Mechanical model of evolution of granular matter force chains

Abstract

Granular models are key for understanding many phenomena in seismology, geophysics and geotechniques. Investigations of granular matters have shown that the scale of activated force chains decreases and a transition from solid-like behavior to liquid-like behavior occurs with the increase of shearing rate, and that at a low shearing rate viscosity is almost inversely proportional to maximal sliding velocity. At present, mechanical models describing the aforementioned behavior of granular matter are still lacking. Here we proposed a mechanical model of granular matter with internal length scale, reflecting the fact that the loading of granular matter is caused by shearing, and the stress relaxation is caused by shear band propagation. In combination with the constancy of shear band propagation speed, relationship between the length of activated force chains and shearing rate is obtained, the inverse proportionality of viscosity to shearing rate is interpreted, and the solid-to-liquid behavior transition shearing rate is predicted very well. This model can provide an effective approach to describe force chain evolution and the transition of granular matter from solid-like behavior to liquid-like behavior.

Graphic abstract

V :

The sliding velocity (mm/s)

V ₀ :

A reference sliding velocity (mm/s)

V _max :

Maximal sliding velocity (mm/s)

η :

Effective viscosity (Pa∙s)

ν :

Relaxation speed (m/s)

c _s :

The propagation speed of the elastic shear wave (m/s)

\(\dot{\gamma }_{d}\) :

The characteristic transition shearing rate corresponding to particle diameter d (m/s)

δ :

The interface gouge granular layer thickness (m)

d :

Particle diameter (m)

l :

Characteristic length (m)

D _c :

The critical slip distance (m)

t _r :

The relaxation time (s)

T _bc :

Binary contact time (s)

t* :

The time for deformation to reach its limit (s)

τ :

Shear stress (MPa)

τ _fric :

A shear stress related to friction (MPa)

τ _vis :

A shear stress related to viscosity (MPa)

σ _n :

Effective normal stress (MPa)

σ :

Consolidating stress (MPa)

σ _I :

Intensity of stress deviator (MPa)

\(s^l_{ij}\) :

Deviatoric stresses corresponding to scale level l (MPa)

G :

Shear modulus (MPa)

E :

Young’s modulus (MPa)

F :

Driving force (N)

ρ :

The density of the medium (kg/m³)

\(\dot{\gamma }\) :

Strain rate

γ ^* :

Crituical hear bands deformation

\(\dot{e}_{ij}\) :

Deviatoric strain rate components

ε* :

Limit strain

\(\dot{\varepsilon }_{I}\) :

Strain rate intensity

μ ₀ :

The steady state friction coefficient at V = V₀

a,b :

Material property parameters

θ :

The state variable

Sa :

Savage number

μ _f :

Friction coefficient

μ :

Poisson’s ratio

The study was supported by the National Natural Science Foundation of China (Nos. 12172036, 51774018), the “973” Key State Research Program (Nos. 2015CB0578005), Program for Changjiang Scholars and Innovative Research Team in University (PCSIRT, IRT_17R06).

Authors and Affiliations

1. Beijing Advanced Innovation Center for Future Urban Design, Beijing University of Civil Engineering and Architecture, Beijing International Cooperation Base for Transportation Infrastructure Construction, Beijing, 100044, China

   Chengzhi Qi & Zefan Wang

2. Institute of Geosphere Dynamics, RAS, Moscow, 119334, Russia

   G. G. Kocharyan

Contributions

Chengzhi Qi: Conceptualization, Methodology, Formal analysis,Investigation, Writing–original draft, Writing–reviewing and Editing, Funding acquisition, Resources, Supervision. Zefan Wang: Formal analysis, Investigation, Writing–original draft, Writing–reviewing and Editing. G.G. Kocharyan: Writing-reviewing and Editing.

Corresponding author

Correspondence to Zefan Wang.

Conflict of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

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