2, based on slip on a
plane. Observed 1-5 mm deformed zone thickness
in gouge is a precursor thickness (i.e., lcr
based on an initial, broad h) not the thickness
of the large shear zone.