This paper deals with the development of concrete water content measuring devices for nuclear civil structures. It proposes a theoretical method to estimate the measurement uncertainty of the monitoring system needed to improve the predictions of the long-term behavior of prestressed concrete containment structures. Assuming a basic model for concrete drying, the errors regarding its parameters calibration when using different sensors arrangements are compared to figure out what are the most suitable systems and what are the devices specifications needed to actually improve the predictions. It turns out that current water content monitoring device should be improved to get a better benefit to containment ageing management. In particular, the measurement uncertainty should be enhanced to enable more relevant concrete creep prediction at the end of containment building lifetime. However, an extensive spatial sampling of the moisture profiles can compensate somehow current lack of water content devices for concrete monitoring.

This paper discusses some reasons for measuring moisture in concrete structures. Within the framework of the prestressed concrete containment monitoring of the French nuclear reactors fleet, a method is pro-posed to assess the possible contribution of concrete moisture monitoring in ageing management strategy. Based on sensitivity and variance analysis, it aims at clarifying the conditions necessary to enhance the identification of some model parameters for concrete shrinkage and creep. In-situ water content monitoring could be beneficial to improve ageing predictions if some conditions are met. However, the estimated measurement uncertainties to reach this goal seem to exceed current devices capabilities. (C) 2020 Elsevier Ltd. All rights reserved.

This paper focuses on the relation between electromagnetic properties of clayrock and its water content, in view of radioactive waste repository monitoring. Final aim is to improve off-the-shelf Time Domain Relfectometry sensing lines, which is basically sensitive to electromagnetic properties of the host material, clayrock in our case. Such parameters are poorly known. In a first time, we developed a new laboratory dielectric measurement device, consisting of a coaxial transmission line, enabling characterization of intact clayrock permittivity over the 50 MHz - 1 GHz frequency range. The study has shown a large variation of complex permittivity with (i) water content, the parameter of interest and (ii) frequency, which could be accurately fitted by a Cole - Cole model. In a second time, we proposed an analytical modeling of the TDR probe using these results as input electromagnetic parameter. Finally, some synthetic data were obtained, they was used to perform an inversion process: which consists to reach accurate estimation of the electromagnetic parameters starting from synthetic measurements. This stage has been made through both use of the analytical and Cole - Cole modeling in the same approach: the five parameters of the Cole-Cole model are least mean square estimated from a frequency sweep containing at least five frequencies.

In this paper, the relevance of the non contact RF evaluation of the complex permittivity of organic material is addressed by means of a computational approach. The authors consider a simple configuration constituted of a single loop RF antenna interacting with a dielectric material mimicking a typical organic tissue (the electrical conductivity is 0.6 S/m and the dielectric constant is 80) which includes a buried inclusion (e.g. a tumor featuring a conductivity of 0.2 to 1.6 S/m and a dielectric constant ranging from 20 to 160). First a three dimensional semi analytical model (DPSM) is implemented in order to evaluate the sensitivity of such an antenna to the complex permittivity of the buried inclusion. Then, the inverse problem which consists in evaluating the complex permittivity, the size and the location of the inclusion is addressed by means of an artificial neural network (ANN) approach. For the considered configuration (5 mm radius antenna, 40 mm radius spherical inclusion buried at a 5 to 20 mm depth within the tissue, antenna operated at 135 MHz), the main conclusions are that the complex permittivity and the depth of the inclusion can be fairly estimated (estimation error smaller than 5%), even in the case of antenna positioning uncertainties, providing the ANN is adequately trained. Also, a double antenna configuration significantly enhances the estimation of the location and size of the inclusion.

The paper reports on a numerical study aiming at assessing the influence of the frequency on the sensitivity of an inductive sensing method dedicated to the non contact dielectric characterization of organic materials. A three dimensional electromagnetic mesh-free modeling of the interactions between a single loop radio frequency antenna and a dielectric material mimicking a tissue (skin) shows that frequencies allowing a loss factor tanδ close to 1 in the material is particularly relevant to sense its complex permittivity. Moreover, the inverse problem which consists in estimating the complex permittivity of the material starting from the antenna impedance changes is carried out using an artificial neural network. Estimation results shows that a combination of three frequencies providing loss factors in the material such as tanδ = 1, tanδ>>1 and tanδ<;<;1 enable to significantly enhance the estimation of the dielectric properties, even if sensor positioning uncertainty is involved.

