International Symposium (NDTCE 2003) NonDestructive Testing in Civil Engineering 2003  
Start > Contributions >Lectures > Pavement: 
Capacitance Sounding: a New Geophysical Method for Asphalt Pavement Quality EvaluationYuly Dashevsky, Institute of Geophysics SB RAS, Novosibirsk, RussiaMichail Filkovsky, GLIF Engineering Device Ltd, Novosibirsk, Russia Vladimir Synakh, Institute of Computational Mathemathics and Mathematical Geophysics SB RAS, Novosibirsk, Russia AbstractA capacitance sounding method has been proposed and developed for evaluation in a realtime on a continuous basis the actual thickness and dielectric permitivity of asphalt pavement. The patented method is based on the measurement of the electrical capacitance between two electrodes. The first one is grounded into the soil immediately adjacent to the side of the road. The second (sensing) electrode is mounted on a motordriven positioner to obtain the capacitance measurements at multiple locations along the direction perpendicular to asphalt surface. A distinguished feature of the proposed technology is that the measured signal depends only on the thickness and the permitivity of the asphalt layer. All underlying layers do not affect the capacitance readings in any way. The EGOZA family of software tools was created for solving forward and inverse problems of the capacitance sounding. An unknown thickness and permitivity are derived from a realtime 2D inversion of the data obtained. A portable laboratory device of EGOZA equipment has been designed and created. Asphalt layer thickness and the dielectric constant measurements were carried out on a hightraffic highway. The comparison of field trial results with core sampling analysis demonstrated the efficiency of the proposed method. State of the ArtWhile rebuilding and paving existing roads that show signs of cracking and significant deterioration or when building new roads or highways, it is important to effectively control the paving process. In the construction of roads various factors affect the quality of the resultant asphalt surface. These factors include a proper mixture of the asphalt components, design thickness of the pavement layer as well as a proper compaction of asphalt. The hot asphalt mixture has three components including aggregate, bitumen, and air voids. The bitumen binds the aggregate particles together after they have been compacted and the asphalt has cooled. Air voids make up approximately 1726% of the volume of the hot mix (Rogge and Jackson, 1999). A proper compaction reduces this percentage to about 5% (Grigas et al., 1999). Currently, the researches are concerned with methods of measuring the strength and deformation properties of the layers that make up the pavement structure. The measurement can be destructive in nature, when samples are tested in laboratory conditions, or nondestructive, when the structure's transient response is measured within the range of known loading conditions. The falling weight deflectometer ( FWD) is commonly used. It applies a dynamic load through a plate that is lowered to the pavement surface. Sensors in contact with the surface measure the downward deflection of the pavement surface. It should be noted that the information collected by a FWD can be adequately processed only if the pavement layer thickness is known. Extensive efforts were made in the past to the nondestructive evaluation (NDE) of the asphalt density characteristics and the asphalt layer thickness. The nuclear density gauges, for example, have been used for several years to measure the bulk density of hot asphalt mixtures quickly and nondestructively. In the field, during the paving operation one can also make use of the surface moisture density gauges utilizing a gamma ray back scattering approach. These devices have some constraints. Accurate density measurement can be obtained only within several minutes making difficult the realtime use on a continuous basis. It occurred that there is significant variability of density test results between the nuclear density gauge and standard core sample approach. In addition, nuclear density gauges involve the use of ionizing radiation, which requires safety precautions, certification of equipment, etc. Groundpenetrating radar (GPR) is a promising NDE technique that has possibilities for realtime asphalt density measuring during the rolling operation. In Finland, the GPR method has been used in road surveys since 1986 covering various fields of application from site investigations to aggregate exploration and from concrete bridge deck deterioration mapping to road structural course thickness surveys and investigation of damage (Saarenketo, 1996). A new field of the GPR applications involves the quality control measurements of new pavements. Apart from the air voids content, the thickness of different layers of the pavement structure can be also interpreted from the measurement results, thus additionally providing the possibility to ensure that the pavement thickness criteria has been taken into account. In the United States the GPR applications in roads have mainly measured thicknesses of the pavement and base layers, but recently efforts have been made to apply the GPR technique in detecting subsurface defects such as stripping and voids or locating sinkholes beneath the highway structure (Saarenketo and Scullion, 1994). Existing horn antennas used in commercial pavement GPR systems are based on old technology and design concepts. In recent years rapid advances have been made in designing planar miniature antennas. The researches are working on the construction of a field unit that will be mounted on a FWD to provide layer thickness information at each test location. Using the GPR approach in pavement density quality control is based on the evaluation of the dielectric value of the pavement. The basic idea behind dielectricity measurements is that compaction reduces the relative air void content of the asphalt mixture and increases the relative proportions of