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COMPARISON OF SIMULTANEOUS BENDER ELEMENTS AND RESONANT COLUMN TESTS ON PORTO RESIDUAL SOIL Ferreira, C. PhD Student, FEUP, University of Porto; cristiana@fe.up.pt

Viana da Fonseca, A. Associate Professor, FEUP, University of Porto; viana@fe.up.pt

Santos, J.A. Assistant Professor, IST, Technical University of Lisbon; jaime@civil.ist.utl.pt ABSTRACT Bender elements are a powerful and increasingly common laboratory tool for determining the shear wave velocity hence the small strain shear stiffness (G0) in soil samples. There are several advantages of the bender element technique, namely its simplicity and ease of use; however, there is no standard developed for this technique as the interpretation of the results involves some uncertainty and subjectivity. Different approaches have been proposed to deal with these issues, especially in terms of the interpretation techniques, based on the time and on the frequency domain. In the present work, a modified resonant column, equipped with bender elements, has been used, where shear wave velocities can be measured independently and different interpretation methodologies of the bender element results can be applied. For this study, natural samples of Porto granitic residual soil were tested, since this geomaterial has been object of research and interest for many years in the University of Porto. The paper will focus on the comparison of simultaneous results of shear wave velocities by the resonant column and the bender elements. It is intended to provide some contribution to the routine laboratory practice using bender elements, with further insight in the interpretation of the results. 1 INTRODUCTION Widely recognised as a reference parameter for the definition of constitutive properties of soils, the maximum shear modulus (G0) or very small strain stiffness can be determined in the laboratory in dynamic tests, by measuring shear wave velocities, namely in the resonant column or in bender element tests. The resonant column (RC) is a classical dynamic laboratory test, in which the vibration frequency can be varied, in order to induce resonance of the system. Its main advantage lies on the reliability of the derived parameters, which are based on one-dimensional wave propagation theory. As an alternative, bender elements (BE) are rapidly becoming common laboratory tools for determining the shear wave velocity in soil samples. The installation of bender elements into a conventional static soil test device, such as the triaxial cell, is relatively easy and the determination of G0 is simpler and performed more rapidly than in the expensive resonant column apparatus (Gordon & Clayton, 1997). There are indeed several advantages of the bender element technique, namely its simplicity and ease of use; however, there is no standard developed for this technique as the interpretation of the results, under different methodologies, involves some uncertainty and subjectivity. Considering the current discussion on the interpretation methods for BE tests, it seems interesting to compare results of the application of both tests (RC and BE), not only on the

