Additive Decomposition of Shear Strength in Cohesive Granular Media from Grain-Scale Interactions

We study cemented granular media by introducing cohesive bonding (sliding or rolling friction and tensile strength) between grains in the framework of the contact dynamics method. We find that, for a wide range of bond parameters, the macroscopic angle of friction at the peak state can be split into three distinct terms of collisional, frictional and dilational origins. Remarkably, the macroscopic tensile strength depends only on the bond tensile strength, and the friction angle at the peak state is proportional to the dilatancy angle which varies linearly with sliding friction.

Figure 1

(a) Shear and torque failure envelopes and (b) cohesive bond.

Figure 2

Shear stress (a) and volumetric strain (b) as a function of shear strain at various confinement levels.

Figure 3

Peak and residual friction angles ${\varphi }_P$ and ${\varphi }_R$ as a function of sliding friction angle ${\varphi }_s$. Full lines (${\varphi }_R$) represent exponential fits whereas dashed lines (${\varphi }_P$) join data points.

Figure 4

(a) Dilatancy angle $\psi$ as a function of $\Delta \varphi$; (b) $\psi$ and $\Delta \varphi$ as a function of the angle of sliding friction ${\varphi }_s$; see the text for definitions.

Figure 5

Macroscopic theoretical tensile strength $A^{*}$ (see inset) as a function of bond tensile strength ${\sigma }_a$.

Figure 6

Schematic representation of the partition of the peak angle of friction.