Estimating the Shear Modulus of Gravelly Soils

A special large-scale torsional resonant column apparatus was used to test gravelly soils. Values of small strain elastic shear modulus $\left(G_{\max }\right)$ and modulus reduction relationships [shear modulus $\left(G\right)$ versus shear strain $\left(\gamma \right)$ ] were measured for specimens of uniform and graded crushed limestone gravel, graded river gravel, standard Ottawa and crushed limestone sands, and gravel–sand–silt mixtures. Measurements of $G_{\max }$ were used to modify existing three-dimensional constitutive equations for soil elasticity for application to gravelly soils. The value of $G_{\max }$ for relatively clean uniform and graded gravels was found to increase with particle size. Soils with a variety of gradations were tested to identify the particular particle size in a graded material that is effective in determining $G_{\max }$ . With respect to modulus reduction, the need to normalize both modulus and strain is demonstrated. Normalization of both modulus and strain ( $G∕G_{\max }$ versus $\gamma ∕{\gamma }_r$ , where ${\gamma }_r$ is defined as reference strain) leads to relationships that are approximately independent of stress level for a given material.