Morphologies of three-dimensional shear bands in granular media

We present numerical results on spontaneous symmetry breaking strain localization in axisymmetric triaxial shear tests of granular materials. We simulated shear band formation using the three-dimensional distinct element method with spherical particles. We demonstrate that the local shear intensity, the angular velocity of the grains, the coordination number, and the local void ratio are correlated and any of them can be used to identify shear bands; however, the latter two are less sensitive. The calculated shear band morphologies are in good agreement with those found experimentally. We show that boundary conditions play an important role. We discuss the formation mechanism of shear bands in the light of our observations and compare the results with experiments. At large strains, with enforced symmetry, we found strain hardening.

Figure 1

(Color online) (a) A granular sample was subjected to axial load and confining pressure. (b) The rubber membrane surrounding the sample was simulated by overlapping spheres initially arranged in a triangular lattice. (c) The neighboring spheres were interconnected with linear springs. The confining pressure acted on the triangular facets.

Figure 2

(Color online) Cross sections (a), (c), (e), (f), (g) of sample C and (b), (d), (h), (i), (j) of sample D shown at 10% axial strain. (k), (l), (m) present CT scans [3] (Experiment No. F2075). The vertical cross sections (a)–(d) were taken at the middle of the sample. The horizontal cross sections were taken at different heights: close to the top (e), (h), (k), at the middle (g), (j), (m), and in between (f), (i), (l). The gray (red) color encodes the local shear intensity (c)–(j) and the local void ratio on (k)–(m). (a), (b) show the velocity field.

Figure 3

Correlation of the local shear intensity $S$ with the local void ratio $(\nu ,\circ )$, the coordination number $(Z,\times )$, and the angular velocity of the grains $(R,+)$. $X$ is one of $\nu$, $Z$, and $R$. $F$ denotes a linear transformation different for each data set. All quantities are scaled by average values $(X_{av},S_{av})$. The data are collected from four samples at $10\%$ axial strain. See text for more details.

Figure 4

(Color online) Stress-strain relation. The stress ratio $\sigma ∕{\sigma }_0$ (where ${\sigma }_0$ denotes the initial stress) measured on the upper platen is shown as a function of the axial strain, for different simulation runs. (See inset for low strains.) For the lower two curves (a) and (c) tilting of the upper platen was enabled, and for the upper two (b) and (d) it was disabled. For (c) and (d) the samples were compressed two times faster than for (a) and (b).

Figure 5

Experimental stress-strain relation from a triaxial compression test exhibiting strain softening and development of shear plane. (Courtesy of Poul V. Lade; reprinted from [19] with permission from Elsevier.)