1. Implementation of a system for measuring velocity of
primary & secondary waves in rocks and soils.
Prashant S Sengar
Department of Electrical and Computer Engineering
Engineering Center (EC)
Florida International University
Miami, Florida- 33174, USA
email: pseng002@fiu.edu
Maryam S. Bhagini
Department of Electrical Engineering
Indian Institute of Technology- Bombay, Powai
Mumbai 400076, India
email: mshojaei@ee.iitb.ac.in
D. N. Singh
Department of Civil Engineering, Geotechnical
Engineering division, Indian Institute of Technology-
Bombay, Powai, Mumbai 400076, India
email: dns@civil.iitb.ac.in
Abstract—Measurement of shear and compression wave
velocities in rock and soil samples play an important role in the
detection of their types and characteristics. The instruments
employed for these measurements are too expensive and bulky.
Thus, a low cost instrument is required to measure the primary
(shear) and secondary (compression) waves velocities in real
time. This paper describes an implementation of an ultrasonic
nondestructive measuring system using Piezoceramic
transducers. The operational frequency of the system is 0.2KHz -
30KHz and 500KHz, 1MHz for measuring shear and
compression wave velocities respectively. It is able to detect the
wave velocities in rock specimens and some compacted soils of
different properties (dry & wet).
Keywords—Piezoceramic element, bender, compression wave,
piezoceramic disc, extender, instrumentation amplifier, filter.
I. INTRODUCTION
Piezoceramic elements are crystalline substances which
generate electrical charges when subjected to mechanical
stress. Conversely, if placed in an electric field they experience
a mechanical strain (Lings and Greening 2001). It is due to this
property, that they can be used as actuators and or sensors for
various geotechnical engineering applications [1]. Piezo-
ceramic transducers are widely used for variety of applications
such as ultrasonic cleaners, atomisers, dynamic force &
pressure measurement, SONAR, accelerometers, flowmeters,
strain gauges, actuators and more. They can be effectively
employed for the shear and compression wave velocity
measurements in rock and soil specimens. These polarized
sensors when connected in different configurations can be used
as bender or extender elements which can generate shear waves
(S) and compression waves (P) respectively. Bender elements
are commonly used for the measurement of shear wave
velocity and the determination of small strain shear modulus
(Gmax) [2]. Whereas, the extender elements are less commonly
used for the compression wave velocity measurement and
determination of Young’s modulus (Emax) & Poisson’s ratio
(ν). Since the extender elements are not efficient for
compression wave velocity measurement, piezoceramic discs
of frequency 500KHz and 1MHz were used for the system
development. Interestingly, both bender element and piezo-
ceramic disc can act as a transmitter or receiver of waves at any
given point of time [3]. Extensive investigations are made to
account for the performance of the piezoceramic elements
according to their configurations, such as the polarization of
the elements and wiring configurations (series or parallel) [1].
The implemented system is divided into three functional
blocks namely, Signal generator, amplifiers-filters and signal
detection (DSO). Bender elements and piezoceramic discs are
included in the amplifiers-filters block. These transducers are
coupled to the surface of rock or soil specimens by using a
coupling gel. The circuitry implemented for sensor system
requires good Common mode rejection ratio (CMRR) and a
precise range of band pass filter for the acquisition of the
signal. Instrumentation amplifiers were employed to improve
the CMRR of the received signal [7]. The operational
amplifiers were chosen according to their slew rates in order to
amplify the desired frequencies.
II. BENDERS AND PIEZOCERAMIC DISCS
Piezoceramic transducers (benders & peizoceramic discs)
used to realize the present system were developed using a Lead
Zirconate Titanate (LZT) based material, SP-5A US DOD
Navy type material-II (Sparkler Ceramics LTD). These low
power operated piezoceramic elements have high dielectric
constant and piezoelectric sensitivity. The quality and strength
of the transmitter signal & receiver signal depends upon the
size of the piezoceramic elements [2]. These elements also
show good response and minimum time lag between the
excitation and wave generation. A bender element (S-wave)
transducer is composed of two piezoceramic plates bonded
together with a central metallic plate [8]. Depending upon the
wiring configuration, the benders can be polarized in series or
parallel type. In order to transmit and receive a S-wave, a
piezoceramic element with the parallel wiring (same
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2. polarization) acts as a transmitter and the other with series
wiring (opposite polarization) act as a receiver [3], depicted in
Fig. 1. The dimensions of the bender elements used as
transmitter and receiver were 15mm x 12mm x 0.65mm.
