Extending TDR Capability for Measuring Soil Density and Water Content for Field Condition Monitoring

Within many developed nations there are a large quantity of geotechnical assets (e.g., earth dams, flood levees, embankments and cuttings, and reinforced walls and pavements), many of which may have been constructed decades, if not a hundred or more years, ago. Soil is, by its very nature, a material that tends to form an equilibrium with the surrounding environmental and loading conditions; changes in these conditions can result in changes in the properties of the soil, which in turn can cause deterioration of the properties of the geotechnical asset. For example, changes in climatic and seasonal conditions (i.e., temperature and rainfall) can result in fine-grained soils (which exhibit plasticity) experiencing changes in volume due to the shrink/swell mechanism. Over a number of years, the soil may experience, for example, nonuniform vertical and horizontal movements, changes in fabric structure, changes in physical properties (water content and shear strength parameters), which can result in deterioration of the geotechnical properties of the geotechnical asset (i.e., weakening of a slope resulting in slippage). The deterioration of geotechnical assets can be related, in part, to change in water content with time (Pritchard et al. 2014; Gunn et al. 2015). The water content is an important parameter when considering the behavior of soils due to a number of factors including changes in the three-phase model for the soil, potential changes in volume, changes in the pore water pressure regime leading to changes in effective stress, and hence changes in shear strength. Numerous methods have been developed for measuring the soil water content in the field. Among these, electromagnetic techniques are the most commonly used due to their accuracy, versatility, and lack of radiation hazard compared to other methods (Topp 2003). Replacement of aging geotechnical assets can be prohibitively expensive, hence monitoring and maintenance (when required) is often the preferred option. Traditional monitoring methods (invasive or noninvasive) tend to be discrete in nature (such as installation and surveying of boreholes or use of surface/borehole geophysical techniques), whereas the installation (either during construction of the geotechnical structure or retrofitted) of relatively inexpensive sensors that permit continuous monitoring could offer an attractive alternative when attempting to determine the relative condition of a potentially vulnerable asset. Time domain reflectometry (TDR) has been used to monitor water content in soils for many years, and more recently, a method was developed to investigate the dry density and water content of compacted soils (ASTM-D6780/D6780M).

TDR has been extensively, and successfully, used in the past both in the laboratory and in the field for assessment of water content of the soil [see Noborio (2001), Jones et al. (2002), and Robinson et al. (2003) for an in-depth overview of the TDR technique]. In summary, TDR sends a broadband electromagnetic (EM) pulse in the frequency range between a few MHz and approximately 1 GHz (Friel and Or 1999) across a coaxial transmission line comprising a coaxial cable and a probe. A TDR probe usually consists of an inner metal rod carrying the signal surrounded by one or more outer rods that contain the EM field (Zegelin et al. 1989). Reflections occur whenever there is a change in the EM properties of the material within the sampling volume of the probe and when the cross-sectional geometry of the inner and outer conductors changes (Clarkson et al. 1977; Yanuka et al. 1988; Feng et al. 1999; Lin 2003; Lin and Tang 2007). TDR measures the amplitude and the time of these reflections. The travel time between the reflections occurring at the start and at the end of the TDR probe is related to the complex relative dielectric permittivity of the medium (hereafter the terms relative and dielectric will be omitted for simplicity), and can be used to measure an apparent permittivity, $K_a$, defined by Eq. (1) (Topp et al. 1980)where ${ϵ}_r^{\prime }(f)$ = frequency dependent real permittivity representing the storage of energy through separation of charges; ${\mu }_r$ = relative magnetic permeability; ${ϵ}_p^{″}(f)$ = frequency dependent imaginary permittivity representing the relaxation losses; ${\sigma }_{dc}$ = static electrical conductivity ($\mathrm{S}/\mathrm{m}$); $f$ = frequency of the signal (Hz); and ${ϵ}_0$ = absolute permittivity of free space ($8.854\times {10}^{-12}\mathrm{F}/\mathrm{m}$). Water has a significantly larger permittivity than the other soil constituents (i.e., solid particles and air); therefore, TDR measurements of soil can be used as a proxy for measuring the soil water content (Topp et al. 1980). Many empirical (e.g., Topp et al. 1980; Ledieu et al. 1986; Malicki et al. 1996; Jacobsen and Schjønning 1993; Wensink 1993; Siddiqui and Drnevich 