X-Ray Tomography Investigation of Cyclically Sheared Granular Materials

We perform combined x-ray tomography and shear force measurements on a cyclically sheared granular system with highly transient behaviors, and obtain the evolution of microscopic structures and macroscopic shear force during the shear cycle. We explain the macroscopic behaviors of the system based on microscopic processes, including particle level structural rearrangement and frictional contact variation. Specifically, we show how contact friction can induce large structural fluctuations and cause significant shear dilatancy effect for granular materials, and we also construct an empirical constitutive relationship for the macroscopic shear force.

Figure 1

(a) Schematic of the experimental setup: granular packing is sheared by the motor on the linear stage, and the macroscopic shear force is measured by the force sensor. (b) Evolutions of the global volume fraction $\varphi$ and shear force $F$ within one cycle (ensemble averaged over 12 realizations).

Figure 2

(a) Variation of fractions of $N$-ring structures $\mathrm{\Delta }{f}_{N\text{-ring}}$ within one cycle with respect to the symmetric states ($\gamma =0$), where $\mathrm{\Delta }{f}_{N\text{-ring}}=f_{N\text{-ring}}(\gamma )-f_{N\text{-ring}}(\gamma =0)$. (b) Volume change $\mathrm{\Delta }{V}_{\text{global}}$ and $\mathrm{\Delta }{V}_{\text{topo}}$ (inset) within one cycle.

Figure 3

(a) Probability distribution functions of the Delaunay tetrahedron free volume $v_f$ at $\gamma =0$ and $\gamma =0.167$. The solid lines denote the exponential fittings on tails. Inset: evolution of the effective temperature $\chi$ within one cycle. (b) Relationship between $\mathrm{\Delta }\ln (N_{N\text{-ring}}/N_{N\text{-ring}})$ and $-1/\chi$. All lines are shifted vertically to have zero intercepts on the vertical axis. (c) Probability distribution functions of Delaunay tetrahedron free volume $v_f$ of different $N$-ring structures at $\gamma =0.167$. Inset: evolution of effective temperatures for different $N$-ring structures within one cycle which are obtained from exponential fittings of their respective tails in the main plot. (d) Relationship between $⟨V_f{⟩}_{N\text{-ring}}$ and $\chi$ for different types of $N$-ring structures.

Figure 4

(a) Evolution of $N_{\text{topo}}$ within one cycle. The arrows are guides to eye to show the increasing trends of $N_{\text{topo}}$ just before and after shear reversal which is analogous to the behavior of shear force $F$ in (c). (b) Evolution of the $A_{\mathrm{xz}}$ component of the fabric tensor within one cycle. (c) Shear force behavior within one cycle and the corresponding empirical fitting using $N_{\text{topo}}$ and $A_{\mathrm{xz}}$. (d) The respective contributions of $N_{\text{topo}}$ and $A_{\mathrm{xz}}$ to shear force $F$, denoted by $F(N_{\text{topo}})$ and $F(A_{xz})$.