(a)
(b)
Fig. 1. (a) Bender element wiring configuration transmitter and receiver
(adapted from Cristiana Maria da Fonseca Ferreira) (b) Dimension of the
bender elements used for the system development.
Piezoceramic disc of resonant frequency 500KHz and
1MHz (Diameter 54mm, thickness 4mm) were employed for
compression wave generation and reception, Fig. 2. A
longitudinal stress wave is generated by the piezoceramic disc
when excited through a pulse generator. The size of the piezo-
ceramic discs and the excitation voltage influence the quality
and strength of the received wave [2].
Fig. 2. Shape, mode, wave motion and direction of polarization of the Piezo-
ceramic discs.
These piezoceramic discs (500KHz & 1MHz), transmitter
and receiver are resonant at particular fundamental frequencies.
It must be noted that when the transmitter transducer is excited
with the resonant frequency, the receiver generates maximum
amount of potential difference around its electrodes. The exact
resonant frequency of the transmitter and receiver pair was
found out by exciting the transmitter with a range of
frequencies at 5 Volts and detecting the output waves in DSO
through receiver, placing a standard test specimen (concrete)
between the transducers. A graph of input frequency at
transmitter verses output voltage at receiver for both 500KHz
and 1MHz piezoceramic transducer are plotted, as shown in the
Fig. 3. It is clear from the graph that the resonant frequency of
the piezoceramic disc transducers pair (transmitter & receiver)
is different from the described frequency of single transducer
(i.e. 563KHz for 500KHz elements and 1.124MHz for 1MHz
elements). This frequency shift is due to the mismatch of
transmitter & receiver disc frequencies. Thus, in order to
retrieve better signal quality and strength from the receiver
transducer, the setup must be operated at the resonant
frequency.
(a)
(b)
Fig. 3. (a)Frequency response of 500KHz piezoceramic transducer pair
(transmitter & receiver with the test specimen concrete). (b) Frequency
response of 1MHz piezoceramic transducer pair (transmitter & receiver with
the test specimen concrete)
III. BENDER & PIEZOCERAMIC DISCS TEST SETUP
The test setup used to measure shear and compression wave
velocity is shown in Fig. 4. The Function generator IC XR-
2206CP was used to develop the sine wave signal generator for
bender elements (0.2KHz - 30KHz) and piezoceramic discs
(500KHz & 1MHz). The operational voltage of the function
generator is from 10V to 24V. Thus, it makes it suitable for the
benders and piezoceramic discs test setup. The output sine
Proceedings of the IEEE SoutheastCon 2015, April 9 - 12, 2015 - Fort Lauderdale, Florida
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3. wave from the function generator has very low waveform
distortion and was fed to an buffer operational amplifier circuit.
The piezoceramic element, bender and piezoceramic disc
generate shear waves (S) and compression waves (P)
respectively. The piezoceramic transducers were directly
interfaced with the buffer circuits for S-wave and P-wave
transmission. These transducers are coupled to the surface of
rock or soil specimens by using a coupling gel or paraffin wax.
S-waves and P-waves are injected to the rock and soil samples
through the transmitter transducer. The received wave (signal)
is detected through the receiver transducer which is filtered and
amplified at the filters & amplifiers block. The signal is then
fed to a dual channel digital signal oscilloscope (DSO) TDS
2001, Tektronics for display of the wave. For storing the
received data, TDS2MEM communication extension module
(consists of USB flash card & a RS232 port for computer
interface) was used. The waves were displayed using
LabVIEW software on the desktop computer which is an
integral part of the DSO, TDS2001.
