Experimental Study on the Soil Electrical Conductivity and Dielectric Constant Properties

Experimental Study on the Soil Electrical Conductivity and Dielectric Constant Properties | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Experimental Study on the Soil Electrical Conductivity and Dielectric Constant Properties Fei Wang, Shuang Nie, Qunfang Hu, Yuankang Mao, Qian Hai, Yanghe Liu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6187477/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Wireless monitoring can effectively enhance the operational safety of underground infrastructures. The electrical conductivity and dielectric constant of soil determine the transmission performance of buried wireless signals. To solve the problem of wireless monitoring signal transmission of underground infrastructure, the variation patterns of soil electrical conductivity and dielectric constant need to be explored. In this study, the effect of different particle size distribution, water content, and dry density on soil conductivity and dielectric constant were investigated by experiments. And the existing soil water content-resistivity and soil water content-dielectric constant models were evaluated and analyzed. The results show that both soil conductivity and dielectric constant increase with increasing water content and soil dry density, but the rate of increase first increases and then decreases with the increase of water content. Due to the varying complexity of surface charges on soils with different particle sizes, the high content of clay and silt with small particle size is helpful to improve soil conductivity and dielectric constant, while the increase of sand content with large particle size leads to the decrease of both. And the sensitivity analysis revealed that soil particle size distribution significantly affects the water content-resistivity and water content-dielectric constant relationship, whereas the impact of dry density is minimal. Based on the experimental data, the existing relational models were evaluated and analyzed. The median particle size (D50) is incorporated into the empirical model to elucidate the physical significance of the model parameters and to develop modified models. The modified models were validated using published data, demonstrating their good accuracy. Soil Electrical Conductivity Dielectric Constant Underground wireless signals Transmission medium modified model Figures Figure 1 Figure 2 Figure 3 Figure 5 Figure 6 Figure 7 Figure 10 Figure 11 1 Introduction Underground wireless monitoring can enhance the operational safety of underground infrastructures such as pipelines and tunnels(2013; Sun et al., 2011 ). The key to acquiring underground facilities monitoring data is in the transmission performance of wireless signals through the soil. Soil electrical conductivity (or resistivity) and dielectric constant are the primary integrated parameters that influence wireless signal propagation in the soil. The dielectric constant of soil is a physical quantity used to characterize the dielectric properties or polarization rate of soil. It is always expressed as a relative dielectric constant, which is the ratio of the real part of the dielectric constant to the vacuum dielectric constant (Xu et al., 2022 ). The dielectric constant mentioned in this paper is also the relative dielectric constant. Soil electrical conductivity and dielectric constant are mainly affected by the properties of the soil such as composition, particle size distribution, water content, and dry density(Akyildiz and Stuntebeck, 2006 ; Corwin and Scudiero, 2016 ; Liu, 2015 ). Therefore, to ensure the effective transmission of wireless monitoring data for underground facilities, it is necessary to explore the variation patterns of electrical conductivity and dielectric constant of soil. Currently, some studies have been conducted on the electrical conductivity and dielectric constant of soil, and revealing some laws. The water content in the soil is the most important factor affecting the soil electrical conductivity and dielectric constant, which will gradually increase with the increase in volume water content (Wei et al., 2013; Xu et al., 2022 ). However, the impact of bound water and free water on electrical conductivity and dielectric constant in soil differs significantly, with the influence of bound water being far less pronounced than that of free water (Boyarskii et al., 2002 ; Chang-Hwan et al., 2017 ). For the conduction of current in soil, there are three pathways, which are Solid, Fluid, and Air. The fluid path provides the main contribution to the flow of electric current(Rhoades et al., 1999 ). When water occupies most of the pores in the soil and is connected, the conductivity will increase significantly. In addition, the different particle size contents in the soil also have a significant impact on the soil electrical properties (electrical conductivity and dielectric constant). Clay and silt have a larger specific surface area, and thus they have a higher charge density, which will lead to an increase in the conductivity of soil(Jayawickreme et al., 2010 ; Seladji et al., 2010). The sand particles have larger grain size than clay and silt, resulting in a high porosity of the soil, and the connectivity between the pores is poor, which reduces the mobility of water and dissolved ions in the soil (Soil), thereby decreasing the electrical conductivity. Additionally, Clays and silt possess fine particle structure, in which small pores can retain more water, increasing the overall water content of the soil, thus enhancing the dielectric constant of the soil (Kabir et al., 2020 ). The compaction of soil particles significantly affects dielectric properties. As the dry density increases, the spacing between soil particles decreases, thereby influencing the polarization of the electric field at the particle surfaces(Xu et al., 2022 ). Water content is the primary factor affecting both conductivity and dielectric constant, therefore, many empirical models have been proposed for soil water content-resistivity and water content-dielectric constant relationship (Archie and G., 1942; Celano et al., 2011 ; Herkelrath et al., 1991 ; Liao et al., 2016 ; Malicki et al., 1996 ; Melo et al., 2021 ; Topp et al., 1980 ; Zhao and Ling, 2016 ), which include the Power model and the Topp model etc. However, the coefficients of these models need to be obtained through fitting experimental data, and their physical meanings are not well understood, making practical application difficult. Soils with different particle size distribution have different charge density and water retention capabilities(Jayawickreme et al., 2010 ; Seladji et al., 2010), and changes in soil dry density can lead to alterations in soil porosity and the arrangement of soil particles. Thus the particle size distribution and dry density of the soil may also have a significant impact on soil water content-resistivity and water content-dielectric constant relationship. Therefore, it is necessary to quantitatively test the effects of soil particle distribution, dry density, and moisture content on soil conductivity and dielectric constant, and to evaluate existing moisture content-conductivity and moisture content-dielectric constant relationship models. And soil particle distribution and dry density will be incorporated into the models to elucidate the physical meanings of the parameters and their impact on the moisture content-conductivity and moisture content-dielectric constant relationships. Ultimately, modified models will be obtained and validated using published data. In this study, the effects of different soil particle distribution, water contents, and dry densities on soil electrical conductivity and dielectric constant were investigated. And the intrinsic mechanisms underlying the variations were analyzed. Additionally, Experimental data was used to evaluate and analyze existing relationship models, and to modify the models, clarifying the physical meanings of the parameters. Finally, the modified models were validated using published data. This provides theoretical support for the application of the models in predictive analysis of target values 2 Experimental Procedure 2.1 Soil sample The properties of different soil layers vary, which can have varying degrees of impact on wireless signal transmission. Therefore, this study investigates soils from layers at different depths. Additionally, according to previous research, the salt concentration of ordinary sites varies slightly(Zhu et al., 2007 ). Therefore, this study adopts the factors with significant influence to explore the electrical properties of soil, including soil particle distribution, dry density, and water content. Two types of soil were obtained from the depth of 0.5 m and 1.5 m near the Weichang River Road in Pudong New Area of Shanghai, and three different particle distributions of soil were prepared by using dry river sand. The soil samples were air-dried and passed through a 2mm sieve to remove impurities, and then the soil samples were placed in a 101-2 type electric thermostatic drying oven for drying, with the drying temperature set at 105°C. The soil treatment process is shown in Fig. 1 . And the specific drying steps are as follows: i. Place the screened and impurity-free soil samples into multiple aluminum dishes; ii. Turn on the drying oven, set the temperature and time, preheat the drying oven, and wait for the drying oven to reach the required temperature; iii. Place the prepared soil samples into the preheated drying oven, ensuring they are evenly distributed in the drying oven to ensure uniform drying; iv. Close the drying oven and start the drying process according to the preset temperature and time; v. Regularly check the state of the soil samples during the drying process to ensure they are neither over-dried nor under-dried; vi. When the drying time is up, turn off the drying oven, remove the soil samples, and let them cool to room temperature to avoid absorbing moisture. The particle size distribution of dried samples was then measured by using laser particle size analyzer (Malvern Mastersizer 2000). The specific soil particle size distribution is shown in Table 1 . The specific water content and density settings are shown in Table 2 . Due to differences in soil types, there are significant variations in soil porosity and particle weight. And the texture and density of the soil are interrelated and cannot be separated independently, so the density of different types of soils is set separately(Topp et al., 1980 ). Table 1 Soil particle size distribution < 0.002mm (%) 0.002-0.05mm (%) 0.05-2.0mm (%) Soil 1 8.31 55.36 36.34 Soil 2 12.89 79.38 7.74 Soil 3 4.80 39.18 56.02 Soil 4 2.62 21.38 76.01 Soil 5 0 0 100 Table 2 Water content and density configuration Dry density(g/cm³) water content(%) Soil 1 1.16 5 10 15 20 25 30 35 40 45 50 55 60 1.22 1.28 Soil 2 1.11 1.17 1.22 Soil 3 1.29 1.35 1.42 Soil 4 1.30 1.36 1.43 Soil 5 1.29 1.35 1.42 2.2 Test method The Time Domain Reflectometry (TDR) technology was used to measure soil water content, when the soil water content reaches its maximum value (i.e., saturation), continuing to add water will result in the measured water content being lower than the actual water content. The excess water will become free water, forming standing water on the soil surface or draining out through gravity. Therefore, the change of water content measured will reduce. Thus, when the increase in the measured water content significantly decreases with the addition of actual water, it is determined that the soil has reached saturation. The specific steps for using TDR to measure soil water content are as follows: i. Insert the TDR probe into the soil to measure the initial water content; ii. Slowly add water and observe whether the readings change until the soil is saturated; iii. Record the water content of each measurement. The process of adding water should be uniform and slow to ensure that the moisture penetrates evenly into the soil. By following these steps, the soil saturation water content is confirmed. In this study, the HydraGO Flex device (See Fig. 2 ) was used to measure conductivity and dielectric constant. The HydraGO Flex is a portable soil dielectric constant and conductivity measurement instrument that measures the real part (true dielectric constant) and the imaginary part (dielectric loss factor) of the soil dielectric constant through its built-in HydraProbe probe. The core measurement principle is based on the Frequency Domain Reflectometry (FDR), which is a technique for measuring soil dielectric properties. The device emits electromagnetic waves of a certain frequency (50 MHz) from the probe, and the electrodes on the probe generate an electromagnetic field around the surrounding soil. The electrodes sense the reflected electromagnetic signals from the soil, allowing the probe to obtain the amplitude attenuation and phase shift of the reflected waves. The Phase shift provides information about the dielectric loss factor, while amplitude variation is related to the actual dielectric constant. Based on this, the soil's dielectric constant (including both the real and imaginary parts) can be calculated. The real dielectric constant (ε') reflects the ability of water molecules in the soil to store electromagnetic wave energy. It is directly related to soil water content, because water molecules can be polarized and respond to changes in the electric field. The imaginary dielectric constant (ε'') also known as the dielectric loss factor, represents the soil's ability to dissipate electromagnetic wave energy. This value is related to the soil's conductivity and frequency, reflecting the energy loss caused by the movement of water and other ions in the soil. Among them, the imaginary dielectric constant (ε'') is related to the soil's conductive characteristics, and the volumetric conductivity (𝜎) is calculated based on the imaginary dielectric constant: σ = 2 πfϵ 0 ε'' (1) Where 𝑓 is electromagnetic wave frequency, 𝜖 0 is permittivity of vacuum. ε'' is imaginary part of the dielectric constant. Test steps (See Fig. 3): i. Insert the probe of HydraGo Flex vertically into the test soil; ii. Then start the device, and the probe will automatically send and receive electromagnetic waves, and record the characteristics of the reflected waves. The built-in software processes the data in real-time according to preset algorithms, then outputting the measured results of permittivity and conductivity. Communication with smart devices is achieved via Bluetooth, and data reading and recording are done using a dedicated application. 3 Results and Discussion 3.1 Soil saturation water content The water content measured by the TDR350 and the actual added water are shown in Fig. 4. When the soil water content reaches the maximum value (saturated state), adding more water will result in the measured water content being lower than the actual water content, thus the point at which the actual water content begins to change from the measured water content is considered the saturation point of the soil. The saturated water contents of Soil 1 and Soil 2 are 50%; the saturated water content of Soil 3 is 45%, and that of Soil 4 is approximately 45%, while the saturated water content of Soil 5 is approximately 35%. 