Strain-accumulation mechanisms in sands under isotropic stress

Determining the pressure dependence of dynamic moduli in unconsolidated sediments is still an open problem in applied geophysics. This is because several petrophysical parameters affect the elastic response of the granular medium during compression. Effective medium theories based on the Hertz–Mindlin contact law estimate the effective moduli from petrophysical parameters. Among them, the Pride and Berryman model assumes that new contacts between grains are progressively created during compression. Furthermore, the gaps around rattlers are distributed following a power law with distance and the global strain can change either linearly or quadratically with the local strain. This identifies two types of strain accumulation. Quadratic strain accumulation is associated with grain rotation.We simplified this model by assuming a flat distribution of gaps around rattlers and we applied this simplified model to published ultrasonic measurements. By means of these measurements, we studied how the strain-accumulation mechanism affects the coordination number during isotropic compression. The coordination numbers were estimated by applying a DEM-based correction to the average-strain model.We observe that the majority of the experimental trends lay between the linear and the quadratic accumulation trends. Based on this result, we assume that the strain accumulation is a combination of the two mechanisms and we propose a formula to estimate the contribution of each mechanism. Furthermore, we note that, in the studied datasets, rotation affects larger grains (diameter approximately 500 m) more than smaller grains (diameter approximately 100 m). If further validated, this correlation could guide the determination of pressure trends for sands.