Complex Permittivity of Adobe Verses Frequency and Water Content

Abstract

The complex permittivity of adobe is measured using a coaxial probe system verses frequency (500 MHz to 7 GHz) and water content (0% to 6%). Measurements are performed using adobe samples collected from abode bricks. The geotechnical properties of the compressed earth bricks are characterized by (1) percentage of gravel, sands, and fines; (2) Atterberg limits; and (3) grain-size distribution. The variation in adobe complex permittivity verses frequency is measured at discrete levels of water content using small adobe samples exposed to controlled levels of constant humidity in an environmental chamber. The typical water content profile verses depth for an adobe brick is also determined.

1. Introduction

Through wall radar is an important field in remote sensing that allows for the imaging or detection of objects located behind a wall. Typically, model-based reasoning is used to design the through wall radar system, where the propagation effects of the wall have major impacts on the performance of the radar [1,2,3,4,5]. Significant variation in the two-way attenuation levels verses frequency for various wall types was demonstrated through measurement in [1], which leads to through wall radar system design tradeoffs relative to resolution and penetration. For solid walls constructed from dense materials such as adobe, the relatively homogeneous wall material may exhibit inhomogeneous properties verses depth into the wall due to water content variation. Thus, reliable simulation models for through wall radar systems in an adobe wall environment requires accurate material properties verses frequency and water content level, along with knowledge of the water content distribution within the wall [5,6]. While information on these properties can be found in the literature for several wall materials [7,8,9,10,11,12,13,14,15,16], a concise representation of the complex permittivity of adobe verses frequency and water content is lacking.

The overall complex permittivity $ϵ$ (in $\mathrm{F}/\mathrm{m}$) of a material is defined by

$$ϵ={ϵ}_o[{ϵ}_r^{\prime }-\mathrm{j}{ϵ}_r^{″}]={ϵ}_o\left[{ϵ}_r-\mathrm{j}{\displaystyle \frac{\sigma }{\omega {ϵ}_o}}\right]$$

(1)

where ${ϵ}_o$ is the free space permittivity $(\mathrm{F}/\mathrm{m})$, $\sigma$ is the material conductivity $(\mathrm{S}/\mathrm{m})$, and $\omega$ is the radian frequency $(\mathrm{rad}/\mathrm{s})$. The bracketed term in the equation above represents the complex relative permittivity of the material. The real part of the complex relative permittivity $\left({ϵ}_r^{\prime }\right)$ is the relative permittivity ${ϵ}_r$, which defines the amount of polarization in the material. The imaginary part of the complex relative permittivity $\left({ϵ}_r^{″}\right)$ represents the dielectric loss factor, which is expressed in terms of the material conductivity. The experimental measurement of the complex relative permittivity for adobe verses frequency and water content is addressed in this study, and the measured results are presented.

2. Materials and Methods

2.1. Adobe Test Articles

Several adobe wall test articles composed of compressed earth blocks were produced by the Engineer Research and Development Center, Geotechnical and Structures Laboratory (ERDC), Concrete Materials Branch. The compressed earth block, hereafter referred to as the adobe brick, was identified by ERDC as a representative abode based on a combination of local availability, sand-to-clay ratio, homogeneity, and consistency. The bricks were formed from a characterized soil/clay mixture and pressed into block using an AECT^® 3500 Series Compressed Earth Block Machine. The bricks were then assembled into walls using a mortar formed from the same sand and soil with the addition of water in a one to three to one ratio by mass, respectively. The geotechnical properties of the adobe bricks were measured and are summarized in the following data. The percentage of gravels, sands, and fines in the bricks are provided in

Table 1. Representative adobe brick composition used during testing.

Gravel
Coarse (%)	Medium (%)	Fine (%)	Total (%)
$0.0$	$0.0$	$0.1$	$0.1$
Sand
Coarse (%)	Medium (%)	Fine (%)	Total (%)
$0.7$	$0.9$	$1.2$	$3.2$
Fines
Silt (%)	Clay (%)		Total (%)
$77.2$	$19.5$		$96.7$

.

