Artículo Científico / Scientific Paper 



https://doi.org/10.17163/ings.n24.2020.02 


pISSN: 1390650X / eISSN: 1390860X 

MOISTURE IN CONCRETE AGGREGATES AND ITS RELATION TO
THE DIELECTRIC CONSTANT 

HUMEDAD Y SU RELACIÓN CON LA ESPECTROSCOPÍA DIELÉCTRICA EN AGREGADOS DE CONCRETO 
Franco Abanto^{1,*}, Pedro Rotta^{1}, Luis LaMadrid^{1}, Juan Soto^{1}, Gerson La Rosa^{1}, José Manrique^{1}, Gaby Ruiz^{1}, William Ipanaque^{1} 
Abstract 
Resumen 
Measurement of moisture content (CH) of concrete aggregates (AOC) in
the manufactury of ready mixed concrete is one of the currently challenges in
the building industry since affect to the final properties of concret. At
present, the methods for measurement of CH in AOC are invasive and
destructive. This paper presents a novel sensing technique using dielectric
espectroscopy (ED), a method that using the propagation of microwaves on the
material allows the correlation of its dielectric constant (CD) and its CH.
In this research is used this method in AOC. Three diferents peruvian
quarries (Moyobamba, Sol sol y Cerro Mocho) have been used. The results shows
that the sensor at the frequency of 1.5GHz is capable of detecting the CH in
AOC with linear regression of R^{2} = 95%. In conclusion, is
available using the ED as a online and no invasive sensing method of CH in
AOC for using in the building industry. 
Medir el contenido de humedad (CH) de los agregados de concreto (ADC) en la fabricación de concreto premezclado es uno de los retos actuales en la industria de la construcción porque afecta a las propiedades finales del concreto. Actualmente los métodos que se utilizan para medir el CH en ADC son invasivos y destructivos. Este artículo presenta una técnica moderna basada en espectroscopía dieléctrica (ED), un método que al propagar microondas en el material correlaciona su constante dieléctrica (CD) y su CH. En esta investigación se ha utilizado este método en ADC. Tres diferentes canteras peruanas de ADC (Moyobamba, SolSol y Cerro Mocho) han sido utilizadas. Los resultados demuestran que el sensor a una frecuencia de 1.5 GHz es capaz de detectar el CH en ADC con una regresión lineal de R^{2}=95%. En conclusión, se puede utilizar la ED como un método de sensado no invasivo y en línea de CH en ADC para ser utilizado en la industria de la construcción. 


Keywords: moisture
contentent, microwaves, dielectric spectroscopy, dielectric contant, concrete
aggregates 
Palabras clave: contenido de
humedad, microondas, espectroscopía dieléctrica,
constante dieléctrica, agregados de concreto

^{1,*}Laboratorio de Sistemas Automáticos de Control, Universidad de Piura, Perú. Corresponding author ✉: fabanto977@hotmail.es. https://orcid.org/0000000293882692 https://orcid.org/0000000264392870 https://orcid.org/0000000000000000 https://orcid.org/0000000191573098 https://orcid.org/0000000168292706 https://orcid.org/0000000203312734 https://orcid.org/0000000338359708 https://orcid.org/0000000340394422 

Received: 14102019, accepted after review: 13042020 Suggested citation: Abanto, F.; Rotta,
P.; LaMadrid, L.; Soto, J.; La Rosa, G.; Manrique,
J.; Ruiz, G. and Ipanaque, W. (2020). «Moisture in Concrete Aggregates and its relation to
the Dielectric Constant». Ingenius. N.◦ 24, (julydecember). pp. 1727.
doi: https://doi.org/10.17163/ings.n24.2020.02. 