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same material under identical conditions, but also if possible in a unique specimen, at the same time. Hence, in an attempt to bring together the benefits of both tests, that is, the reliability of the RC and the usefulness of the BE, simultaneous tests have been carried out, after modification of the resonant column apparatus to accommodate bender elements. Relatively few publications can be found in the literature reporting these experiments. One of the exceptions is the bender elements reference work of Dyvik & Madshus (1985), who found good agreement between G0 derived from the two techniques. Similar observations have been reported by Fam et al. (2002). Before presenting the results of this research, it is worthwhile detailing, even if briefly, the most common techniques for the interpretation of bender element tests, which are the fundamental subject under research. 2 INTERPRETATION METHODS FOR BENDER ELEMENTS TESTS As previously mentioned, the interpretation of bender elements traces involves some uncertainty and it is widely accepted that however simple the transmitted wave is, a far more complex wave will be received (Moncaster, 1997). Arroyo (2001) points out that pulse tests in soils should cope not just with a slow, highly attenuated transmission, but also with an important distortion of the transmitted signal. Different approaches have been proposed to deal with these issues, in terms of the interpretation techniques, usually based on the time or on the frequency domain. The frequency domain method generally produces an estimate of shear wave velocity, which is lower than that from traditional time domain readings (Greening et al., 2003). These discrepancies have not yet been systematized and the reasons are still unclear and diverse. In the present study, first direct arrival (at various input frequencies) and continuous sweep input frequency (using a specific software, ABETS) were applied. A brief description of each of these methodologies is presented as follows. a) Time domain: First direct arrival method, at various frequencies [TD] The first direct arrival method is the most simple, common and usual procedure for interpreting BE measurements. It consists on the identification of the first instant of arrival of the wave in the output signal, similarly to the techniques used in geophysical tests (namely Cross-Hole and Down-Hole). While it is sometimes easy to determine first arrival, it is often the cause of much uncertainty. For instance, Arroyo (2001) has estimated uncertainties of up to 100% in estimation of the small strain shear stiffness (G0). Many authors (Sanchez-Salinero et al., 1986; Viggiani & Atkinson, 1995; Jovicic et al., 1996; Arulnathan et al., 1998; Pennington, 1999) have reported several sources and factors of error and inherent near field effects, which mask and compromise the identification of the arrival point. Several solutions have been proposed in order to minimize the subjectivity of this method. Changing the frequency and shape of the pulse is sometimes advised, either to a square wave (Dyvik and Madshus, 1985; Jamiolkowski et al, 1995), a single pulse, a burst, or to a distorted sinusoidal (Jovicic et al., 1996; Pennington, 1999). On the other hand, it is recommended that a number of technical requirements and boundary conditions are accomplished (Jovicic, 2004; Lee and Santamarina, 2005). These requirements comprise good electronics equipment, well shielding and grounding, properly connected and encased transducers, leak free connections, and noise free environment. It is important to be aware that other issues also play a part, especially spatial conditions, such as alignment of the BE, reflections of the wave on the edges and sides of the sample, near field effects, relative distance between transmitter and receiver; contact between the BE

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and the soil, which might induce poor coupling, especially at low confining pressures; and overshooting, since at high frequencies the bender element changes its mode shape and the response becomes very complex. Recently, analytical approaches (Fratta and Santamarina,1996; Arroyo, 2001; Lee and Santamarina, 2005) and numerical studies have been reported on the propagation of seismic waves in cylindrical specimens, modelled in finite differences, finite elements, and spectral elements (Arroyo et al., 2002; Hardy et al., 2002; Rio et al, 2003). These studies have revealed significant influences of sample geometry and boundary conditions in the shape, frequency, and velocity of the wave travelling through the sample, while highlighting the limitations of time domain interpretations. b) Frequency domain: Continuous sweep input frequency via ABETS [FD] The use of continuous signals which require the shear wave velocity to be decoded from measurements of relative phase of transmitted and received signals has been gaining in popularity (e.g. Brocanelli and Rinaldi, 1998; Blewett et al., 1999; 2000; Greening et al., 2003). While this technique has been used across a wide range of fields, Viggiani and Atkinson (1995) were the first to apply phase-delay method to BE testing. According to Greening et al. (2003), these methods have a number of advantages over traditional pulse-based measurements, namely the possibility of creating an algorithm to determine travel time by establishing the gradient of a graph of phase difference against frequency. Phase delay methods can be performed reliably using “traditional” equipment i.e. a signal generator and oscilloscope (Kaarsberg, 1975), where a continuous harmonic sinusoid is used as the input signal. The frequency of the signal is changed and the frequencies at which the transmitted signal and received signal are exactly in and out of phase with one another (so called π-points) are noted. Greening and Nash (2003) showed that the same information could be established less onerously using a sweep input signal and a spectrum analyser. The continuous sweep input method enables the acquisition of a continuous phase angle versus frequency relationship. Greening et al. (2003) suggested a setup, consisting of a low-cost spectrum analyser system implemented in Microsoft ExcelTM, which makes use of a PC on which a specific software, ABETS (Automatic Bender Element Testing System) is loaded to control a high-speed dual channel data acquisition unit. The software details, namely on data processing, can be found in Greening et al. (2003). Slight modifications have been introduced to the program, namely for post-processing data and analysis. A screenshot of this program, in its Portuguese version, is presented in Figure 1, with an example of the data acquisition results spreadsheet. Best results have been obtained with a sweep sine input signal with a 0-20kHz bandwidth. The first graph on Figure 1 shows the input and output signals in the time domain, where it is unfeasible to determine a direct arrival time. Below it, is the graph of the coherence between the two signals (from 0 to 1) against input frequency; by definition, the coherence of two waves indicates how well correlated the waves are, as quantified by the cross-correlation function, which essentially quantifies the ability to predict the value of the second wave by knowing the value of the first. Hence, the higher the coherence, the more correlated the signals will be. The plots at the right show the relative phase against frequency; in the top one, the phase angle is “wrapped”, ranging from -π to π, while on the

