Ultrasonic Detection of Chloride Ions and Chloride Binding in Portland Cement Pastes
International Journal of Concrete Structures and Materials
Ultrasonic Detection of Chloride Ions and Chloride Binding in Portland Cement Pastes
Arturo Emanuel Ram´ırez-Ort´ız
Prisciliano F. de J. Cano-Barrita
Chloride ions diffuse through the concrete cover and interact with the cement hydration products. As a result, some chloride ions become chemically and/or physically bound. Free chloride ions are the primary cause of steel corrosion in reinforced concrete structures. In this study, ultrasound was used to detect the presence and binding of chloride ions in cement pastes that contained supplementary cementing materials. Four cement pastes with w/c ratio of 0.55 were prepared and cast into cylindrical specimens that were moist cured for 254 days before being oven dried at 105 C. The dried specimens were vacuum-saturated with NaCl solutions at various concentrations. Through-transmission ultrasonic measurements were performed as a function of time using 500 kHz longitudinal wave transducers. The results indicated exponential relationships between energy/amplitude weighted average frequency and the amount of chloride chemically bound by the cement pastes.
ultrasound; X-ray diffraction; cement paste; chloride binding; durability
One of the primary factors that influences the durability of
concrete structures is penetration of aggressive species such
as chloride ions. Chloride ions present in concrete mix
constituents, deicing salts, or marine environments are the
main cause of steel corrosion in reinforced concrete
. Some of the chloride ions that penetrate
the concrete cover become physically and chemically bound
to the hydration products
(Hirao et al. 2005; Marinescu and
Brouwers 2012; Paul et al. 2015; Suryavanshi et al. 1996;
Talero 2012; Thomas et al. 2012)
, while others remain free.
Chemically bound chlorides form Friedel’s salt. Free
chlorides are present in the pore solution and cause corrosion of
reinforcing steel upon reaching it at a certain threshold
(Ann and Song 2007; Glass and Buenfeld
1997; Grantham 2003; Saremi et al. 2002)
Conventional methods of determining the chloride ion
resistance of concrete include the rapid chloride permeability
(ASTM C1202 2012)
, chloride ion migration tests
, and profile grinding to determine the
chloride ion concentration
(NT BUILD-443 1995)
binding isotherms reflect the chloride binding capacity of a
specific cementitious material in concrete
. Most conventional techniques are
destructive, time consuming, and expensive.
Non-destructive techniques have also been used to study
chloride ion ingress in concrete.
Torres-Luque et al. (2014)
classified the non-destructive methods into three main groups:
(i) ion selective electrodes (ISE)
(Angst and Vennesland 2009;
Atkins et al. 1996; Jin et al. 2017)
, (ii) electrical resistivity (ER)
(Gao et al. 2017; Andrade et al. 2014; Hornbostel et al. 2013;
Polder and Peelen 2002)
, and (iii) optical fiber sensors (OFS)
(Falciai et al. 2001; Lam et al. 2009)
. Each technique has
advantages and disadvantages. For instance, the ISE and OFS
methods detect only free chloride ions. In addition, they must
be installed before casting the concrete structure and thus
cannot be used to monitor existing structures. While ER is
easily performed on either new or existing structures, variations
in ER measurements are influenced by various factors such as
the degree of hydration, pore connectivity, moisture content,
and pore solution composition. Magnetic resonance imaging
(Cano et al. 2002)
is a technique suitable for laboratory
profiling of sodium and chloride distribution in cement-based
materials. However, the low NMR sensitivity of 35Cl makes its
detection difficult, thus requiring the use of MRI systems with
high-field superconducting magnets to increase signal
intensity. These types of MRI systems are costly and not widely
available, which restricts the use of MRI in studying
cementbased materials. Recent studies have focused on the application
of ground penetrating radar as a non-destructive method of
studying the presence and penetration of chloride ions in
(De´robert et al. 2017; Hugenschmidt
and Loser 2007; Kalogeropoulos et al. 2013; Senin and Hamid
. Researchers have also considered use of the near- and
far-field microwave methods
(Al-Mattarneh 2016; Chiniforush
et al. 2017)
Ultrasound (US) is a nondestructive monitoring technique
used to assess the strength and deterioration of concrete. It
has been used primarily to characterize concrete strength
(ACI Committee 228 2003)
et al. 2009)
, internal defects such as cracks, honeycombs and
(Jung et al. 2002)
, porosity and permeability
(Lafhaj et al. 2006)
, setting of high performance concrete
(Lee et al. 2004; Trtnik et al. 2013)
and deterioration of
concrete by alkali-silica reactions
(Gong et al. 2014; Ju et al.
