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Response of a granular sandwich to external vibrations: �How to control the transmitted acoustic frequency

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Giuseppe Petrillo

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Giuseppe Petrillo

5 July 2022

Granular media: The Group

H. Herrmann

A. Puglisi, A. Sarracino, A. Plati

E. Lippiello, L. de Arcangelis, A. Sarracino

G. Petrillo

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Giuseppe Petrillo

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The granular sandwich

Confining pressure

Lz

Top plate

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Giuseppe Petrillo

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Two side of the same coin

Solid-like

Fluid-like

Amplitude plays a role of temperature

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Giuseppe Petrillo

5 July 2022

Two side of the same coin

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Giuseppe Petrillo

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Two side of the same coin

Experimental setup

Numerical setup

A.Gnoli, L. de Arcangelis, F.Giacco, E. Lippiello, M. Pica Ciamarra, A. Puglisi and A. Sarracino. Phys. Rev. Lett. 115, 128001

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Giuseppe Petrillo

5 July 2022

Two side of the same coin

A. Plati, L. de Arcangelis, A. Gnoli, E. Lippiello, A. Puglisi and A. Sarracino. Phys. Rev. Res. 115, 128001

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Giuseppe Petrillo

5 July 2022

Two side of the same coin

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Giuseppe Petrillo

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The Problem

Why the stress responsible for seismic failure is usually orders of magnitude smaller than the value expected on the basis of rock fracture mechanics?

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Giuseppe Petrillo

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Remote triggering

Earthquake

Triggered events

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Giuseppe Petrillo

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Acoustic Fluidization

Melosh, H. Dynamical weakening of faults by acoustic fluidization. Nature 379, 601–606 (1996). https://doi.org/10.1038/379601a0

 

 

 

 

 

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Giuseppe Petrillo

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Acoustic Fluidization

1° STEP: Establishing a relationship between strain rate and stress

2° STEP: The energy stored in the crust is released and generate vibrations

WAIT!!

Which is the frequency of the generated vibration??

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Giuseppe Petrillo

5 July 2022

Acoustic Fluidization

F. Giacco, L. Saggese, L. de Arcangelis, E. Lippiello, and M. Pica Ciamarra Phys. Rev. Lett. 115, 128001

Granular sandwich representing the fault gouge

P0 Confining pressure

σ Shear stress

W Width of the fault gouge

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Giuseppe Petrillo

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Acoustic Fluidization

Time evolution of the top plate position

Slips involve the rearrangement of all grains

inside the fault

Slip instabilities correspond to a transition

from a jammed solid-like to an unjammed fluid-like configuration

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Giuseppe Petrillo

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Acoustic Fluidization

Can an acoustic perturbation cause this fluidization?

In absence of perturbation, are there spontaneous acoustic emissions at slip instabilities?

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Giuseppe Petrillo

5 July 2022

Acoustic Fluidization

P0 Confining pressure

σ Shear stress

W Width of the fault gouge

 

 

 

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Giuseppe Petrillo

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Acoustic Fluidization

Time

  1. The frictional weakening is affected only by perturbation at a certain frequency
  2. Acoustic waves at characteristic frequency spontaneously emerge at failure

 

 

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Giuseppe Petrillo

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Acoustic Fluidization

The power spectral density as function of the frequency and the time in absence of perturbation

Time

 

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Giuseppe Petrillo

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Acoustic Fluidization

Time dependence of the spectral density at three different frequencies

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Giuseppe Petrillo

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Acoustic wave in a granular sandwich

What does this characteristic frequency represent?

Standing waves moving up and down in the granular sandwich

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Giuseppe Petrillo

5 July 2022

Acoustic waves in a granular sandwich

Confining pressure

Lz

Top plate

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Giuseppe Petrillo

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Acoustic wave in a granular sandwich

On what length scale we can view a granular medium as an almost homogeneous random medium?

The propagation of an acoustic wave is related to the contact random network of the packing?