other components. Another method for the evaluation of asphalt density involves the use of capacitance energy dissipation equipment. The method measures actual air voids based on the decay rate of energy stored in the asphalt segment compared to the known decay rate of a reference capacitor. One major problem with density testing techniques involves errors from variations in temperature, binder mix and the aggregate. Various "correction factors" are required when utilizing any approach mentioned above. As a result, the user must carry out extended sensor calibrations correcting for these variables to ensure an accurate reading and meaningful results. We can conclude that researchers face two main issues. The first challenge is to bridge the gap between complex and sophisticated laboratory testing and its implementation as routine procedures within the pavement design community. The second challenge is to make the proposed evaluation techniques practical so that they could fit within the organization and time constraints under which pavement designers work. The GPR approach and other NDT procedures are good candidates for this work. GPR can rapidly and continuously scan long lengths of highway. But some problems arise during the interpretation of GPR results. To evaluate the layerspecific dielectric values of the pavement, a surface reflection technique is utilized. In practice the dielectric value is obtained by calculating reflection coefficients from the reflection amplitudes of the pavement surface and then comparing them with the reflections read from a metal plate. A need can therefore be seen for a nondestructive and nonsophisticated device that could carefully monitor dielectric value and thickness of asphalt pavement continuously in a realtime. Such a device should overcome problems found in the prior art: a great amount of errors related to variations in temperature, binder mix and the aggregate. It should also reduce the necessary number of pavement core samples. Asphalt pavements are cored to calibrate NDT measurements and evaluate layer thickness. If the actual measurement is below the design thickness the coring interval is reduced. Coring is expensive and destructive. Coring cannot be eliminated, but should be minimized and restricted to the suspected thin area. Capacitance Sounding: Basic PhysicsRocks, soils and pavements are very complex multiphase materials and their electrical properties, electrical resistivity and dielectric permitivity vary over a very wide range depending on their granularity, porosity, moisture, number of cracks, etc. It is therefore very attractive to base shallow depth geophysical prospecting on the measurement of these properties. This approach has been used widely for more than seventy years but its use is limited. The main logical problem is that the technique requires the electrode to be in good contact with isolating pavement. To overcome the difficulty a straightforward extension of the concept applied in DC electrical prospecting has been developed and capacitive electrodes have been proposed. Since 1986, they have been used in France for archaeology, civil engineering as well as also in permafrost areas of Canada and Russia. The goal of this paper is to propose and develop a new technique  a capacitance sounding method that can be used to evaluate the thickness and the dielectric permitivity of asphalt pavement. A portable apparatus for the capacitance sounding includes a couple of electrodes and electronic equipment to measure capacitance between these electrodes. The equipment operates at a lowfrequency range (~ 1000 Hz). The first electrode is grounded into the soil immediately adjacent to the side of the road. The second one is mounted on a motordriven positioner driven by a stepper motor to obtain capacitance measurements at multiple locations along the direction perpendicular to the asphalt mat surface. Before starting the sounding, the second electrode is located at the point under investigation and disposed in intimate contact with the surface of the asphalt mat. The positioner then moves the electrode upward by 0.025 m and the first capacitance measurement takes place. This procedure is repeated until the electrode position is about 0.04 m above the surface. A set of the capacitance measurements versus the position is considered as capacitance sounding curve. The curve data are saved in the computer and the 2D inverse problem is solved in the realtime mode to obtain the thickness and the dielectric permittivity of the asphalt layer. Upon completing the inversion the sounding is over. The operator can move the assembling with the second electrode across the mat surface to the next sounding site. It should be emphasized that a measured signal depends only on the thickness and the permittivity of the asphalt layer. All underlying layers do not affect the measured capacitance in any way. This conclusion can be easily realized: two above mentioned electrodes form an infinitely long plane capacitor. The plates of the capacitor coincide with asphalt mat boundaries. Assuming a medium to be linear and its response linearly dependent on the electric charges of the two electrodes, a simple theoretical background for a lowfrequency capacitance measurement is the electrostatic case modelling. Capacitance Sounding: Twodimensional Mathematical ModelLet us consider 2D mathematical model for the capacitance sounding (Fig.1). A thin metal disk of radius a is situated above the road so that they are divided with the air layer of thickness h_{a} and an additional isolating disk of thicknessH_{i}. The metal disk potential is U. The parameters e_{a} ,e_{i} denote the corresponding dielectric constants. Unknown quantities are H_{r} and e_{r} thickness and dielectric constant of the asphalt layer, respectively. The rest of the system parameters can be measured directly. One can determine the capacitance Cof this system in two ways:
where the integration is carried out over any surface including the metal disk.
