Anisotropic properties of fracture zone in sandstone inferred from seismic moment tensors of acoustic emissions.

An application of a moment tensor analysis to acoustic emission (AE) is studied to elucidate crack types and orientations of AE sources. In the analysis, simplified treatment is desirable, because hundreds of AE records are obtained from just one experiment and thus sophisticated treatment is realistically cumbersome. Consequently, a moment tensor inversion based on P wave amplitude is employed to determine six independent tensor components. Selecting only P wave portion from the full‐space Green's function of homogeneous and isotropic material, a computer code named SiGMA (simplified Green's functions for the moment tensor analysis) is developed for the AE inversion analysis. To classify crack type and to determine crack orientation from moment tensor components, a unified decomposition of eigenvalues into a double‐couple (DC) part, a compensated linear vector dipole (CLVD) part, and an isotropic part is proposed. The aim of the decomposition is to determine the proportion of shear contribution (DC) and tensile contribution (CLVD + isotropic) on AE sources and to classify cracks into a crack type of the dominant motion. Crack orientations determined from eigenvectors are presented as crack‐opening vectors for tensile cracks and fault motion vectors for shear cracks, instead of stereonets. The SiGMA inversion and the unified decomposition are applied to synthetic data and AE waveforms detected during an in situ hydrofracturing test. To check the accuracy of the procedure, numerical experiments are performed on the synthetic waveforms, including cases with 10% random noise added. Results show reasonable agreement with assumed crack configurations. Although the maximum error is approximately 10% with respect to the ratios, the differences on crack orientations are less than 7°. AE waveforms detected by eight accelerometers deployed during the hydrofracturing test are analyzed. Crack types and orientations determined are in reasonable agreement with a predicted failure plane from borehole TV observation. The results suggest that tensile cracks are generated first at weak seams and then shear cracks follow on the opened joints.

SUMMARY Seismic moment tensors can provide information on the size and orientation of fractures producing acoustic emissions (AEs) and on the stress conditions in the sample. The moment tensor inversion of AEs is, however, a demanding procedure requiring carefully calibrated sensors and accurate knowledge of the velocity model. In field observations, the velocity model is usually isotropic and time independent. In laboratory experiments, the velocity is often anisotropic and time dependent and attenuation might be significant due to opening or closure of microcracks in the sample during loading. In this paper, we study the sensitivity of the moment tensor inversion to anisotropy of P-wave velocities and attenuation. We show that retrieved moment tensors critically depend on anisotropy and attenuation and their neglect can lead to misinterpretations of the source mechanisms. The accuracy of the inversion also depends on the fracturing mode of AEs: tensile events are more sensitive to P-wave anisotropy and attenuation than shear events. We show that geometry of faulting in anisotropic rocks should be studied using the source tensors, since the P- and T-axes of the moment tensors are affected by velocity anisotropy and deviate from the true orientation of faulting. The stronger the anisotropy is, the larger the deviations are. Finally, we prove that the moment tensor inversion applied to a large dataset of AEs can be utilized to provide information on the attenuation parameters of the rock sample. The method is capable of measuring anisotropic attenuation in the sample and allows for detection of dilatant cracking according to the stress regime.

Transgranular microcracking is fundamental for the initiation and propagation of all fractures in rocks. The geometry of these microcracks is primarily controlled by the interaction of the imposed stress field with the mineral elastic properties. However, the effects of anisotropic elastic properties of minerals on brittle fracture are not well understood. This study examines the effects of elastic anisotropy of quartz on the geometry of brittle fracture and related acoustic emissions (AE) developed during indentation experiments on single crystals at ambient pressure and temperature. A Hertzian cone crack developed during blunt indentation of a single crystal of flawless Brazilian quartz parallel to the c axis shows geometric deviation away from predictions based on the isotropic case, consistent with trigonal symmetry. The visible cone crack penetration depth varies from 3 to 5 mm and apical angle from 53° to 40°. Electron backscatter diffraction (EBSD) mapping of the crack tip shows that fracturing initiates along a ∼40 μm wide process zone, comprising damage along overlapping en echelon high‐index crystallographic planes, shown by discrete bands of reduced electron backscatter pattern (EBSP) quality (band contrast). Coalescence of these surfaces results in a stepped fracture morphology. Monitoring of AE during indentation reveals that the elastic anisotropy of quartz has a significant effect on AE location and focal mechanisms. Ninety‐four AE events were recorded during indentation and show an increasing frequency with increasing load. They correspond to the development of subsidiary concentric cracks peripheral to the main cone crack. The strong and complex anisotropy in seismic velocity (∼28% Vp, ∼43% Vs with trigonal symmetry) resulted in inaccurate and high uncertainty in AE locations using Geiger location routine with an isotropic velocity model. This problem was overcome by using a relative (master event) location algorithm that only requires a priori knowledge of the velocity structure within the source volume. The AE location results correlate reasonably well to the extent of the observed cone crack. Decomposition of AE source mechanisms of the Geiger relocated events shows dominantly end‐member behavior between tensile and compressive vector dipole events, with some double‐couple‐dominated events and no purely tensile or compressive events. The same events located by the master event algorithm yield greater percentage of vector dipole components and no double‐couple events, indicating that AE source mechanism solutions can depend on AE location accuracy, and therefore, relocation routine that is utilized. Calculations show that the crystallographic anisotropy of quartz causes apparent deviation of the moment tensors away from double‐couple and pure tensile/compressive sources consistent with the observations. Preliminary modeling of calcite anisotropy shows a response distinct from quartz, indicating that the effects of anisotropy on interpreting AE are complex and require detailed further study.