1. Introduction The moisture
content (MC) of a material is a parameter that many industrial sectors seek to
control in their processes, because it impacts the final characteristics of
the product. In the construction industry, the MC of the concrete is
important since it defines the mechanical properties and the useful life of a
civil project [1]. Studies have been carried out to analyze the durability
and resistance in concrete structures measuring the MC [2], and also in
concrete test tubes [3]. No research studies have been conducted about
systems for measuring the MC of the AOC online, during the mixing process in
the plant. Authors in [4–6] show different techniques to perform the
measurement of the MC of materials. In the present paper it is utilized a
methodology based on dielectric spectroscopy, which has been tested in soil
[7], wool [8], paper [9], fabric [10], flour [11], wood [12–14]. There are various methods for measuring the MC of materials, which are
classified in direct and indirect. In the direct methods the MC is obtained
without correlating with other variables. These are the thermogravimetric and
chemical methods. The thermogravimetric method is not selective [15, 16], the
effective measuring range varies from 0.5 % to 99.9 % for the MC, and its
precision is 0.5 % of the total mass. In contrast, the chemical method
[17–19] is selective, it has a precision of 0.0001 % and a measuring range
from 0.00001 to 99.9 % of MC. The indirect methods require a prior
calibration to obtain the MC using direct methods. The indirect methods are classified in passive and active. The former
utilize elements such as variable resistances or capacitances to determine
the MC, which is by nature an invasive control. The active are those that
emit electromagnetic waves to determine the characteristics of the medium,
thus guaranteeing and online control and the integrity of the sample by not
being invasive nor destructive. The results of different research works in [20–23] in the field of
active methods, demonstrate that there is a relationship between the MC and
the relative permittivity (ε 0 ) or dielectric constant (DC) [24] of a material. The indirect methods use techniques such as the DS, which seeks to
measure the DC of the material, and is also utilized for other purposes such
as characterizing materials. Another indirect technique is the use of
hyperspectral images, which has had good success in bioengineering [25] and
in agroindustry [26–29]. Authors show applications with DS oriented to the agriculture, with
the purpose of estimating the quality of 
their products [30–41], which include applications in seeds, wheat, grains,
nuts, fruits of oil palm and bananas. This paper describes theoretical concepts of the DS and its
relationship with the MC [6]. An application is presented
that uses the DS to seek for the correlation between the MC and the DC of AOC
with different quarries, and verifying the possibility of this new method in
this industry. 1.1. Description
of the electromagnetic waves Electromagnetic
fields refers to the group of fields of electric and magnetic forces produced
by electric charges and currents in movement through the vacuum or any type
of matter. When an electromagnetic field propagates in the space
it is called propagation of electromagnetic waves. The propagation of electromagnetic waves is based on the solution of
Maxwell’s equations.
Where: E is the electric field [V/m] H the magnetic field [A/m] M is the density of magnetic current [V/m^{2}] J is the density of electric current [A/m^{2}] B is the density of magnetic flux [Wb/m^{2}] D is the density of electric flux [Coul/m^{2}] ρ is the density of charge [Coul/m^{3}] In order to solve Maxwell’s equations it is supposed
propagation in free space and, besides, a sinusoidal and harmonic
timedependent field that propagates in the zaxis and is polarized in the
xaxis. By using these assumptions and combining the given equations, it is
generated the second orden equation, known as homogeneous Helmholtz vector
equation for E.
where k is the wave number, which for a lossless medium is expressed
as: 
where: ω is the angular frequency of propagation ε_{0} is the vacuum permittivity µ_{0} is the vacuum permability Solving (5) yields:
which takes the phasor value:
The following expression can be used to give the phasor vector in
sinusoidal form:
Figure 1 shows the
propagation of the electric field in free space, where the given hypotheses
have been been taken into account.
Figure 1. Representation of an electromagnetic wave that
travels in free space [11]. 1.2. Propagation
of the waves in a medium with losses The hypotheses
defined in the preceding subsection consider the propagation of
electromagnetic waves in the vacuum. These are now extended to materials with
losses, i.e., conventional materials. According to their behavior in front of fields, the materials are
classified in good conductors, when they allow electric fields pass through
them, or as dielectrics, when they store electric energy inside and form
polar molecular bonds that are known as electric dipoles. In general, a
material has a conducting part and a dielectric 
part. Their
behavior is determined by means of the complex permittivity of the material,
which is defined as:
Where ε´ is the dielectric constant of the material, that
measures the amount of formed dipolar moments and represents the energy stored
in the material, and ε´´ is the constant of losses that represents the
energy that is not stored in the material, but that is somehow propagated or
reflected, which is represented as:
Where σ is the conductivity of the material such that:
It is obtained an equivalent conductivity that represents all the
losses in the medium.
