S U M M A R YA viscoelastic damage rheology model is presented that provides a generalization of Maxwell viscoelasticity to a non-linear continuum mechanics framework incorporating material degradation and recovery, transition from stable to unstable fracturing and gradual accumulation of non-reversible deformation. The model is a further development of the damage rheology framework of Lyakhovsky et al. for evolving effective elasticity. The framework provides a quantitative treatment for macroscopic effects of evolving distributed cracking with local density represented by an intensive state variable. The formulation, based on thermodynamic principles, leads to a system of kinetic equations for the evolution of damage. An effective viscosity inversely proportional to the rate of damage increase is introduced to account for gradual accumulation of irreversible deformation due to dissipative processes. A power-law relation between the damage variable and elastic moduli leads to a non-linear coupling between the rate of damage evolution and the damage variable itself. This allows the model to reproduce a transition from stable to unstable fracturing of brittle rocks and the Kaiser effect. 3-D numerical simulations based on the model formulation for homogeneous and heterogeneous materials account for the main features of rock behaviour under large strain. The model coefficients are constrained, using triaxial laboratory experiments with low-porosity Westerly granite and high-porosity Berea sandstone samples.

The observation of localized stationary structures, coined oscillons, in granular media has evoked much interest. By parametric excitation of clay suspensions, we demonstrate a hysteretic transition to oscillon-type states in a nongranular medium. When the symmetry of up-down reflection 1 time translation is lost, these states undergo a transition to propagating localized states previously seen in Newtonian fluids. These observations are in accord with recent theoretical predictions of sufficient conditions for oscillon formation. In addition, a novel measurement technique for the effective suspension viscosity demonstrates their shear-thinning properties.

[1] Large-scale crustal deformation in the Levant is mainly related to the DST and the CFS. The former is an active left lateral transform, bounding the Arabian plate and the Sinai sub-plate, and the latter branches out of the former and separates the Sinai sub-plate into two tectonic domains. In this study we obtain the velocities of 33 permanent GPS stations and 145 survey stations that were surveyed in three campaigns between 1996 and 2008. We use a simple 1-D elastic dislocation model to infer the slip rate and locking depth along various segments of the DST. We infer a 3.1-4.5 mm/yr slip rate and a 7.8-16.5 km locking depth along the DST north of the CFS, and a slip rate of 4.6-5.9 mm/yr and locking depth of 11.8-24 km along the Jericho Valley, south of the CFS. Further south, along the Arava Valley we obtain a slip rate of 4.7-5.4 mm/yr and a locking depth of 12.1-23 km. We identify an oblique motion along the Carmel Fault with $0.7 mm/yr left-lateral and $0.6 mm/yr extension rates, resulting in N-S extension across the Carmel Fault. This result, together with the decrease in DST slip velocity from the Jericho Valley to the segment north of the CFS, confirms previous suggestions, according to which part of the slip between Arabia and Sinai is being transferred from the DST to the CFS.

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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.