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Giuseppe Petrillo

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Measuring top grain frequency

The arrival time as a function of the detector distance

The pressure dependence of the sound speed

Somfai et al. Phys. Rev. E https://doi.org/10.1103/PhysRevE.72.021301

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Giuseppe Petrillo

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Measuring top grain frequency

Confining pressure

Lz

Top plate

Top plate oscillation velocity

 

Top plate oscillation frequency

 

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Giuseppe Petrillo

5 July 2022

Measuring top grain frequency

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Giuseppe Petrillo

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System setting up

2 dimensional

1 dimensional

3 dimensional

We consider different type of systems

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Giuseppe Petrillo

5 July 2022

Computing top grain frequency

α = 1

α = 3/2

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Giuseppe Petrillo

5 July 2022

Scaling results: Hertz contact

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Giuseppe Petrillo

5 July 2022

Scaling results: Hertz contact

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Giuseppe Petrillo

5 July 2022

Scaling results: Hertz contact

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Giuseppe Petrillo

5 July 2022

Scaling results: Hertz contact

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Giuseppe Petrillo

5 July 2022

Scaling results: Hooke contact

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Giuseppe Petrillo

5 July 2022

Scaling relation

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Giuseppe Petrillo

5 July 2022

Force chains in a granular medium

Daniels et al. - Sound propagation and force chains in granular materials

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Giuseppe Petrillo

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Force chain in 2D-hexagonal granular media

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Giuseppe Petrillo

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Force chain in 2D-hexagonal granular media

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Giuseppe Petrillo

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Scaling results: Hertz contact

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Giuseppe Petrillo

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Scaling results: Hooke contact

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Giuseppe Petrillo

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Force chain in 2D-hexagonal granular media

Different elastic contant

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Giuseppe Petrillo

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Strong chain in a granular media

2-dimensional bidisperse system with periodic boundary conditions

Red grain -> radius = 1

Yellow grain -> radius = 0.75

Blue grain -> Rigid top plate radius = 1

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Giuseppe Petrillo

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Strong chain in a granular media

2D

3D

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Giuseppe Petrillo

5 July 2022

Strong chain in a granular media

Lc = 8

Lc = 9

Lc = 10

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Giuseppe Petrillo

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Strong chain in a granular media

Characteristic frequency as a function of the width of the sandwich for different stiffest chain lengths

Scatter plot indicate that the sandwich width does not play a role for the acoustic propagation

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Giuseppe Petrillo

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Strong chain in a granular media

Characteristic frequency as a function of the stiffest chain length

The scaling suggests the waveguide effect of the stiffest chain

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Giuseppe Petrillo

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Strong chain in a granular media

1/3

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Conclusion and Perspective

  • The force chain control the acoustic propagation
  • The strong chain control the sound propagation and the resonance frequency
  • We simulate 2D bidisperse system and 3D disordered system
  • Localization of acoustic energy at the end points of stiffest force chain
  • Making strongest chain by changing the mass of the grain

Next steps:

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Giuseppe Petrillo

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Acknowledgment

This work was started by our friend Ferdinando Giacco and these results are dedicated to his memory

Thank you for the attention

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Giuseppe Petrillo

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1D Case – Pile of grains

Increasing angle between grains

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Giuseppe Petrillo

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1D Case – Pile of grains

Free z, frozen xy

Free z, frozen y

z

z

x

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Giuseppe Petrillo

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1D Case – Pile of grains: Angle study, simulations

LAMMPS simulations - frozen xy

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Giuseppe Petrillo

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1D Case – Pile of grains: Angle study, analytical

Defining

Hooke

Hertz

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Giuseppe Petrillo

5 July 2022

1D Case – Pile of grains: Angle study, analytical

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Giuseppe Petrillo

5 July 2022

1D Case – Pile of grains: Angle study, simulations

LAMMPS simulations - frozen y

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Giuseppe Petrillo

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1D Case – Pile of grains: Angle study, analytical

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Giuseppe Petrillo

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1D Case – Pile of grains: Angle study, analytical

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Giuseppe Petrillo

5 July 2022

1D Case – Pile of grains: Angle study, approximations

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Giuseppe Petrillo

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1D Case – Pile of grains: high angly divergence

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Giuseppe Petrillo

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Building 2D from 1D

…

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Giuseppe Petrillo

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Building 2D from 1D

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Building 2D from 1D

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Building 2D from 1D

Eq.(1)

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Giuseppe Petrillo

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Non-rigid top plate

Varying the rigidity of the top plate

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Giuseppe Petrillo

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Non-rigid top plate