3.2 Electrical conductivity 3.2.1 Effect of water content and dry density Figure 5 shows the change of soil conductivity with the increase of water content and dry density. It can be seen from the figure that the conductivity increases with the increase of water content, which is because the current conduction in the soil is mainly relies on the movement of ions in the pore water, and the ions that transport the charge are derived from the ionization of salt in the soil (Rhoades et al., 1999 ). Therefore, the current conduction in the soil mainly depends on the water content in the pores(Samoulian et al., 2005 ). When the water content increases from 0% to about 30%, the increase rate in electrical conductivity is increase. While when the water content increases from about 30%, the rate of increase becomes decrease. This is because when the water content is below about 30%, initially water in the soil mainly adheres to the surface of soil particles in the form of film, and the electrical conductivity is affected by the thickness of the bound water film (Roodposhti et al., 2019 ). At low moisture content, these films are thin and the conductive paths are discontinuous, resulting in lower efficiency of charge transfer. Additionally, there is more air in the soil pores and relatively less water, and air is a poor conductor, which will adversely affect soil conductivity. With water content increases, the thickness of the water film on the surface of soil particles increases, which leads to higher conductivity. However, at low moisture content, a continuous water phase has not yet formed. As water content continues to increase, the amount of free water in the soil pores gradually increases, a continuous water phase will be formed. Consequently, the growth rate of conductivity increases. Under these water content conditions, not only does the water cover the surface of the soil particles, but it also fills the pores, greatly increasing the overall conductivity of the soil. When the water content increases to a certain extent, the conductivity tends to reach its maximum value. This is because the dissolved ions in the soil water (pore water) are the carriers of electric current conduction. With the water in the soil increases, the content of dissolved ions generally also increases, thereby improving the conductivity. However, when the saturated water content is reached, even if more moisture is added, the concentration of dissolved ions may not change significantly. Figure 5 also shows the effect of soil dry density on electrical conductivity under different soil types and water contents. It can be seen from the figure that the effect of water content on electrical conductivity is greater than that of dry soil density, which is consistent with previous research (Melo et al., 2021 ). As the dry density increases, the electrical conductivity increases slightly. This is mainly because water in the soil is primarily distributed as a film on the surface of the soil particles. For soils with higher density, the contact between soil particles is more compact, which means that the water film forms more continuous channels between the particles. These continuous water film channels facilitate the transport of charges, thereby increasing the electrical conductivity. Additionally, soil particles with higher density are more compact and have fewer pores, and the water in these pores can form more effective conductive paths. Compared to low water content, when the water content is higher, the electrical conductivity of soils with different dry densities shows greater differences. This indicates that the effect of dry density on electrical conductivity is related to the water content of the soil, and this effect is more significant at high water contents. 3.2.2 Effect of soil particle distribution Figure 6 shows the distribution of electrical conductivity for different soil particle distribution under various water contents. In Soil 1, Soil 2, and Soil 3, the clay and silt content are relatively higher compared to Soil 4 and Soil 5, and their electrical conductivities are also very close. However, when the water content exceeds 30%, the electrical conductivity of Soil 2 reaches maximum value. This is primarily due to the higher clay and silt content compared to the other soils. And clay and silt have a larger specific surface area, thus resulting in a higher charge density, which leads to an increase in the conductivity of the soil samples (Jayawickreme et al., 2010 ; Seladji et al., 2010). The conductivity of Soil 4 and Soil 5 is significantly lower than that of other soil samples. This is primarily because the sand particles are larger, resulting in a higher soil porosity and poor connectivity between the pores. This structure reduces the mobility of water and dissolved ions within the soil, thereby decreasing the electrical conductivity. Additionally, the sand in the soil has "very low" water absorption capacity, the silt has "low" water absorption capacity, and the clay has "medium" water absorption capacity (Soil), which means that sandy soil generally has poor water retention capacity, and the water easily leaks between the particles. Since the electrical conductivity depends on the concentration of ions in the water, the low water retention capacity will directly affect the electrical conductivity. Moreover, due to the larger specific surface area of clay, the charges on the surface of clay particles result in higher electrical conductivity compared to coarse-textured soils. (Minato, 1999 ; Samoulian et al., 2005 ). That is why sand shows a lower conductivity. 3.2.3 Model analysis Conductivity can also be expressed by resistivity, which are reciprocals of each other. Relationship models are typically expressed as the relationship between water content and resistivity. Archie et al. proposed an empirical relationship (power model, See Eq. 2 ) based on laboratory measurements of resistivity-water content for clean sandstone samples(Archie and G., 1942). This relationship has been successfully used in many studies to estimate soil water content using resistivity(Binley et al., 2002 ; Zhou et al., 2001 ). In addition, the commonly used models for the relationship between soil resistivity and water content include exponential models and logarithmic models (See Eqs. 3 and 4 )(Melo et al., 2021 ). $$\theta ={\text{ }}a\cdot {\rho ^b}$$ 2 $$\theta ={\text{ }}c\cdot exp\left( {\rho d} \right)$$ 3 $$\theta ={\text{ }}e+f\cdot lo{g_{10}}\left( \rho \right)$$ 4 Where a, b, c, d, e, f are the fitting parameters of the model, ρ is the resistivity, θ is water content. Despite the belief that the power model may not be suitable for clay (Calamita et al., 2012 ), numerous experimental studies have found that the power model is still the best statistical model to describe the relationship between resistivity and water content(Celano et al., 2011 ; Melo et al., 2021 ). This study also used experimental data to fit and evaluate the model (see Fig. 7). It was found that the power function model was most applicable with the best fitting degree, with a goodness-of-fit of over 0.9, the goodness-of-fit of logarithmic model is about 0.892, while the exponential model did not converge during the fitting process. From the fitting curves of different soils, it can be seen that although the power function model has a good goodness-of-fit, the fitting parameters are different for different soil particle content. In other words, although the power function model is suitable for the relationship between soil conductivity and water content, the parameters still need to be fitted and determined through experimental data, and the physical meaning is unclear, which makes the equation difficult to understand and apply. The parameters in the power model reflect the total parameter of all factors affecting soil resistivity except for soil water content (Hadzick et al., 2011 ), among which the change of different soil particle content has the most obvious impact from Fig. 5 and Fig. 7. Therefore, based on the experimental data of this study, incorporating soil particle distribution into the formula. The primary reason soil particles affect the model relationship is that different particle sizes result in varying amounts of surface charge (Jayawickreme et al., 2010 ; Seladji et al., 2010). Therefore, the particle distribution is represented by the mean particle diameter D50. D50 represents the particle size at which 50% of the soil particles are smaller by weight. For simplification, we calculate D50 through the proportions of clay, silt, and sand. Assuming that D50 is the weighted average of these three components, it can be calculated using the following Eq. 5 $${D_{50}}=\frac{{{P_{clay}}\cdot {D_{clay}}+{P_{silt}}\cdot {D_{silt}}+{P_{sand}}\cdot {D_{sand}}}}{{{P_{clay}}+{P_{silt}}+{P_{sand}}}}$$ 5 Where P clay , P silt , and P sand represent the content of clay, silt, and sand, respectively. D clay , D silt , and D sand represent the characteristic particle diameters of clay, silt, and sand, respectively, which are 0.002 mm, 0.050 mm, and 0.5 mm. Based on the experimental data, the revised formula is refitted and presented as Eq. 6 . This equation eliminates parameters and quantifies the impact of soil particle size distribution on the model relationship. $$\theta =(235.55 - 10.01\cdot D50)\cdot {\rho ^{( - 0.73+0.16\cdot D50)}}$$ 6 From Table 3 , the goodness of fit for the experimental data exceeds 0.9. Additionally, the revised formula was validated using published data(Celano et al., 2011 ; David et al., 2018), yielding goodness of fit values of 0.709 and 0.824, respectively. The results indicate that the revised relationship model effectively explains the relationship between the physical quantities. Table 3 Fitting results Soil sample Clay (%) Sand (%) Silt (%) D50 R 2 Soil 1 8.31 36.34 55.36 0.210 0.9719 Soil 2 12.89 7.74 79.38 0.079 0.9661 Soil 3 4.80 56.02 39.18 0.300 0.9774 Soil 4 2.62 76.01 21.38 0.391 0.9799 Soil 5 0 100 0 0.500 0.9809 Celano et al. 14.11 64.16 21.73 0.332 0.709 Bertermann et al. 20 10 70 0.085 0.824 3.3 Dielectric constant 3.3.1 Effect of water content and dry density For soil, the dielectric constant is mainly determined by the relative dielectric constants of soil solid particles, water, and air. Among them, the dielectric constant of water (approximately 80) is much higher than that of soil solids (approximately 2–5) and air (approximately 1)(Lu et al., 2016 ). As shown in Fig. 8, the dielectric constant of dry soil is small, and with the water content increases, the dielectric constant increases. It also can be seen from the figure that the water content in soil is the main factor affecting the dielectric properties of soil. When the water content is low, water exists in the form of bound water, and the dielectric constant of bound water is much smaller than that of free water (Hongjian et al., 2019 ). And the dielectric constant of water is dependent on the thickness of the water film covering soil particles (Boyarskii et al., 2002 ). As the thickness of the water film on soil particles increases, the average dielectric constant of the entire aqueous phase (bound water and free water) continues to increase (Friedman and Shmulik, 1998). Although soil particles form the basic framework of the soil, their dielectric constants are less affected by the soil itself. With the water content further increases, the dielectric properties of bound water in the soil approach those of free water, and the polarization of free water increases (Boyarskii et al., 2002 ; Xu et al., 2022 ), causing a significant increase in the dielectric constant. When the water content increases from 0–20%, the rate of increase of dielectric constant is relatively small, while when the water content increases from 20–40%, the rate of increase becomes larger. This is because when the water content is below 20%, during the low water content stage, the water in the soil is mainly distributed as a thin film on the surface of the particles or fills small pores (Boyarskii et al., 2002 ), which limits the contribution of water to the overall dielectric constant. Due to the limited amount of water, the dielectric properties of the soil are more influenced by solid particles and air. Therefore, even with the water content gradually increases, the increase of the dielectric constant is relatively slow. However, when the water content exceeds 20%, more free water accumulates in the soil pores. This free water not only covers the surface of the particles but also fills larger pores, water content becomes the main factor affecting the dielectric constant. At this stage, the high dielectric constant of water significantly increases its contribution to the overall dielectric constant. As the water content continues to increase, the volume and contact area of free water with soil particles also increase significantly, thereby accelerating the rate of increase in the dielectric constant. Figure 8 also shows the effect of soil dry density on the dielectric constant under different soil types and water contents. As dry density increases, the dielectric constant increases. The decrease in pores and increase in particle contact area due to the increase in dry density cause the free water to be compressed to the surface of the soil (Xu et al., 2022 ), leading to an increase of the dielectric constant. Additionally, when the dry density of the soil increases, the content of solid particles per unit volume increases. Soil particles, especially those containing minerals, generally have a higher dielectric constant than air or gases in pores. Furthermore, with the dry density increases, the contact between soil particles becomes more compact, which enhances the efficiency of charge transfer between particles. The dense arrangement of particles enhances the dielectric properties because the electric field is more continuous among soil particles, reducing disruptions in the electric field. 3.3.2 Effect of soil particle distribution Figure 9 illustrates the effect of soil particle distribution on the dielectric constant. It can be seen from the figure that when the water content is high, soil 2 has a relatively large dielectric constant. This is mainly because soil 2 contains more silt and clay. Due to their fine particle, silt and clay can retain more water in smaller pores, increasing the overall water content of the soil, thereby enhancing the dielectric constant of the soil. In addition, silt and clay particles usually carry more surface charges, which can increase the charge distribution and complexity in the soil, thereby enhancing the dielectric response of the soil. When water as a dielectric, these charge characteristics can enhance the dielectric effect, especially under high water content conditions. On the other hand, the dielectric constant of soil 5 (sand) is relatively low. The dielectric properties of sand are significantly lower than those of other soils, this is mainly due to the fact that sand consists of relatively large particles with larger pores. The larger particles reduce the contact area of particles per unit volume, thereby reducing the electric field interactions between particles (Kabir et al., 2020 ). Additionally, sand has weaker adsorption and retention capabilities for water due to its larger particles and lower specific surface area. Under natural conditions with low water content, there is relatively less water in the sand, so the contribution of water to the dielectric constant is limited. Water is one of the main factors that increase the dielectric constant. A lack of sufficient water means that the dielectric constant will remain at a low level. 