Stiffness of clays and silts: Normalizing shear modulus and shear strain

Paul J Vardanega*, Malcolm D. Bolton

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

180 Citations (Scopus)


An analysis is presented of a database of 67 tests on 21 clays and silts of undrained shear stress-strain data of fine-grained soils. Normalizations of secant G in terms of initial mean effective stress p' (i.e., G/p' versus log gamma) or undrained shear strength c(u) (i.e., G/c(u) versus log gamma) are shown to be much less successful in reducing the scatter between different clays than the approach that uses the maximum shear modulus, G(max), a technique still not universally adopted by geotechnical researchers and constitutive modelers. Analysis of semiempirical expressions for G(max) is presented and a simple expression that uses only a void-ratio function and a confining-stress function is proposed. This is shown to be superior to a Hardin-style equation, and the void ratio function is demonstrated as an alternative to an overconsolidation ratio (OCR) function. To derive correlations that offer reliable estimates of secant stiffness at any required magnitude of working strain, secant shear modulus G is normalized with respect to its small-strain value G(max), and shear strain gamma is normalized with respect to a reference strain gamma(ref) at which this stiffness has halved. The data are corrected to two standard strain rates to reduce the discrepancy between data obtained from static and cyclic testing. The reference strain gamma(ref) is approximated as a function of the plasticity index. A unique normalized shear modulus reduction curve in the shape of a modified hyperbola is fitted to all the available data up to shear strains of the order of 1%. As a result, good estimates can be made of the modulus reduction G/G(max) +/- 30% across all strain levels in approximately 90% of the cases studied. New design charts are proposed to update the commonly used design curves. (C) 2013 American Society of Civil Engineers.

Original languageEnglish
Pages (from-to)1575-1589
Number of pages15
JournalJournal of Geotechnical and Geoenvironmental Engineering
Issue number9
Early online date4 Jan 2013
Publication statusPublished - 9 Sept 2013


  • Stiffness
  • Clays
  • Silts
  • Design
  • Deformations
  • Modulus
  • Statistical analysis


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