Monitoring and Calibrating Building Materials Drying Kinetics with Capacitance Sensors

Abstract

Building materials’ moisture content defines the overall durability and serviceability of buildings and infrastructures. Conventionally, moisture content is estimated by weighing the materials before and after drying. In this work, the results of capacitance wired sensors for measuring moisture content were investigated. These sensors facilitate in situ measurement of capacitance values, with the aid of specialized installation equipment, and the results are accessible via a cloud-based software application. In practice, the main drawback associated with the application of these sensors is related to their calibration. Thus, it is important to investigate different algorithms which convert capacitance readings into moisture content values. To address this, various specimens covering a diverse set of building materials were prepared in the laboratory. This study focused on examining two bricks, two sedimentary stones with low and high porosity values. and four different kinds of mortars (with different binders, namely hydrated lime putty, cement, natural hydraulic lime, and hydrated lime powder and pozzolan). The results indicated that a linear model can be recommended for calibrating sensor capacitance to moisture content measurements. This model can be used for the prediction of building material moisture content with high accuracy, from saturated to the dry state, covering the full range of drying kinetics.

1. Introduction

Water in all forms is considered as the major decay factor of building materials and components [1]. The presence of moisture in porous building materials is associated with almost all decay phenomena [2], including electrochemical corrosion of metallic components, chemical deterioration and dissolution of materials, chemical processes, freeze-thaw deterioration, discoloration, volume changes, and biological decay, such as mold [3]. UNI EN 772-1 describes that if moist stones are forced to dry, compressive strength may be reduced by approximately 20% [4,5].

Furthermore, moisture alters the thermal properties of materials impacting heat transfer flows, influencing materials’ insulation properties and human comfort and health. To sustain the building envelopes’ performance, it is important to maintain proper temperature and humidity levels [6]. Thermal conductivity measured for traditional bricks from dry to semi-saturated state can be two times higher, escalating to over 100% in fully saturated conditions. In the case of a more porous material, moisture content between 20–30% may result in a severe loss of thermal resistance [5].

Worldwide, 19–80% of buildings exhibit moisture-, and mold-related damage [7]. Therefore, quantifying moisture content in building materials is critical to accurately diagnose building pathologies for the adoption of appropriate intervention measures and for evaluating the effectiveness of the applied treatment solutions [8].

For measuring moisture content of materials, both direct and indirect methods are used. The gravimetric method is a direct method which requires actual samples, ensuring reliability but limiting its applicability, particularly in historic materials/structures. The gravimetric method is straightforward despite the variety of different testing standards; this method requires weighing a sample in both dry and saturated states [9,10]. Alternatively, indirect (non-destructive) testing methods can be applied. Non-destructive testing for measuring moisture content uses physical properties as proxies for moisture, such as electrical, visual, or thermal measurements [11]. Undoubtedly, the direct gravimetric method is the most accurate method, since factors such as the homogeneity, density, porosity, surface treatments, and degree of material decay may negatively affect the accuracy of indirect methods [12].

Regarding the indirect methods applied in recent years, electrical-based sensors are a very promising technique for obtaining moisture content values of building materials and components. The word “sensor” originates from the Latin word “sensorius”, meaning “to perceive, to feel”. Their function is primarily based on measuring the resistivity or capacitance of building materials. The presence of water changes the conductivity of building materials by allowing the estimation of moisture content by measuring resistivity. Additionally, moisture modifies a material’s dielectric property, allowing the use of capacitance methods to detect these dielectric variations due to the presence of water [13]. The use of capacitance sensors is not new [14]. This method is based on the high dielectric constant (ɛ = 80) of water, in comparison to the low dielectric constant of building materials. Consequently, changes of a material’s dielectric properties can be attributed to its varying moisture content. A European standard has been established for this technique regarding wood products [15], while the European standard EN 16682 [16] has proposed specifications for wood and masonry materials. According to this standard, “the capacitance methods respond to the total amount of water molecules, but the output depends on other factors too, including how the molecules are distributed inside the material, the signal being higher for molecules close to the sensor”. There is a lot of criticism of the application of this method, because the presence of electrolytes in masonry constitutes a limitation for the application of the capacitive method [12].

Several capacitance sensors have been tested for use with different building materials [17,18,19,20,21]. These capacitance sensors use different electronic designs, resulting in various application techniques and calibration approaches.

The dielectric properties are influenced by several different factors, such as material intrinsic factors (mineralogical chemical composition, microstructure, grain size, etc.), but also extrinsic factors, such as environmental conditions. Due to the complexity and variability of these different parameters, it is evident that each material requires individual calibration in order to obtain reliable moisture measurements. The calibration of capacitance sensors for in situ measurements is even more challenging for cultural heritage materials [12].