3.3.3 Model analysis Based on previous research, scholars have proposed many models for soil water content-dielectric constant relationships, which are mainly divided into empirical models (C. et al., 1992; Ren-peng et al., 2008 ). This study collected commonly used existing models as shown in Table 4 . And these existing models are evaluated the based on experimental data. The results are shown in Fig. 10. From the figure, it can be seen that all types of models perform well, with a goodness-of-fit of over 0.9. However, similar to conductivity, the model parameters also need to be obtained through fitting experimental data, thus the model cannot be directly applied. Table 4 Model comparison Model Expression R 2 Topp model(Topp et al., 1980 ) \(\theta ={\text{ }}a+b\varepsilon +c{\varepsilon ^2}+d{\varepsilon ^3}\) 0.97573 Herkelrath model(Herkelrath et al., 1991 ) \(\theta ={\text{ }}\frac{{\left( {\sqrt \varepsilon - b} \right)}}{a}\) 0.96844 Malicki model(Malicki et al., 1996 ) \(\theta =\frac{{\sqrt \varepsilon +a+b{\rho _d}+c{\rho _d}^{2}}}{{d+e{\rho _d}}}\) 0.97783 Zhao model(Zhao and Ling, 2016 ) \(\theta =\frac{{a+\sqrt \varepsilon }}{{b+c\sqrt \varepsilon }}\) 0.97460 Liao model(Liao et al., 2016 ) \(\theta =alg\left( {\varepsilon /b} \right)\) 0.93205 Where θ is water content, ε is dielectric constant, ρ d is dry density From the Fig. 11a, it can be seen that there is an obvious distribution area for the dielectric constant-water content scatter plot, and the upper boundary of the distribution area is θ=-8.7434 + 3.18847 x -0.08522 x 2 + 0.0011 x 3 , lower boundary is θ=-11.35287 + 3.03801* x -0.07804 x 2 + 0.00087961 x 3 . As the water content increases, the distribution range of the relative dielectric constant also expands. This is mainly due to the coupled effects of water content, soil particle content, and dry density. An increase in dry density and water content helps to increase the dielectric constant, while an increase of sand particle content leads to a decrease in the dielectric constant. The distribution area shows a clear pattern of change as the water content increases. By fitting the distribution width-water content relationship, a quantitative law for the variation of regional width with water content was obtained, as shown in Fig. 11b. Since the distribution area is influenced by multiple factors, a sensitivity analysis of the factors affecting the dielectric constant distribution area is conducted. To ensure that variables with different dimensions can be directly compared, the data is standardized. Standardization refers to the process of calculating the standardized value 𝑥′ of a variable 𝑥 in a given dataset 𝑋 using the formula 𝑥′ = (𝑥 − 𝜇) / 𝜎, where 𝑥 is the original data value, 𝜇 is the mean of variable 𝑥, 𝜎 is the standard deviation of variable 𝑥, and 𝑥′ is the standardized data value. After standardization, the mean of each variable is 0 and the standard deviation is 1. Then, a multivariate linear regression model is constructed using the standardized data, with the goal of predicting the width of the distribution range (difference G ). The form of the regression model is as follows: $$G={\beta _0}+{\beta _1}\cdot {P_{clay}}+{\beta _2}\cdot {P_{silt}}+{\beta _3}\cdot {P_{sand}}+{\beta _4}\cdot D+{\beta _5}\cdot {P_{water}}+\sigma$$ 7 Where P clay , P silt , P sand , P water are clay content, silt content, sand content, water content, D is the density, β 0 is the constant term, β1, β2, β3, β4, and β5 are the regression coefficients of the respective variables, and σ is the error term. The regression coefficients of each variable were obtained through a regression model. To evaluate the sensitivity of each factor, the standardized regression coefficient (SRC) is calculated using the following formula: $$SRC{\text{ }}=\frac{{{\beta _i} \times {\text{ }}std\left( {{X_i}} \right)}}{{std\left( Y \right)}}$$ 8 where β i is the regression coefficient, std( X i ) is the standard deviation of the ith independent variable, and std( Y ) is the standard deviation of the dependent variable. The analysis results are shown in Table 5 . The standardized regression coefficient for water content is 0.831, indicating that changes in water content have a significant impact on the difference, and it is the most influential factor. Silt content (-0.140) and sand content (0.110) also have some impact on the difference, but much less than water content. The impact of density (0.092) and clay content (-0.082) is relatively small. Through sensitivity analysis, it was found that water content has the greatest impact on the difference, followed by silt content and sand content. The impact of clay content and density is relatively small. Table 5 Regression coefficient Table of influencing factors Influencing factors Standardized regression coefficient clay content -0.082 silt content -0.140 sand content 0.110 density 0.092 water content 0.831 The increase in water content has a significant impact on the dielectric constant distribution, and it may change the effect of soil particle size distribution and dry density. However, the results obtained through linear regression analysis alone cannot fully explain this interaction effect. Therefore, a regression model that includes interaction terms is constructed. By adding interaction terms to the regression model, the interaction effect between two variables is evaluated. The interaction effects between water content and clay content, silt content, sand content, and dry density are considered separately to construct the following regression model: G = β 0 + β 1 × P clay + β 2 × P silt + β 3 × P sand + β 4 × D + β 5 × P water + β 6 × ( P water × P clay ) + β 7 × ( P water × P silt ) + β 8 × ( P water × P sand ) + β 9 × ( P water × D ) + σ (9) To ensure that variables with different units can be directly compared, data normalization is performed first. Through the above model, the regression coefficients of each interaction term can be interpreted. Water content-Clay Content evaluates the interaction effect between water content and clay content; Water content-Silt Content evaluates the interaction effect between water content and silt content; Water content-Sand Content evaluates the interaction effect between water content and sand content; Water content-Density evaluates the interaction effect between water content and dry density. The larger the standardized regression coefficient, the more significant the impact of the interaction term on the dependent variable. The results are shown in Table 6 . Table 6 Standardized regression coefficients for factor interactions Influencing factors Standardized regression coefficient Water content - Clay Content -7.164689e-10 Water content - Silt Content -2.825982e-08 Water content - Sand Content -4.390623e-08 Water content - Density -2.966624e-14 The standardized regression coefficients for water content and sand content (-4.390623e-08) and water content and silt content (-2.825982e-08) are negative and relatively large, indicating a significant negative interaction effect between water content and sand content and silt content. The standardized regression coefficients for water content and clay content (-7.164689e-10) and water content and density (-2.966624e-14) are smaller, indicating that these interaction effects are weaker. The interaction effects indicate that an increase in water content will weaken the impact of sand content and silt content on the difference. This means that under higher water content conditions, the contribution of sand and silt content to the distribution area will decrease. The direct effects of clay content and density are relatively small, and their interaction with water content is also not significant. Through analysis, it is evident that particle size distribution is the primary factor affecting the distribution of dielectric constants. Therefore, the Herkelrath model with good goodness of fit is used as the foundation, incorporating the influence of particle size distribution into the model, resulting in the following revised model: $$\theta =\frac{{\sqrt \varepsilon - (b0+b1 \times D50)}}{{a0+a1 \times D50}}$$ 10 Where a 0 = 0.1084, a 1 =-0.00001145, b 0 = 0.901, b 1 = 0.0018. The goodness of fit (R²) for the experimental data using this model exceeds 0.8 (show in Table 7 ). Additionally, the model was validated with published data(Jin et al., 2020 ), achieving goodness of fit values also above 0.8, confirming the reliability of the model. Table 7 Fitting results soil sample Clay (%) Silt (%) Sand (%) D50 R 2 Soil 1 8.31 36.34 55.36 0.210 0.9079 Soil 2 12.89 7.74 79.38 0.079 0.8085 Soil 3 4.80 56.02 39.18 0.300 0.9519 Soil 4 2.62 76.01 21.38 0.391 0.9840 Soil 5 0 100 0 0.500 0.9547 Published data 1 13.43 35.06 51.51 0.275 0.9215 Published data 2 8.53 49.51 41.96 0.235 0.8993 Published data 3 13.48 55.89 30.63 0.181 0.9033 Published data 4 19 63.84 17.16 0.118 0.8755 Published data 5 47.38 47.6 5.02 0.050 0.8373 Conclusion This study investigates the variations in soil properties that affect the transmission of underground wireless signals. Specifically, the effects of different particle size distribution, water content, and dry density on soil electrical conductivity and dielectric constant were investigated by experiments, and revealing the underlying mechanisms under the variation of influencing factors. Additionally, the existing soil water content-resistivity and water content-dielectric constant relationship models are evaluated and modified. The main conclusions are as follows: (1) Soil electrical conductivity and dielectric constant both increase with increasing water content and dry density, but the rate of increase first rises and then decreases as water content increases. (2) High clay and silt content can improve soil electrical conductivity and dielectric constant, while an increase in sand content leads to a decrease in both properties. (3) Water content is the main factor affecting the distribution of dielectric constants. An increase in water content weakens the impact of sand and silt content on the dielectric constant distribution range. Under high water content conditions, the contribution of sand and silt content to the distribution range decreases. The direct impact of clay content and density is relatively small, and their interaction with water content is not significant. (4) Through experimental data, models for water content-resistivity and water content-dielectric constant relationships were evaluated and modified. By incorporating D50 into the model parameters, the physical meanings of the parameters were clarified, and a modified model was obtained. The validity of the model was then verified using published data. The findings provide a theoretical basis for the application of wireless monitoring in underground structures, thereby facilitating the optimization of wireless signal propagation prediction and practical implementation. Declarations Funding This work was supported by the National Key R&D Program of China (Grant No.2022YFC3801000) and Shanghai “Science and Technology Innovation Action Plan” project (Grant No.22dz1200402, and Grant No.22dz1201200). Author Contribution Fei Wang and Shuang Nie conceived the idea and drafted the manuscript. Qunfang Hu secured the funding. Qunfang Hu, Yuankang Mao, Qian Hai, and Yanghe Liu revised the manuscript. All authors reviewed the manuscript. References Wireless Sensor Networks for Leakage Detection in Underground Pipelines: A Survey Paper. Procedia Computer Science 2013; 21: 491-498. Akyildiz IF, Stuntebeck EP. Wireless underground sensor networks: Research challenges. Ad Hoc Networks 2006; 4: 669-686. Archie, G. E. The electrical resistivity log as an aid in determining some reservoir characteristics. Transactions of the Aime 1942; 146: 54-62. Binley A, Cassiani G, Middleton R, Winship P. Vadose zone flow model parameterisation using cross-borehole radar and resistivity imaging. Journal of Hydrology 2002; 267: 147-159. Boyarskii DA, Tikhonov VV, Komarova NY. Model of Dielectric Constant of Bound Water in Soil for Applications of Microwave Remote Sensing - Abstract. Journal of Electromagnetic Waves & Applications 2002; 16: 411-412. C., H., ROTH, M., A., MALICKI, et al. Empirical evaluation of the relationship between soil dielectric constant and volumetric water content as the basis for calibrating soil moisture measurements by TDR. Journal of Soil Science 1992; 43: 1-13. Calamita G, Brocca L, Perrone A, Piscitelli S, Lapenna V, Melone F, Moramarco T. Electrical resistivity and TDR methods for soil moisture estimation in central Italy test-sites. Journal of Hydrology 2012; 454-455: 101-112. Celano, Palese, AM, Ciucci, Martorella, Vignozzi, Xiloyannis. Evaluation of soil water content in tilled and cover-cropped olive orchards by the geoelectrical technique. GEODERMA 2011; 2011,163(3-4): 163-170. Chang-Hwan P, Andreas B, Ellsworth LD, Volker W. New Approach for Calculating the Effective Dielectric Constant of the Moist Soil for Microwaves. Remote Sensing 2017; 9: 732. Corwin DL, Scudiero E. Field-scale Apparent Soil Electrical Conductivity. Methods of Soil Analysis 2016. David, Bertermann, Hans, Schwarz. Bulk density and water content-dependent electrical resistivity analyses of different soil classes on a laboratory scale. Environmental Earth Sciences 2018. Friedman, Shmulik P. A saturation degree-dependent composite spheres model for describing the effective dielectric constant of unsaturated porous media. Water Resources Research 1998; 34: 2949-2961. Hadzick ZZ, Guber AK, Pachepsky YA, Hill RL. Pedotransfer functions in soil electrical resistivity estimation. Geoderma 2011; 164: 195-202. Herkelrath WN, Hamburg SP, Murphy F. Automatic, Real-Time Monitoring of Soil Moisture in a Remote Field Area With Time Domain Reflectometry. Water Resources Research 1991; 27: 857-864. Hongjian, Liao, Huan, Dong, Chunming, Ning, et al. A new logarithmic dielectric constant model of soils. Japanese Geotechnical Society Special Publication 2019; 7: 281-286. Jayawickreme DH, Van Dam RL, Hyndman DW. Hydrological consequences of land-cover change: Quantifying the influence of plants on soil moisture with time-lapse electrical resistivity. Geophysics 2010; 75: WA43-WA50. Jin X, Yang W, Gao X, Li Z. Analysis and Modeling of the Complex Dielectric Constant of Bound Water with Application in Soil Microwave Remote Sensing. Remote Sensing 2020; 12: 3544. Kabir H, Khan MJ, Brodie G, Gupta D, Antunes E. Measurement and modelling of soil dielectric properties as a function of soil class and moisture content. Journal of Microwave Power & Electromagnetic Energy A Publication of the International Microwave Power Institute 2020: 1-16. Liao HJ, Sun JY, Zan YW, Zhu QN, Gu F. Dielectric constant model for soil and its application in engineering. Chinese Journal of Geotechnical Engineering 2016. Liu F. Electrical Conductivity in Soils: A Review. 