Mechanics of faulting
Jyr-Ching Hu, Dept. Geosciences National Taiwan University
http://www.sanandre
asfault.org
Strengths of active thrust-belt wedges & their basal
detachments: directly determined from the covariation of
surface slope a with detachment dip b , without strong
assumptions about the specific strength-controlling
Test: Niger delta thrust belt, the active Taiwan mountain
belt, and the thrust that slipped in the M = 7.6 Chi-Chi
earthquake
Suppe, Geology 2007
Absolute fault & crustal strength from wedge tapers
Basal detachments: exceedingly weak, with effective
coefficients of friction (0.04–0.1) that are an order of
magnitude less than most laboratory friction coefficients
(0.6–0.85)
Weak faults & strong crust: wedges are moderately
strong internally, within the range of pressure-dependent
strengths in deep boreholes
Frictional resistance = b x Weight
The classic thrust-fault problem…
The breakup Maximum length ~20 km
Courtesy of John Suppe
Critical-taper wedge mechanics
Courtesy of John Suppe
Critical-taper wedge
taper = ab
Courtesy of John Suppe
Critical-taper wedge mechanics
Courtesy of John Suppe
Actively deforming fold-and-thrust belts & accretionary wedges:
simultaneously at regional failure internally & along their base
Mechanical equilibrium: between the critical taper α + β of a
wedge & the strength of the wedge & its base, where α is the
surface slope and β is the dip of the detachment
taper = ab
Davis, 1983
Wedge theory
1 (1 )
sin1 2(1 )
1 sin
f b b b
f
S gH
C gH
b a b
Wedge theory: infer the magnitudes of strength parameters that
are consistent with observed tapers, e.g., internal & basal friction
coefficients (μ = tanφ, μb) & depth-normalized pore-fluid pressures
(λ = Pf /ρgH).
Mechanically homogeneous Wedge (Dahlen, 1990, equation 99):
Sb & C: non-pressure-dependent parts of the fault and wedge strength H: thickness
Wedge theory
Equations contain a number of average regional-scale fault
& crustal strength parameters, but unfortunately have little
direct constraint in actively deforming regions.
Equations simpified:
(1 )b b bF S gH
Fault-strength terms: 2(1 ) sin 1 sinW
C gH
Wedge-strength terms
1
1
f
f
F
W
b a b
( , )f F Wa b
[1 − (ρf /ρ)]: ratio of the density of the overlying fluid (seawater or air)
to the mean density of rock & is 1 for subaerial wedges & ~0.6 for
submarine wedges
Wedge theory
1
1
f
f
F
W
b a b
(see Dahlen, 1990, equations 88, 90, 91, 97)
F gH
F: regional normalized basal shear traction
1 3W gH
W: normalized differential stress
Wedge theory
If F & W are homogeneous then a & b are linearly related
1 1f fF W
W Wa b
0 sba a b
Get strengths from co-variation of a & b
1
sW
s
0F Wab
11
f
sW
s
Application to active wedges
Dry-sand wedges on a Mylar base,
Two active geologic wedges, Taiwan and
the Niger delta
Approximate the assumption of large-scale
homogeneity
1. Approximate linear covariation of α and β
2. Rather thick (H = 5 – 12 km)
Application to active wedges
Not mechanically homogeneous: thin toes (H < ~1
km) of active accretionary wedges such as the
Nankai trough & Barbados show surface slopes α
that decrease away from the toe, with no
associated change in detachment dip β
Have horizontal gradients in wedge strength, given
the strong lateral variation in porosity, lithification, &
hence cohesion, & probably fluid pressure.
