Universal and Nonuniversal Aperture‐to‐Length Scaling of Opening Mode Fractures Developing in a Particle‐Based Lattice Solid Model

Abstract

AbstractOpening‐mode fractures, such as joints, veins, and dykes, frequently exhibit power‐law aperture‐to‐length scaling, with scaling exponents typically ranging from 0.5 to 2. However, published high quality outcrop data and continuum‐based numerical models indicate that fracture aperture‐to‐length scaling may be nonuniversal, with scaling being superlinear for short fractures and sublinear for long fractures. Here we revisit these published results by means of a particle‐based lattice solid model, which is validated using predictions from linear elasticity and linear elastic fracture mechanics. The triangular lattice model composed of breakable elastic beams, with strengths drawn from a Weibull distribution, is used to investigate the fracture aperture‐to‐length scaling that emerges in a plate subjected to extension. The modeled fracture system evolution is characterized by two stages which are separated by the strain at which peak‐stress occurs. During the pre‐peak‐stress stage, aperture‐to‐length scaling is universal with a power‐law exponent of about one. Shortly after the material has attained its maximum load bearing capacity, which coincides with the formation of a multiple‐segment fracture zone, aperture‐to‐length scaling becomes nonuniversal, with power‐law exponents being consistent with earlier studies. The results presented here confirm that deviation from universal scaling laws is a consequence of fracture interaction. More specifically, the onset of nonuniversal aperture‐to‐length scaling coincides with the formation of a multiple‐segment fracture zone.