Multivariate distribution models of soil electrical resistivity

https://doi.org/10.1016/j.coldregions.2022.103584Get rights and content

Highlights

  • The resistivity test results of 134 soil samples were collected in the literature as a database for this study.

  • The nonlinear Box-Cox method is used to convert the parameters to approximate normal variables.

  • Based on the correlation matrix between soil parameters and resistivity, a multivariate distribution model between soil parameters and resistivity was established.

  • The multivariate distribution model established in this paper is compared with the traditional empirical models, and the prediction results of the proposed multivariate distribution models are obviously better than the traditional empirical models.

Abstract

Soil electrical resistivity is an important parameter in geotechnical engineering. In this paper, a multivariate distribution model is used to predict soil electrical resistivity. The Box-Cox method was used to transform the soil parameters, which were then analysed by a correlation matrix. Multivariate distribution models with different input parameters were established, verified and analysed, and compared with conventional empirical models. The results show that the predictive accuracy of the multivariate distribution models was improved significantly by increasing the number of parameters. The correlation coefficient (R2) of the calibration data increased from 0.05 to 0.88, and that of the validation data increased from 0.06 to 0.83. The model with the best predictive accuracy was the RE−{G, F, Sr} model (R2 = 0.87, E(ε) = 1.22, COV(ε) = 0.98). The predictive accuracy of the multivariate distribution model was obviously higher than that of the conventional empirical model. The multivariate distribution model is an effective and simple way to predict soil electrical resistivity. The proposed model exhibits good performance using limited electrical resistivity data from frozen soils.

Introduction

With the intensification of energy consumption and global warming, the development and utilization of new energy is becoming increasingly important. Fluidized bed design ground reconstruction and urban cable laying are strongly influenced by the electrical resistivity properties of soil. Electrical resistivity (RE) is a physical quantity reflecting the conductivity of soil, which has been used to predict changes in soil salinity, saturation, water content and the degree of freezing and thawing (Shea and Luthin, 1961; McCarter, 1984; Kalinski and Kelly, 1993; Gunnink and El-Jayyousi, 1993). Electrical resistivity is mainly affected by the soil's solid particle mineral composition, particle size and morphology, and saturation and temperature (Abu-Hassanein et al., 1996; Archie, 1942; McCarter and Desmazes, 1997; Fukue et al., 1999; Friedman, 2005). Therefore, in the design and application of electrical structures, it is highly important to understand the electrical resistivity properties of soil.

There has been much research on the properties of soil electrical resistivity and associated models. Wu et al. (1985) studied soil electrical resistivity in situ and concluded that it is influenced by the parent rock and the soil's salt content, texture and type. Singh et al. (2001) developed a generalized model of the relationship between electrical resistivity and thermal conductivity. Fortier et al. (2008) tested the electrical resistivity of frozen soil and used linear regression to establish the relationship between it and unfrozen water and ice contents. Fu et al. (2009) studied the relationship between uniaxial compressive strength and the initial electrical resistivity of frozen soil. Yan et al. (2012) measured the electrical resistivity of bentonite in Guangxi, China, and concluded that the electrical resistivity of expansive soil is a function of its volumetric water content, saturation and pore ratio. Nouveau et al. (2016) tested the electrical resistivity and thermal conductivity of four soils with different particle size distributions and clay contents at temperatures of 20–100 °C. They concluded that electrical resistivity decreases with increases in temperature, while thermal conductivity increases. Many theoretical models of soil electrical resistivity have been proposed (Samui, 2014; Shan et al., 2015; Tang et al., 2018; Hasan et al., 2021). To sum up, the electrical resistivity of soil is affected by many factors. There is a correlation between soil electrical resistivity and thermal conductivity. In order to predict soil electrical resistivity, empirical models of electrical resistivity and other parameters are usually established. Empirical models use mathematical methods to perform regression analysis on soil electrical resistivity test data. They establish the relationships between soil electrical resistivity and thermal conductivity coefficient saturation volume moisture content, porosity ratio and other factors. At present, soil electrical resistivity models comprise both empirical and theoretical models. Theoretical models simplify the conductive process of rock and soil materials on the basis of electricity. Theoretical models involve many parameters and their calculation process is complicated, so they are difficult to use in practical engineering. Empirical models are more practical as they use fewer parameters and have a simpler calculation process; however, their predictive accuracy can be low. Therefore, a novel method is needed to predict soil resistivity accurately and conveniently. To do this, the present study constructs a multivariate distribution model for the prediction of soil electrical resistivity.

This paper investigates the electrical resistivity of soil and transforms and analyses the related parameters. A multivariate distribution model is established to predict the electrical resistivity of soils. The performance of the established prediction model is tested. The prediction results of the model are compared with the traditional empirical relationship model, and the effectiveness and superiority of the prediction model proposed in this paper are clarified.

Section snippets

Electrical resistivity database

This section first introduces the soil electrical resistivity database. A general database of 134 soil electrical resistivity measurements was established. Then, the electrical resistivity database was divided into calibration and verification datasets, which were used to construct and verify a multivariate distribution model of soil electrical resistivity. Finally, three statistical indicators are introduced to evaluate the performance of the predictive model.

Construction of prediction model

The main purpose of this section is to study the influence of soil parameters on electrical resistivity by conducting multivariate statistical analysis and establishing a corresponding predictive model.

Multivariate distribution model of soil electrical resistivity

A multivariate distribution model that predicts RE can be established by using one or more parameters. In the correlation analysis of soil parameters (Section 3), G, F, and Sr were highly correlated with RE. Therefore, a binary correlation model of G, F, Sr and RE was established first, then a multivariate correlation model of soil electrical resistivity was established.

Examples of soil electrical resistivity calculation

his section illustrates the application of the multivariate distribution model with measured data. The measured data of soil sample No. 2 in Table 1 is: G = 2.67, F = 100, w = 1.45, γd = 4.78, Sr = 15.2 and RE = 232.56. A multivariate correlation model with input parameters G, F, and Sr was used to calculate the electrical resistivity of soils RE using the following process.

Step 1 Convert G(X1), F(X2), Sr(X5) into N1, N2, N5 by Eq. (7). The conversion parameters are shown in Table 2, and the

Comparison of calculation models

At present, prediction of soil electrical resistivity is mainly based on theoretical and empirical models. Theoretical models are often impractical because of their many parameters and complicated calculation process. Empirical models are usually used in practical engineering because of their simple calculation process and few parameters. To verify the effectiveness of the multivariate distribution model, its predictions of soil electrical resistivity were compared with those of the models of

Conclusions

In this paper, the electrical resistivity of soil was calculated and studied based on multivariate distribution models, and their performance was analysed. The main conclusions are as follows.

  • (1)

    The soil parameters were converted by Boxcox and the converted parameters obeyed a normal distribution so that a multivariate distribution model could be established. The multivariate distribution model quantitatively considers the influences of electrical resistivity and soil parameters and provides a

Author statement

Caijin Wang: Conceptualization; Methodology; Investigation; Formal analysis; Data Curation; Writing.

Hualei Feng: Investigation; Visualization; Writing.

Meng Wu: Conceptualization; Writing; Supervision.

Guojun Cai: Formal Analysis; Investigation; Data Curation; Visualization; Writing.

Declaration of Competing Interest

None.

Acknowledgements

This paper was supported by the National Natural Science Foundation of China (Grant No. 41877231, No. 42072299).

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