Shear strength of wet granular materials: Macroscopic cohesion and effective stress

Abstract.

Rheometric measurements on assemblies of wet polystyrene beads, in steady uniform quasistatic shear flow, for varying liquid content within the small saturation (pendular) range of isolated liquid bridges, are supplemented with a systematic study by discrete numerical simulations. The numerical results agree quantitatively with the experimental ones provided that the intergranular friction coefficient is set to the value $\mu\simeq 0.09$, identified from the behaviour of the dry material. Shear resistance and solid fraction $\Phi_{S}$ are recorded as functions of the reduced pressure $P^{\ast}$, which, defined as $P^{\ast}=a^{2}\sigma_{22}/F_{0}$, compares stress $\sigma_{22}$, applied in the velocity gradient direction, to the tensile strength $F_{0}$ of the capillary bridges between grains of diameter a, and characterizes cohesion effects. The simplest Mohr-Coulomb relation with $P^{\ast}$-independent cohesion c applies as a good approximation for large enough $P^{\ast}$ (typically $P^{\ast}\ge 2$. Numerical simulations extend to different values of μ and, compared to experiments, to a wider range of $P^{\ast}$. The assumption that capillary stresses act similarly to externally applied ones onto the dry granular contact network (effective stresses) leads to very good (although not exact) predictions of the shear strength, throughout the numerically investigated range $P^{\ast}\ge 0.5$ and $0.05\le\mu\le 0.25$. Thus, the internal friction coefficient $\mu^{\ast}_{0}$ of the dry material still relates the contact force contribution to stresses, $\sigma^{{\rm cont}}_{12}=\mu^{\ast}_{0} \sigma^{{\rm cont}}_{22}$, while the capillary force contribution to stresses, $\underline{\underline{{\sigma}}}^{{\rm cap}}$, defines a generalized Mohr-Coulomb cohesion c, depending on $P^{\ast}$ in general. c relates to $\mu^{\ast}_0$ , coordination numbers and capillary force network anisotropy. c increases with liquid content through the pendular regime interval, to a larger extent, the smaller the friction coefficient. The simple approximation ignoring capillary shear stress $\sigma^{{\rm cap}}_{12}$ (referred to as the Rumpf formula) leads to correct approximations for the larger saturation range within the pendular regime, but fails to capture the decrease of cohesion for smaller liquid contents.

Graphical abstract