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CONTRIBUTION OF CAPACITANCE PROBES FOR NONDESTRUCTIVE
INSPECTION OF EXTERNAL POST-TENSIONED DUCTS
J. Iaquinta
LCPC, Paris, France
Abstract: In bridges, external post-tension habitually comes as cables placed in ducts for which
the residual internal space is (imperfectly) filled with a fluid cement grout. Detecting the
problems of injection is not practicable visually from the outside, and no effective auscultation
tools were found yet. A recent laboratory experiment established that capacitance probes can be
employed, but the main difficulty is to provide a correct interpretation of the measurements in
terms of deterioration of the coating, along with the occurrence of water or grout voids. In order
to understand if the presence of the cable itself can disturb the diagnosis in such proportions that
any inspection is destined to failure, the subject was tackled here from a numerical point of view.
It is shown that the capacitance probe is sensitive to the location of the cable, but that it is still
possible to distinguish typical defects present at low depth. This result is confirmed, from a
qualitative point of view, by tests performed with an actual probe.
Introduction: A lot of bridges and tunnels include "external" post-tension (so called since it is
not in the concrete material, hence potentially accessible for measurement), either originally or a
after reinforcement of structure. The cables are generally placed in High Density Poly-Ethylene
(HDPE) ducts, where the residual space is filled under high pressure with a cement grout intended
to prevent corrosion. This protection being imperfect, cable breaking occurs in non-protected
zones because of the presence of a "white paste" (not hardened grout with a high water content)
or grout voids.
The detection of such defects inside an opaque duct is unachievable visually from the outside.
Furthermore, already existing procedures (Derobert et al., 2002) often involve the damaging
creation of apertures on the duct envelopes to look inside or introduce an endoscope. Another
approach employing gamma-rays radiography is cumbersome and expensive, acoustic methods
are not precise enough, etc. In these conditions, there are few available modus operandi, and the
need for a reliable diagnosis urgently requires the development of effective investigation tools to
prevent unnecessary strengthening and repair, or even replacement (Cavell et al, 2001).
Electromagnetic methods are suited for many purposes, amid, capacitive measurement is
implemented on a regular basis for a quantitative estimation of the water content of soil (Fares
and Alva, 2002), cement (Smith et al., 2002), or agricultural products (Nelson, 1992). This
technique is also appropriate to assess the porosity of volcanic rocks (Rust et al., 1999), voids
fraction in multi-phase flows (Kendoush and Sarkis, 1996), etc. Further, capacitance detectors are
employed for the qualitative differentiation of materials like clear wood from knots and distorted
grain (Steele and Kumar, 1996), to characterize biologic cells (Asami, 2002), to sound snow
packs in avalanche forecast (Louge et al., 1998), and to detect buried plastic landmines
(Mamishev, 1999). Capacitor properties provide non destructive tools (Matiss, 1999) at micro-
scale as well, for instance to inspect electronics products (Ruprecht et al., 2003) or control their
processing integrity (Jeandupeux et al., 2002).
In the same manner, the auscultation of external post-tensioned ducts with a capacitance probe
was found to be workable during laboratory experiments (Dupas et al., 2001). The tests utilized
long transparent proof bodies, containing a steel cable, and acting as duct pieces. Holes allowed
the introduction of water, sand or air, and the emptying. Two rectangular electrodes applied on
the outer surface of the samples were moved around and along the proof axis, repeatedly. An
alternating current being applied between the plates, the system constituted some sort of capacitor
coupled into a high frequency resonant circuit. The resonant frequency shift is indicative of the
nature of the materials inside the duct.
However, without knowledge of the factors susceptible of influencing the measurements,
operators experience and shrewdness are necessary for interpreting the capacitance data.
Moreover, previous sampling and calibrating phases are necessary to have a chance for relating
measured and searched information. Indeed, the case of post-tensioned ducts is complex, since
they appear as an heterogeneous mixing of conductors and dielectrics, and as internal geometry
interferes in an undefined manner. Accordingly, it seems judicious to study first the influence of
each contribution independently, starting from the most important processes, or at least (those
sought to be) governing features.
Actually, the first question we have to answer is: does the presence of the steel cable influences
the measurement in such proportions that any inspection for detecting inclusions is destined to
failure ? The problem was tackled here from an electrostatic point of view, and a model of post-
tensioned duct was used for a numerical evaluation of its dielectric capacitance by solving the
corresponding set of equations with finite elements. After setting up the configuration in the first
part of this paper, several situations are studied in a second section for a sensitivity study in
typical capacitors where the nature of the constituents as well as the location of the post-tensioned
cable both vary. At last, an example of measurement obtained in the laboratory with a capacitance
probe is described as well as the corresponding simulation.
