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Universal and Nonuniversal Aperture‐to‐Length Scaling of Opening Mode Fractures Developing in a Particle‐Based Lattice Solid Model
Author(s) -
Mayrhofer Franziska,
Schöpfer Martin P. J.,
Grasemann Bernhard
Publication year - 2019
Publication title -
journal of geophysical research: solid earth
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.983
H-Index - 232
eISSN - 2169-9356
pISSN - 2169-9313
DOI - 10.1029/2018jb015960
Subject(s) - scaling , exponent , power law , physics , linear elasticity , aperture (computer memory) , lattice (music) , geometry , mechanics , mathematics , statistics , thermodynamics , acoustics , philosophy , linguistics , finite element method
Opening‐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.