Use of Combined Static and Dynamic Testing to Quantify the Participation of Particles in Stress Transmission

A number of research studies have recognized that not all particles in a sand specimen are active in stress transmission, particularly in the case of gap-graded soils. This has implications for the use of the global void ratio ($e$), and variables/parameters that depend upon $e$, to predict the influence of the state on the mechanical behavior of gap-graded soils. This study explores the possibility of comparing the shear stiffness determined in dynamic wave propagation tests ($G_{dyn}$) with stiffness values determined in small-strain probes ($G_{sta}$) to assess the extent to which all the particles in a specimen are actively engaged in stress transmission. The idea is initially developed using three-dimensional discrete element method simulations and considering ideal specimens. The practical application of this approach is then tested in a series of drained triaxial compression tests. The numerical studies considered both specimens with continuous, linear particle size distributions as well as gap-graded soils. The results show that the ratio $G_{sta}/G_{dyn}$ may be associated with the ratio between the bulk density calculated considering only the stress transmitting particles, ${\rho }_m$, and the bulk density calculated considering all particles, $\rho$. The ratio ${\rho }_m/\rho$ is determined by the proportion of inactive particles, which varies with the proportion by mass of finer particles in the soil ($F_{\mathrm{finer}}$) for gap-graded soils. The relationship between $G_{sta}/G_{dyn}(e)$ and $F_{\mathrm{finer}}$ enables a qualitative assessment of the proportion of inactive particles. The corresponding experimental test results show a similar but weaker correlation between the ratio of $G_{sta}/G_{dyn}$ and $F_{\mathrm{finer}}$, this weaker correlation may be attributed to the differences between the simulations and the experimental conditions. However, despite the challenges with experimental implementation, the data presented here support the idea that it may be possible to qualitatively estimate the proportion by volume/mass of inactive particles in physical samples by comparing the stiffness results of static and dynamic testing.