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Bender element transducers are used to determine the small-strain shear stiffness,G0, of soil, by determining the velocity of propagation of mechanical waves through tested samples. They are normally used in the laboratory, on their own or incorporated in geotechnical equipment such as triaxial cells or oedometers. Different excitation signals and...
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... 3. The poor contact between the bender element sensor and the soil material (mainly for the 1 mm sensors length). 4. At small strain test (as in Bender element), both of polyurethane rubber and soft soils showing a similarity in the mechanical behaviour (Rio, 2006). 5. ...
... 6. Many researchers used similar materials such as (Kim & Kweon, 2000;Li et al., 2019;Rio, 2006;Stokoe et al., 1990). ...
... Consequently, the soil specimens were replaced by Extruded Polystyrene specimens (Alshameri et al., 2015a(Alshameri et al., , 2015bLeong et al., 2009;Rio, 2006). The Extruded Polystyrene is a long chain hydrocarbon with a chemical component of styrene as chain (C8H8)n where the n refers to the number of styrene connected in a chain. ...
In the bender element (BE), the variations in the recommended Ltt/λ (wave path length, Ltt and the wavelength, λ) raise questions about the effect of these ratios in the near-field effect. The objectives of this study were sought to verify the efficiency of the Ltt/λ on the near-field effects as well as filling the gap associated with the assessment boundary conditions in both free/flexible and rigid boundaries. To achieve these objectives, the BE technique was implemented in uniform material (polystyrene) to assess both effects using various excitation frequencies, thicknesses, ratios of specimen width (D) to wave path length (Ltt), Ltt/λ, and time-domain interpretation methods. The results showed that both free/flexible and rigid boundary had no significant effects on compression wave velocity while the shear wave velocity was subjected to variation at D/Ltt < 1.15 and D/Ltt < 0.77 in free/flexible and rigid boundary respectively. At the rigid boundary, the reflected compression wave obscured the first-peak of direct shear wave at D/Ltt < 0.77. The outcomes from this study and the variations in the suggested Ltt/λ from previous researchers using different materials indicated that the near-field effects do not entirely depend on Ltt/λ. Nevertheless, the detection of the arrival time is affected by the variation in the frequency. Conclusively, to avoid the effect of boundary conditions, no measurements should be conducted via BE if the D/Ltt is less than 0.77. The first-peak method (using the conditions of Ltt/λ ≥ 5) was recommended to reduce the variations in the results as well as near-field effects. The longer the wave path, the lower the variation in the analysis of the wave velocity.
... The bender elements measure the elastic material zone. These tests could measure the strain range of γ = [10 −6 -10 −5 ] (Ishihara 1996;Rio 2006;Irfan et al. 2020). The elastic zone and part of the elasto-plastic zone of the shear modulus degradation curve could be measured by the RC, which provides information in the strain range of γ = [2×10 −6 :6×10 −3 ] (Ishihara 1996;Molina-Gómez et al. 2020). ...
... It applies a harmonic oscillatory stress or strain signal with a controlled frequency and strain amplitude, measuring the material dynamic properties G and ξ (Villacreses et al. 2020). Table 1 shows a summary of the strain level ranges that some devices could measure based on the references analyzed (Ishihara 1996;d'Onofrio, Silvestri, and Vinale 1999;Rio 2006;Irfan et al. 2020;Molina-Gómez et al. 2020;Villacreses et al. 2020). The rheometer test used in this research is a single device (not a combined method) that can measure a whole strain range from 10 −6 to 10 −2 . ...
The dynamic properties of loose sands under low stresses are an unexplored topic in soil dynamics because these soil conditions are uncommon in most geotechnical structures on Earth.
