Fracture ellipticity as a measure of chemical reaction-controlled fracture growth

Natural fractures are generally viewed as elliptical in shape, consistent with elastic fracture mechanics. To quantify deviations of fracture shape from theoretically predicted elliptical opening distributions and to evaluate processes leading to non-elliptical fracture shapes, we measured aperture profiles of quartz-cemented opening-mode fractures in low-grade metamorphic sandstone. Ellipticity was quantified by the Lamé n-value, with measured n-values deviating significantly from n = 2 for elliptical shapes, ranging from 0.7 for tapered fractures to 3.2 for blunted fractures.

While some deviation from n = 2 can be explained by mechanical interaction with nearby fractures and layer boundaries, we explain the generally observed large variation in n values with competing processes between chemically assisted subcritical fracture propagation, leading to preferred fracture length growth and tapered tips for non-recoverable inelastic fracture opening by solution-precipitation creep, and preferred aperture growth and tip blunting by locally enhanced solution-precipitation creep in the fracture tip region. Using geometric models, we show that preferred length growth with non-recoverable fracture opening strain can lead to tapered fractures with n = 1; Preferred aperture growth and opening increments with Lamé n = 3 result in overall blunted fracture shapes with n > 2. We propose that fracture ellipticity provides a measure of chemically reactive fracture growth processes in geological systems.