INFLUENCE OF CYCLICAL SOAKING IN CHLORIDE BATH
AND DRYING OF MORTAR ON ITS MICROWAVE
DIELECTRIC PROPERTIES: THE FORWARD MODEL
Kristen Munoz and Reza Zoughi
Electrical and Computer Engineering Department, Applied Microwave
Nondestructive Testing Laboratory (amntl), University of Missouri - Rolla, Rolla,
MO 65409, USA
ABSTRACT. Reinforced concrete structures provide a highly alkaline and protective environment for
steel bar reinforcements. The protective environment is destroyed upon the introduction of chloride ions,
allowing for corrosion if moisture and oxygen are present. Microwave nondestructive testing is one
method to detect chloride in cement-based materials. A comprehensive understanding of how chlorides
are deposited in mortar that is exposed to cyclical salt water soaking and oven drying is desired.
Modeling is a necessary component of this process. This paper presents the modeling process using
mixing models and possible salt distributions in conjunction with a multi-layer code that provides
simulated results.
INTRODUCTION
Reinforced concrete structures are commonly used in a large percentage of the
country's infrastructure. Normally, concrete provides an environment in which the
reinforcements will not come into contact with corrosive agents or conditions. Concrete is
highly alkaline and provides protection for reinforcing steel bars from corrosion due to a
submicroscopic passive film that forms at the steel-concrete interface. However, should
chloride ions be introduced into the concrete structure, the protective film will be
destroyed. Subsequently, when moisture and oxygen are present in the concrete, the steel
reinforcing bars corrode through an electrochemical process [1].
Thus, it is important to be able to detect the presence of chloride (i.e. free salt) in
cement-based materials. Microwave nondestructive testing (NDT) is one such detection
method. Microwave NDT methods offer many advantages [2], namely that:
• microwave signals are able to penetrate dielectric media,
• they are sensitive to dielectric, volumetric, and size distribution of a mixture and
its constituents,
• they are sensitive to molecular bonding (i.e. curing and free vs. bound water),
• modeling tools are available to predict dielectric properties of mixtures,
• non-contact, nondestructive, and one-sided measurements are feasible,
• large areas can be inspected with sensor arrays,
• systems are low power, operator friendly, real-time, and in-situ.
CP657, Review of Quantitative Nondestructive Evaluation Vol. 22, ed. by D. O. Thompson and D. E. Chimenti
© 2003 American Institute of Physics 0-7354-0117-9/03/$20.00
470
BACKGROUND
The detection and evaluation of chloride ions (i.e. free salt) in cement-based structures
is important as it relates to the integrity of cement-based structures that come into contact
with salt water. Near-field microwave NDT techniques have shown great promise for
evaluating various properties of cement-based materials including the detection of
chloride ingress in mortar [3-11]. However, a more comprehensive understanding of how
the free salt is deposited in a mortar sample that is exposed to cyclical salt water soaking
and subsequent oven drying is still desired.
The process of cyclically soaking and drying a mortar sample gradually leaves behind
free salt in the pores. Consequently, this process results in a non-uniform gradient of salt
ingress. Electromagnetically, this is equivalent to a mortar sample possessing nonuniform dielectric properties.
To obtain such a sample, cylindrical mortar samples with rectangular cross-sections
will be produced. The samples will be made to fit tightly inside of a shorted rectangular
waveguide sample holder. The samples will then be cyclically exposed to a salt water
solution in such a manner that will provide for a non-uniform salt distribution that varies
only over the sample length. After each soaking and drying cycle, the calibrated
microwave reflection coefficient of the sample will be determined for when the samples
are placed inside a short-circuited rectangular waveguide.
To determine the salt distribution (gradient) within the sample, it is necessary to model
the experimental process. With the soaking and drying process in mind, the sample will
resemble that shown in Figure 1A, which depicts a non-uniform salt penetration. This
sample can then be discretized to have many layers, each with a discrete thickness and
uniform average dielectric properties, as shown in Figure IB. Subsequently, a model
based on evaluating the total electric field inside of each layer along with the application
of boundary conditions at each interface is used to obtain the calculated reflection
coefficient [12,13]. The results of the model and the experimental measurements can then
be compared to arrive at the sought-after information such as the gradient and total salt
content in the sample after each soaking and drying cycle.