However, low densities and low-stress conditions prevail on other planets, like, for instance, the surface of Mars, for which particular attention is presently given through the InSight NASA mission. This work presents a new procedure for measuring the dynamic properties of loose
sand under low stress by using the dynamical mechanical analysis (DMA) tester, a technique commonly used in asphalt engineering but not in geotechnical engineering. Compared to traditional geotechnical methods (resonant column and cyclic triaxial tests), DMA investigates a broader range of strains using a single apparatus. In this work, we assess the dynamical properties of loose fine sand Dr ≈ 0.2, considered a possible Mars regolith analog, by varying the input strain from γ = 10−6 to γ = 10−2 while applying confining pressures from σ3 = 3 kPa to σ3 =30 kPa. The results validate the proposed procedure, showing an increment of the shear modulus as the confining pressure increases. Furthermore, they highlight DMA’s advantages for studying the dynamic properties of granular soils under low stress and strain
... The output signal is more attenuated, distorted, and complex than the input signal, because it incorporates the transfer functions of the transmitter BE, the soil, the receiver BE, and any electronics involved. The most common interpretation of a BE test is made in the time domain as recommended in the ASTM standard (ASTM D8295-19, Standard Test Method for Determination of Shear Wave Velocity and Initial Shear Modulus in Soil Specimens Using Bender Elements); however, the evaluation of the travel time is still the subject of much discussion (Arroyo, Muir Wood, and Greening 2003;Rio 2006;Ferreira 2009;Camacho-Tauta et al. 2015). Several authors have studied different phenomena affecting the performance of BEs, such as the installation and insulation conditions, crosstalk and noise effects, wave dispersion, near-field effects, wave reflections at the boundaries, and vibration modes (e.g., Sánchez-Salinero, Roesset, and Stokoe 1986;Viggiani and Atkinson 1995;Jovičić, Coop, and Simić 1996;Arulnathan, Boulanger, and Riemer 1998;Hardy, Zdravkovic, and Potts 2002;Lee and Santamarina 2005;Viana da Fonseca, Ferreira, and Fahey 2009;Irfan et al. 2020). ...
... For the determination of the seismic wave velocity from BE tests, the only two measurements required are the travel length and the travel time. Different proposals for the definition of the travel length have also been suggested (Fam and Santamarina 1995;Viggiani and Atkinson 1995;Rio 2006). The effective distance is most commonly taken as the BE's tip-to-tip distance, as confirmed by Camacho-Tauta et al. (2015), by comparison with the response of miniature accelerometers. ...
... MONITORING THE BENDER ELEMENT BEHAVIOR Schultheiss (1982) devised the self-monitoring BE by wiring the piezoceramics of the BE transmitter to two independent electric circuits. However, this monitoring procedure suffered from electric leakage that masked its true behavior (Greening and Nash 2004;Rio 2006). Greening and Nash (2004) mounted a strain gauge directly onto the piezoceramic platens and evaluated the resonant frequency of the transducer. ...
Bender elements (BE) have become a routine geotechnical laboratory tool for seismic wave velocity measurements. Since the 1980s, this testing technique has gained popularity, currently being available in many geotechnical laboratories worldwide in a variety of apparatuses. The advantage of simultaneously measuring small and large strain soil stiffnesses in each device, and the easiness and low-cost implementation of BE are the main reasons for their common application. Although there is already a standardized procedure for BE testing (ASTM-D8295, 2019), the use of high frequency pulses for the simultaneous measurement of compressional (VP) and shear (VS) wave velocities is not considered. In contrast, the use of high excitation frequencies is usually discouraged, as they tend to induce spurious participation of high vibration modes in the BE response. However, this work shows that the use of higher vibration modes can be advantageous to evaluate P-wave velocities from standard BE testing. Thus, this paper presents a new approach for the concurrent measurements of VP and VS using a typical installation of BE. The new approach is first demonstrated by experimental measurements, and subsequently validated using high-frequency laser vibrometer measurements of the actual BE deformation (nano-meter scale) under different excitation frequencies. The laser vibrometer measurements show the displacements of the transmitter BE as a function of the input frequency in not only the horizontal but also in the vertical directions; demonstrating the generation of P-waves when higher vibration modes are excited. The measured VP values are shown to be in good agreement with the predicted values using Biot’s equations. Thus, the proposed methodology addresses the current knowledge gap in the use of BE for concurrent P-wave and S-wave velocity measurements. The generated wavelengths are large enough to travel through the soil skeleton instead of the pore water only.
