Coupled evolution of damage and porosity in poroelastic media: theory and applications to deformation of porous rocks

Abstract

S U M M A R YWe address the gradual transition from brittle failure to cataclastic flow under increasing pressures by a new model, incorporating damage rheology with Biot's poroelasticity. Deformation of porous rocks is associated with growth of two classes of internal flaws, namely cracks and pores. Cracks act as stress concentrations promoting brittle failure, whereas pores dissipate stress concentrations leading to distributed deformation. The present analysis, based on thermodynamic principles, leads to a system of coupled kinetic equations for the evolution of damage along with porosity. Each kinetic equation represents competition between cracking and irreversible porosity change. In addition, the model correctly predicts the modes of strain localization such as dilating versus compacting shear bands. The model also reproduces shear dilatancy and the related change of fluid pressure under undrained conditions. For triaxial compression loading, when the evolution of porosity and damage is taken into consideration, fluid pressure first increases and then decreases, after the onset of damage. These predictions are in agreement with experimental observations on sandstones. The new development provides an internally consistent framework for simulating coupled evolution of fracturing and fluid flow in a variety of practical geological and engineering problems such as nucleation of deformation features in poroelastic media and fluid flow during the seismic cycle.

Shear Band Formation in Numerical Simulations Applying a Continuum Damage Rheology Model

“…16-20) could not be satisfied for m \ 0.2. Homogeneous compression and weak localization (or lack of it) in compression tests with high confining stress (i.e., [200 MPa and/or m & 0.2 and therefore n & n 0 ) are in agreement with experimental results (e.g., WONG et al, 1997;WU, 2000;MENENDEZ, 1996), with recent studies of compaction bands and compacting shear bands (CHALLA and ISSEN, 2004;ISSEN 2008) and with theoretical and numerical analysis of a coupled damage-porosity model (HAMIEL et al, 2004b(HAMIEL et al, , 2005. The conditions in which strain is not localized along shear-bands could represent a transition from brittle failure to distributed cataclastic flow in which compaction, pore collapse, strain-hardening and intensive grain crushing is dominant (WU 2000;MENENDEZ 1996).…”

Time-scale invariant changes in atmospheric radon concentration and crustal strain prior to a large earthquake

“…Biot, 1954;Lyakhovsky et al, 1993Lyakhovsky et al, , 1997Ben-Zion and Lyakhovsky, 2002;Turcotte et al, 2003;Hamiel et al, 2004;Nanjo and Turcotte, 2005;. The irreversible thermodynamic model is used to describe the macroscopic viscoelastic (or elastic) behaviour with microscopic damage evolution such as microcracking.…”

“…At α=0, the material is undamaged, and failed at a critical value of α c . Hamiel et al (2004) discussed the deformation of porous rocks by using this damage parameter and the porosity separately. We consider the two parameters as one, and define the porosity to be the volume fraction of interstitial spaces including cracks, pores and their assemblies along wide fissures such as fault zone, without loss of generality as far as irreversible thermodynamics (e.g.…”

“…5.1, let us consider damage mechanics with radon migration, defined by Helmholtz free energy of unit volume F = F (T , ε, α, c, ζ ) where ε is the macroscopic elastic strain, and ζ is the volume of the fluid content (e.g. de Groot and Mazur, 1962;Jou et al, 2001;Hamiel et al, 2004). Then, the total differential of F is given by…”

A Systematic Analysis of Seismic Moment Tensor at The Geysers Geothermal Field, California

“…(2) Strain from an initial shear dislocation could cause elevated pore pressures in a sealed region around the dislocation. If pore pressure could exceed the minimum local stress, the pore fluids could subsequently dilate pathways opened up from faulting damage (Ashby and Sammis, 1990;Lyakhovsky et al, 1997;Johnson and Sammis, 2001;Hamiel et al, 2004;Ben-Zion and Ampuero, 2009). …”