Keywords:

Titre : Surveillance des couches de construction de structures artificielles à l'aide de méthodes microondes Mots clés : Propagation du rayonnement micro-ondes; supports multicouches, méthodes optiques et de résonance pour déterminer les propriétés électriques des supports, simulation informatique, effet de la salinité et de la température sur les propriétés électriques des supports, corrélation des propriétés électriques et mécaniques. Résumé : Dans cette étude, une méthode de détermination des propriétés électrophysiques des sols basée sur la méthode GPR combinée à des approches optiques et des mesures de résonance a été développée. Dans le cadre de l'électrodynamique classique, une méthode a été développée pour déterminer les indices de réfraction absolus des couches structurelles et les coefficients d'atténuation correspondants dans la gamme des micro-ondes de 1200 à 1700 MHz, basée sur le traitement quantitatif des données GPR. La méthode développée de traitement des données GPR est basée sur l'utilisation d'amplitudes d'ondes réfléchies ; il permet de déterminer les constantes diélectriques et les conductivités électriques des couches structurelles avec une erreur ne dépassant pas 10-15%.

Des méthodes de détermination de la constante diélectrique complexe et de l'humidité par la méthode GPR, étalonnées par des mesures en laboratoire, sont proposées et évaluées. L'approche développée permet un diagnostic rapide de l'état des objets étendus, car elle combine les avantages de la méthode GPR à grande vitesse avec un nombre limité de mesures d'étalonnage. Les dépendances de la constante diélectrique et de la conductivité spécifique vis-à-vis de l'humidité ont été étudiées dans un certain nombre de bentonites avec différentes compositions d'ions échangeables. Une corrélation entre ces grandeurs électrophysiques et la plasticité des bentonites est établie.

Contents

Introduction 1

Chapter 1. Literature review 1.1 GPR method 1. 1.1 GPR equipment 1. 1.2 Bibliometric analysis 1. 1.3 Patent analysis 1. 1.4 GPR on transport 1. 1.5 Monitoring the density of soils of the railway road bed by GPR 1. 1.6 GPR method in the construction of subgrade 1.2 Direct methods for measuring the electrophysical properties of soils 1.2.1 Quasi-optical (in free space) methods 1. 2.2 Waveguide methods 1. 2.3 Resonance methods [START_REF]American Society of Civil Engineer Standard Guideline for the Collection and Depiction of Existing Subsurface Utility Data[END_REF] [START_REF]British Standard: Specification for Underground Utility Detection, Verification and Location Institute of Civil Engineer[END_REF]. Equations for calculating the absolute refractive indices of the leveling layer and the invert 2.3 Numerical procedures for determining the coefficients of attenuation of the electromagnetic field and refractive indices 2. 3.1 The use of traces to determine the attenuation coefficients for an example of industrial water 2. 3.2 The use of traces to determine the attenuation coefficients of tunnel structural layers 2. 3.3 Using the amplitude of the signal reflected by the interface of the structural layers of variable thickness to determine the attenuation coefficient of the leveling layer 2.4 Determination of the absolute refractive indices of structural layers 2. 5. Selection of refractive indices using phase analysis of radargrams 2.6 Determination of the attenuation coefficient in the leveling layer by the amplitudes of the signals reflected by its boundaries 2.7 Results and Discussion 2. [START_REF]Subsurface radar issues[END_REF]. [START_REF]American Society of Civil Engineer Standard Guideline for the Collection and Depiction of Existing Subsurface Utility Data[END_REF] Verification of GPR results using alternative methods 2. 7.2 Contrast of construction layers 2.8 Conclusions 3 Chapter 3. Resonance method for determining the electrophysical properties of soils and materials

3.1

Objectives of the study 3.2 Soils model 3.3 Analytical models of dielectric constant in soils 3. 3.1 Water in soils 3. 3.2 Analytical dielectric permittivity models related to the porosity parameter 3.3.3 Models of effective dielectric constant 3.4 Designing a cavity resonator for measuring the properties of materials taken from the core 3. [START_REF]Regulations for Performing Preliminary Surveys with Groundprobling Radar for Before Laying Underground Utilities and Infrastructures[END_REF].1 Creating a computer model of a cavity resonator, in accordance with the prototype, in the software CST Studio Suite 3.5 Software and hardware device for experimental studies of the electrophysical properties of samples 3.5.1 Determination of the resonance frequency of electromagnetic waves transmitted through reference samples with known dielectric constant values 3.6 An integrated study of the dielectric properties of soils of different moistures by volume resonator method and simultaneous GPR measurements at frequencies of 1.4 GHz.

3.7

Determination of the real part of dielectric constant and the conductivity of soil-forming minerals using GPR calibrated method 3.8 Determination of sample moisture using calibrated GPR data 3.9 Conclusions 4 Chapter 4. The effect of soil salinity on the depth of GPR surveys [START_REF]Regulations for Performing Preliminary Surveys with Groundprobling Radar for Before Laying Underground Utilities and Infrastructures[END_REF].1 Materials used 4. 1.1 Cohesionless materials 4. 1.2 Cohesive materials 4.2 Electrophysical properties of sand 4. 2.1 Electrophysical properties of wet sand 4. 2.2 Electrophysical properties of wet saline sand 4. 2.3 Electrophysical properties of wet saline sand at low temperatures 4.3 Some properties of the samples used 4. 3.1 Electrophysical properties of bentonite "Dusch" 4. 3.1.1 Determination of the accuracy of the measurements of electrophysical quantities [START_REF]Regulations for Performing Preliminary Surveys with Groundprobling Radar for Before Laying Underground Utilities and Infrastructures[END_REF]. 3.1.2 The effect of salinity on the electrical properties of the bentonite

Introduction

Modern large-scale construction of roads and railways, renovation of housing and urban development has led to the active development and use of ground penetrating radar (GPR) technologies. Currently, the method of subsurface survey or georadilation is one of the most widely used and rapidly developing methods of non-destructive testing, providing all necessary information about the state of the surveyed environment. At the same time, the efficiency of the method increases significantly when combined with other non-destructive or laboratory methods.

The use of reliable values of dielectric constant and specific conductivity of the medium allows calibrating georadars and creating software and hardware complexes for monitoring engineering infrastructure objects, determining thickness of structural layers and other important characteristics, such as moisture, density, etc.

Analysis of the existing physical methods for measuring the electrical properties of the materials in the microwave range showed that to solve the above mentioned problems, the most promising alternative method for integration with GPR is the resonance method which allows obtaining dielectric constants and specificconductivities of materials and soils with their structure undisturbed.

In this regard, this thesis is devoted to theoretical and experimental study of the propagation of electromagnetic radiation in multilayer environments, the creation of a set of GPR-based methods and the resonance method for determining the dielectric constant and conductivity of materials and soils. In particular, in this thesis, for the frequency of 1700 MHz:

-The possibility of using the GPR method for determining the electrophysical parameters of materials and soils is assessed;

-The methods for designing the resonators for measuring dielectric constants and conductivities are developed;

-The method for determining the dielectric constant and conductivity is developed;

-The equipment and technology for measuring the dielectric constant and specific conductivity of samples are created.

Relevance of the research topic. Physical and geophysical methods for studying multilayer inhomogeneous media (soils) have recently become more and more widely used in engineering. This is primarily due to the fact that the destructive methods used today (penetration, soil sampling by drilling, etc.) do not allow obtaining information about the surveyed medium in the required volume, and are associated with significant time, labor and material costs.

Practically important results for materials and soils used in the construction and maintenance of infrastructure facilities can be obtained by combining these methods with non-destructive testing methods, i.e. GPR, seismic prospecting, electrical sounding, etc. Among geophysical methods, GPR has advantages in speed, and efficiency of use. However, in spite of the obvious attractiveness, there are certain difficulties in its application. For example, when determining the position of the interfaces between medium layers from the reflected GPR signal, the main factor affecting the accuracy of the method is the accuracy of the dielectric constant set during the survey as an external parameter. In addition, the depth of the GPR method is limited by the specific conductivity of the media, the value of which it is desirable to know before starting the survey.

In this regard, the development of methods for measuring the dielectric constant and specific conductivity of media is an important task. Thus, it seems relevant to further study the electrophysical properties of soils by GPR and resonance methods in practically important multilayered moist inhomogeneous media.

In this work, in order to improve the accuracy of the GPR measurements, a resonator (tunable split coaxial resonator with a shortening capacitance) was designed and created for measuring the dielectric constant and conductivity of samples of materials and soils with undisturbed structure at frequencies close to 1700 MHz.

Measurements of electrophysical parameters performed in the work were accompanied by computer simulation of the electric field in the resonator cavity containing samples of materials and soils.

The results of these studies will increase the efficiency and reliability of solving specific applied problems by using the method of subsurface sounding.

The main goals of the work:

-study of the effect of the structure and electrophysical properties of structural layers of artificial structures on the results of the GPR diagnostics;

-development of methods for measuring the electrophysical properties of soils for the refinement of GPR data.

To achieve these goals, the following scientific problems were solved in the thesis:

-a method for quantitative processing of GPR data is developed;

-a method for determining the electrophysical properties of soils is developed;

-electrophysical properties of soils with different degrees of moisture and salinity are investigated;

Scientific novelty of the work. Scientific results for the defense 1. In the framework of classical electrodynamics, a method has been developed for determining the absolute refractive indices of structural layers and corresponding attenuation coefficients in the microwave range of 1200-1700 MHz, based on the quantitative processing of GPR data. The developed method of processing the GPR data is based on the use of amplitudes of reflected waves; it makes it possible to determine dielectric constants and electrical conductivities of structural layers with an error of not more than 10-15%. This makes it promising for the use in software systems for the automatic processing of GPR information when monitoring the state of extended sections of roads and railways.

2. Methods for determining the complex dielectric constant and moisture by the GPR method, calibrated by laboratory measurements, are proposed and assessed. The developed approach allows rapid diagnosing the state of extended ob-jects, since it combines the advantages of the high-speed GPR method with a limited number of calibration measurements. [START_REF]British Standard: Specification for Underground Utility Detection, Verification and Location Institute of Civil Engineer[END_REF]. The dependences of the dielectric constant and specific conductivity on the moisture have been investigated in a number of bentonites with different composition of exchangeable ions. A correlation between these electrophysical quantities and the plasticity of bentonites is established.

Reliability of the results obtained is determined by the use of modern, reliably developed ideas of electromagnetic radiation theory in theory and practice of GPR, by application of modern methods of computing and data processing, and by the use of libraries of approved computer algorithms. All theoretical conclusions and the results obtained are confirmed by laboratory and field tests.

Scientific and practical significance of the work is in developing of a set of methods, including GPR and resonant measurements, for determining electrophysical values of materials and soils; these methods are effective for practical application. The developed approaches are aimed at the quantitative processing of the results of the GPR measurements at frequencies close to 1700 MHz.

Approbation of the work. Principal results of this thesis are reported and discussed at a number of All-Russian and International conferences: Chapter 1. Literature review

GPR method

The GPR method belongs to non-destructive methods that are widely used to examine the subsurface space when solving a wide range of engineering problems. In Russia, the use of the GPR method is regulated by normative documents [START_REF]American Society of Civil Engineer Standard Guideline for the Collection and Depiction of Existing Subsurface Utility Data[END_REF][START_REF]Standard Guide for Using the Surface Ground Penetrating Radar Method for Subsurface Investigation[END_REF][START_REF]British Standard: Specification for Underground Utility Detection, Verification and Location Institute of Civil Engineer[END_REF][START_REF]Regulations for Performing Preliminary Surveys with Groundprobling Radar for Before Laying Underground Utilities and Infrastructures[END_REF][5].

The GPR method is based on the emission of broadband pulses of electromagnetic radiation and recording of signals reflected by media separation interfaces or objects placed in a ground or in structural layers of artificial structures [START_REF]Ground penetrating radar applications, principles, procedures[END_REF][START_REF]Subsurface radar issues[END_REF].

The interlayer interfaces in the media under study are, for example, the contact between dry and moisture-saturated soils (groundwater level), contacts between rocks of different lithological composition, between rock and material of artificial construction, between frozen and thawed soils, between bedrock and sedimentary rocks, etc.

GPR pulse contains harmonics whose spectrum depends on the pulse duration. In GPR, the spectrum contains frequencies in the range from 10 to 5000 MHz.

A wave propagating in a medium can experience reflection and refraction on the interfaces between the media layers with different relative dielectric constant, diffract on objects whose dimensions are smaller than the prevailing wavelength, decay due to angular divergence and absorption in the medium.

Important characteristics of media that affect the description of the propagation of electromagnetic pulses are propagation velocity and attenuation coefficient.

Electromagnetic waves propagation speed depends on the relative dielectric and magnetic permeabilities. For the most of media encountered in practice the relative magnetic permeability differs little from unity. Therefore, the speed of wave propagation in the medium is determined by the formula:

 C V 
, where C is the speed of light in vacuum or air, and ε is the relative dielectric constant of the medium.

Wave attenuation is associated with the presence of charge carriers in the medium, and their mobility. The higher the frequency of the applied field, the fewer are the obstacles to the movement of charges. Therefore, the specific electric conductivity of the medium increases with increasing frequency; this causes an increase in the attenuation coefficient of the medium and a restriction on the use of GPR in some types of soil [START_REF]Ground penetrating radar applications, principles, procedures[END_REF][START_REF][END_REF].

Another important characteristic of GPR is resolution. The resolution of the GPR antenna unit is the ability to distinguish two closely located objects. The resolution of the GPR is determined by the wavelength and is usually taken to be equal to its fourth part.

GPR survey is most often used in GPR profiling mode when the distance between the receiving and transmitting antennas does not change [START_REF]Ground penetrating radar applications, principles, procedures[END_REF][START_REF]Subsurface radar issues[END_REF]. In the process of moving, the transmitting antenna emits electromagnetic pulses that, propagating in the medium, are reflected from the contrasting interfaces of the soil layers or local objects and get into the receiving antenna. At each point, a signal is recorded, i.e. the direct passage signal from the transmitting antenna to the receiving one, and the secondary signal scattered by medium inhomogeneites. In this case, inhomogeneity is understood as the interface between media with different dielectric permeabilities 1

 and 2  .

Moving the antenna module above the heterogeneity surface leads to the fact that a hyperbole is observed on the GPR section (also called radargram, see Figure 1.1), which is described by the following equation:

, 2 2 ) ( 2 2 V h x V L x t   
where L is the path traveled by the wave, V is the speed, h is the depth of the object, x is the displacement of the GPR unit from the projection of the inhomogeneity onto the boundary of the half-spaces. The use of GPR method has several reasons. The first reason is the ability to perform studies of the internal spatial structure of soil layers with relatively high resolution (up to about 1 cm), which is related to the frequency range used in this method. In addition, the GPR method allows obtaining continuous information on the surveyed environment, which makes this method promising for creating software and hardware methods for monitoring the subsurface space and searching for communication lines and their networks [START_REF] Davis | Ground-penetrating radar for high resolution mapping of soil and rock stratigraphy: geophysical prospecting[END_REF][START_REF] Daniels | Ground Penetrating Radar[END_REF][START_REF] Conyers | Ground-penetrating Radar[END_REF][START_REF] Jol | Ground penetrating radar theory and applications[END_REF][START_REF] Benedetto | Civil engineering applications of ground penetrating radar[END_REF][START_REF] Slob | Surface and borehole ground-penetrating-radar developments[END_REF].