... Studies on bender transducer-soil sample interaction are rather limited in the literature. Laser vibrometers were used by Rio (2006) and Greening et al. (2007) to measure the response of T x in air and under embedded conditions in a synthetic rubber specimen (that replicated a soil specimen); a hole was created in the rubber specimen to let the laser beam reach the T x . Rio (2006) showed that because of the confinement in the rubber specimen, the resonant frequency f o and damping ratio ξ of the T x increased whereas the amplitude of vibration decreased. ...
... Laser vibrometers were used by Rio (2006) and Greening et al. (2007) to measure the response of T x in air and under embedded conditions in a synthetic rubber specimen (that replicated a soil specimen); a hole was created in the rubber specimen to let the laser beam reach the T x . Rio (2006) showed that because of the confinement in the rubber specimen, the resonant frequency f o and damping ratio ξ of the T x increased whereas the amplitude of vibration decreased. Pallara et al. (2008) used a laser vibrometer and showed that the shape of T x response in air is different from the shape of the input signal. ...
The response of a bender transmitter to sinusoidal excitations in air, liquids, and transparent soil is investigated using a novel laser vibrometer technique. The purpose of the study is to investigate how benders vibrate in different media so that the bender-soil interaction can be better understood. This may help in more accurate determination of the travel time of shear waves in soil and in more reliable prediction of the wave velocity. The study is important because, currently, there is no standardization of the bender element (BE) test available because the bender's behavior is not well understood when it is embedded in soil. BE test results depend on the critical assumption that the bender transducer behaves as a cantilever beam. It is shown for the first time through experimental modal analysis that benders actually vibrate as plates and higher modes of plate vibration play a significant role in bender-soil interaction. The participation of the different modes depends on the confining stresses present in the soil sample. The hydrodynamic interactions of the bender transmitter in different liquids show that the added mass effect of the liquids impact the frequency and, more importantly, the damping of the bender vibration. The changes in vibration mode and damping with a change in confinement have practical implications because the signal-to-noise ratio of bender vibration gets altered by these changes (thereby increasing the error in the estimation of shear waves), which impacts the interpretation of the BE test results. Thus, the study provides important insights into the bender behavior in terms of its displacement, velocity, resonant frequencies, damping ratios, and mode shapes.
... The setup and an example of test results is shown in Figure 6. For the bender element test, the interpretation procedure developed at NPRA evaluates the wave travel times in the same manner as for the SCPTu, by comparing the source wave and registered response within a given window using equation (3). The shear wave velocity is then calculated as ...
... These include adjusting either the travel time for the wave, adjusting the travel distance or adjusting both. On the topic of travel distance, a comprehensive study of previous work is found in [3], where it is stated that estimating the travel distance is commonly considered less problematic than determining the travel time and that a variety of authors have assumed that the tip-to-tip distance should be used as the travel distance. This is challenged by the author, who finds that the height should be measured between the center of dynamic pressure of the transducers, which is estimated to be roughly at 60% of the embedded bender element height. ...
... This would suggest that the cell pressures can have created a small gap between the sensors. Correcting vs with the first tc registration is in agreement with both the case where the travel distance is selected as the distance between the center of dynamic pressure for the elements [3] and the center to center distance (our initial assumption). The 60% embedded bender element height assumption is about the same as the average of the two others and is selected as the representative value from the bender test. ...