1995; Curtis 2001) and physically based (e.g., Birchak et al. 1974; Dobson et al. 1985; Roth et al. 1990) relationships linking the TDR measured $K_a$ to the soil water content have been described in the literature. However, due to the heterogeneous nature of soils, a universal relationship has not been found that can produce accurate results for every soil. For projects where accuracy is of primary importance, it is therefore still advisable to perform a soil-specific calibration (Thring et al. 2014). TDR has also been shown capable of measuring the low frequency bulk electrical conductivity (BEC, $S/m$) from the attenuation of the signal after reaching a steady-state level (Giese and Tiemann 1975; Topp et al. 2000). Given that TDR measures a volume of soil, it is used to measure the soil volumetric water content. The soil water content, often also called soil moisture, can be defined either as volumetric water content $\theta$ [Eq. (2a)] or as gravimetric water content, $w$ [Eq. (2b)], both usually expressed as percentage by volume and by mass, respectively. The use of one or the other term varies across the disciplines but should always be specified to avoid confusion. In geotechnical engineering, the use of $w$ is preferred because it can be easily and accurately measured in the laboratory using the oven-drying method (BSI 1999b) and can be directly linked to the mechanical behavior of the soil. The volumetric and gravimetric water contents are linked through Eq. (2c)where $V_w$ = volume occupied by the water (${\mathrm{m}}^3$); $V_t$ = total volume of soil investigated (${\mathrm{m}}^3$); $m_w$ = mass of water (g); $m_s$ = mass of soil contained in the investigated sample (g); ${\rho }_d$ = soil dry density, defined as the ratio between $m_s$ and $V_t$ ($\mathrm{Mg}/{\mathrm{m}}^3$); and ${\rho }_w$ = density of the water ($\mathrm{Mg}/{\mathrm{m}}^3$). More recently, TDR was shown capable of measuring the soil ${\rho }_d$ and $w$ and therefore making it more appealing to geotechnical engineers. Thring et al. (2014) proposed simple methods for converting $\theta$ to $w$ by using the information contained in the soil description and other available soil data. Although quick and inexpensive, these methods only provide estimates of these parameters and are unlikely to be as accurate as direct measurements. Siddiqui and Drnevich (1995) proposed a method for measuring both ${\rho }_d$ and $w$ in the field by taking two separate TDR measurements, one in the soil in situ and one in a sample of the soil that has been excavated and compacted in a mold of known volume (for which the soil bulk density could be determined directly on site using a balance). This results in two water content values and one bulk density being obtained; assuming no water loss during the procedure, the method uses the two separate measurements to determine the ${\rho }_d$ and $w$ of the in situ soil. The method was validated by other studies (Lin et al. 2000; Siddiqui et al. 2000) and led to the creation of the ASTM-D6780 standard (ASTM 2003). An improved method was subsequently developed (Yu and Drnevich 2004; Drnevich et al. 2005) that avoided the need for two separate field measurements and did not require the excavation of the soil sample, reducing testing time and effort. For this reason the method has become known as the one-step method and was included in an updated version of the ASTM-D6780 standard (Procedure B, ASTM 2005). This method involves the measurement of $K_a$ and BEC by TDR. As both are related to $w$, if normalized by ${\rho }_d$, they can be used together to determine these parameters following a soil-specific laboratory calibration. The procedure includes a temperature correction, if testing outside the normal room temperature range, and an adjustment of BEC to account for the fact that the pore fluid conductivity of the soil in the field is generally different from the pore fluid conductivity obtained in the laboratory. Despite the one-step method proposed by Yu and Drnevich (2004) typically producing satisfactory results, it has been found to be sensitive to the compactive effort and dependent on the adjustment for BEC, making it potentially less accurate when applied in the field. Independent studies reported satisfactory results in the laboratory but unsatisfactory results in the field that have been attributed to soil disturbance during probe insertion and to theoretical flaws in the adjustment for BEC (Lin et al. 2012). Hence, the method was improved by Jung et al. (2013a, b), who introduced a new type of calibration relationship that was shown to be relatively independent of the compactive effort and produced better accuracy. This method forms the current ASTM-D6780/D6780M (ASTM 2012) standard and is described in more detail in the next section. The main issue with ASTM-D6780/D6780M is that it requires a specific type of TDR probe. If the use of TDR is to be expanded into geotechnical asset monitoring, then it would