MODEL
In order to model the reflection coefficient of such a sample, some indication of the
distribution of the salt in the sample after each soaking and drying cycle is necessary. To
this end, three distribution functions were chosen as shown in Figure 2. If it is found that
these three functions do not exactly describe how the salt is distributed within the sample,
it is believed that the final distribution function will lie within the boundaries of the three
distributions shown in Figure 2 [14,15]. The importance of this is that any distribution
that accurately depicts the actual salt distribution can be used in this model, allowing for
the implementation of any distribution function.
FIGURE 1A. Depiction of a non-uniform salt distribution
471
FIGURE IB. Depiction of discretized non-uniform salt distribution.
———— 1st Distribution
— — 2nd Distribution
- 3rd Distribution
10
8
6
4
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10
.
20
30
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40
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Sample Length (mm)
FIGURE 2. Salt distribution curves as a function of sample length.
The distributions, shown along the sample length in Figure 2, are for salt with a
maximum volume content of 8%. This is also the maximum porosity of the sample. This
relationship exists because when the salt water penetrates the sample and then evaporates,
the free salt left behind will fill the sample pores. This particular value for porosity was
used since it is within reported limits for porosity in mortar [16].
Assuming the sample is discretized along its length into 100 layers, each with a 0.5
mm thickness (total sample length 50 mm), the dielectric properties for each layer must be
determined for incorporation into the layered model. The dielectric properties for each
layer depend on the volume fraction (content) of mortar, air (porosity), and free salt in
each layer. Dielectric mixing models provide for the effective dielectric properties of such
a mixture by knowing the dielectric properties (relative to free space) of mortar (em = 5 jO.5), salt (es = 3 - jO.3) and air (ea = 1 - jO.O) and their respective volume fractions [17].
The volume fraction of salt comes from the distributions shown in Figure 2. The volume
fractions of mortar and air are related to the volume fraction of salt.
Three different mixing models were used to determine the dielectric properties of each
layer [18]. These mixing models are shown in Equations 1, 2 and 3, where fs is the
volume fraction of salt, fm is the volume fraction of mortar, andfa is the volume fraction of
air. The volume fractions of salt and air are a function of sample length, t.
l (0 = /, (0 £, + /X + fa
a)
(2)
(3)
The three mixing models shown above are obviously different, yet when used for this
investigation, the equations do not behave so differently. In [17], it is shown that mixing
models, such as these listed above, behave similarly at the endpoints; that is, when the
porosity (air included in the sample) is a small or large percentage of the total sample
volume, the equations converge. However, using these three equations provides for a
472
degree of diversity in the way the dielectric properties of the salt and mortar mixture may
behave.
These mixing models were applied to each of the 100 layers of the discretized sample
to produce effective dielectric properties eefj(t) that differ for each layer. These effective
dielectric properties are shown over the entire sample length for each of the mixing
models in Figures 3,4 and 5.
RESULTS
Since the number of layers, thickness of each layer, and the effective dielectric
properties of each layer are known, the reflection coefficient as a function of frequency
can be calculated, as depicted in Figures 6, 7 and 8 [12]. The frequency band used for the
calculations is S-band (2.6-3.95 GHz). This frequency band has shown great promise for
detecting chloride ingress in mortar [8-11,19]
-0.432
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20
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40
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Sample Length (mm)
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Sample Length (mm)
FIGURE 3. Effective dielectric properties using the 1st salt distribution and all three mixing models.
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Sample Length (mm)
FIGURE 4. Effective dielectric properties using the 2nd salt distribution and all three mixing models.
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FIGURE 5. Effective dielectric properties using the 3rd salt distribution and all three mixing models.
473
50
——— 1st Distribution —•
- — 2nd Distribution
- 3rd Distribution
——— 1st Distribution
— — 2nd Distribution
- 3rd Distribution
0.8
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0
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2.9
3.19
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Frequency (GHz)
2.9
3.19
3.48
3.77
Frequency (GHz)
FIGURE 6. Simulated microwave reflection properties at S-band using the 1st mixing model and all 3 salt
distributions.
——— 1st Distribution
— — 2nd Distribution
- 3rd Distribution
——— 1 st Distribution
— — 2nd Distribution
—— — 3rd Distribution
0.8
0.64
CD
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2.61
2.9
3.19
3.48
2.61
3.77
Frequency (GHz)
2.9
3.19
3.48
3.77
Frequency (GHz)
FIGURE 7. Simulated microwave reflection properties at S-band using the 2nd mixing model and all 3 salt
distributions.
