# A Noninvasive TDR Sensor to Measure the Moisture Content of Rigid Porous Materials

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{3}/cm

^{3}) and expanded uncertainty (0.01–0.02 cm

^{3}/cm

^{3}depending on moisture) was established along with calibration of the applied sensor. The obtained values are comparable to, or even better than, the features of the traditional invasive sensors utilizing universal calibration models. Both, the TDR and capacitive (FD) sensor enabled monitoring of capillary uptake phenomenon progress. It was noticed that at the end of the experiment the TDR readouts were 4.4% underestimated and the FD readouts were overestimated for 12.6% comparing to the reference gravimetric evaluation.

## 1. Introduction

_{ω}—real part of dielectric permittivity of medium at ω frequency [-], ε″

_{ω}—imaginary part of dielectric permittivity of medium at ω frequency [-], i—imaginary unit (i

^{2}= −1), σ

_{0}—electrical conductivity [S/m], ε

_{0}—dielectric permittivity of vacuum (ε

_{0}= 8.85 × 10

^{−12}F/m), ω—angular frequency of the external electric field [1/s].

_{p}—travel time along the TDR sensor [s], L—length of measuring elements of the TDR sensors [m].

^{3}/cm

^{3}, which may be caused by the differences of solid phase structure of the examined material. According to Černý [11], standard uncertainty of moisture estimation by the Topp’s model equals 0.0468 cm

^{3}/cm

^{3}. Additionally, it should be considered that Equation (3) is applicable for porous media with bulk density close to 1500 kg/m

^{3}, only for volumetric moisture content below 0.5 cm

^{3}/cm

^{3}and should not be used for organic soils or mineral soils containing organic material and clay [24,40].

## 2. Concept of the Surface TDR Sensor

- construction of TDR probes of significant size, consisting of steel rods of the required diameter and durable head [4];
- construction of the TDR surface sensor.

^{3}/cm

^{3}. On the other hand, the idea of sensors proposed by Perrson and Berndtsson [15] was based on application of the typical three-rod probes covered by the properly carved dielectric of known thickness and dielectric characteristics, allowing determination of dielectric parameters, thus water content, of medium located below the cover. This solution was rather primitive but it enabled, to some extent, the non-invasive determination of moisture in porous medium.

## 3. Materials and Methods

#### 3.1. Details of the Developed Sensor

#### 3.2. Measuring Setup

- Aerated concrete, dry apparent density 600 kg/m
^{3}; - Laboratory oven VO-500 (Memmert, Schwabach, Germany);
- Bitumen isolation;
- Laboratory scale WPT 6C/1 (RADWAG, Radom, Poland);
- Multifunctional scale WPW 30/H3/K (RADWAG, Radom, Poland),
- Water reservoir equipped with necessary equipment to sustain the constant water level;
- TDR equipment including laboratory multimeter LOM (ETest, Lublin, Poland);
- TDR sensor presented in this article, concentric cable;
- Personal Computer for meter control and data management;
- Capacitive moisture meter LB-796, (LABEL, Reguły, Poland);
- Atomizer (for calibration procedure).

#### 3.3. Preliminary Research

_{n}—mass of wet sample [kg], m

_{s}—mass of dry sample [kg], θ

_{V}—volumetric water content [cm

^{3}/cm

^{3}], V

_{W}—volume of water [cm

^{3}], V

_{tot}—total volume of the sample [cm

^{3}].

#### 3.4. Calibration the Sensor

#### 3.5. Model of Regression

^{3}/cm

^{3}]; $\overline{{\epsilon}_{eff}}$—mean effective dielectric permittivity obtained by reflectometric measurements [-], $\u03f5$—random error of normal distribution, p—critical level of significance (* p < 0.05; ** p < 0.01; *** p < 0.001).

