Absolute fault and crustal strength from wedge tapers Suppe, Geology, 2007 Let’s begin with a...

Absolute fault and crustal strength from wedge tapers

Suppe, Geology, 2007

Let’s begin with a review of the history of FTB...

1st pb : Overthrusting faults with displacement from a mile to more than 50 miles?

1815 : Hall demonstrated that a horizontal compression force was necessary to create folds.

First overthrust recognized by Weiss in 1826, near Dresden.

1843: Rogers brothers described the structure of the Appalachian mountains in Virginia and Pennsylvania as thrusts.

Scotland : thrust faults in northwest highlands of scotland first reported in 1861 by Nicol.

1875 : Eduard Suess proposed that horizontal movements could be the result of a lateral compression. Based on Elie de Beaumont work (1852), considering a contraction of the earth : the earth getting colder, it contracts and the crust becoming too big, folds and thrusts are formed.

1883 : Callaway described a displacement in the scotisch fold and thrust belt over one mile.1884 : Peach et Horne : thrust over 16 miles

Overthrusting faults with displacement from a mile to more than 50 miles ?

Hall, 1815, 1976, http://cnrs.fr/cw/dossiers/dosgeol/01 decouvrir

First analogue model of FTB :

1890 : Cadell : noticed that rocks in FTB seem to behave like rigid blocks sliding.Experiences with material able to fold and to break :wet sand and plaster compressedFirst demonstration of the wedge theory

1912 : Wegner, plate tectonics theory, overthrusting over large distances finally accepted.

Except by mechanicians !

2nd pb : How to explain overthrusting faults with displacement from miles to more than 50 miles?

Cadell, 1890http://cnrs.fr/cw/dossiers/dosgeol/01 decouvrir

Overthrusting faults with displacement from a mile to more than 50 miles ?

How to displace kilometers of rocks over such distances ?

1st ideas : gravity forces : need décollement dips equivalent to the internal friction !

1951 : Hafner calculated the internal stress distribution with elasticity equations, showed stress trajectories.

1959 : Hubbert and Rubbey for a rectangle with a basal decollement governed by a coulomb criterion, pushed by a horizontal force : Impossible to displace 5 km of rocks over these distances !

introduced the pore fluid pressure : Water acts as a lubricant and reduces the coefficient of sliding friction. Clays and fault gouge also.

Mechanical paradox of overthrusts

1978 : Chapple : Wedge-shaped concept, based on field observations

Wedge dues to horizontal compression, no need to appeal for gravity.

Jura

Appalaches

Roeder et al., 1978, Homberg et al., 2002


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1983 : Davis et al. : Mechanics of wedge analogue to soil or snow in front of a moving bulldozer.

Nankai

Morgan and Karig, 1994

The critical Taper

QuickTime™ et undécompresseur Photo - JPEG

sont requis pour visionner cette image.

QuickTime™ et undécompresseur Photo - JPEG


Unstable wedge

Supercritical wedge

The critical Taper

Coulomb criterion : Rock deformation in the upper lithosphere is governed by pressure dependent and time independent coulomb behavior ie by brittle fracture (Paterson, 1978) or frictional sliding (Byerlee, 1978).

Thin-skinned structures allow small angles approximations :

Force equilibrium : Gravitational body force, pressure of water, frictional resistance to sliding along the basal decollement, compressive push :

The critical Taper

No length scale : scale independent

The critical Taper

No weak basal decollement considered !basal friction = 0.85, internal friction = 1.1 !

Formula for dry and cohesionless sand :

Sandbox validation :

Application to taiwan wedge :

The critical Taper

http://www.cnrs.fr/cw/dossiers/dosgeol/01_decouvrir/02_subduction/03_prismes

QuickTime™ et undécompresseur Sorenson Video


QuickTime™ et undécompresseur Sorenson Video


Some results of the theory

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QuickTime™ et undécompresseur TIFF (non compressé)


Jolivet

QuickTime™ et undécompresseur TIFF (non compressé)


Jolivet

Some results of the theory

Infinite solutions for a set of a/b

The exact solution

The exact solution

Applications : strength of wedges and faults ?

Dahlen 1990 exact solution :

Fault-strength term :

Wedge-strength term :

Simplified equation :

F is the normalized basal traction :

W is the normalized differential stress :3

Strength of wedges and faults, Suppe, 2007

Validation with sandbox experiments of Davis et al. 1983 :

Sand dry and cohesionless > basal and internal frictions directly determined

> F = basal friction

> W = internal friction


For real structures > only F and W can be determined :

W= 0.6 and 0.7 F= 0.08 and 0.04


Application to Niger and Taiwan wedges :

And if only a single taper measurement?