Broadband electromagnetic frequency or time domain sensor techniques present high potential for quantitative water content monitoring in porous media. Prior to in situ application, the impact of the relationship between the broadband electromagnetic properties of the porous material (clay-rock) and the water content on the frequency or time domain sensor response is required. For this purpose, dielectric properties of intact clay rock samples experimental determined in the frequency range from 1 MHz to 10 GHz were used as input data in 3-D numerical frequency domain finite element field calculations to model the one port broadband frequency or time domain transfer function for a three rods based sensor embedded in the clay-rock. The sensor response in terms of the reflection factor was analyzed in time domain with classical travel time analysis in combination with an empirical model according to Topp equation, as well as the theoretical Lichtenecker and Rother model (LRM) to estimate the volumetric water content. The mixture equation considering the appropriate porosity of the investigated material provide a practical and efficient approach for water content estimation based on classical travel time analysis with the onset-method. The inflection method is not recommended for water content estimation in electrical dispersive and absorptive material. Moreover, the results clearly indicate that effects due to coupling of the sensor to the material cannot be neglected. Coupling problems caused by an air gap lead to dramatic effects on water content estimation, even for submillimeter gaps. Thus, the quantitative determination of the in situ water content requires careful sensor installation in order to reach a perfect probe clay rock coupling.

The distributed point source method, or DPSM, developed in the last decade has been used for solving various engineering problems-such as elastic and electromagnetic wave propagation, electrostatic, and fluid flow problems. Based on a semi-analytical formulation, the DPSM solution is generally built by superimposing the point source solutions or Green's functions. However, the DPSM solution can be also obtained by superimposing elemental solutions of volume sources having some source density called the equivalent source density (ESD). In earlier works mostly point sources were used. In this paper the DPSM formulation is modified to introduce a new kind of ESD, replacing the classical single point source by a family of point sources that are referred to as quantum sources. The proposed formulation with these quantum sources do not change the dimension of the global matrix to be inverted to solve the problem when compared with the classical point source-based DPSM formulation. To assess the performance of this new formulation, the ultrasonic field generated by a circular planer transducer was compared with the classical DPSM formulation and analytical solution. The results show a significant improvement in the near field computation.

The electromagnetic characterization of dielectric media is a major issue in many industrial fields. Non-contact radiofrequency (RF) inductive techniques are well suited for the non-invasive evaluation and monitoring of dielectric media. In this paper, we investigated the relevance of a semi-analytical modeling technique, so-called distributed point source method (DPSM) to model the interactions of a RF single loop antenna with a dielectric medium containing a dielectric inclusion. The resistance of the antenna, which is related to the conductivity of the investigated media, can be estimated using DPSM. A series of experiments were carried out to validate the computed results. Furthermore, a simple system constituted of two RF single loop antennas is considered to locate the position of an inclusion. The DPSM was used to study the ability of such a system to locate the inclusion.

This paper deals with the problem of imaging defects in metallic structures through eddy current (EC) inspections, and proposes an original process for a possible tomographical crack evaluation. This process is based on a semi analytical modeling, called “distributed point source method” (DPSM) which is used to describe and equate the interactions between the implemented EC probes and the structure under test. Several steps will be successively described, illustrating the feasibility of this new imaging process dedicated to the quantitative evaluation of defects. The basic principles of this imaging process firstly consist in creating a 3D grid by meshing the volume potentially inspected by the sensor. As a result, a given number of elemental volumes (called voxels) are obtained. Secondly, the DPSM modeling is used to compute an image for all occurrences in which only one of the voxels has a different conductivity among all the other ones. The assumption consists to consider that a real defect may be truly represented by a superimposition of elemental voxels: the resulting accuracy will naturally depend on the density of space sampling. On other hand, the excitation device of the EC imager has the capability to be oriented in several directions, and driven by an excitation current at variable frequency. So, the simulation will be performed for several frequencies and directions of the eddy currents induced in the structure, which increases the signal entropy. All these results are merged in a so-called “observation matrix” containing all the probe/structure interaction configurations. This matrix is then used in an inversion scheme in order to perform the evaluation of the defect location and geometry. The modeled EC data provided by the DPSM are compared to the experimental images provided by an eddy current imager (ECI), implemented on aluminum plates containing some buried defects. In order to validate the proposed inversion process, we feed it with computed images of various acquisition configurations. Additive noise was added to the images so that they are more representative of actual EC data. In the case of simple notch type defects, for which the relative conductivity may only take two extreme values (1 or 0), a threshold was introduced on the inverted images, in a post processing step, taking advantage of a priori knowledge of the statistical properties of the restored images. This threshold allowed to enhance the image contrast and has contributed to eliminate both the residual noise and the pixels showing non-realistic values.