2.2. Details of Measurement Procedures

The experimental procedures for sample preparation and complex permittivity measurement are described in detail in what follows. The specific procedures described here are (1) the validation of water content homogeneity within the abode samples, (2) the complex permittivity measurements for the abode samples, and (3) the determination of a representative water content profile for an abode brick.

2.2.1. Validation of Water Content Homogeneity within the Adobe Samples

An adobe sample with uniform water content throughout is required to accurately correlate the measured complex permittivity of the sample to a single adobe water content. The selection of the abode sample size is actually a tradeoff between (1) a sample small enough to sustain a homogeneous moisture and (2) a sample large enough to ensure an accurate complex permittivity measurement (see Section 2.2.2). Adobe samples of a cubic shape with a dry mass in the range of 20 to 40 g were found, through testing, to satisfy the given requirements. The adobe samples were exposed to a controlled (constant) humidity environment in a humidity-controlled chamber [Electro-Tech Systems 5503-11 Benchtop Humidity Chamber, Perkasie, PA, USA]. Oven-dried adobe samples were placed in the humidity chamber for a period of time required for the sample to reach a constant weight for the given humidity level. The adobe samples were then broken into smaller pieces, which were then tested gravimetrically to obtain the water content levels associated with the components. The water content levels of the sample components were found to be within $\pm 0.18\%$ of that for the overall sample. Gravimetric analysis is typically used to measure the material water content, and has been shown to be one of the most accurate methods for water content measurement of solids [12,17,18]. The water content $\mathrm{\Psi }$ is defined

$$\mathrm{\Psi }={\displaystyle \frac{{\mathrm{m}}_{\mathrm{w}}}{{\mathrm{m}}_{\mathrm{d}}+{\mathrm{m}}_{\mathrm{w}}}}\times 100\%$$

(2)

where ${\mathrm{m}}_{\mathrm{w}}$ is the mass of the sample containing water and ${\mathrm{m}}_{\mathrm{d}}$ is the mass of the dried sample. Generally, a sample is dried in an oven at 103–$110°\mathrm{C}$ for an hour and allowed to cool to room temperature in a desiccator. The sample is then heated again for 30 min, allowed to cool, and weighed a second time. The procedure is then repeated until successive weightings agree to within 0.3 mg [18].

To achieve the water content levels presented herein, all adobe samples were first oven dried to their constant weight following common gravimetric analysis procedures [18]. The samples at their constant weight are considered to contain a 0% water content level. Then, the oven dried, constant weight samples are subjected to a constant relative humidity level maintained in an environmental chamber until the samples reach a constant weight for the given humidity level. This allows both maximum water content absorption within the material samples at a given humidity level, in addition to providing a uniform water content profile throughout the sample, which ensures the material assumption of the dielectric measurement procedure. The water content levels achieved at the constant humidity levels for the samples used during the experiments are shown in Figure 1. The overall relationship between the adobe sample water content and the relative humidity of the surrounding environment is nonlinear, especially at high humidity levels. The information in Figure 1 can be used to determine the relative humidity environment required to produce a given adobe sample water content.

2.2.2. Complex Permittivity Measurements

The complex permittivity measurements on the abode samples were collected using a coaxial probe system (Agilent 85070E Dielectric Probe Kit, Santa Clara, CA, USA) in conjunction with Agilent E8362B Network Analyzer, Santa Clara, CA, USA. The dielectric probe kit consists of several open-ended coaxial probes, application software, calibration standards, cables, and adapters. The network analyzer sweeps the transmitted signal in frequency and measures the signal reflected from the probe/sample interface. The software then uses the reflected signal ($S_{11}$) to calculate the complex permittivity. Of the probes included in the dielectric probe kit, the “Slim Form Probe” (Option 030—manufactured by Agilent, Santa Clara, CA, USA) was used for the results presented herein, but it is noted that both the “High Performance Probe” and “High Temperature Probe” were used systematically to confirm measurement consistency across samples [19]. That is, after a set of measurements were conducted, another probe type was calibrated and used to measure different samples in order to verify measurement agreement/consistency. The dimensions of the probes, which operate over a frequency range of 500 MHz to 50 GHz, are shown in Figure 2a. The open-ended coaxial probe is placed in contact with the sample under test, which is assumed to be nonmagnetic, isotropic, and homogeneous. Thus, the adobe samples must have a smooth surface on which to place the probe, which is achieved by cutting the samples with a masonry saw using a diamond blade. This is an important step in the measurement process as adobe brick’s material composition is not well suited for measurement techniques that require high precision during sample preparation such as the transmission line or free space measurement techniques. Adobe samples extracted for water content measurements (described in Section 2.2.3) are shown in Figure 2b to illustrate the “softness” of adobe material and emphasis the necessity for the coaxial probe method of dielectric measurement. To ensure consistent probe-to-sample contact, a probe stand/mounting bracket is employed. The equations used to determine the complex permittivity from the S11 measurement assumes a “semi-infinite” sample size, which translates into a minimum recommended sample thickness equal to the diameter of the probe [19].

