Craters and Granular Jets Generated by Underground Cavity Collapse

We study experimentally the cratering process due to the explosion and collapse of a pressurized air cavity inside a sand bed. The process starts when the cavity breaks and the liberated air then rises through the overlying granular layer and produces a violent eruption; it depressurizes the cavity and, as the gas is released, the sand sinks under gravity, generating a crater. We find that the crater dimensions are totally determined by the cavity volume; the pressure does not affect the morphology because the air is expelled vertically during the eruption. In contrast with impact craters, the rim is flat and, regardless of the cavity shape, it evolves into a circle as the cavity depth increases or if the chamber is located deep enough inside the bed, which could explain why most of the subsidence craters observed in nature are circular. Moreover, for shallow spherical cavities, a collimated jet emerges from the collision of sand avalanches that converge concentrically at the bottom of the depression, revealing that collapse under gravity is the main mechanism driving the jet formation.

Figure 1

(a) Schematic view of the experimental setup. (b)–(d) Different craters produced by cavity collapse: (b) with a central peak, (c) with terraces, (d) with conical profile.

Figure 2

Typical stages of the cratering process by cavity collapse: (a) cavity perforation ($t=0.000\mathrm{s}$) and emergence of a growing mound (0.052 s), (b) corona explosion and outgassing (0.130 s), (c) surface subsidence and corona collapse (0.312 s), (d) collimated jet emergence (0.373 s), (e) maximum jet height (0.488 s), (f) jet collapse under gravity and central peak formation (0.798 s).

Figure 3

(a) $D_{\text{crat}}$ and $H_{\text{crat}}$ (inset) vs $V_{\text{cav}}$ for different values of pressure and depth. All of the data are proportional to ${V_{\text{cav}}}^{1/3}$ (the black lines). (b) $D_{\text{crat}}$ (the black squares) and $D_{\text{cor}}$ (red points) as a function of $D_{\text{cav}}$; the black and red lines have slopes of 2 and 1, respectively. (c) $H_{\text{crat}}$ vs $D_{\text{crat}}$; the slope $m$ indicates an aspect ratio $D_{\text{crat}}/H_{\text{crat}}=m^{-1}=6.83\pm 0.59$ independent of $P_{\text{cav}}$ and $S$. (d),(e) A shadow projection technique was used to determine the crater profile. (f) Profile fitted with a hyperbola (green), a parabola (blue), and a semicircle (red). (g) $V_{\text{crat}}$ as a function of $V_{\text{cav}}$ for a hyperboloid (▾, green), a paraboloid (▴, blue), a spherical dome (•, red), and a cone (▪, black). (h),(i) Aspect ratio $L/W$ of craters created by nonspherical cavities: an elongated balloon located at different depths $S$ (•) and a red rectangular cavity of depth $h$ (□). Note that $L/W$ goes to 1 as $S$ or $h$ increases.

Figure 4

(a)–(d) Jet shapes observed at different pressures; see the text. (e) Linear dependence of $h_{\text{jet}}$ vs $D_{\text{cav}}$ with slope $1.97\pm 0.16$. (f),(g) Top (lateral) view of the cavity collapse and jet formation in a 3D (2D) system.