Shear localization due to thermal pressurization of pore fluids in rapidly sheared granular media

Transcription

1 BIOT-5 Conference, Vienna, July 2013, Symposium MS02, Mechanics of fluid-infiltrated earth materials - in memory of Terzaghi and Biot Session MS02-2, Localization and failure, presentation MS02-2.1, 10 July, 2:00-2:20 pm Shear localization due to thermal pressurization of pore fluids in rapidly sheared granular media John D. Platt (Harvard University, USA) James R. Rice (Harvard University, USA) John W. Rudnicki (Northwestern University, USA)

2 Earthquake shear is highly localized Punchbowl PSS, composite based on Chester & Chester [Tectonophys 98] & Chester & Goldsby [SCEC 03] [Rice, JGR 2006] 5 mm

3 [Heermance, Shipton & Evans, BSSA, 2003] Core retrieved across the Chelungpu fault, which hosted the 1999 Mw 7.6 Chi-Chi, Taiwan, earthquake: Suggests slip at 328 m depth traverse was accommodated within a zone ~ μm thick.

4 Two other Chelungpu Fault,Taiwan boreholes [Boullier et al., GGG 2009, GSL 2011]: Principal Slip Zone (PSZ) localized within black gouges Hole A, fault at 1111 m depth: PSZ is ~2 cm thick A Hole B, fault at 1136 m depth: PSZ is ~3 mm thick PSZ layering defined by variations in concentrations of clay minerals and clasts, comparable to structures produced in high-rate rotary shear experiments. B

5 Median Tectonic Line Fault, Japan k, h 3 mm Wibberley (2003) q = k η f ( p ρ f g) = fluid flux relative to solid host

6 τ = f x (σ n p) Statically strong but dynamically weak faults, e.g., due to thermal weakening in rapid, large slip: Process expected to be important from start of seismic slip: - Thermal pressurization of in-situ pore fluid, reduces effective stress. Process that may set in at large enough rise in T: - Thermal decomposition, fluid product phase at high pressure (e.g., CO 2 from carbonates; H 2 O from clays or serpentines). Ultimately: - Melting at large slip, if above have not limited increase of T.

7 Two non-yielding half-spaces are moved relative to each other at a speed V. All deformation accommodated in gouge layer, leading to a nominal strain rate, γ 0 = V h.

8 Rice, Rudnicki & Platt (in prep for JGR 2013) To model the deforming gouge layer we use, Mechanical equilibrium Conservation of energy Conservation of fluid mass τ y = 0, σ n y = 0 2 T = τ γ ρc T t α th p t α hy y 2 2 p y 2 = Λ T t Shear stress modeled using the effective stress and rate-strengthening friction, γ τ = f ( γ )(σ n p) f ( γ ) = f 0 + (a b)log γ 0 ( We assume a b ( γ df ( γ )/d γ ) γ = γ > 0) 0

9 Shear between moving rigid blocks of perfectly insulating, impermeable material : Exact homogeneous shear solution (Lachenbruch, JGR, 1980,version ignoring dilatancy): τ(t) = f o ( σ n p(t) ) = f o σ n p a ( γ o = V / h) Linearized perturbation analysis : Λ ( )exp f o ρc γ ot, Is that solution stable to small perturbations? Not unless h is very small! Stable only if h W crit Typically, π f o a b f o a b >> 2 W crit π 2 a b f o 2 ( ) ρc α th + α hy f o Λ V ρc α th + α hy Λ V [W crit = λ shr / 2, where λ shr = longest wavelenth λ for stable linearized response to infinitesimal exp(2πiy / λ) perturbation].. h σ n V / 2 V / 2 τ(t) u(y,t) = γ o y = V h y Rice, Rudnicki & Platt (in prep for JGR 2013)

10 Estimates of maximum stable shear layer thickness (i.e., localized zone width) W crit : W crit = π f o a b Results, using f o = 0.4, ( ) ρc α th + α hy f o Λ V (indep. of σ n, but Λ, α hy, etc. may vary with σ n ) f o a b = 20, V = 1 m s, α th = 0.7 mm2, ρc = 2.7 MPa s ºC : Corresponding to ~ 7 km depth : Low estimate (Based on lab properties of intact Median Tectonic Line gouge [Wibberley and Shimamoto, 2003] at effective confining stress = 125 MPa and T = 200ºC): Λ = 0.70 MPa ºC, and α hy = 1.5 mm2 W crit = 3-5 μm s High estimate (Accounts very roughly for fresh damage of the initially intact fault gouge, introduced at the rupture front just before and during shear, by increasing permeability k to k dmg = 5-10 k, and increasing drained compressibility β d to β d dmg = βd ): Λ 0.34 MPa ºC, and α hy 3.5 mm2 s W crit μm Corresponding to ~ 1 km depth : Low estimate : W crit 25 μm High estimate : W crit 200 μm Rice, Rudnicki & Platt (in prep for JGR 2013)

11 Platt, Rudnicki & Rice (in prep for JGR 2013) Two non-yielding half-spaces are moved relative to each other at a speed V. All deformation accommodated in gouge layer leading to a nominal strain rate, γ o = V h

12 Platt, Rudnicki, and Rice (in prep for JGR 2013) Simulations using representative physical values show that strain localization does occur. Gouge layer y W Deformation has localized to a zone much thinner than the layer, W << h (43 μm << 1,000 μm). W nonlin. calc. is comparable to W lin. pert..