The effectiveness of the GPR equipment and technology are related to the type of antenna design. There are three main types of antennas: "butterfly", horn and dipole [15][START_REF] Congedo | Modified bowtie antenna for GPR applications[END_REF][START_REF] Turk | Hyper-wide band tem horn array design for multi band ground-penetrating impulse radar // Microwave and Optical Technology Letters[END_REF][START_REF] Yavna | Broadband directional antennas for monitoring the state of the ballast section of a railway track // Abstracts of the reports of the second international scientific-practical conference[END_REF].

Butterfly-type antennas make it possible to obtain a sufficiently high resolution, which is necessary for accurate positioning of subsurface objects and media interface boundaries [START_REF] Rial | Resolution of GPR bowtie antennas: An experimental approach[END_REF][START_REF] Xu | Statistical method to detect subsurface objects using array ground-penetrating radar data[END_REF]. The use of a horn-type design allows one to generate narrowly directed and more intense radiation. Suppression of external interference is possible by using the screen [15] made of metal attenuating external electromagnetic radiation.

To improve the quality of information, phased antenna arrays have recently been used [START_REF] Xu | Statistical method to detect subsurface objects using array ground-penetrating radar data[END_REF][START_REF] Kikuchi | Improved imaging capability of phased array antenna in Ground Penetrating Radar[END_REF][START_REF] Lutz | Phased-array transmitters for GPR surveys[END_REF]. Another direction to increase the effectiveness of the GPR method is the use of combinations of several operating frequencies [START_REF] Huston | Tri-band ground penetrating radar for subsurface structural condition assessments and utility mapping[END_REF][START_REF] Brunzell | Dual-antenna impulse radar for improved detection of buried land mines[END_REF].

GPR sections (radargrams) obtained during the survey are the sets of single tracks recorded for individual points of the GPR unit position [START_REF][END_REF][START_REF] Daniels | Ground Penetrating Radar[END_REF].

Engineers apply various methods of processing radargrams based on the use of standard object patterns [START_REF] Rachmana | Interpretation target pattern of a buried basic object on surface Ground Penetrating radar system[END_REF], neural networks and fuzzy logic [START_REF] Al-Nuaimy | Automatic detection of buried utilities and solid objects with GPR using neural networks and pattern recognition[END_REF][START_REF] Shihab | Image processing and neural network techniques for automatic detection and interpretation of ground penetrating radar data[END_REF][START_REF] Ahmadi | Estimating geometrical parameters of cylindrical targets detected by ground-penetrating radar using template matching algorithm[END_REF][START_REF] Lanka | Use of approximate reasoning techniques for locating underground utilities // Tunnelling and Underground Space Technology[END_REF], pattern recognition [START_REF] Simi | Hough transform based automatic pipe detection for array GPR: Algorithm development and on-site tests[END_REF]. Least square approximations [START_REF] Dolgiy | Optimal Radius Estimation for Subsurface Pipes Detected by Ground Penetrating Radar[END_REF][START_REF] O'leary | Direct and specific least-square fitting of hyperbolae and ellipses[END_REF] in fitting the GPR patterns by hyperbolas [START_REF] Ristic | A new method to simultaneously estimate the radius of a cylindrical object and the wave propagation velocity from GPR data[END_REF][START_REF] Shihab | Radius estimation for cylindrical objects detected by ground penetrating radar // Subsurface Sensing Technologies and Applications[END_REF][START_REF] Jafrasteh | Automatic extraction of geometrical characteristics hidden in ground-penetrating radar sectional images using simultaneous perturbation artificial bee colony algorithm[END_REF][START_REF] Mertens | Automated detection of reflection hyperbolas in complex GPR images with no a priori knowledge on the medium[END_REF] are used to determine the geometry and dimensions of cylindrical objects. In [START_REF] Liu | Estimation of subsurface cylindrical object properties from GPR full-waveform inversion[END_REF], the authors use a new method of three-dimensional complete inversion of the wave field in the frequency domain to determine both the geometric parameters of a cylindrical object and its dielectric properties. The latter allows determining the type of material.

GPR equipment

Currently, most of the domestic market is representad by the equipment of the following manufacturers: LLC "LOGIS" (Russia), LLC "VNIISMI" (Russia), LLC "Timer" (Russia), HTP "TENSOR" and FSUE "RosdorNII" (Russia), FSUE SKB IRE RAS (Russia), LLC "GEOLOGORAUTH" (Russia), Transient Technologies Ltd. (Ukraine), Spetsavtomatika LLC (Ukraine), GSSI (USA), Sensor and Software Inc. (Canada), Era Technology (England), MALA (Sweden), Radar Systems Inc (Latvia), Ingegneria Dei Sistemi (IDS) (Italy). Table 1.1 presents the GPR equipment and the frequencies of the antenna units used.

. Bibliometric analysis

The GPR method is used to solve a wide class of geophysical and engineering problems. To assess its demand, we will limit ourselves to solving only one task, namely, we will consider publications on the use of engineering methods for determining the location and depth of existing underground networks. The search was performed in the Scopus database. Dynamics of the distribution of scientific publications by year, country, scientific research areas is shown in Figure 1. [START_REF]Standard Guide for Using the Surface Ground Penetrating Radar Method for Subsurface Investigation[END_REF].

Number of publication

Publishing year

GPR method

Pipelines and cable searchers

Electric resistance method

Metal detectors

Optical methods It can be seen From figure 1.3 that the greatest number of inventions is related to the GPR-based method, 39%.

Thermovision methods

Magnetic methods

Acoustic methods

GPR on transport

The method of broadband GPR [START_REF]Ground penetrating radar applications, principles, procedures[END_REF][START_REF] Daniels | Ground Penetrating Radar[END_REF][START_REF] Vladov | Introduction to the GPR[END_REF][START_REF] Grinev | Sub-surface radar issues[END_REF] is currently used to survey the state of the railway track and engineering infrastructure facilities. Infrastructure transport objects are sources of secondary scattered electromagnetic waves, therefore, the use of GPR for their survey sets additional requirements for the interference protection of receiving and transmitting antennas, and increasing the overall information content in the subsequent mathematical processing of measurement results.

Chapters of the monograph [START_REF] Craddock | Antennas for Ground-penetrating Radar (Book Chapter)[END_REF] are devoted to the problem of antenna design for GPR. Research in this direction is carried out constantly. In [START_REF] Khakiev | Improving GPR monitoring of track ballast and railway structural integrity / Z.B // First break[END_REF], interference from the infrastructure, increasing the depth and resolution of surveys was achieved via the use of a horn design of the receiving and transmitting antennas;

refs. [17.42] discuss the possibilities of using Vivaldi antennas for examining the state and determining the electrical properties of infrastructure objects. In [START_REF] Ahmed | Incorporating transmitter-receiver offset to interpret pavement layer thicknesses by GPR[END_REF], experimental and theoretical studies of the effect of the distance between the antenna units on the accuracy of determining the thickness of pavement layers were performed.

Improving the informativity of the GPR method is significantly related to the progress of mathematical methods for processing radargrams; these are being developed in several directions. In recent years, significant progress in interpreting the data has been achieved using neural networks. In [START_REF] Shangguan | Pattern recognition algorithms for density estimation of asphalt pavement during compaction: A simulation study[END_REF], this approach was used to control the density of the asphalt-concrete pavement, and the study [START_REF] Tong | Recognition, location, measurement, and 3D reconstruction of concealed cracks using convolutional neural networks[END_REF] demonstrated the applicability of the approach for solving the problem of identifying hidden cracks. Another direction in the mathematical processing of radargrams is the automation of their interpretation [START_REF] Xie | An automatic recognition algorithm for GPR images of RC structure voids[END_REF]. Such methods lead to the creation of computer codes that work as part of hardware and software systems used in the diagnostics of extended transport infrastructure objects. Relevant technologies are developed by the following organizations and firms: U.S. Federal Railroad Admin-istration (USA), Safe Rail System (Germany), Zetica Rail (ZARR) United Kingdom, Roadscanners Oy (Finland), IDS (Italy), GSSI (USA).

World experience of using GPR on railways has shown their high efficiency when examining the ballast layer and the road bed. As a rule, railway track surveys are carried out by multichannel GPR systems combined with global positioning and video recording systems [START_REF]The development of a multi-channel GPR system for roadbed damage detection[END_REF]. Ref. [START_REF]An innovative vehicle-mounted GPR technique for fast and efficient monitoring of tunnel lining structural conditions[END_REF] introduced a six-channel GPR complex mounted on a mobile unit and used to survey the tunnel lining at speeds up to 175 km/h.

Several studies report on determining the parameters of the materials used for ballasting the railway track by the GPR method. The work [START_REF]Evaluating the effectiveness of methods based on reflected GPR signal for determining the clogging of the ballast layer[END_REF] is devoted to determining the informativeness of the amplitude and frequency analysis of the GPR signals reflected from the soil surface. It is shown that the methods based on the amplitude analysis of a signal are more informative than those using frequency characteristics. In [START_REF]Identification of type and degree of railway ballast fouling using ground coupled GPR antennas[END_REF], the dependence of the dielectric constant of the contaminated ballast material on the chemical composition of the pollutants was carried out, and [START_REF] Benedetto | Railway ballast condition assessment using ground-penetrating radar -An experimental, numerical simulation and modelling development[END_REF] investigated the dependence of the dielectric constant of the ballast on the concentration of the pollutant (siltysoil). In [START_REF] Bold | Benchmarking large scale GPR experiments on railway ballast[END_REF], the analysis of the scatter of the GPR waveforms was used to predict the ballast pollution index.

Attention to the inspection of roadbeds of roads and railways the foundations of artificial structures is caused by the danger of deformations of the upper structure of roads and buildings. To solve the problem of diagnostics of subgrade, the authors of [START_REF] Khakiev | GPR determination of physical parameters of motor road and railway structural layers[END_REF] developed a method for determining the refractive index and conductivity of structural layers of artificial structures using the results of GPR surveys. The developed methods were successfully used to monitor seasonal changes in the structural layers on several sections of railway. The authors of [54] developed a method for estimating seasonal changes in moisture of the structural layers of a railway track. In [START_REF]Determination of the complex permittivity and soil moisture by GPR[END_REF], the GPR method is combined with the resonance method for determining the electrophysical properties of soils. The method allows, in a short time interval, to diagnose the condition of extended objects as it combines the advantages of the high-speed GPR method with a limited number of veri-fying measurements of the dielectric constant by the resonant method, and the measurements of moisture content by laboratory methods.

Ref. [START_REF] Marecos | Assessing the pavement subgrade by combining different non-destructive methods[END_REF] is devoted to the determination of the anomalous zones of the subgrade by the method of GPR and load tests. The results showed good agreement between the two methods of non-destructive testing (GPR and load tests) in identifying the anomalous zones. In [START_REF] Wang | Experimental study of soil compaction effects on GPR signals[END_REF], the correlation between the density of soil and the results of GPR surveys is established. It is noted that the dielectric constant of the soil in its natural state depends on the water content, and an increase in the bulk density of the soil usually reduces its content. Thus, the process of changing the density of the soil, occurring during the construction of artificial structures or the current maintenance of artificial structures, affects the speed of propagation of electromagnetic radiation and can be studied by GPR.

Technogenic development of the territory with unfavorable conditions led to the study of properties of permafrost soils [START_REF]Investigation of the freeze-thaw states of foundation soils in permafrost areas along the China-Russia Crude Oil Pipeline (CRCOP) route using groundpenetrating radar (GPR)[END_REF] the degradation of which can cause significant damage to transport communications. In addition, numerous freeze-thaw cycles lead to a change in the geometry of the railway track due to frost heaving of the soil, which can lead to a limitation of the speed of trains and reduce the intensity of the turnover. In [START_REF] Silvast | Identifying frostsusceptible areas on Finnish railways using the ground penetrating radar technique[END_REF], for planning preventive maintenance in areas with frost heaving, a technique was proposed for examining the road bed of railways in order to identify frost-sensitive sub-ballast and ground layers using frequency-based GPR analysis techniques.

In recent years, research has been intensively developing to apply the GPR method to diagnose the state and determine the physical properties of quasihomogeneous finely dispersed media (concrete structures and asphalt-concrete road surface coverings). Such studies are aimed at monitoring the quality of construction work and monitoring the state of objects, which is necessary for determining their residual life The GPR method was employed in [START_REF] Ameri | Comparison of the field measurements of asphalt concrete densities obtained by ground-penetrating radar, pavement quality indicator and the borehole coring methods[END_REF] to measure the density of asphalt-concrete mixtures. In [START_REF] Dong | Rapid detection methods for asphalt pavement thicknesses and defects by a vehiclemounted ground penetrating radar (GPR) system[END_REF], according to laboratory experiments and simulation analysis, a theoretical method was proposed for determining the degree of compaction and delamination at the interfaces between structural layers.

Field tests showed its satisfactory accuracy. Work [START_REF]Estimation of in-situ density and moisture content in HMA pavements based on GPR trace reflection amplitude using different frequencies[END_REF] is devoted to the study of the density of the material of the asphalt pavement with drainage properties, and the identification of the presence of moisture in the layer under study by antennas operating at frequencies of 1.0 and 2.0 GHz. In [START_REF]GPR abilities in investigation of the pavement transversal cracks[END_REF], a library of radargrams obtained from coatings with different types of cracks was created, and a method for detecting local cracks was developed. Detection of cracks in the early stages of their development seems to be quite an important task because they contribute to the accumulation of moisture and chemical compounds, corrosion of reinforcement, weakening of the concrete monolith due to periodic processes of freezing and thawing of water. In refs. [START_REF] Trela | Non-destructive imaging of reinforcement bars in circular concrete columns using radar technique[END_REF][START_REF] Lachowicz | Application of GPR method in diagnostics of reinforced concrete structures[END_REF] high efficiency of the GPR method for solving the problem of determining the geometric dimensions of layers and positioning the reinforcement cage in reinforced concrete structures is noted. In [START_REF] Wiwatrojanagul | A new method to determine locations of rebars and estimate cover thickness of RC structures using GPR data[END_REF], a GPR method was proposed for automatic localization of reinforcement in reinforced concrete structures, based on a modified hyperbolic model of image formation. The method allows estimating the thickness of the protective layer with an average accuracy of up to 3.12%. The proplem of positioning pipes in a multilayer medium was solved in [START_REF]Robust adaptive detection of buried pipes using GPR[END_REF].

In [START_REF]A three dimensional approach for tracking cracks in bridges using GPR [Текст] /Andrea Benedetto[END_REF]69] the studies are carried out to identify cracks and determine corrosion of reinforcement in concrete structures of bridges using broadband georadars, and ref. [START_REF]Field observations and numerical models of GPR response from vertical pavement cracks [Текст] /Nectaria Diamanti[END_REF] is devoted to identifying cracks in road pavement (asphalt, concrete) using georadars at frequencies of 250 and 1000 MHz. Various types of cracks were simulated which allowed to describe their features in the GPR data.

