The effect of nonelliptical cracks on the compressibility of rocks

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.