# Dynamic Characterization of Cohesive Material Based on Wave Velocity Measurements
## 2 Methods and Materials
### Test Setup and Procedure  
The test procedure followed that of a drained isotropic resonant column test. An upright cylindrical specimen of soil, with an aspect ratio of 2:1 (length:diameter), was employed. The proportions between length and diameter were as follows: 140 mm \(\times\) 70 mm. Undisturbed material was set up in the resonant column cell, then saturated by the back pressure method in order to achieve the level of full saturation and subsequently consolidated to predetermined isotropic stress levels of 30, 120, 180, 240, 360 and 410 kPa. Back pressure was increased slowly, in order to ensure the proper saturation of the sample, until Skempton's \(B\) value reached 0.84. This represents, with respect to Head [36], the saturation level being equal to approximately 97%. During the consolidation stage, the axial deformation and volume change of the sample were measured. The back pressure was kept at a constant level of 290 kPa. At the end of each consolidation stage, seismic wave velocities were checked, in the undrained conditions, as well as using the bender elements located at the top and bottom of the soil specimen. The BE transmitter was excited with a sine pulse, whose magnitude equaled 15 V. A change of voltage applied to the transmitter caused bending and transmission of a shear wave through the sample. The receiver, located at the other end of the specimen, registered the arrival of the shear wave as a change in voltage [37; 38; 39]. For each isotropic confining pressure level, a range of input frequencies between 100 and 1 kHz was tested, in order to identify the value of greater amplification in the received signals. This value should represent the clearest output signals. In the case of some input frequencies, particularly the higher ones, compression wave velocity was measured additionally. Due to the limitations of the software and hardware (S- and P-waves were transmitted by the same piezoelectric element) provided by the GDS company, the authors were unable to conduct the measurements in the same period (\(T\)) of S- and P-waves. Hence, there is an apparent limit in the predetermined period or frequency of propagating various waves through the soil sample. In Figure 7, the oscilloscope data obtained during the discussed studies are shown. The input signals at different frequencies were sent under the same stress conditions. During the analysis of this figure, it appeared to the authors, that at higher frequencies, the determination of the arrival time was more precise. Changes in the input signal frequency did not produce any change of polarization in the shear waves. For all applied frequencies, the input and output signals indicated the same amount of polarization. Figure 6: Grain size distribution of the tested soils. To interpret the BE results, the authors applied two commonly-known techniques used in time domain methods, which they described in the earlier subsection. For the start-to-start method, the noise level is very significant. [PERSON] _et al._[PERSON] _et al._ (2016) verified the criteria for the improvement of the interpretation of the BE test, among which there is the signal-to-noise ratio (SNR) criterion. According to their research, the SNR should be of at least 4 dB for the receiver signal. In the authors' research, the average SNR for the start-to-start method was equal to 10.44 dB. This level of the SNR allowed picking a very reliable and comfortable wave onset. Values of the wave velocity were calculated on the basis of the tip-to-tip distance between the transmitter and the receiver bender element ([PERSON], 2016). The shear wave velocity was evaluated from the relationship presented below ([PERSON], 2016; [PERSON] _et al._, 2016):  
\[\upsilon_{S}=\frac{h}{t} \tag{5}\]  
where \(h\) is the distance between the transmitter and the receiver and \(t\) is the travel time. Figure 7: The oscilloscope signals at various frequencies of input signals: (**a**) 20 kHz, (**b**) 10 kHz, (**c**) 2 kHz, (**d**) 1 kHz and at the same effective stress value.