Development of constitutive models for linear and nonlinear shear modulus and material damping relationships of uncemented soils
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For many decades, hundreds of soil samples recovered from North America and other parts of the world have been tested in the Soil and Rock Dynamics (SRD) Laboratory at The University of Texas at Austin using combined resonant column and torsional shear (RCTS) equipment. Dynamic soil property relationships determined in this study include: (1) linear relationships of log G[subscript max] - log σ₀ and log D[subscript min] - log σ₀, and (2) nonlinear relationships of G/G[subscript max] - log γ and D - log γ. These relationships are important in geotechnical design, especially for geotechnical earthquake engineering and soil dynamics. More recently, higher resolution measurements have been made over shear strains ranging from about 1×10⁻⁶ to 0.3 %. Most recently, measurements of the initiation of pore-water pressure generation in nearly to saturated poorly-graded sands and low-plasticity silts have been conducted during torsional shear (TS) testing. A significant database has been developed involving all types of uncemented soil specimens tested in the SRD Laboratory since the late 1980's. The effects of soil type, index properties, density, confining state and strain level on the dynamic properties have been quantified through multivariable regression analyses performed on the database. Four sets of empirical models for log G[subscript max] - log σ₀, G/G[subscript max] - log γ, log D[subscript min] - log σ₀ and D - log γ relationships are presented in this study. These models are composed of simple equations that incorporate the key parameters controlling linear soil behavior as well as nonlinear soil behavior. The process used to develop the parameters in the models employed a residual analysis procedure in a staged manner. Both the mean values of the empirical models and the uncertainty associated with these values are presented. Those empirical models show significant improvements in accuracy and applicable range compared to previous models. The application ranges of these models and sparse portions of the associated database are also discussed for the sake of appropriate utilization and future updates. The influence of number of loading cycles, confining pressure and soil type (sand or low-plasticity silt) on the initiation of pore-water pressure generation during TS testing are briefly discussed. A preliminary model for the r[subscript u] - log γ relationship is presented. This model focuses on determination of the threshold strain at which pore pressure generation is triggered, γ[subscript t][superscript pp], and the early stages leading towards soil liquefaction.