Application to active wedges
Basal coefficient of friction of F = μb = 0.27 & a wedge
strength W = 1.9, which corresponds to a cohesionless
internal friction of μ = tanφ = 0.57.
predicts µ = 0.57
measured µ = 0.58
predicts µb = 0.27
measured µb = 0.3
Davis et al. (1983)
h=v
Taiwan Main Detachment
Carena et al.,
geology
2002
Stepping down to deeper detachments to East…
Courtesy of John Suppe
Linear regressions of taper measurements
Carena et al. (2002)
Bilotti & Shaw (2005)
Deep-water
compressive toe of
the Niger delta
Central Taiwan
Summary
W = (σ1 − σ3)/ρgH based on the regression slopes &
obtain similar results for both wedges.
Taiwan gives W = 0.6 & the Niger delta gives W = 0.7
Normalized basal shear traction F = σ /ρgH:
F = 0.08 for Taiwan and F = 0.04 for the Niger delta.
Observed ratio of fault strength to wedge strength F/W
= σ /(σ1 − σ3):
0.13 for Taiwan and 0.06 for the Niger delta.
These results show that the basal detachments are
exceedingly weak absolutely and relative to the wedge
strengths.
Comparison with deep borehole data
Borehole stress measurements
SAFOD pilot hole: strong
decrease with depth; suggesting
that the measurements, which
are at a depth of 1–2 km in
granite, are still within the near-
surface boundary layer in which
cohesion dominates
Cohesive strength C = ~46 MPa:
A factor of four less than the
borehole-scale cohesion estimated
for the SAFOD pilot hole at 197–
212 MPa (Hickman & Zoback,
2004).
Comparison with deep borehole data Borehole stress measurements
W* is relatively
constant
as a function of depth,
indicating that the KTB
region is dominated by
pressure-dependent
strength, with W* = 1.0
± 0.2 to a depth of 8 km.
KTB borehole σ2 is vertical, whereas in compressive wedges
σ3 is vertical
Constraint of a single taper
1 ( )fF Wa a b 0 sba a b
Constraint of a single taper
Courtesy of John Suppe
Wedge-strength constraints
Courtesy of John Suppe
Courtesy of John Suppe
Thermal anomaly in post Chi-Chi boreholes
Courtesy of John Suppe
Constraint of Chi-Chi thermal anomaly
Tanaka et al. GRL 2006
Post Chi-Chi borehole stress measurements
Hung et al. Tectonophysics
2009
W*=0.75-0.95
Constraint of borehole thermal anomaly
Courtesy of John Suppe
Summary Upper bound on upper-crustal strength: Byerlee’s law (μ
= 0.85) with hydrostatic pore-fluid pressures (λ = 0.4),
then W ≤ 2.2 & F ≤ 0.21, which is a weak detachment
Chinshui Shale detachment: exceedingly weak, & best
estimate is in the range F = σ /ρgH = 0.07–0.11
Chelungpu thrust ramp is even weaker based on shear
tractions σ estimated from post Chi-Chi borehole
thermal anomalies and W* observed by Tanaka et al.
(2006), Hung et al. (2009), and Kano et al. (2006) (F* =
σ /σn = 0.03–0.05).
Summary
These extreme fault weaknesses are especially striking
in light of the observation that the regional pore-fluid
pressures surrounding the Chinshui Shale detachment
and thrust ramp are hydrostatic (λ = 0.4) (Yue, 2007).
Therefore, the static ambient Hubbert & Rubey (1959)
fluid-pressure hypothesis is not the cause of the
weakness of the Chinshui Shale detachment or thrust
ramp.
Furthermore, the wedge is strong in spite of the very
weak thrust ramp within it, presumably because of the
internal strength of the thrust sheets in bending
Why are the faults so weak & the crust so strong???
W 1 3
gH 0.6 .0.95
F gH 0.040.09
F
W
1 3
0.04 0.15
Are pore-fluid pressures the solution to the weak fault problem???
The classic Hubbert-Rubey hypothesis…
F (1 )b
where
Pf gz
need
(1 ) 0.1 or
0.9
The Chinshui shale detachment is above fluid-retention depth ZFRD
…therefore not classic Hubbert & Rubey fluid-pressure mechanism
Courtesy of John Suppe
Relationship between ZFRD and Hubbert & Rubey effect….