The use of electromagnetic sensors such as Time Domain Reflectometry (TDR) probes has gained increasing importance for long term monitoring of the water content in radioactive waste repositories. TDR probes are sensitive to changes in electromagnetic properties of the surrounding material, a clay rock in our case. Prior to the in situ application, it is mandatory to have an accurate relationship between the electromagnetic properties of the intact host clay rock and the water content. For this purpose, the dielectric properties of intact clay rock samples were systematically studied at frequencies from 1 MHz to 10 GHz with network analyzer technique in combination with coaxial transmission line cells. Samples were conditioned to achieve a water saturation range from 16 % to nearly saturation. The relaxation behavior was quantified based on a generalized fractional relaxation model under consideration of an apparent direct current conductivity assuming three relaxation processes: a high-frequency water process and two interfacial processes which are related to interactions between the aqueous pore solution and mineral particles (adsorbed/hydrated water relaxation, counter ion relaxation and Maxwell-Wagner effects). In a second step, these data are introduced in 3-D numerical frequency domain finite element field calculations to model the one port broadband frequency or time domain transfer function for a three rode based TDR-probe embedded in the clay rock. The results are analyzed with classical travel time analysis (onset/inflection) which under/overestimates the value of the permittivity compared to effective permittivity at 1 GHz. Indeed, apparent permittivity contains not only the water-content contribution but also effects due to water-mineral interaction processes. The results demonstrate the capabilities of a combined TD/FD analysis procedure for the monitoring of physical and chemical properties of materials with high frequency electromagnetic sensor techniques.

In this paper, the authors report on the implementation of a simplified and computationally efficient electromagnetic modeling of the interactions that take place between an eddy current imaging device and a metallic assembly, in the context of the non destructive evaluation of defects in metallic parts. The model is implemented in the case of the evaluation of a millimetric defect buried in a three plate aluminum assembly, for eddy current frequencies ranging from 300Hz to 3kHz. The model is validated against experimental data in terms of two-dimensional distributions of the computed magnetic field, as well as in terms of modulus and phase of the magnetic extrema observed in the images, in the whole frequency range. The obtained result provides promising prospects for the use of such model for the automatic characterization of defects in the context of the eddy current imaging of metallic parts.

This paper deals with an innovative implementation of a semi-analytical modeling method, called the Distributed Points Source Method (DPSM), in the case of an eddy current problem. The DPSM has already shown great potentialities for the versatile and computationally efficient modeling of complex electrostatic, electromagnetic or ultrasonic problems. In this paper, we report a new implementation of the DPSM, called differential DPSM, which shows interesting prospects for the modeling of complex eddy current problems such as met in the non-destructive imaging of metallic parts. In this paper, the used eddy current imaging device is firstly presented. It is composed of an eddy current (EC) inducer and a magneto optical set-up used to translate the magnetic field distribution appearing at the surface of the imaged part, into a recordable optical image. In this study, the device is implemented for the time-harmonics (900 Hz) imaging of a two-layer aluminum based assembly, featuring surface-breaking and buried defects. Then, the basics of the time-harmonics DPSM modeling are recalled, and the differential approach is presented. It is implemented for the modeling of the interactions of the eddy current imaging device with the considered flawed assembly in the same operating conditions as the experimental implementation. The comparison between experimental and computed data obtained for millimetric surface and buried defects is presented in the form of complex magnetic cartographies and Lissajous plots. The obtained results show good agreement and open the way to the modeling of complex EC problems. Furthermore, the low computational complexity of the differential DPSM modelings makes it promising to consider for the solving of EC inverse problems.

