Bridging the Gap III (2015)
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ACOUSTIC FLUIDIZATION: WHAT IT IS, AND IS NOT. H. J. Melosh1 1Earth Atmosphere and Planetary
Sciences, Purdue University, West Lafayette IN 47907. [email protected]
Acoustic Fluidization: I introduced the concept of
acoustic fluidization in 1979 to explain the astonishingly low strength and viscosity exhibited by the collapse of impact craters and the formation of central
peaks in lunar craters [1]. The name I gave to this process was not well chosen for the geologic community—“vibrational fluidization” might have been more
apt--but that name was already in use in another context and would have proven confusing [2].
The principal motivation for introducing this process was to explain the transition from simple to complex craters on the Moon. Mechanical analysis of the
collapse of simple craters indicates that the strength of
the underlying material is only about 3 MPa [3]. Furthermore, the rise of central peaks in craters larger than
about 15 km diameter on the Moon suggests that the
post-impact debris can flow as a fluid with a viscosity
in the vicinity of about 109 Pa-sec [4], implying a
Bingham rheology for the material surrounding the
crater. How could dry, broken rock debris on the surface of a planet lacking water, air or even clay minerals
flow like a liquid? My solution was to invoke the action of strong vibrations in the rock debris broken by
the shock from the impact, which I proposed could
briefly fluidize the debris. The reality of such strong
vibrations near an impact is supported by ground motion measurements near large explosions on Earth [5],
and the nonlinear dependence of strain rate on stress
predicted by the theoretical model is consistent with
the phenomenological Bingham rheology [6]. Moreover, the predicted relation between stress and strain
rate as a function of the amplitude of vibrations was
verified by measurements with a rotational viscometer
[7], as shown in Figure 1.
The acoustic fluidization model has been widely
applied to hydrocode modeling of impact crater collapse through the approximate scheme of the “Block
Model” [8], with great success, although at the cost of
introducing three empirical parameters; one that relates
the amplitude of the vibrations to the strength of the
initial shock wave, another that specifies an effective
viscosity (it essentially chooses an effective frequency
or wavelength of the vibrations) and one that specifies
the decay rate of the vibrational energy.
The full acoustic fluidization model also envisions
a feedback between flow and the vibrational energy
field [9,10], which is not captured by the Block Model.
A recent study has finally begun to lift this restriction
[11] and provides a more accurate model of how craters collapse.
Figure 1. Strain rate vs. stress in sand fluidized by
strong vibrations at a frequency of about 300 Hz. Σ is
the ratio between the rms vibration amplitude and the
overburden pressure, and the yield stress is measured
in the absence of vibrations. The solid theoretical
curves are fit to the data with no free parameters.
Tests of Acoustic Fluidization? A recent study [12]
argues against the efficacy of acoustic fluidization in
the formation of a well-exposed central peak of a crater
on Mars on the basis of the mapped exposures’ failure
to conform to the assumptions of the Block Model. In
particular, it was stated that the apparent continuity of
the mapped units and the lack of matrix separating
observable discrete blocks is evidence against the process. However, I believe that this is a case of taking a
simplified heuristic model too literally. The Block
Model, with its discrete blocks separated by thick layers of matrix is only a conceptual model to motivate
equations that are similar to those of the full acoustic
fluidization model, which never postulated such a
structure. Acoustic fluidization only supposes that a
mass of dry rock debris, which is potentially quite homogeneous, is fluidized by the fluctuating pressures
induced by strong vibrations (acoustic waves) traversing the mass. Individual clasts or larger rock units,
normally pushed tightly against each other by the pressure of overlying rock debris, suddenly become free to
slip during a transient fluctuation of the pressure field
to low pressure. The mechanism is very similar to one
proposed (and observationally verified) for the flow of
rock debris in muddy debris streams [13,14], where
pore pressure fluctuations relieve the overburden pressure within the normally clast-supported matrix.
