Elastic wave propagation in dry granular media: effects of probing characteristics and stress history
Static probing allows to understand the path dependency of the elastic moduli, i.e., the stress response to small strain increments, as well as their degradation behavior, for medium-to-large probing strains. Complementarily, dynamic probing provides insights into the acoustic properties (dispersion relations) at different wavelengths, for various probing characteristics. The wave velocities extracted from the space-time evolution of particle motion are sensitive to travel distance and input waveform, but converge to the same long-wavelength velocities far away from the source, where short wavelengths are dispersed and attenuated. Analyzing the same space-time data in the frequency domain leads to the same results, much less dependent on the probing characteristics than in the time domain, and much faster than static probing.
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. 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.
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. |
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Influence of load mode on particle crushing characteristics of silica sand at high stresses
We performed a series of high-pressure compression tests with various stress paths in monotonic and cyclic loading conditions. Particle crushing characteristics of silica sand in dense state was analyzed. Different stress paths were chosen to investigate the influences of mean and shear stress on particle crushing. The results show that the degree of particle crushing increases with the stress level and is markedly affected by the stress paths. For each compression test following a designated stress path, an increase in the cyclic loading number also enhances the degree of particle crushing. Particle morphology is affected by the accompanying occurrence and evolution of grain damage. The relative breakage expresses a linear relationship with the maximum volumetric strain during monotonic and repeated compression loadings. A good correlation between the relative breakage and plastic work per unit volume is obtained for silica sand at various mean stresses regardless of the stress history. However, this correlation is affected by cyclic loading number because of different crushing mechanisms.
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DEM simulation of anisotropic granular materials: elastic and inelastic behavior
In this work, Discrete Elements Method simulations are carried out to investigate the effective stiffness of an assembly of frictional, elastic spheres under anisotropic loading. Strain probes, following both forward and backward paths, are performed at several anisotropic levels and the corresponding stress is measured. For very small strain perturbations, we retrieve the linear elastic regime where the same response is measured when incremental loading and unloading are applied. Differently, for a greater magnitude of the incremental strain a different stress is measured, depending on the direction of the perturbation.
In the case of unloading probes, the behavior stays elastic until non-linearity is reached.Under forward perturbations, the aggregate shows an intermediate inelastic stiffness, in which the main contribution comes from the normal contact forces. That is, when forward incremental probes are applied the behavior of anisotropic aggregates is an incremental frictionless behavior. In this regime we show that contacts roll or slide so the incremental tangential contact forces are zero. |