#### 3.6. Calculation of Uncertainty

^{2}(X’X)

^{−1}. The second source is a consequence of fact, that it is not possible to reveal the true dependence between the selected predictors and the dependent variable—fitted volumetric water content value may differ from the true value of θ because it is impossible to control all variables affecting it [60]. Uncertainties type B are neglected from the investigation because they are of lower level comparing to the uncertainty of A type. In the assumed model four factors affect measurement uncertainty: estimators β

_{0}, β

_{1}, β

_{2}, and the dielectric permittivity:

_{p}—coverage factor, calculated from t-student distribution for α = 0.05, depending on the number of degrees of freedom, it oscillates around 2.

#### 3.7. Capillary Suction Test

^{3}and was higher than declared by the producer. The determined mass of the moist concrete sample after capillary rise test was equal to 16.91 kg, thus the increase of 4.52 kg was observed in relation to mass before the test.

_{eff}were converted into the volumetric moisture content, using the calibration formula obtained within the calibration test (Section 3.4 and Section 3.5). The FD sensor readouts were performed in the similar manner, simultaneously to the TDR measurements, according to the producer’s guidelines. The FD meter was pre-calibrated by the producer, which enabled reading ready values of moisture content. Since the FD results are presented as the gravimetric water content, the readouts were converted to volumetric water content.

## 4. Results

#### 4.1. Preliminary Test Results

#### 4.2. Calibration of the TDR Sensor

#### 4.3. Combined Standard and Expanded Measurement Uncertainty

^{3}/cm

^{3}. Only in nearly dry and saturated conditions its value is higher, 0.015 and 0.02 cm

^{3}/cm

^{3}, respectively.

#### 4.4. Capilary Suction Results

^{3}/cm

^{3}and 0.02 cm

^{3}/cm

^{3}when determined by the TDR and FD sensors, respectively. The reported initial readouts slightly greater than zero may be caused by the manner of sample preparation (drying in 105 °C to constant mass) and measurement uncertainty of applied sensors for the assumed model of regression.

^{3}/cm

^{3}for the TDR sensor and 0.2 cm

^{3}/cm

^{3}for FD one, are visible. No increase in water content was observed by both of the probes in the reference point at the height of 30 cm.

## 5. Discussion

#### 5.1. Discussion on the Calibration Results and Uncertainty Calculations

^{3}/cm

^{3}the effective apparent permittivity determined using the surface TDR sensor reaches the values in the range between 3 and 4. This is the consequence of the values of apparent permittivity of solid phase of material and apparent permittivity of polyoxymethylene that equals 3.8. In the higher ranges of moisture the readouts of apparent permittivity by the TDR surface sensor show the greater moisture than values read by the traditional invasive probe using Topp’s or Malicki’s calibration formulas. This is mainly caused by the influence of the polyoxymethylene covering the waveguides and significantly decreases the effective apparent permittivity read by the surface sensor at the particular level of the sample. The estimated calibration Equation (12) considers this influence and precisely reproduces the dependence between the examined moisture and readouts of apparent permittivity by the surface TDR sensor. This is also confirmed by the statistical characteristics of the applied model, mainly coefficient of determination which equals 0.986 and Residual Standard Error (RSE) = 0.014 cm

^{3}/cm

^{3}. Also, the linear formula of regression presented in Figure 6b has the following features: slope value equal 0.994 and y-intercept value equal 0.002. Levels of significance of particular parameter estimators in the Equation (10) are lower than 0.001 in case of β

_{0}and β

_{1}. Only in the case of estimator β

_{2}the significance level is below 0.05. Simultaneously, the analysis of F Statistic (p < 0.001) confirms the statistical significance of the applied model. Root mean square error (RMSE), the frequently used measure of uncertainty, equals 0.013 cm

^{3}/cm

^{3}and is lower that could be found in the literature concerning even the invasive probes. According to the data presented by Ju et al. [46] using the Topp’s model in relation to the selected soils caused uncertainties expressed as RMSE in the range of 0.01–0.066 cm

^{3}/cm

^{3}. The RMSE value for the model proposed by Roth et al. [37] was in the range of 0.008–0.037 cm

^{3}/cm

^{3}depending on material, while the RMSE for moisture estimation using the Malicki’s model [16] equals 0.03 cm

^{3}/cm

^{3}. The RMSE value obtained for the described surface TDR sensor is smaller than presented in the cited literature, anyway it must be remembered that discussed formulas are universal and because of that the quality of data fitting may be worse. The model presented in this article is individual, dedicated to the particular sensor and material, which may explain the better projection of the discussed dependence ε

_{eff}-θ. Analyzing the RMSE value established for the presented sensor it should be mentioned that it is located in the range of RMSE values established by Udawatta et al. [42] for individual models estimated for traditional invasive probes and different materials (0.008–0.034 cm

^{3}/cm

^{3}).

