Dissipation in quasistatically sheared wet and dry sand under confinement

We investigated the stress-strain behavior of sand with and without small amounts of liquid under steady and oscillatory shear. Since dry sand has a lower shear modulus, one would expect it to deform more easily. Using a new technique to quasistatically push the sand through a tube with an enforced parabolic (Poiseuille-like) profile, we minimize the effect of avalanches and shear localization. We observe that the resistance against deformation of the wet (partially saturated) sand is much smaller than that of the dry sand, and that the latter dissipates more energy under flow. This is also observed in large-amplitude oscillatory shear measurements using a rotational rheometer, showing that the effect is robust and holds for different types of flow.

Figure 1

(a) Tube experiment's measurement cell containing granular matter (dark red); a volume change $\Delta V$ provokes a difference between $p_1$ and $p_2$, the pressures in the adjacent chambers; $D$ and $L$ are the cell diameter and length, respectively. (b) Cup-plate rotational rheometric setup. (c) Differential pressure curves with increasing shear amplitudes for wet sand$.$ The measured parameters for each curve are $\tau$ and $\Delta V$.

Figure 2

(a) Differential pressure curves for dry and wet sand measured with the setup of Fig. 1a. In blocks (b)–(d) Lissajous characteristics are shown for polystyrene beads with and without silicon oil under confinement measured with the standard rheometric setup of Fig. 1 for bead diameters (b) 250, (c) 500, and (d) 140 $\mu$m. The liquid content $w$ indicates the wet loop. The strain amplitude ${\gamma }_{\max }$ is indicated in (a) and (b).

Figure 3

Studies with the tube experiment, $\tau$ vs ${\gamma }_{\max }$ behavior and corresponding fit for the dissipative flow range for dry sand with different packing fractions $\phi$ and wet sand ($0.01\le w\le 0.03,$ $\phi =0.63$). The inset shows the corresponding range ${\gamma }_{\max }<0.1$. The second inset shows the characteristic energy $E_0$ vs the packing fraction $\phi$ (triangles) compared with the wet sand (squares).

Figure 4

Dissipated energy per unit volume $E_d$ vs strain amplitude ${\gamma }_{\max }$: (a) for the range ${\gamma }_{\max }>0.1,$ calculated from the area of the differential pressure curve loop; and (b) integrating $E_d$ from Lissajous loops for polystyrene beads. In both figures, squares represent wet sand, triangles dry sand. The insets show the same graphs in linear scale.

Figure 5

(a) Confinement pressure vs strain amplitude for the tube experiment. (b) Normal stress vs strain amplitude for the cup-plate rheometric setup.