Research Papers

Interaction Model for “Shelled Particles” and Small-Strain Modulus of Granular Materials

[+] Author and Article Information
Shun-hua Zhou

Key Laboratory of Road and Traffic Engineering
of the State Ministry of Education,
Tongji University,
Shanghai 200092, China
e-mail: zhoushh@tongji.edu.cn

Peijun Guo

Key Laboratory of Road and Traffic Engineering
of the State Ministry of Education,
Tongji University,
Shanghai 200092, China;
Department of Civil Engineering,
McMaster University,
Hamilton L8S 4L7, ON, Canada
e-mail: guop@mcmaster.ca

Dieter F. E. Stolle

Department of Civil Engineering,
McMaster University,
Hamilton L8S 4L7, ON, Canada
e-mail: stolle@mcmaster.ca

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received March 25, 2018; final manuscript received May 22, 2018; published online June 27, 2018. Assoc. Editor: Thomas Siegmund.

J. Appl. Mech 85(10), 101001 (Jun 27, 2018) (11 pages) Paper No: JAM-18-1170; doi: 10.1115/1.4040408 History: Received March 25, 2018; Revised May 22, 2018

The elastic modulus of a granular assembly composed of spherical particles in Hertzian contact usually has a scaling law with the mean effective pressure p as KGp1/3. Laboratory test results, however, reveal that the value of the exponent is generally around 1/2 for most sands and gravels, but it is much higher for reclaimed asphalt concrete composed of particles coated by a thin layer of asphalt binder and even approaching unity for aggregates consisting of crushed stone. By assuming that a particle is coated with a thin soft deteriorated layer, an energy-based simple approach is proposed for thin-coating contact problems. Based on the features of the surface layer, the normal contact stiffness between two spheres varies with the contact force following knFnm and m[1/3,1], with m=1/3 for Hertzian contact, m=1/2 soft thin-coating contact, m=2/3 for incompressible soft thin-coating, and m=1 for spheres with rough surfaces. Correspondingly, the elastic modulus of a random granular packing is proportional to pm with m[1/3,1].

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Grahic Jump Location
Fig. 1

Variation of exponent n with the coefficient of uniformity and mean particle size d50

Grahic Jump Location
Fig. 2

Contact between coated elastic bodies: (a) a rigid sphere and an elastic layer bonded on a rigid substrate and (b) two coated rigid spheres

Grahic Jump Location
Fig. 3

Contact of rigid spheres coated by incompressible elastic layers: (a) εr=εθ=0 and (b) εz+εr+εθ=0

Grahic Jump Location
Fig. 4

Contact of a rigid frictionless sphere with a thin incompressible layer bounded on a semi-infinite rigid substrate: (a) εr=εθ=0 and (b) εz+εr+εθ=0

Grahic Jump Location
Fig. 5

Particle size distribution of the virgin aggregate and select RAPs

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Fig. 6

Influence of RAP content on the variation of resilient modulus with bulk stress for different aggregate-RAP blends: (a) virgin aggregate and aggregate-RAP 3 blends and (b) virgin aggregate and aggregate-RAP 1 blends

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Fig. 7

Variation of K2 with RAP content

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Fig. 8

Contact of rough surfaces (after Ref. [31]): (a) A random rough surface according to Greenwood and Williamson (1966) and (b) contact of a rough surface composed of cone-shaped asperities



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