^{3}/cm

^{3}, according to Černý [11]—0.0269 cm

^{3}/cm

^{3}, Malicki et al. [16] 0.004–0.018 cm

^{3}/cm

^{3}and finally Roth et al. [37] 0.011–0.013 cm

^{3}/cm

^{3}. The expanded uncertainty obtained for the presented noninvasive sensor and the tested material is within the values declared by the cited authors for the traditional invasive sensors or even lower. In the opinion of the authors of this elaboration, the beneficial measuring parameters of the prototype non-invasive TDR sensor are the consequence of the following reasons:

- model of regression is individual;
- most of the cited models were developed for soil media, less homogenous in comparison to the tested building material (autoclaved aerated concrete).

#### 5.2. Discussion on Capillary Uptake Experiment Results

^{3}/cm

^{3}) and high measurement uncertainty for the low range of determined water content. All observed differences between both techniques of moisture detection are the consequence of their indirect character and the potential influence of some disturbances which not always could be minimized or eliminated, for example ionic conductivity, contact condition and nonhomogeneous degree of material saturation.

- moisture readouts at points located at low height about the water table (5 and 10 cm) were higher for the TDR noninvasive sensor;
- at the height of 15 cm moisture content determined by capacitive probe was slightly higher that one indicated by the TDR sensor which is confirmed by the slope of regression higher than 1 and positive value of the y-intercept;
- for low saturation conditions the FD probe showed higher moisture readouts than the TDR surface sensor;
- both of the tested probes showed high measurement instability for low saturation (close to dry), which is visible in Figure 10 for the reference level at 30 cm, with the negative coefficient of regression;
- the maximal noted standard deviation for the TDR sensor was equal to 0.012 cm
^{3}/cm^{3}with the maximal standard deviation for the FD probe was higher, reaching 0.037 cm^{3}/cm^{3}.

^{3}, lower than tested in this paper, so installation of the invasive TDR probes could be easier. The probes were installed at the following heights over the water table 15, 30, 45, 60, 75 and 90 mm, lower and with smaller spacing than applied in our research. Thus, the first registered readouts of water content for the lowest level, 5 cm above water level, were observed after approx. an hour and after 5 h the conditions near full saturation were noted. The increase in water content for higher levels were observed respectively later. To compare the dynamics of the studied processes, the readouts of water content at the height of 90 mm reported by Hansen [47] and 100 mm obtained during the presented studies were analyzed. In case of the surface TDR probe the appearance of water was observed after approx. 20 h and the full saturation after approx. 80 h, while the comparable values were reported by Hansen [47] after approx. 60 and 100 h, respectively. But, the full saturation was probably not achieved, because lower sensors showed higher values of moisture readouts in several points.

^{3}. The initial conditions showed volumetric water content at the level of 0.1 m

^{3}/m

^{3}. The TDR FP/mts probes were installed at the heights of 5, 10, 15 and 20 cm above the water table, similarly to the experiment concerning application of the FD and surface TDR sensors. The reported experiment lasted 20 days. The maximum value of water content at the end of the experiment was equal to 0.34 cm

^{3}/cm

^{3}and was comparable to readouts by the surface TDR and FD sensors (0.357 and 0.338 cm

^{3}/cm

^{3}, respectively). The increase in moisture to full saturation determined by the TDR FP/mts probes appeared at given tested heights after 3, 5, 10 and 20 days, respectively.

^{3}/cm

^{3}. Contrary, both, the surface TDR and FD, sensors showed values of standard deviation equal to 0.005 cm

^{3}/cm

^{3}, respectively. However, it should be underlined that all the determined values of standard deviations were below the extended uncertainty of TDR method. The observed differences in readouts of porous material water contents were caused by the different physical properties of tested specimens, various characteristics of sensors and varies character of the performed research.

