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1

Thermodynamics with rotation motions: Fragmentation and slip

Majewski E., Teisseyre R.

Acta Geophysica

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2013

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Vol. 61, no. 2

281--310

EN

Basing on the Asymmetric Continuum Theory, we develop the thermodynamics including fragmentation spin fracture processes; applications for the earthquake source processes are considered. The fracture band model is used to describe a dislocation and disclination superlattice. The Gibbs free energy of defect formation is specified. A dynamic spin fracture criterion was formulated. Consequently, a dynamic model of rock fracture employing dislocations, disclinations, and cracks was constructed to describe slip and fragmentation fracture processes in the earthquake sources.

2

Induced strains and defect continuum theory: Internal reorganization of load

Teisseyre R., Górski M.

Acta Geophysica

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2012

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Vol. 60, no. 1

24-42

EN

Induced strains play an important role in mining regions and water dam areas. We consider a mechanism of reorganization of the applied stress load by some changes in rock-body defect distribution caused by human activity. A defect content increases with increasing stress load and related deformations; hence, a relationship could appear between seismic risk and deformation level. Recent progress in the Asymmetric Continuum Theory permits to consider some internal reorganization of the applied load due to internal defect content and distribution; in this paper we consider an increase of internal defect densities due to mining works and the appearance of reorganized internal stress distribution. A generalization of the Peach–Koehler forces acting on the defects makes it possible to define formation of induced strains; a character of resulting strains may essentially differ from the applied load. In the case of an axial load, this approach helps to understand formation of shear or rotational micro-fractures, usually recognized as fragmentation and slip motions.

3

Fluid theory with asymmetric molecular stresses: Difference between vorticity and spin equations

Teisseyre R.

Acta Geophysica

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2010

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Vol. 58, no. 6

1056-1071

EN

We present a new development in fluid theory, incorporating into it the velocity and spin fields; special attention is given to the structure of transport.The theory includes asymmetric molecular stresses and independent rotation velocity, i.e., spin. Our approach is based on our former studies on the asymmetric continuum theory with the balance and constitutive laws for displacement velocity and independent rotation motion, and points out the role of a related characteristic length unit. It is assumed that the vorticity caused by velocities can induce a spin transport counterpart. Thus, under certain conditions, an additional transport term due to rotational velocity fields may be incorporated to the velocity transport, which may lead to the vortex fields included directly into the theory. The Coriolis effect, important for the vortex processes, is considered and it is demonstrated that the motion equations in our asymmetric theory include this effect automatically. When confinining to 2D case, some compatibilities are found between the relations derived for the rotation motions and the moment formed by the Coriolis forces and applied to such motions. This is an important argument supporting our approach. The obtained nonlinear vortex equations (solitons) are derived and discussed for a stationary case.