. Several factors such as moisture content
, matrix density and porosity
(Punurai et al.
, and pore fluid viscosity
measurements of cement-based materials. Increasing the
NaCl concentration increases the solution density and
(Lin and Brown 1993)
, which in turn increases the
ultrasonic pulse velocity (UPV) and decreases the signal
(Herzfeld and Litovitz 2013)
This paper proposes the basis for an experimental
monitoring technique based on US that identifies the presence and
binding of chloride ions in four hydrated cement pastes. These
pastes exhibited differing chloride binding mechanisms and
capacities, as determined via conventional chloride binding
isotherms and by the height of the X-ray diffraction (XRD)
peak that corresponded to Friedel’s salt. After moist curing for
254 days, the samples were oven-dried at 105 C and then
vacuum saturated with NaCl solutions at concentrations of 0,
2.8, and 5.6 mol/L. US response signals from cement pastes
were acquired from the vacuum saturated samples as
functions of time for up to 200 days. The UPVs, energies, and
average frequencies of the US signals were related to the
presence and binding of chloride ions.
2. Experimental Investigation
Ordinary Portland cement (OPC), type F fly ash (FA), and
silica fume (SF) were used with distilled water to prepare
cement pastes. Table 1 provides the chemical compositions
of the Portland cement and supplementary cementing
2.2.1 Preparation and Conditioning of the Cement
Four cement pastes with water-to-cement ratio (w/c) of
0.55 were prepared using 100% OPC, 90% OPC ? 10% SF,
80% OPC ? 20% FA, and 60% OPC ? 40% FA. They
were labeled as OPC, 10SF, 20FA, and 40FA, respectively.
The cement pastes were prepared according to the ASTM
(ASTM C305 2011)
and the proportions
associated with cement replacement were determined by
weight. Replacement of OPC with supplementary cementing
materials produced cementitious systems with different
chloride binding mechanisms. Physical binding of C–S–H
dominated in the hydrated 10SF cement paste due to its high
specific surface area
(Byfors et al. 1986)
. Chemical chloride
binding was more significant than physical adsorption in the
20FA and 40FA cement pastes
A total of 64 cylindrical cement paste specimens
measuring 65 mm in diameter and 100 mm in length were cast
using plastic molds. The molds were filled in two layers,
each of which was compacted by tapping its base to expel
trapped air. The specimens were then placed in a device
designed to rotate at 7 rpm in order to minimize
sedimentation in the fresh cement pastes. After 1 day, the specimens
were demoulded and moist cured at 23 ± 2 C via
immersion in a saturated lime solution for 254 days. This long
moist curing process was performed to obtain a high degree
of hydration such that the effects of cement hydration during
ultrasonic measurements would be negligible.
At 254 days, the specimens stored in saturated lime
solutions were cut to 100 mm in length and further vacuum
saturated (- 20 in-Hg) with deionized water for at least 1 h.
After their masses were measured, the specimens were
covered with Parafilm to avoid water loss. This stage of the
process was marked as day - 4. Subsequently, the Parafilm
was removed and the specimens were oven dried at 105 C
until constant mass was achieved. This stage was marked as
day - 1. The specimens were cooled and vacuum saturated
(- 20 in-Hg) with NaCl solutions at concentrations of 0,
2.8, and 5.6 mol/L (day 0). Vacuum saturation was used to
accelerate chloride ion ingress, and consequently chloride
binding. The specimens were covered with Parafilm to
prevent moisture loss.
After vacuum saturation of the specimens (day 0), the
solutions left in the containers were brownish and included
suspended particles that precipitated after 1 day. A Fourier
transform infrared (FTIR) spectroscopy analysis of these
particles indicated the presence of calcium carbonate
produced by the reaction between the calcium hydroxide within
the specimens and the carbon dioxide present in the solution.
2.2.2 Chloride Binding Isotherms
Chloride binding isotherms were determined for the four
cement pastes in accordance with the technique proposed by
Luping and Nilsson (1993)
. In this technique, the central
regions of the specimens were cut into discs 5 mm thick,
which were ground before being passed through a No. 8
sieve (2.5 mm) and retained in a No. 60 sieve (0.25 mm).
