Effects of sample size on bender-based axial G₀ measurements

Abstract

Bender elements are piezoelectric transducers frequently employed for the measurement of the small-strain shear modulus of soils. The measurement is based on transmission of a mechanical signal through a soil sample. A very common set-up involves transmission along the axis of a cylindrical sample, with source and receiver transducers mounted, for instance, in the end platens of a triaxial apparatus. Current test interpretation is generally based on the assumption of plane wave transmission between transducers. However, this model does not explain the heavily distorted transmission usually observed. The result is substantial measurement uncertainty. Although other phenomena do play a role, it is here proposed that a main culprit for signal distortions is sample-size effects due to lateral boundary reflections. To support this hypothesis, results from a series of numerical 3D simulations of the problem are analysed. Velocity estimates obtained from the simulated traces using plane-wave based time and frequency domain methods are compared with the known exact value. Errors in velocity determination are shown to be very important and directly related to lateral boundary influences. Comparison with some experimental data confirms the need to include sample-size effects in a renewed interpretative framework for bender tests.

A Framework Interpreting Bender Element Tests, Combining Time-Domain and Frequency-Domain Methods

“…These ratios are such that near-field effects are more likely to affect the output signals, being less than the value of 3.0 suggested by Arroyo et al (2006) as the limit above which such effects should not be present. Ideally, this would be overcome using higher frequencies, but in this case, the response at higher frequencies was too weak to allow sensible analysis.…”

“…It has been pointed out by a number of authors (e.g., Lee and Santamarina, 2005;Arroyo et al 2006) that side reflections of P-waves are less likely in a saturated triaxial sample than in a dry one, because the impedance difference between the saturated soil and the cell water is much smaller than between the same dry soil and cell water.…”

“…For the lower frequencies used here, the L / ratio is smaller than the minimum value (3.0) required to avoid near-field effects (e.g., Arroyo et al 2006). Nevertheless, there is still considerable benefit to be derived within the presented framework in considering these lower frequencies, as the information provided allows an appreciation of the complete response.…”

Application of Bender Elements Technique in Testing of Anthropogenic Soil—Recycled Concrete Aggregate and Its Mixture with Rubber Chips

“…The reliability of BE technique is influenced by different factors, e.g., near-field effects [49], directivity [48], travel distance [50], boundary effects [51], sample geometry and size [52], cross-talking [53]. The difficulty lies as well in accurately evaluating the travel time (tt) of shear wave from the source BE to the receiver BE, whereas a distance between elements (L TT ), accepted as the tip-to-tip distance, can be precisely measured.…”

Two-dimensional discrete element modelling of bender element tests on an idealised granular material

“…In a physical test uncertainty about the magnitude of the bender deflection and the nature of the contact between the bender element and the soil, amongst other issues, add to this complexity. There is therefore merit in creating simpler, numerical models of the system to isolate the various sources of complexity, motivating the continuum based numerical analyses of Arroyo et al [7] and Rio [8]. While these studies have advanced understanding of the mechanics of bender element tests, they are restricted as they assume the material to be a solid continuum, and do not explicitly consider the particulate nature of soil.…”