Osmotic Ion Concentration Control of Steady-State Sub-critical Fracture Growth in Shale

Hoang T. Nguyen, Zdeněk P. Bažant

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations


The mechanism of formation of natural cracks in sedimentary rocks in the geologic past is an important problem in hydraulic fracturing. Why are the natural cracks roughly parallel and equidistant, and why is the spacing in the order of 10 cm rather than 1 cm or 100 cm? Fracture mechanics alone cannot answer these questions. Here it is proposed that fracture mechanics must be coupled with the diffusion of solute ions (Na+ and Cl are considered here), driven by an osmotic pressure gradient. Parallel equidistant cracks are considered to be subcritical and governed by the Charles-Evans law. The evolution in solute concentration also affects the solvent pressure in the pores and cracks, altering the resistance to frictional sliding. Only steady-state propagation and periodic cracks are studied. An analytical solution of the crack spacing as a function of the properties of the rock as well as the solvent and solute, and the imposed far-field deformation is obtained. Finally, the stability of the growth of parallel cracks is proven by examining the second variation of free energy. Stability of the periodic growth state is also considered.

Original languageEnglish (US)
Title of host publication56th U.S. Rock Mechanics/Geomechanics Symposium
PublisherAmerican Rock Mechanics Association (ARMA)
ISBN (Electronic)9780979497575
StatePublished - 2022
Event56th U.S. Rock Mechanics/Geomechanics Symposium - Santa Fe, United States
Duration: Jun 26 2022Jun 29 2022

Publication series

Name56th U.S. Rock Mechanics/Geomechanics Symposium


Conference56th U.S. Rock Mechanics/Geomechanics Symposium
Country/TerritoryUnited States
CitySanta Fe

ASJC Scopus subject areas

  • Geochemistry and Petrology
  • Geophysics


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