Setting up: A sketch of external post-tension duct containing a seven-tendons steel cable at the
bottom is shown on Figure-1. Here, the volume of the HDPE envelope is imperfectly filled of
cement grout, with an air pocket and a water saturated material layer (i.e., not hardened paste), as
may occur frequently.
Cable
Air
Electrodes
Water saturated
material
Grout
HDPE
duct Figure-1: Example of post-tension duct having a steel
cable and various materials inside, with the sensing
and driven electrodes outside.
The electrodes of the probe are slid on the duct, in order to allow measurements longitudinally,
referred hereafter as the z coordinate, and transversely by rotation θ of around the z-axis. For the
moment, displacements of the sensor are carried out manually, but in a short term a completely
autonomous (motorized) probe is planned.
Regarding the different constituents of the system, some (steel, for instance) are excellent
electrical conductors, other are insulators (HDPE), and between the extremes, most materials are
more or less conductors. Indeed, their effective dielectric constant is highly sensitive to water
content, since the relative dielectric constant of water is several orders of magnitude higher.
The investigation frequency (and alternating electric field) can be properly selected, based on
information about the materials electromagnetic properties thoroughly measured individually
over a broad range, in particular for the cement grout (Al-Qadi et al., 1995; Al-Qadi et al., 1997).
But in the end, the frequency dependence of the mix (Priou, 1992) cannot be only attributed to the
intrinsic properties of each material (one of the reasons being the interfacial polarization
mechanisms). However this intricate point is out of the scope of the present work, so the
dielectric constants of pure (not combined) constituents are set to fixed values for conducting the
preliminary computations.
The configuration of a "conventional" parallel plate capacitor would require a contact with the
material under test from two opposite sides. The variation here is that the electrodes of the sensor
are placed next to one another (see on Figure-2), so as to provide a sufficient penetration depth of
the electric field between sensing and driven devices, and to allow measurement in situations
where accessibility is difficult (Diefenderfer et al., 1998).
Considering the shape of the electrodes, it was shown (Xu et al., 1999) that the sensing range of
similar systems narrows slightly when their length (along the main line, parallel to the z-axis)
decreases to less than 150 mm, whereas the reduction of the corresponding capacitance value
makes it more difficult to measure. Accordingly, a geometry was chosen after performing several
experiments, and for the sensitivity analysis we used rectangular sensing items of length 150 mm.
The width of the electrodes was taken as θe=20° arc following the roundness of the duct, with a
∆θe=10° separation space between them.
+ -
+ -
c)
+ -
a)
b)
Figure-2: The configuration of the sensor can be seen as the result of two processes: gradually
open the angle between the electrodes of a parallel plate capacitor from situation a) to c), then
add a slight curvature to adapt their shape to the roundness of the duct (c).
We handled here a three-dimensional electrostatics model of the system based on linear
homogeneous isotropic materials, defining as many independent sub-domains. For the numerical
resolution of the problem using finite elements we implemented the FEMLAB 2.3 package
(COMSOL AB., http://www.comsol.com). This software was running with the MATLAB 6.5
interface (The Mathworks Inc., http://www.mathworks.com).
Basically, modeling of the electric field is carried out using the electric potential V, calculated
from the Laplace equation. Appropriate boundary conditions are straightforward: the electrodes
are equipotential surfaces, and the remainder is insulated electrically. The capacitance of the
system is achieved by means of a calculation of the electrostatic energy.
Actually, spaces on both sides of the electrodes intervene, so that the resulting layout does not
constitute a single capacitor but two capacitors in parallel, which corresponds to type "external
electrodes without radial screen" in the classification of Yang (1997). The first one (capacitance
Ci) being formed by the duct (capacitance Cd) plus the material inside (capacitance Cm), in series,
and the second (Ce) by the surrounding environment (principally air and plexiglas making up the
probe), and the total capacitance (Ct) is the sum (see Figure-3).
C
C
C
C +
+
=
+
e
1
+
=
+
= 1
1
i
e
C
C
C
C
C
e
t C
d
m
C
d
m
d
m Ct
=
Ce
Cd Cm
Ci
Figure-3: Simplified model of the system and the associated representation.
