Rock Mechanics and Rock Engineering

, Volume 47, Issue 5, pp 1613–1623 | Cite as

Combined Scaling of Fluid Flow and Seismic Stiffness in Single Fractures

  • C. L. Petrovitch
  • L. J. Pyrak-Nolte
  • D. D. Nolte
Original Paper


The connection between fluid flow and seismic stiffness in single fractures is governed by the geometry of the fracture through the size and spatial distributions of the void and contact areas. Flow and stiffness each exhibit scaling behavior as the scale of observation shifts from local to global sample sizes. The purpose of this study was to explore the joint scaling of both properties using numerical models. Finite-size scaling methods are used to extract critical thresholds and power laws for fluid flow through weakly correlated fractures under increasing load. An important element in the numerical fracture deformation is the use of extended boundary conditions that simulate differences between laboratory cores relative to in situ field studies. The simulated field conditions enable joint scaling of flow and stiffness to emerge with the potential to extrapolate from small laboratory samples to behavior on the field scale.


Hydromechanical scaling Scaling Fracture deformation Rock fractures Fracture 



This work is supported by the Geosciences Research Program, Office of Basic Energy Sciences US Department of Energy (DEFG02-97ER14785, DE-FG02-09ER16022), by the Geo Mathematical Imaging Group at Purdue University, the Purdue Research Foundation, and from the Computer Research Institute at Purdue University.


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Copyright information

© Springer-Verlag Wien 2014

Authors and Affiliations

  • C. L. Petrovitch
    • 1
  • L. J. Pyrak-Nolte
    • 2
    • 3
    • 4
  • D. D. Nolte
    • 2
  1. 1.Applied Research Associates Inc.RaleighUSA
  2. 2.Department of PhysicsPurdue UniversityWest LafayetteUSA
  3. 3.School of Civil EngineeringPurdue UniversityWest LafayetteUSA
  4. 4.Department of Earth, Atmospheric and Planetary SciencesPurdue UniversityWest LafayetteUSA

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