1032
Proceedings of the 18
th
International Conference on Soil Mechanics and Geotechnical Engineering, Paris 2013
2005) observed in physical specimens. In DEM simulations the
displacement and velocity of each individual particle can be
monitored, allowing for the specification of multiple wave
receivers at arbitrary locations. Figure 1 shows five particles
along the central axis of the cylindrical specimen that were
selected as S-wave receivers.
Figure 1. A DEM specimen with S-wave transmitting layer and
receivers (for clarity, only half of the specimen is shown).
2.2
Interpretation of travel time
Accurate determination of signal travel time has been the
subject of considerable research in laboratory S-wave velocity
measurements (e.g., Styler and Howie 2012). Many factors,
such as cross-talk between the source and the receiver (Lee and
Santamarina 2005), system delay (Yang and Gu 2012),
fabrication defects in the testing device (Montoya et al. 2012),
and electric and environmental noise add to the uncertainties
and the difficulties in the interpretation of receiving signal.
In DEM simulations, most of these aforementioned influence
factors can be eliminated. Figure 2 shows ‘clean’ source and
receiving signals from a typical DEM S-wave propagation
simulation. The amplitude of the signal is a representation of the
displacement of particles in the direction of the excitation
(along x-axis in Figure 2). It can be seen that the receivers’
respond to the excitation at different times. The delays of the
first arrival between equally spaced receivers are almost the
same. The receiving signals have identical wave forms but
attenuate as the distance to the source increases.
In laboratory, S-wave velocity is typically calculated from the
travel time and the distance between wave transmitter and
receiver, while in DEM simulations it is also possible to
calculate S-wave velocity between the receivers. The common
start-to-start and peak-to-peak methods can be applied between
source and receiver and between any two receivers. In
simulation, when applying the cross-correlation method
(Viggiani and Atkinson 1995) between receiving signals, it is
expected to be ‘cleaner’ to interpret compared to laboratory data
because they contain less noise and there is a very high
similarity between the waveforms.
In the bender element test, the wave motion is indirectly
expressed in the change of voltage, which means that the initial
polarization between the input and the output signal does not
necessarily reflect the relative direction of wave motions at the
wave source and at the receiver. It is for the reason that the
polarity of the signal is not only determined by the direction that
the bender element curves but also affected by the wiring of the
bender element electrodes. Unlike in the bender element test,
the polarity of the signal in the current simulations directly
represents the direction of wave motion, which helps to identify
whether the initial deflection of the receiving signal is caused by
the S-wave (which results in the same polarity as the source
signal) or by the P-wave reflected from the side boundaries
(which results in an inverse polarity of the source signal). From
Figure 2, it can be seen that the initial deflection of the
receiving signals has the same polarity as the source signal,
which indicates little P-wave interference to the first arrival of
the receiving signal. The S-wave velocities shown in this
manuscript were determined as follows: the travel times
between the source layer and the two far most receivers (to
avoid near-field effects; Sanchez-Salinero et al. 1986) were
determined by the start-to-start method; second, the final
representative S-wave velocity was determined by averaging the
travel times obtained in step one.
S-wave transmitting layer
Figure 2. Source signal and receiving signals from a typical DEM S-
wave propagation simulation (D
50
= 2.0 mm; e = 0.63; σ'
3
= 150 kPa.
Note: for clarity, the amplitudes of the receiving signals are upscaled to
facilitate comparison)
3 EFFECTS OF EXCITATION FREQUENCY
In bender element tests, the response of the receiver bender
element is enhanced when the frequency of the input signal
approaches the resonant frequency of the bender element-soil
system (Lee and Santamarina 2005). The resonant frequency
can be determined in the laboratory by sweeping the excitation
frequency of a sine pulse. The DEM models were excited by
sine pulse with different frequencies to approximately identify
the resonant frequency. Figure 3 shows the response from one
of the receivers in a DEM specimen excited by sine pulse
signals with a frequency range from 1 kHz to 100 kHz.
From Figure 3 it is apparent that the response of the receiver is
rather weak under excitation frequencies of 1 kHz and 2 kHz.
The strongest response is achieved at 5 kHz. Thus, the resonant
frequency is located in the range 2-10 kHz. This agrees with
published laboratory findings (Santamarina and Fam 1997). The
response signals are strong with similar waveform across a wide
range of excitation frequencies from 5 kHz to 100 kHz.
Frequency domain analyses were also used to investigate the
effect of excitation frequency (Figure 4). It can be seen that the
highest amplitude occurs at around 3 kHz, consistent with the
observations from time domain analyses. Figure 4 also shows
that the receiving signal contains a range of frequency
components though the transmitted signal is a sine pulse. When
the frequency of the transmitted signal is lower than the
resonant frequency (3 kHz), the predominant frequency of the
corresponding receiving signal is identical to the frequency of
the transmitted signal. However, when the frequency of the
transmitted signal is higher than the resonant frequency, the
predominant frequency of the corresponding receiving signal is
roughly equal to the resonant frequency. The DEM specimen
works as a low-pass filter, rejecting frequency components
higher than the cut-off frequency, which is found to be the
resonant frequency discussed above. The analytical illustration
of this low-pass filtering effect in discrete media can be found
R2
R1
R3
R4
R5
Receivers