Ref. [START_REF] Hong | Experimental monitoring of chlorideinduced reinforcement corrosion and chloride contamination in concrete with ground-penetrating radar[END_REF] presents the results of laboratory experiments aimed at identifying GPR signs of corrosion of reinforcement in concrete. It is shown that the growth of corrosion leads to an increase in the amplitude of the reflected signal in the time domain, but does not change the frequency of the peak in the frequency domain;

pollution with chlorides weakens the signal and lowers the frequency of the peak.

In [START_REF] Hasan | An experimental study for quantitative estimation of rebar corrosion in concrete using ground penetrating radar[END_REF], the corrosion of reinforcement was accelerated in laboratory conditions, which was accompanied by GPR studies; this made it possible to propose a method for determining the corrosion rate by measuring the maximum amplitude of the GPR signal.

An important direction of GPR research is the refinement of the values of the electrophysical parameters of the structural layers. Measurements of the dielectric constant of asphalt concrete pavements in the frequency range 1.7-2.0 MHz were carried out in refs [START_REF] Kulizhnikov | Dielectric values of various types of asphalt concrete pavements[END_REF]74], and the behavior of the dielectric constant of various bitumen materials was investigated depending on weather conditions [START_REF] Kulizhnikov | Dielectric values of various types of asphalt concrete pavements[END_REF]. The service life of reinforced concrete structures is directly related to water permeability, because almost all destructive reactions, such as corrosion of reinforcement and concrete, require the presence of liquid water or water vapor. The correlation between the depth of water penetration into concrete and the characteristics of the GPR wave pattern was studied in [START_REF] Rodríguez-Abad | Water penetrability in hardened concrete by GPR[END_REF][START_REF] Rodríguez-Abad | Application of ground-penetrating radar technique to evaluate the wa-127 terfront location in hardened concrete[END_REF], and the gradient of the mass of water absorbed by concrete structures through capillaries was studied in [START_REF] Xiao | Use of electromagnetic twolayer wave-guided propagation in the GPR frequency range to characterize water transfer in concrete[END_REF]. Since the parameters of the wave GPR picture of the medium are significantly dependent on the presence of water, the method for determining its concentration during the formation of concrete structures was proposed in [START_REF] Johnson | Non-destructive assessment of the rate of hydration and strength gain of concrete[END_REF]. In that work, the degree of correlation between the values of dielectric constant and strength was studied on the example of 45 samples of three types of concrete.

Monitoring the density of soils of the railway road bed by GPR

The normative state of the roadbed of roads and railways should provide uniform elastic and dissipative properties under the action of loads from automobiles and railway rolling stock, respectively. During the operation of roads and railways, residual deformations should be absent, and elastic deformations should not exceed 30% of the total elastic deformation of the railway track [START_REF] Lysyuk | Reliability of a railway track[END_REF].

To assess the possibility of using the GPR method for determining the strength characteristics of soils, a set of field and laboratory work was performed in [START_REF] Shapovalov | Monitoring the density of the subgrade soil by the GPR method. Way and track facilities[END_REF], which allowed the GPR method to be calibrated to determine the density of soil.

In [START_REF] Pupatenko | Density distribution in the bulk model of a railway subgrade. / Pupatenko V.V[END_REF], the density of soils in the body of a railway embankment was estimated from seismic data. The authors proposed a method for obtaining the value of density of soils from the measured values of the propagation velocity of seismic longitudinal and transverse waves. In [START_REF] Lobanov | Approaches to the study of the strength characteristics of soils as a factor of stability of floodplain-channel complexes (on an example of the basin of the upper Dniepr river)[END_REF], the dependences of the average frequency of the maximum of the reflected GPR signal with a center frequency of 400

MHz on the type of soil were obtained. In [START_REF] Neradovskiy | Determination of the strength properties of sedimentary and intrusive rocks in the cryolithozone of southern Yakutia using the GPR method[END_REF], GPR field and laboratory studies to determine the strength properties of sedimentary and intrusive rocks were carried out. The dependences of the speed of propagation and attenuation of electromagnetic radiation on the strength of granite, dolomite and sandstone are obtained. The authors of [START_REF] Wang Ping | Experimental study of soil compaction effects on GPR signals[END_REF] performed experiments to determine the effect of soil type on the shape of the reflected GPR signal. The velocities and amplitudes of the signal in various media, including multilayer ones, have been studied. The effect of density, moisture and soil mineralization on the formation of the reflected signal is estimated.

In [START_REF] Forte | A new fast methodology to estimate the density of frozen materials by means of common offset GPR data[END_REF], the authors proposed methods for determining the propagation velocity of electromagnetic radiation in a medium and associated it with the density of frozen materials. The problems of determining the dielectric constant and reflection coefficient from the change in the signal amplitude were considered.

GPR method in the construction of subgrade

During the construction of the roadbed of roads and railways, it is necessary to observe the geometrical parameters of the structure, as specified by the standards and laid down in the project, and to ensure uniform distribution of the strength characteristics of soils along the path under construction and into its depth. According to the norms, the compaction of the subgrade soil is carried out layer by layer at optimum moisture making a certain number of passes of sealing machines along the same track. It is known that soils are three-phase systems consisting of a soil skeleton and pores filled with water or air.

Porosity and soil moisture affect soil's condition, and with a decrease in porosity due to mechanical compaction of the soil, the strength and stability of the subgrade increases. Due to the importance of the density of the soil during the con-struction of the embankment norms the control of its values during construction is obligatory. In this regard, it is necessary to quickly monitor the density of a given profile to obtain continuous information. Such information will allow achieving a uniform compaction in accordance with the desiredn density values in the entire volume of the roadbed and to prevent leaving uder-or overcomacted areas.

One of the methods that can be applied to solve such a problem is the GPR method [START_REF]Ground penetrating radar applications, principles, procedures[END_REF][START_REF]Subsurface radar issues[END_REF][START_REF][END_REF][START_REF] Davis | Ground-penetrating radar for high resolution mapping of soil and rock stratigraphy: geophysical prospecting[END_REF][START_REF] Daniels | Ground Penetrating Radar[END_REF]. In [START_REF] Shapovalov | Approaches to the determination of the density of the subgrade soil by means of a geradiolocation method during construction[END_REF], the possibility of using GPR to determine the density of the subgrade soil of a railway under construction was studied.

Direct methods for measuring the electrophysical properties of soils

Methods for studying the properties of materials and soils using radio wave technology are sufficiently studied and tested. According to [START_REF] Brandt | Study of dielectrics at microwave frequencies[END_REF], they can be classified as waveguide, resonance, and free space methods. The choice of measurement method is determined by a number of factors, which include the frequency range, phase composition and properties of the material under study, temperature, etc.

When choosing a method, it is important to take into account the range of variation of values since methods for measuring samples with low permeability may not be suitable for samples with high dielectric constant and dielectric loss tangent. A detailed description of the theoretical concepts on the dielectric properties of substances, analysis of methods for calculating the principal dispersion parameters (relaxation time, distribution coefficient of relaxation times, thermodynamic functions, etc.), description of various methods for measuring dielectric constant and dielectric losses are given in monographs and review articles [89 -92].

In the tasks set in the dissertation research, it is assumed to obtain materials and soils with undisturbed structure obtained by boring. To substantiate the choice of methods for measuring the electrophysical parameters of the samples in the microwave range, we briefly describe the main methods for determining the dielectric constant.

Quasi-optical (in free space) methods

When using the quasi-optical method to determine the complex dielectric constant, the sample is located between the horn emitting and receiving antennas. During measurements, propagation characteristics of electromagnetic waves are recorded, such as attenuation and phase of the wave. The advantage of the quasi-optical method is that it is a non-destructive non-contact measurement methods. Using these methods does not impose strict requirements on the size, accuracy and roughness of the samples.

Waveguide methods

When using waveguide methods, the sample of the material under study is placed inside a coaxial or rectangular segment of the waveguide. The shape of the sample must exactly match the profile of the waveguide, which in the case of soils is difficult to implement, and leads to errors. When measuring in a coaxial waveguide, the samples should be cylindrical with a through hole in the center. The diameter of the coaxial waveguide is small compared with the diameter of the sampler. To measure in this waveguide, the selected samples must be crushed, which leads to disruption of the soil structure. The dielectric constant of the soil, as a complex multi-phase material, depends on the dielectric properties of the mineral composition of the solid, chemical nature, structure and composition of soil particles, their shape and size, as well as on the dielectric features of porous air and moisture.

Each of the phasessolid, liquid, and gaseousby entering in various combinations and ratios into the volume of the soil, contributes to the value of the effective dielectric constant of the soil as a whole complex of elements. To measure and calculate the dielectric constant of the system, knowledge of the structure, density, dispersion, porosity, moisture, chemical and mineralogical composition is necessary. In addition, it is necessary to understand the nature and the character of electrical interactions and bonding forces between atoms and molecules of soil material. It should be remembered, as noted earlier, that there are all kinds of conductivity in the soil: weak electronic (for well-conducting components of the solid phase), dielectric (for poorly conducting elements of the mineral part of the soil) and especially ionic (for soil solution). As a result of the above factors it can be seen that the violation of the structure of the soil leads to a change in the dielectric constant and conductivity. When the waveguides are filled with a sample to be measured, another problem arises: the waveguide mismatch, which leads to additional reflections and dissipated energy.

Waveguides of this type are connected according to two schemes (depending on the type of the wave, reflected or transmitted) "for reflection", and "for passage".

Resonance methods

In the resonance method, the sample under study is placed in a microwave resonator. A resonator is a volume completely enclosed by metal walls containing two small communication holes, through one of which electromagnetic fields are excited in the resonator. The dependence of the amplitude of the electromagnetic field on the frequency of the incident radiation characterizes the resonant curve of the resonator. This curve has maxima at the resonant frequencies of the resonator.

When measuring, the resonance curve is recorded first without a sample, and then with the sample. In the presence of a sample, a shift of the maxima of the resonance curve towards lower frequencies and a change in the shape of the resonance curve is observed. It becomes wider and lower in comparison with the resonant curve of an empty resonator. The shift of the resonance frequency and the widening of the resonance curve caused by the presence of the sample are used to calculate its complex permittivity [START_REF] Yavna | Broadband directional antennas for monitoring the state of the ballast section of a railway track // Abstracts of the reports of the second international scientific-practical conference[END_REF]. Measurements are possible for samples in the form of cylinders and discs. The advantage of the resonance method is the possibility of measuring the soil samples with undisturbed structure, high moisture and salinity (W up to 20%).

Conclusions

The above methods for determining the electrophysical properties of soil materials significantly expand the capabilities of the GPR method. The introduction of these methods in the practice of diagnostics of soil and structural layers of artificial structures will allow developing of an indicator method for GPR into a geophysical measurement method.

However, these techniques require refinement, comprehensive testing and admission in the prescribed manner to use in geophysical surveys. In this regard, in this study, the aim is to create a GPR method for determining the electrophysical properties of soils based on the use of optical approaches.

Comparison of the wave and resonance methods for determining the complex dielectric constant showed that resonance methods are preferable for evaluating the dielectric constant and conductivity of cylindrical core samples of large diameter. Of greatest interest is the method of a volumetric tunable resonator with a shorting capacitance, in which the directly recorded parameters are the shift of the resonant frequency and quality factor.

In this regard, this study develops a method for determining the electrophysical properties based on the resonance method of core samples of soil materials. Compared with the waveguide method, it has the following advantages:

-the resonance method requires small volumes of the investigated soil, the technology of preparation of which for measurements has been developed;

-the use of ditches with the test soil speeds up the measurement process;

-the internal dimensions of the resonator coincide with the internal dimensions of the sampler, which allows preparing samples for electrophysical measurements with minimal deformation of their natural internal structure and preservation of natural humidity.

In this regard, this study aims to create a GPR method for determining the electrophysical properties of soils based on the use of optical approaches and resonant measurements.

Chapter 2. Application of GPR for determining electrophysical properties of structural layers and materials

Organization of timely implementation of anti-deformation and repair work in tunnels and other objects of transport infrastructure requires a detailed analysis of the physical state of structures and their individual elements. In recent years, a nondestructive ground penetrating radar (GPR) method has been increasingly used for this purpose. In this Chapter I present the results of GPR determination of electrophysical characteristics (refractive indices and attenuation coefficients for electromagnetic radiation averaged within structural layers) of the highway road concretes in the tunnel using 1200-1700 MHz microwave radiation. The method of processing the GPR data is based on classical electrodynamics and, for practical implementation, it does not require additional integration with other geophysical or destructive methods. When performing calculations of electrophysical parameters of structures' concretes, various approaches are implemented, this made it possible to estimate the errors of the computational schemes and approximations. The results obtained are applied to clarify the dimensional parameters of the layers and determine the volumetric moisture content of structures' concretes.

Method of experimental studies

GPR tracking measurements were performed using the "OKO" georadar at a frequency of 1700 MHz after removal of the asphalt pavement from the roadway of the tunnel. Technical parameters of the equipment and the software for registration and primary GPR signal processing are given on the website of the manufacturer of the equipment: http://www.logsys.ru. According to the information of the equipment manufacturer, this radar provides the depth of examination up to 1 m with a resolution of up to 0.03 m. During the survey, the receiving antenna was kept in contact with the surface of the rigid base (the first concrete structural layer), the scanning time discrimination was chosen equal to 24 ns, and averaging over 16 independent measurements was performed during the registration of traces. It is known that the number of independent measurements in the registration of traces significantly affects the signal-to-noise ratio, which determines the depth of measurement and the quality of the GPR data. In this study, the selection of 16 independent measurements for recording the traces is optimal for the conditions and speed of the GPR measurements. Positioning of the GPR traces was carried out in manual mode by making marks on the radargrams through each meter of the trajectory.

The processing of experimental GPR sections obtained in this work was performed in the same manner as it is done in the Geoscan32 computer software package developed by Logis Ltd. The processing included the following steps. Initially, a part of the GPR section of interest was selected from the experimental material. To increase the contrast of the anomalies of the examined structure, the average trace determined on the section of 100 traces including the current one, was subtracted from the trace of the GPR section. Then, using direct and inverse Fourier transforms, low frequencies of up to 0.5 MHz were suppressed in the frequency spectrum of the traces. At the final stage of processing, the amplitudes of the trace ( ) ( exp  E ) were subjected to exponential amplification:

   е E E ) ( ) ( exp 
, where τ is the time of recording the point of the path, and  is the gain parameter chosen from the condition of the best representation of GPR information.

A general view of thus processed radargram obtained at 1700 MHz in the transverse direction of the carriageway is shown in Fig. 2.1 after applying a low frequencies filtering procedure (up to 0.5 MHz).

Theory of the method

Determination of structural layers' refractive indices: general case

Here we confine ourselves to considering the normal incidence of electromagnetic radiation on the boundary of the upper structural layer (incidence at α = 0), as in Fig. 2.2 for the general case.

The application of the approximation of normal incidence of the GPR pulse is valid in the case when the aperture of the antenna is substantially smaller than its distance from the boundaries of the structural layers. Consider the case where the antenna unit is placed at a certain height above the surveyed structure and the forward signal is reliably distinguished in the trace.