Then, 15 g of ground paste was placed in 125 mL plastic
bottles and vacuum saturated for 2 h. The bottles were filled
with 60 mL of NaCl solutions at seven different
concentrations (0.1, 0.3, 0.5, 0.7, 1.0, 2.0, and 3.0 mol/L), sealed and
stored at 23 ± 1 C. The changes in the chloride ion
concentrations of NaCl solutions with initial concentrations of
3.0 mol/L were monitored as functions of time until the
solution concentrations were constant, indicating that no
further binding was occurring
(Thomas et al. 2012)
amount of bound chlorides Cb, given in mg Cl/g of sample,
was determined according to Eq. (1):
where V is the volume of the external solution (mL), Ci is the
initial chloride ion concentration of the external solution
(mol/L), Ce is the concentration of free chloride ions in
equilibrium with the external solution (mol/L), 35.453 is the
molar mass of the chloride ion, W11 is the mass of the sample
(g) and n11 is the evaporable water content (g). The last two
parameters were determined at a relative humidity of 11%.
XRD measurements were performed in order to verify the
formation of Friedel’s salt. Friedel’s salt is the main product
of chemical chloride binding. The XRD spectra were
obtained after the chloride binding isotherm experiments
were complete. The cement pastes were dried at 105 C for
24 h and then ground and passed through a No. 100 sieve
2.2.3 Ultrasonic Signal Acquisition
Through-transmission ultrasonic measurements with
500 kHz longitudinal wave transducers were performed on
specimens saturated with the three NaCl solutions (0, 2.8,
and 5.6 mol/L) 0, 1, 3, 7, 14, and 200 days after vacuum
saturation. Measurements were also performed at - 4 and
- 1 days. The specimen masses were measured before each
ultrasonic measurement to detect significant moisture loss.
Sodium chloride solutions with concentrations of 0, 0.7,
1.4, 2.1, 2.8, 3.5, 4.2, 4.9, and 5.6 mol/L, contained in an
extruded polystyrene vessel (65 mm in width 9 65 mm in
height 9 100 mm in length) were subjected to ultrasonic
pulses and their responses were recorded. Longitudinal wave
contact transducers (500 kHz) were used in direct contact
with the solutions. The UPVs
(ACI Committee 228 2003)
and signal energies
were calculated for all
solutions. The energies were calculated as the sums of the
squares of the amplitudes of the time-history responses. The
resulting UPV and signal energy behavior detected in the
solutions helped us to better understand the responses
observed from the saturated cement paste specimens.
The excitation pulses used in all of the measurements were
generated by an Olympus pulser/receiver model 5058PR
with a voltage of 200 V, 20 Hz repetition rate, 500 X
damping, and gains of 40 and 60 dB (applied to the OPC,
10SF samples; and to the 20FA, 40FA samples,
respectively). Each condition had three replicate specimens. All of
the pulse generation and the response signal acquisition
parameters remained constant throughout the experiment.
3. Results and Discussion
3.1 Properties of the Hydrated Cement Pastes
The OPC, 10SF, and 20FA pastes had average moisture
contents of 31% at 254 days, while the 40FA paste had an
average moisture content of about 40%. The average
variation in specimen moisture content (measured by mass)
between the various testing days was about 0.033%,
indicating negligible moisture loss during the ultrasonic
measurements. Figure 1 presents the oven-dried bulk densities of
the cement pastes, as well as their porosities. The higher
porosity and lower density of the cement paste containing
40% FA results primarily from the relatively high cement
replacement rate and the presence of unreacted fly ash,
which acts as a low-density filler.
3.2 Chloride Binding
Variations in the external NaCl solution concentrations
over time until equilibrium are shown in Fig. 2. Typically,
when the ground cement pastes are immersed in a 3.0 mol/L
NaCl solution, the external solution concentration stabilizes
during the 3rd week. This is consistent with the stabilization
times obtained by other researchers who used cement pastes
with w/c values of 0.50
(Thomas et al. 2012; Zibara 2001)
and 0.45 (Delagrave et al. 1997).