This study investigated the low-temperature self-healing behaviour of asphalt mixtures modified with 5% Styrene–Butadiene-Styrene (SBS) and subjected to 10 freeze–thaw cycles, with and without a 12-hour resting period between cycles. Acoustic Emission and semicircular bending tests were conducted under three fracture modes (Mode I, Mode II, and mixed Mode I/II) at temperatures of −12°C. The Acoustic Emission tests revealed that SBS modification enhanced the self-healing index by 16% in samples with resting time and by 11% in those without. The semicircular bending tests showed that the healing index varied depending on resting time, mixture type, and fracture mode. SBS-modified mixtures demonstrated improvements of approximately 15% in fracture energy, 10% in secant modulus, 11% in stress intensity factor, and 12% in flexibility index compared to control samples. A comparison of the Acoustic Emission and semicircular bending test results indicated that the resting period in mixed Mode I/II fracture aligns with the findings from the Acoustic Emission tests.

Bi-modular properties of sandstone inferred from seismic moment tensors of acoustic emissions

The decomposition of moment tensors into isotropic (ISO), double-couple (DC) and compensated linear vector dipole (CLVD) components is a tool for classifying and physically interpreting seismic sources. Since an increasing quantity and quality of seismic data allow inverting for accurate moment tensors and interpreting details of the source process, an efficient and physically reasonable decomposition of moment and source tensors is necessary. In this paper, the most common moment tensor decompositions are revisited, new equivalent formulas of the decompositions are derived, suitable norms of the moment tensors are discussed and the properties of commonly used source-type plots are analysed. The Hudson skewed diamond plot is introduced in a much simpler way than originally proposed. It is shown that not only the Hudson plot but also the diamond CLVD–ISO plot and the Riedesel–Jordan plot conserve the uniform distribution probability of moment eigenvalues if the appropriate norm of moment tensors is applied. When analysing moment tensor uncertainties, no source-type plot is clearly preferable. Since the errors in the eigenvectors and eigenvalues of the moment tensors cannot be easily separated, the moment tensor uncertainties project into the source-type plots in a complicated way. As a consequence, the moment tensors with the same uncertainties project into clusters of a different size. In case of an anisotropic focal area, the complexity of moment tensors of earthquakes prevents their direct interpretation, and the decomposition of moment tensors must be substituted by that of the source tensors.

SUMMARYTo investigate the influence of fluid viscosity on the fracturing process, we conducted hydraulic fracturing experiments on Kurokami-jima granite specimens with resins of various viscosities. We monitored the acoustic emission (AE) activity during fracturing and estimated the moment tensor (MT) solutions for 54 727 AE events using a deep learning technique. We observed the breakdown at 14–22 MPa of borehole pressure, which was dependent on the viscosity, as well as two preparatory phases accompanying the expansion of AE-active regions. The first expansion phase typically began at 10–30 per cent of the breakdown pressure, where AEs occurred three-dimensionally surrounding the wellbore and their active region expanded with time towards the external boundaries of the specimen. The MT solutions of these AEs corresponded to crack-opening (tensile) events in various orientations. The second expansion phase began at 90–99 per cent of the breakdown pressure. During this phase, a new planar AE distribution emerged from the borehole and expanded along the maximum compression axis, and the focal mechanisms of these AEs corresponded to the tensile events on the AE-delineating plane. We interpreted that the first phase was induced by fluid penetration into pre-existing microcracks, such as grain boundaries, and the second phase corresponded to the main fracture formation. Significant dependences on fluid viscosity were observed in the borehole pressure at the time of main fracture initiation and in the speed of the fracture propagation in the second phase. The AE activity observed in the present study was fairly complex compared to that observed in previous experiments conducted on tight shale samples. This difference indicates the importance of the interaction between the fracturing fluid and pre-existing microcracks in the fracturing process.

