Development of Constitutive Models for Linear and Nonlinear Shear Modulus and Material Damping Ratio of Uncemented Soils

The shear modulus ($G$) is the parameter commonly used to describe soil stiffness and to calculate shear deformations at small-to-moderate strains ($\gamma <0.5\%$). The material damping ratio ($D$) is the parameter commonly used along with $G$ to analyze the response of the geotechnical materials to dynamic shearing motions. The following four sets of empirical models are presented in this study: (1) small-strain shear modulus ($G_{\max }$), (2) nonlinear shear modulus ($G/G_{\max }–\log \gamma$) relationships, (3) small-strain material damping ratio ($D_{\min }$), and (4) nonlinear material damping ratio relationships ($D–\log \gamma$). The associated database included all traceable uncemented soil specimens tested in the Soil and Rock Dynamics Laboratory at The University of Texas at Austin using the combined resonant column and torsional shear (RCTS) equipment since the late 1980s. The effects of soil type, index properties, density, confining state, and strain level on the shear modulus and material damping ratio have been quantified through multivariable regression analyses performed in a staged manner. The staged outcomes provide options of models with user-preferred levels of complexity and corresponding accuracy. In conclusion, these empirical models for $G_{\max }$, $G/G_{\max }–\log \gamma$ relationships, $D_{\min }$, and $D–\log \gamma$ relationships perform well in fitting the database and can be applied to predict the shear behavior of uncemented soils at small-to-moderate strains ($\gamma <0.5\%$).