Rock Mechanics and Rock Engineering

, Volume 48, Issue 6, pp 2551–2566 | Cite as

Attenuation Properties of Fontainebleau Sandstone During True-Triaxial Deformation using Active and Passive Ultrasonics

  • S. D. Goodfellow
  • N. Tisato
  • M. Ghofranitabari
  • M. H. B. Nasseri
  • R. P. Young
Original Paper


Active and passive ultrasonic methods were used to study the evolution of attenuation properties in a sample of Fontainebleau sandstone during true-triaxial deformation. A cubic sample of Fontainebleau sandstone (80 mm \(\times\) 80 mm \(\times\) 80 mm) was deformed under true-triaxial stresses until failure. From the stress state: \(\sigma _3 = 5\) MPa and \(\sigma _1 = \sigma _2 = 35\) MPa, \(\sigma _1\) was increased at a constant displacement rate until the specimen failed. Acoustic emission (AE) activity was monitored by 18 piezoelectric sensors and bandpass filtered between 100 kHz and 1 MHz. A source location analysis was performed on discrete AE data harvested from the continuous record where 48,502 events were locatable inside the sample volume. AE sensors were sequentially pulsed during periodic P-wave surveys among 135 raypaths. Analytical solutions for Biot, squirt flow, viscous shear, and scattering attenuation were used to discuss to observed attenuation at various stages of the experiment. We concluded that initial attenuation anisotropy was stress induced and resulted from friction and squirt flow. Later attenuation of the high-frequency spectrum was attributed to scattering as a result of the formation of large macroscopic vertical fractures. Passive (AE) ultrasonic data produced similar information to that from active data but with enhanced temporal and spacial resolution.


Acoustic emission True-triaxial Attenuation Ultrasonic 

List of symbols

\(\sigma _1\)

Maximum principal stress (Pa)

\(\sigma _2\)

Intermediate principal stress (Pa)

\(\sigma _3\)

Minimum principal stress (Pa)

\(\epsilon _1\)

Strain in the \(\sigma _1\) direction (\(\%\))

\(\epsilon _2\)

Strain in the \(\sigma _2\) direction (\(\%\))

\(\epsilon _3\)

Strain in the \(\sigma _3\) direction (\(\%\))


Ultrasonic P-wave velocity (m/s)


Ultrasonic S-wave velocity (m/s)


Ultrasonic P-wave velocity in the \(\sigma _1\) direction (m/s)


Ultrasonic P-wave velocity in the \(\sigma _2\) direction (m/s)


Ultrasonic P-wave velocity in the \(\sigma _3\) direction (m/s)


Ultrasonic energy (J)


Energy flux (m\(^2\)/s)


Attenuation quality factor



The authors wish to thank Laszlo Lombos (formerly of ErgoTech Ltd.) and Applied Seismology Consultants for their technical support. The Itasca Education Partnership is acknowledged. In addition, we are grateful to Hamed Ghaffari for many useful discussions and input. The funding for the creation and operation of the Rock Fracture Dynamics Facility at the University of Toronto was provided by the Canada Foundation for Innovation and the Province of Ontario (Grant No. 0000302419) and the Natural Sciences and Engineering Research Council of Canada (Grant No. 0000300001), respectively.


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Copyright information

© Springer-Verlag Wien 2015

Authors and Affiliations

  • S. D. Goodfellow
    • 1
  • N. Tisato
    • 2
  • M. Ghofranitabari
    • 3
  • M. H. B. Nasseri
    • 1
  • R. P. Young
    • 1
  1. 1.Department of Civil EngineeringUniversity of TorontoTorontoCanada
  2. 2.Department of Geological SciencesThe University of Texas at AustinAustinUSA
  3. 3.Department of PhysicsUniversity of TorontoTorontoCanada

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