## 6. Conclusions

- (1)
- For proper recalculation of reflectometric moisture readouts, the noninvasive, surface TDR sensors require individual calibration.
- (2)
- Due to influence of polyoxymethylene cover of the sensor, apparent permittivity read by the noninvasive sensor is lower than one read by the traditional probe in relation to the same moisture level. These differences can be abolished by application of the individual calibration.
- (3)
- Residual mean squared error (RMSE) for the calibration formula developed for the discussed sensor and material equals 0.013 cm
^{3}/cm^{3}and is smaller than found in the literature for the traditional invasive probes utilizing the standard empirical calibration formulas. - (4)
- Expanded uncertainty of the discussed sensor equals 0.01 cm
^{3}/cm^{3}in the most of the range of material moisture which is lower value than found in the literature for the invasive sensors utilizing the traditional empirical calibration formulas. - (5)
- Expanded uncertainty of the tested sensor is higher at nearly dry and nearly saturated states of the measured material.
- (6)
- In the range of high moisture values, water content readouts by the TDR surface sensor were higher than those acquired by the capacitive sensor.
- (7)
- In the range of average and low moisture values, water content readouts by the TDR surface sensor were lower than those acquired by the capacitive sensor.
- (8)
- During the comparison of the indirect, electric estimation of moisture using noninvasive TDR and FD sensors with the gravimetric evaluation it was noticed that the TDR readouts were underestimated for 4.4% and the FD readouts were overestimated for 12.6%.
- (9)
- Comparing the maximal standard deviations in both tests using electric techniques of moisture detection it was noted, that capacitive sensors are characterized by greater values of this parameter.