Titration of the seven NaCl solutions was performed in
order to obtain the chloride binding isotherms presented in
Fig. 3. The 40FA cement paste has the highest chloride
binding capacity, followed in descending order by 10SF,
20FA, and OPC. These isotherms are in general agreement
with behavior reported in the literature for these types of
supplementary cementing materials
(Delagrave et al. 1997;
Thomas et al. 2012)
. The free chloride versus bound chloride
data was plotted and fitted to Freundlich and Langmuir
isotherms. The best fit is obtained with the Freundlich
isotherm, which achieves a higher coefficient of determination
(R2 = 0.99) than the Langmuir isotherm (R2 = 0.96). This
is consistent with the results obtained by Zibara (2001), who
found that data related to this level of NaCl concentration
(higher than 0.01 mol/L) is best represented by the
Freundlich isotherm (Eq. 2).
Cb ¼ aCfb
where a and b are binding constants and Cf is the
concentration of free chloride ions (mol/L).
Friedel’s salt is the result of chemical binding of chlorides
to aluminates. Figure 4 presents XRD patterns that reveal
the presence of Friedel’s salt via peaks located at 2h = 11.3
with a net spacing of d = 7.8 A˚. The peak intensities are
related to the amount of Friedel’s salt generated, which
depends on the amount of tricalcium aluminate (C3A) in the
cement and alumina present in the supplementary cementing
. The 40FA paste produces the
highest peak intensity, followed by 20FA, OPC, and 10SF. In
addition, various levels of calcium hydroxide are observed in
the cement pastes as a result of the pozzolanic reaction. This
reaction reduces the amount of calcium hydroxide in pastes
containing SF and FA.
Figure 5 shows the Friedel’s salt XRD peak intensity and
the alumina content, versus the amounts of bound chlorides
in the pastes. Both graphs show that the bound chlorides
increase with the alumina content in all cement pastes except
for 10SF, which contains slightly less Al2O3 than OPC but
provides the second highest binding capacity of the materials
studied (Fig. 3). This confirms that SF contributes to binding
by increasing chloride ion adsorption on the additional C–S–
H produced by the pozzolanic reaction
(Luping and Nilsson
. Generation of Friedel’s salt is the dominant chloride
binding process in the other cement pastes, as shown in
Fig. 5. These results are consistent with those reported in the
(Thomas et al. 2012; Zibara 2001)
, except that the
literature indicates lower binding capacities among
specimens that contain silica fume.
3.3 Ultrasonic Measurements
3.3.1 Signal Energies and UPVs in NaCl Solutions
Figure 6 presents ultrasonic characterizations of the NaCl
solutions. Figure 6a and b show signal attenuation that arises
from the fact that the solution viscosities increase with the
(Uedaira and Suzuki 1979)
frequency domain spectra of these signals show the ‘‘filtering’’
effect that higher concentration solutions apply to the
ultrasonic response. Figure 6c shows the mean signal
energies and mean UPVs of the tested solutions. The energy
decreases as the NaCl concentration increases. This is
because signal attenuation is enhanced when higher NaCl
concentrations increase solution viscosities. In contrast, the
UPV increases linearly when solution densities increase due
to higher NaCl concentrations. These observations aid in
interpretation of the results obtained with cement pastes. The
porosities of the cement pastes are relatively high and thus
their responses to ultrasonic pulses are significantly
Fig. 5 Percentage of Al2O3 present in each paste and the
Friedel’s salt maximum intensity peak from XRD,
versus the bound chlorides in cement pastes.
influenced by the characteristics of the solutions used for
3.3.2 Effect of NaCl Solution Concentration on the Ultrasonic Responses of Cement Pastes
Figure 7 shows UPVs measured at various times before
(day - 4) and after vacuum saturation (day 0) with
deionized water and NaCl solutions at various concentrations.
From the insets, it is evident that all of the pastes exhibit
UPV decreases as a result of microcracking produced at day
- 1 when the samples are oven-dried 105 C
Wittel 2011; Wu et al. 2015)
. The effect of microcracking is
so significant that the UPV does not recover to its initial
value even after the cement pastes are vacuum saturated (day
0). After the specimens are vacuum saturated, the OPC,
10SF, and 20FA cement pastes exhibit nearly constant UPVs
from days 1 through 200. In addition, slightly lower UPV
values are observed in samples saturated with a 5.6 mol/L
NaCl solution than in those saturated with 0 and 2.8 mol/L
solutions. The 40FA cement paste samples saturated with
NaCl solutions present similar but more noticeable UPV
behaviors. They exhibit relatively low UPV values from
days 1 through 14, which increase from days 14 through
200. At days 0 and 1, only the 40FA cement paste exhibits
UPV values that are consistent with the positive relationship
between UPV and the NaCl concentration shown in Fig. 6c.