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bottom one, it is “unwrapped”, starting near zero, and continuously increasing. The travel time is derived directly from the slope of this curve, given from the best fit line, for a selected range of frequencies. Such selection is evidenced by the vertical lines of the bottom right graph.

Frequency range :

f1 = 8000

f2 = 16000

travel time = 0.305783328 ms

corr. coeff. = 0.99552152

distance = 105 mm

density = 1977 kgm-3

wave velocity, Vs = 343.380 ms-1

estimate G0 = 233.108 MPa0

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Figure 1 – Data acquisition results using ABETS A non-linear relationship between the relative phase and the signal frequency can be generally observed, showing that the 0-20kHz range is too broad to provide reasonable results. However, this is useful as an overview of the full coherence function as well as the complete unwrapped phase against frequency relationship, with the purpose of deciding the most adequate ranges to select. A selection of a high coherence range is necessary to obtain low dispersion in the results, thus a high correlation coefficient of the best fit line. 3 BE AND RC TESTS ON RESIDUAL SOIL SAMPLES 3.1 Outline of the tests In this research, the RC apparatus is a Hardin oscillator, manufactured by Seiken (Japan) and installed at the Geotechnical Laboratory of IST, in Lisbon. The modifications in the platens for the BE were designed by the authors and new platens were made by the manufacturer. The bender elements were manufactured at COFS (in UWA, University of Western Australia) and consist of a T-shaped pair encased in a stainless steel casing. The electronic equipments used for BE measurements comprise a programmable function generator; input and output multiplexers (also specifically developed at COFS); an oscilloscope connected to a PC or, alternatively, a data acquisition with spectral analyser device (PICOScope), also connected to a PC, acquiring on ABETS. In each test, simultaneous measurements of the RC and BE were made, using the two interpretation

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methodologies for the BE results, in order to identify any discrepancies in the measured shear wave velocity, towards determining which method most closely estimates the true travel time. In Figure 2 a photograph of the apparatus is shown, with emphasis to the modified platens equipped with a T-shaped pair of bender elements.

a) b) Figure 2 – Resonant column device with bender elements: a) test apparatus; b) modified platens Porto granitic residual soil has been selected on this work as it is regionally dominant and has been thoroughly studied for many years. Residual soils result from physical, chemical and mechanical weathering processes acting on rocks and, in the present case, this soil is a weathered granite. A reference work on its characterization has been presented by Viana da Fonseca (2003). The typical Porto granite is a leucocratic alkaline rock, with two micas and of medium to coarse grain size. The natural variability of the rock generates a fairly heterogeneous mass in macro scale. This soil is characterised by the presence of a bonded structure and fabric that has significant influence on its engineering behaviour. For the present research, it is relevant to mention its wide grain size distribution, usually defined in the Unified Classification of Soils (ASTM D 2487-85), as silty (SM) or well graded (SW) sands, or more rarely as clayey sands (SC). The presence of fines adds higher compressibility than that of sands, though permeability is relatively high (k=10-6-10-5 m/s). Four simultaneous RC and BE tests were carried out on natural samples of Porto residual soil, which will be analysed in this work. The main properties of the test specimens are summarized in Table 1 and it must be emphasized that each of these were fairly homogeneous in texture and fabric. Table 1 - Identification and soil index properties of the residual soil samples