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Topp, G.C.; Ferré, T.P.A. Time-Domain Reflectometry. In Encyclopedia of Soils in the Environment; Hillel, D., Ed.; Elsevier: Amsterdam, The Netherlands, 2005; pp. 174–181. ISBN 978-0-12-348530-4. [Google Scholar]
- Rubio-Celorio, M.; Garcia-Gil, N.; Gou, P.; Arnau, J.; Fulladosa, E. Effect of temperature, high pressure and freezing/thawing of dry-cured ham slices on dielectric time domain reflectometry response. Meat Sci.
**2015**, 100, 91–96. [Google Scholar] [CrossRef] [PubMed] - Nasraoui, M.; Nowik, W.; Lubelli, B. A comparative study of hygroscopic moisture content, electrical conductivity and ion chromatography for salt assessment in plasters of historical buildings. Constr. Build. Mater.
**2009**, 23, 1731–1735. [Google Scholar] [CrossRef] - Sobczuk, H.; Plagge, R. Time Domain Reflectometry Method in Environmental Measurements; Polska Akademia Nauk. Komitet Inzynierii Srodowiska: Lublin, Poland, 2007; Volume 39, pp. 1–114. ISBN 83-89293-51-X. [Google Scholar]
- Malicki, M.A.; Campbell, E.C.; Hanks, R.J. Investigations on power factor of the soil electrical impedance as related to moisture, salinity and bulk density. Irrig. Sci.
**1989**, 10, 55–62. [Google Scholar] [CrossRef] - Topp, G.C.; Davis, J.L.; Annan, A.P. Electromagnetic determination of soil water content: Measurements in coaxial transmission lines. Water Resour. Res.
**1980**, 16, 574–582. [Google Scholar] [CrossRef] - Skierucha, W.; Wilczek, A.; Alokhina, O. Calibration of a TDR probe for low soil water content measurements. Sens. Actuators A Phys.
**2008**, 147, 544–552. [Google Scholar] [CrossRef] - Topp, G.C.; Davis, J.L.; Annan, P. Electromagnetic determination of soil water content using TDR: I. Applications to wetting fronts and steep gradients. Soil Sci. Soc. Am. J.
**1982**, 46, 672–678. [Google Scholar] [CrossRef] - Malicki, M.A.; Skierucha, W.M. A manually controlled TDR soil moisture meter operating with 300 ps rise-time needle pulse. Irrig. Sci.
**1989**, 10, 153–163. [Google Scholar] [CrossRef] - Zegelin, S.J.; White, I.; Jenkins, D.J. Improved field probe for soil water content and electrical conductivity measurement using time domain reflectometry. Water Resour. Res.
**1989**, 25, 2367–2376. [Google Scholar] [CrossRef] - Černý, R. Time-domain reflectometry method and its application for measuring moisture content in porous materials: A review. Measurement
**2009**, 42, 329–336. [Google Scholar] [CrossRef] - Blonquist, J.M.; Jones, S.B.; Robinson, D.A. A time domain transmission sensor with TDR performance characteristics. J. Hydrol.
**2005**, 314, 235–245. [Google Scholar] [CrossRef] - Noborio, K. Mesurement of soil water content and electrical conductivity by time domain reflectometry: A review. Comput. Electron. Agric.
**2001**, 31, 213–237. [Google Scholar] [CrossRef] - Selker, J.S.; Graff, L.; Steenhuis, T. Noninvasive time domain reflectometry moisture measurement probe. Soil Sci. Soc. Am. J.
**1993**, 57, 934–936. [Google Scholar] [CrossRef] - Perrson, M.; Berndtsson, R. Noninvasive water content and electrical conductivity laboratory measurements using time domain reflectometry. Soil Sci. Soc. Am. J.
**1998**, 62, 1471–1476. [Google Scholar] [CrossRef] - Malicki, M.A.; Plagge, R.; Roth, C.H. Improving the calibration of dielectric TDR soil moisture determination taking into account the solid soil. Eur. J. Soil Sci.
**1996**, 47, 357–366. [Google Scholar] [CrossRef] - Sobczuk, H.; Suchorab, Z. Calibration of TDR instruments for moisture measurement of serated concrete. In Monitoring and Modelling the Properties of Soil as Porous Medium; Skierucha, W., Walczak, T., Eds.; Institute of Agrophysics, Polish Academy of Sciences: Lublin, Poland, 2005; pp. 156–165. ISBN 9788387385958. [Google Scholar]
- Lee, J.; Horton, R.; Noborio, K.; Jaynes, D.B. Characterization of preferential flow in undisturbed, structured soil columns using a vertical TDR probe. J Contam. Hydrol.