Moment tensor analysis of the acoustic emission source in the rock damage process

Application of the shear-tensile source model to acoustic emissions in Westerly granite

TS6d6 - DETERMINATION OF CRACK KINEMATICS BY ACOUSTIC EMISSION

Elastic waves emitted by microfracturing are called acoustic emission (AE). Recently AE techniques have been extensively applied to concrete engineering as a non–destructive testing (NDT) method. A key aspect of AE is that the nucleation of internal cracks is directly detected by a surface observation. In conventional AE techniques, such AE parameters as event count (activity), amplitude, energy and spectra are correlated with the failure process of materials. Thus, AE characteristics are utilized for NDT. The AE source (crack) is also located by employing a multichannel (more than 5) AE detecting and recording system. In this Paper an advanced AE analysis procedure is proposed. In addition to crack locations, crack types and crack orientations are determined from AE relative amplitudes of the first motions. The procedure classifies cracks into tensile cracks and shear cracks. Based on information of the crack type, the crack orientation is determined; this is the direction of crack opening in the case of tensile cracks, and the direction of sliding motion in the case of shear cracks. The proposed procedure is applied to a pull-out test of an anchor–bolt from a concrete block and a cylinder–tensile test. In the pull out test the opening directions of the tensile cracks is perpendicular to the failure surface, while the directions of sliding motion of the shear cracks are parallel to the failure surface. In the cylinder–tensile test the opening directions of the tensile cracks are perpendicular to the loading direction and all sources are located near the final plane. The proposed procedure is therefore able to determine the microcrack kinematics generated in concrete.

Source kinematics of acoustic emission based on a moment tensor

Theoretical treatment of acoustic emission (AE) source is investigated in the disbonding process of stainless steel overlay from base metal. Source representations of AE due to disbonding are studied in the simulation analysis based on a generalized theory. Taking into account a crack size, a point dislocation model for a tensile crack is considered as an AE source. The effects of crack shape and crack expansion on waveforms are clarified. Following Eshelby’s process, penny-shaped tensile cracks are mainly employed as AE sources due to disbonding. An attempt to estimate pressure of hydrogen intrusion suggests that preexisting infinitesimal flaws coalesce as a tensile crack in the disbonding process. The effect of crack orientation is studied by using a moment tensor representation. Since crack orientations can be determined from the eigenvalue analysis of a moment tensor, a technique to determine moment tensor components is applied to simulated waveforms due to inclined cracks. These results confirm that the theoretical treatment of AE waveform is useful for clarifying fundamental mechanisms of microfracturing.

Acoustic Emission (AE) is a phenomenon caused by the emission and propagation of elastic waves generated from micro-cracking. A procedure named “SiGMA” (simplified Green's function for moment tensor analysis) to identify the crack kinematics from AE waveforms has been developed recently. Using this procedure, the crack location, crack orientation and crack type can be determined. Computer software for the SiGMA procedure has been developed and applied in practice. To apply the SiGMA procedure for AE source inversion in a thin plate and other two-dimensional (2D) models, the SiGMA-2D procedure is proposed in this paper. The most distinctive feature of this procedure is projection of 3D moment tensor components onto a plane. For confirmation of SiGMA-2D solutions in practical AE waveforms, the in-plane uniaxial compression tests of plates, which are made by mortar having an internal through-thickness slit, are carried out. The results confirm the applicability of the SiGMA-2D procedure for elucidating the crack mechanisms in 2D models. Further, estimation of crack volume is proposed. For this purpose, the AE sensors are quantitatively calibrated using the Davies-bar technique. A laser opto-interferometer is used to measure the oscillation at the bar end. These results are applied to determination of micro-crack volume.

As a diagnostic application of the acoustic emission (AE) waveform analysis, crack inspection based on the moment tensor analysis is proposed. Because moment tensor components contain information on crack kinematics, the decomposition of eigenvalues of the moment tensor is possible and the contributions of shear motion and tensile motion to crack nucleation can be determined from the ratio of eigenvalues. Thus, cracks are classified into the type of dominant motion. After the crack types are determined, crack orientations can be decided from the directions of eigenvectors.The procedure developed was applied to a pull-out test of anchor bolt and a cylindrical tension test. The results confirm the applicability of the procedure to inspecting internal cracks by the quantitative AE waveform analysis based on the moment tensor inversion.