Acoustical Society of America
ICA/ASA '98 Lay Language Papers


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The Remarkable Nonlinearities of Rock

James A. TenCate - tencate@lanl.gov
Koen E.A. VanDenAbeele, Eric Smith, Thomas J. Shankland, and Paul A. Johnson

EES-4, MS D443, Los Alamos National Laboratory
Los Alamos, NM 87545

Popular version of paper 3aPAb10
Presented Wednesday morning, 24 June 1998
135th ASA Meeting/16th International Congress on Acoustics, Seattle, WA

In contrast to air or water, rocks and other earth materials are remarkably nonlinear. Furthermore, the nonlinearity is quite complex and is the reason that several different, clearly distinct behaviors are observed. For example, we see nonlinearity in rock at incredibly low levels (where wave motions are on atomic scales) and memory effects at higher levels. The point of our study is to learn more about the properties of rocks by studying the various types of nonlinear behavior present in rock. It also may turn out that understanding cracked materials like rock will lead to an increase of our understanding of fatigue and cracking in common engineering materials.

Our experiments are simple. A long thin rod of rock--like an organ pipe--has a resonance frequency. (It's even conceivable that one could build a small organ out of various sizes and types of rocks! ) By putting a lightweight piezoelectric source at one end (see the figure at the right), we can drive the rod at successively increasing frequencies, listen for the resonance peak (with a device which measures the acceleration at the end), and plot an entire resonance curve for different driving amplitudes. We've done these sorts of experiments with several types of rocks. In what follows we'll show results we obtained on Berea sandstone, a common, easily obtained oil/gas reservoir rock.

The figure below shows how different a sandstone rod is compared to a rod made of a linear material. A set of resonance curves taken on a lucite rod (shown in left hand side of the figure) shows that the lucite behaves much like an organ pipe. It has a single resonance frequency no matter how "loud" we make the drive. Constrast the lucite resonance curves with those of a Berea sandstone rod (right hand side of the picture). If an organ pipe behaved like the sandstone shown below, the resonance frequency would drop the louder you blew on the pipe. A drop in resonance frequency with increasing drive means that the rock is getting softer, i.e., not as stiff, at higher drives. There are other more complex behaviors one can see in the picture: the shape of the resonance curves changes and frequency sweeps up and down through resonance aren't the same.

 

Two behaviors. We've found two rather different and distinct nonlinear behaviors in the samples we've examined. The picture to the right shows approximately where each behavior dominates. One such regime occurs at very low strains (shown by the green bar on the right hand side). Here it's likely that only a small number of grains are participating in the resonance and any actual movement (e.g., opening and closing of cracks, fluid movement within cracks and pore spaces) is on atomic scales. At higher strains (shown by the yellow bar), the rock's nonlinearity starts to become much more obvious (and very different in character as well).


At very low strains, we find nonlinearity. To our knowledge, this has never been reported elsewhere. The picture to the left is a plot of the resonance frequency as the drive level is increased. The plot shows something very interesting and unexpected: the rock never shows linear behavior! As the drive amplitude is increased, the rock first stiffens and then begins to soften (which continues up to and into the next regime). Such nonlinearity is rare in acoustics. We hope that studying nonlinearity at these low strains will tell us much about the rock's microstructure.

At higher strains, the resonance frequency shifts, resonance-curve shapes change, and different up and down resonance curves begin to appear. What causes these effects? It appears as if the rock has memory. We find that when you drive a rock hard, it softens (becomes like a softer spring) and stays that way for some period of time. In fact, you can devise an experimental recipe which demonstrates this nicely. Start with a virgin rock, measure its initial resonance frequency at a low amplitude, then drive it hard for a period of time. The result should be a softer rock. To test, turn the large-amplitude drive off, plot a series of successive small-amplitude resonance curves (see the figure below), and watch the rock gradually stiffen. The rock should finally end in the state it started (several minutes or hours later, depending on the rock).


For further information on various other aspects of nonlinearity, see our web site via the following URL: http://www.ees4.lanl.gov/Nonlinear


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