The shear wave velocity (v s ) is an important soil and rock property that can both be used in several geotechnical problems including for evaluation of dynamic properties of soils as well as in determining the maximum value of soil stiffness at small strain. This property is also seen to give good correlations with other soil parameters used in settlement and stability analyses. The Norwegian Public Roads Administration (NPRA) has recently invested in equipment to measure this fundamental soil property both in the laboratory using bender elements and out in the field using a seismic CPTu (SCPTu). NPRA has also developed internal procedures and techniques to standardize logical interpretations. To assist with this standardization procedure, NPRA has conducted soil investigations at a site in Fredrikstad municipality in the southern part of Norway. The investigations included SCPTu and extraction of high quality mini-block samples. The shear wave velocity is estimated after consolidation in the triaxial apparatus. The laboratory program was done right after the sample extraction and repeated on stored samples a couple of weeks later. Comparison of v s measured in the laboratory was then made with the field measurements with SCPTu. The work gives comparison of the field and laboratory measurements. Correct interpretation approaches are necessary for the laboratory tests as these are found to be more sensitive to small changes in experimental conditions than the SCPTu. Recommendations on how to reduce discrepancies between laboratory and field data are given.
... Arroyo [22] stated that the sample size could produce (a) effects introduced by end rebounds which provoke interferences and signal overlap, and (b) effects due to the cylindrical boundary that produce and interfered with signal where each frequency travels at a different velocity especially when wavelengths are comparable with the size of the specimen. Rio [23] in his thesis stated that the best results are obtained for slenderness ratios greater than 2. Therefore, specimens with small diameters are more affected by reflections from lateral boundaries [21]. ...
After obtaining the value of shear wave velocity (VS) from the bender elements test (BET), the shear modulus of soils at small strains (Gmax) can be estimated. Shear wave velocity is an important parameter in the design of geo-structures subjected to static and dynamic loading. While bender elements are increasingly used in both academic and commercial laboratory test systems, there remains a lack of agreement when interpreting the shear wave travel time from these tests. Based on the test data of 12 Warsaw glacial quartz samples of sand, primarily two different approaches were examined for determining VS. They are both related to the observation of the source and received BE signal, namely, the first time of arrival and the peak-to-peak method. These methods were performed through visual analysis of BET data by the authors, so that subjective travel time estimates were produced. Subsequently, automated analysis methods from the GDS Bender Element Analysis Tool (BEAT) were applied. Here, three techniques in the time-domain (TD) were selected, namely, the peak-to-peak, the zero-crossing, and the cross-correlation function. Additionally, a cross-power spectrum calculation of the signals was completed, viewed as a frequency-domain (FD) method. Final comparisons between subjective observational analyses and automated interpretations of BET results showed good agreement. There is compatibility especially between the two methods: the first time of arrival and the cross-correlation, which the authors considered the best interpreting techniques for their soils. Moreover, the laboratory tests were performed on compact, medium, and well-grained sand samples with different curvature coefficient and mean grain size. Investigation of the influence of the grain-size characteristics of quartz sand on shear wave velocity demonstrated that VS is larger for higher values of the uniformity coefficient, while it is rather independent of the curvature coefficient and the mean grain size.
... Thus, the studies conducted after Schultheiss's original research have reported quite contrasting results in terms of both the specimens and the air. Rio (2006), however, pointed out that the motion of the BE following the input signals is questionable and it must be modeled as a single-degree-of-freedom (SDOF) response, where the system can simply be described by a mass, a spring, and a damper, because it is assumed to behave as a cantilever plate. He also reported that such results, as seen in Jovičić et al. (1996) or Wang et al. (2007), can be explained by electric leakage where the input electric signal reaches the wiring circuit for monitoring the BE motion directly. ...
... Meanwhile, Greening and Nash (2004) observed the BE motion without using the self-monitoring technique. They mounted a strain gauge onto a BE before epoxy resin encapsulation, deriving similar results to those of Schultheiss (1982), while successfully excluding the potentiality that Rio (2006) mentioned. Recently, similar techniques have been conducted for measuring the BE motion independent of any wiring circuit for the BE (Rio, 2006;Irfan et al., 2020). ...
... They mounted a strain gauge onto a BE before epoxy resin encapsulation, deriving similar results to those of Schultheiss (1982), while successfully excluding the potentiality that Rio (2006) mentioned. Recently, similar techniques have been conducted for measuring the BE motion independent of any wiring circuit for the BE (Rio, 2006;Irfan et al., 2020). By using a laser velocimeter, they showed transfer functions with clear peaks and phase lags, deriving a multi-modal response for the BE motion. ...