The complex permittivity measurements were collected over a frequency range of 500 MHz to 7 GHz using a uniform frequency step of 1 MHz. Prior to each set of measurements, the dielectric probe was calibrated to three known standards (air, water, and a short circuit). Additionally, measurements were taken of two materials with known dielectric properties (i.e., water and Teflon) to validate and monitor measurement accuracy throughout the adobe measurement trial. For each water content level, five abode samples were used with measurements collected at five locations per sample. Thus, the complex permittivity measurements presented here represent the average of 25 distinct measurements for a given water content level.

2.2.3. Measurement of Adobe Brick Water Content Profile

The process for measuring the water content profile of an adobe brick verses depth in an adobe wall is summarized in Figure 3. First, an adobe wall test article is exposed to a constant humidity environment for an extended period (several days). The adobe wall test article considered in this paper was stored in an indoor laboratory prior to the water content profile measurements. An adobe brick near the center of the wall is extracted and cut in half relative to the longest dimension of the brick. The dimensions of the adobe bricks considered in this work are $35.6\times 17.8\times 10.2\mathrm{cm}$. Assuming a TWRI application with normal incidence (wave propagation is in a direction perpendicular to the surface of the wall), the sliced brick exposes an internal surface that can now be measured along the path of wave propagation. Complex permittivity measurements are performed at discrete points along the center-line of the exposed surface in the direction of normal incidence, as shown in (3) of Figure 3. The spacing between the measurement locations is uniform, with the first and last points chosen close to the outer surfaces of the brick. The results of these measurements are a permittivity profile verses depth for the abode brick. By correlating the permittivity measured at the discrete points in the adobe wall to the water content results found in using homogeneous samples of known water content, one obtains the water content profile of the abode wall.

3. Results

A summary of all adobe complex permittivity measurement results are shown in Figure 4 and Figure 5 for the discrete water content levels considered here, which ranged from approximately 0 to $6\%$. The ranges of permittivity and conductivity for a given water content level are presented in horizontal bar-chart format. That is, the horizontal bars indicate the variation of dielectric values measured for a given water content level across the 25 measurements and illustrate adobe’s frequency dispersion. The square and diamond markers on each line represent the mean of the measured values at 500 MHz and 7 GHz. respectively. Note that, in general, the change in the adobe relative permittivity over the range of 500 MHz to 7 GHz is relatively small when compared to the change in the adobe conductivity, demonstrating that the abode water content impacts conductivity more significantly than relative permittivity. The variation in measurements of the adobe relative permittivity and conductivity shown in Figure 4 and Figure 5 can be attributed to limits in the probe accuracy as well as the inherent granular inhomogeneity of the adobe, as defined in Table 1. As the position of the probe on the sample is varied, slightly different percentages of adobe components contribute to each measurement, yielding variations in the measured adobe properties. An accurate homogeneous model for the adobe is found by employing a sufficient number of measurements. Overall, the adobe brick measurements included in these results fall within the typical accuracy of the Agilent probe (${ϵ}^{\prime }={ϵ}^{\prime }\pm 0.05\left|ϵ\right|$) and (${ϵ}^{″}={ϵ}^{″}\pm 0.05\left|ϵ\right|$) [19]. Note that the electric conductivity values measured for brick samples at $0\%$ water content are not displayed as this abode sample falls below the minimum recommended loss tangent of $0.05$ [19].

