The Phase-Shift Method for
Studying Nonlinear Acoustic Behaviors of Soils

Popular version of paper 4pPA3
Presented Thursday afternoon, October 20, 2005
ASA/NOISE-CON 2005 Meeting, Minneapolis, MN

It is generally believed that nonlinear parameters are more sensitive than linear parameters, such as sound speed, attenuation, impedance, and other commonly-used physical quantities, to small changes in material properties caused by structural disturbance and environmental variations. Nonlinear behavior can be used as a powerful tool for material characterization and for non-destructive evaluation. In comparison with intact solids and fluids, porous materials such as rocks, sands, sandstones, sediments, soils, and other cracked materials have much stronger nonlinear responses.

One of the important characteristics of nonlinear behaviors is the amplitude-dependent phenomenon, i.e. the physical properties of a material change with the amplitude of a mechanical vibration or a sound. For example, the resonant frequency of a cylindrical rock bar driven by a frequency-sweeping source shifts towards a lower frequency as the amplitude of the signal increases. The physics behind the phenomenon can be explained as a result of nonlinearity in which elastic modulus is reduced in responding to an increment of sound pressure. By measuring the resulting frequency shift in a resonant bar, the nonlinear behaviors can be studied. This method is called the frequency shift method.

Another method is proposed in this study that measures the phase shift as well as the frequency shift when the sample tested is excited by a sweeping frequency of increasing amplitude. This method, hereafter called the phase shift method, uses three acoustic transducers serving as transmitter, reference, and receiver, respectively. The phase difference between the received signal that travels through a test sample and the reference signal that detects the source vibration caused by the transmitter is measured by a lock-in amplifier with high accuracy. Due to nonlinear effects, a variation in the phase difference, or a phase shift, occurs as the excitation level increases. The variation in phase shift as a function of sound pressure or dynamic strain can be used to calculate the nonlinearity parameter, an important parameter to quantify the degree of the nonlinearity of a material, by curve-fitting the equation of state.

In this presentation, the nonlinear acoustic behaviors of soils are studied and typical nonlinear phenomena such as resonant frequency shift and phase shift are observed. The study also found that rich, high-order harmonics up to fifth harmonic are generated and serve as the evidence that energy is transferred from the fundamental frequency component to high harmonics. The nonlinearity parameter of a soil is measured and compared using both frequency shift and phase shift methods. The results are comparable.

This research is sponsored by the USDA Agricultural Research Service under Specific Cooperative Agreement 58-6408-5-084.