Fig. 4. The block diagram of the piezoceramic transducer test setup (Block
diagram adapted from A. patel, D.N. Singh).
Bender elements are placed on top and bottom surface of
the specimen by creating a thin slit at the center of each of the
two planes. It is ensured that the bender elements are placed in
the same axis, parallel to each other. Piezoceramic disc have a
large flat plane which can be easily coupled using gel with the
top and bottom flat surfaces of the specimen.
IV. SIGNAL GENERATOR, FILTERS & AMPLIFIRES
The electronics involved for the test setup of measuring shear
and compression wave velocity in rocks and soils consists of a
function generator, filters, instrumentation amplifiers,
oscilloscopes and data storage/ processing device. Function
generator equipments are bulky and fail to provide high
strength signals. Thus, a signal (sine wave) generator was
developed for the testing purposes. A sine wave generator
circuit can provide high strength and quality waves required by
the piezoceramic transducers.
A. Signal generator
The Function generator IC XR-2206CP was used to develop
the sine wave signal generator for bender elements (0.2KHz -
30KHz) and piezoceramic discs (500KHz & 1MHz), shown in
Fig. 5. The operational voltage of the function generator is
from 10V to 24V. The output sine wave from the function
generator (XR-2206CP) has very low waveform distortion and
was fed to an non-inverting buffer operational amplifier
LM358 circuit. The sine waves of frequency 0.1Hz to 2MHz
with more than 20Vpeak to peak can be generated.
Fig. 5. Sine wave generator and Op amp buffer.
B. Filters and Amplifiers for Benders.
An input sine wave of 20Vp-p from the signal generator
having a frequency between 0.5 KHz to 20 KHz is given to the
transmitter which injects this signal to the soil or rock sample.
The signal received from the receiver transducer is then fed to
filters and amplifiers in order to eliminate noise and to increase
the amplitude of the received attenuated waves. The R C filters
and amplifiers implemented consist a combination of three
operational amplifiers ICs (INA121, OP07 and TL082).
INA121 is an instrumentation amplifier that provides high
input impedance and amplification to the signal from the
transducer. For eliminating DC errors which may arise during
amplification of the signal, the high pass filter was used. The
low pass and high pass cut-off frequencies were fixed as 150
KHz and 1 KHz, respectively.
The output waves received from the sample after
excitation of the bender setup is passed to an active High pass
filter having a cut-off frequency of 1 KHz, allowing only high
frequencies over 1KHz to pass through it. The filtered wave is
amplified using an operational amplifier OP07 which has
typical slew rate of 0.3V/µs and very low input offset voltage
(75μV max for OP07E). The low offsets and high open-loop
gain makes OP07 useful for high-gain instrumentation
applications. The output of high pass filter is given as an input
to the low pass filter having a cut off frequency of 150 KHz.
The active low pass filter is also implemented using R C
components and IC OP07 which allows frequencies only up to
150 KHz to pass. Both the operational amplifiers (IC OP07)
were operated in non- inverting mode as shown in Fig. 6.
Fig. 6. Filters and Amplifiers circuit diagram for Bender transducers.
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4. The output from the filter stage is amplified using IC TL082CP
which is a high speed, dual JFET input operational amplifiers.
It requires low supply current yet maintains a large gain
bandwidth product and fast slew rate of about 13V/µs. In order
to get correct and clear waveforms, various gain levels were
tried for the output signal, by placing a potentiometer as a
variable feedback resistor to the amplifier. Further the output
signal from the amplifier is displayed and stored using DSO
and in desktop computer (LabVIEW) for signal analysis.
C. Filters and Amplifiers for Piezoceramic discs.
A piezoceramic disc of 500 KHz or 1 MHz when excited with
its resonant frequency, it injects maximum amount of
longitudinal stress wave through the rock and soil samples [6].
The test setup utilized for the rock sample is shown in Fig. 7.
(a) (b)
Fig. 7. (a) 500KHz Piezoceramic disc transducers with granite sample test
setup. (b) 1MHz Piezoceramic disc transducers with granite sample test setup.