**2001**, 51, 131–144. [Google Scholar] [CrossRef] [Green Version] - Lins, Y.; Schanz, T.; Fredlund, D.G. Modified pressure plate apparatus and column testing device for measuring SWCC of sand. Geotech. Test J.
**2009**, 32, 450–464. [Google Scholar] [CrossRef] - Skierucha, W.; Wilczek, A.; Szypłowska, A.; Sławiński, C.; Lamorski, K. A TDR-based soil moisture monitoring system with simultaneous measurement of soil temperature and electrical conductivity. Sensors
**2012**, 12, 13545–13566. [Google Scholar] [CrossRef] [PubMed] - Davis, J.L.; Annan, A.P. Ground-penetrating radar for high-resolution mapping of soil and rock stratigraphy. Geophys. Prospect.
**1989**, 37, 531–551. [Google Scholar] [CrossRef] - Skierucha, W.; Malicki, M.A. TDR Method for the Measurement of Water Content and Salinity of Porous Media; Institute of Agrophysics, Polish Academy of Sciences: Lublin, Poland, 2004. [Google Scholar]
- Wilczek, A.; Szypłowska, A.; Kafarski, M.; Skierucha, W. A Time-Domain Reflectometry Method with Variable Needle Pulse Width for Measuring the Dielectric Properties of Materials. Sensors
**2016**, 16, 191. [Google Scholar] [CrossRef] [PubMed] - Jones, S.B.; Wraith, J.M.; Or, D. Time domain reflectometry measurement principles and applications. Hydrol. Proc.
**2002**, 16, 141–153. [Google Scholar] [CrossRef] - De Loor, G.P. Dielectric properties of heterogeneous mixtures containing water. J. Microw. Power
**1968**, 3, 67–73. [Google Scholar] [CrossRef] - Tinga, W.R.; Voss, W.A.G.; Blossey, D.F. Generalized approach to multiphase dielectric mixture theorie. J. Appl. Phys.
**1973**, 44, 3897–3902. [Google Scholar] [CrossRef] - Dobson, M.C.; Ulaby, F.T.; Hallikainen, M.T.; El-Rayes, M.A. Microwave dielectric behavior of wet soil. Part 2: Dielectric mixing models. IEEE Trans. Geosci. Remote Sens.
**1985**, 23, 35–46. [Google Scholar] [CrossRef] - Noborio, K.; Horton, R.; Tan, C.S. Time Domain Reflectometry probe for simultaneous measurement of soil matric potential and water content. Soil Sci. Soc. Am. J.
**1999**, 63, 1500–1505. [Google Scholar] [CrossRef] - O’Connor, K.M.; Dowding, C.H. Geomeasurements by Pulsing TDR Cables and Probes; CRC Press: Boca Raton, FL, USA, 1999; ISBN 9780849305863. [Google Scholar]
- Moret, D.; Lopez, M.V.; Arrue, J.L. TDR application for automated water level measurement from Mariotte reservoirs in tension disc infiltrometers. J. Hydrol.
**2004**, 297, 229–235. [Google Scholar] [CrossRef] [Green Version] - Topp, G.C.; Reynolds, W.D. Time Domain Reflectometry: A seminar technique for measuring mass and energy in soil. Soil Tillage Res.
**1998**, 47, 125–132. [Google Scholar] [CrossRef] - Jones, S.B.; Or, D. Modeled effects on permittivity measurements of water content in high surface area porous media. Physica B
**2003**, 338, 284–290. [Google Scholar] [CrossRef] - Skierucha, W. Accuracy of Soil Moisture Measurement by TDR Technique. Int. Agrophys.
**2000**, 14, 417–426. [Google Scholar] - Rayleigh, L. On the influence of obstacles arranged in rectangular order upon the properties of the medium. Philos. Mag.
**1892**, 34, 481–502. [Google Scholar] [CrossRef] - Maxwell Garnett, J.C. Colours in Metal Gases and Metal Films; Transactions of the Royal Society: London, UK, 1904; Volume 203, pp. 385–420. [Google Scholar]
- Polder, D.; van Santen, J.H. The effective permeability of mixtures of solids. Physica
**1946**, 12, 257–271. [Google Scholar] [CrossRef] - Roth, K.; Schulin, R.; Flühler, H.; Attinger, W. Calibration of time domain reflectometry for water content measurement using a composite dielectric approach. Water Resour. Res.
**1990**, 26, 2267–2273. [Google Scholar] [CrossRef] - Whalley, W.R. Consideration on the use of Time Domain Reflectometry (TDR) for measuring soil water content. Eur. J. Soil Sci.
**1993**, 44, 1–9. [Google Scholar] [CrossRef] - Schapp, M.G.; de Lange, L.; Heimovara, T.J. TDR calibration of organic forest floor media. Soil Technol.
**1996**, 11, 205–217. [Google Scholar] [CrossRef] - Skierucha, W. Wpływ Temperatury Na Pomiar Wilgotności Gleby Metodą Reflektometryczną; Acta Agrophysica, Rozprawy i Monografie, Polska Akademia Nauk: Lublin, Polska, 2005. (In Polish) [Google Scholar]
- Quinones, H.; Ruelle, P. Operative calibration methodology of a TDR sensor for soil moisture monitoring under irrigated crops. Subsurf. Sens. Technol. Appl.