Since the introduction of bender element tests to soil testing, the reliability of the estimated travel time has been the most serious problem. The author has previously shown a potential solution whereby removing the response of the bender element subsystem from the whole response could dramatically improve the accuracy of the travel time estimation. In order to lay the foundation for estimating the response of the bender element subsystem, this paper examines the correlation between the displacements of the element and the induced feedback signals by employing a self-monitoring element. The response of the self-monitoring element is modeled as a transfer function involving two internal transfer functions that relate the input signals to the displacements and the displacements to the feedback signals, respectively. Using a laser displacement sensor, the displacements are directly measured through the entire surface and reveal the three-dimensional bending motion of the element oscillating in both longitudinal and width directions. The feedback signals are similar to, but inconsistent with, the tip displacements, and an attempt is made to correct the feedback signals. Finally, a conclusion is given on the potential for estimating the response of the bender element subsystem using the self-monitoring element.
... Piezoceramic bender element tests in soils are very useful in determining various soil properties and many of the researchers [1][2][3][4][5][6][7] have worked in this area in the past. However, interpretation of waves obtained from the Bender-Extender elements in these soils has been a challenging task always. ...
... In this context it is expected that the numerical simulation of bender element test is going to be very useful in supporting the experimental results and moreover revealing the hidden phenomena of wave propagation, boundary wall reflections etc. which otherwise facilitate to understand the complex and highly non-linear behavior at a certain level. However, the numerical analysis of bender element test simulation is less focused and only a few researchers have studied the different aspects such as non-linear dynamics of element-soil system using different numerical approaches [6,7,[14][15][16][17][18][19]. As such, the analysis by using different software packages in literature indicated much variation in the results. ...
... Sample geometry and the boundary conditions are inevitable and primary components in numerical analysis which requires special attention while selection. To achieve this, two different specimen geometries were adopted to check the effect of using with and without absorbing lateral boundary conditions according to [6]. Fig. 1 shows the sample geometry considered in the finite element analysis. ...
Shear and Compression wave velocities (Vs and Vp, respectively) are considered to be very useful for determining various dynamic properties of soils such as small strain shear modulus, Gmax, elastic modulus, Emax and the Poisson’s ratio, ν. Moreover, the index as well as engineering properties of the soil mass can be directly or indirectly correlated to Vs and
Vp. However, the bender-extender element and soil interaction during wave propagation stage is difficult to monitor due to various sequential transformations as an electromechanical system. The experimental analysis is unable to reveal the hidden phenomena of wave propagation, boundary wall reflections etc. which otherwise
facilitate to understand the complex and highly non-linear behavior at a certain level. The numerical analysis of bender element test simulation is less focused and very few researchers have studied the different aspects such as non-linear dynamics of element-soil system using different numerical approaches. In present study, a numerical code AbaqusTM based on finite element method (FEM) was used to simulate the bender element tests. Shear wave velocity was determined experimentally for six different types of soils and the results were compared with that obtained from numerical modeling. The objective of FE analysis in this research is to arrive at an accurate approximation of laboratory shear wave velocity in different soil materials modelled at varying input frequencies.
... A few experimental studies have been performed to hypothesise the actual behaviour of BEs inside soil specimens. Rio (2006) measured, using a laser velocimeter, the response of transmitters in air and under embedded conditions inside a synthetic rubber specimen. Rio (2006) showed that, when BEs are embedded in synthetic rubber specimens, the natural frequency and damping ratio of transmitter vibration are greater and the amplitude of vibration is less than the corresponding quantities measured when the BEs are in air. ...
... Rio (2006) measured, using a laser velocimeter, the response of transmitters in air and under embedded conditions inside a synthetic rubber specimen. Rio (2006) showed that, when BEs are embedded in synthetic rubber specimens, the natural frequency and damping ratio of transmitter vibration are greater and the amplitude of vibration is less than the corresponding quantities measured when the BEs are in air. The first mode resonance frequency in air of one of the benders (dimensions 1·5 mm  6 mm  8 mm) studied by Rio (2006) was 3·4 kHz. ...