A relationship between the measured capacitances and corresponding resonant frequency shifts
can be obtained, knowing the inductance of the electronic circuit. However, for the sake of
convenience, we'll only deal with the capacitance of the inside volume in the rest of the paper. In
practice, some precautions must be taken in order to prevent the so-called "hands effect" or
interference of external electrical fields: metallic screen to shield the electrodes from external
fields (Yang et al., 1995), radial earthed screens between the plates to decrease the inter-electrode
capacitance external to the duct (Yang and York, 1999), etc.
Results and discussion: The first considered configuration, to evaluate the influence of the
location of the cable (Figure-4), is that of a duct perfectly filled with cement grout (no void or
"white paste") where the whole steel cable is moved from the center towards the edge (at the
bottom). The electrodes are rotated around the z-axis, starting from the top (θe=0°), while passing
by bottom (θe=180°), with a return to the initial point.
Figure-4: Influence of the location of the cable on the
resulting capacitance of the system. The axes indicate
the angular location of the sensor θe, and that of the
cable in the duct. Cable close
to the duct
Cable in
the center
When the cable is in the center of the duct, the capacitance obviously remains the same, whatever
the location of the electrodes. A cable shift generates a surge of the capacitance value in the
corresponding half part of the duct: the increase approximately affects modeled capacitances in
the range of θe∈[90°, 270°]. The auscultation depth being roughly 20 mm in this construction, it
turns out that the cable acts as a screen when it approaches the edge. Therefore, phenomena
occurring behind may be invisible in certain configurations but the rest of the duct should be
properly sensed.
To study the effect of air and water layers, consider one of the curves taken from the situation
already examined, with the HDPE duct, the steel cable close to the bottom of the duct, and the
grout (Figure-5). On both sides of the graphs (θe<90° or θe>270°), the capacitance is about 5 pF,
and as long as it remains in the sensed area, the influence of the cable dominates. The maximal
value is obtained when the steel cable is near the outer surface of the duct (having its center
located at 24 mm), in the vicinity of the electrodes (at an angle of about 180°). When a horizontal
air layer is formed above the grout, the capacitance drops off drastically (something like a -50 %
fall): this sudden decrease of the values is undoubtedly indicative of the presence of air in the
volume. In the last case, we took into account the presence of material simulating "white paste",
between the grout and air regions. As the electrodes approach this layer with a high water content,
there is an increase of the capacitance compared to the previous arrangement. The phenomena in
particular affects the response of the device when it is located exactly above the considered zone,
with little bumps on each sides of that are due to the cable.
As a result, we can suspect that a capacitance value lower than that of the configuration where
there is only grout and a cable in the middle of the duct, is a distinguishing attribute of grout
voids. However, the signature of the "white paste", generating a larger capacitance, is similar to
that of the cable itself, but generally with a smaller extent. Accordingly, and without any
indications about the precise location of the cable, the interpretation of the measurements may be
confusing.
Fortunately, the course of the cables in the duct between two spacers is well known, and the
formed undulation is rather regular, which is not true for randomly occurring flaws with a much
smaller size. Furthermore, because of the inclination of the ducts (Leroy et al., 2000), occurrence
of grout voids and "white paste" takes place about the higher part, in general. Therefore, this a
priori information will help discriminating between the cable and zones with a high moisture
content, by considering capacitance changes as a function of the location along the duct axis.
Hence, smooth variations will be related to the cable, whereas more chaotic changes correspond
to defects with a smaller extent.
Figure-5: Capacitance calculated for three
configurations: cable + grout only (solid line), cable
+ air (dashed line), cable + water + air (dotted line).
Only grout
Grout + water
+ air
Grout + air
The flaws considered in the previous section were very extended horizontally, but what would
happen for the detection of inclusions with dimensions much smaller than that of the electrodes
(Figure-6a) ? Here we assume that a grout void (i.e., bubble), or a water saturated material region
(for simulating "white paste") are formed in the grout, in the upper part of the duct (for θb=0°),
and at an abscissa zb=0, while the steel cable is in the center. For several angular position θe all
around (between 0° and 180°, the other side is symmetrical), the electrodes are moved along the
z-axis.
a) Defect b)
Electrodes
at 0°
30°
90°
60°
Air
c)
Electrodes
at 0°
30°
60°
Water
90°
Figure-6: Detection of insulating injection defects (as
shown on the sketch a) in the case of a grout void (b),
and the same with water saturated material (c).
As long as the capacitive sensor is "far" from the inclusion, either longitudinally (|ze| larger than
about 180 mm) or angularly (from θe≈60°) there is no nearly sensitivity. However, when the
electrodes are near the defect (i.e., when it is located just below the electrodes, on the other side
of the HDPE duct) the response is noticeable. For a grout void, the decrease of capacitance value
is smaller than in the case of the horizontal air layer because of a smaller extent. A comparable
behavior is observed for water, but this time with an increase.
