Joint pattern development: Effects of subcritical crack growth and mechanical crack interaction

TLDR: In this paper, a subcritical fracture growth model is used to generate equilibrium crack geometries, where fracture length distributions and spacing are modeled as proportional to the n-th power of the mode I stress intensity.

Abstract: Fracture networks are examined in the light of subcritical crack growth theory. Examples of equilibrium crack geometries are generated using a fracture mechanics model that explicitly tracks the propagation of multiple fractures. It is determined that propagation velocity as modeled using a subcritical fracture growth law exerts a controlling influence on fracture length distributions and spacing. Velocity is modeled as proportional to the n-th power of the mode I stress intensity. Numerous, closely spaced, similar length fractures result for n=1, with many en echelon arrays forming due to fracture interaction. Increasing the value of n results in the growth of fewer fractures that are more widely spaced. Fractures tend to cluster in narrow zones, with limited fracture growth in the intervening areas. The spacing between zones is controlled by the stress shielding effects of longer fractures on shorter ones. The amount of time required for fracture pattern development is also influenced by the subcritical velocity exponent, n. At low n, patterns take seconds to minutes to develop, while patterns generated at higher n can require hundreds of years or more.