[Paper Review] A Model for Athermal Strain Localization in Dry Sheared Fault Gouge

Xiao Ma, Ahmed Elbanna|arXiv (Cornell University)|Jan 11, 2017

earthquake and tectonic studies62 references3 citations

TL;DR

This paper presents a physics-based continuum model using Shear Transformation Zone (STZ) theory to simulate athermal strain localization in dry, sheared fault gouge. The model reveals that higher confining pressure, lower dilatancy, and looser initial conditions promote ductile shear banding, while lower pressure, higher loading rates, and higher dilatancy lead to brittle failure with significant strength drops.

ABSTRACT

Shear banding is widely observed in natural fault zones as well as in gouge layers in laboratory experiments. Understanding the dynamics of strain localization under different loading conditions is essential for quantifying strength evolution of fault gouge, energy partitioning during earthquakes and characterizing rheological transitions and fault zone structure changes. To that end, we develop a physics-based continuum model for strain localization in sheared granular materials. The grain-scale dynamics is described by the Shear Transformation Zone (STZ) theory, a non-equilibrium statistical thermodynamic framework for viscoplastic deformation in amorphous materials. Using a finite strain computational framework, we investigate the initiation and growth of complex shear bands under a variety of loading conditions and identify implication for strength evolution and ductile to brittle transition. Our numerical results show similar localization patterns to field and lab observations and suggest that shear zones show more ductile response at higher confining pressures, lower dilatancy and loose initial conditions. Lower pressures, higher loading rates and higher dilatancy favor a brittle response and larger strength drops. These findings shed light on a range of mechanisms for strength evolution in dry sheared gouge and provide a critical input to physics-based multiscale models of fault zone instabilities.

Motivation & Objective

• To develop a continuum-scale model that captures the dynamics of strain localization in dry, sheared fault gouge.
• To understand how varying confining pressure, loading rate, and initial density influence the transition from ductile to brittle behavior.
• To link microscale grain dynamics (via STZ theory) to macroscale fault zone rheology and strength evolution.
• To provide a predictive framework for fault zone instabilities and energy partitioning during earthquakes.
• To bridge the gap between laboratory observations and physics-based multiscale models of fault mechanics.

Proposed method

• The model is grounded in Shear Transformation Zone (STZ) theory, a non-equilibrium statistical thermodynamic framework for viscoplastic deformation in amorphous materials.
• A finite strain computational framework is employed to simulate the evolution of strain localization under various boundary conditions.
• Grain-scale plasticity is modeled through STZ activation, which governs localized shear band nucleation and growth.
• The model incorporates dilatancy effects and initial density variations to capture the influence of material state on deformation mode.
• Loading conditions—confining pressure, strain rate, and initial porosity—are systematically varied to assess their impact on failure behavior.
• Numerical simulations track the development of complex shear band patterns and quantify strength drops during localization.

Experimental results

Research questions

• RQ1 How does confining pressure influence the transition from ductile to brittle strain localization in dry fault gouge?
• RQ2 What role do initial density and dilatancy play in determining the mode of deformation (ductile vs. brittle) during shear localization?
• RQ3 How do loading rates affect the magnitude of strength drops during strain localization in granular fault gouge?
• RQ4 To what extent can STZ-based continuum modeling reproduce observed shear band patterns in laboratory and field settings?
• RQ5 What are the implications of these deformation modes for energy partitioning and fault zone rheology during seismic events?

Key findings

• The model reproduces complex shear band patterns consistent with both laboratory experiments and natural fault zone observations.
• Higher confining pressure leads to more ductile response, with localized strain distributed over broader zones.
• Lower confining pressure and higher loading rates promote localized, brittle-like failure with sharp strength drops.
• Increased initial dilatancy enhances the likelihood of brittle failure and larger strength reductions during localization.
• Loose initial conditions favor ductile deformation, whereas denser initial states promote earlier and more intense strain localization.
• The model demonstrates that strength evolution is strongly governed by the interplay between confining pressure, strain rate, and material state (density and dilatancy).