Elastic waves in fractured rocks under periodic compression (original) (raw)
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Acoustical Physics, 2005
The interrelated elastic and inelastic fast and slow effects of acoustic wave interaction with cracks are discussed from a unified point of view. Special attention is given to the dissipative manifestations of the presence of cracks and to the effects of the symmetrically time-reversible slow dynamics observed for acoustically activated cracks. These effects can be more pronounced than the conventionally discussed nonlinear elastic effects (such as higher harmonic generation). Taking into account the main geometric features of cracks, a thermoelastic mechanism is proposed to consistently interpret the experimental data. Consequences of the results of these studies for seismics are discussed, and the possibilities of using the observed effects for nonlinear acoustic diagnostics of cracks are discussed.
The analysis of the wave propagation in layered rocks masses with periodic fractures is tackled via a twoscale approach in order to consider shape and size of the rock inhomogeneities. To match the displacement fields at the two scales, an approximation of the micro-displacement field is assumed that depends on the first and second gradients of the macro-displacement through micro-fluctuation displacement functions obtained by the finite element solution of cell problems derived by the classical asymptotic homogenization. The resulting equations of motion of the equivalent continuum at the macro-scale result to be not local in space, thus a dispersive wave propagation is obtained from the model. The simplifying hypotheses assumed in the multi-scale kinematics limit the validity of the model to the first dispersive branch in the frequency spectrum corresponding to the lowest modes.
Science China Earth Sciences
Rocks in earth's crust usually contain both pores and cracks. This phenomenon significantly affects the propagation of elastic waves in earth. This study describes a unified elastic wave theory for porous rock media containing cracks. The new theory extends the classic Biot's poroelastic wave theory to include the effects of cracks. The effect of cracks on rock's elastic property is introduced using a crack-dependent dry bulk modulus. Another important frequency-dependent effect is the "squirt flow" phenomenon in the cracked porous rock. The analytical results of the new theory demonstrate not only reduction of elastic moduli due to cracks but also significant elastic wave attenuation and dispersion due to squirt flow. The theory shows that the effects of cracks are controlled by two most important parameters of a cracked solid: crack density and aspect ratio. An appealing feature of the new theory is its maintenance of the main characteristics of Biot's theory, predicting the characteristics of Biot's slow wave and the effects of permeability on elastic wave propagation. As an application example, the theory correctly simulates the change of elastic wave velocity with gas saturation in a field data set. Compared to Biot theory, the new theory has a broader application scope in the measurement of rock properties of earth's shallow crust using seismic/acoustic waves. poroelasticity, wave propagation, cracked medium, rockphysics Citation: Tang X M. A unified theory for elastic wave propagation through porous media containing cracks-An extension of Biot's poroelastic wave theory.
Seismic wave scattering in non-homogeneous geological deposits with cracks
WIT Transactions on State of the Art in Science and Engineering, 2014
This work is a study of seismic wave scattering by cracks in inhomogeneous geological continua with depth-dependent material parameters and under conditions of plane strain. A restricted case of inhomogeneity is considered, with a Poisson's ratio of 0.25 and both shear modulus and density profiles varying proportionally. Also, time-harmonic conditions are assumed to hold. For this type of material, elastic wave speeds remain macroscopically constant and it becomes possible to recover exact Green functions for the crack-free inhomogeneous continuum using an algebraic transformation as a first step. Subsequently, the complete elastodynamic fundamental solution, along with its spatial derivatives and an asymptotic expansion for small arguments, are all derived in closed-form using the Radon transform. Next, a non-hypersingular, traction-based boundary element method formulation is implemented for solving the planar boundary value problem with internal cracks. This formulation is used for computing stress intensity factors and scattered wave displacement field amplitudes for the case of an inclined line crack in a continuously inhomogeneous medium swept by either pressure (P) or vertically polarized shear (SV) waves at an arbitrary angle of incidence. The numerical results show substantial differences between homogeneous and inhomogeneous materials containing a crack in terms of their dynamic response, with the latter case being a more realistic representation for geological deposits. Finally, these types of results are useful within the context of earthquake engineering, since they can account for the influence of geological cracks in modifying seismically-generated ground motions.
Stress-induced ultrasonic wave velocity anisotropy in fractured rock
Ultrasonics, 1988
The closure of cracks in rock under an applied compressive stress can significantly affect the permeability of the rock. Crack closure may be monitored using ultrasonic wave velocities, since these are significantly reduced in the presence of open cracks. When a non-hydrostatic compressive stress is applied to a rock, an initially isotropic distribution of cracks will become anisotropic and the rock will display an elastic anisotropy determined by the orientation distribution of those cracks remaining open. The crack orientation distribution function gives the probability of a crack having a given orientation with respect to a set of axes fixed in the rock. The coefficients W,,,,, of a series expansion of this function in generalized Legendre functions can be obtained to order /=4 from the angular variation of the elastic wave velocity. This allows construction of microfracture pole figures, which specify the orientation distribution of open cracks. The theory is applied to the measurements of Nur and Simmons, who applied a uniaxial compressive stress to a sample of Barre granite. Cracks with normals aligned along the stress direction are closed preferentially in agreement with the theory of Walsh. However, for crack normals perpendicular to the applied stress there is some evidence of crack opening that is not predicted by the theory. This is also observed in the electron microscope study of Batzle et al. and a possible mechanism is discussed.
