Softening of Granular Packings with Dynamic Forcing

TL;DR

This study uses numerical simulations to explore how dynamic forcing softens granular packings, reducing wave velocities and contact numbers, with implications for understanding seismic and structural responses during earthquakes.

Contribution

It demonstrates that dynamic forcing decreases the resonant frequency and contact number in granular packings, revealing elastic softening mechanisms consistent with experimental observations.

Findings

Resonant frequency decreases with increasing dynamic amplitude.

Elastic wave velocity decreases as contact number reduces.

Localized soft spots become more prevalent with higher dynamic forcing.

Abstract

We perform numerical simulations of a two-dimensional bidisperse granular packing subjected to both a static confining pressure and a sinusoidal dynamic forcing applied by a wall on one edge of the packing. We measure the response experienced by a wall on the opposite edge of the packing and obtain the resonant frequency of the packing as the static or dynamic pressures are varied. Under increasing static pressure, the resonant frequency increases, indicating a velocity increase of elastic waves propagating through the packing. In contrast, when the dynamic amplitude is increased for fixed static pressure, the resonant frequency decreases, indicating a decrease in the wave velocity. This occurs both for compressional and for shear dynamic forcing, and is in agreement with experimental results. We find that the average contact number $Z_c$ at the resonant frequency decreases with increasing dynamic amplitude, indicating that the elastic softening of the packing is associated with a reduced number of grain-grain contacts through which the elastic waves can travel. We image the excitations created in the packing and show that there are localized disturbances or soft spots that become more prevalent with increasing dynamic amplitude. Our results are in agreement with experiments on glass bead packings and earth materials such as sandstone and granite, and may be relevant to the decrease in elastic wave velocities that has been observed to occur near fault zones after strong earthquakes, in surficial sediments during strong ground motion, and in structures during earthquake excitation.