be much better if it could be used with off-the-shelf probes that are more suitable for burial (three-rod TDR probes can be buried and the surrounding soil more easily compacted). Multiplexers are also necessary in field monitoring applications as multiple TDR probes are likely to be required to monitor a relatively large zone of soil, and these must be connected to the TDR (it would be prohibitively expensive to pair one TDR per probe buried on site). Therefore, the aim of this study was to evaluate the ASTM-D6780/D6780M method using commercially available (and comparatively inexpensive) three-rod TDR probes, with and without the addition of two levels of multiplexers, thus making it much more attractive for long-term field monitoring. It was found that the method was less than ideal in this experimental setup, and an improved method has been developed. This could open up a major avenue of exploitation for the TDR technique, including the long-term condition monitoring of geotechnical assets, such as dams, embankments and other earth structures.

The basis for the current calibration procedure reported in the ASTM-D6780/D6780M standard (ASTM 2012) has been described in detail by Jung et al. (2013a, b). As $K_a$ is directly related to $\theta$ and the conversion factor between $w$ and $\theta$ is the density term ${\rho }_d/{\rho }_w$ [Eq. (2c)], it is appropriate to express the relationship between $K_a$ and $w$ with Eq. (3) (Siddiqui and Drnevich 1995; Siddiqui et al. 2000; Yu and Drnevich 2004; Drnevich et al. 2005). It should be noted that the subscript 1 has been added to the calibration coefficients (i.e., $a_1$ and $b_1$) to indicate the first step of the calibration procedure

A number of authors have demonstrated that the inclusion of a density term improves the relationship between $K_a$ and $\theta$, indicating that this relationship is also affected by the soil density (Ledieu et al. 1986; Roth et al. 1992; Dirksen and Dasberg 1993; Jacobsen and Schjønning 1993; Malicki et al. 1996; Gong et al. 2003; Thring et al. 2014). For this reason, Eq. (3) is thought to be superior compared to other empirical equations relating $K_a$ (or $\surd K_a$) directly to $\theta$ (Siddiqui and Drnevich 1995; Siddiqui et al. 2000; Drnevich et al. 2005). However, to calculate $w$ and $\theta$, a value of ${\rho }_d$ is required. Hence, Jung et al. (2013a) proposed an independent relationship relating a voltage and density normalization term to the $K_a$ measured by TDR and expressed by Eq. (4) (it should be noted that the subscript 1 on the coefficients (i.e., $c_1$, $d_1$, and $f_1$) has been kept the same as in Jung et al. (2013a) for consistency reasons, although this forms the second step of the calibration procedure)where $V_r$ = ratio between the first voltage drop, $V_1$, occurring between the start and the end of the probe [Fig. 1(a)], and the final steady-state voltage level $V_f$ obtained after all the multiple reflections have attenuated [Fig. 1(b)]. By re-arranging Eq. (4) and using the calibrated coefficients $c_1$, $d_1$, $f_1$, the soil ${\rho }_d$ can be calculated and used in Eq. (3) together with the calibrated coefficients $a_1$ and $b_1$ to find $w$. $\theta$ can also be calculated from Eq. (2c). Eqs. (3) and (4) form the first and second step of the calibration procedure proposed by Jung et al. (2013a) and are incorporated in the ASTM-D6780/D6780M standard (ASTM 2012). The methodology was tested on a number of ASTM reference soils and was demonstrated to be a significant improvement over the previous methods developed for the calculation of ${\rho }_d$ and $w$ with TDR. To the knowledge of the authors, this method was only tested using a specifically developed probe, also referred to as multiple rod probe (MRP), originally introduced by Siddiqui and Drnevich (1995) and further described by Siddiqui et al. (2000). This probe design, featuring a detachable head, is well suited to in situ field measurements where repeated insertions and withdrawals are required and has the advantage that it simulates well a coaxial transmission line having one central rod surrounded by three external rods (Zegelin et al. 1989). The MRP was on the market for a limited number of years, but at the present time it cannot be purchased commercially. However, although it can easily be built in a workshop, it would be preferable to be able to use off-the-shelf probes to enable more widespread use of the method. In addition, the application of the calibration procedure using common and inexpensive three-rod TDR probes could potentially extend its applicability to field monitoring (i.e., measurements being taken over a period of time). In fact, probes with two or three parallel rods and with a nondetachable head are more suited to continuous monitoring in the field and have been used extensively by a number of authors (Herkelrath et al. 1991; Delin and Herkelrath 2005; Rajkai and Ryden 1992; Bittelli et al. 2008; Curioni et al. 2017).

