mechanics of faulting - 國立臺灣大學 · 2017. 4. 26. · critical-taper wedge mechanics...

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

Critical-taper wedge

taper = ab


Critical-taper wedge mechanics


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)


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.


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…


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


Wedge-strength constraints


Thermal anomaly in post Chi-Chi boreholes


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


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


Relationship between ZFRD and Hubbert & Rubey effect….

(1 ) 0.6ZFRD

Z

need Z > 5ZFRD or ~10-15 km for Taiwan


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…


Continual deformation of new rock along axial surfaces….

Weak faults and strong crust…



Fault bends must be the locus of crustal strength…


Contrasting crustal strengths…


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


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

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,

mechanics of faulting - 國立臺灣大學 · 2017. 4. 26. · critical-taper wedge mechanics...

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