In this case, the equation for the amplitude of the electromagnetic wave reflected from the upper boundary of the rigid base has the form [START_REF] Born | Principles of Optics, 7th[END_REF]:

, 1 1 1 1 0 1    n n Ε Ε (2.1)
where E 0 is the amplitude of the electromagnetic wave incident on the upper boundary, n 1 is the absolute refractive index of the rigid base; refractive index of air is taken equal to unity.

When calculating the amplitude of the electromagnetic wave reflected from the upper boundary of the leveling layer "b" (Fig. 2.2), the relations describing the following processes are taken into account. When propagating from the transmitting antenna, an electromagnetic wave can pass from the air into a rigid base through the interface "a" (Fig. 2.2), weaken in its material and be reflected from

invert   1 E 2 E 3 E 0 E 1 E 4 E 0 E A B 0 E  0 E  0 E   2 E  3 E  3 E   4 E 
the interface "b" (Fig. 2.2). The electromagnetic wave reflected in the direction of the receiving antenna undergoes attenuation once again in the material of the rigid base, passes through the interface "a" (Fig. 2.2) into the air and consequently the amplitude takes the form:

  2 1 2 1 2 2 1 1 2 1 1 1 4 n n n n е n n Ε Ε h p 0      , (2.2)
where n 2 is the refractive index of the leveling layer, 1 h is the thickness of the rigid base, p 1 is the attenuation coefficient of the electromagnetic radiation in the rigid base.

An expression for the amplitude of the wave reflected by the upper boundary of the invert (surface "c", Fig. 2.2), and reaching the receiving antenna, can be obtained in the same manner. In this case, when deriving the expression for the amplitude from equation 2, the process of reflection from the interface "b" is excluded (Fig. 2.2). Additionally, the following processes are considered: transmission of electromagnetic radiation through the interface "b" (Fig. 2.2), attenuation in the material of the leveling layer, reflection from the interface "c" (Fig. 2.2), repeated attenuation in the material of the leveling layer, and exit into the air through the interface "a" (Fig. 2.2):

    3 2 3 2 2 2 2 2 1 2 1 2 1 1 3 2 2 1 1 4 1 4 n n n n е е n n n n n n Ε Ε h p h p 0        , ( 2.3)
where 2 h is the thickness of the leveling layer, n 3 is the refraction index of the invert, and p 2 is the coefficient of attenuation of electromagnetic radiation in the leveling layer.

The solution of the system of equations ( 2 3) implies a selfconsistent procedure in the case when the values of h 1 and h 2 are unknown. Realization of a self-consistent procedure implies taking into account in (2.1-2.3) the module of a complex refractive index instead of its real part.

Additional equations for the determination of refractive indices

Direct measurement of the amplitude of the electromagnetic wave E 0 incident on the upper boundary may encounter significant difficulties due to the features of the formation and recording of an electromagnetic wave in the near-field region. In addition, in measurements with the movement of the antenna unit along the boundary of the surveyed structure, it is difficult to isolate the value 1 Ε against the background of the direct transmission signal. These circumstances make it difficult to apply the equations (2.1-2.3) directly to the calculation of the refractive indices. In such cases, it is necessary to use additional information that can be contained in radargrams, and lead to a change in the set of equations for calculating the refractive indices of multilayered structures.

GPR images of local objects

In this work, the absolute refractive index of the rigid base (n 1 ) is determined by plotting the hyperbolas reflecting the positions of local objects near their lower boundary by the method employed in the Geoscan32 software package. The method is illustrated in Fig. 2.3, where an antenna block with a linear coordinate x is displayed moving along the upper boundary of the medium in which a local reflecting object with the coordinates x 0 , z 0 is located.

It is evident from Fig. 2.3 that

      , ) , 0 ( ) , ( ( 2 0 0 2 0 2 0 0 z R z x x z x x R L       (2.4)
where L and z 0 are the shortest distances from the media interface to the reflecting surface of the object, and

) , ( 0 0 z x x R 
is the distance from the center of mass of the reflecting object to its reflecting surface. , where c is the speed of propagation of electromagnetic radiation in vacuum, t and t 0 are the propagation time of a pulse of electromagnetic radiation in a medium with a refractive index n when the antenna unit is placed in positions with linear coordinates x and x 0 . Then expression (2.4) can be reduced to the form:

) , ( ) , 0 ( 2 ) ( 2 0 0 2 0 0 2 0 z x x R x R n ct x x c n t             . ( 2.5)
It can be seen from equation (2.5) that the local objects create a hyperbolic image on the radargram, and that this allows, with a known function

) , ( 0 0 z x x R 
, to restore the value of n, seeking agreement between theoretical and experimental values of t.

In this work, cracks in the invert that extend to the lower boundary of the rigid base (Fig. 2.4) and the reinforcement placed at a small depth in the invert (Fig. 2.5) are selected as local objects. The curves t = t(x) are constructed for 10 local objects. The absolute refractive index is assumed to be equal to the average value for all the objects examined and it is found to be n 1 = 3.16±1. 5. The scatter in the results of individual measurements can be explained by the used mode of binding the radargrams to the trajectory of the antenna unit movement. As mentioned above, in this study, the binding was performed manually, and the scatter in the number of traces between the marks marking the one-meter segments along the path of the antenna unit was about 10%. In addition, the variation in the size of the local objects used can lead to a scatter when determining the refractive index.

The dependence of the hyperbola shape of the GPR feature of a local object of circular cross section on its radius was studied of [START_REF] Dolgiy | Optimal Radius Estimation for Subsurface Pipes Detected by Ground Penetrating Radar[END_REF]. Determining the n values for local objects of arbitrary shape with

) , ( 0 0 z x x R 
dependent on x via solving equation (2.5) requires the analysis of the amplitudes of reflected waves, and it would be a separate study outside the frame of the study.

In this work, when determining n, the finite dimensions of the local objects were not taken into account. The relative error in the refractive index and the permittivity introduced by this approximation is evaluated for the case

m z x x R z R 01 . 0 ) , ( ) , 0 ( 0 0 0   
, with relative errors δt = δt 0 = 0.

For the relative error of the refractive index, one can obtain the following expression using (2.5):

      n ct z R n ct z x x R z R n ct x x z R n ct x x z x x R z x x R z R n ct x x z R z R z R n ct n 2 ) , 0 ( 2 ) , ( ) , 0 ( 2 ) , 0 ( 2 ) , ( ) , ( ) , 0 ( 2 ) , 0 ( ) , 0 ( ) , 0 ( 2 0 0 0 0 0 2 0 0 2 0 2 0 0 2 0 0 0 0 0 2 0 1 0 2 0 0 0 0 0                                                               (2.6) Assuming R z x x R z R       ) , ( ) , 0 ( 0 0 0 , x 0 -x = z 0 =0.2m
, and

m z x x R z R 01 . 0 ) , ( ) , 0 ( 0 0 0    , (2.6) gives R n   13 . 0 
. Then the uncertainty of the shape of the reinforcement cross section in the case under consideration can give a maximum contribution to the error in refracting index (at 1  R



) of up to 15%.

Contact of the rigid base and the invert

The use of a leveling layer in the construction of automobile tunnels is connected with the need to provide required slope to the rigid base. In this situation, on the curved sections of the road, the areas of contact between the rigid base and the leveling layer can be replaced by the regions of direct contact between the rigid base and the invert ("d" in Fig.

  3 1 3 1 2 2 1 1 4 1 1 1 4 n n n n е n n Ε E h p 0      , (2.7)
where E 4 is the amplitude of the signal reaching the receiving antenna after reflection from the boundary between the rigid base and the invert.

Equations for calculating the absolute refractive indices of the leveling layer and the invert

Homogeneity of the dimensions and properties of the rigid base, and the determination of its absolute refractive index according to subsection 2.2.2.1, allow moving the point of comparison of amplitudes from the upper boundary of the structure ("a", Fig. 2.2) to the upper boundary of the leveling layer ("b", Fig. 2.2), or the invert ("d", Fig. 2.2).

According to the above notation, near these boundaries, the incident radiation has an amplitude ' 0 Ε , the magnitude of which can be obtained from 0 Ε taking into account the process of passing the electromagnetic wave from the air into the rigid base through the interface "a" (Fig. 2.2), and its attenuation in the material of the rigid base. Then the desired amplitudes of radiation can be obtained by excluding from equation (2.2) and (2.7) the processes of attenuation of electromagnetic radiation in the material of the rigid base and the exit into the air through the interface "a" (Fig. 2.2); they have the form:

2 1 2 1 ' 0 2 n n n n Ε E     , (2.8) 3 1 3 1 ' 0 4 n n n n Ε E     , ( 2.9)
where, as before, Similarly, from equation (2.3) we can get the amplitude of the wave reflected by the upper boundary of the invert. We take into account that the radiation reflected by the interface between the leveling layer and the invert passes twice through the interface between the rigid base and the leveling layer, and it weakens while spreading through the leveling layer. We denote the corresponding attenuation coefficient with p 2 .

Then the amplitude at the observation point is determined by the relation:

  . 4 3 2 3 2 2 2 1 2 2 1 ' 0 ' 3 2 2 n n n n е n n n n Ε Ε h p      (2.10)

Numerical procedures for determining the coefficients of attenuation of the electromagnetic field and refractive indices

The technology of the GPR tracking measurements used in this work makes the use of equation (2.1) impossible because of the complexity of measuring E 0 in the near-field region. In this case, the system of equations for the calculation of n 2 , n 3 , and the amplitude E 0 will include equations (2.8-2.10). The solution of these implies an independent determination of the attenuation coefficients p 1 , p 2 , as well as the determination of the amplitudes ' 1 Ε , ' 2 Ε and ' 3 Ε from the radargrams.

In the case of conducting media, the systems of equations ( 2

       р с n 
, where c is the speed of light in vacuum, ω is the central value of the circular frequency of the GPR pulse. In this case, it is necessary to additionally determine the attenuation coefficients p 1 and p 2 .

Let us consider possible approaches to the determination of the attenuation coefficients.

The use of traces to determine the attenuation coefficients for an example of industrial water

In this section, the possibility of determining the electromagnetic radiation attenuation coefficient via the processing of traces in the case of a 0.2 m thick layer of industrial water is demonstrated. For this purpose, GPR measurements were carried out in laboratory conditions with the antenna unit placed 0.05 m above the water surface. During the examination, as before, the sweep value was chosen to be 24 ns, and during the registration of traces, the averaging was performed over 16 measurements. Registered traces of a total of 100 are averaged and subjected to the Hilbert transform, which converted the values of the traces to the values proportional to the module of the complex amplitude of the electromagnetic field. This relationship is approximated by

) ( 2 0 | ) ( | r r p Aе Ε Н    , (2.11)
where r is the current coordinate, and r 0 is the initial point of the approximation. To estimate the accuracy of the proposed procedure for calculating the electromagnetic waves attenuation coefficient, an independent determination of the attenuation coefficient is made using the amplitudes of the waves reflected by upper and lower boundaries of the water layer. The ratio of equations of the form (2.10) and (2.8) written for a layer of water leads to the following expression for determining the electromagnetic radiation attenuation coefficient p: The values of attenuation coefficients for water obtained with the use of formulas (2.11) and (2.12) are given in Table . 2.1. Comparison of the data in Table 2.1 allows estimating the accuracy of the mathematical procedure for the processing of traces to be about 20%.

  , ln          

The use of traces to determine the attenuation coefficients of tunnel structural layers

To determine the attenuation coefficients of electromagnetic radiation of the rigid base p 1 , the leveling layer p 2 and the invert p 3 , the radargram shown in Fig. 2.1 makes it possible to estimate the error of the numerical routine to be about 15%.

Determination of the absolute refractive indices of structural layers

The amplitudes ' 2 Ε , ' 3 Ε and ' 4 Ε of the reflected waves formed at the interfaces of structural layers (Fig. 2.2) required for the calculation of the refractive indices are given in Table 2. [START_REF]Standard Guide for Using the Surface Ground Penetrating Radar Method for Subsurface Investigation[END_REF]. For their determination, intervals of the GPR section are identified that do not contain local objects that could distort the wave pattern from the interface between the media. To improve the accuracy of the numerical procedure, averaging was performed over 10 traces of this profile and over three adjacent GPR sections of the same type. Table 2.2 also lists all possible relationships between the refractive indices of the rigid base, the leveling layer and the invert, and the solutions of equations ( 2

Selection of refractive indices using phase analysis of radargrams

To select the solutions among the possible options given in Table 2

      t s t s arctg t i i i    , ( 2.13)
where   t si  is the orthogonal complement of the trace defined by the Hilbert transform:

. ) ( ) ( ) (            d t s t s i i Function   t si  satisfies the relation       0 ) ( ) ( dt t s t s i i Calculated   t i 
are shown in Fig. 16 together with the traces from the domains of the radargram designated as a, b and c. It can be seen that near the interfaces of the rigid base and the leveling layer (position a), there is no change in the phase of the reflected signal meaning that n 1 > n 2 . At the same time, the phase change is seen at the interface between the leveling layer and the invert (position b), as well as at the interface between the rigid base and the invert (position c). Inversion of phase at these boundaries means a greater value of the absolute refractive index of the invert n 3 compared to that of the leveling layer, n 2 ; this allows us to choose the solution (n 1 > n 2 <n 3 , n 1 <n 3 ) as physically justified. (2.14)

The value of the attenuation coefficient p 2 , calculated with (2.15) for h 2 = 0.15 m is given in Table 2.1.

Results and Discussion

Verification of GPR results using alternative methods

GPR studies and the proposed methods for the data processing discussed above made it possible to determine the absolute refractive indices n 1 , n 2 , n 3 and the attenuation coefficients p 1 , p 2 , p 3 for electromagnetic radiation in the structural layers of the roadway of the automobile tunnel made of concrete of different brands.

 

             ' 3 ' 2 1 2 2 3 1 2 2 3 2 1 2 2 ) ( 4 ln 2 1 E E n n n n n n n n n n h p 53
The verification of the obtained results was performed as follows. The refractive index n 1 was used to calculate the thickness of the rigid base, which is found to be h 1 = 0.19 m. The thickness of the rigid base made after its disassembly is measured directly and found to be 0.20 -0.22 m. Comparison of the thicknesses thus obtained gives an estimate of the accuracy of the GPR method for determining the refractive index,

% 10 1  n 
. Comparison of calculated thickness of the leveling layer and the results of its direct measurement leads to a similar estimate of the error of the refractive index n 2 .

To assess the accuracy of the GPR determination of the attenuation coefficient for electromagnetic radiation in the leveling layer, we compare the results of calculations performed by different methods and given in Table 2. [START_REF]American Society of Civil Engineer Standard Guideline for the Collection and Depiction of Existing Subsurface Utility Data[END_REF]. It is clear that those results are similar; the average value is p 2 = 7.24 m -1 with an error less than 5%.

At the same time, solving the system of equations (2.8-2.10) provides the significantly different values of the refractive indices of the rigid base and the invert made of concrete of the same B25-type (Table 2.2). This can be explained by the overmoisture of the invert, which was confirmed by the excavation work of the rigid base and the leveling layer (Fig. 2.17).

To determine possible moisture of the concrete of the invert we confine ourselves to the approximation of independent media. In this approximation, the optical density of water-saturated concrete is a sum of the optical densities of the concrete frame, and the pore water.