2015. Lu H, Jiang W, Zhao Y, Zeng Z. Relationship between volumetric water content and effective dielectric permittivity of Nanning expansive soil. Rock and Soil Mechanics 2016; 37: 2145-2150. Malicki MA, Plagge R, Roth CH. Improving the calibration of dielectric TDR soil moisture determination taking into account the solid soil. European Journal of Soil Science 1996; 47. Melo LBBD, Silva BM, Peixoto DS, Chiarini TAP, Curi N. Effect of compaction on the relationship between electrical resistivity and soil water content in Oxisol. Soil and Tillage Research 2021; 208: 104876. Minato MF. The micro-structures of clay given by resistivity measurements. Engineering Geology 1999; 54. Ren-peng, CHEN1, Yun-min, CHEN1, Wei, XU1, et al. A new equation for dielectric permittivity of saturated soils based on polarization mechanics. Journal of Zhejiang University 2008. Rhoades JD, Corwin DL, Lesch SM. Geospatial Measurements of Soil Electrical Conductivity to Assess Soil Salinity and Diffuse Salt Loading from Irrigation: Assessment of Non-Point Source Pollution in the Vadose Zone, 1999. Roodposhti HR, Hafizi MK, Kermani MRS, Nik MRG. Electrical resistivity method for water content and compaction evaluation, a laboratory test on construction material. Journal of Applied Geophysics 2019; 168: 49-58. Samoulian A, Cousin I, Tabbagh A, Bruand A, Richard G. Electrical resistivity survey in soil science: a review. Elsevier 2005. Seladji, Cosenza, Tabbagh, Ranger, Richard. The effect of compaction on soil electrical resistivity:a laboratory investigation. EUR J SOIL SCI 2010. Soil D. testing procedures and testing equipment—determination of water absorption. Sun Z, Wang P, Vuran MC, Al-Rodhaan MA, Al-Dhelaan AM, Akyildiz I. MISE-PIPE: Magnetic induction-based wireless sensor networks for underground pipeline monitoring. Ad Hoc Networks 2011; 9: 218-227. Topp GC, Davis JL, Annan AP. Electromagnetic determination of soil water content: Measurements in coaxial transmission lines. Water Resources Research 1980; 16: 574-582. Wei, Bai, Lingwei, Kong, Aiguo, Guo. Effects of physical properties on electrical conductivity of compacted lateritic soil. Journal of Rock Mechanics and Geotechnical Engineering 2013. Xu XQ, Wang HJ, Qu X, Li C, Cai B, Peng GC. Study on the dielectric properties and dielectric constant model of laterite. Frontiers in Earth Science 2022; 10. Zhao Y, Ling DS. Study on a calibration equation for soil water content in field tests using time domain reflectometry. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering) 2016; 17: 240-252. Zhou QY, Shimada J, Sato A. Three-dimensional spatial and temporal monitoring of soil water content using electrical resistivity tomography. Water Resources Research 2001; 37: 273-285. Zhu JJ, Kang HZ, Gonda Y. Application of Wenner Configuration to Estimate Soil Water Content in Pine Plantations on Sandy Land. PEDOSPHERE 2007; 17: 12. Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6187477","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":427139169,"identity":"21a6eb52-f6f3-4946-97be-33e4b00452da","order_by":0,"name":"Fei Wang","email":"","orcid":"","institution":"Tongji University","correspondingAuthor":false,"prefix":"","firstName":"Fei","middleName":"","lastName":"Wang","suffix":""},{"id":427139170,"identity":"3f4d1625-4fd9-4016-8e1d-3d3875765c51","order_by":1,"name":"Shuang Nie","email":"","orcid":"","institution":"Tongji University","correspondingAuthor":false,"prefix":"","firstName":"Shuang","middleName":"","lastName":"Nie","suffix":""},{"id":427139171,"identity":"1384066d-796c-444d-b72c-09da0294adaf","order_by":2,"name":"Qunfang Hu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA1ElEQVRIiWNgGAWjYBACAzBpYwPhJDAwMDYQpyUtTYJkLYclYAKEtZhLJG+TLkg4X8cv3X6h4AGDjeyGA8zPHuDTYjkjrUx6RsJtCck5ZwqADksz3nCAzdwAr8Nu5JhJ8/64LQFkJAC1HE7ccICHTYKgFp6EczAt/4nWcgCoJf0AUMsBIrSceVZszZOQLDlzRg4wkA2SjWceZjPDr+V48sbbPAl2/PwS6c8Mf1TYyfYdb36GVwsDLGoYGHjMDMBsZgLqkbSwP35AWPEoGAWjYBSMRAAAYNVHJL3xYXwAAAAASUVORK5CYII=","orcid":"","institution":"Tongji University","correspondingAuthor":true,"prefix":"","firstName":"Qunfang","middleName":"","lastName":"Hu","suffix":""},{"id":427139172,"identity":"267eeb83-be60-4b72-ad94-00b1d6445078","order_by":3,"name":"Yuankang Mao","email":"","orcid":"","institution":"Tongji University","correspondingAuthor":false,"prefix":"","firstName":"Yuankang","middleName":"","lastName":"Mao","suffix":""},{"id":427139173,"identity":"b6bea012-5f3c-4218-afe0-1be98a55df4a","order_by":4,"name":"Qian Hai","email":"","orcid":"","institution":"Tongji University","correspondingAuthor":false,"prefix":"","firstName":"Qian","middleName":"","lastName":"Hai","suffix":""},{"id":427139174,"identity":"429b755c-40c5-4834-a40a-328ff36cfd9d","order_by":5,"name":"Yanghe Liu","email":"","orcid":"","institution":"Tongji University","correspondingAuthor":false,"prefix":"","firstName":"Yanghe","middleName":"","lastName":"Liu","suffix":""}],"badges":[],"createdAt":"2025-03-09 08:08:14","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6187477/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6187477/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":78416334,"identity":"2d940fac-1e0b-40d1-8063-e99bb4e82123","added_by":"auto","created_at":"2025-03-13 04:49:18","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":346473,"visible":true,"origin":"","legend":"\u003cp\u003eSoil treatment\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-6187477/v1/884831c0b2888181c4002695.png"},{"id":78416332,"identity":"64218224-3e74-475a-8011-257287867bd8","added_by":"auto","created_at":"2025-03-13 04:49:18","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":118312,"visible":true,"origin":"","legend":"\u003cp\u003eHydraGo Flex（HydraGo Flex probe 6cm）\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-6187477/v1/54ed31cca60d7bf0065f8501.png"},{"id":78417429,"identity":"4d8decf6-4734-45b6-ba2c-1fc80a57cbab","added_by":"auto","created_at":"2025-03-13 05:05:18","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":568068,"visible":true,"origin":"","legend":"\u003cp\u003ea: Soil sample; b: Soil conductivity and dielectric constant test\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-6187477/v1/bee5566e94dd1f132fddaa1a.png"},{"id":78416335,"identity":"17d7fb6e-8011-428d-9fec-c755a9a7b164","added_by":"auto","created_at":"2025-03-13 04:49:18","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":114108,"visible":true,"origin":"","legend":"\u003cp\u003eSoil Electrical Conductivity a: Soil 1, b: Soil 2, c: Soil 3, d: Soil 4, and e: Soil\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-6187477/v1/1bcdb3d169cab0edbe5da65f.png"},{"id":78417191,"identity":"46078200-0f4c-411c-ac2b-e108cf0f7aa7","added_by":"auto","created_at":"2025-03-13 04:57:18","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":19483,"visible":true,"origin":"","legend":"\u003cp\u003eConductivity of different soil types\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-6187477/v1/1e0fb50932b0e7674d1273ed.png"},{"id":78416339,"identity":"5bdd4b49-8407-4071-94e7-2bb4e9ca10f4","added_by":"auto","created_at":"2025-03-13 04:49:18","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":68075,"visible":true,"origin":"","legend":"\u003cp\u003eFitting Relationship a: Soil 1, b: Soil 2, c: Soil 3, d: Soil 4, and e: Soil 5\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-6187477/v1/881d3fa3a23b7e9439abf80d.png"},{"id":78417437,"identity":"3017c4e5-1309-4274-9ea3-72b871b478bd","added_by":"auto","created_at":"2025-03-13 05:05:19","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":68697,"visible":true,"origin":"","legend":"\u003cp\u003eModel comparison a: Topp model, b: Herkelrath model, c: Zhao model, d: Liao model, e: Liao model\u003c/p\u003e","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-6187477/v1/827feaf461a9d7483a7b79b3.png"},{"id":78417431,"identity":"9f8a0ead-7630-4cb1-b886-b1538f69640e","added_by":"auto","created_at":"2025-03-13 05:05:18","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":28020,"visible":true,"origin":"","legend":"\u003cp\u003ea: Dielectric constant distribution range; b: Relationship between distribution width and water content.\u003c/p\u003e","description":"","filename":"11.png","url":"https://assets-eu.researchsquare.com/files/rs-6187477/v1/7ce8191eb0297a60b5e771a6.png"},{"id":87285668,"identity":"4f30ae9a-c239-4cd3-81bc-e57792aa0e14","added_by":"auto","created_at":"2025-07-22 10:32:01","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2377922,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6187477/v1/a0fed0b2-590f-4e4a-9717-a6fe79505411.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Experimental Study on the Soil Electrical Conductivity and Dielectric Constant Properties","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eUnderground wireless monitoring can enhance the operational safety of underground infrastructures such as pipelines and tunnels(2013; Sun et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2011\u003c/span\u003e). The key to acquiring underground facilities monitoring data is in the transmission performance of wireless signals through the soil. Soil electrical conductivity (or resistivity) and dielectric constant are the primary integrated parameters that influence wireless signal propagation in the soil. The dielectric constant of soil is a physical quantity used to characterize the dielectric properties or polarization rate of soil. It is always expressed as a relative dielectric constant, which is the ratio of the real part of the dielectric constant to the vacuum dielectric constant (Xu et al., \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). The dielectric constant mentioned in this paper is also the relative dielectric constant. Soil electrical conductivity and dielectric constant are mainly affected by the properties of the soil such as composition, particle size distribution, water content, and dry density(Akyildiz and Stuntebeck, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2006\u003c/span\u003e; Corwin and Scudiero, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Liu, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). Therefore, to ensure the effective transmission of wireless monitoring data for underground facilities, it is necessary to explore the variation patterns of electrical conductivity and dielectric constant of soil.\u003c/p\u003e \u003cp\u003eCurrently, some studies have been conducted on the electrical conductivity and dielectric constant of soil, and revealing some laws. The water content in the soil is the most important factor affecting the soil electrical conductivity and dielectric constant, which will gradually increase with the increase in volume water content (Wei et al., 2013; Xu et al., \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). However, the impact of bound water and free water on electrical conductivity and dielectric constant in soil differs significantly, with the influence of bound water being far less pronounced than that of free water (Boyarskii et al., \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2002\u003c/span\u003e; Chang-Hwan et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). For the conduction of current in soil, there are three pathways, which are Solid, Fluid, and Air. The fluid path provides the main contribution to the flow of electric current(Rhoades et al., \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e1999\u003c/span\u003e). When water occupies most of the pores in the soil and is connected, the conductivity will increase significantly. In addition, the different particle size contents in the soil also have a significant impact on the soil electrical properties (electrical conductivity and dielectric constant). Clay and silt have a larger specific surface area, and thus they have a higher charge density, which will lead to an increase in the conductivity of soil(Jayawickreme et al., \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; Seladji et al., 2010). The sand particles have larger grain size than clay and silt, resulting in a high porosity of the soil, and the connectivity between the pores is poor, which reduces the mobility of water and dissolved ions in the soil (Soil), thereby decreasing the electrical conductivity. Additionally, Clays and silt possess fine particle structure, in which small pores can retain more water, increasing the overall water content of the soil, thus enhancing the dielectric constant of the soil (Kabir et al., \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). The compaction of soil particles significantly affects dielectric properties. As the dry density increases, the spacing between soil particles decreases, thereby influencing the polarization of the electric field at the particle surfaces(Xu et al., \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Water content is the primary factor affecting both conductivity and dielectric constant, therefore, many empirical models have been proposed for soil water content-resistivity and water content-dielectric constant relationship (Archie and G., 1942; Celano et al., \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; Herkelrath et al., \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e1991\u003c/span\u003e; Liao et al., \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Malicki et al., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e1996\u003c/span\u003e; Melo et al., \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Topp et al., \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e1980\u003c/span\u003e; Zhao and Ling, \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2016\u003c/span\u003e), which include the Power model and the Topp model etc. However, the coefficients of these models need to be obtained through fitting experimental data, and their physical meanings are not well understood, making practical application difficult.\u003c/p\u003e \u003cp\u003eSoils with different particle size distribution have different charge density and water retention capabilities(Jayawickreme et al., \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; Seladji et al., 2010), and changes in soil dry density can lead to alterations in soil porosity and the arrangement of soil particles. Thus the particle size distribution and dry density of the soil may also have a significant impact on soil water content-resistivity and water content-dielectric constant relationship. Therefore, it is necessary to quantitatively test the effects of soil particle distribution, dry density, and moisture content on soil conductivity and dielectric constant, and to evaluate existing moisture content-conductivity and moisture content-dielectric constant relationship models. And soil particle distribution and dry density will be incorporated into the models to elucidate the physical meanings of the parameters and their impact on the moisture content-conductivity and moisture content-dielectric constant relationships. Ultimately, modified models will be obtained and validated using published data.