Capacitance methods remain a pioneer among various indirect methods due to their high operation speed and good accuracy, automation of measurements and data processing [22]. However, despite their advancements, capacitance-based methods for determining moisture content have some disadvantages compared to other methods These issues are related to the need for calibration in order to determine the gravimetric to capacitance correlation. Additionally, sensor placement within building materials may be inconsistent across different installations, introducing potential measurement errors. Furthermore, after events where building materials may be saturated, the material must reach a steady state to reliably obtain a consistent measurement.

Despite the wide variety of techniques available for calculating moisture content, measuring and monitoring moisture using a minimally destructive method, in real time, remains a challenge for both historical and modern buildings [23,24]. Although advanced imaging technologies and computational methods are widely used in building investigations, the determination of moisture content is still in need of further elaboration [25]. Additionally, climatic change, along with its accompanied phenomena, such as sea level rise, extreme weather conditions, floods, etc., constitutes a challenge for conventional methods. Consequently, only permanent monitoring of moisture content can evaluate the risk of decay or damage and support decision-making for the preventive conservation of structures [26].

The main objective of this study was to investigate the monitoring of materials’ moisture content measured simultaneously by direct and indirect methods. For this reason, different building materials comprised of main structural elements were selected (such as bricks and stones), but also different kinds of mortars (cement, lime, and hydraulic lime-based), most frequently used in historic and modern buildings. More specifically, the materials’ moisture content was measured in the laboratory using both the gravimetric method and the application of embedded capacitance sensors. The main task of the investigation was to evaluate the capacitance sensor measurements in relation to the gravimetric results during a dynamic drying test experiment. A calibration model was developed which correlates a material’s actual moisture content to capacitance values for the entire range of drying, from completely saturated to dry state, in constant environmental conditions.

2. Materials and Methods

2.1. Capacitance Sensors

In this work, sensors designed to create a fringing electric field are used to estimate the values for moisture content through capacitance measurements. The sensor used consists of a pair of flexible stainless-steel flattened conductors that can be easily inserted into a mortar joint or suitably adjusted for application to a brick or stone surface [27]. In Figure 1a, the twin tape capacitance sensor is presented. The advantage of this type of sensor is its length (25 cm), which can supply more reliable information when embedded inside masonry in comparison with most available sensors that measure at specific points or are limited in size. In Figure 2b, a characteristic specimen representing each of the three different categories of materials under investigation is presented, cement mortar, stone, and brick. In the mortar, the sensor is embedded within its mass, while in the case of stones and bricks, the sensors are inserted and held in place using tight straps. The sensors are then connected with wires to a datalogger that records the voltage variations. When examining samples from a historic building, special attention should be paid to the dimension of the samples. The samples should have at least a length greater than 25 cm, which is the length of the sensors, resulting in a configuration as shown in Figure 1b.

The capacitance sensing tape connects to a 5 MHz sensing circuit via a coaxial cable connected to a datalogger where both the tape sensor and reference capacitor are measured.

Figure 2 illustrates the coupling of the electrodes to the material through a fringing electric field. When an electric field is applied, the material within this coupled system functions as the dielectric medium of the capacitor. The upper surface of the two electrodes (D/S) interacts with the material with the dielectric constant ε_m, while the downward surface material has a dielectric constant equal to ε_s. The capacitance C(D/S) is then estimated by Equation (1) [27]:

$$C\left(DS\right)=\frac{{\epsilon }_o\left(\frac{{\epsilon }_m+{\epsilon }_s}{2}\right)k\left(\sqrt{1-\frac{a^2}{b^2}}\right)}{k\left(\frac{a}{b}\right)}+{\epsilon }_o{\epsilon }_a\frac{t}{a}$$

(1)

where:

${\epsilon }_o,$ electric constant (permittivity of free space);

${\epsilon }_m$, material dielectric constant;

${\epsilon }_s$, substrate dielectric constant;

${\epsilon }_a$, dielectric constant of material between two electrodes (air);

k, Coulomb constant;

a, inner distance between the two electrodes, 4.5 mm;

b, outer distance between the two electrodes, 14 mm.

