A Unified Formula for Small-Strain Shear Modulus of Sandy Soils Based on Extreme Void Ratios

Small-strain shear modulus ($G_0$) is a fundamental property required in dynamic analyses. For sandy soils, $G_0$ may be affected strongly by particle characteristics such as uniformity coefficient ($C_u$), mean particle size ($d_{50}$), fines content (FC), and particle shape. Based on an extensive experimental study of the mechanical behavior of coral sands, this paper proposes a new formula for predicting $G_0$ for sandy soils with various $C_u$, $d_{50}$, FC, and particle shapes. A notable feature of the new formula is the use of the extreme void ratios (maximum void ratio $e_{\max }$ and minimum void ratio $e_{\min }$) as the indexes, which were shown to be able to account for the effects of the various factors in a simple yet collective manner. Power-law correlations were established between the minimum small-strain shear modulus $G_{0\min }$ and $e_{\max }$ as well as between the maximum small-strain shear modulus $G_{0\max }$ and $e_{\min }$. The wide applicability of this formula was validated further using extensive data from the literature from resonant column, bender element, and torsional shear tests on siliceous, calcareous, and coral sandy soils.