Description

On the downside, the wave propagation induced by piezoelectric transducers is physically more complex, hindering the standardization of the experimental setup and the interpretation of the output signal, and limiting their use in the industry. Regarding the experimental setup, open issues include the best location of the transducers, their optimal geometry and the nature of the excitation. Regarding the interpretation of the output signal, the difficulties are related with three main issues: the dissimilarity of the input and output signals, due to high frequency damping and spurious boundary reflections (back into the sample) and radiation (into the surroundings); the residual motion of the emitter transducer, which continues to vibrate due to its own inertia after the electrical signal ends; and the solid continuum assumption in the moduli computation, which may be inadequate for multi-phase materials. Consequently, the purely experimental approach to the piezoelectric transducers testing only offers (partial) knowledge of the input and output signals and essentially leaves the analyst to guess what goes on between the input and output readings.

The objective of this project is to change the way piezoelectric testing is approached, by coupling experimental and numerical techniques toward a reliable characterization of wave propagation in geomaterials. Numerical modelling will offer insight that cannot be acquired by simply analyzing the lab data, and serve as a tool for assessing the impact of various setup options on the quality of the output signal.

The conclusions, once confirmed experimentally, will enable the optimization of the experimental setup, paving the way for its future CEN standardization. Moreover, the geometry of the transducers will be optimized in order to reduce the residual motion of the emitter and to increase the quality of the readings of the receiver. Prototypes will be produced and tested, and the best solutions patented. Finally, model updating techniques will be used to study the correlation between the simulation and experimental data for the automatic recovery of the shear modulus. This feature will be included in a computational toolbox, to be made available to the geotechnical community.

Numerical modelling of piezoelectric transducer testing using conventional techniques is hindered by the high frequency of the excitation and the complexity of the material behaviour. Pulse input signals of high frequency require the use of very small time steps for their correct modelling. Moreover, when conforming displacement finite elements are used in the model, their size must not exceed 1/10 of the wavelength, which is typically of the order of millimetres. To avoid such complications, hybrid-Trefftz finite elements will be used for the numerical models. Hybrid-Trefftz elements are roughly 30 times less wavelength-sensitive than the conforming elements. This feature endorses the use of very coarse meshes which do not need to be locally refined as the wave propagates. Moreover, hybrid-Trefftz elements use physically meaningful approximation bases, tailored for each specific problem. This feature enables the numerical filtering of waves of a certain type (e.g. shear waves in bender element testing), thus eliminating the output signal pollution. Finally, the use of a novel wavelet-based time integration technique endorses the use of very large time steps.