The system illustrated in Figure 3 operates at 5 MHz. The basic principle is based on the comparison of the charging duration between the sensor and reference RC circuit. The electric signal generated by this circuit exhibits different phases and amplitudes corresponding with variations in capacitance. Cr is a fixed capacitor, RCr is the reference, and RCs are the capacitance sensing side. An electric pulse is produced where its width correlates to the RC of the sensing circuit. After passing through a low pass filter, two output voltages, Va and Vb, are generated. The voltage output Va is stable, while Vb alters according to the sensing capacitance, Cs. The capacitance variation of the sensing capacitor (Cs) corresponds to the differential voltage between Va and Vb. These two output values are transmitted to the datalogger, where the analog data are converted to digital data via an analog to digital converter.

2.2. Preparation of Test Samples

Three different types of building materials were investigated, bricks, stones, and mortars. Samples’ dimensions were 4 cm × 4 cm × 30 cm; the 30 cm length is to accommodate the sensors’ 25 cm length. More specifically, two different kinds of bricks were investigated, BRI and BRM. These bricks are fired, handmade, and predominately used in historic buildings. Traditional bricks were selected on account of their appropriate size, as well as their compactness and absence of holes. The stones selected are of sedimentary type, commonly used in construction works (codes SRY, SST). Regarding mortars, it was decided to prepare samples with the four different binders most frequently used, one with hydrated lime putty binder (ML), one with natural hydraulic lime (MHL) binder, one with lime powder and pozzolan (MLP), and one with cement binder (MC). The different mortar binders were chosen to be characteristic for both historical and modern structures. The samples total height was 4 cm. For bricks and stones, the sensor was placed between two samples measuring 2 cm × 2 cm × 30 cm, secured firmly together (Figure 1b). The sensors during the preparation of the mortars were placed at 2 cm height and width, in the middle of the sample. The different materials used in the investigation are presented in

Table 1. Materials under investigation.

Material	Code	Type
Brick–Italy	BRI	Fired, handmade
Brick–Greece	BRM	Fired, handmade
Limestone	SRY	Quarry stone
Travertine	SST	Quarry stone
Lime	ML	Hydrated lime putty, river sand, 1:3 per weight
Hydraulic lime	MHL	Natural hydraulic lime 3.5, commercial premixed mortar
Lime	MLP	Hydrated lime powder with artificial pozzolan, commercial premixed mortar
Cement	MC	Cement binder (CEMII/B-M), river sand, 1:3 per weight

.

2.3. Measurements/Calibration

In this work, the different building materials examined are typically found in historic and modern buildings, such as traditional and modern mortars, bricks, and stones. The main aim of the investigation is to calibrate the moisture content as measured by the capacitance sensors based on correlation with the results obtained using the gravimetric method, while drying the samples at constant conditions (T = 21 ± 1 °C and RH (%) = 50 ± 5%). The materials’ microstructure characteristics were investigated with the aid of a mercury porosimeter (MIP, Pascal 140, 440, Thermo Electron Corporation, Waltham, MA, USA), in a pressure range of 0.01–200 MPa. During the experiment, capacitance changes as the different materials are conditioned to the different specific moisture content levels from 100% saturated state to dry state. Dry building materials are usually electrically insulating resulting in a weak dielectric response to the electric field, with a dielectric constant ranging between 1 and 5. However, their porosity leads to moisture absorption and storage. The high dielectric constant (80) of water results in a higher dielectric constant for the moisture-containing materials relative to their dry state. The overall dielectric constant increases with the amount of moisture. Thus, the dielectric constant can be an indicator of the moisture content in these materials. The moisture content (MC) can be determined by measuring the change of the dielectric constant in relation to moisture content [20,22].

For each material, three samples underwent two series of drying measurements:

• After measuring the mass of dried samples, the samples were immersed in distilled water. Then, their weight was recorded every hour, using a precision balance (RADMAG, PS 10100.R2.M), with an accuracy of 0.01 g. The moisture content X (kg/kg db) (db: dry base), for each material is estimated as:

$$X=\frac{Xsaturation-Xdry}{Xdry}\times 100$$

(2)

2.

After drying, samples were saturated with immersion in water, and then were left in the same environmental conditions (T = 21 ± 1 °C and RH (%) = 50 ± 5%) to dry. This time, the difference between the reference voltage Vb_ref and Va was measured V (mV/mV db) as:

$$V=\frac{Va-Vb\_ref}{Vb\_ref}$$

(3)

Then, the two dimensionless values were correlated for the different materials.

Usually, sensor calibration tests are performed for specific moisture content levels when the material is either completely wet or dry. For example, Weiss and Sass (2022) tested eight different types of sensors, including two types of capacitance sensors, for measuring the moisture content of sandstone. The capacitance sensors were calibrated when samples were fully saturated with water and after drying [16]. This gravimetric calibration method considers only discrete moisture thresholds and does not capture the entire range of the drying process. The advantage of the present investigation is that the calibration was performed for the dynamic drying phenomenon, and not only for specific moisture contents.

