Stiffness of Clays and Silts: Normalizing Shear Modulus and Shear Strain

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 $p\prime$ (i.e., $G/p\prime$ versus $\text{log}\hspace{0.17em}\gamma$) or undrained shear strength $c_u$ (i.e., $G/c_u$ versus $\text{log}\hspace{0.17em}\gamma$) are shown to be much less successful in reducing the scatter between different clays than the approach that uses the maximum shear modulus, $G_{\text{max}}$, a technique still not universally adopted by geotechnical researchers and constitutive modelers. Analysis of semiempirical expressions for $G_{\text{max}}$ 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 $G_{\text{max}}$, and shear strain $\gamma$ is normalized with respect to a reference strain ${\gamma }_{\text{ref}}$ 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 ${\gamma }_{\text{ref}}$ 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 $G/G_{\text{max}}\pm 30\%$ across all strain levels in approximately 90% of the cases studied. New design charts are proposed to update the commonly used design curves.