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DSSS: The Critical Link: Fracture Stiffness as Nexus


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Dr. Laura J. Pyrak-Nolte is a Professor in the Physics Department, College of Science, at Purdue University.  She holds courtesy appointments in the School of Civil Engineering and in the Department of Earth, Atmospheric and Planetary Sciences, also in the College of Science.  Prior to arriving at Purdue in 1997, she was an Assistant Professor at the University of Notre Dame in the Department of Civil Engineering and Geological Sciences.  Dr. Pyrak-Nolte holds a B.S. in Engineering Science from the State University of New York at Buffalo, an M.S. in Geophysics from Virginia Polytechnic Institute and State University, and a Ph.D. in Materials Science and Mineral Engineering from the University of California at Berkeley.  Her interests include applied geophysics, experimental and theoretical seismic wave propagation, rock mechanics, micro-fluidics, particle swarms, and fluid flow through Earth materials.  In 1995, Dr. Pyrak-Nolte received the Schlumberger Lecture Award from the International Society of Rock Mechanics.  She received Young Investigator Awards from the National Science Foundation and the Office of Naval Research, and in 2001, Purdue recognized Dr. Pyrak-Nolte’s accomplishments with a University Scholar Award.  In 2012, she was appointed to the Department of Energy Earth Sciences Council, the Board of the American Rock Mechanics Association and to the Council for the International Society of Porous Media.  In 2013, she was made a Fellow of the American Rock Mechanics Association.


The hypothesis that the hydraulic, mechanical and seismic properties of fractures are all interrelated has been indirectly implied by research performed by the hydrology, geomechanics and geophysics communities—but with each community providing a partial view into the behavior of fractures and fracture networks.  For example in the hydrology community, fluid flow through fractures and fracture networks has established that fluid flow through a fracture depends on length scales associated with the size and spatial distribution of the connected apertures (that depend on stress) within a fracture or fracture network.  In the geomechanics community, it has been independently shown that fracture deformation is controlled by length-scales associated with the size and spatial distribution of contacts between the two surfaces of a fracture and depends on the loading condition. On the other hand, the geophysics community views fractures either as discrete features that give rise to converted modes, or as sources of moduli reduction that depend on stress-dependent fracture specific stiffness and the wavelength of the seismic probe.  Fracture specific stiffness, in turn, depends on both contact area and aperture distribution of the fracture, which comes full circle back to hydrology and geomechanics.  Ultimately, all three fields have demonstrated that each physical property of interest to their community depends on the geometry of the voids and contact area that define the fracture, and thus should be implicitly linked through the fracture geometry.

In this presentation, results from a finite-size scaling analysis are presented that reveal a fundamental scaling relationship between fracture stiffness and fracture fluid flow.  Computer simulations extract the dynamic transport exponent that is used to collapse the flow-stiffness relationship onto a universal scaling function.  Near the critical percolation threshold, the scaling function displays a break in slope that is governed by the topology of the stressed flow paths.  The resulting hydromechanical scaling function provides a link between fluid flow and the seismic response of a fracture, which suggests that seismic techniques may provide a means for remote sensing of fracture permeability.  To fulfill this potential, deeper understanding of the origins and dynamics of fracture seismic stiffness is still required.  Recent results will be presented on the seismic response of the intersections between multiple fractures, which represent a newly uncovered contribution to the compliance of a rock mass.