The effect of nonelliptical cracks on the compressibility of rocks

Abstract

Dislocation theory is used to study the deformation of nonelliptical thin cracks in a loaded elastic material. The cracks considered are two-dimensional with nonblunted, tapered ends such that opposite faces are tangent to each other at points of contact. Under compression the cracks shorten by closing near the crack tips, the proportion of crack surface area in contact becoming gradually larger. Some cracks make contact between the crack tips, becoming multiple cracks. Normal stresses on the crack surface vary rapidly over the closed portions from zero near the open surfaces to a peak value at the original crack tip. Stresses remain finite everywhere. At a given load the effective rock compressibility due to arbitrarily shaped, tapered cracks depends only on crack length, giving results identical to a distribution of elliptical cracks of the same lengths. However, at different loads the varying length causes the modulus to vary. As a result, interpretation of features like porosity and modulus under varying applied stress will depend on the specific crack model chosen. In particular, a single aspect ratio of a simply-tapered crack yields the same nonlinear effect as a flat distribution of elliptical cracks. Consequently, estimates of crack spectra from nonlinear strain data are totally nonunique.

Report on THMC Modeling of the Near Field Evolution of a Generic Clay Repository: Model Validation and Demonstration

“…However, this proportionality is in fact not always constant in many cases, but rather stress-dependent (e.g., Cazacu, 1999;Lionço and Assis, 2000;Brown et al, 1989;Johnson and Rasolofosaon, 1996;Brady, 1969). A number of efforts have been made to relate this stress-dependent behavior to the microstructures of "cracks" in porous rock (Walsh, 1965;Nur, 1971;Mavko and Nur, 1978). An excellent review of these efforts is provided in a chapter entitled "Micromechanical Models" in Jaeger et al (2007).…”

Nonlinear acoustoelastic constants of dry and saturated rocks

“…In this paper we are only interested in describing how velocities increase with stress. Most theoretical models of this effect have been based upon closure of microcracks or compression of grain contacts [Walsh, 1965;O'Connell and Budiansky, 1974;Mavko and Nur, 1978]. More recently, third-order nonlinear elasticity theory has been applied to rocks [Johnson and Shankland, 1989;Meegan et.…”

Random polycrystals of grains containing cracks: Model of quasistatic elastic behavior for fractured systems

“…Phenomenology for other crack shapes may differ somewhat from the discussion presented here [20]. However, other shapes are beyond our present scope and will necessarily be treated elsewhere.…”