Frictional mechanics of granular materials

collaboration with W. Losert and J. P. Gollub

Introduction

Dry granular materials exhibit solid-like frictional properties. The result holds true for immersed granular materials. It is even more surprizing as the interstitial fluid is expected to lubricate the contacts between the grains in this case.

The frictional response of bidisperse granular materials depends on the mixing ratio. The experimental results could be relevant for explaining the segregation process of granular materials.

The following material is taken from a talk I gave on the subject in Japan (May 2001).

Table of content

Principle of the measurements
Experimental setup
Immersed granular materials
Dynamic frictional force
Dilation
Phenomenological model
Binary mixtures

The frictional response of granular material is tested experimentally by sliding a plate across the free surface of a horizontal layer with the help of a spring. The control parameters are the driving velocity V and the stiffness of the spring k. The typical behavior of the elongation d of the spring as a function of time t is recorded (The typical behavior observe in the case of a dry granular layer is given above). The frictional force F is deduced from d(t).

The experimental setup consists of a frame pushing a cantilever at constant velocity V. Both the bending of the cantilever d and the vertical position of the sliding plate h are recorded. The setup makes possible to work with a dry or immersed granular layer.

In the case of immersed granular material, we observe a continuous sliding of the plate after a transient regime during which the plate rises up (dilatancy). The static frictional force is defined to be the maximum value the frictional force reaches during the transient regime.

The frictional force, measured during the continuous sliding of the plate (dynamic frictional force), is proportional to the normal applied stress (weight of the sliding plate), and does not depend on the driving velocity. The immersed granular material exhibits solid-like frictional properties.

During the transient regime, the sliding plate rises up. The vertical position of the plate increases exponentially with the sliding distance x. The experimental characteristic length equals the radius R of the beads the granular material is made of.

A simple phenomenological model successfully describes the response of the material to the applied horizontal stress as long as the plate slides significantly.

A significant increase of the static frictional force is oberved when the plate remains at rest for a long period of time t before measurement. In the case of glass beads immersed in water, this aging is due to the formation of solid bridges between the grains.

The static frictional coefficient measured in the case of bidisperse granular materials is always larger than that of the monodisperse materials.

The dynamic frictional coefficient measured in the case of bidisperse granular materials can be either larger or smaller than those of the monodisperse material.

In the case of bidisperse granular materials, the underlying characteristic length of the system is given by the mean radius (by weight) of the grains.

Related publications

Frictional mechanics of wet granular material,
Géminard J.-C., Losert W. and Gollub J. P., Phys. Rev. E 59 (1999) 5881.

Mechanism for slow strengthening in granular materials,
Losert W., Géminard J.-C., Nasuno S. and Gollub J. P., Phys. Rev. E 61 (2000) 4060.

Frictional properties of bidisperse granular matter : Effect of mixing ratio,
J.-C. Géminard, and W. Losert, Phys. Rev. E 65 (2002) 041301.