The original aim of this study was to test the recently proposed calibration method by Jung et al. (2013a) (i.e., ASTM-D6780/D6780M) using conventional and inexpensive three-rod TDR probes together with multiplexers, which would make the method applicable to continuous field monitoring. However, it was found that this method did not always produce reliable results and was affected by the addition of multiplexers due to the suboptimal performance of the second step of the calibration. Hence, a number of new empirical relationships were tested, and a modification of the current relationship was found to be more suitable for the calibration of ${\rho }_d$. Fig. 4 shows the steps necessary for developing a soil-specific calibration with TDR. Fig. 4(a) shows the standard compaction curves for the soils studied, indicating the wide range of conditions tested. Using the combination of the measured ${\rho }_d$ and $w$ an empirical calibration against $w$ (Step 1) was developed for each soil according to Eq. (3). These results showed some scatter, indicating slightly different relationships depending on the soil type, and demonstrate the need for soil-specific calibrations to obtain better accuracy. In addition, the scatter increased marginally with two levels of multiplexers (mux2) due to the higher uncertainty in the determination of $K_a$. In general, the results from this first step of the calibration were satisfactory, and because Eq. (3) has a theoretical foundation (Siddiqui and Drnevich 1995; Siddiqui et al. 2000; Drnevich et al. 2005), it was not modified in this study. Fig. 4(c) shows the relationship between the voltage and density normalization parameter suggested by Jung et al. (2013a) versus $K_a$. As for Step 1, each soil showed a unique relationship, but significant scattering was present that yielded inaccurate predictions of ${\rho }_d$ and subsequently $w$. The effect of multiplexers is also evident in the results. Both $K_a$ and the voltage ratio $V_r$ were affected by the increased attenuation caused by the use of two levels of multiplexers and therefore produced less accurate results. As mentioned earlier, it was thought that a better relationship with improved precision and accuracy could be developed, which would also reduce the influence of multiplexers. A number of alternative empirical relationships were tested, and the proposed one is expressed by Eq. (7) and shown in Fig. 4(d)where $a_2$, $b_2$, and $c_2$ = calibration coefficients (the subscript 2 was used to indicate the second step of the calibration procedure). Similar to Eq. (4), this relationship makes use of the density and voltage normalization factor and relates it to a quantity consisting of a combination of both $K_a$ and $V_1$ measured by TDR. Although this form was obtained empirically, it is justified by the fact that both $V_1$ and $K_a$ are affected by changes in ${\rho }_d$. The use of the squared root of $K_a$ and $V_1$ was found to improve the accuracy of the relationship. Previous authors showed that $V_1$ increases with increasing ${\rho }_d$ while keeping $w$ constant (Yu and Drnevich 2004; Jung et al. 2013a) and improved calibrations between $\theta$ and $K_a$ (or between $\theta$ and $\surd K_a$) have been reported by several authors (e.g., Ledieu et al. 1986; Dirksen and Dasberg 1993; Jacobsen and Schjønning 1993; Malicki et al. 1996; Thring et al. 2014), demonstrating that $K_a$ is indeed affected by ${\rho }_d$. For a given $w$, $K_a$ is expected to increase slightly with increasing ${\rho }_d$ due to the reduced volume occupied by air (Gong et al. 2003). Similar to Jung et al. (2013a), a physical constraint (i.e., $V_1=0$ in air) was added to the model and was found to further improve the results. Therefore, the relationship was simplified by setting the coefficient $a_2$ equal to zero. The remaining coefficients $b_2$ and $c_2$ were obtained by minimizing the sum of squares of the differences between measured and calculated values using Eq. (7). Table 2 shows the calibrated coefficients for the soils studied using Eqs. (3), (4), and (7). Due to the limited nature of the data