(1 ) 0.6ZFRD
Z
need Z > 5ZFRD or ~10-15 km for Taiwan
Courtesy of John Suppe
Chi-Chi earthquake…
Yue, Suppe & Hung, 2005
Earthquake slip is confined to geometric segments…
Coseismic folding in Chi-Chi earthquake…
Fault bends must be the locus of crustal strength…
Courtesy of John Suppe
Coseismic folding in Chi-Chi earthquake…
Courtesy of John Suppe
Continual deformation of new rock along axial surfaces….
Weak faults and strong crust…
Courtesy of John Suppe
Coseismic folding in Chi-Chi earthquake…
Fault bends must be the locus of crustal strength…
Courtesy of John Suppe
Contrasting crustal strengths…
Courtesy of John Suppe
Areas of very thick deforming sediments…
Gulf of Mexico Niger delta Borneo Sumatra Nankai trough Cascadia Bangladesh/Myanmar Makran Gulf of Alaska New Zealand Taiwan
Courtesy of John Suppe
Low strength of deep San Andreas fault gouge from
SAFOD core
David A. Lockner, Carolyn Morrow, Diane
Moore & Stephen Hickman
Nature, 472, 82–85, 2011
Weakness of the San Andreas Fault Zone
Absence of a heat flow anomaly (Brune et al.,
1969; Lachenbruch & Sass, 1980; Williams et
al., 2004)
Stress orientation across the fault (Zoback et
al., 1987; Mount and Suppe, 1987),
Hypotheses
Fault zone consists of clay gouge (Wu et al., 1975; Wu,
1978; Wang et al., 1978), especially a montmorillonite rich
clay gouge that has frictional coefficients as low as ~0.1
(e.g., Wang and Mao, 1979; Chu et al., 1981; Carpenter et
al., 2011; Lockner et al., 2011)
Fault zone has a normal frictional coefficient but is
dynamically weakened during earthquakes by shear heating
& other physicochemical processes (e.g., Lachenbruch,
1980; Di Toro et al., 2011)
Frictional coefficient of the fault is ‘normal’, but high
porepressure in the fault zone lowers the effective normal
stress on the fault and thus its frictional resistance to sliding
(Rice, 1992; Byerlee, 1990)
SAFOD: San Andreas
Fault Observatory at
Depth
Study the physical &
chemical processes
controlling faulting &
earthquake generation
along an active, plate-
bounding fault at depth
SAFOD
San Andreas Fault
Fault Contact at 10,063 ft
Highly Deformed Siltsone
Granite Cobble
Conglomerate
Clay Gouge
2.5 cm
Direct measurement
of the processes
that control
earthquakes
San Andreas Fault Observatory at Depth (SAFOD)
North
American
Plate
A 15-year effort of
Mark Zoback,
Steve Hickman,
and Bill Ellsworth
Steve Steve
Location of SAFOD site SAFOD site: located at the NW end of the rupture zone of the 1966
and 2004 M 6 Parkfield earthquakes, in the transition between the
creeping and locked sections of the SAF
At surface, the fault is creeping
at a rate of 1.8 cm/yr.
Numerous earthquakes occur
directly on the SAF at 3-12 km
Geophysical logs & generalized lithology from phase 2 of the SAFOD project
SAF is a broad
zone of
anomalously low
P- and S-wave
velocity and
resistivity
Why Parkfield? Transition between the locked portion of the fault to the SE & the segment of the fault to the NE where slip dominantly occurs by aseismic creep
Geologic cross-section parallel to the trajectory of the SAFOD borehole
San Andreas Fault damage zone: SDZ, CDZ, & NBF
56
2007 => creeping strands:
southwest deforming zone (SDZ)
central deforming zone(CDZ)
Depth:2.7 km,
damage zone:200 m wide
Methods
•1.6 m and 2.6 m fault gouge of 31 m of core
•Powder(
X-Ray Diffraction
SDZ & CDZ:
porphyroclasts of serpentinite
and sedimentary rock
dispersed in a matrix of Mg-
rich clays
X-Ray Diffraction
CDZ:Sap (>60%)
SDZ:Sap, Cor, Q , F
The two gouge zones: product of
shearing-enhanced metasomatic
reactions between serpentinite &
adjoining sedimentary rocks.
