Difference between static and dynamic small strain shear stiffness of anisotropic granular materials: a DEM study

The shear stiffness at small strain is an essential mechanical property of granular materials. Whether the static shear stiffness (G_sta) derived from stress-strain relationship equals the dynamic shear stiffness (G_dyn) obtained through shear wave velocity measurement is a question of significant interest. A marked discrepancy between G_sta and G_dyn has been widely reported, yet its underlying causes remain unclear. This study therefore aims to elucidate the difference between G_sta and G_dyn using theoretical analyses and discrete element method (DEM) simulations. A cross-anisotropic elastic framework is established first to derive the shear moduli in the vertical and horizontal planes (G_vh and G_hh) from conventional triaxial (CT) tests, namely $G_{\text{vh}}^{\text{sta},\text{CT}}$ and $G_{\text{hh}}^{\text{sta},\text{CT}}$. Then, DEM simulations are performed on assemblies of sphere and clump particles under various stress states. Small strain CT tests are conducted to measure G_sta, including the conventional static secant shear modulus G_sec, $G_{\text{vh}}^{\text{sta},\text{CT}}$ and $G_{\text{hh}}^{\text{sta},\text{CT}}$, while bender element tests are simulated to measure G_dyn, including $G_{\text{vh}}^{\text{dyn}}$ and $G_{\text{hh}}^{\text{dyn}}$. It is found that G_sec is highly path-dependent, particularly under anisotropic conditions. The analysis reveals that the difference between static and dynamic shear stiffness arises from the distinction between G_sec and G_vh. It also highlights a coupled effect of initial anisotropy and induced anisotropy on shear stiffness.