Suppose that the volume of the invert V contains the volume of water where the volumetric moisture of concrete is determined by the relation: ; it compares with the value obtained from (2.15) with an accuracy of 18%.

V V w O H / 2  .
The proximity of the obtained moisture values can serve as an indirect evidence of reliability for the proposed methods for processing GPR data in obtaining the numerical values of

Contrast of construction layers

According to the tunnel construction project, a B25-type concrete was used to form the rigid base and the invert, and the leveling layer is made of a B15-type concrete.

The concretes used can have significant variations both in the composition of the ingredients and in their electrical properties. It is therefore advisable to check the validity of the relation n 1 > n 2 in laboratory conditions, for example by the method [START_REF]Determination of the complex permittivity and soil moisture by GPR[END_REF]. In addition, the approximate relationship between the refractive indices of these layers can be estimated at the frequencies of the GPR measurements by the relation: The possibility of determining the electrophysical quantities without using any additional information makes the proposed method promising for the use in the software systems for automatic processing of GPR information when monitoring 57 extended sections of roads and railways. Electrophysical quantities and moistures determined during surveying allow estimating the rate of degradation of structural layers' materials which is necessary for timely repairs.

Further development of the method, along with the development of the selfconsistent procedures for the solution of equations (2.1-2.3, 2.7) or (2.8-2.10), may be associated with the refinement of physical assumptions, namely, with the rejection of the approximation of normal incidence, with additional consideration of the spectral features of the incident radiation, and dispersion dependences of electrophysical quantities.

The practical use prospect of the developed monitoring method depends significantly on the accuracy of obtaining and processing the GPR data, which, in turn, is associated with the technical capabilities of the GPR equipment and surveying techniques.

Chapter 3. Resonance method for determining the electrophysical properties of soils and materials.

Objectives of the study.

The presence of water in the structural layers of engineering structures, roadbed layers of roads and railways can adversely affect the stability of the structures. In this regard, it is important to quantitatively characterize the soil moisture both at individual points of the structure [START_REF] Makeeva | Dielectric properties of composite materials 129 based on cement of different genesis[END_REF] and along its extended sections [START_REF] Khakiev | GPR determination of physical parameters of motor road and railway structural layers[END_REF].

Traditionally, the density and humidity of soils are determined by destructive methods, for example, by drilling and sampling. These methods are characterized by high accuracy of measurements, however, they are relatively expensive and time consuming; they also require stopping the traffic on the surveyed site during the measurements. To overcome these difficulties, it is increasingly recommended to use non-destructive geophysical methods [START_REF] Makeeva | Dielectric properties of composite materials 129 based on cement of different genesis[END_REF][START_REF] Dane | Methods of Soil Analysis, Part 4 Physical Methods[END_REF].

An important place among geophysical methods is occupied by the GPR method, which allows obtaining continuous information about the state of soil layers, both in the mode of detailed diagnostics, and as part of specialized diagnostic mobile tools (railway cars, mortises, and automobiles). For its effective use in solving the problems of quantitative diagnostics of infrastructure facilities, the procedure of integration of the GPR methods and the methods of direct measurements of electrophysical properties of soils and materials seems promising.

In this regard, this chapter solves the problem of developing a technique for resonant measurements of the dielectric constant and specific conductivity of soilforming minerals at different humidity at a frequency of 1400 MHz.

For solving the problem, the following studies have been performed.

1) Designing a cavity resonator for measuring the properties of materials extracted from the core.

2) Determination of the dependence of the resonant frequency on the dielectric constant of samples with known values of basic electrophysical parameters.

3) Creating a computer model of the cavity resonator, in accordance with the prototype, using the software CST Studio Suite.

4) Determination of the resonance frequency of electromagnetic waves that have passed through the reference samples with known dielectric constant values.

The second problem of the research is connected with the creation and use of a number of methods, including GPR and resonance measurements, for determining the electrophysical properties of soil media and materials at different values of moisture.

To solve it, the following studies were performed.

1) Integrated study of dielectric properties of soil-forming minerals with different moisture using the cavity resonator method, and simultaneous GPR measurements at a frequency of 1.4 GHz.

2) Determination of the real part of dielectric constant and the conductivity of soil-forming minerals by the developed set of methods.

Soils model

The principal components of the soil are soil-forming minerals, air, water in various aggregative states, aqueous solutions of salts, organic and inorganic impurities. The diversity of the pore space structure and different nature of surfaces of the soil particles lead to specific features of their interaction with water vapor and water. The mechanism of absorption and retention of moisture depends on the size and shape of their pore space, as well as on the surface area, and surface hydrophilicity. Water in grounds, rocks and soils can be in a free or a bound state.

Free water is water under the action of gravity in non-capillary-sized macropores and rock cracks, as well as water held in pores and cracks by capillary forces. In contrast, the bound water is retained in soils due to chemical and physicochemical forces acting from the surface of the particles and changing its properties in comparison to the free water [START_REF] Benedetto | Water content evaluation in unsaturated soil using GPR signal analysis in the frequency domain[END_REF].

Analytical models of dielectric constant in soils

Water in soils

Natural dispersed structures, including rocks and soils, are complex polydisperse formations with a diverse structure of the pore space and different nature of the surface of the particles forming them. In this regard, the soils have specific features when interacting with water vapor and liquid water (Fig. 3.1). The absorption and retention of moisture depends on the size and the shape of their pore space, as well as on the area of their surface, and its hydrophilicity. 2) adsorbed -physically absorbed from solutions by soil particles;

3) hygroscopic -absorbed by soil particles from the air.

Tightly bound water is not capable of moving in the soil without its heating or compaction.

II.

Loosely bound water is water that envelops soil particles with a film of different thickness and it moves along the film as a liquid from areas with greater film thickness to areas with smaller thickness.

III.

Free water is divided into:

1) gravitational water -its movement in the pores under the action of gravity is not hampered by capillary and electromolecular forces; water in separately localized pores larger than 1 mm also belong to this kind;

2) capillary water held in pores and cracks by capillary forces.

It is believed that all water, except chemically bound, can be removed from the soil by heating it to a temperature of 105-110 ° C.

According to an alternative classification, there are the following types of water in soil: 1. "Osmotically" absorbed water -absorbed due to selective diffusion of water in the direction of the surface of the particles ("surface osmosis"). The layer of "osmotically" absorbed water experiences some influence of surface forces, which can affect its structural features. In this case, in the water layer of up to 10-6 cm, not only the ordered arrangement of its molecules is possible, but also the formation of a transition ("melted") layer of moisture with a "disordered" arrangement of molecules in it. In the case of high salinity of the solution interacting with the rock, "osmotic" water is not formed.

Capillary water (capillary condensation and absorption

) is water in the capillary-sized pores (<1 mm), absorbed by capillary pressure and held by the capillary forces of the meniscus at the inter-phase boundary: water -air -solid surface.

III. Free water (closed in large pores and flowing). Water in a liquid state ("gravitational"), which is exclusively under the action of gravity in non-capillarysized macropores and rock cracks (> 1 mm), and water in closed macropores.

All of these types of water are found in soils of different composition, and the greater the specific surface area of the solid component (the surface area of particles in 1 g of soil) and the lower the soil moisture, the greater is the role played by bound water.

The variety of water types in the soil is characterized by several parameters.

The main parameter is the weight moisture of the soil, which is determined as the ratio of the mass difference of a soil sample before and after drying at 105-110 ° C

to the absolutely dry state to the mass of absolutely dry soil sample;is expressed in fractions or in percent. Along with the weight moisture, there exists the parameter of volumetric moisture, which is the volume of water in a unit volume of soil.

Analytical dielectric permittivity models related to the porosity parameter

To create a model that describes the distribution of the dielectric constant in a real environment (soil, clay, sand), we use the porosity parameter (ϕ). The porosity of the soil is the ratio of volume occupied by the soil voids, to the total volume of the soil with natural moisture. Using the relationship of the refractive index and die-

lectric constant r n   (3.1)
one can express the refractive index in the approximation of non-interacting phases that make up the soil:

,,

(1 )

r r g w w w r a n S S              (3.2)
where ϕ is the soil porosity, S w is the degree of humidity,

w box w soil SV W m      , (3.3)
where V box is the volume of the cubic form in which the sample is placed,  w is the density of water, , m soil is the mass of the sample.

Models of effective dielectric constant

Consider soil samples as diverse systems of microparticles. If any macroscopic parts of this system exceed characteristic dimensions of its components, and the distances between them are large, then the so-called effective model can be used to describe its properties. In this model, the soil is considered as a homogeneous medium (matrix) having its macroscopic characteristics, and inclusions (Fig. 3.3)

[100-101].

Figure3. [START_REF]British Standard: Specification for Underground Utility Detection, Verification and Location Institute of Civil Engineer[END_REF]. Schematic representation of the real heterosystem (left) and its effective model (right). Consider the matrix of a medium with a dielectric constant ε having isolated inclusions (for convenience, we assume that all the inclusions are spherical) with a dielectric constant ε 1 . We assume that all inclusions have the same macroscopic properties and their volume fraction f 1 is much smaller than that of the matrix. Due to the rarity of inclusions, it is assumed that in an electric field, the resulting polarization in the sphere will not affect the polarization of the matrix as a whole. In this case, each selected sphere is placed in a uniform electric field and surrounded by a medium with dielectric constant ε. Then the polarization inside this sphere is calculated as: 0 [START_REF]British Standard: Specification for Underground Utility Detection, Verification and Location Institute of Civil Engineer[END_REF] 2

eff eff P       (3.4)
On the other hand, this polarization is the sum of polarizations of all the inclusions:

11 01 11 [START_REF]American Society of Civil Engineer Standard Guideline for the Collection and Depiction of Existing Subsurface Utility Data[END_REF] 33 22

k k P E V f E V                , ( 3.5)
where

1 1 k k fV V
  is the volume fraction of inclusions and k numbers the inclu- sions.

From the equality of the right-hand sides of equations (3.4) and (3.5) follows the expression for the effective dielectric constant:

1 1 1 22 eff eff f           or 1 1 1 1 1 1 (1 2 ) 2 (1 ) , (1 ) (2 )
eff ff ff           (3.6)
At f 1 →0, (3.6) is reduced to .

eff

 

The models described make it possible to calculate the dielectric constant of various media for small and large volume contents of inclusions. In the calculation, a finite elements integration method was used, implemented using the "Eigenmode Solver" software block with the division of space into discrete cells of hexahedral form. With its help, the natural frequencies and respective distributions of electromagnetic fields of systems with different electrophysical parameters are determined (Figures 3.6 -3.10).

field has the maximum value of the vector E = 2.72·10 8 V/m (Fig. 3.6). Thus, the design of the resonator has limitations on the range of the measured dielectric constant of the samples, which can be estimated by   30.

Software and hardware device for experimental studies of the electrophysical properties of samples.

The necessary measurement tools for experimental studies of the electrophysical properties of samples (see Fig. 3.10) include the P2M-04 transmitter and reflection modulus meter, operating in the frequency range 10 MHz -4 GHz (a), a brass resonator containing the sample container (б) made of plastic with a dielectric constant of 2.98, as well as a computer with a specialized software (в).

The R2M-04 device includes hardware and software parts. The hardware part performs a number of basic functions that determine the measurement modes.

The software part provides the implementation of the user-selected measurement mode, control of measurements, and display of measurement results. When plotting the calibration curve, materials with guaranteed dielectric permeabilities were used: Fluoroplast with ε = 2.08, PCT-3 with ε = 3, Polystyrene with ε = 2.6, FLAN 2.8 with ε = 2.8, glass fiber laminate with ε = 6 and FLAN 10 with ε = 10. These materials were used to make discs with the diameter d 0 =19 mm and the thickness of l = 2 mm.

The results are presented in Figure 3.11. It can be seen that the accuracy of the computer model and the numerical procedure can be estimated at 0.5%. Combination of these physical quantities allows us to calculate the attenuation coefficient determined by the processes of absorption and scattering of electromagnetic radiation ( ), and the refractive index ( ), with the expressions [START_REF] Born | Principles of Optics, 7th[END_REF]:

(

where 𝜔 is the most probable value of the chiclic frequency, c is the speed of light in vacuum, and μ 0 is the magnetic permeability of vacuum. Since the radiation of the GPR pulse is not monochromatic, the most probable circular frequency was used in the calculations by formulas (3.9-3.10). For the radiation of the AB-1700 antenna of the "OKO" series GPR used in this work, it is determined to be 𝜔 = 2πf = 8.79 10 9 s -1 .

Algebraic transformations of expressions (3.9-3.10) allow us to associate the absorption coefficient and specific conductivity by the relation:

(

For a given soil condition, from the results of the GPR measurements, we determine the intensity of the reflected signal E * , the position of the interface between the soil layers, and the attenuation coefficient of electromagnetic radiation .

Electromagnetic radiation propagating in medium undergoes angular divergence, the value of which depends on the antenna design and the properties of the medium, as shown in Figure 3.12. We define the attenuation coefficient associated with the spatial divergence of electromagnetic radiation in the sample by .

(3.12)

* e p * n               2 2 4 2 0 2 2 1 ω σ с μ ε ε с ω p              2 2 4 2 0 2 2 2 1 ω σ с μ ε ε n c pn 0 2    * p * * e p p p   
The basis for determining the value of the complex dielectric constant of the sample is a comparison of the results of direct measurements of signal's frequency and quality factor with the results of their computer simulation with specified dielectric permeability and conductivity. When the container with the soil is placed in the cavity of the resonator, and with the increase of soil's moisture, the dielectric losses increase. To take them into account in a computer model, in addition to the real part of the dielectric constant, additional parameters of the sample are introduced: conductivity (σ) or dielectric loss tangent (tanδ).

In this work, calibration of the results of georadar survey of sand placed in a volume of cubic shape with a side of 0.5 m was performed. The antenna unit was placed above the surface of the sand at a height of 0.15 m. The sand humidity was . Conductivity is determined by the formulas:

 * =- ст ,
, where  is the specific conductivity of the sample placed in the container,  ст = 0.92 10 -3 S/м is the specific conductivity of the container without sand, is the width of the resonance curve at half height .

) (r F F  )) ( ( r F G G  ) ( 0 * )) 0 ( ( )) ( ( r r p e F G r F G    0 )) ( (  r F G , h r  h 0 r 0,0 0, 2 0,4 0,6 0 2000 4000 E, отн.ед. h, м 3.7.
Determination of the real part of dielectric constant and the conductivity of soil-forming minerals using GPR calibrated method.

Determination of electrophysical properties of soils after a change in their state, which may be caused by thea change of moisture, is carried out using the calibrated GPR method.

Implementation of the method is related to determining the intensity of the reflected signal E 0 , the position of the corresponding interface and the attenuation coefficient of electromagnetic radiation.

The calculation of the dielectric constant of the soil in a new physical state is performed using the expressions:

(

Calculated refractive indices for sand of different moisture are given in Table 3. [START_REF]Standard Guide for Using the Surface Ground Penetrating Radar Method for Subsurface Investigation[END_REF]. The table also shows attenuation coefficients determined by analogy with section

      n n A (3.17) (3.16) , ) 1 ( ) 1 ( 2 2 2 2 
In the (3.16) the following notation is used:

The data shown in Figure 3.16 allows us to estimate the relative deviation of the calculated and experimental values of relative intensities with a value of 0.10 -0.15%.

