Test Bender Interpretacion

[Ermelindo Klatt]

Benderelement (BE) testing has become a widely used technique to evaluate S-wave velocities and to derive shear moduli from them in laboratory tests. Results of BE tests depend heavily on the proper identification of the S-wave travel time from waveforms often affected detrimentally by factors such as the near-field effect, crosstalk, noise, or drift. The authors have performed BE tests on soil specimens of Texcoco Clay over the last few years in triaxial cells and oedometers and have sometimes dealt with waveforms influenced by those undesirable factors thus, it was observed that the using of different available techniques to evaluate the S-wave travel time are often prone to errors. This paper shows that the S-wave travel time can be assessed unambiguously from the distance between the inflection points present in both the source and the received signals when waveforms generated with different input frequencies are superimposed, even in signals affected by the near-field effect, crosstalk, noise, or drift. This approach, named here the Wave Inflection Method (WI method), yields good results, at least when applied to data obtained from BE tests on soft Texcoco Clays. The method was validated by applying it to synthetic signals and experimental waveforms obtained from triaxial and oedometer tests equipped with BE. When applied to previously published waveforms on a wide range of soil types, our results suggest that the WI method significantly reduces subjectivity and produces improved reliability in evaluating the S-wave travel time.

Time-domain (TD) methods aim to identify two characteristic points in both the input and the output waveforms and the time subtraction between them is the S-wave travel time (Δt). Figure 1 shows examples of the TD methods that have been widely used and reported in the literature (Viggiani and Atkinson 1995; Jovičic et al. 1996; Pennington et al. 2001). These include the start-to-start, the minimum peak-to-peak, and the maximum peak-to-peak methods. It should be noted that personal judgment affects interpretation procedures and, hence, results may vary from one user to another. Some researchers have proposed alternative TD techniques for identifying Δt, based on applying a correction to the wavelength of the received signal (Khan et al. 2019, 2020). Finally, it has been observed on a stiff material such as compacted lime-treated silt that the S-wave arrival time can be assessed at a frequency higher than 20 kHz since the S-wave arrival point can be identified by referring to the P-wave received signal (Wang et al. 2017).

Frequency domain techniques (FD), that allow the automatic acquisition and interpretation of S-wave travel times in BE tests, have also been used (Greening and Nash 2004; Styler and Howie 2014), even though these methods can involve complex manipulation of data (Chan 2012). FD techniques usually use a continuous sinusoidal waveform as input and are based on finding the phase delay between in time series using the Fourier transform. An alternative method in the FD relies on identifying the arrival of the shear wave using a sliding Fourier transform and the predominant frequency of the received signal (Kumar and Shinde 2019). However, it has been reported that FD techniques can underestimate Vs, and some authors recommend that the results of this method be assessed by comparing them with the results obtained by applying other interpretation techniques, usually in the time domain (Viana da Fonseca et al. 2009; Yamashita et al. 2009). It was also reported that the Vs assessed using the cross-spectrum technique in the FD can vary substantially and erratically with the frequency of the transmitted wave (Hasan and Wheeler 2015); variations in observed S-wave travel times may be caused by the system response (Ogino 2019). Thus, removing the response of the BE subsystems from the whole response could dramatically improve the accuracy of travel time evaluation even for the time domain approaches.

It should be mentioned that S-wave travel times can seldom be obtained under optimal conditions. In experimental waveforms, the output signals can be significantly influenced by various factors, including the near-field effect, crosstalk, or noise that can distort the waveforms.

Electromagnetic coupling (crosstalk) is an early quasi-simultaneous component of the input signal that appears in the output signal due to inefficient transducer grounding, and it may be quite important in highly conductive solids such as saturated soils (Lee and Santamarina 2005). To prevent crosstalk, it is necessary to cover the BE with a conductive layer and connect it to the neutral segment of the coaxial cable to ground the electromagnetic field that may be generated in the soil. However, in highly conductive soils, this option may not be sufficient, and crosstalk may still be observed.

