Craters produced by explosions in a granular medium

We report on an experimental investigation of craters generated by explosions at the surface of a model granular bed. Following the initial blast, a pressure wave propagates through the bed, producing high-speed ejecta of grains and ultimately a crater. We analyzed the crater morphology in the context of large-scale explosions and other cratering processes. The process was analyzed in the context of large-scale explosions, and the crater morphology was compared with those resulting from other cratering processes in the same energy range. From this comparison, we deduce that craters formed through different mechanisms can exhibit fine surface features depending on their origin, at least at the laboratory scale. Moreover, unlike laboratory-scale craters produced by the impact of dense spheres, the diameter and depth do not follow a $1/4$-power-law scaling with energy, rather the exponent observed herein is approximately 0.30, as has also been found in large-scale events. Regarding the ejecta curtain of grains, its expansion obeys the same time dependence followed by shock waves produced by underground explosions. Finally, from experiments in a two-dimensional system, the early cavity growth is analyzed and compared to a recent study on explosions at the surface of water.

Figure 1

Explosions in granular media: Snapshots taken from high-speed video sequences of (a) an explosion in a 3D bed setup with $m=0.4$ g, (b) an explosion in a quasi-two-dimensional (2D) cell with $m=0.2$ g, and (c) early cavity growth in the 2D cell for $m=0.2$ g, recorded at 20 000 fps. See also the supplemental videos [32].

Figure 2

(a) Crater produced by an explosive with $m=0.4$ g of gunpowder, and its surface profile obtained with a laser line. (b) Crater profiles produced by different explosive masses $m$ (solid lines). Craters have raised rims and a hyperbolic shape approaching almost a conical depression (dashed lines). (c) The crater aspect ratio $\alpha =D/H$ is nearly independent of $m$, although it decreases slightly for larger values of $m$. (d) Rim height $H_{\text{rim}}$ measured from $z=0$ as a function of $m$.

Figure 3

(a) Crater volume $V$ as a function of mass $m$. The linear fit predicts $m_0\approx 0.076$ g. (b) Crater diameter $D$ vs $m$. The log-log plot (inset) reveals a power-law $D=A{(m-m_o)}^{0.30}$.

Figure 4

(a) Corona growth in 3D explosions for different values of $m$. (b) $D_{\text{cor}}$ measured at the surface level as a function of time follows a growth power law $D_{\text{cor}}=A{t}^{0.30}$, with $A=(56.1\pm 0.5){(m-m_0)}^{1/3}$ determined in the inset.

Figure 5

(a) Inset: $R_{\text{cav}}$ vs $t$ in 2D explosions for different masses. Main plot: the case $m=0.2$ g (solid points) is compared with three models: $R_{\text{cav}}=R_{\text{max}}(1-e^{-t/\tau })$ (solid lines), isothermal model (red dashed line), and power-law model $R\left(t\right)=A{t}^{2/5}$ (green dotted line). (b) $R_{\text{cav}}/R_{\text{max}}$ vs $t/\tau$. The heuristic model describes fairly well the growth process with the average value $\tau =1.127$ ms. The inset shows that $R_{\text{max}}\propto {(m-m_0)}^{1/2}$.