The «tangent of losses» is a measure of the power losses in the medium, and is defined as.
Therefore, the solution of Maxwell’s equations through the homogeneous Helmholtz vector equation for E takes the form:
where k_{c} is the complex wave number, i.e., that takes the
complex value of the permittivity of the medium, which behaves in phasor mode
when taking a sinusoidal electric field. Besides, the vacuum permittivity is
expressed as a real value, since it will have no losses:
Therefore, this form of behavior of the materials makes the electromagnetic waves to attenuate at the moment of hitting them; part of the energy will be stored in the polar bonds and part will leave as energy losses. As 
a result, the
concept of propagation constant is defined as:
Using the definition of tangential loss:
Where α is the constant of attenuation and β is the constant of phase. Then, the primary solution given in vacuum is written as:
which takes the phasor value:
where:
Figure 2 shows the representation of this attenuation of an electric
field that hits a material with losses. 
Figure 2. Representation of an electric field that travels in
a medium with losses [11]. The energy lost at the moment of the propagation on the material is
called this way, because it is stored in the material forming polar bonds;
part of this energy is reflected from the material and part goes through it,
according to the value of its conductivity. This is seen in Figure 3. It is
observed an incident electric field (in green) that collides in the medium
(blue lines), and part of it is reflected (in red) and part is propagated by
the field (in orange). All this is quatified in the complex permittivity. In all this analysis it is assumed that the material is isotropic,
i.e., that the dipolar moments or that the polar bonds occur in the direction
of the electric field; this does not occur in anisotropic materials, but this
analysis is not taken into account in this research, because isotropic AOC
have been considered. 
Figura 3. Comportamiento de la propagación de una onda electromagnética frente a un cambio de medio [11]. 
The reflected part of the field can be related with respect to the
incident field by means of the reflection coefficient Γ, which relates the reflected wave and the incident
wave of the field
Replacing the equation of the wave to express it in terms of the
electric field, yields:
The equation of the magnetic field of the propagated and reflected
wave is directed in the direction orthogonal to the electric field:
It is possible to measure the electric field that hits a material, the
propagated field and the reflected field, in accordance with the equations
given in the theory. With all this it can be assumed
that it is possible to deduce the values of DC that will take the material
when analyzing the relationship between these quantities. 1.3. Dielectric
properties of the molecule of water The water is a
dielectric, i.e., it contains in its structure polar molecules that form
dipolar moments when being in contact with an electric field, and thus a greater
amount of water will result in a greater measured DC. A dry material will have a behavior established according to its
molecular structure, and will be normally homogeneous if this structure
remains unalterable when subject to a temperature increase or when mixed with
water. The AOC, due to their shape and properties, have a homogeneous
structure. Therefore, their dielectric constant will remain unalterable when
moistened. However, a higher moisture will increase the dipolar moment of the
mixture due to the water present, which will produce a change in the DC of
such mixture due to the increase in water. Therefore, the DC of the mixture
will be related with the MC of the AOC, and if the MC and the DC of the
mixture can be measured, it will be possible to determine a correlation
between them for future prediction and use as a sensing system. 2. Methodology It was seen in
the previous section that it is possible to correlate the value of the MC of
the AOC with the DC of 
the mixture,
because the quantity of dipolar moments will increase according to its MC. In
addition, it has been theoretically seen that it is possible to determine the
DC of the mixture using Maxwell’s equations and their solution for media with
losses. This section presents the experimental methodology which was followed
to determine such correlation. It should be noted that the field emmited is the field that collides
with the material, and the propagated field is the one that goes through the
material. 2.1. Materials The DC uses
frequencies in the microwave range for the propagation of the electromagnetic
fields; therefore, two aperture antennas are utilized to emit and receive the
incident and propagated fields, respectively (see Figure 4).