\u003c/p\u003e \u003cp\u003eIn this study, the effects of different soil particle distribution, water contents, and dry densities on soil electrical conductivity and dielectric constant were investigated. And the intrinsic mechanisms underlying the variations were analyzed. Additionally, Experimental data was used to evaluate and analyze existing relationship models, and to modify the models, clarifying the physical meanings of the parameters. Finally, the modified models were validated using published data. This provides theoretical support for the application of the models in predictive analysis of target values\u003c/p\u003e"},{"header":"2 Experimental Procedure","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Soil sample\u003c/h2\u003e \u003cp\u003eThe properties of different soil layers vary, which can have varying degrees of impact on wireless signal transmission. Therefore, this study investigates soils from layers at different depths. Additionally, according to previous research, the salt concentration of ordinary sites varies slightly(Zhu et al., \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2007\u003c/span\u003e). Therefore, this study adopts the factors with significant influence to explore the electrical properties of soil, including soil particle distribution, dry density, and water content. Two types of soil were obtained from the depth of 0.5 m and 1.5 m near the Weichang River Road in Pudong New Area of Shanghai, and three different particle distributions of soil were prepared by using dry river sand. The soil samples were air-dried and passed through a 2mm sieve to remove impurities, and then the soil samples were placed in a 101-2 type electric thermostatic drying oven for drying, with the drying temperature set at 105\u0026deg;C. The soil treatment process is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. And the specific drying steps are as follows: i. Place the screened and impurity-free soil samples into multiple aluminum dishes; ii. Turn on the drying oven, set the temperature and time, preheat the drying oven, and wait for the drying oven to reach the required temperature; iii. Place the prepared soil samples into the preheated drying oven, ensuring they are evenly distributed in the drying oven to ensure uniform drying; iv. Close the drying oven and start the drying process according to the preset temperature and time; v. Regularly check the state of the soil samples during the drying process to ensure they are neither over-dried nor under-dried; vi. When the drying time is up, turn off the drying oven, remove the soil samples, and let them cool to room temperature to avoid absorbing moisture. The particle size distribution of dried samples was then measured by using laser particle size analyzer (Malvern Mastersizer 2000). The specific soil particle size distribution is shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. The specific water content and density settings are shown in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. Due to differences in soil types, there are significant variations in soil porosity and particle weight. And the texture and density of the soil are interrelated and cannot be separated independently, so the density of different types of soils is set separately(Topp et al., \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e1980\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eSoil particle size distribution\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.002mm (%)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.002-0.05mm (%)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.05-2.0mm (%)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSoil 1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e8.31\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e55.36\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e36.34\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSoil 2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e12.89\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e79.38\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e7.74\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSoil 3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4.80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e39.18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e56.02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSoil 4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2.62\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e21.38\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e76.01\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSoil 5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eWater content and density configuration\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"15\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c12\" colnum=\"12\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c13\" colnum=\"13\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c14\" colnum=\"14\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c15\" colnum=\"15\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colspan=\"1\" nameend=\"c4\" namest=\"c2\"\u003e \u003cp\u003eDry density(g/cm\u0026sup3;)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"13\" nameend=\"c15\" namest=\"c5\"\u003e \u003cp\u003ewater content(%)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eSoil 1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\" morerows=\"14\" rowspan=\"15\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" morerows=\"14\" nameend=\"c5\" namest=\"c4\" rowspan=\"15\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\" morerows=\"14\" rowspan=\"15\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\" morerows=\"14\" rowspan=\"15\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\" morerows=\"14\" rowspan=\"15\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\" morerows=\"14\" rowspan=\"15\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\" morerows=\"14\" rowspan=\"15\"\u003e \u003cp\u003e35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\" morerows=\"14\" rowspan=\"15\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\" morerows=\"14\" rowspan=\"15\"\u003e \u003cp\u003e45\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\" morerows=\"14\" rowspan=\"15\"\u003e \u003cp\u003e50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\" morerows=\"14\" rowspan=\"15\"\u003e \u003cp\u003e55\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\" morerows=\"14\" rowspan=\"15\"\u003e \u003cp\u003e60\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.22\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.28\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eSoil 2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.11\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.17\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.22\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eSoil 3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.29\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.35\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.42\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eSoil 4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.30\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.36\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.43\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eSoil 5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.29\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.35\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.42\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Test method\u003c/h2\u003e \u003cp\u003eThe Time Domain Reflectometry (TDR) technology was used to measure soil water content, when the soil water content reaches its maximum value (i.e., saturation), continuing to add water will result in the measured water content being lower than the actual water content. The excess water will become free water, forming standing water on the soil surface or draining out through gravity. Therefore, the change of water content measured will reduce. Thus, when the increase in the measured water content significantly decreases with the addition of actual water, it is determined that the soil has reached saturation. The specific steps for using TDR to measure soil water content are as follows: i. Insert the TDR probe into the soil to measure the initial water content; ii. Slowly add water and observe whether the readings change until the soil is saturated; iii. Record the water content of each measurement. The process of adding water should be uniform and slow to ensure that the moisture penetrates evenly into the soil. By following these steps, the soil saturation water content is confirmed.\u003c/p\u003e \u003cp\u003eIn this study, the HydraGO Flex device (See Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e) was used to measure conductivity and dielectric constant. The HydraGO Flex is a portable soil dielectric constant and conductivity measurement instrument that measures the real part (true dielectric constant) and the imaginary part (dielectric loss factor) of the soil dielectric constant through its built-in HydraProbe probe. The core measurement principle is based on the Frequency Domain Reflectometry (FDR), which is a technique for measuring soil dielectric properties. The device emits electromagnetic waves of a certain frequency (50 MHz) from the probe, and the electrodes on the probe generate an electromagnetic field around the surrounding soil. The electrodes sense the reflected electromagnetic signals from the soil, allowing the probe to obtain the amplitude attenuation and phase shift of the reflected waves. The Phase shift provides information about the dielectric loss factor, while amplitude variation is related to the actual dielectric constant. Based on this, the soil's dielectric constant (including both the real and imaginary parts) can be calculated. The real dielectric constant (ε') reflects the ability of water molecules in the soil to store electromagnetic wave energy. It is directly related to soil water content, because water molecules can be polarized and respond to changes in the electric field. The imaginary dielectric constant (ε'') also known as the dielectric loss factor, represents the soil's ability to dissipate electromagnetic wave energy. This value is related to the soil's conductivity and frequency, reflecting the energy loss caused by the movement of water and other ions in the soil. Among them, the imaginary dielectric constant (ε'') is related to the soil's conductive characteristics, and the volumetric conductivity (\u0026#120590;) is calculated based on the imaginary dielectric constant:\u003c/p\u003e \u003cp\u003e \u003cem\u003eσ\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2\u003cem\u003eπfϵ\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e\u003cem\u003eε''\u003c/em\u003e (1)\u003c/p\u003e \u003cp\u003eWhere \u0026#119891; is electromagnetic wave frequency, \u0026#120598;\u003csub\u003e0\u003c/sub\u003e is permittivity of vacuum. ε'' is imaginary part of the dielectric constant.\u003c/p\u003e \u003cp\u003eTest steps (See Fig.\u0026nbsp;3): i. Insert the probe of HydraGo Flex vertically into the test soil; ii. Then start the device, and the probe will automatically send and receive electromagnetic waves, and record the characteristics of the reflected waves. The built-in software processes the data in real-time according to preset algorithms, then outputting the measured results of permittivity and conductivity. Communication with smart devices is achieved via Bluetooth, and data reading and recording are done using a dedicated application.\u003c/p\u003e "},{"header":"3 Results and Discussion","content":"\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Soil saturation water content\u003c/h2\u003e \u003cp\u003eThe water content measured by the TDR350 and the actual added water are shown in Fig.\u0026nbsp;4. When the soil water content reaches the maximum value (saturated state), adding more water will result in the measured water content being lower than the actual water content, thus the point at which the actual water content begins to change from the measured water content is considered the saturation point of the soil. The saturated water contents of Soil 1 and Soil 2 are 50%; the saturated water content of Soil 3 is 45%, and that of Soil 4 is approximately 45%, while the saturated water content of Soil 5 is approximately 35%.\u003c/p\u003e\u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Electrical conductivity\u003c/h2\u003e \u003cdiv id=\"Sec8\" class=\"Section3\"\u003e \u003ch2\u003e3.2.1 Effect of water content and dry density\u003c/h2\u003e \u003cp\u003eFigure\u0026nbsp;5 shows the change of soil conductivity with the increase of water content and dry density. It can be seen from the figure that the conductivity increases with the increase of water content, which is because the current conduction in the soil is mainly relies on the movement of ions in the pore water, and the ions that transport the charge are derived from the ionization of salt in the soil (Rhoades et al., \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e1999\u003c/span\u003e). Therefore, the current conduction in the soil mainly depends on the water content in the pores(Samoulian et al., \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2005\u003c/span\u003e). When the water content increases from 0% to about 30%, the increase rate in electrical conductivity is increase. While when the water content increases from about 30%, the rate of increase becomes decrease. This is because when the water content is below about 30%, initially water in the soil mainly adheres to the surface of soil particles in the form of film, and the electrical conductivity is affected by the thickness of the bound water film (Roodposhti et al., \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). At low moisture content, these films are thin and the conductive paths are discontinuous, resulting in lower efficiency of charge transfer. Additionally, there is more air in the soil pores and relatively less water, and air is a poor conductor, which will adversely affect soil conductivity. With water content increases, the thickness of the water film on the surface of soil particles increases, which leads to higher conductivity. However, at low moisture content, a continuous water phase has not yet formed. As water content continues to increase, the amount of free water in the soil pores gradually increases, a continuous water phase will be formed. Consequently, the growth rate of conductivity increases. Under these water content conditions, not only does the water cover the surface of the soil particles, but it also fills the pores, greatly increasing the overall conductivity of the soil. When the water content increases to a certain extent, the conductivity tends to reach its maximum value. This is because the dissolved ions in the soil water (pore water) are the carriers of electric current conduction. With the water in the soil increases, the content of dissolved ions generally also increases, thereby improving the conductivity. However, when the saturated water content is reached, even if more moisture is added, the concentration of dissolved ions may not change significantly.