... Rio (2006) showed that, when BEs are embedded in synthetic rubber specimens, the natural frequency and damping ratio of transmitter vibration are greater and the amplitude of vibration is less than the corresponding quantities measured when the BEs are in air. The first mode resonance frequency in air of one of the benders (dimensions 1·5 mm  6 mm  8 mm) studied by Rio (2006) was 3·4 kHz. Rio (2006) estimated that the maximum shear strain from the peak BE displacements was of the order of 10 À3 %, which is inconsistent with the maximum shear strain in BE testing given by previous researchers (Pennington et al., 2001;Leong et al., 2005;Camacho-Tauta et al., 2015). ...
Bender elements (BEs) are commonly used by geotechnical laboratories worldwide to measure the shear-wave velocity of soils. However, the actual behaviour of BEs inside the soil specimen has never been directly measured. There is experimental, numerical and analytical evidence that the shape and frequency content of the actual transmitter movement are different from the shape and frequency content of the input voltage signal, although this disparity has never been validated for BEs placed inside a soil specimen. In order to systematically investigate the disparity between the input signal and the actual transmitter response and to advance the understanding of the frequency response of the transmitter inside the soil, an experimental programme is designed to measure, for the first time, the responses of BEs placed inside soil specimens. To capture the transmitter response when placed inside the soil, a transparent granular soil is used to allow penetration of a laser beam from a laser vibrometer. The results show that, contrary to common assumptions, the transmitter response inside the soil specimen is different from the input excitation signal. The time delay between input excitation and transmitter response is found to be a function of frequency and the surrounding medium. Moreover, the vibration modes of BEs are studied by analysing the transmitter response to different input signals. These observations are used to understand the actual behaviour of the BEs placed inside the soil.
... Despite the extensive popularity of this technique, the interpretation of the arrival time of the shear wave, however, still remains controversial (Wang et al. 2007). Bender element test results are affected by different issues arising from (i) near-field effects (Sanchez-Salinero et al. 1986;Arroyo et al. 2003), (ii) directivity (Lee and Santamarina 2005), (iii) travel distance in relation to wavelength (Brignoli et al. 1996), (iv) boundary effects (Arulnathan et al. 1998), (v) specimen geometry and size (Rio et al. 2003;Arroyo et al. 2006;Rio 2006), and (vi) cross-talking (Lee and Santamarina 2005). By considering these different effects, several methods have been proposed to interpret bender element tests data, such as (i) first time of arrival (Dyvik and Madshus 1985;Arulnathan et al. 1998;Yamashita et al. 2009), (ii) first peak to peak (Arulnathan et al. 1998;Yamashita et al. 2009), (iii) cross-correlation (Viggiani and Atkinson 1995;Arulnathan et al. 1998; Kumar and Madhusudhan 2010;Airey and Mohsin 2013), and (iv) analysis of the two signals in a frequency domain to determine their phase difference (Blewett et al. 1999;Nash 2004, Da Fonseca et al. 2009). ...
Identification of the arrival point of the shear wave in bender element tests is a task that can have ambiguous results. The contamination of the received shear wave signal with a weak P-wave component, which can emerge either directly from the transmitter or reflect from the side boundary, makes the judgement involved in this task dubious. The different available procedures to mark the arrival times of the shear wave are often prone to errors. A method is proposed to identify the time of the arrival of the shear wave. The predominant frequency of the received signal is first evaluated and then, with the help of the sliding Fourier transform approach, the arrival of the shear wave is identified. The method does not require any manual intervention. The proposed approach is applied to bender element tests performed on dry and saturated sand and glass beads by varying (i) input frequency of the signal, (ii) confining pressure, and (iii) void ratio. Results for different cases, including those obtained by using resonant column tests, are found to be very promising.