13 Weakening of the gouge layers during localization τ f o (σ n p a ) Platt, Rudnicki & Rice (in prep for JGR 2013) Vt / h Closely follows slip on a plane analysis of Rice [JGR, 2006], see also Mase & Smith [JGR,1987] Localization leads to additional weakening. τ = f o (σ n p a )exp Vt L * erfc Vt L * where L * = 2ρc f o Λ 2 ( α hy + α ) 2 th V

14 τ = f x (σ n p) Statically strong but dynamically weak faults, e.g., due to thermal weakening in rapid, large slip: Process expected to be important from start of seismic slip: - Thermal pressurization of in-situ pore fluid, reduces effective stress. Process that may set in at large enough rise in T: - Thermal decomposition, fluid product phase at high pressure (e.g., CO 2 from carbonates; H 2 O from clays or serpentines). Ultimately: - Melting at large slip, if above have not limited increase of T.

15 Examples, thermal decomposition: Dolomite, CaMg(CO 3 ) 2 (De Paola et al., Tectonics, 2008, Geology, 2011; Goren et al., J. Geophys. Res., 2010): At T ~ 550ºC, dolomite decomposes to calcite, periclase, and carbon dioxide: CaMg(CO 3 ) 2 CaCO 3 + MgO + CO 2 At T ~ ºC, the calcite further decomposes to lime and carbon dioxide: CaCO 3 CaO + CO 2 Many clays and hydrous silicates (Brantut et al., J. Geophys. Res., 2010): At T ~ 500ºC (~300ºC for smectite, ~ 800ºC for chlorite), decomposition releasing H 2 O starts. Gypsum, CaSO 4 (H 2 O) 2 ) (Brantut et al., Geology, 2010): At T ~ 100ºC, gypsum dehydrates to form bassanite: CaSO 4 (H 2 O) 2 CaSO 4 (H 2 O) H 2 O At T ~ 140ºC, bassanite turns into anhydrite CaS 4 (H 2 O)0.5 CaSO H 2 O

16 [Han, Shimamoto, Hirose, Ree & Ando, Sci., 2007]: Carbonate Faults Simulated faults in Carrara Marble at subseismic to seismic slip rates)

17 To model the deforming gouge layer we use, based on J. Sulem and co-workers (Vardoulakis, Brantut, Ghabezloo, Famin, Lazar, Noda, Schubnel, Stefanou, Veveakis, ), T t = τ γ ρc + α th p t = Λ T t + α hy 2 T y 2 E r 2 p y 2 + P r ξ t ξ t We assume that the reaction follows an Arrhenius kinetic law, ξ t = A( 1 ξ)exp Q RT Platt, Brantut & Rice (AGU, Fall 2011; in prep 2013 for JGR)

18 Platt, Brantut & Rice (AGU, Fall 2011; in prep 2013 for JGR) μ Linear perturbation estimate, localization zone width W, high T, fast reaction rate limit: W lin. pert. = π 2 α hy V (a b) f o 2 ρce r P r

19 Now we consider nonlinear simulations for a finite width gouge layer sheared between two non-yielding poroelastic half-spaces. Platt, Brantut & Rice (AGU, Fall 2011; in prep 2013 for JGR)

20 Platt, Brantut & Rice (AGU, Fall 2011; in prep 2013 for JGR) Distance from fault center, mm We now solve the system numerically for a 1 mm wide gouge layer. s -1 Accumulated slip, mm Accumulated slip, mm When the reaction becomes important, we observe significant strain localization (W nonlin. calc. of order ~ 2 x W lin. pert. ). Platt, Brantut & Rice (AGU, Fall 2011; in prep 2013 for JGR)

21 Distance from fault center, mm Our linear stability analysis predicts the localized zone width is independent of kinetic parameters. To test this we increase A by three orders of magnitude. s -1 Accumulated slip, mm Accumulated slip, mm The localized zone width has only decreased by a factor of two. Platt, Brantut & Rice (AGU, Fall 2011; in prep 2013 for JGR)

22 Distance from fault center, mm Now we investigate a case for which depletion of reactant is important. s -1 Accumulated slip, mm Accumulated slip, mm Depletion causes the zone of localized straining to migrate. The strain rate and reaction rate profiles are strongly coupled. Platt, Brantut & Rice (AGU, Fall 2011; in prep 2013 for JGR)

23 This localized zone migration leads to a complex, non-monotonic, strain history. Distance from fault center, mm Accumulated slip, mm Platt, Brantut & Rice (AGU, Fall 2011; in prep 2013 for JGR)

24 Courtesy of T. Mitchell -- dolomite rich clay gouge

25 o o o o o o

26 Particle size distribution for Ultracataclasite gouge hosting the Punchbowl pss [Chester et al., Nature, 2005] N(D)/A = number of particles per unit sample area with 2D /3< diameter < 4D /3. N(D)/A c / D 2 for 30 nm < D < 70 μm. In 3D: ˆN(D)/V ĉ / D 3 D 50 (= size such that 50% by mass are larger/smaller) ~ 1 μm. Standard granular material guideline (for narrow size range): thinnest possible shear zone ~5 to 10 D 50 5 to 10 μm