For calibrating the dynamic drying phenomenon, it is necessary to have ‘curve shapes’, as in Figure 4 [28]. The shape of these curves reveals, optically, the quality of the calibration process [11]. An ideal calibration curve is of a linear shape (Figure 4a), in which the sensor records the whole range of moisture content with high accuracy. Figure 4b corresponds to non-linear relationships, with better accuracy for higher and lower water contents. Figure 4c presents the measurement thresholds, with no specific information about the relationship between the two variables, while Figure 4d corresponds to an unreliable, unstable calibration. Many factors can be responsible for these inconsistencies, such as material characteristics, limitations of the sensors, and operational errors. The shape of the calibration curves reveals effortlessly the accuracy of the measurements of the sensors.

3. Results and Discussion

3.1. Materials’ Microstructural Characteristics

The materials’ microstructural characteristics, as calculated with the aid of mercury intrusion porosimetry, are presented in

Table 2. Materials microstructural properties.

Material	Total Cumulative Volume V (mm3/g)	Bulk Density dbulk (g/cm3)	Total Open Porosity P (%)	Average Pore Radius r (µm)	Total Specific Surface Area s (m²/g)
BRI	85.0	2.06	17.5	0.97	0.43
BRM	174.0	1.87	32.6	2.01	1.46
SRY	197.0	1.79	35.2	2.83	2.28
SST	15.7	2.49	3.91	10.7	0.28
ML	169.2	1.77	29.9	19.3	1.20
MHL	210.4	1.60	33.6	23.9	2.23
MLP	85.0	1.85	28.4	0.03	6.28
MC	174.0	2.20	14.8	0.18	3.85

. In addition, Figure 5 shows the distribution of mercury relative volume (Rel. Vol. (%)) for different selected pore ranges.

The bricks, although both fired and handmade, present totally different microstructural characteristics. BRI presents an open total porosity of about 17.5%, while for BRM this percentage is about 32.6%. Concerning their pore size distribution, both materials present a unimodal distribution around the pore average radius. For BRI, the highest percentage of pores is found in the range of 0.1–1.0 µm, while for BRM it is found in the 2.0–5.0 µm pore range.

As far as stones are concerned, the two sedimentary stones also exhibit completely different microstructures. SRY presents a high open porosity value (35.2%), while SST is a very low-porosity stone, with a percentage of 3.91%. Although both stones present their highest percentage of pores in the 0.1–1.0 µm range, SRY presents in general smaller pores, in a unimodal distribution around its average pore radius of 2.83 µm, while SST has larger-sized pores, distributed throughout the whole pore range, with an average pore radius of about 10.7 µm.

The mortars also show different microstructural characteristics. The natural hydraulic lime mortar (MHL) presents the highest open porosity value (about 33.6%), with a bimodal distribution, with a main peak around its average pore radius of 23.9 µm and a second peak at 0.3 µm. ML also presents high porosity value (29.9%), with a bimodal distribution around its average pore radius of 19.3µm and around 1µm. The MLP mortar presents a porosity of about 28.4%, with a bimodal distribution around its average pore radius 0.03 µm and around 0.8 µm. The cement-based mortar (MC) presents the lowest open porosity, about 14.8%, with a unimodal pore size distribution around its average pore radius of 0.2 µm.

In general, it is known that the drying rate of building materials is controlled by a material’s microstructural parameters, in conjunction with the effect of environmental conditions [29].

3.2. Drying Moisture Content Results

In general, drying processes involve two basic parts [30]. Many different mathematical models are proposed for describing the process of drying. In general, drying kinetics of building materials depend on the environmental conditions (air temperature, relative humidity, air velocity), material, and surface characteristics [31].

• The drying rate is constant up to critical moisture content. This period depends mainly on the material’s microstructure and the boundary conditions;
• The falling drying rate period. This is the period of unsaturated surface drying, determined by the difference between material moisture content and the surrounding water vapor pressures [32].

The moisture content Xsat (%) and voltage difference Vsat are the values for the saturated samples, at the beginning of the experiment, while Xo (%), Vo are the corresponding values at the end of the experiment, which correspond to the equilibrium values for the environmental conditions under investigation. These values are shown in

Table 3. Different materials’ moisture content and voltage difference values for the samples saturated with water.