Figure 4. Aperture antennas utilized in MC measuring tests. A system for analyzing vector signals has been also utilized to emit the
electromagnetic field, as it is seen in Figure 5. The phase and
amplitude variation of the signal is analyzed, to further etermine the DC.
Figure 5. Wavetester equipment for analyzing vector signals. The analyzer of vector signals utilizes a software for data detection.
A sensing platform has been also constructed to carry out the
experimentation, on which the AOC has 
been placed to
measure its DC and its MC. Other utilized materials include: scales,
measuring containers, drying oven, etc. The sample is placed between the receiver and trasnmitting antennas,
where it is measured the effect on the AOC of the wave propagating in free
space between the two antennas. 2.2.
Experimentation Three Peruvian
quarries of AOC have been utilized to perform the calibration of the system:
Cerro Mocho, Moyobamba and SolSol. To determine the correlation between MC
and DC it has been proceeded the following way: An initial mass (m_{0}) has been defined as the total mass of AOC provided by the quarry. Then a thermogravimetric drying has been carried out to obtain the value of dry mass (m_{s}), i.e., without MC. This value of ms has been divided into 4, and each of theses samples has been named sampling dry mass and have been numbered from 1 to 4 (m_{smx}), where the subscript x corresponds to the number of the subsample. Then the sample m_{sm1} is selected and placed on the sensing platform, the electromagnetic field is emitted on the material, and with the help of the signal analyzer the value of the DC for m_{sm1} is measured. This value of DC corresponds to the value of 0 % of MC. The mass of water (m_{H2O}) corresponding to 0.5 % m_{sm1} is added to m_{sm1}, and the same procedure is carried out for measuring its DC. Then 0.5 % m_{sm1} is added again and the DC is measured, which corresponds to 1 % of its MC. This procedure is repeated until reaching 10 % of MC
It should be clarified that the following relationships are met in the
experimentation:
The distance between antennas was 23 cm, the thickness of the sample
was established in 40 mm, and the frequency of emission of the
electromagnetic field was 1.5 GHz. 
m_{sm1} and m_{sm2} were utilized to make the curves
of correlation, and m_{sm3} and m_{sm4} to validate the
results. It should be remarked that, at all times, the DC of the mixture of
the moistened AOC is measured. 3. Results With the values
of DC vs. MC obtained for each quarry, the calibration curve is fitted by
means of linear regression models. In this fit the MC is set as the dependent
variable, and the DC as the independent variable with different effects:
linear, quadratic, cubic and of fourth order. The «Stepwise Forward» method was applied for selecting the linear
regressiong model, to determine which of the effects of the DC better fits
with the MC. This classical method for the selection of variables initiates
with an empty model, and in each iteration evaluates incorporating some of
the defined effects of the dielectric constant: linear, quadratic, cubic and
of fourth order. It is decided to incorporate some of the aforementioned
effects if it meets the defined significance level: P Value smaller than
0.05. The «Stepwise Forward» method finalizes when no more effects can be
incorporated, because they do not meet the significance level. In order to
evaluate the level of significance of the effects, a hypothesis test with
«TStudent» is carried out. In this test it is verified if the estimated
coefficient of the effect is equal or different than zero.
If the null hypothesis is rejected (b_{i} ≠ 0), the
effect is significant. In hypothesis contrasting, it is calculated the relationship between
the estimated coefficient of the effect (b_{i}) and its standard
deviation (S_{bi}), and it is compared with the critical t for a
confidence level of 95% (α = 0, 05).
If the relationship is met, the null hypothesis is rejected. In this
condition it is met that the «P value» is smaller than 0.05. 
In fitting the regression model it was also found necessary to apply
the CochraneOrcutt iterative procedure, to correct the autocorrelation
present in the data. This autocorrelation is the result of sequentially
adding the variation of the moisture, and with this correction the estimation
of the parameters is improved. The results of the tests are presented in the following. 3.1. Cerro Mocho
quarry The model was selected by means of «Stepwise Forward», where it is
obtained
In this model, the linear effect of the dielectric coefficient with
respect to the expected value of moisture results significant. Table 1 shows
the results of the hypothesis contrasting, where the «P value» of the linear
effect is smaller than 0.05. It was obtained a linear regression model of R^{2}
= 95.8057 % and a standard error of 0.382134.
