Slow drag in granular materials under high pressure

The resistance offered by a cylindrical rod to creeping cross flow of granular materials under pressure is investigated. The experimental system consists of a confined bed of granular particles, which are compacted under high pressure to consolidate the granular medium. A cylindrical rod is pulled at a constant and slow rate through the granular medium, and the measured pulling resistance is characterized as a drag force. The influence of various parameters such as the velocity of the cylindrical rod, the rod diameter and length, the granular particle size, and the compaction pressure on the required drag force is investigated experimentally. Nondimensional analysis is performed to simplify the relationships between these variables. The results show that the drag force is independent of the drag velocity, is linearly proportional to compaction pressure and rod diameter, and increases with rod length and particle size. Additional compaction experiments show that the effective density of the granular bed increases linearly with pressure, and similar behavior is noted for all particle sizes. These results should prove useful in the development of constitutive equations that can describe the motion of solid objects through compacted granular media under high pressure, such as during ballistic penetration of soils or ceramic armors.

Figure 1

Schematic of the device used for compression experiments.

Figure 2

Schematic of the device used for drag experiments. (a) Application of compaction pressure. (b) Dragging cylinder through granular bed. (c) Detailed view of the cylinder.

Figure 3

Compression behavior at various velocities for (a) $1092\mu \mathrm{m}$, (b) $483\mu \mathrm{m}$, and (c) $165\mu \mathrm{m}$ granules.

Figure 4

Generalized behavior during drag experiments, including compaction (part I), steady drag (part II), and cylinder approaching top cover (part III). Parameters for this experiment were $p=3.13\text{MPa}$, $D=4.76\text{mm}$, and $L=44.45\text{mm}$.

Figure 5

The effect of (a) rod diameter and (b) rod length on drag force, for different particle sizes. All experiments are at $p=3.13\text{MPa}$. For the experiments in (a), $L=49.53\text{mm}$. For the experiments in (b), $D=4.76\text{mm}$.

Figure 6

The effect of pressure on drag force, for different particle sizes. All experiments are for $D=4.76\text{mm}$ and $L=44.45\text{mm}$.

Figure 7

The effect of particle size on drag force, for different compaction pressures. All experiments are for $D=4.76\text{mm}$ and $L=44.45\text{mm}$.

Figure 8

Micrographs of (a) $1092\mu \mathrm{m}$, (b) $483\mu \mathrm{m}$, and (c) $165\mu \mathrm{m}$ particles before (left) and after (right) drag experiments. All micrographs are for $p=5.63\text{MPa}$, $D=4.76\text{mm},$ and $L=44.45\text{mm}$.

Figure 9

Normalized drag force as a function of (a) $D_g$, (b) $D∕D_g$, and (c) $LD∕\left(D_g^2\right)$. Note that the axes in (b) and (c) are logarithmic.