A sine wave of frequency 563 KHz and 1.124 MHz having
10Vp-p voltage is given to the piezoceramic discs (transmitter)
of 500 KHz and 1 MHz respectively. The output signal from
the rock sample is fed to an active band pass filter having
centre frequencies equal to the respective resonant frequencies
of the piezoceramic discs that is 563 KHz and 1.124 MHz [5].
The filtered signal is amplified by using operational amplifiers
ICs TL082, LM318. Two band pass filters and amplifiers were
implemented for both the piezoceramic disc of 500 KHz and 1
MHz. Filter amplifier circuit implemented for 500 KHz piezo-
ceramic discs is as shown in Fig. 8. The centre frequency of
band pass filter was kept as 563 KHz and a bandwidth of 50
KHz. IC TL082 having a slew rate of 13V/µS was used for the
amplification of the filtered signal. A potentiometer of 10KΩ
was placed at the feedback path of the amplifier in order to
vary gain of the received waves within ±5V range. The
equations used to determine the resistor values of the filter are
as follows:
R1 = Q / (G*C*2*Pi*F),
R2 = Q / ((2*Q^2)-G)*C*2*Pi*F), ... equation (1)
R3 = (2*Q) / (C*2*Pi*F),
Q = Center frequency/ Bandwidth
Center frequency = √(Lower freq. * Upper freq.)
where Q is the Quality factor.
The filtered and amplified output waves can be seen on DSO
which can also be transferred to the computer for further
analysis. LabVIEW software which is provided with the DSO
(Tektronix, USA) was utilized for the storage and analysis of
waves.
Fig. 8. Filters and Amplifiers circuit diagram for 500KHz Piezoceramic disc
transducers
Band pass filter and amplifier circuit for 1MHz piezoceramic
discs was implemented in a same manner as shown in Fig. 9.
The centre frequency of the band pass filter was kept as 1.124
MHz with a bandwidth of 50 MHz [5]. The resistor values
were determined with the same equations (refer equation (1))
used before for 500 KHz piezoceramic discs. Operational
amplifier ICs AD797 and LM318 were utilized for filter and
amplification purposes due to their high slew rate, very low
noise, low distortion and wide gain bandwidth. IC AD797 has
a slew rate of 20 V/μs and a 110 MHz gain bandwidth, which
makes it highly suitable for our low frequency ultrasonic
application. The output gain can be varied by using a
potentiometer as variable feedback resistor to the amplifier IC
LM318 which has a high slew rate of 60 V/μs.
Fig. 9. Filters and Amplifiers circuit diagram for 1MHz Piezoceramic disc
transducers.
V. SIGNAL GENERATOR, FILTERS & AMPLIFIERS BOX
The signal generator, filter and amplifier circuitry for benders
and piezoceramic discs (500KHz & 1MHz) was implemented
in a single sided printed circuit board which was a general
purpose board of 10×8cm. A 15×10 cm Acrylic box was fitted
with four potentiometers, each for adjusting gain of the output
waves and six bores were made for receiver, transmitter,
function generator, DSO inputs & outputs as shown in Fig. 10.
(a)
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5. (b)
Fig. 10. (a) Internal view of the developed system. (b) Fully fuctional Signal
generator, Filters and Amplifiers Box .
VI. RESULTS
The transmitter transducer was excited with the continuous
sine wave produced by the signal generator. Also a single
sinusoidal pulse wave generator using a timer circuit was
employed for the rock and soil testing. The developed system
was tested with four types of granite rocks and two types of
compacted soils.
(A) Bender elements
Bender element circuit was tested with a granite rock and a soil
sample. The wave velocity in the granite and soil sample
obtained were in accordance with the standard values [1]. It
must be noted that the circuit developed for the bender element
is for low power application, thus the rock & soil samples were
reduced dimensionally. An input sine wave of 20Vp-p from the
signal generator having a frequency between 0.5 KHz to 20
KHz is given to the transmitter. The wave travels through the
sample with some distortion and acquires a time lag before
being detected at the receiver. This 'Time Lag' is observed
through the DSO by comparing the transmitted and the
received wave. In order to find the wave velocity in the sample,
the distance between the transducers is divided by the transit
time of the wave (time lag). Fig. 11 shows the wave acquired
on LabVIEW when tested with the granite rock sample.
