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 : 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 : Callaway described a displacement in the scotisch fold and thrust belt over one mile : Peach et Horne : thrust over 16 miles Overthrusting faults with displacement from a mile to more than 50 miles ? Hall, 1815, 1976, 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 compressed First 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, 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 : 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 Mechanical paradox of overthrusts

: 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

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

Some results of the theory

13 Some results of the theory

Infinite solutions for a set of a/b 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 : Sand dry and cohesionless > basal and internal frictions directly determined > F = basal friction > W = internal friction Strength of wedges and faults, Suppe, 2007

For real structures > only F and W can be determined : W= 0.6 and 0.7 F= 0.08 and 0.04 Strength of wedges and faults, Suppe, 2007 Application to Niger and Taiwan wedges :

And if only a single taper measurement? Strength of wedges and faults, Suppe, 2007

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? Strength of wedges and faults, Suppe, < 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 solution but : problem with displacement discontinuities Hardy et al., 2009 Simple but : not the result of a mathematical theory needs 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 Upper bound on the tectonic force Other studies : Limit Analysis

effect of the basal friction : Parameters: α = 4°, β = 3.5°, internal friction = 30° (0.57), weakening= 15° (0.26) Basal friction : Other studies : Limit Analysis

effect of the ramp weakening : Parameters: α = 4°, β = 3.5°, internal friction = 30° (0.57), basal friction = 15° (0.26) Ramp friction : Other studies : Limit Analysis

> 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) Other studies : Limit Analysis Applications : Nankai

Other studies : Limit Analysis Applications : Taiwan

Other studies : Limit Analysis Applications : Taiwan

Other studies : Limit Analysis Applications : Taiwan

Other studies : Limit Analysis Applications : Taiwan

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