This paper deals with modeling in electromagnetism in the field of eddy current for Non Destructive Evaluation. Several techniques could be used to diagnose structural damages. In eddy current application, a magnetic field generates by an excitation coil (or primary coil), interacts with a conductive target and generates eddy current. Variations in the phase and the magnitude of these eddy currents can be monitored using a second “receiver” coil. Variations in the physical properties (electrical conductivity, magnetic permeability,..) or the presence of any flaw in the target will cause a change in eddy current and a corresponding change in the phase and amplitude of measured signal. The interpretation of the signals requires a good understanding of the interaction between eddy current and structure. Therefore, researchers need analytical or numerical techniques to obtain a clear understanding of wave propagation behaviors. However, modeling of wave scattering phenomenon by conventional numerical techniques such as finite elements requires very fine mesh and heavy computational power. To go further, an innovative implementation of a semi-analytical modeling method, called the Distributed Points Source Method (DPSM), has been developed and used. The DPSM has already shown great potentialities for the versatile and computationally efficient modeling of complex electrostatic, electromagnetic or ultrasounic problems. In this paper, we report on a new implementation of the DPSM, called differential DPSM, which shows interesting prospects for the modeling of complex eddy current problems. In parallel, an Eddy Current Imager (ECI) has been recently developed in our laboratory in the aim of imaging cracks in metallic structures. In this paper, a simplified modeling of the ECI is presented using DPSM technique, the basics of DPSM formalism being firstly developed. A comparison between experimental and computed data obtained for a millimetric surface defect is presented in the form of complex magnetic cartographies. The obtained results show good agreement. Then, imaging in the case of a buried object in a metallic target is discussed. The effect of 2 parameters (the conductivity and the depth of the buried object) on the magnetic field which is computed at the surface of the material through our DPSM modeling is presented. The objective is to predict the sensor behavior for different values of these parameters, and to plot some arrays of curves, which can be used as calibration curves for the sensor’s user.

A Cryogenic Current Comparator (CCC) used as a SET current amplifier with a maximum current ratio of 30 000 : 1 has been developed at LNE. The equivalent input current noise was found lower than 2 fA/Hz1/2 over a frequency range 1 Hz to 350 Hz in both operating modes. A new matrix method allows the analytical determination of the electrical behavior of the CCC to estimate the AC current ratio error. The error on 30 000:1 ratio is estimated less 10-8 at 1 Hz.

The water content in concrete (nuclear structures and nuclear waste repositories ) is a major topic to understand and predict the behaviour at the end of the operating period. That is th e reason why ANDRA and EDF are involved in research programs dedicated to concrete Thermo-Hydro Mechanical (THM) modeling and to in situ water content assessment technologies [1]. Another example concerns the bridges which incl ude “external” post-tensioned cables to reinforce these structures. These cables are not into the concrete material, hence potential ly accessible for measurement. They are generally placed in High Density Poly-Ethylene (HDPE) ducts, w here the residual space is filled under high pressure with a cement grout intended to preven t corrosion. Nevertheless, in some cases, the cables breaking occur in non-protected zones [2, 3 ] due to the presence of a “white paste” or grout voids. To remote diagnosis anywhere and in real time of post tensioned ducts or to measure the water content in concrete, we propose a structural health monitoring method based on Frequency Dom ain Reflectometry (FDR). Today’s, advanced reflectometry methods provide an efficient solution for the fault-detection and for their diagnosis in electric transmission lines [4 , 5]. This paper presents a direct model of the FDR method based on T elegrapher’s equations. An analysis of these signals, based on scattering theory, enables one to retrieve the impedan ce distribution of the electric line. The impedance distribution depends on damage into the duct or the wa ter content in concrete. An inversion algorithm is realized with software ISTL provided by INRIA. FDR method has been applied to two real cases: measurement of the water content in concrete and the diagnost ic of the external post tensioned duct.

The use of a capacitive probe as a non-destructive investigative technique for controlling the post tensioned ducts of bridges has gained increasing acceptance in France since several years. A field campaign measurement made in 2006 has shown the performance of the capacitive probe developed by the IFSTTAR. Nevertheless, some results are not understood, and in particular the behaviour of the probe when cement exudation product are present in the duct. Without an accurate knowledge of the electromagnetic properties of those products it is impossible to quantitatively assess the results of our capacitive probe. This paper reports the development of a coaxial transmission line feature. It was designed to allow the evaluation of a large type of material (liquid, paste or granular) over a large frequency range (50MHz–4GHz at maximum). A calibration scheme developed before at the Fresnel Institute was used. Using a two port S parameter instrument, the complex permittivity and magnetic permeability were evaluated by frequency domain measurement. The electromagnetic characterization of cement paste, cement exudation products and injection wax has brought us some key results in the interpretation of the capacitive probe signal. The results of this characterization were then used in a 3D semi analytical modelling of the problem. The studies of configurations with exudation products are presented and compared to experimental results obtained with our capacitive probe on laboratory duct.