Combined use of formulas (3.16) and (3.17) made it possible to determine the electric field strength of the incident wave on the sample surface during the GPR surveys of this work:

. The possibility to estimate the electric field strength of an incident wave at different distances from the emitter can be used in evaluating the efficiency of designing antenna units.

Determination of sample moisture using calibrated GPR data

The solution of the problem of determining the correlation between the complex dielectric constant and the moisture content of soil samples has been addressed in [103], where this correlation dependence is approximated to a high degree of accuracy 𝛿 < 10% by a third-order polynomial where the parameters A, B, C and D depend on the composition of the sample, but at the same time their ratio being 1: 9: 60: 30.

It can be seen that the main contribution to the approximation of the dielectric constant is comes from the quadratic term. This suggests that the dependence of the refractive index on moisture and is close to linear. The dependence of the refractive index on moisture for sand obtained in this work is shown in Figure 3.17. It is obvious that the tangent of the slope of the straight line will depend on the composition of the samples, therefore the calibration of the GPR data should be carried out at two points.

0

E E A  p c    % 10 15000 0   E , 3 2 DW CW BW A      1.

Conclusions

In this work, a method has been developed for determining the complex dielectric constant and soil moisture by the resonant method, the results of which are used for calibrating the GPR measurements.

To this end:

-a numerical model of a cavity resonator was developed in the software product CST Studio Suite;

-the cavity resonator for measuring the properties of materials taken from the core is designed;

-the dependences of the resonance frequency on the dielectric constant of samples with known values of the basic electrophysical parameters are determined;

-the resonance frequencies of electromagnetic waves transmitted through reference samples with known dielectric constants are measured.

Methods for determining the complex dielectric constant and moisture by the GPR method calibrated by laboratory measurements of these values, have been proposed and laboratory tested. The assessment of the accuracy of determining the electrophysical properties of soils allowed formulating requirements for improving the resolution of the equipment used and its capabilities. As a result, recommendations can be developed to optimize the operation of railways, to make plans for repair and rehabilitation works that are adequate to infrastructure objects current state, to also monitor seasonal and weather changes in reflectivity which can provide a criterion for evaluating the effectiveness of drainage systems. In addition, the data obtained can help interpret observed disorders of railways and provide necessary information on the nature and volume of repair work needed.

The developed method allows, in a shorter time, to diagnose the state of extended objects, since it combines the advantages of the high-speed GPR method with a limited number of calibration measurements of the dielectric constant and moisture by laboratory methods.

The use of GPR methods for monitoring extended sections of railways using mobile diagnostic tools leads to the need to process and interpret a large amount of information. As a result, recommendations can be developed for optimizing the operating conditions of railways; repair and rehabilitation works can be planned that are adequate objects current state.

In particular, the control of seasonal and weather changes of reflectivity can give a criterion for evaluating the effectiveness of functioning of drainage systems.

Chapter 4. The effect of soil salinity on the depth of GPR surveys.

As noted in the previous chapter, non-destructive geophysical methods are used to overcome technological difficulties associated with the monitoring of soils and structural layers of artificial structures with destructive methods. An important place among these methods is occupied by the GPR method which allows obtaining continuous information on the state of local and extended objects. For its effective use in solving problems of quantitative diagnostics when planning experiments, it is necessary to take into account the depth limitations that are directly related to the conductivity of soils and materials. This physical characteristic, in turn, is determined by the moisture and mineralization of soils and materials. High depth of GPR research in sands, ice and rocks is known, as well as low depth in low-ohm clays.

In this regard, in this chapter, the effect of humidity and salinity on the conductivity of some soil-forming minerals is studied using the method of resonance measurements.

The reliability of transport and civil engineering structures is significantly dependent on the accuracy of determination of plasticity and other mechanical properties of cohesive soil materials. Currently, when designing the construction of artificial structures, these measurements are carried out using standard methods set forth in international and national regulatory documents. At the same time, it is known that the accuracy of plasticity determination is not always acceptable, and the problem of its enhancement using infrared spectroscopy methods is discussed in the literature [104,105].

In this chapter, the studies have been performed to establish the correlation between the plastic and electrophysical properties of soil-forming materials determined in the microwave range of electromagnetic waves.

Electrophysical properties of sand

Electrophysical properties of wet sand

In this section, the electrophysical properties of sand are studied depending on its moisture in the moisture range including the optimum value. As the upper limit of the range, a value of 16% is chosen since the further addition of water leads to its release in natural conditions.

Samples for measurements were prepared from pre-washed with distilled

Electrophysical properties of wet saline sand

In this section, the effect of salt impurities on the electrophysical properties of sand is studied. Measurements are performed for a sand with moisture content of 5%. At this value of moisture, the dielectric constant of sand was 4.50, and the specific conductivity, 0.00574 S/m. The salts used in the experiment, as well as some features of the preparation of samples for measurements, are listed in Table 4. 5. To interpret the results obtained, we take into account that the conductivity associated with the mobility of ions formed during the dissociation of salts in aqueous solutions is determined by the relation:

𝜎 = 𝛼𝑒𝑛(𝑣 𝑘 + 𝑣 𝑎 ),
where  is the degree of dissociation, e = 1,602 10 -19 C is the elementary charge, n is the number of salt molecules in the solution, v k is cations mobility, v a -anions mobility.

Calculate the concentration of salt molecules by the expression:

n= mN А /(V),
where m is the salt mass, N A is the Avogadro number,  is the molar mass, and V is the sample volume.

Suppose that the degree of dissociation is close to unity for all the salts used.

We calculate the conductivity of salts under the assumption that the mobility of ions does not depend on the frequency of the electromagnetic field. The calculation results are given in table 4.7. From a comparison of the data given in table 4.7, one can conclude that the results of measurements and calculations in the approximations described differ by less than 10%.

Electrophysical properties of wet saline sand at low temperatures

In this section, electrophysical properties of the sand sample in different states at low temperature are studied. The following reference samples were used: dry sand (exposure at a temperature of 105˚ for 3 hours), sand at a moisture of 5%, and sand at a moisture of 5% with a salt concentration of NaCl of 0.268%. The samples for studying the effects of low temperatures were obtained by exposure of reference samples for 24 hours at a temperature of -5 ˚C. Table 4.8 shows the obtained values of dielectric constant and conductivity. -an increase in sample moisture leads to an increase in dielectric constant and conductivity;

-the introduction of NaCl in the sample of sand with a moisture of 5% leads to an increase in the specific conductivity of up to 3 times while the value of the dielectric constant does not change;

-the change in conductivity with the introduction of salt ions allows one to create a method for determining the salinity of construction materials;

-binding of ions by freezing free water leads to a decrease in the specific conductivity while the dielectric constant varies inly within the measurement error interval.

Some properties of the samples used

In this work, the objects of study were:

-Bentonite Dusch (Figure 4. Similarly, the bentonites "Dusch" and "Zir" can be attributed to the alkaline earth bentanites with a predominance of calcium and magnesium ions. It can be seen from the figures that the scatter in measured values is about 10%. Not more than 10% of experimental points fall out of this error range.

The effect of salinity on the electrical properties of the bentonite of type "Dusch"

To study the electrical properties and assess the effect of additional salinity of bentonite "Dusch" on the results of measurements of dielectric constant and conductivity, the samples of different moisture were used. When preparing samples of a given moisture, bentonite was mixed with a specified amount of NaCl salt solution of a certain concentration. Before measurements, the samples were kept in hermetic laboratory glassware for at least one day in order to undergo possible consolidation processes. The measurement results are presented in Figures 4.11 The approximating line is shown in red color.

To determine the degree of the approximation polynomial, we apply the expression from [START_REF] Born | Principles of Optics, 7th[END_REF], reflecting the change in the dielectric constant when conduction is present:

𝜀 → The smallness of ∝ allows to bring the expression (4.1) to the form:

𝜺 → 𝜺 + 𝝁 𝟎 𝟐 с 𝟒 𝝈 𝟐 𝟐𝜺𝝎 𝟐 (4.2)
Suppose that the conductivity depends linearly on the concentration of ions in the solution (Fig. 4.14). Since the second term in expression (4.2) contains in the denominator the dielectric constant which is also dependent on the concentration of ions, and the square of the conductivity in the numerator, it can be approximated by a polynomial, the degree of which can vary in the range from one to two. In this paper, a first-degree polynomial is used to approximate the experimental values. -the use of a 10% solution of NaCl at moistures lower than 50% does not lead to a noticeable change in the electrophysical values; this may indicate a slight dependence of conductivity on salinity at low humidity of the samples.

Electrical and mechanical properties correlation

In figures 4.11 and 4.12, the vertical lines show the moistures values at the platic and liquid limits of the "Dusch"bentonite, given in table 4. [START_REF] Daniels | Ground Penetrating Radar[END_REF]. It is known that with an increase in the moisture content of the sample from values close to zero, the formation of the H 2 O layers on the surface of clay particles begins. At these values of moisture, a monotonic increase in the dielectric constant and conductivity is observed.

The formation of surface-bound water is completed when the moisture is that of the plastic limit when dry friction between clay particles gives way to the friction associated with the interaction of water layers on the surfaces of the particles. As seen from Figs. 4.11 and 4.12, Near this moisture values, special points (local maxima) are observed on the plots of the dielectric constant and specific conductivity against moisture. Starting from this moisture, the dielectric constant increases with moisture is not so rapidly; this it may be due to:

-the peculiarities of the measurement technique, in particular with the displacement of the field from the volume occupied by water;

-with the swelling of the sample and reducing the influence of the properties of bentonite on the properties of the sample as a whole.

In this range of moisture variation, the specific conductivity decreases due to the replacement of clay particles with water molecules at a constant sample mass.

The transition to a liquid state is characterized by a further pushing the field from the volume of the conductor, which leads to an apparent decrease in the dielectric constant and specific conductivity of the sample.

Correlation of electrical properties and temperature

To determine the effect of temperature on the electrophysical parameters of bentonite "Dusch", an independent series of measurements was performed, the results of which are shown in table [START_REF]Regulations for Performing Preliminary Surveys with Groundprobling Radar for Before Laying Underground Utilities and Infrastructures[END_REF] The results obtained at room temperature differ from those obtained earlier and used in the plots of Figures 4.9-4.12 by about 10%. The results given in Table 4.11 show that when the sample humidity exceeds the plastic limit, and the temperature drops down to under zero degrees Celsius, then ice is formed; this results in a decrease in the dielectric constant. At the same time, the ions mobility decreases, which is reflected in a decrease in the specific conductivity to values characteristic of dry bentonite.

Electrophysical properties of the "Kutch" bentonite

To study the electrical properties and assess the effect of additional salinity of the Kutch type bentonite on its dielectric constant and conductivity, the samples of different moistures were used that were obtained according to the technology described in Sections 4. In Figures 4.17 4. [START_REF] Daniels | Ground Penetrating Radar[END_REF]. As in the case of the "Dusch" bentonite, the moisture at the plastic limit is characterized by a value less than 50%. At this moisture, local maxima of the dielectric constant (Figure 4.17) and conductivity (Figure 4.18) are formed.

The liquid limit moisture value of the "Kutch" bentonite (158.4) differ little from that of the bentonite "Duch" (163.2). In the vicinity of this moisture value special points are seen in the dielectric constant and conductivity graphs.

Comparison of electrophysical properties of bentonites

For a quantitative comparison of the electrophysical properties of bentonites, their dielectric constant and conductivity are shown in Figures 4.19 Comparison of the above data allows to note that:

-at the moisture regions near the plastic limits, the position of special points (local maxima) on the plots of dielectric constant and conductivity at W = 50%, 60% and 30%, correlates with respective values from Table 4.10 (39.4%, 47.7%, and 39.4%);

-the scatter of the experimental dielectric constant and specific conductivity for bentonites that differ in the composition of exchange ions, with the exception of a few points, is about 20%.

Electrophysical properties of kaolinite "KZHV"

The kaolin concentrate Zhuravliniy Log is characterized by the presence of the main rock-forming mineral kaolinite (89-92%), quartz (5-7%), microcline up to 4%, as well as the presence of an irregular smectite phase. The composition contains kaolinite, illite, quartz and microcline. Montmorillonite (smectite), as an independent mineral phase, has not been found.

To study the electrophysical properties and to assess the effect of additional salinity of the "KZhV" type kaolinite on dielectric constant and conductivity, the samples of different moisture were used, obtained according to the technology described in sections 4. [START_REF]British Standard: Specification for Underground Utility Detection, Verification and Location Institute of Civil Engineer[END_REF] Measurement of the electrophysical properties of samples with a NaCl concentration of 10% was performed only at moistures less than 35%, since a further increase in moisture at such salinity leads to the pushing the field out of the sample, which complicates the interpretation of the experimental results.

At salinities of 1% and 2%, the variation of electrophysical quantities of the "KZhV" kaolinite with moisture qualitatively coincides with their behavior in bentonites. The most noticeable difference is the increase in electrophysical parameters at humidities above the plastic limit. This circumstance should be taken into account when interpreting the GPR data.

It can be seen from Figure 4.26 that at moistures under 15%, specific conductivity of bentonite differs from that of sand approximately two times, and from that of kaolinite, four times. A further increase in moisture content up to the liquid limit of kaolinite leads to an increase in the difference in specific conductivities of clays based on montmorillonite and kaolinite. This circumstance explains the limited applicability of the GPR method in low-resistance clays that are in a natural state of humidity. A further increase in the moisture content of bentonite leads to a decrease in the value of specific conductivity, which may be due to a decrease in the density of ions in the sample, the number of which is determined by the composition of bentonite.

Conclusions

1. At moistures under 15%, the dielectric constant and specific conductivity of the sand studied in the work allows linear approximation.

2. The introduction of additional ions of salts of NaCl, KCl and BaCl 2 to the sand at a salt concentrations under 0.3%, does not lead to the changes in dielectric constant within the accuracy of 10%. The variation in conductivity obeys a linear law.

3. The introduction of ions into NaCl in the sample of sand with a moisture content of 5% leads to an increase in the specific conductivity up to 3 times while maintaining the value of the dielectric constant. [START_REF]Regulations for Performing Preliminary Surveys with Groundprobling Radar for Before Laying Underground Utilities and Infrastructures[END_REF]. The change in conductivity with the introduction of salt ions allows creating a method for determining the salinity of construction materials;

5. The binding of ions by freezing free water leads to a decrease in the specific conductivity while the dielectric constant do nit vary within the measurements error.

6. For samples of the "Dusch" type bentonite prepared using 1% and 2% NaCl solution, there is a tendency to increase in dielectric constant and conductivity 7. The use of a 10% NaCl solution for the manufacturing the "Dusch" bentonite samples with moisture under 50% does not lead to a noticeable change in the electrophysical values; this indicates a slight dependence of conductivity on salinity at low samples moisture.