	Xsat (%) (kg/kg db)	Stdev (kg/kg db)	Xo (%) (kg/kg db)	Stdev (kg/kg db)	Vsat (mV/mV db)	Stdev (mV/mV db)	Vo (mV/mV db)	Stdev (mV/mV db)
BRI	8.39	0.005	0.20	0.0004	0.390	0.019	0.192	0.026
BRM	12.9	0.014	0.18	0.00005	0.393	0.134	0.122	0.001
SRY	13.3	0.050	0.73	0.005	0.649	0.011	0.159	0.029
SST	3.80	0.009	0.45	0.040	0.350	0.031	0.231	0.007
ML	13.2	0.002	0.83	0.060	0.646	0.008	0.169	0.029
MHL	14.7	0.676	1.80	0.160	0.639	0.033	0.186	0.044
MLP	15.8	0.090	1.10	0.090	0.635	0.003	0.160	0.005
MC	7.70	0.160	1.01	0.120	0.636	0.013	0.271	0.006

.

As the moisture content of the materials increases, the capacitance increases as well. In Figure 6, the results for the variations of the materials’ moisture content in relation to time are presented, with the average values for each material. For some materials, like ML and MC, the beginning of the experiment showed no change due to the calibrated range of the measurement circuit. There were no changes for the first few hours, as the capacitance circuit was tuned for a maximum range of 600 mV [22]. Especially for the cement mortar, although it presents lower moisture content in respect to the other mortars, the values of voltage difference remain at a high level even after 41 h.

3.3. Correlation of Moisture to Capacitance Values

In this work, the primary objective is to calibrate the capacitance sensors. In Figure 7, Figure 8 and Figure 9, the results of the linear correlation model between moisture content and the differences in voltage are presented with compact lines, while with dotted lines are shown the levels of confidence of 5%. The diagrams describe the entire drying process spectrum reflecting the materials’ moisture content, ranging from fully saturated with water to its dry state.

For the ML and the MC mortars, the correlation (Figure 9) was performed for a longer time span after the experiment’s initiation, 31 h for ML and 41 h for MC. In

Table 4. Linear regression equations for all materials under investigation.

Material	Equation	R2	Sd (kg/kg db)	Rsd (%)
BRI	$X=1.519\times V-0.29$	0.93	0.0027	7.69
BRM	$X=0.841\times V-0.124$	0.98	0.0018	3.09
SRY	$X=0.427\times V-0.066$	0.99	0.0012	2.31
SST	$X=0.670\times V-0.115$	0.97	0.0006	4.39
ML	$X=0.146\times V-0.017$	0.99	0.0005	1.69
MHL	$X=0.297\times V-0.028$	0.97	0.0033	4.20
MLP	$X=0.514\times V-0.099$	0.97	0.0034	5.43
MC	$X=0.073\times V-0.011$	0.99	0.0002	1.00

, the linear regression equations for each material are presented, along with the standard deviation (Sd) and the relative standard deviation Rsd (%). In this work, a good residual sum of squares was considered a value greater than 0.92 R-squared, with very small Sd values. All materials under investigation resulted in low Rsd values (<10%), corresponding to a narrow spread within the estimated values.

As shown in Table 3, a linear regression model is found to be suitable for the calibration of the sensors’ measurements to moisture content for all materials. Based on these linear relationships, the moisture content of the materials under investigation can be estimated easily for different water content levels. The equations’ constants depend on the material’s microstructural characteristics and its chemical-mineralogical composition.

In practice, these models can easily be applied to obtain accurate and reliable moisture values from voltage values for a range of moisture content.

4. Conclusions

The capacitance sensing system tested in this work is a very promising and effective tool for structural health monitoring of buildings and components. This is due to the impracticality and destructive nature of performing gravimetric testing to determine the moisture content of materials, as well as the unpredictable conductivity of various building materials. This system facilitates in situ measurements and real-time data processing from the cloud for a variety of different construction types, from historic to modern structures.

The calibration process encompassed the entire spectrum of moisture content during the drying process. By simultaneously measuring capacitance and material weight, as expressed by the dimensionless moisture content and voltage signal, it was evident that the relationship between moisture content and capacitance (derived from the voltage signal) can be described by a linear model for all materials under investigation, with high accuracy. These linear equations offer high accuracy in predicting moisture content throughout the entire range of the dynamic drying process and not only at specific water content levels, with a very high degree of reliability.

In future works, the effect of environmental variations could be evaluated to supply an integrated model covering diverse environmental conditions. This research could yield even more reliable and accurate results, enabling the full exploitation of this valuable tool for monitoring the health of buildings and infrastructure.