**2001**, 2, 31–45. [Google Scholar] [CrossRef] - Udawatta, R.P.; Anderson, S.H.; Motavalli, P.P.; Garrett, H.E. Calibration of a water content reflectometer and soil water dynamics for an agroforestry practice. Agrofor. Syst.
**2011**, 82, 61–75. [Google Scholar] [CrossRef] - Mastrorilli, M.; Katerji, N.; Rana, G.; Nouna, B.B. Daily actual evapotranspiration measured with TDR technique in Mediterranean conditions. Agric. For. Meteorol.
**1998**, 90, 81–89. [Google Scholar] [CrossRef] - Ren, T.; Noborio, K.; Horton, R. Measuring soil water content, electrical conductivity, and thermal properties with a thermo-time domain reflectometry probe. Soil. Sci. Soc. Am. J.
**1999**, 63, 450–457. [Google Scholar] [CrossRef] - Soncela, R.; Sampaio, S.; Vilas Boas, M.A.; Tavares, M.H.F.; Smanhotto, A. Construction and calibration of TDR probes for volumetric water content estimation in a Distroferric Red Latosol. Eng. Agríc.
**2013**, 33, 919–928. [Google Scholar] [CrossRef] [Green Version] - Ju, Z.; Liu, X.; Ren, T.; Hu, C. Measuring Soil Water Content with Time Domain Reflectometry: An Improved Calibration Considering Soil Bulk Density. Soil Sci.
**2010**, 175, 469–473. [Google Scholar] [CrossRef] - Hansen, M.H. TDR measurement of moisture content in aerated concrete. In Proceedings of the 6th Symposium on Building Physics, Trondheim, Norway, 17–19 June 2002. [Google Scholar]
- Suchorab, Z.; Widomski, M.; Łagód, G.; Sobczuk, H. Capillary rise phenomenon in aerated concrete. Monitoring and simulations. Proc. ECOpole
**2010**, 4, 285–290. [Google Scholar] - Suchorab, Z.; Barnat-Hunek, D.; Franus, M.; Łagód, G. Mechanical and Physical Properties of Hydrophobized Lightweight Aggregate Concrete with Sewage Sludge. Materials
**2016**, 9, 317. [Google Scholar] [CrossRef] [PubMed] - Pavlík, Z.; Fiala, L.; Černý, R. Determination of Moisture Content of Hygroscopic Building Materials Using Time Domain Reflectometry. J. Appl. Sci.
**2008**, 8, 1732–1737. [Google Scholar] [CrossRef] - Wraith, J.M.; Robinson, D.A.; Jones, S.B.; Long, D.S. Spatially characterizing apparent electrical conductivity and water content of surface soils with time domain reflectometry. Comput. Electron. Agric.
**2005**, 46, 239–261. [Google Scholar] [CrossRef] - Ito, Y.; Chikushi, J.; Miyamoto, H. Multi-TDR probe designer for measuring soil moisture distribution near the soil surface. In Proceedings of the 19th World Congress of Soil Sciences, Brisbane, Australia: Soil Solutions for a Changing World, Brisbane, Australia, 1–6 August 2010. [Google Scholar]
- Choi, C.; Song, M.; Kim, D.; Yu, X. A New Non-Destructive TDR System Combined with a Piezoelectric Stack for Measuring Properties of Geomaterials. Materials
**2016**, 9, 439. [Google Scholar] [CrossRef] [PubMed] - Sobczuk, H. Sonda Do Pomiaru Wilgotności Ośrodków Porowatych, Zwłaszcza Materiałów Budowlanych. Available online: https://rejestr.io/patenty/212837 (accessed on 13 November 2018).
- Sobczuk, H.; Suchorab, Z. Sonda Do Pomiaru Wilgotności Przegród Budowlanych, Zwłaszcza O Chropowatych Powierzchniach. Available online: https://rejestr.io/patenty/225640 (accessed on 13 November 2018).
- Sobczuk, H.; Suchorab, Z. Sonda Do Pomiaru Wilgotności, Zwłaszcza Elementów O Powierzchniach Wypukłych. Available online: https://rejestr.io/patenty/225641 (accessed on 13 November 2018).
- Sobczuk, H.; Suchorab, Z. Sonda Do Pomiaru Wilgotności, Zwłaszcza Elementów O Zakrzywionych Powierzchniach. Available online: https://rejestr.io/patenty/225639 (accessed on 13 November 2018).
- Knight, J.H. Sensitivity of time domain reflectometry measurements to lateral variations in soil water content. Water Resour. Res.
**1992**, 28, 2345–2352. [Google Scholar] [CrossRef] - Suchorab, Z.; Sobczuk, H.; Cerny, R.; Pavlik, Z.; De Miguel, R.S. Sensitivity range determination of surface TDR probes. Environ. Prot. Eng.
**2009**, 35, 179–189. [Google Scholar] - Majerek, D.; Widomski, M.; Garbacz, M.; Suchorab, Z. Estimation of the measurement uncertainty of humidity using a TDR probe. AIP Conf. Proc.
**2018**, 1988, 020027. [Google Scholar] [CrossRef] - JCGM 100:2008, GUM 1995 with Minor Corrections, Evaluation of Measurement Data—Guide to the Expression of Uncertainty in Measurement. Available online: http://www.bipm.org/utils/common/documents/jcgm/JCGM_100_2008_E.pdf (accessed on 24 September 2018).
- Wu, S.Y.; Zhou, Q.Y.; Wang, G.; Yang, L.; Ling, C.P. The relationship between electrical capacitance-based dielectric constant and soil water content. Environ. Earth Sci.
**2010**, 62, 999–1011. [Google Scholar] [CrossRef] - Topp, G.C.; Davis, J.L.; Bailey, W.G.; Zebchuk, W.D. The measurement of soil water content using a portable TDR hand probe. Can. J. Soil. Sci.
**1984**, 64, 313–321. [Google Scholar] [CrossRef] - Amato, M.; Ritchie, J.T. Small spatial scale soi water content measurement with time-domain reflectometry. Soil Sci. Soc. Am. J.
**1995**, 59, 325–329. [Google Scholar] [CrossRef]