After 1 day, this behavior changes only for the paste
saturated with deionized water. It exhibits an exponential
increase in UPV similar to that seen in typical cement
(Boumiz et al. 1996; Hewlett 2003)
to 200 days.
Due to the levels of FA replacement and w/c ratios, the
degree of cement hydration may be low
(Lam et al. 2000)
may be the extent of the pozzolanic reaction
and Tangtermsirikul 2004)
. After microcracking due to oven
drying, unhydrated cement particles might become exposed
and react with the saturating solution, generating new
hydration products along these microcracks. Therefore, the
UPV of the 40FA cement paste increases (Fig. 7d). It appears
that rehydration is limited in samples that contain NaCl
solutions and therefore is not high enough to seal the
microcracks. This is in contrast to the behavior observed in the
samples that are vacuum saturated with deionized water.
Now, let us use the energies of the ultrasonic signal
response to identify the three NaCl solution concentrations
within the cement pastes. The responses were recorded at
- 4, - 1, 0, 1, 3, 7, 14, and 200 days. Figure 8 shows the
signal energy evolution over time. Data for the OPC paste at
day 0 saturated with the 5.6 mol/L NaCl solution was not
recorded because the vacuum saturation period was longer
than those of the rest of the specimens. Regardless of the
type of cement paste, similar energy levels are observed
from day - 4 (water saturated) to day - 1 (oven dried),
which suggests similar paste microstructures after oven
drying. However, the pastes exhibit distinct behaviors as
time passes. There is an overall trend towards signal energy
reduction as the NaCl concentration increases. Higher
concentrations attenuate the signal (see Fig. 6c) by increasing
the pore fluid viscosity
(Lin and Brown 1993)
in the cement
pastes. Upon comparing the distinct cement pastes, it is
interesting to note the significant decreases in the energies of
the 20FA and 40FA pastes compared to the OPC and 10SF
pastes. This attenuation may be explained by chloride
binding and scattering. Chloride binding produces a lower
solution viscosity while generating Friedel’s salt. Based on
the low energies obtained with 20FA and 40FA, it is
suggested that this reduction is produced by scattering
caused by spherical particles of unreacted FA (Fig. 9) and
Friedel’s salt. The energy reductions observed in the 20FA
and 40FA cement pastes vacuum saturated with deionized
water are related to a similar process that occurs without
generation of Friedel’s salt. In the 40FA cement paste
vacuum saturated with deionized water, the attenuation
described also overcomes possible increases caused by new
generation of hydration products along the microcracks. The
behavior of the 10SF paste differs from that described,
probably because its chloride binding process (physical
adsorption) is different from those of the other cement pastes
Figure 10 shows the signal energies of all of the cement
pastes at day 14 after vacuum saturation. The energies of the
OPC and 10SF pastes are significantly higher than those of
the 20FA and 40FA pastes at each NaCl concentration. The
only exception is the OPC saturated with a 5.6 mol/L NaCl
solution. As mentioned, the energy reductions in 20FA and
40FA are probably caused by chloride binding and
scattering. Figure 2 suggests that most of the chloride ions should
already be bound by day 14. This is indicated by the
constant chloride concentrations of the external solutions. The
pastes that have been treated with 0 and 2.8 mol/L NaCl
solutions exhibit only moderate decreases in their signal
energies. Distinctions between 2.8 and 5.6 mol/L are evident
only for OPC. The change in the 10SF cement paste signal
energy is less sensitive to the effects of NaCl concentration
than the others. This is consistent with the fact that this
cement paste undergoes a different chloride binding process
and therefore impacts the energy of the ultrasonic signal
3.3.3 Ultrasonic Identification of Chloride Binding
The signal energy is presented in Fig. 11 as a function of
testing time. This plot corresponds to pastes with a NaCl
concentration of 2.8 mol/L (close to the maximum
concentration of 3.0 mol/L used for the chloride binding isotherms).
Before vacuum saturation (days - 4 and - 1) with the
chloride solution, all of the pastes exhibit the same energy
behavior. Thus, oven drying causes no significant
differences between the microstructures of the cement pastes.
After vacuum saturation ([ 0 days), the pastes containing
20FA and 40FA exhibit lower energies than the OPC and
10SF pastes. The larger volume of NaCl solution contained
in the FA pastes (due to their higher porosities) might
explain the more extensive decreases in the signal energies
of these specimens. In addition, scattering caused by
unreacted FA and the amorphous Friedel’s salt generated might
contribute to these energy decreases.
