Predictive Analysis of Acoustic Demining Efforts, 14-R9658

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Principal Investigators
Jerome A. Helffrich
Walter M. Gray
James D. Walker

Inclusive Dates:  10/01/06 – 04/01/08

Background - There is a need for detectors that can sense non-ferrous land mines and improvised explosive devices (IEDs) that may be buried in roadways. One proposed method of finding these usually plastic devices is to project seismic waves from rollers that are pushed along the roadway and scan the undulations of the road ahead using a laser beam. This approach relies upon some assumed properties of the soil underlying the roadway to facilitate quick detection of the response of the mine. Previous researchers in this arena have been unable to do more than come up with a phenomenological explanation of how it works, based on two adjustable parameters. This is insufficient for field use; what is needed is a more detailed model of the interaction of seismic waves and buried objects, and a way to condense this model into a few simple heuristics that can be put into hardware.

Approach - This work was targeted at illuminating the interaction between a buried land mine and covering soil under vibrational excitation, as would be encountered in the use of some proposed acoustic-based land mine detection schemes. The work presented here concentrated mainly on a land mine simulant buried in sand, but also comprised measurements on the behavior in moist sand and moist clay. The results show that sand is apparently nonlinear in its mechanical characteristics even at low vibration levels, and that this nonlinear behavior is difficult to model with existing finite element modeling software. Results are presented that show both classical nonlinear behavior (resonance softening) and nonclassical behavior (hysteretic behavior in response to excitation level changes) in this system.

Accomplishments - The project's goal was to conduct measurements of the vibrational resonances of a land mine simulant in a controlled soil environment that could be modified and whose conditions could be monitored with relative ease. Because of the difficulties of working with electronics and variable soil moisture outdoors, an indoor chamber was deemed preferable to a test bed outdoors. To connect the measurements with a theory for how buried mines should behave when vibrated, extensive numerical (finite element) analyses of the mechanical behavior of the chamber with sand fill material were conducted with the goal of reproducing the experimental results, and then the mathematics involved was approximated in the numerical simulations with a few simple equations.

The finite element modeling concentrated on (1) the prediction of natural frequencies of oscillation of the fill material (generally sand); (2) prediction of the natural frequencies of the upper surface of the sand in the experimental apparatus; and, (3) prediction of the response (frequency content) along the upper surface of the sand in the experimental apparatus given an input excitation at the base plate of known frequency content. First, the natural frequencies were calculated to compare with the observed values as determined by the laser and geophone sensors. Then, the fill material and base plate properties were adjusted to align the measured resonances as closely as possible with the numerically computed values.

A solid model of the experimental apparatus was developed and implemented in LS-DYNA to investigate resonance frequencies of the mine stimulant and natural and forced oscillations. For the initial simulations all materials were assumed to be linear elastic, thus the MAT_ELASTIC material model available in LS-DYNA was used. In an effort to make the material model more realistic, and to base it upon the measurable properties of density, porosity and water content, a pressure-dependent sand model was created that assumed elastic, perfectly plastic behavior (no strain hardening). In this model, the yield behavior is determined from a curve of pressure vs. volumetric strain. The project team searched for material property data useable in a crushable foam model, and common properties such as density, shear and bulk modulus were extracted from various sources. Data describing the pressure dependence of volumetric strain and yield stress (pressure constants) required by the model were not readily available for either sand type. However, using equation-of-state and constitutive relationships, estimates of the required parameters were obtained from the triaxial compression data. Volumetric strain as a function of pressure was obtained by assuming uniform deformation (same in all axes).

The same two excitation signals (1.6 kiloHertz, 160+182 Hertz) used in the linear model were input to the pressure-dependent model (Figures 1 and 2). The results reveal that the pressure-dependent crush up of the sand alters or removes much of the higher frequency content of the input signal with only low frequencies (less than 20 Hertz) observed in the response of the sand surface. This result contrasts sharply with experimental observations; thus the pressure-dependent model does not appear to provide a realistic representation of the actual sand experiments. However, the actual excitation amplitudes utilized in the experiments are on the order of 0.0005 inch versus the 0.05-inch amplitudes assumed in the simulations. The higher amplitude may be creating an excessive "crush-up" not experienced in the experiments.

Figure 1. Composite input signal consisting of 160 Hertz and 182 Hertz sine waves used to generate amplitude and frequency response shown in Figure. 2.
Figure 2. Amplitude and frequency response of the pressure-dependent model resulting from a 160 Hertz and 182 Hertz input signal. Note the lack of an expected difference frequency signal appearing in the output, possibly due to intense attenuation of the input signals.

For the experiments, the mine simulant was constructed as a copper-clad fiberglass plate, supported on its edges by a tubular column extending up from the base of the chamber (Figure 3). This construction incorporated two key features of the actual mines being simulated, in that it had a generally plastic top of the correct diameter (6.5 inches), and the top was supported at the edge by a clamped support, similar to the way that the molded cover of a real mine would be. The test chamber was built on an elevated platform so that a shaker could be put beneath it to vibrate the chamber from below. This shaker has the capability of applying 112-N force to the underside of the chamber in the vertical direction, at frequencies up to 5 kHz. Displacement sensors were located at five points underneath the mine simulant plate. Two geophones were buried in the fill material next to the plate, one at the bottom of the test chamber and one just below the surface of the fill material. A laser vibrometer scanned across the surface of the fill material, allowing us to measure the vertical component of the vibration velocity at any point on the surface of the chamber.

