Bubble-induced cave collapse.
Bottom Line:
Using familiar theories for the strength of flat and arched (un-cracked) beams, we first show that the flat ceiling of a submerged limestone cave can have a horizontal expanse of 63 meters.Using familiar bubble dynamics, fluid dynamics of bubble-induced flows, and accustomed diving practices, we show that a group of 1-3 divers submerged below a loosely connected ceiling rock will quickly trigger it to fall causing a "collapse".In these experiments, a metal ball represented the rock (attached to the cave ceiling with a magnet), and the bubbles were produced using a syringe located at the cave floor.
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PubMed Central - PubMed
Affiliation: Geophysical Fluid Dynamics Institute, The Florida State University, Tallahassee, Florida, United States of America.
ABSTRACT
Conventional wisdom among cave divers is that submerged caves in aquifers, such as in Florida or the Yucatan, are unstable due to their ever-growing size from limestone dissolution in water. Cave divers occasionally noted partial cave collapses occurring while they were in the cave, attributing this to their unintentional (and frowned upon) physical contact with the cave walls or the aforementioned "natural" instability of the cave. Here, we suggest that these cave collapses do not necessarily result from cave instability or contacts with walls, but rather from divers bubbles rising to the ceiling and reducing the buoyancy acting on isolated ceiling rocks. Using familiar theories for the strength of flat and arched (un-cracked) beams, we first show that the flat ceiling of a submerged limestone cave can have a horizontal expanse of 63 meters. This is much broader than that of most submerged Florida caves (~ 10 m). Similarly, we show that an arched cave roof can have a still larger expanse of 240 meters, again implying that Florida caves are structurally stable. Using familiar bubble dynamics, fluid dynamics of bubble-induced flows, and accustomed diving practices, we show that a group of 1-3 divers submerged below a loosely connected ceiling rock will quickly trigger it to fall causing a "collapse". We then present a set of qualitative laboratory experiments illustrating such a collapse in a circular laboratory cave (i.e., a cave with a circular cross section), with concave and convex ceilings. In these experiments, a metal ball represented the rock (attached to the cave ceiling with a magnet), and the bubbles were produced using a syringe located at the cave floor. No MeSH data available. Related in: MedlinePlus |
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Mentions: Substituting this into (Eq 4) yields,F = 2W / 3π(5)Note that we have horizontal and vertical forces at points A and B. First, let’s calculate the bending moment (M) at any point on the beam. By taking about any point on the beam (equivalent to point C (Fig 5b) but with known Ax and Ay at point A) and using (Eq 5), we find the total bending moment (M) at any angle (θ) to beM= (w / 4)Rasin2θ– (2W/ 3π)Rasin θ(6)Noting that the maximum moment function (Mmax) occurs when sin θ = 1, we getMmax= (W/ 4)Ra– (2W/ 3π)Ra(7)Further noting that, by definition, the maximum stress (σmax) is given byσmax=Mmaxy/I(8)we get using (Eq 7),σmax=(3π−4)Ra2ρ'g/h(9)Finally, we use (Eq 9) to find the maximum span (L) to beL=2Ra=4hσmax /(3π−4)ρ'g(10)which, for h = 20 m, ρ′ = 1700 kg/m3, and σmax = 70 MPa (maximum compressive strength of limestone), gives L = 248.9m. As expected, this is considerably larger than both the flat beam case (Fig 6) and typical values found in Florida caves. This implies, once again, that Florida caves are structurally stable. |
View Article: PubMed Central - PubMed
Affiliation: Geophysical Fluid Dynamics Institute, The Florida State University, Tallahassee, Florida, United States of America.
No MeSH data available.