Fig. 11. Signal displayed in the LabVIEW front panel. Time Lag observed was
29.5 microseconds.
Considering the time lag observed through DSO or LabVIEW
software and the distance between the transducers which was
7.3cms, shear wave velocity was calculated. The shear wave
velocity obtained was 2471.2 m/s for the granite rock which
approximately matched the standard known values [4]. Table
no. I, Fig. 14 refers to the calculated and known shear wave
velocity in granite rock sample.
(B) Piezoceramic discs
Sine wave of frequency 563 KHz and 1.124 MHz having
10Vp-p voltage is given to the piezoceramic discs (transmitter)
of 500 KHz and 1 MHz respectively. The graph below, Fig. 12
shows the transmitter transducer input voltage versus output
voltage at receiver transducer for both 500 KHz and 1 MHz
piezoceramic discs.
(a)
(b)
Fig. 12. (a) Input voltage at transmitter verses output voltage at receiver for 500
KHz transducers, (b) Input voltage at transmitter verses output voltage at
receiver for 1 MHz transducers.
Granite rock samples were tested for the verification of the
piezoceramic disc transducer system. Fig. 13 depicts the waves
obtained in DSO for a test granite sample. The distance
between the transducers was approximately 6.8 cms for 500
KHz piezoceramic discs and 1.8cm for 1 MHz piezoceramic
discs.
The time lag between the transmitted (yellow) and received
(blue) wave is 15.5 μs for 500 KHz and 3.88 μs for 1 MHz
transducers. The compression wave velocity (P-waves)
calculated from piezoceramic disc transducer test setup
matched closely with the known granite P-wave velocity
values. Below is the result table obtained through the
developed system, refer Fig. 14.
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6. (a)
Yellow- Input wave 1.124MHz
(b) Blue- Output wave 1.125MHz
Fig. 13. (a) Input (top) and output (bottom) waves displyed on the DSO for 500
KHz and (b) 1 MHz piezoceramic transducer test setup.
TABLE I.
Transducer Frequ-
ency
Transducer
distance
(cm)
Time
lag
(μs)
Calculated
value of
Granite
(m/s)
Known
value of
(Granite)
(m/s)
Benders
(S-
wave)
0.1 -
30KHz
7.3 29.5 2471.2
2500 -
3300
Piezo-
ceramic 500KHz 6.8 15.5 4427.3
4200-
6000
discs (P-
wave)
1MHz 1.8 3.88 4483.2 4200-
6000
Fig. 14. Table for calculated and known shear and compression wave velocities
in granite rock sample.
Thus, it is clear from the above table that the shear wave (S)
and compression wave (P) velocities calculated by using the
developed system matches the known granite values. The wave
velocity values obtained through the test is beneficial in
determination of Young’s modulus (Emax) & Poisson’s ratio
(ν). This system can also detect the S & P wave velocities in
concrete and various stiff rocks.
VII. CONCLUSION
A system consisting of signal generator, filters and amplifiers
was successfully implemented to measure primary
(compression) and secondary (shear) wave velocities in rock or
soil samples using piezoceramic transducers. The system
developed is for low power, laboratory applications. It is
handy, portable and can be utilized for in-situ rock & soil
testing. High quality sine waves are produced by signal
generator which drives the piezoceramic transducers for signal
transmission. The received signal is filtered and amplified to
detect the desired waves which travelled through the sample
for the determination of sample type and its characteristics
(small strain shear modulus (Gmax), Young’s modulus (Emax) &
Poisson’s ratio (ν)), refer equation (2).
..... equation (2)
where, Cp is longitudinal pulse velocity.
Detection of quality waves depend upon the size of the piezo-
ceramic transducers. Waves detected through the developed
system were stored and analyzed using LabVIEW software.
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