Figure 3. Test chamber used in conducting measurements of the acoustic properties of buried mine simulants. The fiberglass plate simulating the top of the mine has been removed in this photograph.

The test chamber was used for two types of experiments. In the first type, the system was excited by a swept sine tone at the base plate, and the response at the excitation frequency was measured. This kind of testing is in general useful for obtaining the response of a nonlinear system as a function of amplitude, because only one frequency of signal is present in the system at any time. In this way, the team able to observe shifts in the vibration resonance peaks as a function of amplitude, which would be obscured if noise or chirp type excitations were used. In the second type of experiment, the system was driven with a sine wave at a series of increasing and decreasing levels, of a frequency near the fundamental resonance of the simulant plate (Figure 4).

Figure 4. In these experiments, the objective was to observe the change in the system response with time after the signal input changes level. This kind of nonlinear, or stair-stepped, response is due to hysteresis and thermal effects in the material (sand or dirt) and is infrequently observed in laboratory experiments, as far as we know. Typical input waveform (base plate accelerometer signal) to the test chamber when nonlinearity in the time domain is being studied.

Another point of comparison between our measurements and the literature is in the shift of the resonance frequency with amplitude of excitation. In linear systems, the resonance frequency is independent of the amplitude of excitation (shaking), but in nonlinear systems it is not uncommon to see a hardening (frequency shift up) or softening (frequency shift down) of the resonance with increasing excitation amplitude. In severely nonlinear systems, this can result in the resonance frequency being different when the amplitude is increasing from when it is decreasing. Such an experiment was conducted to see whether such nonlinearity existed in the sand-mine system, and an attempt was made to extract the nonlinear frequency shift with excitation amplitude from that (Figure 5). The results are significant in that it fits theories of nonlinear behavior of rocks pretty well, but with a larger nonlinear behavior ( J. Acoust. Soc. Am., Vol. 117, No. 1, January 2005 P. Johnson and A. Sutin: "slow dynamics and nonlinear fast dynamics in diverse solids"). This idea has also come up in recent work on earthquakes, where the shocks delivered to buildings during earthquakes can be explained better by a model that treats the soil above the subsurface rock as a nonlinear medium that can accelerate the objects on top of it as if they were bouncing off a trampoline. The result is greater damage one would anticipate just by looking at the seismograph plots.

Figure 5. Shift of resonance frequency of the buried mine simulant with amplitude of shaker excitation. The data fit very well to a straight line with slope -5100 Hertz/(meters/second). In terms of strain amplitude, the shift is 5.5 Hertz per microstrain.

Eigenvalues (resonant frequencies) were calculated by finite element analysis techniques using LS-Dyna®. Interest was focused on the behavior of these resonances at different vibration amplitudes, since this is a classical way of evaluating the force-displacement curve of a nonlinear oscillator. The team ran a series of experiments that mapped the response of the fundamental plate/soil resonance mode as the excitation amplitude was increased and then decreased (Figure 6). The effect was highly reproducible at different depths of sand, and followed the same trajectory when the excitation amplitude was swept down.

Figure 6. Springs that soften as they are pushed and stretched farther are represented here as nonlinear softening (downward frequency shift) of buried mine simulant resonance with increasing excitation amplitude.

In conclusion, three different signatures of nonlinear behavior were observed in the buried-mine system:

  • Harmonic generation in the fill mixture increased in level as the excitation level was increased, but not always monotonically. Nonlinear behavior of the sand (or soil) covering the mine was a prominent feature of the measurements, and needed to be included in the finite element modeling for agreement with results at amplitudes greater than 2x10-5 m/sec.
     
  • Nonlinear "softening" of the principal mine resonance occurred as the driving amplitude was increased, from which was extracted the nonlinearity parameter α for this soil. The fact that this parameter was not greatly different from that of sandstone suggests that the nonlinearity is intrinsic to the fill material and not a result of the loss of contact between the fill material and the plate. This is further supported by the fact that the excitation levels used were at least a factor of 20 below what would create accelerations of -1 g in the fill material. This observation supports the general use of harmonic detection for finding buried land mines.
     
  • Hysteresis in the response of the system to changes in drive level was measured, indicating there is a response time constant on the order of 0.01 to 0.1 seconds, during which the system adjusts to a new drive condition. The effects of this are very complex and need more advanced data analysis. This should be considered when selecting finite element material model for sand or soil.

Objects that are buried in soil have a variety of physical behaviors that are rich in nonlinearities, and the nonlinear behavior of the mine simulant buried in sand appeared to be dominated by the nonlinear behavior of the sand itself, and not by contact nonlinearities with the simulant. This is significant, as it refutes a current model of harmonic generation that was based on a discontinuity in the contact forces with the mine. The impact of this is significant in that a currently popular acoustic mine detection technique is to search for nonlinear signals being generated above the mine, in the area of contact between the mine and the covering soil.

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