# A Computational Platform for Automatic Signal Processing for Bender Element Sensors +
## 1 Introduction  
In geomechanics, the small strain shear modulus is an essential parameter for the dynamic characterisation of both cohesive and cohesionless geomaterials, and bender elements are one of the main techniques to measure it experimentally [1]. The use of bender elements as an alternative to the well-known resonant column test has been fuelled by their affordable price and flexible installation in various geotechnical testing devices. A ready-to-use bender element equipment costs tens of times less than a resonant column apparatus, and can be installed in codometers [2], triaxial devices [3], and Rowe cells [4], among others. Field applications have also recently been reported [5]. On the other hand, bender elements induce unknown levels of (very small) strain in the geomaterial, so they can only be used to measure the shear modulus, not to relate it with the level of strain, as is the case of the resonant column. Moreover, the interpretation of the test is notoriously challenging and substantially depends on the experience of the analyst [6]. A typical experimental configuration consists of two bender elements, inserted on opposite sides of the sample: a transmitter whose lateral vibration (input signal) generates a transient shear wave, and a receiver which is triggered by the vibration of the materialand generates the corresponding electrical signal (the output signal). The objective of the experiment is to use the information on the input and output signals to derive the shear modulus of the material [7]. This has mainly been achieved using two classes of interpretation techniques, namely time domain techniques and frequency domain techniques. Time domain approaches use pulse input signals and aim at either reading the arrival time of the shear wave directly from the output signal or obtaining it by cross-correlating input and output signals. From the travel time, the shear wave velocity is calculated, from which the small strain shear modulus is found by using a well-known equation of the Theory of Elasticity [8] (from this point on, the term _shear modulus_ is used instead of small strain shear modulus, to keep the presentation simple). Conversely, frequency domain approaches generally use continuous harmonic input signals and measure the wavelength as a function of the input frequency from which the wave velocity is calculated [9]. Hybrid methods have also been reported [10]. Both time and frequency domain interpretation methods rely on the assumption that input and output signals are similar. This is not the case, however, as the output signal is strongly affected by the dispersion of the travelling waves, boundary reflection and radiation [11], as well as by the pollution of the main (shear) wave with secondary (compression) waves, byproducts of the lateral motion of the transmitter. For this reason, the peak on the output signal that marks the arrival of the shear wave may not be the first nor the highest local maximum, so its accurate identification using conventional time domain methods may be quite arduous. On the other hand, frequency domain methods assume that the wavelength is constant throughout the sample, which is generally not true due to wave distortion. These issues induce considerable subjectivity in the interpretation of the output signal, which is notoriously uncertain [6]. Between 2003 and 2006, an International Parallel Test took place in 23 geotechnical laboratories from 11 countries to test the consistency of the shear modulus measurements of the same samples of Toyoura sand. The specimens were tested under different state conditions (saturation, consolidation patterns, confining pressures). The results are known as one of the most convincing displays of uncertainty of the bender element predictions published to date [12]. The consistency of the results was particularly problematic for low confining pressures (50 kPa).