Bender-based G0 measurements: A coupled numerical–experimental approach

Abstract

Bender elements are shear wave transducers, widely used for the experimental identification of the small-strain shear moduli of geomaterials. They offer good coupling with the sample and controllable loading signal and frequency, but some of their design and signal interpretation features are still under investigation. The research of these features has been approached mainly on experimental grounds and, in most cases, the conclusions were not consensual. This study aims at laying the foundations for a coupled, numerical–experimental approach to the problem. It uses hybrid-Trefftz finite elements to model the bender element test and the output signal obtained in the laboratory to validate the model.

Two main reasons justify the choice of the hybrid-Trefftz finite elements. First, hybrid-Trefftz elements are considerably less wavelength-sensitive than conforming displacement elements. This feature endorses the use of the same (coarse) mesh for modelling waves of very different types and frequencies, thus eliminating the need for time-consuming mesh refinements. Second, hybrid-Trefftz elements use physically meaningful approximation bases. This feature enables the numerical filtration of the spurious compression waves propagating laterally from the emitter and of their reflections from the envelope of the sample. Hybrid-Trefftz finite elements are shown to recover adequately the output signal obtained experimentally, for pulse excitations of various frequencies and two sets of boundary conditions. The decomposition of the output signal into its shear and compression components endorses the clear identification of the shear wave arrival and the amount of compression wave pollution.