Least-squares linear regression approximations are applied to the means of the dielectric measurements in order to combat outliers within the measured data and more clearly bring out frequency dependencies. In the case of modeling the adobe wall’s dielectric properties, the linear regression model is of the form

$${\epsilon }_r^i={\beta }_0+{\beta }_1{\mathrm{\Psi }}_i+{\beta }_2{f}_i+{\beta }_3{\mathrm{\Psi }}_i{f}_i$$

(3)

where $\beta$ is the regression coefficients, ${\epsilon }_r^i$ is the relative permittivity, $\mathrm{\Psi }$ is the water content, and f is the frequency of the ith observation (measurement). Similarly, the regression model for electrical conductivity follows the same format, but replacing ${\epsilon }_r^i$ with ${\sigma }^i$ in Equation (3). The regression models of the adobe relative permittivity and electrical conductivity are shown in Figure 6 and Figure 7, respectively, along with uncertainty margins corresponding to the maximum and minimum measured values at each frequency. The regression models follow the expected patterns for the relative permittivity and conductivity verses frequency and water content.

The results for the adobe wall water content profile measurements are summarized in

Table 2. Water content, relative permittivity, and conductivity of the adobe brick as a function of position.

Distance from Brick Edge (cm)	Water Content (%)	${\mathit{\epsilon }}_{\mathit{r}}$ (500 MHz, 7 GHz)	$\mathit{\sigma }$ (S/m) (500 MHz, 7 GHz)
0.1	3.11	4.61, 3.86	0.073, 0.13
2.3	3.09	4.38, 3.74	0.071, 0.11
4.5	3.04	4.23, 3.63	0.069, 0.10
6.7	2.78	3.90, 3.42	0.054, 0.10
8.9	2.56	3.87, 3.35	0.048, 0.075
11.1	2.98	4.00, 3.45	0.062, 0.082
13.3	3.17	4.64, 3.89	0.063, 0.11
15.5	3.22	4.69, 3.92	0.071, 0.12
17.7	3.25	4.70, 3.92	0.075, 0.13

and Figure 8. The individual adobe samples in these measurements, each extracted from the adobe brick, are characterized by a slightly inhomogeneous water content profile. The measured relative permittivity and conductivity for each sample represents that obtained for the slightly inhomogeneous region below the tip of the measurement probe. The water content of the extracted sample represents the average value of the inhomogeneous water content distribution throughout the volume of the sample. As shown in Figure 3, a total of nine samples are used over the 17.8 cm depth of the adobe brick. The nine probe positions are defined relative to the edge of the brick, as given in Table 2. The adobe brick measured water content profile is found to be slightly asymmetric, decreasing with depth into the brick and reaching a minimum value at the center of the brick. The adobe brick relative permittivity and conductivity follow the same pattern as the water content profile verses depth, reaching a minimum value at the brick center for both the minimum frequency of 500 MHz and the maximum frequency of 7 GHz. A comparison of the extracted brick sample measurements and the uniform water content sample measurements shows close agreement for the relative permittivity and conductivity. The relative permittivity and electrical conductivity measurements are plotted in Figure 9, where the square and diamond points represent measurements taken at 500 MHz and 7 GHz, respectively. The vertical lines represent the range of values measured over this frequency and consequently illustrates the frequency dispersion at the relative position in the adobe brick sample. The shape of the water content profile of the adobe brick matches well with the measured dielectric properties and reinforces the necessity of incorporating this information when considering transmission waveforms designed to enhance TWRI applications considering adobe walls.

4. Conclusions

The complex permittivity of adobe has been measured using a coaxial probe system over a frequency range of 500 MHz to 7 GHz and water content from 0% to 6% using samples collected from abode bricks. The geotechnical properties of the compressed earth bricks have been characterized by (1) percentage of gravel, sands, and fines; (2) Atterberg limits; and (3) grain-size distribution. The variation in the adobe complex permittivity verses frequency was measured at discrete levels of water content using small adobe samples exposed to controlled levels of constant humidity in an environmental chamber. The typical water content profile verses depth for an adobe brick has also determined. Future efforts in this work will explore utilization of deep learning techniques such as the use of fuzzy layers that take advantage of characterized materials in improving through-the-wall radar imaging as well as material design applications [21,22].