Results for FTB in central western Taiwan :

CCL :Pore fluid pressure not a suficiant argument to explain weakness of faults :Dynamc mechanisms operating during EQ?


0.07 < F < 0.11

Mean used for the topography slope and for the décollement dip, Effects of small topographic variations on the critical state ?

Formula for critical state, how to determine basal and internal friction for supercritical wedges ?

What about ramps and their frictions?What about sequence of thrusts? How to localise thrusts? What

controls spacing, lifetime, number of thrusts?

Limitations of the critical taper theory :

FEM Discret element models Minimization of dissipation

Other studies :

Complete mechanical solutionbut :

problem with displacement discontinuities

Hardy et al., 2009

Simplebut :

not the result of a mathematical theoryneeds predetermination of fault position

(Hardy et al., 1997)

Hardy et al., 1998

Based on : force equilibrium and the theory of

maximum rock strength.

The external approach of LA : searchs for un upper bound of the tectonic

force necessary to obtain a rupture.

Other studies : Limit Analysis

Adopted kinematics : ramp and backthrust

Research of the optimal thrust system yielding to the lower upper bound

Rigid translation along dicontinuities

New thrust system adopted if lower upper bound

Sequence of thrusts predicted

Sequence of thrusts predicted

Positions and dips of ramp and back thrust predicted.

Positions and dips of ramp and back thrust predicted.

Parameters : α = 4°, β = 3.5°, basal friction = 5°, internal friction = 30°, weakening = 15°

Shortening δ

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effect of the basal friction :

Parameters: α = 4°, β = 3.5°, internal friction = 30° (0.57), weakening= 15° (0.26)

0.087

0.17

0.26

Basal friction :


effect of the ramp weakening :

Parameters: α = 4°, β = 3.5°, internal friction = 30° (0.57), basal friction = 15° (0.26)

0.26

0.36

0.46

Ramp friction :


> by inversion, we can retrieve ramp and basal frictions (assuming the internal friction) Avtge : weak ramp

> by inversion, if 2 active thrusts, same force, friction of each ramp (assuming the basal friction)


Applications : Nankai


Applications : Taiwan

Hall J. (1815), On the vertical position and convolution of certain strata, and their relation with granite, Transactions of the Royal Society, London, 7, p. 79-108.

Cadell H. M. (1888), Experimental researches in mountain building, Royal Soc. Edinburgh Transactions, 35, 337-360.

Hafner, W., (1951), Stress distributions and faulting, Bulletin of the Geological Society of America, 62, 373-398.

Hubbert and Rubbey (1959), Role of fluid pressure in mechanics of overthrust faulting, BGSA, vol. 70, 115-166

Davis, D., J. Suppe and F.A. Dahlen (1983), Mechanics of Fold-and-Thrust Belts and Accretionary Wedges, J. Geophys. Res., 88, B2, 1153-1172.

Dahlen, F.A. (1984), Noncohesive critical Coulomb wedges : an exact solution, J. Geophys. Res., 89, B12, 10125-10133.

Lallemand, S.E., P. Schnurle and J. Malavieille (1994), Coulomb theory applied to accretionary and nonaccretionary wedges : Possible causes for tectonic erosion and/or frontal accretion, J. Geophys. Res., 99, B6, 12,033-12,055.

Suppe J. (2007),

Buiter, S.J.H., A.Y. Babeyko, S. Ellis , T.V. Gerya, B.J.P. Kaus, A. Kellner, G. Schreurs and Y. Yamada (2006), The numerical sandbox : comparison of model results for a shortening and an extension experiment, in Analogue and numerical model ling of crustal-scale processes, edited by S.J.H. Buiterand G. Schreurs, 29-64, London Geol. Soc. Spec. Publ.

Hardy, S., C. Duncan, J. Masek and D. Brown (1998), Minimum work, fault activity and the growth of critical wedges in fold and thrust belts, Basin Research, 10, 365-373.

Hardy

Cubas N., Leroy Y.M., Maillot B. (2009), Prediction of thrusting sequences in accretionnary wedges, Journal of Geophysical Research.

Yue, Suppe, Hung (2005), Structural geology of a classic thrust belt earthquake: the 1999 Chi-Chi earthquake Taiwan (MwZ7.6) , 27, 2058–2083

Absolute fault and crustal strength from wedge tapers Suppe, Geology, 2007 Let’s begin with a...

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