Specimen Borehole γ kN/m3

w % e Sr % wL

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<2um %

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01CRBE S2 [6.25-6.50m] 19.5 22.4 0.64 93 n/a n/a 5.0 42.0 94.5

02CRBE S2 [2.00-2.30m] 19.3 19.4 0.62 83 30 26 5.5 36.9 89.8

03CRBE S1 [2.20-2.30m] 19.5 22.9 0.65 94

04CRBE S1 [2.10-2.20m] 19.4 23.0 0.66 93

32 25 7.3 46.4 88.4

The tests comprised the application of isotropic and (or) anisotropic confining pressures, at various stages, as outlined in Table 2. All tests were drained, but the samples were almost

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but not fully saturated during testing, maintaining the natural moist. After a stabilization period of about 30 minutes, RC readings of the resonance frequency were made, followed by the acquisition of the wave traces for the time and frequency domain with the BE. Table 2 - Testing conditions for each specimen Specimen Testing conditions 01CRBE Anisotropic consolidation (Kc = 0.5): 6 stages up to σ’v = 400kPa 02CRBE Anisotropic consolidation (Kc = 0.5) and shear: 7 stages up to σ’v = 120kPa 03CRBE Isotropic consolidation: 8 stages up to σ’c = 400 kPa 04CRBE Isotropic consolidation: 8 stages up to σ’c = 400 kPa, with creep (for 48 days) The final results of the variation of the shear modulus, determined by RC and BE measurements, with mean effective stress are shown in Figure 3, for the four specimens.

GBE(TD) = 4.310 p' 0.624

R2 = 0.917

GBE(FD) = 3.467 p' 0.658

R2 = 0.892

GRC = 4.535 p' 0.619

R2 = 0.904

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Figure 3 – Variation of G0 with p’ for all samples, from RC and BE readings The results exhibit significant similarities in terms of the G0 versus p’ relation and the dispersion between RC and the two BE results are very small. The derived equations for this relation, respective to each method, evidence good convergence. These equations are merely indicative for the dependence of G0 with p’, as it is beyond the scope of this paper to examine this relation. It is assumed that the obtained constants (multiplier and exponent) incorporate very important contributions from void ratio, structure, stress history, among others, which must be addressed separately. It is interesting to note that, despite having being followed diverse stress paths in each test, the overall curve for each method closely matches the individual points. This is, however, the final graph obtained after careful analyses of the acquired data. The RC test is known to be very accurate dynamic test and the experience from these (and previous) tests confirm it. The margin of error from one operator to another is generally less than 1Hz for the resonant frequency under standard testing conditions. BE readings are clearly more controversial: time domain results remains subjective and the frequency domain technique, despite being automated and clearly more objective, still requires judgement and an “experienced eye” for post-processing the data. It is therefore worthwhile taking a closer look at one of the tests, to understand the underlying requirements towards good and reliable results.

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3.2 Analysis and Discussion of the Results As an example of the BE test procedure and analysis, test 04CRBE will be examined in detail. In the present tests, the first arrival method was used and several input frequencies at relevant levels were applied, in order to minimize the sources of errors. Figure 4 illustrates the BE traces for 2, 4, 8, 10 and 15kHz input pulse sine waves, for stage #02, corresponding to an isotropic effective stress of 50kPa.