According to Fig. 2, the chloride binding processes
stabilizes by day 14 in all of the pastes studied. As chemical
binding of chlorides is closely related to the presence of
aluminates, the relationship between the amounts of alumina
and bound chlorides and the corresponding signal energies
are presented in Fig. 12. Both relationships are similar,
except in the case of bound chlorides where the cement paste
containing SF behaves differently due to its different
chloride binding mechanism. It is an outlier in the bound
Figure 13 shows the bound chlorides as functions of the
amplitude weighted average frequency. The range of
frequencies considered is limited by the sampling rate
(25 MHz) and the duration of the signal (2.6214 ms). One
Fig. 8 Evolution of the energy over time of the specimen ultrasonic response (the error bars indicate ± one standard deviation),
pastes a OPC, b 10SF, c 20FA, and d 40FA.
Fig. 9 Randomly distributed unreacted fly ash shown as
hollow spherical particles in the 40FA cement paste.
can note similarities between Figs. 5 and 12. In this case, the
different chloride binding process in the 10SF paste is also
evident. This demonstrates that the US signal response
contains information related to both solid and pore fluid
changes. Changes in the solid phase of the hydrated cement
paste are produced via the generation of Friedel’s salt. On
the other hand, changes in the pore fluid occur due to
Fig. 10 Energy of the ultrasonic response at day 14 (the error
bars indicate ± one standard deviation).
reductions in chloride ion concentrations as chemical and
physical binding occur.
Figure 14, a combination of Figs. 5 and 13, shows that the
amplitude weighted average frequency from the ultrasonic
measurements is related to the amounts of alumina and
Friedel’s salt present in the cement pastes. These results
demonstrate that the ultrasonic responses of
containing cement pastes can be used to non-destructively
study the chloride binding properties of cement-based
This paper proposes the basis for an experimental
monitoring technique based on US that can identify the presence
of chloride solutions and their binding in four hydrated
cement pastes. The ultrasonic responses of cement pastes
after vacuum saturation with NaCl solutions of various
concentrations were analyzed to identify relationships
between the ultrasonic signal characteristics and binding
capacities of the cement pastes. Based on the results
obtained in the present research, the following conclusions
Fig. 13 Amplitude weighted average frequencies obtained
from the Fourier spectra of ultrasonic response
signals and the chloride binding capacities of the
cement pastes (data correspond to pastes 14 days
after vacuum saturation with a 2.8 mol/L NaCl
(1) UPV measurements cannot detect either the type of
fluid present in the cement pastes or the changes caused
by chloride binding.
(2) The energy of the ultrasonic signal response allows
identification of the NaCl solution concentration only
for the OPC cement paste 14 days after vacuum
(3) There is an exponential decay relationship between the
bound chlorides (governed by chemical reaction) and
the signal energy, as well as between the alumina
content and the signal energy.
(4) There is an exponential relationship between the
amplitude weighted average frequency and the quantity
of bound chloride (regulated by chemical reaction) in
the cement paste.
(5) The amplitude weighted average frequency is directly
proportional to the quantities of alumina and Friedel’s
salt generated by chemical chloride binding.
Although analysis of the results was challenging, especially
with regard to the effect of microcracking on the energy
results, promising non-destructive techniques for monitoring
the durability of concrete structures may rely on the
relationships found between signal energy (or amplitude
weighted average frequency) and bound chloride (or alumina
content). These relationships are valid only for those cement
pastes which bind chlorides primarily via chemical reactions.
The authors acknowledge CONACyT and the Instituto
Politecnico Nacional for financial support of the project
(CONACyT CB Grant number 154552 and Grant number
SIP 20131009, respectively). P. Cano acknowledges
CONACyT of Mexico for financial support of the project with
Grant Number 239727. Arturo Ramirez acknowledges
CONACyT for his graduate studies scholarship. The authors
acknowledge Dr. Mario F. Cosmes-L o´pez for his assistance
during ultrasonic data acquisition.
This article is distributed under the terms of the Creative
Commons Attribution 4.0 International License (http://
creativecommons.org/licenses/by/4.0/), which permits unre
stricted use, distribution, and reproduction in any medium,
provided you give appropriate credit to the original
author(s) and the source, provide a link to the Creative
Commons license, and indicate if changes were made.
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