Q = quartz
Cc = calcite
K = K feldspar
Pl = plagioclase
(albite?)
Chl = chlorite
Km = K - micas
Srp = serpentine
Sap = saponite
Cor = corrensite
SW side
NE side
X-Ray Diffraction
CDZ:Sap (>60%)
SDZ:Sap, Cor, Q , F
The two gouge zones: product of
shearing-enhanced metasomatic
reactions between serpentinite &
adjoining sedimentary rocks.
Q = quartz
Cc = calcite
K = K feldspar
Pl = plagioclase
(albite?)
Chl = chlorite
Km = K - micas
Srp = serpentine
Sap = saponite
Cor = corrensite
SW side
NE side
Sample strength: in situ
μ:coefficient of friction τ :shear stress σn :effective normal stress p:pore pressure
σn = 122 MPa
V = 1.15 μm/s
Compositional
change
SW => NE
SDZ & CDZ:
0.13≦ μ ≦0.21
Saponite (μ
~0.05)
Strength & sliding rate
Serpentinite porphyroclast from
the SDZ: a − b = +0.0004 ± 0.0014
All other core samples have
positive rate sensitivity:
1. Outside the foliated gouge zone:
+0.001 o => stable creep
Low frictional strength (µ ≈ 0.15) of foliated gouge:
(1) lack of an observed heat flow anomaly
(2) maximum compressive stress oriented at a high angle to the fault trace
(3) no evidence of pore pressure elevated in fault zone
The positive dependence of strength on slip rate of the fault gouge material is consistent with deformation by creep rather than by earthquakes.
Stable creep and low strength
Boness & Zoback, 2006
Argument
Stress state
Tembe et al., 2009 77 °
Depth : 2.7km
τ = 17 MPa , σn = 122 MPa p = 27
Summary
The laboratory strength measurements of the SAFOD
fault core materials at in situ conditions, demonstrating
that at this locality & this depth the San Andreas fault is
profoundly weak (μ = 0.15) owing to the presence of
the smectite clay mineral saponite, which is one of the
weakest phyllosilicates known.
This Mg-rich clay is the low-temperature product of
metasomatic reactions between the
quartzofeldspathic wall rocks and serpentinite blocks in
the fault.
Deformation of the mechanically unusual creeping
portions of the San Andreas fault system is controlled
by the presence of weak minerals rather than by high
fluid pressure or other proposed mechanisms
References 11. Zoback, M. D., et al. (1987), New evidence on the state of stress of
the San Andreas Fault, Science, 238, 1105–1111.
2. Scholz, C. H. (2000), Evidence for a strong San Andreas fault,
Geology, 28, 163– 166.
3. Zoback, M. D. (2000) Strength of the San Andreas. Nature 405, 31–32
4. Carpenter, B. M., C. Marone, and D. M. Saffer (2011) Weakness of the
San Andreas Fault revealed by samples from the active fault zone,
Nature Geoscience, doi: 10.1038/ngeo1089.
5. Wang, C-Y (2011) High pore pressure, or its absence, in the San
Andreas Fault, Geology, 39, 1047-1050, doi: 10.1130/G32294.1.
6. Zoback, M., Hickman, S. Ellsworth, W. and the SAFOD Science Team
(2011) Scientific Drilling Into the San Andreas Fault Zone — An Overview
of SAFOD’s First Five Years, doi:10.2204/iodp.sd.11.02.2011
7. Collettini, C., Niemeijer, A., Viti C. & Marone, C. (2009) Fault zone
fabric and fault weakness, Nature 462, 36,