# A Computational Platform for Automatic Signal Processing for Bender Element Sensors +
## 6 Conclusions  
GeoHyTE is a new computational toolbox for the automatic shear modulus extraction from the output signal provided by bender element sensors. GeoHyTE searches for the shear modulus that maximises the correlation between the output signals obtained experimentally and using a finite element model. The hybrid-Trefftz finite elements implemented in GeoHyTE are ideally suited to highly transient problems involving large solution gradients, as typical for bender element tests. They are nearly wavelength-insensitive, meaning that the well-known requirement of calibrating the leading dimension of the finite elements to cover at most \(1/6\) of a wavelength needs not be observed. For this reason, good shear modulus predictions can be obtained using very coarse finite element models. GeoHyTE was thoroughly tested and validated using a well-known granular geomaterial, and its predictions were compared with all mainstream interpretation techniques. The shear moduli produced by GeoHyTE compare well with other time domain interpretation techniques and with the bulk of the results reported in an International Parallel Test  
Figure 29: Horizontal displacement fields obtained with the coarse model. that was used as a benchmark. The procedures built into GeoHyTE can be used for clays, too. However, since clays typically have very low permeability, the seepage between solid and fluid phases is generally neglected and they are modelled as single-phase materials. In this sense, using hybrid-Trefftz elements based on the [PERSON]'s theory is not economical from a computational perspective. Future releases of GeoHyTE will include finite elements for single-phase media which will be able to model clays at a lower computational price. GeoHyTE is highly insensitive to the starting point of the maximisation process and able to converge to a global maximum of the correlation despite the presence of local extrema. Moreover, the derivative of the (single) fixed point of the update function is close to zero, meaning that it is an attractor and the convergence is very fast. The maximum number of iterations needed to converge was four, despite the vast differences between the starting points essayed in this study. As opposed to most conventional techniques used for the interpretation of bender element tests, the procedure implemented in GeoHyTE is objective (as it does not depend on the experience of the analyst) and physically consistent (as it correlates signals of the same nature, obtained taking into account the physical features of the experiment). GeoHyTE is user-friendly, featuring graphical user interfaces for all phases of the definition of the model, and highly flexible, as it enables the use of localised basis refinements, meaning that different refinements of the domain and boundary bases can be defined on different elements and essential boundaries. It uses implicit parallel processing techniques to improve its computational efficiency and outputs detailed descriptions of all fields at every iteration, which can be used to visualise the solutions after (and even during) the execution. A beta version of the software is available to the scientific community upon request [20]. We believe that this paper will enable GeoHyTE to become a mainstream signal interpretation technique for bender element sensors. Conceptualization, I.D.M. and A.G.C. ; methodology, I.D.M. ; software, I.D.M. and A.A.; validation, I.D.M. and A.A.; investigation, I.D.M., A.A. and A.G.C. ; resources, A.A. and A.G.C. ; data curation, A.A.; writing--original draft preparation, I.D.M. ; writing--review and editing, I.D.M., A.A. and A.G.C. ; supervision, I.D.M. and A.G.C. ; project administration, I.D.M. and A.G.C. ; funding acquisition, I.D.M. and A.G.C. All authors have read and agreed to the published version of the manuscript.