——— 1 st Distribution
— — 2nd Distribution
—
——— 1st Distribution
— — 2nd Distribution
- 3rd Distribution
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2.61
2.9
3.19
3.48
2.61
3.77
2.9
3.19
3.48
3.77
Frequency (GHz)
Frequency (GHz)
FIGURE 8. Simulated microwave reflection properties at S-band using the 3rd mixing model and all 3 salt
distributions.
The calculated results point to many important issues. For example, the mixing model
used has an important effect on the results. For a given mixing model, the calculated
reflection coefficient from each of the three salt distributions differs from one another.
However, the 3rd mixing model provides the most difference. This shows the importance
474
of choosing the mixing model that not only provides for an accurate effective dielectric
distribution but also an adequate difference between different distributions.
The results can also be used to determine which frequencies are optimal for the
experimental procedure. Consider the results shown in Figure 8. If the measurements
were to be conducted in the lower end of the frequency band, the difference between the
different distributions is not nearly as apparent as the difference between the different
distributions in the upper part of the band, particularly between 3.5 GHz and 3.8 GHz.
Therefore, choosing an appropriate frequency of operation plays an important role in
optimizing the experimental procedure.
Another comparison that may provide insight for choosing the optimal frequency of
operation is a comparison between the sample with and without salt ingress. Figures 9
and 10 show the phase and phase difference of such a comparison respectively.
Figure 9 depicts the phase of reflection coefficient using the 1st mixing model and the
rd
3 salt distribution for the cases with and without salt. It is important to note that if the
sample did not have any salt ingress, the sample would consist only of mortar and air.
According to the 1st mixing model, the effective (no-salt) dielectric properties based on the
above mentioned dielectric properties of air and mortar is sno.sait = 4.68 - J0.44. It can be
seen that there is a difference in the calculated results between the cases with and without
salt. This difference is seen easily when the phase difference of the two cases is
examined, as shown in Figure 10. The results are shown over the frequency range that
holds the greatest difference in phase between the two cases, namely between 3 and 4
GHz. It can be seen that a maximum phase difference of nearly 30 degrees occurs at
approximately 3.6 GHz, providing an indication as to where in the frequency band
experimental procedures should be carried out.
w/out salt
— — with salt
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FIGURE 9. The phase of the reflection coefficient for the cases with and without salt using mixing model 1
and salt distribution 3.
30
24
18
Q
CD
12
6
3
3.2
3.4
3.6
Frequency (GHz)
FIGURE 10. Phase difference between the salt and no-salt cases.
475
3.8
CONCLUSION
Reinforced concrete is commonly used in many areas of today's infrastructure.
The penetration of free salt (chloride ions) along with moisture and oxygen can cause steel
reinforcements to corrode. It is important then to have information regarding how free salt
is deposited inside cement-based materials. Microwave NDT techniques have shown
promise for obtaining such information. Consequently, it is proposed to cyclically expose
a mortar sample to salt water and then make calibrated reflection coefficient
measurements to characterize the deposited free salt distribution after the sample is oven
dried.
In order to fully understand this process, modeling of the experimental effort must be
completed as well. This is done by discretizing the free salt distribution, applying mixing
models, and incorporating the resulting effective dielectric properties into a multi-layer
code. The multi layer code then provides the calculated reflection coefficient. The
mixing models consider the dielectric properties of the mortar, air, and salt along with the
volume fraction (content) of each.
A number of salt distributions as well as dielectric mixing models were considered.
The dielectric profiles, obtained via mixing models, were calculated. Subsequently, the
calculated microwave reflection properties were provided. The results showed that the
frequency of operation, salt distribution function used, and mixing model chosen all have
an important role to play. The thickness of the sample may also have an effect on the
results.
The calculated results also showed a difference between a sample with and without
salt. The final difference will depend upon the actual distribution by which salt ingresses
into the sample. The number of soaking cycles will have an effect on the final salt
distribution profile as well. Cyclical freezing and thawing of the samples may also be
considered in the future. The overall approach, both experimental and modeling, shows
promise for understanding the way by which salt penetrates into cement-based materials.
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