Time-lapse reconstruction of the fracture front from diffracted waves arrivals in laboratory hydraulic fracture experiments*

Summary 4D acoustic imaging via an array of 32 sources / 32 receivers is used to monitor hydraulic fracture propagating in a 250 mm cubic specimen under a true-triaxial state of stress. We present a method based on the arrivals of diffracted waves to reconstruct the fracture geometry (and fluid front when distinct from the fracture front). Using Bayesian model selection, we rank different possible fracture geometries (radial, elliptical, tilted or not) and estimate model error. The imaging is repeated every 4 seconds and provide a quantitative measurement of the growth of these low velocity fractures. We test the proposed method on two experiments performed in two different rocks (marble and gabbro) under experimental conditions characteristic respectively of the fluid lag-viscosity (marble) and toughness (gabbro) dominated hydraulic fracture propagation regimes. In both experiments, about 150 to 200 source-receiver combinations exhibit clear diffracted wave arrivals. The results of the inversion indicate a radial geometry evolving slightly into an ellipse towards the end of the experiment when the fractures feel the specimen boundaries. The estimated modelling error with all models is of the order of the wave arrival picking error. Posterior estimates indicate an uncertainty of the order of a millimeter on the fracture front location for a given acquisition sequence. The reconstructed fracture evolution from diffracted waves is shown to be consistent with the analysis of 90○ incidence transmitted waves across the growing fracture.

Hydrodynamic descriptions for surface roughness in fracture front propagation

Fracture is ubiquitous in a crystalline material. Inspired by the observed phenomenological similarities between the spatial profile of a fractured surface and velocities in hydrodynamic turbulence, we set up a hydrodynamic description for the dynamics of fracture surface propagation mode I or opening fracture front. We consider several related continuum hydrodynamic models and use them to extract the similarities between the profile of a fractured surface and velocities in hydrodynamic turbulence. We conclude that a fractured surface should be generically self-similar with an underlying multifractal behaviour. This article is part of the theme issue ‘Statistical physics of fracture and earthquakes’.

Spatially-ordered nano-sized crystallites formed by dehydration-induced single crystal cracking of CuCl2·2(H2O)

The dehydration of CuCl2·2(H2O) crystals is studied as an example of a fracture-assisted chemical reaction. The structure of the combined reaction–fracture front undergoes a spontaneous morphology transition, leading to spatial ordering and 8-fold acceleration of the reaction.

Fault Growth and Acoustic Emissions in Confined Granite

The failure process in a brittle granite was studied by using acoustic emission techniques to obtain three dimensional locations of the microfracturing events. During a creep experiment the nucleation of faulting coincided with the onset of tertiary creep, but the development of the fault could not be followed because the failure occurred catastrophically. A technique has been developed that enables the failure process to be stabilized by controlling the axial stress to maintain a constant acoustic emission rate. As a result the post-failure stress-strain curve has been followed quasi-statically, extending to hours the fault growth process that normally would occur violently in a fraction of a second. The results from the rate-controlled experiments show that the fault plane nucleated at a point on the sample surface after the stress-strain curve reached its peak. Before nucleation, the microcrack growth was distributed throughout the sample. The fault plane then grew outward from the nucleation site and was accompanied by a gradual drop in stress. Acoustic emission locations showed that the fault propagated as a fracture front (process zone) with dimensions of 1 to 3 cm. As the fracture front passed by a given fixed point on the fault plane, the subsequent acoustic emission would drop. When growth was allowed to progress until the fault bisected the sample, the stress dropped to the frictional strength. These observations are in accord with the behavior predicted by Rudnicki and Rice’s bifurcation analysis but conflict with experiments used to infer that shear localization would occur in brittle rock while the material is still hardening.

The fracture of glassy polymers

The fracture of glassy polymers starts with the separation of molecule bundles which then form a craze; this is followed by the fracture or rupture of the craze by sliding of the molecule bundles. The first process has the approximate characteristics of brittle fracture, the second those of viscous flow; at low velocities, therefore, the crack extends by the essentially viscous mechanism in the craze layer, whereas at higher velocity the stress required for this rises so high that either a quasi-brittle fracture occurs between the craze and the adjacent bulk polymer (for example, in polystyrene), or patches of craze arise in the bulk ahead of, and away from, the propagating fracture front, as in cast polymethylmethacrylate (PMMA). When the craze wedge ahead of the ‘ viscous ’ crack in the craze layer suddenly peels off the adjacent bulk polymer, either multiple crazes and cracks arise, radiating from its edge, or a new craze wedge is initiated. In either case only one craze wedge propagates, and it drops off the adjacent bulk when the rate of stretching of the craze (normal to its plane) reaches a critical magnitude. The repetition of this process results in the well known striation of the surface of fracture in polystyrene and other polymers. Since the fracture mechanism includes an essentially velocity-dependent viscous process, the Griffith theory cannot be applied to glassy polymers even as an approximation. The work of fracture oscillates by orders of magnitude within microseconds in the region of striations.