Basic Mechanical Properties of Wet Granular Materials: A DEM Study

Numerical simulations, by the discrete element method (DEM), of a model granular assembly, made of spherical balls, are used to investigate the influence of a small amount of an interstitial wetting liquid, forming capillary bridges between adjacent particles, on two basic aspects of granular material rheology: (1) the plastic response in isotropic compression, and (2) the critical state under monotonic shear strain, and its generalization to steady, inertial flow. Tensile strength $F_0=\pi \mathrm{\Gamma }a$, in contacts between beads of diameter $a$ joined by a small meniscus of a liquid with surface tension $\mathrm{\Gamma }$, introduces a new force scale and a new dimensionless control parameter, $P^{*}=a^{2}P/F_0$, for grains of diameter $a$ under confining stress $P$. Under low $P^{*}$, as cohesion dominates, capillary cohesion may stabilize very loose structures. Upon increasing pressure $P$ in isotropic compression, such structures gradually collapse. The resulting irreversible compaction is well described by the classical linear relation between $\log P^{*}$ and void ratio in some range, until a dense structure forms that retains its stability without cohesion as confinement dominates for large $P^{*}$. In steady shear flow, with uniform velocity gradient $\dot{\gamma }=\partial v_1/\partial x_2$ under normal stress $P={\sigma }_{22}$, the apparent internal friction coefficient, which is defined as ${\mu }^{*}={\sigma }_{12}/{\sigma }_{22}$, depends on $P^{*}$ and inertial number (reduced shear rate) $I=\dot{\gamma }\sqrt{m/aP}$, and so does solid fraction $\mathrm{\Phi }$. The material exhibits, as $P^{*}$ decreases, a strongly enhanced resistance to shear (larger ${\mu }^{*}$). In the quasistatic limit, for $I\to 0$, it is roughly predicted by a simple effective pressure assumption by which the capillary forces are deemed equivalent to an isotropic pressure increase applied to the dry material as long as $P^{*}\ge 1$, while the yield criterion approximately assumes the Mohr-Coulomb form. At lower $P^{*}$, such models tend to break down as liquid bonding, causing connected clusters to survive over significant strain intervals, strongly influences the microstructure. Systematic shear banding is observed at very small $P^{*}$.