The material used corresponds to a sand with a content of calcium carbonate (CaCO3) of about 50% (CA50). Due to the difficulty in obtaining naturally carbonated sands, CA50 was produced by combining a quartz sand (QZ) and a commercially acquired carbonate sand, whose calcium carbonate content is about 80% (CA80). Carbonate sands produced artificially are representative since data from naturally cemented carbonate sediments are often highly dispersed [21]. The particle size curve for this material is shown in Fig. 1.

Figure 1 Source: The authors.

It is observed that the granulometry of the sand did not interfere in the CA50 curve by the incorporation of CA80 to QZ. The CaCO₃ content, maximum and minimum voids, curvature coefficient (CC), non-uniformity coefficient (CNU), relative density of the grains (G_S) and strength parameters of the CA50 are shown in Table 1.

Table 1

Source: The authors.

Regarding the bender elements used in this work, they were manufactured by GDS and they present dimensions in mm of 1,5 x 3 x 11 with speed data acquisition of 2 Mega samples/second.

The specimen of 5 cm in diameter and 11.1 cm in height, with base and top cap, was placed and fixed in the triaxial chamber. After applying the vacuum and removing the mold, the desired confining tension was applied by filling the triaxial cell with water and the sample was left to consolidate for 60 minutes. Fig. 3 shows the experimental apparatus of the procedure.

Figure 3 Source: The authors.

Electric excitation was applied to the emitting BE through a wave generator at the desired frequency. The generated data is checked simultaneously and, if satisfactory, is recorded. For each confining stress, this process is repeated at each input frequency.

Loading and unloading tests were carried out at the effective confining stress of 50 kPa, 100 kPa, 300 kPa, 600 kPa and 800 kPa; cycling stress of 50 kPa and 800 kPa. Sine (SIN) and square (SQR) signals were performed at frequencies of 6 kHz, 8 kHz, 10 kHz, 12 kHz and 15 kHz in both samples, to ensure repeatability of the tests.

Although the determination of the travel time of the shear wave imposes subjectivity when calculating the wave velocity, the distance covered by the waves also requires some care. Some authors [12,24] consider the BE's tip-to-tip distance to provide the best accuracy, but in the case of triaxial samples, this distance changes as the sample deforms. Therefore, the heights were corrected for each tension tested by measuring the volume change.

Regarding the measurement of the travel time of the shear wave, near-field effects are of special relevance for time domain analyzes [25-27]. These are interferences in the output signal, which can mainly mask the identification of the shear wave point of arrival [16]. To mitigate this effect, readings that did not meet the L/λ> 2 ratio were excluded, as suggested by [28]; where λ is the wavelength.

The delay (Δ𝑡_𝑑) equal to 11 μs was considered in travel times measured for the three methods during this work.

For this method, despite the subjectivity of the choice of the considered point, the determination by the crossing point on the x-axis resulted in a small dispersion of the values obtained, as observed in the graph (Fig. 5), which contains the standard deviation value for the means of V_S presented along the graph.

Figure 5 Source: The authors.

It is important to highlight the good agreement observed when comparing the time values (Δt_FA) obtained for the two samples (01CA50 and 02CA50). The results showed that the procedure and the interpretation considered are adequate considering the low standard deviations obtained for both samples tested. Although the presence of the near-field effect can make it difficult to identify the travel time, the zero crossing of the waves for the various frequencies tested occurred almost simultaneously regardless the input frequency for all the tests performed.

The time intervals determined by the peak-to-peak method indicated an increase in dispersion with an increase in the confining tension. However, even so, the samples showed good agreement (Fig. 6).

Figure 6 Source: The authors.

Fig. 5-6 also allow us to observe the similar trend of the shear wave velocity as the confining tension increases.

For the Japanese method using average between methods, the velocities obtained were evaluated based on the input frequency for the loading tests and the results are shown in Fig. 7.

Figure 7 Source: The authors.

It is observed for the same frequency, the increase in the confining tension implied an increase in the V_S. In addition, it is noted that the variation in the values of V_S over the range of frequencies studied seems to be more susceptible to higher confining stresses (above 300 kPa). This is probably related to the near-field effects that are most effective in higher confining tensions. As already mentioned, in these conditions there was an increase in V_S and, consequently, an increase in wavelength (especially for lower frequencies).

This may indicate that, at these stress levels, to keep the L/λ ratio as far away from 2 as possible, it should be considered increasing the distance between BE’s or the excitation frequency of the signal.

The graph of V_S versus σ_c allows the visualization of the behavior found with the plotted standard deviation values shown in Fig. 8. The results obtained showed good agreement of the Vs values for both samples, and the behavior was similar when compared with the previous methods, showing an increase in V_S with an increase in σ_c. The deviations shown in Fig. 8 have intermediate values between the FA and PP methods.

Figure 8 Source: The authors.

An evaluation of the velocities obtained was also performed based on the input frequency (f) for this method. Fig. 9 shows the graphs of V_S versus f for each tested confining stresses. Distinctly the evaluation allowed by Fig. 7, there is a better convergence of the velocity values for the different frequencies, which was already expected considering that the CC method is less susceptible to variation in this parameter.

Figure 9 Source: The authors.

Given the presented, the following points can be highlighted: i) the increasing trend of V_S with increasing σ_c can be perceived in the three methods used for the tested samples; ii) the results presented over the previous items allow to validate the experimental procedure carried out given the good agreement of the values obtained for both samples; iii) the evaluation by the CC method resulted in V_S values from 13% to 16% lower than the average adopted according to the Japanese proposal for the average of the methods.

Vs results for carbonate sand were accessed in the literature for comparison with results obtained by the present study. [33] obtained for an average confining stress of 50 kPa and 100 kPa in Quiou sand (about 75% of CaCO₃ content), a range of velocities varying from 200 m/s to 270 m/s (with a relative density from 18% to 85%). For higher values of confining stresses (700 kPa), [34] found for Kenia sand (DR = 96% and CaCO₃ content = 97%) a velocity of 445 m/s. Despite the difference between the calcium carbonate content and the relative density of the samples, the velocity values are in accordance with the findings in the present work, except for the V_S for CC method (Fig. 8) at higher levels of stress.

Fig. 10 shows the results obtained for sample 01CA50 for lower, intermediate, and higher confining stresses (50, 300 and 800 kPa, respectively) in the three methods for the different frequencies.

Figure 10 Source: The authors.

Fig. 11 shows a comparison of V_S versus σ_c obtained for loading (C) and unloading (D). It is noticed that the unloading velocity form an envelope of points with higher values at the same confining stress; a behavior that was verified in both samples.

Figure 11 Source: The authors

In addition, a visual inspection shows that there was no significant difference between the values found for the stress of 600kPa and 800kPa, however, for the lower stresses, this difference reached 18% in the confining stress of 100kPa. Thus, for carbonated sand CA50 it is notable that the discharge influences the wave velocity and, consequently, the shear stiffness.

This difference may be related to the high relative density of sample preparation (80% reference DR). In addition, the increasing of these parameters is probably due to change on soil’s density during the loading and unloading process. In the case of carbonate materials this influence may be related to the nature of the grains and their break during the increasing load.

Fig. 12 shows the V_S results for the carbonated sand submitted to the six loading and unloading cycles. Note that the cycles generated did not significantly influence the parameters for the 800kPa stress. For the 50kPa, an increase in dynamic parameters is noted, however, this increase coincides with that generated during the first discharge (Figs. 11-12).

Figure 12 Source: The authors