Acoustic waves in granular packings at low confinement pressure

Abstract

Elastic properties of a granular packing show nonlinear behavior determined by its discrete structure and nonlinear inter-grain force laws. Acoustic waves show a transition from constant, pressuredependent sound speed to a shock-wave like behavior with amplitude-determined propagation speed. This becomes increasingly visible at low static confinement pressure as the transient regime shifts to lower wave amplitudes for lower static pressure. In microgravity, confinement pressure can be orders of magnitude lower than in a ground based experiment. Also, the absence of hydrostatic gradients allows for much more homogeneous and isotropic pressure distribution. We present a novel apparatus for acoustic wave transmission measurements at such low packing pressures. A pressure control loop is implemented by a microcontroller that monitors static force sensor readings and adjusts the position of a movable wall with a linear motor until the desired pressure is reached. Measurements of acoustic waves are possible using accelerometers embedded in the granular packing as well as piezos. For excitation we use a voice coil-driven wall, with a large variety of signal shapes, frequencies and amplitudes. This enables experiments both in the linear and strongly nonlinear regime.

Propagation and attenuation of pulses driven by low velocity normal impacts in granular media

“…However, the mean sand grain size is about an order of magnitude smaller than the size of the millet grains and Equation 18predicts D ∝ d g . The C W values are about an order of magnitude larger than expected (in comparison to experimental measurements by Langlois and Jia 2015;Tell et al 2020), as we previously estimated in Section 3.10. The initial durations we use for the dotted orange and dashed brown lines have ∆t Rc at r = R Cr that are 3 times and 1.5 times R cr /v P for the millet and sand experiments, respectively.…”

“…Figure 10 shows that pulses initially broaden with an estimated diffusion coefficient that exceeds that which we would have estimated using relations by Langlois and Jia (2015); Tell et al (2020), with C W ∼ 1, by about an order of magnitude. Past about 15 cm from the impact site, pulses are weaker and the widths could be affected by reflections, so we are not concerned by the low durations measured from the accelerometers more distant from the impact site.…”

“…The travel speed of a pressure pulse may also depend on the pulse amplitude or peak pressure P pk with a power law scaling, v P ∝ P β P pk with index β P ≈ 1/6 and this is predicted theoretically and observed in experiments (Gilles and Coste, 2003;van den Wildenberg et al, 2013;Santibanez et al, 2016;Tell et al, 2020). As the pulse pressure amplitude decreases, P pk P 0 , the pulse propagation speed undergoes a transition from a nonlinear and shock-like propagation regime, where the speed depends on the peak pressure, to a linear propagation regime where the propagation speed depends on the ambient or confinement pressure (van den Wildenberg et al, 2013;Santibanez et al, 2016;Tell et al, 2020). To show the possible dependence of travel speed on pressure, in Figures 7a,b we also show a dashed brown line which has pulse speed dependent on pressure in the pulse to the 1/6 power.…”

“…Figure 9 illustrates that the pulses in our experiments broaden as they travel through the granular medium. In a strongly scattering medium, pulse broadening can be described with a diffusion model, (Page et al, 1995;Tell et al, 2020). Both advection and diffusion are required because the pulses broaden as they travel.…”

Seismic waves in the asteroid environment

“…The dynamics of all the other cases are similar and have the same underlying Physics, but there are of course different numerical values. This non-linear behaviour at very low confining pressure has been predicted by the theory [14] and found experimentally [15]. However, the results have not been applied to the evolution of small asteroids in the Solar System or to space exploration missions.…”