\u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;5 also shows the effect of soil dry density on electrical conductivity under different soil types and water contents. It can be seen from the figure that the effect of water content on electrical conductivity is greater than that of dry soil density, which is consistent with previous research (Melo et al., \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). As the dry density increases, the electrical conductivity increases slightly. This is mainly because water in the soil is primarily distributed as a film on the surface of the soil particles. For soils with higher density, the contact between soil particles is more compact, which means that the water film forms more continuous channels between the particles. These continuous water film channels facilitate the transport of charges, thereby increasing the electrical conductivity. Additionally, soil particles with higher density are more compact and have fewer pores, and the water in these pores can form more effective conductive paths. Compared to low water content, when the water content is higher, the electrical conductivity of soils with different dry densities shows greater differences. This indicates that the effect of dry density on electrical conductivity is related to the water content of the soil, and this effect is more significant at high water contents.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section3\"\u003e \u003ch2\u003e3.2.2 Effect of soil particle distribution\u003c/h2\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e6\u003c/span\u003e shows the distribution of electrical conductivity for different soil particle distribution under various water contents. In Soil 1, Soil 2, and Soil 3, the clay and silt content are relatively higher compared to Soil 4 and Soil 5, and their electrical conductivities are also very close. However, when the water content exceeds 30%, the electrical conductivity of Soil 2 reaches maximum value. This is primarily due to the higher clay and silt content compared to the other soils. And clay and silt have a larger specific surface area, thus resulting in a higher charge density, which leads to an increase in the conductivity of the soil samples (Jayawickreme et al., \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; Seladji et al., 2010). The conductivity of Soil 4 and Soil 5 is significantly lower than that of other soil samples. This is primarily because the sand particles are larger, resulting in a higher soil porosity and poor connectivity between the pores. This structure reduces the mobility of water and dissolved ions within the soil, thereby decreasing the electrical conductivity. Additionally, the sand in the soil has \"very low\" water absorption capacity, the silt has \"low\" water absorption capacity, and the clay has \"medium\" water absorption capacity (Soil), which means that sandy soil generally has poor water retention capacity, and the water easily leaks between the particles. Since the electrical conductivity depends on the concentration of ions in the water, the low water retention capacity will directly affect the electrical conductivity. Moreover, due to the larger specific surface area of clay, the charges on the surface of clay particles result in higher electrical conductivity compared to coarse-textured soils. (Minato, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e1999\u003c/span\u003e; Samoulian et al., \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2005\u003c/span\u003e). That is why sand shows a lower conductivity.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section3\"\u003e \u003ch2\u003e3.2.3 Model analysis\u003c/h2\u003e \u003cp\u003eConductivity can also be expressed by resistivity, which are reciprocals of each other. Relationship models are typically expressed as the relationship between water content and resistivity. Archie et al. proposed an empirical relationship (power model, See Eq.\u0026nbsp;\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e2\u003c/span\u003e) based on laboratory measurements of resistivity-water content for clean sandstone samples(Archie and G., 1942). This relationship has been successfully used in many studies to estimate soil water content using resistivity(Binley et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2002\u003c/span\u003e; Zhou et al., \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2001\u003c/span\u003e). In addition, the commonly used models for the relationship between soil resistivity and water content include exponential models and logarithmic models (See Eqs.\u0026nbsp;\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e3\u003c/span\u003e and \u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e4\u003c/span\u003e)(Melo et al., \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\theta ={\\text{ }}a\\cdot {\\rho ^b}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\theta ={\\text{ }}c\\cdot exp\\left( {\\rho d} \\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\theta ={\\text{ }}e+f\\cdot lo{g_{10}}\\left( \\rho \\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003cp\u003e\u003c/p\u003e \u003cp\u003eWhere a, b, c, d, e, f are the fitting parameters of the model, \u003cem\u003eρ\u003c/em\u003e is the resistivity, \u003cem\u003eθ\u003c/em\u003e is water content.\u003c/p\u003e \u003cp\u003eDespite the belief that the power model may not be suitable for clay (Calamita et al., \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2012\u003c/span\u003e), numerous experimental studies have found that the power model is still the best statistical model to describe the relationship between resistivity and water content(Celano et al., \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; Melo et al., \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). This study also used experimental data to fit and evaluate the model (see Fig.\u0026nbsp;7). It was found that the power function model was most applicable with the best fitting degree, with a goodness-of-fit of over 0.9, the goodness-of-fit of logarithmic model is about 0.892, while the exponential model did not converge during the fitting process. From the fitting curves of different soils, it can be seen that although the power function model has a good goodness-of-fit, the fitting parameters are different for different soil particle content. In other words, although the power function model is suitable for the relationship between soil conductivity and water content, the parameters still need to be fitted and determined through experimental data, and the physical meaning is unclear, which makes the equation difficult to understand and apply. The parameters in the power model reflect the total parameter of all factors affecting soil resistivity except for soil water content (Hadzick et al., \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2011\u003c/span\u003e), among which the change of different soil particle content has the most obvious impact from Fig.\u0026nbsp;5 and Fig.\u0026nbsp;7. Therefore, based on the experimental data of this study, incorporating soil particle distribution into the formula. The primary reason soil particles affect the model relationship is that different particle sizes result in varying amounts of surface charge (Jayawickreme et al., \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; Seladji et al., 2010). Therefore, the particle distribution is represented by the mean particle diameter D50. D50 represents the particle size at which 50% of the soil particles are smaller by weight. For simplification, we calculate D50 through the proportions of clay, silt, and sand. Assuming that D50 is the weighted average of these three components, it can be calculated using the following Eq.\u0026nbsp;\u003cspan refid=\"Equ4\" class=\"InternalRef\"\u003e5\u003c/span\u003e\u003c/p\u003e\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$${D_{50}}=\\frac{{{P_{clay}}\\cdot {D_{clay}}+{P_{silt}}\\cdot {D_{silt}}+{P_{sand}}\\cdot {D_{sand}}}}{{{P_{clay}}+{P_{silt}}+{P_{sand}}}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003cp\u003e\u003c/p\u003e \u003cp\u003eWhere \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003eclay\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003esilt\u003c/em\u003e\u003c/sub\u003e, and \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003esand\u003c/em\u003e\u003c/sub\u003e represent the content of clay, silt, and sand, respectively. \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003eclay\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003esilt\u003c/em\u003e\u003c/sub\u003e, and \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003esand\u003c/em\u003e\u003c/sub\u003e represent the characteristic particle diameters of clay, silt, and sand, respectively, which are 0.002 mm, 0.050 mm, and 0.5 mm.\u003c/p\u003e \u003cp\u003eBased on the experimental data, the revised formula is refitted and presented as Eq.\u0026nbsp;\u003cspan refid=\"Equ5\" class=\"InternalRef\"\u003e6\u003c/span\u003e. This equation eliminates parameters and quantifies the impact of soil particle size distribution on the model relationship.\u003c/p\u003e\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$$\\theta =(235.55 - 10.01\\cdot D50)\\cdot {\\rho ^{( - 0.73+0.16\\cdot D50)}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e\u003cp\u003e\u003c/p\u003e \u003cp\u003eFrom Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, the goodness of fit for the experimental data exceeds 0.9. Additionally, the revised formula was validated using published data(Celano et al., \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; David et al., 2018), yielding goodness of fit values of 0.709 and 0.824, respectively. The results indicate that the revised relationship model effectively explains the relationship between the physical quantities.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eFitting results\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e\u003ccolgroup cols=\"6\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSoil sample\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eClay (%)\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSand (%)\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSilt (%)\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eD50\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSoil 1\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e8.31\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e36.34\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e55.36\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.210\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.9719\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSoil 2\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e12.89\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e7.74\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e79.38\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.079\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.9661\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSoil 3\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4.80\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e56.02\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e39.18\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.300\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.9774\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSoil 4\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2.62\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e76.01\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e21.38\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.391\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.9799\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSoil 5\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.500\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.9809\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCelano et al.\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e14.11\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e64.16\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e21.73\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.332\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.709\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBertermann et al.\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e70\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.085\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.824\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e \u003cp\u003e\u003c/p\u003e\u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Dielectric constant\u003c/h2\u003e \u003cdiv id=\"Sec12\" class=\"Section3\"\u003e \u003ch2\u003e3.3.1 Effect of water content and dry density\u003c/h2\u003e \u003cp\u003eFor soil, the dielectric constant is mainly determined by the relative dielectric constants of soil solid particles, water, and air. Among them, the dielectric constant of water (approximately 80) is much higher than that of soil solids (approximately 2–5) and air (approximately 1)(Lu et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). As shown in Fig.\u0026nbsp;8, the dielectric constant of dry soil is small, and with the water content increases, the dielectric constant increases. It also can be seen from the figure that the water content in soil is the main factor affecting the dielectric properties of soil. When the water content is low, water exists in the form of bound water, and the dielectric constant of bound water is much smaller than that of free water (Hongjian et al., \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). And the dielectric constant of water is dependent on the thickness of the water film covering soil particles (Boyarskii et al., \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2002\u003c/span\u003e). As the thickness of the water film on soil particles increases, the average dielectric constant of the entire aqueous phase (bound water and free water) continues to increase (Friedman and Shmulik, 1998). Although soil particles form the basic framework of the soil, their dielectric constants are less affected by the soil itself. With the water content further increases, the dielectric properties of bound water in the soil approach those of free water, and the polarization of free water increases (Boyarskii et al., \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2002\u003c/span\u003e; Xu et al., \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2022\u003c/span\u003e), causing a significant increase in the dielectric constant. When the water content increases from 0–20%, the rate of increase of dielectric constant is relatively small, while when the water content increases from 20–40%, the rate of increase becomes larger. This is because when the water content is below 20%, during the low water content stage, the water in the soil is mainly distributed as a thin film on the surface of the particles or fills small pores (Boyarskii et al., \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2002\u003c/span\u003e), which limits the contribution of water to the overall dielectric constant. Due to the limited amount of water, the dielectric properties of the soil are more influenced by solid particles and air. Therefore, even with the water content gradually increases, the increase of the dielectric constant is relatively slow. However, when the water content exceeds 20%, more free water accumulates in the soil pores. This free water not only covers the surface of the particles but also fills larger pores, water content becomes the main factor affecting the dielectric constant. At this stage, the high dielectric constant of water significantly increases its contribution to the overall dielectric constant. As the water content continues to increase, the volume and contact area of free water with soil particles also increase significantly, thereby accelerating the rate of increase in the dielectric constant.