**Figure 2.**Example of TDR waveforms for dry (

**top**) and moist (

**bottom**) material acquired from an ETest LP/ms TDR probe (own elaboration based on calibration tests). Left-hand side—control peaks, right-hand side—measuring peaks.

**Figure 4.**Electric response of the developed sensor for different environments: upper trace—air-dry sample, bottom trace—saturated sample.

**Figure 6.**Calibration test results: (

**a**) dependence between effective dielectric permittivity and material moisture, (

**b**) comparison of data obtained gravimetrically and by reflectometric evaluation.

**Figure 7.**Combined standard and expanded measurements uncertainties of the TDR surface sensor for aerated concrete.

**Figure 10.**Comparison of capillary rise measurements results obtained by surface TDR sensor and FD capacitive sensor for aerated autoclaved concrete.

Apparent Density [kg/m^{3}] | Saturated Volumetric Water Content [cm^{3}/cm^{3}] | Saturated Gravimetric Water Content [kg/kg] |
---|---|---|

612.2 ± 11.2 | 0.363 ± 0.007 | 0.593 ± 0.007 |

Determination Coefficient R ^{2} | Residual Standard Error RSE [cm ^{3}/cm^{3}] | Root Mean Square Error RMSE [cm ^{3}/cm^{3}] | F-Model Linearity Test Statistic |
---|---|---|---|

0.986 | 0.014 (df = 16) | 0.013 | 580.752 *** (df = 2; 18) |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Suchorab, Z.; Widomski, M.K.; Łagód, G.; Barnat-Hunek, D.; Majerek, D.
A Noninvasive TDR Sensor to Measure the Moisture Content of Rigid Porous Materials. *Sensors* **2018**, *18*, 3935.
https://doi.org/10.3390/s18113935

**AMA Style**

Suchorab Z, Widomski MK, Łagód G, Barnat-Hunek D, Majerek D.
A Noninvasive TDR Sensor to Measure the Moisture Content of Rigid Porous Materials. *Sensors*. 2018; 18(11):3935.
https://doi.org/10.3390/s18113935

**Chicago/Turabian Style**

Suchorab, Zbigniew, Marcin Konrad Widomski, Grzegorz Łagód, Danuta Barnat-Hunek, and Dariusz Majerek.
2018. "A Noninvasive TDR Sensor to Measure the Moisture Content of Rigid Porous Materials" *Sensors* 18, no. 11: 3935.
https://doi.org/10.3390/s18113935