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Figure 4 - Time domain results in stage #02 of test 04CRBE Despite the diverse configurations of the response waves for different input frequencies, it is possible to identify a “most likely” arrival point, even if questionable. The distortions in the traces evidence effects of different nature as frequency increases. More relevant to the discussion is to observe the aspect of the output waves with the increase of applied confining pressure, as shown in Figure 5. For clarity, the complete set of frequencies acquired is not displayed, and only selected frequencies of the input waves are shown for each test stage. Since the travel time is decreasing as a consequence of higher effective stresses, the most relevant frequencies of the input wave change and need to be readjusted. This comment is based on experience and is theoretically confirmed by the requirement of a minimum normalised distance from the source, defined . The recording of several frequencies, by default, evidences and safeguards this important “rule of thumb”.

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Similarly, it is interesting to compile the results of the application of the frequency domain technique into a single graph, as presented in Figure 6. As an example, the curves of unwrapped phase angle versus frequency for selected stages of 04CRBE are depicted, where the best fit line is also represented, for the selected range of frequencies of each test stage, from which the travel time of the shear wave is calculated.

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Figure 6 – Travel time determination from the unwrapped phase angle versus frequency It can be seen that in the time domain, changes in confining pressure are noticeable in the shape of the wave, yet more subtle in the distinction of travel time. In the frequency domain, the slope variation is clearer and more illustrative of such stress variations. An interesting and useful analysis of the frequency domain results consists on selecting different ranges of frequencies in order to observe the changes in the travel time. With the purpose of further understanding this variation of travel time with this method, another approach has been investigated. This consists on a different method of representing the travel time from the sweep results. A simple Visual Basic program was implemented, to manipulate the sweep data considering “unbiased” and objective pre-established ranges of frequencies and to calculate the respective best fit line. The frequency ranges considered were 0.2, 1, 2, and 4kHz. The generated graph of travel time versus frequency, called “time chart”, is presented in Figure 7, where the corresponding first arrival results are included, within the respective frequency range. For the purpose of comparison, the coherence plot, which gives an indication of the dependence of the received signal on the input signal, is combined in the same chart, in a secondary vertical axis. It is only reasonable to compute the travel time for frequencies of highest coherence, near unity. The time charts show that the lowest range selections are highly variable and very sensitive to noise. Nevertheless, this works well as reference to the original data trends. All charts exhibit significant fluctuation on the travel time calculation, with lower variability for higher frequency ranges. Obviously, these tend to smooth down and average the results. On the other hand, the principle of unity coherence is not sufficient to guarantee a stable and unequivocal determination of the travel time. Correspondence between the variability of the two plots is clear, but only partly does it justify the inconsistencies of the time chart. It can also be noted that the fluctuations of travel time with frequency for the various ranges decrease substantially with the stress increase, as well as the differences with the travel time measured by the first arrival method. This fact is likely to be associated with a higher coupling between the soil and the BE, aided by the stiffening of the soil.

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Having shown the analysis process for the BE methods, it is now important to address the main topic of this work, which resides on the comparison of RC and BE tests. As illustrated in Figure 3, the results from both tests show good agreement and convergence. Taking as reference the RC results for the G0 values, it is relevant to assess the relative distance between methods. Figure 8 provides such information and enables to conclude that the FD domain technique results on G0 values that deviate from those measured by the RC by less than 1% in average. The time domain has provided values of G0 that are within an average of 2% of the RC values. The lower and upper limits of the ratio between G0 values for the FD compared with the RC are of about 58% and 110%, respectively. These limits are similar to the ones measured in the TD, which are 58% and 125%, respectively.

GBE(TD) = 0.982 GRC - 0.734

R2 = 0.969

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R2 = 0.981

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Figure 8 – G0 values derived from the RC versus from the two BE methods Based on these results, it can be stated that the bender element tests provide good and valid results, comparable to the resonant column. It is acknowledged that the methods currently available, and herein applied, have some subjectivity and still require some judgement, but at a much lower degree than that associated with a first peak detection on a single pulse reading. CONCLUSIONS The use of bender elements in the laboratory as means to determine the shear wave velocity hence the small strain stiffness continues to increase worldwide. Recent and old discussions on the inherent subjectivity of the interpretation of its results continue to leave room for improvement and research. This paper has analysed the performance of the two most common interpretation techniques for the BE test, by comparing the results with the resonant column test, which is renowned for the quality of its measurements of the dynamic parameters. This has been made by modifying a RC apparatus to accommodate BE and by performing simultaneous readings of the RC frequency and the BE waves in the time and the frequency domain.