The forward problem is to obtain the solution to the Laplace equation Ñ^{2}u=0 with the boundary conditions on the disk surface and in infinity and the junction conditions along all the surfaces dividing a heterogeneous material. We used a version of the residual correction method for the numerical solution of the Laplace equation (Synakh, 2001). Some precautions were made to check the validity of the results of the calculations (Dashevsky and Voronkov, 1995). The capacitance C was obtained from the calculated field u by the two ways: using the volume integral (1) and the surface integral (2). The relative difference of these quantities did not exceed 0.05% in all the cases. The correctness of transferring the boundary conditions from the infinity to the finite distance can be confirmed in such a way: the quarter of the computational domain contains about 95\% of the total field energy and the half of this volume contains not less than 99.5\%. Resolving Capabilities of a Capacitance Sounding Method. Spatial Distribution of the Electric Field Energy.In exploration geophysics one is often asked to make a definitive statement regarding the depth of investigation of a particular method and it's resolving capabilities. A fundamental limitation that prevents us to achieve an arbitrary great resolution and considerable penetration using a given method in a specific environment is imposed by the level of geological noise that is present relative to the signal of interest. The signal of interest is that portion of the measured response that is produced by the target. The geological noise is the part of the response produced by components of the earth excluding the target. In order to quantitatively describe the ability of the measured signal to resolve differences of a particular target parameter, it is convenient to use a sensitivity function. For example, a sensitivity h_{H} of the capacitor parameter C to the spacing H of its plates is:
The sensitivity h_{e} is defined in a similar manner. Our experience gained in solving inverse problems of the surface and the borehole electromagnetic methods brought us to the following conclusion. Evaluation of a particular target parameter is possible with a reasonable practical accuracy if the sensitivity of measured response to this parameter exceeds 0.2. Of course, the sensitivity analysis is a necessary, but not sufficient condition to investigate the potential of a particular sounding method. The analysis of geological noise and signal/noise (S/N) level is also very important. We spent a lot of time travelling on highways and roads and measuring the capacitance for different equipment configurations. Two basic conclusions can be drawn from the results of our field experiments, 2D forward modelling and sensitivity analysis.
Geophysical surveying on a different scale shares an important characteristic: the instrument frequently averages, or smears, observations over distances larger than the targeted object. Therefore, among other things, the possibility to estimate a lateral resolution of a particular geoelectrical method is of great importance. Here it is convenient to introduce the concept of a locality characteristic of a method. Qualitatively, this concept is strongly linked to the relative contribution of different parts of the investigated medium to the measured signal. The smaller the contribution from the medium parts situated far from the measurement point, the higher the locality feature, and vice versa. From the above reasoning, we can turn to the quantitative estimation of the locality characteristic inherent to the capacitance sounding method. In order to evaluate this feature, one can draw on the spatial distribution pattern of electrical field energy. With this purpose in mind, a special attention should be given to Fig.1. Let us draw mentally a circular cylinder of radius R. The size of this body in z direction is h_{a} + H_{P}. The axes of the cylinder coincide with direction z the cylinder surface is marked with a dash line in Fig.1. Suppose that W_{R} and W_{¥} stand for portions of the electrical field energy enclosed in the cylinder of radius R and R = ¥, respectively. The notation w denotes the W_{R} / W_{¥} ratio and the designation R_{a} specifies the cylinder radius normalized to that of the metal disk:R_{a} = R / a . It should be noted that H_{i} = 0 in our case. Since the partial contribution of elementary volumes to the energy integral decreases as the distance R increases one can use the parameter R_{a} as a measure of locality. Let us consider, for example, the value of R_{a} = R^{*}, which results in w being equal, say, to 0.99. Then one can advocate that elementary volumes situated at distances of R_{a}³ R^{*} from z axes do not practically contribute to the measured signal. As consequence the measured capacitance would not be sensitive to any target located within these distant regions. The following comment can be done. The description of any electromagnetic method comprises the definition of a measuring point. For example, the location of a measurement point can be either a receiver point or a midpoint of the array if the DC methods are considered. As far as the capacitance sounding is concerned, it is appropriate to consider the point of intersection of the axis of symmetry of the disk and the pavement surface as a measurement point. Relying on such a definition and based on the analysis of computational results we came to the following