# A Computational Platform for Automatic Signal Processing for Bender Element Sensors +
## 1 Introduction
For instance, for isotropically consolidated specimens, the standard deviation of the readings was larger than half of their average value, with measurements ranging from 25 MPa to 140 MPa. Such findings highlight the need for consistency and objectivity in bender element tests, both in respect to the experimental setup and to the interpretation of the output signal. A standardisation effort was made in 2019, with the publication of the ASTM D8295-19 standard [13]. However, the standard only specifically addresses the triaxial setup (although the procedure can be extended to other geotechnical testing devices), and two time domain interpretation techniques, both based on the direct observation of the output signal. Therefore, their application is subjective and requires experienced analysts. In 2016, a new, coupled numerical-experimental paradigm was proposed by the authors to improve the experimental setup and enhance the quality and objectivity of the interpretation of the output signal. Numerical models taking into account the multi-phase nature of geomaterials are used to describe in detail the wave propagation patterns and endorse the clear identification of the arrival time. The demonstration of the capacity of the numerical model to accurately recover the output signal obtained in the laboratory [14], even in two dimensions, was followed by the development of a mathematical framework for the automatic extraction of the shear modulus based on a fixed point model updating technique [15] and the optimisation of the experimental setup using the information gathered from the numerical models. Conventional numerical modelling of piezoelectric testing is hindered by the high frequency of the input signal and the complexity of material behaviour. For this reason, the numerical models that fuelled the coupled, numerical and experimental paradigm were based on hybrid-Trefftz finite elements. These elements belong to a wider family of (non-conventional) hybrid finite elements [16] and are ideally suited for modellinghigh-frequency wave propagation. Unlike conform displacement elements, hybrid-Trefftz elements use domain approximations that satisfy the differential equation governing the problem. Consequently, they are frequency-insensitive and distinguish naturally between the various types of waves that enter the dynamic response of the sample. On the other hand, hybrid-Trefftz finite elements are very rare in public or commercial software [17; 18]. Therefore, there is a need for public and user-friendly computational tools based on hybrid-Trefftz finite elements to bring the advantages of the new numerical-experimental approach to the fingertips of researchers and practitioners worldwide. This paper reports on the novel computational platform GeoHyTE, a user-friendly toolbox for the automatic extraction of the shear modulus from the output signal of bender element sensors. GeoHyTE implements the fixed-point model updating technique reported in reference [15], its computations powered by hybrid-Trefftz elements for porous elastodynamics. GeoHyTE is the first and currently the only automatic and physically consistent interpretation toolbox for bender element experiments. The beta version of GeoHyTE was recently released at the International Conference \"Trends on Construction in the Post-Digital Era\" [19] and can be downloaded upon request [20]. Besides the presentation of GeoHyTE, the paper is aimed to coin model updating techniques for shear modulus extraction as a mainstream class of interpretation methods, along with the time and frequency domain methods. The study of the mathematical properties of the updating function demonstrates its excellent convergent properties and is a theoretical novelty in respect to reference [15]. Considering two particularly problematic testing configurations reported in the International Parallel Test [12], the paper compares the shear moduli obtained using a wide range of time and frequency domain interpretation methods with those predicted by GeoHyTE and check the latter for consistency.