Figure 6 shows the relationship between the dielectric constant and
the moisture; Figure 7 shows the relationship between real and predicted
values of moisture.
Figure 6.
Plot of the fitted model 
Figure 7. Graphical relationship between observed and predicted
values of moisture. 3.2. Moyobamba
quarry The model was
selected by means of «Stepwise Forward», where the linear, quadratic and
cubic effects of the dielectric constant with respect to the expected value
of moisture are significant. (CH %) =
38.55+18.15×CD−2.52×CD^{2}+0.13×CD^{3} Table 2 shows the results of the hypothesis contrasting, where the «P
value» of the effects is smaller than 0.05. Table 2. Significance of the effect of the variables
It was obtained a linear regression model of R^{2} =99.5097 %
and a standard error of 0.201714.
Figure 8. Plot of the fitted model. 
Figure 8 shows the relationship between the dielectric constant and the
moisture; Figure 9 indicates the relationship between real and predicted
values of moisture.
Figure 9. Graphical relationship between observed and
predicted values of moisture. 3.3. SolSol
quarry The model was selected by means of «Stepwise Forward».
Where the linear and quadratic effects of the dielectric constant with
respect to the value of moisture resulted significant. Table 3 shows that the
«P value» of the effects is smaller than 0.05. Table 3. Significance of
the effect of the variables
It was obtained a linear regression model of R^{2} = 97.1325 %
and a standard error of 0.297068. Figure 10 shows the relationship between the dielectric constant and
the moisture, while Figure 11 shows the relationship between real and
predicted values of moisture. 
Figure
10. Plot of the fitted model.
Figure 11. Graphical relationship between observed and
predicted values of moisture. 4. Discussion of results From the results
obtained in the previous section, it is interesting to see that in the
frequency of 1.5 GHz, the linear regression correlations maintain an R2>95
%, as seen in Table 4. Table 4. Comparison of results
It can be also seen that there is a direct relationship between the MC
and the DC, i.e., a greater MC results in a larger value of DC. 
Comparing the equations for predicting the MC, it can be observed
that, depending on the origin of the AOC, it is defined its calibration curve,
which can vary between linear, quadratic or cubic; hence, for practical
purposes, the AOC should be first calibrated according to a specific quarry
before carrying out the measurement and this curve cannot be used for another
quarry, since the values of DC differ between quarries. This was expected
because the DC depends on the molecular properties and on the energy storage
capacity, which means that each AOC has a different structure at a molecular
level. 5. Conclusions The measurement
of MC with devices that utilize microwaves has advantages over invasive
methods, because they do not damage the material. The measurement of the DC
with this methodology analyzes internally the behavior of the material to
define its DC, since it studies the dipolar moments formed when
electromagnetic fields are induced in the material. It can be used in the
presence of vapors or in dirty environments, while the AOC is not molecularly
changed, since these do not interfere with the microwave signals. Therefore,
the DS enables the measurement of a broad range of materials, whether they
are solids, gases or liquids. The measurement is carried out without contact with the material. The
method is not invasive nor destructive. The meaurement is carried out in real
time and online with the process. It is interesting to observe the relationship found by different
authors. In [17] the author defines a linear or polynomial relationship. The
parameters that influence the calculation of the dielectric constant, and the
relationship between the moisture content and the temperature are shown. It has been verified that with the methodology based in DS at 1.5 GHz,
linear correlation values of high precision (R^{2}>95 %) are
obtained for each of the quarries. The system has been validated in a
horizontal conveyor with fine aggregate and antennas arranged vertically. The results obtained show the relationship between the MC and the DC
in AOC, and it has been observed a variation in the calibration curve between
different quarries. This sensing system exhibits a high potential to be used for measuring
the MC in AOC, in the process of concrete production. 
Acknowledgements
This paper has
been funded by Concytec and Sencico, in the project «Facilitation
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