Bridging the Gap III (2015)
I have also suggested that acoustic fluidization is
responsible for the low coefficients of friction observed in large-volume rock avalanches, termed longrunout landslides or sturzstrom [1,9,15]. These large,
rapid mass movements have much in common with
crater collapse, including Bingham rheology, low coefficients of friction and laminar viscous deformation
[16]. Figure 2 illustrates the debris lobe of one such
avalanche that exhibits many of the characteristics of
the units mapped by Johnson and Sharpton [12].
Figure 2. Debris lobe of the McGinnis Peak, AK
sturzstrom that was initiated by the 2002 Denali earthquake. Note the coherent, but highly deformed, contacts of distinct debris units in the landslide lobe [17].
It has long been noted that such avalanches, in spite
of speeds from 50 to 70 m/sec, flow in an apparently
laminar fashion that does not mix distinct rock units, in
spite of very large strains incurred as the broken rock
mass flows between its source area and final debris
lobe [18].
From a distance, one might infer that the rock in
the slide lobe remained intact, as is suggested by geologic maps of many impact crater central peaks. However, close inspection reveals that the rock is thoroughly shattered and lacks any appreciable tensile strength.
Coherent block sizes can range from centimeters to
many meters and, in still larger collapses occurring in
impact craters, might even approach tens or hundreds
of meters, as suggested by the boreholes into the
Puchezh-Katunki crater’s central peak [19]. Although
the flow incorporated large (but evidently deformed)
“blocks”, there is seldom evidence of a finer matrix
between these units: They are typically separated only
by narrow faults and fractures, consistent with the requirements of the acoustic fluidization model. Similar
observations have also been reported from the wellexposed central peak of the 12 km diameter Kentland,
IN (USA) impact crater [20] as well as other craters
[21], in which the deformation is largely due to numerous small-scale fractures whose motion would
normally be opposed by friction and thus require a
temporary relief of overburden pressure to slide.
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I thus believe that the Martian crater observations
of Johnson and Sharpton [12] as well as the more detailed observations possible at terrestrial craters, are
entirely consistent with the action of acoustic fluidization. On the other hand, the apparent absence of melt
sheets bounding the deformed blocks forming the central peaks of terrestrial craters mitigates strongly
against alternative weakening models that appeal to
discrete planes of melting in collapsing rock units [22].
References: [1] H. J. Melosh, Journal of Geophysical Research 84, 7513 (1979). [2] T. R. H. Davies,
Rock Mechanics 15, 9 (1982). [3] H. J. Melosh, in
Impact and Explosion Cratering, edited by D. J. Roddy
et al. (Pergamon Press, New York, 1977), pp. 1245–
1260. [4] H. J. Melosh, Journal of Geophysical Research 87, 371 (1982). [5] E. S. Gaffney et al., J. Geophys. Res. Solid Earth 87, 1871 (1982). [6] H. J.
Melosh et al., Journal of Geophysical Research 88, 830
(1983). [7] H. J. Melosh et al., Transactions of the
American Geophysical Union, EOS 76, suppl., F270
(1995). [8] H. J. Melosh et al., Annual Review of Earth
and Planetary Sciences 27, 385 (1999). [9] G. S. Collins et al., J. Geophy. Res. 108, doi: 10.1029 (2003).
[10] H. J. Melosh, Nature 379, 601 (1996). [11] H.
Hay et al., 45th Lunar and Planetary Science Conference 1938 (2014). [12] M. K. Johnson et al., 46th Lunar and Planetary Science Conference 46, 1280 (2015).
[13] R. M. Iverson et al., Science 246, 796 (1989). [14]
R. M. Iverson, Reviews of Geophysics 35, 245 (1997).
[15] H. J. Melosh, Acta Mechanica 64, 89 (1986). [16]
W. B. Dade et al., Geology 26, 803 (1998). [17] R. W.
Jibson et al., Earthquake Spectra 20, 669 (2004). [18]
R. L. Shreve, Science 154, 1639 (1966). [19] B. A.
Ivanov et al., Lunar Planet. Sci. Conf. XXVII, 589
(1996). [20] R. T. Laney et al., In: Lunar and Planetary
Science Conference 9, 2609 (1978). [21] T.
Kenkmann, Geology 30, 231 (2002). [22] L. E. Senft
et al., Earth and Planetary Science Letters 287, 471
(2009).