Propagation of long elastic waves in porous rocks with crack-like inclusions
International Journal of Engineering Science, 2008
Heterogeneous porous rocks containing flattened soft (crack-like) inclusions with high hydraulic permeability are considered. The Biot linear poroelastic theory is used for description of wave propagation in such materials. A self-consistent effective field method (EFM) is developed for calculation of the effective dynamic characteristics (elastic moduli, density, and permeability coefficients) of the considered heterogeneous materials. Propagation of long elastic waves in the rocks with randomly oriented or aligned crack-like inclusions is studied. Explicit expressions for the velocities and attenuation coefficients of various types of waves are obtained and compared with experimental data available in the literature.
Journal of Geophysical Research: Solid Earth, 2017
We present a comparative study of crack damage evolution in dry sandstone under both conventional (σ 1 > σ 2 = σ 3), and true triaxial (σ 1 > σ 2 > σ 3) stress conditions using results from measurements made on cubic samples deformed in three orthogonal directions with independently controlled stress paths. To characterize crack damage, we measured the changes in ultrasonic compressional and shear wave velocities in the three principal directions, together with the bulk acoustic emission (AE) output contemporaneously with stress and strain. We use acoustic wave velocities to model comparative crack densities and orientations. In essence, we create two end-member crack distributions; one displaying cylindrical transverse isotropy (conventional triaxial) and the other planar transverse isotropy (true triaxial). Under the stress conditions in our experiments we observed an approximately fivefold decrease in the number of AE events between the conventional and true triaxial cases. When taken together, the AE data, the velocities, and the crack density data indicate that the intermediate principal stress suppresses the total number of cracks and restricts their growth to orientations subnormal to the minimum principal stress. However, the size of individual cracks remains essentially constant, controlled by the material grain size. Crack damage is only generated when the differential stress exceeds some threshold value. Cyclic loading experiments show that further damage commences only when that previous maximum differential stress is exceeded, regardless of the mean stress, whether this is achieved by increasing the maximum principal stress or by decreasing the minimum principal stress.
Long-Wavelength Elastic Wave Propagation Across Naturally Fractured Rock Masses
Rock Mechanics and Rock Engineering, 2014
Geophysical site investigation techniques based on elastic waves have been widely used to characterize rock masses. However, characterizing jointed rock masses by using such techniques remains challenging because of a lack of knowledge about elastic wave propagation in multijointed rock masses. In this paper, the roughness of naturally fractured rock joint surfaces is estimated by using a three-dimensional (3D) image-processing technique. The classification of the joint roughness coefficient (JRC) is enhanced by introducing the scan line technique. The peakto-valley height is selected as a key indicator for JRC classification. Long-wavelength P-wave and torsional S-wave propagation across rock masses containing naturally fractured joints are simulated through the quasi-static resonant column (QSRC) test. In general, as the JRC increases, the S-wave velocity increases within the range of stress levels considered in this paper, whereas the P-wave velocity and the damping ratio of the shear wave decrease.
Detailed analysis of acoustic emission activity during catastrophic fracture of faults in rock
Journal of Structural Geology, 2004
The detailed time-space distribution of acoustic emission (AE) events during the catastrophic fracture of rock samples containing a preexisting joint or potential fracture plane is obtained under triaxial compression using a high-speed 32-channel waveform recording system, and the results are discussed with respect to the prediction and characterization of catastrophic fault failure. AE activity is modeled quantitatively in terms of the seismic b-value of the magnitude -frequency relation, the self-excitation strength of the AE time series, and the fractal dimension of AE hypocenters. Consistent with previous studies on rock samples containing a fracture plane with several asperities, the present analyses reveal three long-term phases of AE activity associated with damage creation on heterogeneous faults, each clearly identifiable based on the above parameters. A long-term decreasing trend and short-term fluctuation of the b-value in the phase immediately preceding dynamic fracture are identified as characteristic features of the failure of heterogeneous faults. Based on the experimental results it is suggested that precursory anomalies related to earthquakes and other events associated with rock failure are strongly dependent on the heterogeneity of the fault or rock mass. A homogeneous fault or rock mass appears to fracture unpredictably without a consistent trend in precursory statistics, while inhomogeneous faults fracture with clear precursors related to the nature of the heterogeneity. q