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Research Papers

Strain Localization and Slip Instability in a Strain-Rate Hardening, Chemically Weakening Material

[+] Author and Article Information
N. Brantut1

 Department of Earth Sciences, University College London, Rock and Ice Physics Laboratory, WC1E 6BT London, UK; Laboratoire de Géologie, CNRS UMR 8538École Normale Supérieure, 24 rue Lhomond, 75005 Paris, Francenicolas.brantut@normalesup.org

J. Sulem

CERMES, UR NavierÉcole des Ponts ParisTech,  Université Paris-Est,6, 8 avenue Blaise Pascal, 77455 Marne-la-Vallée Cedex 2, Francejean.sulem@enpc.fr

1

Corresponding author.

J. Appl. Mech 79(3), 031004 (Apr 05, 2012) (10 pages) doi:10.1115/1.4005880 History: Received June 30, 2011; Revised January 11, 2012; Posted February 06, 2012; Published April 04, 2012; Online April 05, 2012

The stability of steady slip and homogeneous shear is studied for rate-hardening materials undergoing chemical reactions that produce weaker materials (reaction-weakening process), in drained conditions. In a spring- slider configuration, a linear perturbation analysis provides analytical expressions of the critical stiffness below which unstable slip occurs. In the framework of a frictional constitutive law, numerical tests are performed to study the effects of a nonlinear reaction kinetics on the evolution of the instability. Slip instabilities can be stopped at relatively small slip rates (only a few orders of magnitude higher than the forcing velocity) when the reactant is fully depleted. The stability analysis of homogeneous shear provides an independent estimate of the thickness of the shear localization zone due to the reaction weakening, which can be as low as 0.1 m in the case of lizardite dehydration. The potential effect of thermo-chemical pore fluid pressurization during dehydration is discussed, and shown to be negligible compared to the reaction-weakening effect. We finally argue that the slip instabilities originating from the reaction-weakening process could be a plausible candidate for intermediate depth earthquakes in subduction zones.

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Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 6

Contours of strain rate as a function of time and space

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Figure 7

Strain rate (solid line) and reaction extent (dotted line) profiles at the peak localization. The theoretical prediction is shown in red.

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Figure 8

Maximum real part of the normalized growth rate as a function of the normalized perturbation wavelength, computed from Eq. (76). Parameter values are reported in Table 1; hydraulic diffusivity is equal to thermal diffusivity. In the reaction weakening regime (β > 0, here β = 0.83, solid lines), thermal pressurization (TP) does not affect the stability condition and the critical wavelength. In absence of reaction weakening (β = 0, dotted lines), localization is driven by thermal pressurization (see Refs. [26-28]). The black dotted line never crosses the s̃ = 0 line.

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Figure 4

Regularized reaction kinetics used in the numerical stability analysis

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Figure 5

Numerical illustration of the transition from slip instability (solid red and black lines) to slip stability (dotted and dashed block lines). The critical stiffness calculated from Eq. 39 is kcr  = 5.75 × 108 Pa/m. For k = 3 × 108 Pa/m (solid black line), the growth rate of the instability is low, and the reactant is rapidly fully depleted.

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Figure 9

Non-dimensional critical stiffness Kcr as a function of chemical pressurisation parameter Π, for various hydraulic diffusivities. The shaded area corresponds to realistic values of Π. At low values of Π, the critical stiffness converges to a fixed value corresponding to the drained case.

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Figure 1

Schematic of the spring-slider configuration. The fault zone (thickness h) is loaded remotely through an elastic medium of equivalent stiffness k. The constant effective normal stress is σ′ = σ - p, where p is the pore pressure.

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Figure 2

Linearization of the Arrhenius law around Teq ; the cutoff temperature Tc is the intersect of the slope with the T axis

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Figure 3

Constitutive relation for the reacting rock. (a) For constant strain rate, the shear stress decreases as reaction progresses. (b) At a given extent of reaction, the shear stress increases with increasing strain rate.

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