Absolute fault and crustal strength from wedge tapers

Absolute fault and crustal strength from wedge tapers Suppe, Geology, 2007 Let’s begin with a review of the history of FTB. . .

Overthrusting faults with displacement from a mile to more than 50 miles ? 1 st 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 Hall, 1815, 1976, http: //cnrs. fr/cw/dossiers/dosgeol/01 decouvrir

Overthrusting faults with displacement from a mile to more than 50 miles ? 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 plaster compressed First demonstration of the wedge theory 1912 : Wegner, plate tectonics theory, overthrusting over large distances finally accepted. Except by mechanicians ! 2 nd pb : How to explain overthrusting faults with displacement from miles to more than 50 miles? Cadell, 1890 http: //cnrs. fr/cw/dossiers/dosgeol/01 decouvrir

Mechanical paradox of overthrusts How to displace kilometers of rocks over such distances ? 1 st 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

Mechanical paradox of overthrusts 1978 : Chapple : Wedge -shaped concept, based on field observations Wedge dues to horizontal compression, no need to appeal for gravity. Appalaches Jura Roeder et al. , 1978, Homberg et al. , 2002

The critical Taper 1983 : Davis et al. : Mechanics of wedge analogue to soil or snow in front of a moving bulldozer. Nankai 7 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). Force equilibrium : Gravitational body force, pressure of water, frictional resistance to sliding along the basal decollement, compressive push : Thin-skinned structures allow small angles approximations :

The critical Taper No length scale : scale independent

The critical Taper Sandbox validation : Formula for dry and cohesionless sand : Application to taiwan wedge : No weak basal decollement considered ! basal friction = 0. 85, internal friction = 1. 1 !

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

Some results of theory 13

The exact solution Infinite solutions for a set of a/b

The exact solution

Applications : strength of wedges and faults ?

Strength of wedges and faults, Suppe, 2007 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

Strength of wedges and faults, Suppe, 2007 Application to Niger and Taiwan wedges : 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 And if only a single taper measurement?

Strength of wedges and faults, Suppe, 2007 Results for FTB in central western Taiwan : 0. 07 < F < 0. 11 CCL : Pore fluid pressure not a suficiant argument to explain weakness of faults : Dynamc mechanisms operating during EQ?

Limitations of the critical taper theory : 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?

Other studies : FEM Discret element models Minimization of dissipation Hardy et al. , 2009 Hardy et al. , 1998 Complete mechanical solution but : problem with displacement discontinuities Simple but : not the result of a mathematical theory needs predetermination of fault position (Hardy et al. , 1997)

Other studies : Limit Analysis Based on : force equilibrium and theory of maximum rock strength. The external approach of LA : searchs for un upper bound of the tectonic force necessary to obtain a rupture. Adopted kinematics : ramp and backthrust Research of the optimal thrust system yielding to the lower upper bound Positions and dips of ramp and back thrust predicted. Rigid translation along dicontinuities New thrust system adopted if lower upper bound Sequence of thrusts predicted

Upper bound on the tectonic force Other studies : Limit Analysis Shortening δ Parameters : α = 4°, β = 3. 5°, basal friction = 5°, internal friction = 30°, weakening = 15°

Other studies : Limit Analysis effect of the basal friction : Basal friction : 0. 26 0. 17 0. 087 Parameters: α = 4°, β = 3. 5°, internal friction = 30° (0. 57), weakening= 15° (0. 26)

Other studies : Limit Analysis effect of the ramp weakening : Ramp friction : 0. 46 0. 36 0. 26 Parameters: α = 4°, β = 3. 5°, internal friction = 30° (0. 57), basal friction = 15° (0. 26)

Other studies : Limit Analysis Applications : Nankai > 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 : 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, B 2, 1153 -1172. Dahlen, F. A. (1984), Noncohesive critical Coulomb wedges : an exact solution, J. Geophys. Res. , 89, B 12, 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, B 6, 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 (Mw. Z 7. 6) , 27, 2058– 2083