The output signal can also be influenced by noise spikes (background noise) that are visible as high-frequency components that disturb the time series. These spikes are highly irregular (sawtooth waveforms), have a modest variation of amplitude, and as a result, mask the S-wave arrival. Background noise can be mainly associated with deficiencies in grounding, electrical insulation, and mechanical protection (Santamarina et al. 2001). Background noise may also affect detrimentally input signals with frequencies that comply with LT/λ values to avoid the near-field effect. Even though Finas et al. (2016) proposed a methodology for an automatic Vs evaluation in BE test based on approaches developed for seismogram analyses, it was observed that the main limitation of these algorithms is for signals with a signal-to-noise ratio smaller than 4.

Finally, drift is a low-frequency disturbance and waveforms displaying this condition are usually rejected because arrival time values derived from them are generally erroneous. In BE tests drift may be attributed to rotation and tilting of the bender elements, amplitude-dependent electrical or mechanical hysteresis in the sensor, or cross-feed due to misalignment of piezoelectric transducers.

The authors have performed BE tests on soil specimens of Texcoco Clay over the last few years in triaxial cells and oedometers and have sometimes dealt with waveforms influenced by the undesirable effects explained previously. In the following paragraphs, we describe the manner in which some of these effects can affect waveforms in these very soft clays.

The pore water in Texcoco Clays contains rather high amounts of dissolved salts, with an average concentration of around 54.000 ppm of carbonates and sodium bicarbonate, chlorides, and other compounds (Carrillo 1969). High concentrations of dissolved salts enhance electric conductivity throughout the clay specimens and, consequently, crosstalk may affect output signals since electric signals intended for the source bender element can be conducted through the specimen, reaching the receiver bender element at a very high rate.

The experimental data from BE tests performed in these soft clays by the authors also show that the amplitude of output signals is largely attenuated when input frequencies are higher than 7 kHz (Flores-Guzmn et al. 2014; Diaz and Ovando-Shelley 2015; Chamorro-Zurita 2016; Fernndez-Lavn and Ovando-Shelley 2020). This matter can be attributed to the fact that attenuation in wet soils, is much higher than in dry soils, as observed previously by Patel et al. (2010). Under those circumstances, S-wave arrivals can be masked by noise, leading to erroneous S-wave arrival evaluations. Furthermore, in the tests performed in a larger than conventional oedometer built with steel, waveforms were usually affected by noise due to device conductivity since steel is capable of picking up environmental noise (electromagnetic signals), and from the electronic gear of the test set-up. It is also important to mention that the influence of the near field effect in output signals acquired in Texcoco Clay specimens with an input frequency less than 4 kHz is significant and masks the S-wave arrival, as noted previously (Flores-Guzmn et al. 2014; Diaz and Ovando-Shelley 2015; Chamorro-Zurita 2016; Fernndez-Lavn and Ovando-Shelley 2020).

The authors have observed that the approaches presented previously for assessing the S-wave travel time in signals acquired on BE tests performed on soft Texcoco Clay specimens are often prone to induce errors since those waveforms are often influenced by the undesirable factors listed before. To improve the accuracy of S-wave travel time evaluation, this article presents a time-domain method, the wave inflection method (WI method). The S-wave travel time is obtained in the time domain by comparing the time interval between characteristic points of the input and output wave signals. The proposed method is first presented and its theoretical background is discussed next. The WI method was applied to synthetic signals to validate the approach. Finally, in order to illustrate the reliability and accuracy of the S-wave travel time evaluation, the WI method is applied to experimental waveforms, that were affected by the near-field effect, crosstalk, noise, and drift, acquired on the triaxial and oedometer apparatus. Even in signals affected by those detrimental factors, the WI method is shown to yield accurate estimates of travel times.

The WI method was first tested by generating synthetic output signals from sinusoidal pulse input waveforms, similar to those used in routine BE testing with input frequencies varying from 1 to 7 kHz. The synthetic output signal is:

The propagation medium was characterized by properties given in Table 1 which are representative of actual Texcoco Clays in wet conditions. Data obtained from resonant column tests in undisturbed Texcoco Clay specimens, show that small strain damping ratio (Dmin) can vary from 1.9 to 3.2% (Fernndez-Lavn 2020). The parameter for the bender-element damping ratio is the one used by Wang et al. (2007).

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