quantitative assessment of the capacitance sounding locality. Values of the dielectric constant e_{r} and the thickness H_{r} of the asphalt layer derived from the solution of the inverse problem of the capacitance sounding (electrode of radius a = 18.5 cm) are valid over the distances of order 40 cm from the measurement point. Field Trials of the EGOZA EquipmentInstitute of Geophysics SB RAS and the GLIF Engineering Device Ltd. have designed and created a laboratory device of EGOZA equipment  a portable apparatus for the capacitance sounding of asphalt pavements and other nonconductive media. A flat sensing plate is placed on the pavement surface. Then a positioner device starts moving the plate automatically upward. While this takes place, a specially designed multimetre measures the electrical capacitance of the system "moving plateasphalt layer bottom". The thickness and the dielectric constant of the layer are derived in real time from solving the 2D inverse problem with the EGOZA software tools. The EGOZA family of software tools is a group of interactive, graphically oriented, forward and inverse realtime modelling programs. It can be implemented for 2D inversion of the capacitance sounding data acquired at a single station or within the profile. The inversion process uses the NelderMead and the HookeJeeves approaches of nonlinear least squares curve fitting. The error function is given by:
Here p is the vector of model parameters; the vectors g, f are observational and modelling signal, respectively; A is a covariance matrix. Masking option enables the user to keep unwanted data points as part of the data set, while excluding them from the forward (percent error) and the inverse calculations. Prior to the inversion, the user may constrain parameters of the starting model so that they are not adjusted by the inversion algorithm, or so that their adjustment is limited. It should be noted that the NelderMead and HookeJeeves approaches perform the fitting process without calculations of derivatives and are free of any constraints in the values of model parameters. In many instances, we may have a very good reference model. Thus, in the inversion we impose the restriction that the model does not strongly deviate from the prior model. This can be obtained by using the constraints in the model parameters:
where M is the number of model parameters. Contradiction between the necessity to carry out the constraint inversion using the search methods without constraints can be curcumvented using a specially designed transformation. The latter maps a finite range of allowed values of parameter p^{(i)} on the infinite interval (¥, ¥) and vice versa. A special attention should be given to the amount of the CPU time required to solve the 2D forward problem. It is evident that a finite difference code is impractical for simulating the capacitance tool response in realtime. With the purpose of providing a good payoff between the available computer resources and the execution time needed for the realtime simulation, we conducted the so called "preservation" of the forward modelling results. As a theoretical signal depends only on three parameters (e_{r},H_{r },e_{a}) the proposed approach includes two stages:
If this matrix has been prepared and stored, then a spline interpolation of the matrix data can be done instead of the calculations based on a finite difference code. The sensitivity analysis was made resulting in constructing an irregular grid of the parameter values to provide the required accuracy of the realtime forward modelling. In such a case, a minimum size of the stored matrix would be about 50 Kb. Now let us consider the results of the field trials of the capacitance sounding technique. The pilot experiments on the evaluation of the asphalt pavement thickness and the dielectric constant of materials were carried out in the Siberian State Road Academy (Omsk, Russia) on the trial road intended specially to provide teaching and research activity. This trial road is an artificial construction with a roof: the rectangular foundation area is filled with loamy soil. The size of the construction are 25 x 3.5 x 1.5 m. This road includes the parts with different pavements (concrete, asphalt, etc.) and the crushed rock aggregate bases (limestone, granite, basalt, gravel, etc.)
The example of sounding data which consist of 10 measurements of differential capacitance within the sensing electrode separation range of 0.25  2.5 cm is shown in Fig. 2. The vertical bars represent data errors. This picture shows a comparison between the field data and the synthetic data (solid line) predicted by the best fit model derived from the inversion. It can be seen that the field and the theoretical signals are in good fitting if H_{r} = 6.5 cm and e_{r} = 7.9. In this case the mean square error is 3.5%. It should be noted that the design thickness of the asphalt pavement within the measurement point is 6.5  7.0 cm. The asphalt pavement thickness and the dielectric constant measurement tests were performed with the EGOZA equipment in Summer, 2002. One of our first objectives was to verify the concept of capacitance soundings on a heavytraffic highway. Measurements were taken along the center line of the road. The length of the measurement interval was 22 m. According to the design, the driving lanes of the road were constructed of quite possible area material, overlain by 30 cm of granite crush rock base and 12 cm of asphalt.