8. The formation of surface-bound water is completed in cohesive soils at moisture at the plastic limit. In the vicinity of this moisture, special points are observed on the plots of dielectric constant and specific conductivity against moisture. [START_REF] Davis | Ground-penetrating radar for high resolution mapping of soil and rock stratigraphy: geophysical prospecting[END_REF]. At the moistures of plastic limits of bentonites (Dusch, Kutch, Zir) the positions of the specific points (local maxima) on the graphs of dielectric constant and conductivity at moistures of 50%, 60% and 30% correlate with the plastic limit values W p equal to 39 , 4, 47.7% and 39.4%. [START_REF] Daniels | Ground Penetrating Radar[END_REF]. The scatter of experimental results for the dielectric constant and specific conductivity for bentonites, differing in the composition of exchange ions, except for a few points, is about 20%. [START_REF] Conyers | Ground-penetrating Radar[END_REF]. At moisture under 15%, the dielectric constants of sand and bentonite differ slightly and are approximately twice as large as that of kaolinite. This relationship between the dielectric constant of bentonite and kaolinite can be seen up to a moisture close to the liquid limit (46.1%), when free water begins to be formed in the sample of kaolinite. This circumstance should be taken into account when interpreting GPR data.

12. At moistures under 15%, the specific conductivity of bentonite differs from that of sand by about two times, and from that of kaolinite, by four times. A further increase in moisture content up to the kaolinite liquid limit leads to an increase in the difference in the specific conductivities of clays based on montmorillonite and kaolinite. This circumstance explains the limited applica-bility of the GPR method in low-resistance clays that are in a natural state of humidity.

tics of infrastructure facilities, the procedure of integration of GPR methods and the methods of direct measurements of electrophysical properties of soils and materials seems promising. In this regard, Chapter 3 solves the problem of developing a technique for resonant measurements of the dielectric constant and specific conductivity of soil-forming minerals at different moistures at a frequency of 1400

MHz. As a result, Methods for determining the complex dielectric constant and moisture by the GPR method, calibrated by laboratory measurements, are proposed and assessed. The developed approach allows rapid diagnosing the state of extended objects, since it combines the advantages of the high-speed GPR method with a limited number of calibration measurements.

In order to effectively apply the GPR method for solving problems of quantitative diagnostics, when planning experiments, it is necessary to take into account depth limitations that are directly related to the specific conductivity of soils and materials. This physical characteristics, in turn, are determined by the moisture and mineralization of soils and materials. High-depth of GPR research in sands, ice and rocks are possible, whereas only low depth GPR studies in low-resistivity clays are feasible. In this regard, in Chapter 4, the effect of moisture and salinity on the conductivity of some soil-forming minerals is studied using the method of resonance measurements. The dependences of the dielectric constant and specific conductivity on the moisture have been investigated in a number of bentonites with different composition of exchangeable ions. A correlation between these electrophysical quantities and the plasticity of bentonites is established

1 .

 1 V. Yavna, A. Kasprgitsky, G. Lazjrenko, A. Kochur, S.Sulavko. Rapid method of determining the physical properties of clay soils according to infrared spectroscopy. Abstract book: 3rd International Conference on Railway Engineering: Construction and Maintnance of Railway Infrastructure in Complex Environment (ICRE2014), 2-3 august, 2014, Beijing, China. -Beijing: China Railway Publishing House. -P. 114-117. 2. V.A. Yavna, A.S. Kasprzhitsky, G.I. Lazorenko, S.N. Sulavko. Determination of the limits and the plasticity number of clay soils using infrared spectroscopy. Ab-stracts of the tenth scientific-practical conference and exhibition "Engineering Geophysics-2014", Gelendzhik, April 2014. DOI: 10.3997 / 2214-4609.20140358 4. Khakiev ZB, Okost MV, Kasprzhitsky AS, Sulavko S.N., Indicative method for estimating seasonal changes in the moisturet of the road bed according to GPR data. Abstracts of the eleventh scientific-practical conference and exhibition "Engineering Geophysics-2015", Gelendzhik, April 2015. DOI: 10.3997 / 2214-4609.201412259 5. Z.B. Khakiev, V.A. Yavna, S.N.Sulavko, K.Yu. Kislitsa. Determination of complex dielectric constant and soil moisture by GPR. Abstracts of the twelfth scientific-practical conference and exhibition "Engineering Geophysics-2016", Anapa, April 25-29, 2016 April 2016. DOI: 10.3997 / 2214-4609.201600315 6. Victor Yavna, Zelimkhan Khakiev, Georgiy Lazorenko, Anton Kasprzhitskii, Sergey Sulavko. Quantitative GPR inspection of quasi-homogeneous ground layers. MATEC Web Conf. Volume 251, 14 December 2018, VI International Scientific Conference "Integration, Partnership and Innovation in Construction Science and Education" (IPICSE-2018). https://doi.org/10.1051/matecconf/201825102025 The dissertation materials are published in the following papers: 1. A.S. Kasprzhitsky, G.I. Lazorenko, S.N. Sulavko, V.A. Yavna, A.G. Kochur. Study of the interaction of water and kaolinite by the methods of IR spectroscopy. Optics and Spectroscopy, 2016, Vol. 121, No.

3 .

 3 Vladimir Shapovalov, Victor Yavna, Andrei Kochur, Zelimkhan Khakiev, Sergey Sulavko, Philippe Daniel, Alexander Kruglikov. Application of GPR for determining electrophysical properties of structural layers and materials. Applied Geophys. 2019 (paper sent to the journal after recommended revision) Personal contribution of the author of the thesis -analysis of the state of problems and setting research objectives (together with the scientific co-advisors V.A. Yavna and P. Daniel); -performing laboratory and field tests and studies; -theoretical studies applied to GPR practice (together with the scientific coadvisors V.A. Yavna and P. Daniel); -theoretical studies of the characteristics of the propagation of electromagnetic waves in inhomogeneous media of different moisture and salinity (together with the scientific co-advisors V.A. Yavna and P. Daniel); -systematization and generalization of results (together with the scientific coadvisors V.A. Yavna and P. Daniel).

Figure 1 .

 1 Figure 1.1 shows the GPR images of localized underground objects.

Figure 1 . 1 .

 11 Figure 1.1. Localization of underground communication lines on the radarogram.

LLC

  Technologies LLC, VIY 70, 125, 300, 500, 700

Figure 1 . 2 . 70 papers per year. 1 . 1 . 3 .

 1270113 Figure 1.2. Dynamics of publication activity in the field of technologies and technical solutions for determining the location and depth of existing underground networks of engineering and technical support by non-destructive methods for the last 30 years according to the Scopus bibliographic database as of August 2018.

Figure 1 . 3 .

 13 Figure 1.3. Distribution of patents by methods in the period 1988-2018 according to the database esp@cenet

Figure 2 . 1 .

 21 Figure 2.1. Patterns of the objects and the cracks in the body of the roadway

Figure 2 . 2 .

 22 Figure 2.2. Propagation of electromagnetic radiation during examination of two types of the roadway structures of a tunnel

3 n 1 Ε , 2 Ε and 3 Ε

 3123 implies an independent determination of the attenuation coefficients p 1 , p 2 , and the amplitude 0 Ε , as well as the measurement of the amplitudes , in radargrams. A rigorous solution of the system of equations (2.1-2.

Figure 2 . 3 .

 23 Figure 2.3. Forming a hyperbolic image of a local object

Figure 2 . 4 .

 24 Figure 2.4. GPR image of cracks (1 and 2) in the invert, and their reconstructed hyperbolic images (a and b)

  2.2).Examples of this are the road sections near the points a and b on the radargram as shown in Fig.2.6.

Figure 2 . 6 .

 26 Figure 2.6. GPR image of a leveling layer of variable thickness

3 n

 3 are the absolute refractive indices of the rigid base, the leveling layer, and the invert, respectively.

Figure 2 .

 2 Figure 2.7 shows the module of the Hilbert transform amplitude H(E)

  The results of fitting |H(E)| for r 0 = 0.024 m are shown in Fig.2.7 by the solid red line. The approximating function(2.11) reflects the attenuation of a plane wave in a medium with an attenuation coefficient p. At the same time, the attenuation of the experimentally determined module of the complex amplitude against depth can differ from this dependence. In this connection, the numerical values of the constants A and p in the approximating function(2.11) depend on the choice of r 0 .Calculated attenuation coefficient p as function of r 0 is shown in Fig.2.8. The asymptotic value of the expression is p =10.1 m -1 (Table2.1).

Figure 2 . 7 .Figure 2 . 8 .

 2728 Figure 2.7. Module of the Hilbert transform of the radargram of industrial water. Solid line shows the result of fitting with (2.11) at r 0 = 0.024 m

Fig. 2 . 2 

 22 Fig. 2.9 shows the module of the Hilbert transform of the signal of the "OKO" antenna unit with a center frequency of 1700 MHz. The depth scale is cal-

Figure 2 . 9 .

 29 Figure 2.9. Module of the Hilbert transform of direct penetration signal from the antenna unit at a frequency of 1700 MHz.

2 where

 2 refractive index of industrial water, h is the thickness of the water layer, E 1 and E 2 are the amplitudes of the electromagnetic waves reflected by the upper and lower boundaries of the water layer, respectively. The absolute refractive index of industrial water entering (2.12) is determined from the relation: c is the speed of light in vacuum, and Δτ is the time interval during which the signal travels from the lower boundary of the water layer to the receiving antenna located near its upper boundary. The quantities Δτ, E 1 and E 2 required for the calculations, are determined from radargrams. The positioning of upper and lower boundaries of the water layer on the radargram, and the known thickness of the water layer, made it possible to estimate the refractive index of water at a frequency of 1700 MHz,

2 . 6 treated

 26 via the method described in Sect. 1 is additionally subjected to the Hilbert transform. The result of the transformation is shown in Fig.2.10.

Figure 2 .

 2 Figure 2.10. GPR image of the module of Hilbert transform of the radargram shown in Fig. 2.6

Figure 2 . 11 .

 211 Figure 2.11. Module of the Hilbert transform of radargrams in the region of the rigid base.

Figure 2 . 12 . 1 .

 2121 Figure 2.12. Module of the Hilbert transform of radargrams in the region of the leveling layer.

Figure 2 . 13 . 2 . 3 . 3 .Figure 2 . 14

 213233214 Figure 2.13. Module of the Hilbert transform of radargrams in the region of the invert.

Figure 2 .

 2 Figure 2.14 shows the modules of Hilbert transforms of signals reflected from the boundary between the leveling layer and the invert (Fig.2.10) obtained at points spaced 0.5 m apart. The results of fitting of the obtained values with the function (2.11) are given inTable 2.1. Comparison of the attenuation coefficients of the leveling layer given in Table 2.1 makes it possible to estimate the error of

.

  It should be noted that the analysis of the phase of electromagnetic radiation reflected from interfaces requires imple-mentation of numerical procedures for phase analysis; this will be done below. In this section, we consider all possible combinations of the phases of ' 2 of equations (2.8-2.10) does not give any new physically meaningful values of refractive indices, and reduces to the inversion of

Figure 2 . 2 Ε , ' 3 Ε , and ' 4 Ε

 2234 Figure 2.15 shows the variation in n 2 and n 3 depending on the amplitudes of ' 2 Ε , ' 3 Ε

Figure 2 .

 2 Figure 2.15. Changes in the values of the refractive indices n 2 (circles) and n 3 (squares) depending on the variation of amplitudes ' 2 Ε , ' 3 Ε and ' 4 Ε . Experimental values are marked with a vertical line.

51

 51

Figure 2 . 16 .

 216 Figure 2.16. The phases of traces in the radargram shown in Fig. 2.6 calculated with (2.13). Horizontal segments on the scale on the right indicate positive values of the trace amplitudes in the absence of media interfaces.

2. 6 .

 6 Determination of the attenuation coefficient in the leveling layer by the amplitudes of the signals reflected by its boundaries Determination of the refractive indices of structural layers by solving the system of equations (2.8-2.10) makes it possible to calculate the leveling layer's attenuation coefficient from the amplitudes of the waves reflected from the interfaces. The ratio of equations (2.10) and (2.8) leads to the following expression for the attenuation coefficient of electromagnetic radiation in the leveling layer:

  n c , n s , n cs and m c , m s , m cs are refractive indices and mass concentrations of cement, sand and crushed stone, respectively, the stroke indicates the components of the B15-type concrete.

Figure 2 . 17 .

 217 Figure 2.17. Water in the area of local dismantling of the rigid base and leveling layer

Figure 3 . 1 .

 31 Figure 3.1. Orientation of water molecules dipoles on the adsorption centers of the mineral surface

I .

 . Bound water. It is retained in the soil due to chemical and physicochemical forces acting from the surface of the particles and changing its properties in comparison with free water (Fig.3.2). It is subdivided into two types:1. Water of the lattice (constitutional, crystallization-bound). This water is part of minerals in the form of ions in the molecule of the mineral, or in the form of molecules in the crystal lattice of the mineral.

2 .Figure 3 . 2 .

 232 Figure 3.2. Bound water in the soil: 1 -soil particles; 2 -capillary water; 3air; 4 -adsorption water

  are the real parts of the dielectric constant of soil, water and air, respectively. The degree of moisture can be determined with water soil m W m  by the relation:

3. 4 . 8 )

 48 Designing a cavity resonator for measuring the properties of materials taken from the core. Depending on the size of the sample, various types of resonators and measurement methods are used. Since in this work the sample taken from the core is a cylinder with a diameter of d 0 = 19.7 mm and a height of l = 8.04 mm, the cavity resonator designed should be a limited segment of a circular waveguide with transverse dimensions close to the dimensions of the sample under study. For the correct measurement of the properties of materials, a cavity resonator with the oscillation of H 01p type for samples in the form of a disk was used. The operating frequency range in which the resonator should operate was determined from the frequency range at which diagnostics of the structural layers of the transport infrastructure is carried out; it ranges from 0.4 GHz to 1.7 GHz. The most common in practice are quarter-wave resonators,  is the wavelength of the electromagnetic signal, L is the length of the res- onator, n = 1,2,3 ... Accordingly, choosing the working resonant frequency f p = 1.4 GHz and usthe cavity length L = 53.57 mm for n = 1. For n = 2, the length of the resonator is L = 160.71 mm, for n = 3, L = 268.85 mm. When using the expression (3.7), we take the cross-sections of the resonator having outer and inner diameters D and d, but these are limited by the condition of the absence of higher types of waves: The values of the diameters, in addition to the condition (3.8), determine the losses in the walls of the resonator and, therefore, affect the magnitude of the intrinsic quality factor Q 0 . The size of the internal diameter d is determined by the size of the sample. The value of the external diameter D of the resonator is selected based on the condition (3.8). In this study, the internal diameter of the resonator should be d  20 mm, and corresponding external diameter, D >30 mm (3.8).The drawing of the resonator and the specification of its structural materials are presented in Fig.3.4.

Figure. 3 . 4 . 3 . 4 . 1 .

 34341 Figure. 3.4. Drawing of the resonator and specification of sits tructural materials

Figure 3 . 5 .

 35 Figure 3.5. Schematic representation of a resonator with a sample. a-resonator, бplastic cup, вsample, гport 1, дport 2

Figure 3 . 6 .

 36 Figure 3.6. Penetration of the field. Sample ε = 1 With the increase in the dielectric constant of the sample, the field is pushed out of its volume (Figures 3.7 -3.9). As the dielectric constant in the sample increases, the electric field is pushed out of the sample more and more strongly, and, at  30, it practically does not pass through it.

Figure 3 . 7 .

