Role of interparticle friction and particle-scale elasticity in the shear-strength mechanism of three-dimensional granular media

The interlink between particle-scale properties and macroscopic behavior of three-dimensional granular media subjected to mechanical loading is studied intensively by scientists and engineers, but not yet well understood. Here we study the role of key particle-scale properties, such as interparticle friction and particle elastic modulus, in the functioning of dual contact force networks, viz., strong and weak contacts, in mobilizing shear strength in dense granular media subjected to quasistatic shearing. The study is based on three-dimensional discrete element method in which particle-scale constitutive relations are based on well-established nonlinear theories of contact mechanics. The underlying distinctive contributions of these force networks to the macroscopic stress tensor of sheared granular media are examined here in detail to find out how particle-scale friction and particle-scale elasticity (or particle-scale stiffness) affect the mechanism of mobilization of macroscopic shear strength and other related properties. We reveal that interparticle friction mobilizes shear strength through bimodal contribution, i.e., through both major and minor principal stresses. However, against expectation, the contribution of particle-scale elasticity is mostly unimodal, i.e., through the minor principal stress component, but hardly by the major principal stress. The packing fraction and the geometric stability of the assemblies (expressed by the mechanical coordination number) increase for decrease in interparticle friction and elasticity of particles. Although peak shear strength increases with interparticle friction, the deviator strain level at which granular systems attain peak shear strength is mostly independent of interparticle friction. Granular assemblies attain peak shear strength (and maximum fabric anisotropy of strong contacts) when a critical value of the mechanical coordination number is attained. Irrespective of the interparticle friction and elasticity of the particles, the packing fraction and volumetric strain are constant during steady state. Volumetric strain in sheared granular media increases with interparticle friction and elasticity of the particles. We show that the elasticity of the particles does not enhance dilation in frictionless granular media. The results presented here provide additional understanding of the role of particle-scale properties on the collective behavior of three-dimensional granular media subjected to shearing.

Figure 1

(Color online) Variation of the normal stress contribution of strong and weak contacts to ${\sigma }_{11}$ in hard (a) and soft (b) sheared granular assemblies.

Figure 2

(Color online) Variation of the normal stress contribution of strong and weak contacts to ${\sigma }_{33}$ in hard (a) and soft (b) sheared granular assemblies.

Figure 3

(Color online) Variation of the tangential stress contribution of strong and weak contacts to ${\sigma }_{11}$ in hard (a) and soft (b) sheared granular assemblies.

Figure 4

(Color online) Contribution of strong and weak contacts to principal stresses and deviator stress $(\mu =0.1)$ in hard (a) and soft (b) granular assemblies under shearing.

Figure 5

(Color online) Contribution of strong and weak contacts to principal stresses and deviator stress $(\mu =0.25)$ in hard (a) and soft (b) granular assemblies under shearing.

Figure 6

(Color online) Contribution of strong and weak contacts to principal stresses and deviator stress $(\mu =0.50)$ in hard (a) and soft (b) granular assemblies under shearing.

Figure 7

(Color online) Shear stress ratio at peak and steady states.

Figure 8

(Color online) Measure of relative indices (RIs).

Figure 9

(Color online) Variation of (a) packing density and (b) mechanical coordination number of the assemblies during shearing.

Figure 10

(Color online) Variation of measures of fabric-coordination numbers during shearing. The plots show the variations of apparent coordination number $\left(Z_a\right)$ and mechanical coordination number $\left(Z_m\right)$ versus the deviator fabric of all the contacts (a) and the deviator fabric of strong contacts (b). In soft systems, the variation of $Z_m$ and $Z_a$ were almost identical and hence presented as single plots for different values of $\mu$.

Figure 11

(Color online) Variation of sliding fraction in the assemblies.

Figure 12

(Color online) Variation of volumetric strain (a) and maximum dilation rate (b) during shearing.