Fig. 3 shows the asphalt pavement thickness and the dielectric constant profiles obtained in the neighbourhood of Novosibirsk, on the 35th km of the Chuya high road, near the Station 14 + 48. These diagrams represent the solution of the inverse problem of capacitance soundings. The first measurement point is at the Station 12 + 48. Twelve soundings spaced at 2 m were made. The vertical bars show possible thickness deviations from the design asphalt thickness value. Based on these data, one can conclude that the asphalt layer is irregular in thickness and the represented set of thickness values can be approximated with a regression equation. Namely, from the first point onward, the thickness of asphalt pavement monotonically increases from 9 to 13 cm. The same is valid for the dielectric permitivity: a mean value of the constant increases from 10.4 to 13.4. Consider the behaviour of the dielectric constant diagram along the measurement line. A specific feature of this graph is essential deviations of individual values (up to 30 %) from those predicted with the regression equation. We relate this phenomenon either to the cracks, barely perceptible and distributed on the pavement surface in a random manner or to the initial heterogeneity of the asphalt mixture. The second phase of our study includes sample measurements. Here, it seems to be appropriate to consider available devices for measuring the dielectric permitivity of asphalt pavement. For example, the company Adek Ltd (Estonia) manufactures the Percometer: easytouse instrument for the dielectric constant and the electrical conductivity measurements of materials indoors and outdoors. The dielectric constant is calculated from the change of the capacitance of the probe caused by the material under test. The measurement frequency for the dielectric measurements is 4050 MHz. The penetration depth is about 23 cm. The Percometer is a good candidate for the application in GPR surveys, but there exist some limitations for the usage of this device, which can be essential in our case. EGOZA equipment operates at low frequencies. Therefore, bearing in mind a possible frequency dispersion of the dielectric constant, we should use a proper, lowfrequency approach to evaluate a sample dielectric value. The capacitance sounding is based on the assumption that the asphalt pavement consists of a homogeneous material of given dielectric permitivity. It should be noted that in our case a crushed rock aggregate component of the asphalt mixture consists of the particles whose size varies from 1 to 2 cm. One can see that the penetration depth and the average particle size are, practically, about the same. That is why we faced the problem to develop a reliable, easytouse, lowfrequency method for the dielectric value measurements that satisfying the two conditions:
The proposed scheme for measuring dielectric constants of asphalt cores consists in placing a sample of an irregular shape between the electrodes followed by measuring the capacitance of this capacitor. It is important to emphasise that, unlike conventional approaches requiring a good contact at the electrode/sample interface, in our scheme both electrodes are free from it. Suppose that the shape and the dielectric constant have been specified. Then we can formulate the forward and the inverse problems for such a modification of the capacitance sounding of the confined dielectric sample. The EGOZA family software includes tools with the friendly user interface for evaluating a dielectric value of the cylindrical shape cores taking advantage of the abobe presented approach. Five cores of diameter 10 cm were extracted along the measurement line. The solution of the inverse problem for each sample provides the following dielectric constant values: 10.8, 12.8, 10.2, 11.7, 11.3. The average value is 11.3 and almost coincides with that (11.9) obtained from the capacitance soundings of asphalt pavement. The vertical size of the cores have confirmed the calculated data for their thickness. ConclusionsA capacitance sounding method has been proposed and developed for the realtime evaluation of the actual thickness and dielectric permitivity of the asphalt pavement. The distinguished feature is that the measured signal depends only on the thickness and the electrical permitivity of the asphalt layer, so that all underlying layers affect the measured capacitance in no way. The proposed method is based on a profound mathematical background. This includes the formulation of the corresponding 2D mathematical model, the algorithms to solve forward and inverse problems and the EGOZA software to realise them. The effective method of "preserving" the results of the 2D forward mathematical simulation makes it possible to provide the realtime 2D inversion of the capacitance sounding data. An extensive feasibility study of the capacitance sounding method has been carried out. A laboratory model of EGOZA equipment has been designed and constructed. A possibility to obtain the dielectric constant and the thickness of the asphalt pavement as the solution of the inverse problem allows to circumvent the problems found in the prior art: a great amount of errors caused by variations in temperature, binder mixture and the aggregate. Another advantage of the method is a decrease in the number of pavement core samples needed. The capacitance sounding method shows a very good lateral resolution: about 40 cm from the measurement point. The trial field tests were performed with the EGOZA equipment on heavytraffic road in the neighbourhood of Novosibirsk. The comparison of the field trials results with the core samples analysis has confirmed the efficiency of the proposed method. The research leading to this paper was funded by the Ministry of Education of Russia under grant no. E028.040 References