sets involved, the proposed equation was derived empirically, rather than probabilistically, although simple statistical approaches (such as curve fitting using $R^2$ values) were used. It is noted that an empirical approach was previously successfully used when developing ASTM-D6780/D6780M [i.e., Eq. (4)] and is commonly used when deriving relationships that apply to the behavior of soils. The proposed equation was selected because it yielded robust results (based on $R^2$ values and performance during cross-validation) and due to its simplicity; it only requires two unknown coefficients, $b_2$ and $c_2$, after constraining $a_2$ to zero. The number of unknown coefficients and the curvature of this equation were small compared to other models, and this made the method more robust and less dependent on the number of data points used to develop it. This is a clear practical advantage over other models. Fig. 5 shows the second step of the calibration relationship for all the soils from the current data set using the Jung et al. (2013a) method [Eq. (4)] and the new modified relationship [Eq. (7)]. Eq. (7) demonstrated an improvement compared to Eq. (4), with a reduced effect due to multiplexers and a better fit to the data. As will be discussed later, it was also found that Eq. (7) was more robust and less dependent on the number of data points used for the calibration than Eq. (4). By re-arranging Eq. (7), ${\rho }_d$ can be calculated using Eq. (8)

Once the ${\rho }_d$ measured by TDR is known, $w$ can be obtained by rearranging Eq. (3) into Eq. (9)

The aim of this investigation was to determine if TDR could be used in long-term geotechnical asset condition monitoring. For this to be suitable, the probes would have to be relatively inexpensive and survive burial without compromising the reinstatement of the ground (presumably via compaction). In addition, it is envisaged that multiple probes would require burial and, to ensure the system is cost effective, multiplexers would be required. It was apparent from the outcomes of this study (investigating a range of fine-grained soils using commercially available three-rod TDR probes and, in certain tests, two levels of multiplexers) that the method reported in ASTM-D6780/D6780M (specifically, the second step of the method) did not provide very consistent results and was affected by the addition of the multiplexers. Thus, if TDR is to be used in long-term geotechnical asset condition monitoring, the TDR methods for determining both water content and dry density would have to be modified. A new modified relationship has been proposed that replaces Step 2 of the calibration in ASTM-D6780/D6780M. This yields improved precision and accuracy and is less affected by the use of multiplexers. The typical accuracy for the investigated soils was to within an error of $\pm 5\%$ for ${\rho }_d$, and $\pm 2\%$ for $w$, both with and without multiplexers, although occasionally larger errors were measured, but these were still consistently smaller than the errors produced by ASTM-D6780/D6780M. It has been confirmed that the TDR parameters must be corrected for temperature to improve the accuracy; therefore, temperature sensors should be employed alongside the TDR probes when attempting to monitor the relative condition of geotechnical assets with TDR. The TDR probes and multiplexers used in this study are commercially available and well suited to field monitoring, thus it is believed that the proposed relationship could extend the potential uses of TDR to geotechnical applications for monitoring of geotechnical assets (such as earth dams, embankments, and slopes), and as such has provided a significant avenue for further exploitation of this technique.

The authors would like to thank the UK’s Engineering and Physical Sciences Research Council (EPSRC) and the “Assessing the Underworld” (ATU) project (Grant No. EP/KP021699/1) for the financial support provided and the University of Birmingham for access to soil samples and testing equipment. Special thanks go to the technicians of the Civil Engineering laboratories for their essential support.