Directional dependence of P- and S-wave propagation and polarization in foliated rocks from the Kola superdeep well: Evidence from laboratory measurements and calculations based on TOF neutron diffraction

We have measured P- and S-wave velocities on two amphibolite and two gneiss samples from the Kola superdeep borehole as a function of pressure (up to 600 MPa) and temperature (up to 600 °C). The velocity measurements include compressional (Vp) and shear wave velocities (Vs1, Vs2) propagating in three orthogonal directions which were in general not parallel to inherent rock symmetry axes or planes. The measurements are accompanied by 3D-velocities calculations based on lattice preferred orientation (LPO) obtained by TOF (Time Of Flight) neutron diffraction analysis which allows the investigation of bulk volumes up to several cubic centimetres due to the high penetration depth of neutrons. The LPO-based numerical velocity calculations give important information on the different contribution of the various rock-forming minerals to bulk elastic anisotropy and on the relations of seismic anisotropy, shear wave splitting, and shear wave polarization to the structural reference frame (foliation and lineation). Comparison with measured velocities obtained for the three propagation directions that were not in accordance with the structural frame of the rocks (foliation and lineation) demonstrate that for shear waves propagating through anisotropic rocks the vibration directions are as important as the propagation directions. The study demonstrates that proper measurement of shear wave splitting by means of two orthogonal polarized sending and receiving shear wave transducers is only possible when their propagation and polarization directions are parallel and normal to foliation and lineation, respectively.     

Simplified Method for the Assessment of the Stiffness Anisotropy of Rocks at Small Strains

Summary A new, practically applicable method for characterizing the stiffness anisotropy of rocks is presented. The anisotropy of geo-materials is often ignored in engineering applications, with potentially serious ramifications, because of the number of parameters required for characterization. The elastic anisotropy has often been considered to be a function of mathematical symmetry, and the restrictions due to layering, microcracking and granularity of the materials have not been considered in the assessment of the anisotropy. The practicality of the method proposed here is achieved by rationally reducing the number of independent anisotropy parameters, typically 9 for orthotropic anisotropy, to a system of 4 independent parameters through a systematic theoretical and experimental analysis of these structural restrictions. These 4 parameters are shown to be sufficient for describing the anisotropy of some rocks and sands at small strains, and parameter determination by back-analysis is demonstrated to be stable using appropriate measurement systems involving 9 elastic wave velocities even when the directions of anisotropic axes are unknown and the velocity data contains appreciable error.     

An approach to model the mechanical behavior of transversely isotropic materials

The present work proposes an approach to adapt existing isotropic models to transversely isotropic materials. The main idea is to introduce equivalence relations between the real material and a fictitious isotropic one on which one can take all the advantages of the well‐established isotropic theory. Two applications of this approach are presented here: a failure criterion and a damage model that takes into account the load‐induced anisotropy. In both cases, theoretical predictions are in agreement with the experimental data. In the present paper, the developed approach is applied to sedimentary rock materials; nevertheless, it can be generalized to any material that exhibits transverse isotropy. Copyright © 2015 John Wiley & Sons, Ltd.     

Anisotropic damage of rock joints during cyclic loading: constitutive framework and numerical integration

This work describes a constitutive framework for modeling the behavior of rough joints under cyclic loading. Particular attention is paid to the intrinsic links between dilatancy, surface degradation, and mobilized shear strength. The framework also accounts for the important effect of shear‐induced anisotropy. The resulting approach is fully three‐dimensional and is not restricted to plane‐displacement kinematics. Both the governing formulation and an algorithm for implicit numerical integration are presented. While the proposed methods are general, we also postulate a specific model that is compared with experimental data. It employs relatively few free parameters but shows good agreement with laboratory tests. Copyright © 2013 John Wiley & Sons, Ltd.