\u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;8 also shows the effect of soil dry density on the dielectric constant under different soil types and water contents. As dry density increases, the dielectric constant increases. The decrease in pores and increase in particle contact area due to the increase in dry density cause the free water to be compressed to the surface of the soil (Xu et al., \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2022\u003c/span\u003e), leading to an increase of the dielectric constant. Additionally, when the dry density of the soil increases, the content of solid particles per unit volume increases. Soil particles, especially those containing minerals, generally have a higher dielectric constant than air or gases in pores. Furthermore, with the dry density increases, the contact between soil particles becomes more compact, which enhances the efficiency of charge transfer between particles. The dense arrangement of particles enhances the dielectric properties because the electric field is more continuous among soil particles, reducing disruptions in the electric field.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section3\"\u003e \u003ch2\u003e3.3.2 Effect of soil particle distribution\u003c/h2\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e9\u003c/span\u003e illustrates the effect of soil particle distribution on the dielectric constant. It can be seen from the figure that when the water content is high, soil 2 has a relatively large dielectric constant. This is mainly because soil 2 contains more silt and clay. Due to their fine particle, silt and clay can retain more water in smaller pores, increasing the overall water content of the soil, thereby enhancing the dielectric constant of the soil. In addition, silt and clay particles usually carry more surface charges, which can increase the charge distribution and complexity in the soil, thereby enhancing the dielectric response of the soil. When water as a dielectric, these charge characteristics can enhance the dielectric effect, especially under high water content conditions. On the other hand, the dielectric constant of soil 5 (sand) is relatively low. The dielectric properties of sand are significantly lower than those of other soils, this is mainly due to the fact that sand consists of relatively large particles with larger pores. The larger particles reduce the contact area of particles per unit volume, thereby reducing the electric field interactions between particles (Kabir et al., \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Additionally, sand has weaker adsorption and retention capabilities for water due to its larger particles and lower specific surface area. Under natural conditions with low water content, there is relatively less water in the sand, so the contribution of water to the dielectric constant is limited. Water is one of the main factors that increase the dielectric constant. A lack of sufficient water means that the dielectric constant will remain at a low level.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section3\"\u003e \u003ch2\u003e3.3.3 Model analysis\u003c/h2\u003e \u003cp\u003eBased on previous research, scholars have proposed many models for soil water content-dielectric constant relationships, which are mainly divided into empirical models (C. et al., 1992; Ren-peng et al., \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2008\u003c/span\u003e). This study collected commonly used existing models as shown in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. And these existing models are evaluated the based on experimental data. The results are shown in Fig.\u0026nbsp;10. From the figure, it can be seen that all types of models perform well, with a goodness-of-fit of over 0.9. However, similar to conductivity, the model parameters also need to be obtained through fitting experimental data, thus the model cannot be directly applied.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eModel comparison\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e\u003ccolgroup cols=\"3\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eModel\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eExpression\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTopp model(Topp et al., \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e1980\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\theta ={\\text{ }}a+b\\varepsilon +c{\\varepsilon ^2}+d{\\varepsilon ^3}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.97573\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHerkelrath model(Herkelrath et al., \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e1991\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\theta ={\\text{ }}\\frac{{\\left( {\\sqrt \\varepsilon - b} \\right)}}{a}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.96844\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMalicki model(Malicki et al., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e1996\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\theta =\\frac{{\\sqrt \\varepsilon +a+b{\\rho _d}+c{\\rho _d}^{2}}}{{d+e{\\rho _d}}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.97783\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eZhao model(Zhao and Ling, \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2016\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\theta =\\frac{{a+\\sqrt \\varepsilon }}{{b+c\\sqrt \\varepsilon }}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.97460\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLiao model(Liao et al., \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2016\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\theta =alg\\left( {\\varepsilon /b} \\right)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.93205\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e \u003cp\u003e\u003c/p\u003e \u003cp\u003eWhere \u003cem\u003eθ\u003c/em\u003e is water content, \u003cem\u003eε\u003c/em\u003e is dielectric constant, \u003cem\u003eρ\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e is dry density\u003c/p\u003e \u003cp\u003eFrom the Fig.\u0026nbsp;11a, it can be seen that there is an obvious distribution area for the dielectric constant-water content scatter plot, and the upper boundary of the distribution area is θ=-8.7434 + 3.18847\u003cem\u003ex\u003c/em\u003e-0.08522\u003cem\u003ex\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e + 0.0011\u003cem\u003ex\u003c/em\u003e\u003csup\u003e3\u003c/sup\u003e, lower boundary is θ=-11.35287 + 3.03801*\u003cem\u003ex\u003c/em\u003e-0.07804\u003cem\u003ex\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e + 0.00087961\u003cem\u003ex\u003c/em\u003e\u003csup\u003e3\u003c/sup\u003e. As the water content increases, the distribution range of the relative dielectric constant also expands. This is mainly due to the coupled effects of water content, soil particle content, and dry density. An increase in dry density and water content helps to increase the dielectric constant, while an increase of sand particle content leads to a decrease in the dielectric constant. The distribution area shows a clear pattern of change as the water content increases. By fitting the distribution width-water content relationship, a quantitative law for the variation of regional width with water content was obtained, as shown in Fig.\u0026nbsp;11b.\u003c/p\u003e \u003cp\u003eSince the distribution area is influenced by multiple factors, a sensitivity analysis of the factors affecting the dielectric constant distribution area is conducted. To ensure that variables with different dimensions can be directly compared, the data is standardized. Standardization refers to the process of calculating the standardized value 𝑥′ of a variable 𝑥 in a given dataset 𝑋 using the formula 𝑥′ = (𝑥 − 𝜇) / 𝜎, where 𝑥 is the original data value, 𝜇 is the mean of variable 𝑥, 𝜎 is the standard deviation of variable 𝑥, and 𝑥′ is the standardized data value. After standardization, the mean of each variable is 0 and the standard deviation is 1. Then, a multivariate linear regression model is constructed using the standardized data, with the goal of predicting the width of the distribution range (difference \u003cem\u003eG\u003c/em\u003e). The form of the regression model is as follows:\u003c/p\u003e\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e\n$$G={\\beta _0}+{\\beta _1}\\cdot {P_{clay}}+{\\beta _2}\\cdot {P_{silt}}+{\\beta _3}\\cdot {P_{sand}}+{\\beta _4}\\cdot D+{\\beta _5}\\cdot {P_{water}}+\\sigma$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e7\u003c/div\u003e\u003c/div\u003e\u003cp\u003e\u003c/p\u003e \u003cp\u003eWhere \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003eclay\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003esilt\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003esand\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003ewater\u003c/em\u003e\u003c/sub\u003e are clay content, silt content, sand content, water content, \u003cem\u003eD\u003c/em\u003e is the density, \u003cem\u003eβ\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e is the constant term, β1, β2, β3, β4, and β5 are the regression coefficients of the respective variables, and \u003cem\u003eσ\u003c/em\u003e is the error term.\u003c/p\u003e \u003cp\u003eThe regression coefficients of each variable were obtained through a regression model. To evaluate the sensitivity of each factor, the standardized regression coefficient (SRC) is calculated using the following formula:\u003c/p\u003e\u003cdiv id=\"Equ7\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ7\" name=\"EquationSource\"\u003e\n$$SRC{\\text{ }}=\\frac{{{\\beta _i} \\times {\\text{ }}std\\left( {{X_i}} \\right)}}{{std\\left( Y \\right)}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e8\u003c/div\u003e\u003c/div\u003e\u003cp\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cem\u003eβ\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e is the regression coefficient, std(\u003cem\u003eX\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e) is the standard deviation of the ith independent variable, and std(\u003cem\u003eY\u003c/em\u003e) is the standard deviation of the dependent variable.\u003c/p\u003e \u003cp\u003eThe analysis results are shown in Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. The standardized regression coefficient for water content is 0.831, indicating that changes in water content have a significant impact on the difference, and it is the most influential factor. Silt content (-0.140) and sand content (0.110) also have some impact on the difference, but much less than water content. The impact of density (0.092) and clay content (-0.082) is relatively small. Through sensitivity analysis, it was found that water content has the greatest impact on the difference, followed by silt content and sand content. The impact of clay content and density is relatively small.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eRegression coefficient Table of influencing factors\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e\u003ccolgroup cols=\"2\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eInfluencing factors\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eStandardized regression coefficient\u003c/p\u003e \u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eclay content\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-0.082\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003esilt content\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-0.140\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003esand content\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.110\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003edensity\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.092\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ewater content\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.831\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e \u003cp\u003e\u003c/p\u003e \u003cp\u003eThe increase in water content has a significant impact on the dielectric constant distribution, and it may change the effect of soil particle size distribution and dry density. However, the results obtained through linear regression analysis alone cannot fully explain this interaction effect. Therefore, a regression model that includes interaction terms is constructed. By adding interaction terms to the regression model, the interaction effect between two variables is evaluated. The interaction effects between water content and clay content, silt content, sand content, and dry density are considered separately to construct the following regression model:\u003c/p\u003e\u003cp\u003e \u003cem\u003eG\u003c/em\u003e = \u003cem\u003eβ\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e + \u003cem\u003eβ\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e × \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003eclay\u003c/em\u003e\u003c/sub\u003e + \u003cem\u003eβ\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e × \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003esilt\u003c/em\u003e\u003c/sub\u003e + \u003cem\u003eβ\u003c/em\u003e\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003e × \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003esand\u003c/em\u003e\u003c/sub\u003e + \u003cem\u003eβ\u003c/em\u003e\u003csub\u003e\u003cem\u003e4\u003c/em\u003e\u003c/sub\u003e × \u003cem\u003eD\u003c/em\u003e + \u003cem\u003eβ\u003c/em\u003e\u003csub\u003e\u003cem\u003e5\u003c/em\u003e\u003c/sub\u003e × \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003ewater\u003c/em\u003e\u003c/sub\u003e + \u003cem\u003eβ\u003c/em\u003e\u003csub\u003e\u003cem\u003e6\u003c/em\u003e\u003c/sub\u003e × (\u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003ewater\u003c/em\u003e\u003c/sub\u003e × \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003eclay\u003c/em\u003e\u003c/sub\u003e) + \u003cem\u003eβ\u003c/em\u003e\u003csub\u003e\u003cem\u003e7\u003c/em\u003e\u003c/sub\u003e × (\u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003ewater\u003c/em\u003e\u003c/sub\u003e × \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003esilt\u003c/em\u003e\u003c/sub\u003e) + \u003cem\u003eβ\u003c/em\u003e\u003csub\u003e\u003cem\u003e8\u003c/em\u003e\u003c/sub\u003e × (\u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003ewater\u003c/em\u003e\u003c/sub\u003e × \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003esand\u003c/em\u003e\u003c/sub\u003e) + \u003cem\u003eβ\u003c/em\u003e\u003csub\u003e\u003cem\u003e9\u003c/em\u003e\u003c/sub\u003e × (\u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003ewater\u003c/em\u003e\u003c/sub\u003e × \u003cem\u003eD\u003c/em\u003e) + \u003cem\u003eσ\u003c/em\u003e (9)\u003c/p\u003e \u003cp\u003eTo ensure that variables with different units can be directly compared, data normalization is performed first. Through the above model, the regression coefficients of each interaction term can be interpreted. Water content-Clay Content evaluates the interaction effect between water content and clay content; Water content-Silt Content evaluates the interaction effect between water content and silt content; Water content-Sand Content evaluates the interaction effect between water content and sand content; Water content-Density evaluates the interaction effect between water content and dry density. The larger the standardized regression coefficient, the more significant the impact of the interaction term on the dependent variable. The results are shown in Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eStandardized regression coefficients for factor interactions\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e\u003ccolgroup cols=\"2\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eInfluencing factors\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eStandardized regression coefficient\u003c/p\u003e \u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWater content - Clay Content\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-7.164689e-10\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWater content - Silt Content\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-2.825982e-08\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWater content - Sand Content\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-4.390623e-08\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWater content - Density\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-2.966624e-14\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e \u003cp\u003e\u003c/p\u003e \u003cp\u003eThe standardized regression coefficients for water content and sand content (-4.390623e-08) and water content and silt content (-2.825982e-08) are negative and relatively large, indicating a significant negative interaction effect between water content and sand content and silt content. The standardized regression coefficients for water content and clay content (-7.164689e-10) and water content and density (-2.966624e-14) are smaller, indicating that these interaction effects are weaker. The interaction effects indicate that an increase in water content will weaken the impact of sand content and silt content on the difference. This means that under higher water content conditions, the contribution of sand and silt content to the distribution area will decrease. The direct effects of clay content and density are relatively small, and their interaction with water content is also not significant.