The influence of crack shape on the effective elasticity of fractured rocks (original) (raw)
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Effective elasticity of fractured rocks: A snapshot of the work in progress
GEOPHYSICS, 2006
Exploration and development of naturally fractured reservoirs rely on understanding and interpretation of certain signatures associated with seismic waves propagating through cracked rocks. This understanding comes primarily from the effective media theories that predict an overall elastic behavior of a solid containing many inhomogeneities (cracks, in particular) whose sizes are too small to be “seen” individually by the waves. To model seismic responses of fractured formations, a geophysicist typically has a choice between the effective media schemes of Hudson and Schoenberg. While the two predictions usually deviate slightly for liquid-filled cracks, the differences are significant when the fractures are dry. Explaining the origin of these differences and selecting a more accurate scheme is the first goal of this tutorial. Our second, more challenging task, is to prove that simply adding the compliance contributions of cracks as if they were isolated and noninteracting remains su...
Tectonophysics, 2001
An account on the role of higher order strain gradients in the mechanical behavior of elastic-perfectly brittle materials, such as rocks, is given that is based on a special grade-2 elasticity theory with surface energy as this was originated by Casal and Mindlin and further elaborated by the authors. The fundamental idea behind the theory is that the effect of the granular and polycrystalline nature of geomaterials (i.e. their microstructural features) on their macroscopic response may be modeled through the concept of volume cohesion forces, as well as surface forces rather than through intractable statistical mechanics concepts of the Boltzmann type. It is shown that the important phenomena of the localization of deformation in macroscopically homogeneous rocks under uniform tractions and of dependence of rock behavior on the specimen's dimensions, commonly known as size or scale effect, can be interpreted by using this ‘non-local’, higher order theory. These effects are demonstrated for the cases of the unidirectional tension test, and for the small circular hole under uniform internal pressure commonly known as the inflation test. The latter configuration can be taken as a first order approximation of the indentation test that is frequently used for the laboratory or in situ characterization of geomaterials. In addition, it is shown that the solution of the three basic crack deformation modes leads to cusping of the crack tips that is caused by the action of ‘cohesive’ double forces behind and very close to the tips, that tend to bring the two opposite crack lips in close contact, and further, it is demonstrated that the fracture toughness depends on the size of the crack, and thus it is not a fundamental property of the material. This latter outcome agrees with experimental results which indicate that materials with smaller cracks are more resistant to fracture than those with larger cracks.
Nonlinear Processes in Geophysics
Results of examination of experimental data on non-linear elasticity of rocks using experimentally determined pressure dependences of P- and S-wave velocities from various literature sources are presented. Overall, over 90 rock samples are considered. Interpretation of the data is performed using an effective-medium description in which cracks are considered as compliant defects with explicitly introduced shear and normal compliances without specifying a particular crack model with an a priori given ratio of the compliances. Comparison with the experimental data indicated abundance (∼ 80 %) of cracks with the normal-to-shear compliance ratios that significantly exceed the values typical of conventionally used crack models (such as penny-shaped cuts or thin ellipsoidal cracks). Correspondingly, rocks with such cracks demonstrate a strongly decreased Poisson ratio including a significant (∼ 45 %) portion of rocks exhibiting negative Poisson ratios at lower pressures, for which the con...
Limits to crack density: The state of fractures in crustal rocks
SEG Technical Program Expanded Abstracts 1993, 1993
Shear-wave splitting in sedimentary basins and above small earthquakes in a wide range of geological and tectonic domains typically displays evidence for azimuthal shear-wave velocity anisotropy of between 1% and 5%. Interpreted as the effects of parallel vertical fractures, microcracks, and preferentially oriented pore-space, these percentages of anisotropy are equivalent to crack densities of = 0.01 and 0.05 with normalized mean crack diameters of 0.43 and 0.74, respectively. The only exceptions are percentages of anisotropy exceeding 10% > 0.1) observed in near-surface rocks where there is pronounced jointing.
Models of polygonal crack systems in rocks
Journal of Mining Science, 1999
A model of a polygonal crack system which is formed in the fiat layer subjected to nonuniform biaxial tension is constructed. The cracks may develop from various points, the coordinates of which are assumed to be random. The influence of the unloading regions is considered. After implementing the model, the statistical properties of the structures obtained are studied. It is shown that the mean length and size of block are stable characteristics.
Avoiding biases of geometric crack representations in rocks
First International Meeting for Applied Geoscience & Energy Expanded Abstracts
The properties of cracks in low porosity rocks determine their elastic and transport properties, and therefore are highly relevant to the monitoring of hydrocarbon and geothermal recovery processes. Processes that generate large crack densities can cause large and disparate reductions in P-and S-wave velocities with negligible porosity development. Thus, rock physics models that go beyond the classic velocity-porosity relationship are necessary to accurately interpret seismic surveys from stimulated geothermal, oil, and gas reservoirs. Traditionally, specific inclusion shapes such as spheroids with small aspect ratios have been used to mimic cracks. However, when these pores are dry it has been shown that they all exhibit the same normal-to-shear compliance ratio (Bn/Bt)-regardless of aspect ratio ()-and therefore impact the bulk and shear moduli in a predetermined and highly-constrained manner. As such they are inadequate for describing many of the complementary evolutions of P-and S-wave velocities that transpire with the generation of cracks. Using a differential model of decoupled compliances, we analyze published velocities on dry and brine-saturated limestone cores to quantify their normal and shear compliances and find that in both cases they are inconsistent with conventional crack models. We also explicitly contrast these results with those using a differential effective medium approach to highlight the biases of specific geometries and to suggest a way forward.