Rupture cascades in a discrete element model of a porous sedimentary rock

We investigate the scaling properties of the sources of crackling noise in a fully-dynamic numerical model of sedimentary rocks subject to uniaxial compression. The model is initiated by filling a cylindrical container with randomly-sized spherical particles which are then connected by breakable beams. Loading at a constant strain rate the cohesive elements fail and the resulting stress transfer produces sudden bursts of correlated failures, directly analogous to the sources of acoustic emissions in real experiments. The source size, energy, and duration can all be quantified for an individual event, and the population analyzed for their scaling properties, including the distribution of waiting times between consecutive events. Despite the non-stationary loading, the results are all characterized by power law distributions over a broad range of scales in agreement with experiments. As failure is approached temporal correlation of events emerge accompanied by spatial clustering.Comment: 5 pages, 4 figure

Bose-Einstein condensates with attractive 1/r interaction: The case of self-trapping

Amplifying on a proposal by O'Dell et al. for the realization of Bose-Einstein condensates of neutral atoms with attractive $1/r$ interaction, we point out that the instance of self-trapping of the condensate, without external trap potential, is physically best understood by introducing appropriate "atomic" units. This reveals a remarkable scaling property: the physics of the condensate depends only on the two parameters $N^2 a/a_u$ and $\gamma/N^2$, where $N$ is the particle number, $a$ the scattering length, $a_u$ the "Bohr" radius and $\gamma$ the trap frequency in atomic units. We calculate accurate numerical results for self-trapping wave functions and potentials, for energies, sizes and peak densities, and compare with previous variational results. As a novel feature we point out the existence of a second solution of the extended Gross-Pitaevskii equation for negative scattering lengths, with and without trapping potential, which is born together with the ground state in a tangent bifurcation. This indicates the existence of an unstable collectively excited state of the condensate for negative scattering lengths.Comment: 7 pages, 7 figures, to appear in Phys. Rev.

Permeability evolution during progressive development of deformation bands in porous sandstones

[1] Triaxial deformation experiments were carried out on large (0.1 m) diameter cores of a porous sandstone in order to investigate the evolution of bulk sample permeability as a function of axial strain and effective confining pressure. The log permeability of each sample evolved via three stages: (1) a linear decrease prior to sample failure associated with poroelastic compaction, (2) a transient increase associated with dynamic stress drop, and (3) a systematic quasi-static decrease associated with progressive formation of new deformation bands with increasing inelastic axial strain. A quantitative model for permeability evolution with increasing inelastic axial strain is used to analyze the permeability data in the postfailure stage. The model explicitly accounts for the observed fault zone geometry, allowing the permeability of individual deformation bands to be estimated from measured bulk parameters. In a test of the model for Clashach sandstone, the parameters vary systematically with confining pressure and define a simple constitutive rule for bulk permeability of the sample as a function of inelastic axial strain and effective confining pressure. The parameters may thus be useful in predicting fault permeability and sealing potential as a function of burial depth and faul

The dilatancy-diffusion hypothesis and earthquake predictability

The dilatancy-diffusion hypothesis was one of the first attempts to predict the form of potential geophysical signals that may precede earthquakes, and hence provide a possible physical basis for earthquake prediction. The basic hypothesis has stood up well in the laboratory, where catastrophic failure of intact rocks has been observed to be associated with geophysical signals associated both with dilatancy and pore pressure changes. In contrast, the precursors invoked to determine the predicted earthquake time and event magnitude have not stood up to independent scrutiny. There are several reasons for the lack of simple scaling between the laboratory and the field scales, but key differences are those of scale in time and space and in material boundary conditions, coupled with the sheer complexity and non-linearity of the processes involved. 'Upscaling' is recognized as a difficult task in multi-scale complex systems generally and in oil and gas reservoir engineering specifically. It may however provide a clue as to why simple local laws for dilatancy and diffusion do not scale simply to bulk properties at a greater scale, even when the fracture system that controls the mechanical and hydraulic properties of the reservoir rock is itself scaleinvariant. © The Geological Society of London 2012

Acceleration and localization of subcritical crack growth in a natural composite material

Catastrophic failure of natural and engineered materials is often preceded by an acceleration and localization of damage that can be observed indirectly from acoustic emissions (AE) generated by the nucleation and growth of microcracks. In this paper we present a detailed investigation of the statistical properties and spatiotemporal characteristics of AE signals generated during triaxial compression of a sandstone sample. We demonstrate that the AE event amplitudes and interevent times are characterized by scaling distributions with shapes that remain invariant during most of the loading sequence. Localization of the AE activity on an incipient fault plane is associated with growth in AE rate in the form of a time-reversed Omori law with an exponent near 1. The experimental findings are interpreted using a model that assumes scale-invariant growth of the dominating crack or fault zone, consistent with the Dugdale-Barenblatt “process zone” model. We determine formal relationships between fault size, fault growth rate, and AE event rate, which are found to be consistent with the experimental observations. From these relations, we conclude that relatively slow growth of a subcritical fault may be associated with a significantly more rapid increase of the AE rate and that monitoring AE rate may therefore provide more reliable predictors of incipient failure than direct monitoring of the growing fault

A Poisson model for earthquake frequency uncertainties in seismic hazard analysis

Frequency-magnitude distributions, and their associated uncertainties, are of key importance in statistical seismology. When fitting these distributions, the assumption of Gaussian residuals is invalid since event numbers are both discrete and of unequal variance. In general, the observed number in any given magnitude range is described by a binomial distribution which, given a large total number of events of all magnitudes, approximates to a Poisson distribution for a sufficiently small probability associated with that range. In this paper, we examine four earthquake catalogues: New Zealand (Institute of Geological and Nuclear Sciences), Southern California (Southern California Earthquake Center), the Preliminary Determination of Epicentres and the Harvard Centroid Moment Tensor (both held by the United States Geological Survey). Using independent Poisson distributions to model the observations, we demonstrate a simple way of estimating the uncertainty on the total number of events occurring in a fixed time period.Comment: 9 pages, 3 figures; accepted by GRL after minor addition