\u003c/p\u003e \u003cp\u003eThrough analysis, it is evident that particle size distribution is the primary factor affecting the distribution of dielectric constants. Therefore, the Herkelrath model with good goodness of fit is used as the foundation, incorporating the influence of particle size distribution into the model, resulting in the following revised model:\u003c/p\u003e\u003cdiv id=\"Equ8\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ8\" name=\"EquationSource\"\u003e\n$$\\theta =\\frac{{\\sqrt \\varepsilon - (b0+b1 \\times D50)}}{{a0+a1 \\times D50}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e10\u003c/div\u003e\u003c/div\u003e\u003cp\u003e\u003c/p\u003e \u003cp\u003eWhere \u003cem\u003ea\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e = 0.1084, \u003cem\u003ea\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e=-0.00001145, \u003cem\u003eb\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e = 0.901, \u003cem\u003eb\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e = 0.0018. The goodness of fit (R²) for the experimental data using this model exceeds 0.8 (show in Table\u0026nbsp;\u003cspan refid=\"Tab7\" class=\"InternalRef\"\u003e7\u003c/span\u003e). Additionally, the model was validated with published data(Jin et al., \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2020\u003c/span\u003e), achieving goodness of fit values also above 0.8, confirming the reliability of the model.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003ctable float=\"Yes\" id=\"Tab7\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 7\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eFitting results\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e\u003ccolgroup cols=\"6\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003esoil sample\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eClay (%)\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSilt (%)\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSand (%)\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eD50\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSoil 1\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e8.31\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e36.34\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e55.36\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.210\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.9079\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSoil 2\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e12.89\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e7.74\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e79.38\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.079\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.8085\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSoil 3\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4.80\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e56.02\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e39.18\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.300\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.9519\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSoil 4\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2.62\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e76.01\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e21.38\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.391\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.9840\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSoil 5\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.500\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.9547\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePublished data 1\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e13.43\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e35.06\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e51.51\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.275\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.9215\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePublished data 2\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e8.53\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e49.51\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e41.96\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.235\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.8993\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePublished data 3\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e13.48\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e55.89\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e30.63\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.181\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.9033\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePublished data 4\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e19\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e63.84\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e17.16\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.118\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.8755\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePublished data 5\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e47.38\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e47.6\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e5.02\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.050\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.8373\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e \u003cp\u003e\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"Conclusion","content":"\u003cp\u003eThis study investigates the variations in soil properties that affect the transmission of underground wireless signals. Specifically, the effects of different particle size distribution, water content, and dry density on soil electrical conductivity and dielectric constant were investigated by experiments, and revealing the underlying mechanisms under the variation of influencing factors. Additionally, the existing soil water content-resistivity and water content-dielectric constant relationship models are evaluated and modified. The main conclusions are as follows:\u003c/p\u003e\u003cp\u003e(1) Soil electrical conductivity and dielectric constant both increase with increasing water content and dry density, but the rate of increase first rises and then decreases as water content increases.\u003c/p\u003e\u003cp\u003e(2) High clay and silt content can improve soil electrical conductivity and dielectric constant, while an increase in sand content leads to a decrease in both properties.\u003c/p\u003e\u003cp\u003e(3) Water content is the main factor affecting the distribution of dielectric constants. An increase in water content weakens the impact of sand and silt content on the dielectric constant distribution range. Under high water content conditions, the contribution of sand and silt content to the distribution range decreases. The direct impact of clay content and density is relatively small, and their interaction with water content is not significant.\u003c/p\u003e\u003cp\u003e(4) Through experimental data, models for water content-resistivity and water content-dielectric constant relationships were evaluated and modified. By incorporating D50 into the model parameters, the physical meanings of the parameters were clarified, and a modified model was obtained. The validity of the model was then verified using published data.\u003c/p\u003e\u003cp\u003eThe findings provide a theoretical basis for the application of wireless monitoring in underground structures, thereby facilitating the optimization of wireless signal propagation prediction and practical implementation.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eFunding\u003c/h2\u003e \u003cp\u003eThis work was supported by the National Key R\u0026amp;D Program of China (Grant No.2022YFC3801000) and Shanghai \u0026ldquo;Science and Technology Innovation Action Plan\u0026rdquo; project (Grant No.22dz1200402, and Grant No.22dz1201200).\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eFei Wang and Shuang Nie conceived the idea and drafted the manuscript. Qunfang Hu secured the funding. Qunfang Hu, Yuankang Mao, Qian Hai, and Yanghe Liu revised the manuscript. All authors reviewed the manuscript.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eWireless Sensor Networks for Leakage Detection in Underground Pipelines: A Survey Paper. Procedia Computer Science 2013; 21: 491-498.\u003c/li\u003e\n\u003cli\u003eAkyildiz IF, Stuntebeck EP. Wireless underground sensor networks: Research challenges. Ad Hoc Networks 2006; 4: 669-686.\u003c/li\u003e\n\u003cli\u003eArchie, G. E. The electrical resistivity log as an aid in determining some reservoir characteristics. Transactions of the Aime 1942; 146: 54-62.\u003c/li\u003e\n\u003cli\u003eBinley A, Cassiani G, Middleton R, Winship P. Vadose zone flow model parameterisation using cross-borehole radar and resistivity imaging. Journal of Hydrology 2002; 267: 147-159.\u003c/li\u003e\n\u003cli\u003eBoyarskii DA, Tikhonov VV, Komarova NY. Model of Dielectric Constant of Bound Water in Soil for Applications of Microwave Remote Sensing - Abstract. 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Journal of Microwave Power \u0026amp; Electromagnetic Energy A Publication of the International Microwave Power Institute 2020: 1-16.\u003c/li\u003e\n\u003cli\u003eLiao HJ, Sun JY, Zan YW, Zhu QN, Gu F. Dielectric constant model for soil and its application in engineering. Chinese Journal of Geotechnical Engineering 2016.\u003c/li\u003e\n\u003cli\u003eLiu F. Electrical Conductivity in Soils: A Review. 2015.\u003c/li\u003e\n\u003cli\u003eLu H, Jiang W, Zhao Y, Zeng Z. Relationship between volumetric water content and effective dielectric permittivity of Nanning expansive soil. Rock and Soil Mechanics 2016; 37: 2145-2150.\u003c/li\u003e\n\u003cli\u003eMalicki MA, Plagge R, Roth CH. Improving the calibration of dielectric TDR soil moisture determination taking into account the solid soil. European Journal of Soil Science 1996; 47.\u003c/li\u003e\n\u003cli\u003eMelo LBBD, Silva BM, Peixoto DS, Chiarini TAP, Curi N. 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PEDOSPHERE 2007; 17: 12.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Soil Electrical Conductivity, Dielectric Constant, Underground wireless signals, Transmission medium, modified model","lastPublishedDoi":"10.21203/rs.3.rs-6187477/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6187477/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWireless monitoring can effectively enhance the operational safety of underground infrastructures. The electrical conductivity and dielectric constant of soil determine the transmission performance of buried wireless signals. To solve the problem of wireless monitoring signal transmission of underground infrastructure, the variation patterns of soil electrical conductivity and dielectric constant need to be explored. In this study, the effect of different particle size distribution, water content, and dry density on soil conductivity and dielectric constant were investigated by experiments. And the existing soil water content-resistivity and soil water content-dielectric constant models were evaluated and analyzed. The results show that both soil conductivity and dielectric constant increase with increasing water content and soil dry density, but the rate of increase first increases and then decreases with the increase of water content. Due to the varying complexity of surface charges on soils with different particle sizes, the high content of clay and silt with small particle size is helpful to improve soil conductivity and dielectric constant, while the increase of sand content with large particle size leads to the decrease of both. And the sensitivity analysis revealed that soil particle size distribution significantly affects the water content-resistivity and water content-dielectric constant relationship, whereas the impact of dry density is minimal. Based on the experimental data, the existing relational models were evaluated and analyzed. The median particle size (D50) is incorporated into the empirical model to elucidate the physical significance of the model parameters and to develop modified models. The modified models were validated using published data, demonstrating their good accuracy.\u003c/p\u003e","manuscriptTitle":"Experimental Study on the Soil Electrical Conductivity and Dielectric Constant Properties","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-03-13 04:49:13","doi":"10.21203/rs.3.rs-6187477/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"62c88b68-b9b1-40f7-8883-1b631cfc3b99","owner":[],"postedDate":"March 13th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-07-22T10:23:50+00:00","versionOfRecord":[],"versionCreatedAt":"2025-03-13 04:49:13","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6187477","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6187477","identity":"rs-6187477","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}