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Results show that the two testing methods compare well. Both BE interpretation techniques can yield very close values of travel time, though its determination cannot be fully automated nor unambiguous, even for the frequency domain. In effect, both techniques require some degree of judgement and experience that has not yet been eliminated. Data acquisition and post-processing procedures are suggested, as these have proven to lead to reliable values of G0 in the light of the close agreement obtained between RC and BE test results. ACKNOWLEDGEMENTS This work was developed under the research activities of CEC from FEUP (POCTI/ECM/55589/2004) and ICIST of IST, supported by multi-annual funding from FCT (Portuguese Science and Technology Foundation). Special thanks are due to Eng. Gouveia, for his technical support during setup and laboratory testing. REFERENCES Arroyo, M. (2001). Pulse tests in soil samples. PhD thesis, University of Bristol, UK. Arroyo, M.; Medina, L. and Muir Wood, D. (2002). Numerical modelling of scale effects in

bender-based pulse tests. NUMOG VIII, Pande, G.N. & Pietruszczak, S. (eds), pp. 589-594. Arulnathan, R.; Boulanger, R.W. and Riemer, M.F. (1998). Analysis of Bender Element Tests.

Geotechnical Testing Journal, Vol. 21, No. 2, pp. 120-131. Blewett, J.; Blewett, I.J. and Woodward, P.K. (1999) Measurement of shear wave velocity using

phase sensitive detection techniques. Canadian Geotechnical Journal 36, pp. 934-939. Blewett, J.; Blewett, I.J. and Woodward, P.K. (2000). Phase and amplitude responses associated

with the measurement of shear-wave velocity in sand by bender elements. Canadian Geotechnical Journal, Vol. 37, pp. 1348-1357.

Brocanelli, D. and Rinaldi, V. (1998). Measurement of low strain material damping and wave velocity with bender elements in the frequency domain. Canadian Geotechnical Journal, Vol. 35, pp. 1032–1040.

Dyvik, R. and Madhsus, C. (1985). Lab measurements of Gmax using bender elements. Proceedings ASCE Annual Convention: Advances in the art of testing soils under cyclic conditions, Detroit, Michigan, pp. 186-197.

Fam, M. A.; Cascante, G. and Dusseault, M. B. (2002). Large and Small Strain Properties of Sands Subjected to Local Void Increase. Journal of Geotechnical and Geoenvironmental Engineering, Vol. 128, No.12, pp. 1018-1025.

Fratta, D. and Santamarina, J.C. (1996). Wave propagation in soils: Multi-mode, wide-band testing in a waveguide device. Geotechnical Testing Journal, Vol. 19, No. 2, pp. 130-140.

Gordon, M.A.and Clayton, C.R.I (1997). Measurement of stiffness of soils using small strains triaxial testing and bender elements. Modern Geophysics in Engineering Geology. McCann, D.M.; Eddleston, M.; Fenning, P.J. & Reeves, G.M. (eds.). Geological Society Engineering Geology Special Publication, No. 12, pp. 365-371.

Greening, P.D. and Nash, D.F.T. (2004). Frequency domain determination of G0 using bender elements ASTM Geotechnical Testing Journal, Vol. 27, No. 3, pp. 288-294.

Greening, P.D.; Nash, D.F.T.; Benahmed,N.; Viana da Fonseca, A. and Ferreira, C. (2003). Comparison of shear wave velocity measurements in different materials using time and frequency domain techniques Proceedings of Deformation Characteristics of Geomaterials, Lyon, France, 22-24 September, Lyon, France:Balkema, pp. 381-386.

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