It seems that, with the geometry of the electrodes used, the discrimination of the two inclusion
types is possible. The localization is fine, and a rough estimation of the dimension is also
allowed. A more detailed sensitivity study should bring soon additional information about the
most appropriate electrodes shape as a function of the minimal size of the imperfections to be
detected.
For laboratory measurements, a sample was especially prepared with a HDPE duct, hardened
grout at the bottom (no steel cable), an inclined layer of not hardened grout, and air at the top (see
Figure-7).
gap
"White
paste"
Grout
HDPE
duct a)
Left
Right b) Air
Figure-7: Sample prepared for capacitance measurements: a) distribution of materials inside
the HDPE duct, with grout at the bottom, an inclined layer of "white paste" above, and an air
gap on the top (from the left and right sides); b) corresponding model used for numerical study.
In the actual probe, electrodes are 165 mm long, with a 10° arc width, and a 10° separation, so we
considered the same geometry for the numerical calculations below. Furthermore, as this version
of the probe implemented an automatic compensation (including different calibrations and a
readjustment), a point-to-point comparison is not possible. Note that such data processing
(software and associated electronics) will be changed in the next release of the sensor (for getting
absolute values), but we are restricted here to have a qualitative comparison only.
The sensor was rotated around the proof for characterizing different cross-sections: above the air
gap and "white paste" overlaying the grout on the left side (Figure-8a), and only "white paste"
plus grout on the right side of the sample (Figure-8b). Small icons on each graph present the
measured resonant frequency shift, for information. Data are somewhat disturbed, but the
behavior seems to be comparable for the model and the experimentation.
a)
Grout
Air
"White
paste" b)
Grout
Air
"White
paste"
Figure-8: Polar plots of computed capacitance values for cross-sectional areas located on the
left (a) and right (b) sides of the proof body (thick line). The circles correspond ducts only filled
of air (dashed line), grout (dotted line) or "white paste" (dotted-dashed line). Icons on the right
of the graphs display the corresponding resonant frequency shift, for a qualitative comparison.
Straightforwardly, for a duct completely filled with either air, grout or "white paste", the
capacitance measured when rotating the probe would remain the same (concentric circles on the
graphs). Moreover, as already shown, occurrence in the sampled volume of a substance having a
high or a low permittivity should increase or decrease the corresponding capacitance values,
respectively.
Regarding the left cross-section (Figure-8a), the little bumps on both sides of the plot (at about
+/- 45°) can be attributed to the "white paste" layer, and the depression at the top (0°) is related to
air (with a decrease of the capacitance value, compared to the adjacent points). On the right cross-
section (Figure-8b), there is no more gap, and the presence of the high moisture content material
is noticeable as the plot follows the "white paste" curve in the range of approximately +/- 20°. In
the rest of the plot, the capacitance is close to the only-grout case.
Conclusions: Evaluating the actual state of civil engineering infrastructures is a priority for their
administrators, knowing the high cost of the construction compared to that of maintenance. For
post-tensioned concrete bridges with internally grouted tendons, there was a lack of tools able of
revealing the presence of grout voids and high moisture content regions resulting in most of the
common pathologies. In this context, the capacitance method appears as a powerful non-
destructive approach, and the device proved efficient to find grout injection defects; Information
about an elementary tendon failure or substantial cable corrosion analysis should be also
potentially achievable in the same way.
Indeed, in spite of a small penetration depth, this method can be fully exploited in complex
situations involving a combination of conductive and resistive materials, where no other system is
usable. Furthermore, it is possible to adjust the investigation volume, by varying both the
arrangement and geometry of the electrodes. This point is still subject to researches, in particular
to prevent erroneous measurements due to fringing effects, or to improve the axial evenness by
adding appropriate guard rings (Yang et al., 1999).
The applications of this atypical technique have remained marginal in the field of civil
engineering, because of the difficulties for interpreting the measurements. Furthermore, the
behavior of the sensor may be disturbed by a variety of factors, for instance the presence of thin
air layers inside the duct (because of grout shrinking when drying), frequency dispersion,
phenomenon of interfacial polarization of the electrodes, imperfect contacts with the duct
envelope, etc. These points are now being considered from a physical modeling point of view,
and we can expect technical advances (via the implementation of array sensors, as an example) as
well as an evolution of the data-processing.
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