Small-strain stiffness, shear-wave velocity, and soil compressibility

Minsu Cha*, J. Carlos Santamarina, Hak Sung Kim, Gye Chun Cho

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

91 Scopus citations


The small-strain shear modulus depends on stress in uncemented soils. In effect, the shear-wave velocity, which is often used to calculate shear stiffness, follows a power equation with the mean effective stress in the polarization plane Vs=α(σ'm/1 kPa)β, where the α factor is the velocity at 1 kPa, and the β exponent captures the velocity sensitivity to the state of stress. The small-strain shear stiffness, or velocity, is a constant-fabric measurement at a given state of stress. However, parameters α and β are determined by fitting the power equation to velocity measurements conducted at different effective stress levels, so changes in both contact stiffness and soil fabric are inherently involved. Therefore, the α and β parameters should be linked to soil compressibility CC. Compiled experimental results show that the a factor decreases and the b exponent increases as soil compressibility CC increases, and there is a robust inverse relationship between α and β for all sediments: β≈0.73-0.27 log[α/(m/s)]. Velocity data for a jointed rock mass show similar trends, including a power-type stress-dependent velocity and inverse correlation between α and β however, the α-β trend for jointed rocks plots above the trend for soils.

Original languageEnglish (US)
Article number06014011
JournalJournal of Geotechnical and Geoenvironmental Engineering
Issue number10
StatePublished - Oct 1 2014
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2014 American Society of Civil Engineers.


  • Compression index
  • Contact effects
  • Coordination number
  • Granular fabric
  • Shear-wave velocity
  • Velocity-stress power relations

ASJC Scopus subject areas

  • General Environmental Science
  • Geotechnical Engineering and Engineering Geology


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