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Collaborating Authors
Abell, Bradley C.
ABSTRACT Simulation of elastic-wave propagation in rock requires knowledge of the elastic constants of the medium. The number of elastic constants required to describe a rock depends on the symmetry class. For example, isotropic symmetry requires only two elastic constants, whereas transversely isotropic symmetry requires five unique elastic constants. The off-diagonal elastic constant depends on a wave velocity measured along a nonsymmetry axis. The most difficult barrier when measuring these elastic constants is the ambiguity between the phase and group velocity in experimental measurements. Several methods to eliminate this difficulty have been previously proposed, but they typically require several samples, difficult machining, or complicated computational analysis. Another approach is to use the surface (Rayleigh) wave velocity to obtain the off-diagonal elastic constant. Rayleigh waves propagated along symmetry axes have phase and group velocities that are equal for materials with no frequency dispersion, thereby eliminating the ambiguity. Using a theoretical secular equation that relates the Rayleigh velocity to the elastic constants enable determination of the off-diagonal elastic constant. Laboratory measurements of the elastic constants in isotropic and anisotropic materials were made using ultrasonic transducers (central frequency of 1 MHz) for the Rayleigh-wave method and a wavefront-imaging method. The two methods indicated agreement within 1% and 3% for isotropic and transversely isotropic samples, respectively, demonstrating the ability of the Rayleigh-wave method to measure the off-diagonal elastic constant. The surface-wave approach eliminates the need for multiple samples, expensive computational calculations, and most importantly, it removes the ambiguity between the phase and group velocity in the measured data for materials with no frequency dispersion because all measurements are made along symmetry axes.
- Geology > Geological Subdiscipline > Geomechanics (1.00)
- Geology > Rock Type > Sedimentary Rock (0.94)
ABSTRACT: Fractures in rock masses influence strongly the mechanical and hydraulic properties of a rock mass. Thus, the detection and characterization of fractures using geophysical methods is of critical importance for maintaining the integrity of sub-surface infrastructure and subsurface waste or storage repositories. While the effects of single fractures or sets of parallel fractures on seismic wave propagation have been studied by many scientists and engineers, little research has been performed to determine the role of fracture intersections on seismic wave attenuation and velocity. A fundamental question is whether the specific stiffness or compliance of an intersection is the same or differs from the stiffness of any of the individual fractures within two intersecting sets of fractures. In this paper, we show from experimental and numerical studies that the stiffness of fracture intersections can be less than, equal to, or greater than the stiffness of the individual fractures depending on the applied bi-axial loading conditions. 1. INTRODUCTION Rock fractures often occur in sets, as networks, or singly on nearly all length scales. Although many fracture sets contain parallel fractures, sets with orthogonal intersecting fractures are also common. Orthogonal fractures are prevalent in many geologic formations found in Norway, the United States, the United Kingdom, and even on extraterrestrial bodies such as the Moon [1-4]. Extensive theoretical, computational and experimental research has examined the effect of single fractures and fracture sets in isotropic and anisotropic media on seismic wave propagation [5-13]. Hydraulic studies on similar fractures have also been conducted as well as for intersecting fractures [14-23]. It is surprising then, that so little work has been done on characterizing orthogonal fracture intersections seismically. From the aforementioned studies on single and parallel sets of fractures, fractures give rise to converted modes, guided modes, and anisotropy.
- Research Report > New Finding (0.34)
- Research Report > Experimental Study (0.34)
- North America > United States > California > Monterey Formation (0.99)
- Europe > Netherlands > Bergen Area (0.99)
Fracture Intersections And Interface Waves
Pyrak-Nolte, Laura J. (Purdue University) | Abell, Bradley C. (Purdue University) | Wu, Fan (Purdue University)
ABSTRACT Laboratory experiments were performed on synthetic orthogonal fractures to determine the effect of intersections on fracture interface waves. Compressional and shear waves were propagated along fractures as well as along an intersection for a range of normal stresses (1.4 MPa to 14). At an intersection, the bulk shear was quenched and the existence of interface waves was independent of the polarization of the shear wave source. These intersection waves were observed to be highly sensitive to stress concentrations along the intersection including the orientation of the applied stress.
ABSTRACT We performed laboratory experiments on synthetic orthogonal fractures to determine the effect of intersections on fracture interface waves. A seismic array was used to propagate compressional and shear waves along fracture planes as well as along an intersection. Measurements were made for a range of normal stresses (1.4 MPa to 14 MPa). Intersections quench bulk shear waves and produce interface waves independent of the polarization of the shear wave source. Furthermore, these intersection waves are highly sensitive to stress concentrations along the intersection. INTRODUCTION A major difference between working with single fractures and orthogonal fracture networks is the existence of fracture intersections. Fracture intersections enable the formation of three-dimensional dominant flow paths and they act as potential sources of additional seismic wave scattering not observed for single fractures or parallel sets of fractures. A main challenge in working with orthogonal fracture sets is how to determine the connectivity or properties of fracture intersections. Fracture intersections act as either barriers to flow or paths of high conductivity and are difficult to characterize with non-invasive or destructive measurements. The goal of this study is to determine if the intersection between two fractures exhibited a seismic response that differs from that measured along fracture planes. In this paper, we explore the potential use of fracture interface waves to interrogate the properties of fracture intersections and fractures. Fracture interface waves are generalized Rayleigh waves that propagate along fractures [1-5]. The existence and velocity of fracture interface waves depend on the normal and shear stiffness of the fracture, and on the polarization of the shear wave. The velocity of these waves ranges from the Rayleigh wave velocity for a free surface to the bulk shear wave velocity for non-effervescent interface wave modes. As mentioned, the existence of fracture interface waves depends on the polarization of the shear components of the excitation source [3], i.e. interface waves exist when the shear-wave polarization is perpendicular to the fracture plane. However, at an intersection, fracture interface waves should always exist for both parallel and perpendicular shear wave polarizations (relative to one of the intersecting fractures) because each component is perpendicular to one of the orthogonal fractures. In this paper, we demonstrate that interface waves along fracture intersections always exist and the waves are sensitive to stress concentrations along the intersection. EXPERIMENTAL SET-UP Samples Experiments were performed on aluminum samples measuring approximately 100 mm by 150 mm by 150 mm. Aluminum was used to ensure that the effects observed were from the fractures and not the background matrix. Two samples were used in this study: (1) an intact piece of aluminum that was used as a standard; and (2) a “fracture” sample containing two intersecting fractures (Figure 1). Intersecting fractures in the fracture sample were produced by quartering a solid piece of aluminum. After quartering, the fracture sample was machined to the same external dimensions as the intact specimen. The fracture surfaces were smooth, i.e. no apparent roughness is visible to the naked eye.