Pure cross-anisotropy for geotechnical elastic potentials

The pure cross-anisotropy is understood as a special scaling of strain (or stress). The scaled tensor is used as an argument in the elastic stiffness (or compliance). Such anisotropy can be overlaid on the top of any elastic stiffness, in particular on one obtained from an elastic potential with its own stress-induced anisotropy. This superposition does not violate the Second Law. The method can be also applied to other functions like plastic potentials or yield surfaces, wherever some cross-anisotropy is desired. The pure cross-anisotropy is described by the sedimentation vector and at most two constants. Scaling with more than two purely anisotropic constants is shown impossible. The formulation was compared with experiments and alternative approaches. Static and dynamic calibration of the pure anisotropy is also discussed. Graphic representation of stiffness with the popular response envelopes requires some enhancement for anisotropy. Several examples are presented. All derivations and examples were accomplished using the algebra program Mathematica.

Measuring SHmax with Stress-Induced Anisotropy in Nonlinear Anelastic Behavior

Mechanical stress acting in the Earth`s crust is a fundamental property that has a wide range of geophysical applications, from tectonic movements to energy production. The orientation of maximum horizontal compressive stress, SHmax can be estimated by inverting earthquake source mechanisms and directly from borehole-based measurements, but large regions of the continents have few or no observations. Available observations often represent a variety of length scales and depths, and can be difficult to reconcile. Here we present a new approach to determine SHmax by measuring stress induced anisotropy of nonlinear susceptibility. We observe that nonlinear susceptibility is azimuthally dependent in the Earth and maximum when parallel to SHmax, as predicted by laboratory experiments. Our measurements use empirical Green’s functions that are applicable for different temporal and spatial scales. The method can quantify the orientation of SHmax in regions where no measurements exist today.

A hyperelastic model for soils with stress-induced and inherent anisotropy

In this paper, modelling of the superposition of stress-induced and inherent anisotropy of soil small strain stiffness is presented in the framework of hyperelasticity. A simple hyperelastic model, capable of reproducing variable stress-induced anisotropy of stiffness, is extended by replacement of the stress invariant with mixed stress–microstructure invariant to introduce constant inherent cross-anisotropic component. A convenient feature of the new model is low number of material constants directly related to the parameters commonly used in the literature. The proposed description can be incorporated as a small strain elastic core in the development of some more sophisticated hyperelastic-plastic models of overconsolidated soils. It can also be used as an independent model in analyses involving small strain problems, such as dynamic simulations of the elastic wave propagation. Various options and features of the proposed anisotropic hyperelastic model are investigated. The directional model response is compared with experimental data available in the literature.

Distinguishing between Stress-induced and Structural Anisotropy at Mount Ruapehu Volcano

We have created a benchmark of spatial variations in shear wave anisotropy around Mount Ruapehu, New Zealand, against which to measure future temporal changes. Anisotropy in the crust is often assumed to be caused by stress-aligned microcracks, and the polarization of the fast quasi-shear wave (φ) is thus interpreted to indicate the direction of maximum horizontal stress, but can also be due to aligned minerals or macroscopic fractures. Changes in seismic anisotropy have been observed following a major eruption in 1995/96 and were attributed to changes in stress from the depressurization of the magmatic system. Three-component broadband seismometers have been deployed to complement the permanent stations that surround Ruapehu, creating a combined network of 34 three-component seismometers. This denser observational network improves the resolution with which spatial variations in seismic anisotropy can be examined. Using an automated shear wave splitting analysis, we examine local earthquakes in 2008. We observe a strong azimuthal dependence of φ and so introduce a spatial averaging technique and two-dimensional tomography of recorded delay times. The anisotropy can be divided into regions in which φ agrees with stress estimations from focal mechanism inversions, suggesting stress-induced anisotropy, and those in which φ is aligned with structural features such as faults, suggesting structural anisotropy. The pattern of anisotropy that is inferred to be stress related cannot be modeled adequately using Coulomb modeling with a dike-like inflation source. We suggest that the stress-induced anisotropy is affected by loading of the volcano and a lithospheric discontinuity. Copyright 2011 by the American Geophysical Union.

Distinguishing between Stress-induced and Structural Anisotropy at Mount Ruapehu Volcano

We have created a benchmark of spatial variations in shear wave anisotropy around Mount Ruapehu, New Zealand, against which to measure future temporal changes. Anisotropy in the crust is often assumed to be caused by stress-aligned microcracks, and the polarization of the fast quasi-shear wave (φ) is thus interpreted to indicate the direction of maximum horizontal stress, but can also be due to aligned minerals or macroscopic fractures. Changes in seismic anisotropy have been observed following a major eruption in 1995/96 and were attributed to changes in stress from the depressurization of the magmatic system. Three-component broadband seismometers have been deployed to complement the permanent stations that surround Ruapehu, creating a combined network of 34 three-component seismometers. This denser observational network improves the resolution with which spatial variations in seismic anisotropy can be examined. Using an automated shear wave splitting analysis, we examine local earthquakes in 2008. We observe a strong azimuthal dependence of φ and so introduce a spatial averaging technique and two-dimensional tomography of recorded delay times. The anisotropy can be divided into regions in which φ agrees with stress estimations from focal mechanism inversions, suggesting stress-induced anisotropy, and those in which φ is aligned with structural features such as faults, suggesting structural anisotropy. The pattern of anisotropy that is inferred to be stress related cannot be modeled adequately using Coulomb modeling with a dike-like inflation source. We suggest that the stress-induced anisotropy is affected by loading of the volcano and a lithospheric discontinuity. Copyright 2011 by the American Geophysical Union.