 37 Figure 3.7. Penetration of the field. Sample ε = 10, σ = 5.5E-06.

Figure 3 . 8 .

 38 Figure 3.8. Penetration of the field. Sample ε = 30, σ = 5.5E-06.

Figure 3 . 9 .

 39 Figure 3.9. Penetration of the field. Sample ε = 50, σ = 5.5E-06.

Figure 3 . 10 . 3 . 5 . 1 .

 310351 Figure 3.10. Setup for resonant measurements

Figure 3 . 11 .

 311 Figure 3.11. Dependence of resonance frequency on dielectric constant. The errors of experimental measurements of 0.5% are shown.

3. 6 .

 6 An integrated study of the dielectric properties of soils of different moistures by volume resonator method and simultaneous GPR measurements at frequencies of 1.4 GHz. Сalibration of the GPR method by resonant measurements is based on determining the values of the real part of the dielectric constant and conductivity by the resonant method and simultaneous GPR measurements of soil properties. Here and *  *  below, the sign (*) indicates that the parameters belong to the physical state of the soil at which the GPR data were calibrated by resonance measurements.

Figure 3 . 12 .

 312 Figure 3.12. Antenna unit (1) and angular divergence (3) of electromagnetic radiation in a medium bounded by a surface (2)

Figure 3 . 13 . 3 . 1 .

 31331 Figure 3.13. Approximation of the trace segment when calculating the attenuation coefficient

Figure 3 . 14 .Figure 3 .Figure 3 . 16 .

 3143316 Figure 3.14. Specific conductivity of sand of different moisture

Figure 3 . 17 .

 317 Figure 3.17. Moisture of sand samples against the refractive index

  For this research, career sand was used; its physical characteristics were obtained during the tests in the laboratory "Testing and monitoring in civil and transport construction", accreditation certificate RA.RU.21PS69 issued February 18, 2016.The physical characteristics of the soil and the test methods used are presented in Tables 4.1-4.4 and in Fig.[START_REF]Regulations for Performing Preliminary Surveys with Groundprobling Radar for Before Laying Underground Utilities and Infrastructures[END_REF].1.

Figure 4 . 1 . 4 . 1 . 2 .

 41412 Figure 4.1. Results of determining the maximum density and optimum moisture of sand. Standard compaction curve

Fig. 4 . 2 .

 42 Fig. 4.2. Montmorillonite lattice structure

Fig. 4 . 3 -

 43 Fig. 4.3 -Kaolinite unit cell

  water and dried according to GOST 22733-2016 sand by adding distilled water.When performing measurements, a constant mass of 4.269 g was used at any humidity. The samples were placed in a container with a volume of 2833.85 mm 3 , made of the ABS plastic (acryl butadiene styrene -solid, impact-resistant, thermoplastic industrial resin based on a copolymer of acrylonitrile with butadiene and styrene), which was previously used to calibrate the resonator.Measured dielectric constant and conductivity determined according to Chapter 3, are shown in Figures4.4 and 4.5.

Figure 4 . 4 .Figure 4 . 5 .

 4445 Figure 4.4. Dielectric constant of sand as a function of moisture

Figure 4 . 7 .

 47 Figure 4.7. Measured conductivity of sand at moisture of 5% as a function of the salt concentration.

  8.a) The Dash-Salakhninsky deposit (Azerbaijan Republic, Gazakh river, Dash-Salakhny village); it belongs to the calciummagnesium type. The active surface reaches 700-800 m 2 /g and the cation exchange capacity is 80-150 mmol/100g [28]. -Bentonite Kutch (Figure 4.8.b) of the Kutch deposit (Gujarat state, India) of the alkaline type with the main exchange cation Na+ and Ca++. Cation exchange capacity is 90.54 mmol/100g -Bentonite Zir (figure 4.8.c) of the Zyryanovskoye field (st. Zyryanovka, Kurgan region); it belongs to the calcium-magnesium group has low binding capacity, active surface of 700-800 m2/g, and a cation exchange capacity of 80-150 mmol/100g. The compressive strength in the wet state is up to 0.1 MPa [113].-Kaolinite of dry enrichment from "Zhuravlinny Log" field (Figure4.4.g), fraction <5 microns. The chemical formula is Al4(OH)8[Si4O10] [114].

Fig. 4 . 8 .

 48 Fig. 4.8. Samples of bentonite clays and kaolinite

4. 3 . 1 . 4 . 3 . 1 . 1 .Fig. 4 . 9 .

 31431149 Fig. 4.9. The results of two series of experiments on measuring the dielectric constant are shown in red and black. Vertical bars indicate errors of 10%.

Fig. 4 . 10 .

 410 Fig. 4.10. The results of two series of experiments on measuring the specific conductivity are shown in red and black. Vertical bars indicate errors of 10%.

Fig. 4 . 11 .Fig. 4 . 12 .

 411412 Fig. 4.11. Dielectric constant measured at different concentrations of NaCl additionally introduced into the sample. In the figure, the following notations are used: • -non-saline sample, • -1% solution, • -2% solution, • -10% solution. Vertical bars indicate the errors of 10%. Vertical lines mark the moisture at the plastic limit (W p ) and liquid limit (W l ).

Figures 4. 13

 13 Figures 4.13and 4.14 show the dependences of the dielectric constant

  Figures 4.13and 4.14 show the dependences of the dielectric constant and specific conductivity on salinity at a fixed sample moisture of 100%.

Fig. 4 .

 4 Fig.[START_REF]Regulations for Performing Preliminary Surveys with Groundprobling Radar for Before Laying Underground Utilities and Infrastructures[END_REF].[START_REF] Benedetto | Civil engineering applications of ground penetrating radar[END_REF]. Dielectric constant measured at different concentrations of NaCl additionally introduced into the sample. Vertical segments reflect measurement errors of 10%. The approximating line is shown in red color.

Fig. 4 . 14 .

 414 Fig. 4.14. Specific conductivities measured at different concentrations of NaCl additionally added to the sample. Vertical bars reflect measurement errors of 10%.The approximating line is shown in red color.

Figures 4. 11

 11 Figures 4.11and 4.12 demonstrate that

  Figures4.11 and 4.12 demonstrate that -for samples prepared using 1% and 2% NaCl solution, there is a tendency to increase of the measured electrophysical parameters.

Fig. 4 .

 4 Fig. 4.15. Dielectric constant measured at different concentrations of NaCl additionally introduced into the sample. In the figure, the following notations are used: • -non-saline sample, • -1% solution, • -2% solution, • -10% solution. Vertical bars indicate errors of 10%. Vertical lines mark the moistures at the plastic limit (W p ) and liquid limit (W l ).

Fig. 4 . 17 .

 417 Fig. 4.17. Dielectric constant measured at different concentrations of NaCl additionally introduced into the sample. In the figure, the following notations are used: • -non-saline sample, • -1% solution, • -2% solution, • -10% solution. Vertical bars indicate errors of 10%.Vertical lines mark the moistures at the plastic limit (W p ) and liquid limit (W l ).

Fig. 4 . 18 .

 418 Fig.[START_REF]Regulations for Performing Preliminary Surveys with Groundprobling Radar for Before Laying Underground Utilities and Infrastructures[END_REF].[START_REF] Yavna | Broadband directional antennas for monitoring the state of the ballast section of a railway track // Abstracts of the reports of the second international scientific-practical conference[END_REF]. Specific conductivities measured at different concentrations of NaCl additionally introduced into the sample. In the figure, the following notations are used: • -non-saline sample, • -1% solution, • -2% solution, • -10% solution. Vertical bars indicate errors of 10%. Vertical lines mark the moistures at the plastic limit (W p ) and liquid limit (W l ).

  and4.18, the vertical lines show the moisture values at the plastic and liquid limits of the «Zir» bentonite given in Table

  and 4.20 along with lines marking the moisture values at the plastic (W p ) and liquid (W l ) limits.

Fig. 4 .

 4 Fig.[START_REF]Regulations for Performing Preliminary Surveys with Groundprobling Radar for Before Laying Underground Utilities and Infrastructures[END_REF].[START_REF] Rial | Resolution of GPR bowtie antennas: An experimental approach[END_REF]. Dielectric constant of bentonites (• -Duch; • -Kutch; • -Zir). Vertical bars indicate errors of 10%. Vertical lines mark the moistures at plastic limits (W p ) and liquid limits (W l ).

Fig. 4 .

 4 Fig. 4.20. Specific conductivity of bentonites (• -Duch; • -Kutch; • -Zir). Vertical bars indicate errors of 10%. Vertical lines mark the moistures at plastic limits (W p ) and liquid limits (W l ).

Fig. 4 . 21 .

 421 Fig. 4.21. Dielectric constant measured at different concentrations of NaCl additionally introduced into the sample. In the figure, the following notations are used: • -non-saline sample, • -1% solution, • -2% solution, • -10% solution. Vertical bars indicate errors of 10%. Vertical lines mark the moistures at the plastic limit (W p ) and liquid limit (W l ).

Fig. 4 . 22 .

 422 Fig.[START_REF]Regulations for Performing Preliminary Surveys with Groundprobling Radar for Before Laying Underground Utilities and Infrastructures[END_REF].[START_REF] Lutz | Phased-array transmitters for GPR surveys[END_REF]. Specific conductivities measured at different concentrations of NaCl additionally introduced into the sample. In the figure, the following notations are used: • -non-saline sample, • -1% solution, • -2% solution, • -10% solution. Vertical bars indicate errors of 10%. Vertical lines mark the moistures at the plastic limit (W p ) and liquid limit (W l ).

4. 6 .Figures 4 . 23

 6423 Figures 4.23and 4.24 show the dielectric constant and specific conductivity

  Figures 4.23and 4.24 show the dielectric constant and specific conductivity of the bentonites used in this work and additionally salted with a 2% NaCl solution.

Figure 4 .

 4 Figure 4.23 shows that the introduction of additional ions in the considered range of humidity:-do not lead to a difference in dielectric permeabilities within the error intervals with the exception of the W = 90% point; -it does not allow distinguishing the predominant mineral (montmorillonite or kaolinite) in samples.

Fig. 4 . 23 .

 423 Fig.[START_REF]Regulations for Performing Preliminary Surveys with Groundprobling Radar for Before Laying Underground Utilities and Infrastructures[END_REF].[START_REF] Huston | Tri-band ground penetrating radar for subsurface structural condition assessments and utility mapping[END_REF]. Dielectric constant of samples with a 2%concentration of salt NaCl additionally introduced into the sample. In the figure, the following notations are used:(bentonites: • -Dusch; • -Kutch; • -Zir, and • -KZhV kaolinite).

Fig. 4 . 24 .

 424 Fig.[START_REF]Regulations for Performing Preliminary Surveys with Groundprobling Radar for Before Laying Underground Utilities and Infrastructures[END_REF].[START_REF] Brunzell | Dual-antenna impulse radar for improved detection of buried land mines[END_REF]. Specific conductivity of samples with a 2% concentration of salt NaCl additionally introduced into the sample. In the figure, the following notations are used: (bentonites: • -Dusch; • -Kutch; • -Zir, and • -KZhV kaolinite).

Figure 4 .

 4 Figure[START_REF]Regulations for Performing Preliminary Surveys with Groundprobling Radar for Before Laying Underground Utilities and Infrastructures[END_REF].[START_REF] Brunzell | Dual-antenna impulse radar for improved detection of buried land mines[END_REF] shows that the introduction of additional ions in the moisture range up to 50%, the specific conductivities of bentonites are approximately twice as large as those of kaolinite.In Figures4.25 and 4.26 dielactric constants and specific conductivities of

and 4 .Fig. 4 .Fig. 4 . 26 .

 44426 Fig. 4.25. Dielectric constant of minerals. The following notations are used in the figure: (• -Dusch; • -KZhV; • -sand). Vertical bars indicate errors of 10%.

Figure 4 .

 4 Figure[START_REF]Regulations for Performing Preliminary Surveys with Groundprobling Radar for Before Laying Underground Utilities and Infrastructures[END_REF].[START_REF] Rachmana | Interpretation target pattern of a buried basic object on surface Ground Penetrating radar system[END_REF] shows that at moistures under 15%, the dielectric constant of sand and bentonite differs slightly, and it is approximately two times greater than that of kaolinite. This relationship between the dielectric constant of bentonite and

Table 1 .

 1

	1 -The main characteristics of ground penetrating radars
	Manufacturer, device name	Antenna unit frequencies, MHz
	LLC LOGIS, OKO-3	2000, 1700, 1200, 2500, 1000, 400,
		900, 700, 250, 150, 90, 100, 50

  .1-2.3, 2.7) or (2.8-2.10) should include the modules of the complex refractive indices [94],

		2
	which is achieved by replacing n with	2

Table 2 . 1 .

 21 Fit parameters in formula(2.11) approximating the modules of Hilbert transforms of radargrams and electromagnetic radiation attenuation coefficients in structural levels of the tunnel

	Structural level

Table 2 .

 2 2. Values and relations between the absolute refractive indices of the structural layers calculated by solving the equations (2.8-2.10) with experimental values of the amplitudes'

		Ε , ' Ε , ' Ε .
		2	3	4
		Relation be-		' 2 Ε	Ε	' 3	4 ' Ε	1 n	2 n	3 n	0 Ε
		tween n 1 , n 2 , n 3
	1	n 1 >n 2 >n 3		243 95	541	No solution found **
	2	n 1 >n 3 >n 2		243 -95	541	No solution found **
	3	n 1 >n 2 >n 3 , n 1 <n 3 243 95	-541 Solution impossible*
	4	n 3 >n 1 >n 2		243 -95	-541 3.16	2.73	4.41	3293
	5	n 2 >n 1 >n 3		-243 95	541	3.16	3.67	2.27	3293
	6	n 1 <n 2 <n 3 , n 1 >n 3 -243 -95	541	Solution impossible*
	7	n 2 >n 3 >n 1		-243 95	-541 No solution found **
	8	n 1 <n 2 <n 3		-243 -95	-541 No solution found **
	*there is a contradiction between the relative values of the refractive indices and
	the phases of experimental amplitudes of the waves ' 2 Ε , ' Ε , and 3	' 4	.

Ε

** Refractive indices found have no physical meaning, for example, they become less than unity.

Table 2 .

 2 [START_REF]British Standard: Specification for Underground Utility Detection, Verification and Location Institute of Civil Engineer[END_REF]. Solutions of equations (2.8-2.10) for the E 0 wave amplitude and the values of the absolute refractive indices of structural layers absent in Table2.2.

	Relation be-	' 2 Ε	Ε	' 3	4 ' Ε	1 n	2 n	3 n	0 Ε
	tween
	n 1 , n 2 , n 3
	n 1 >n 2 >n 3	243	37	541	3,16 2,72 2,26 3249
	n 1 >n 3 >n 2	443	-12,5	341	3,16 2,28 2,46 2742
	n 2 >n 3 >n 1	-443	12.5	-341	3,16 4,38 4,06 2743
	n 1 <n 2 <n 3	-243	-37	-541	3,16 3,67 4,42 3252

Table 2 .

 2 3 illustrates the attempts to obtain a solution for the "no solution found" cases in Table.2.2 by variation of ' Ε , and p 2 and are determined from the radargrams.

	3 Ε , ' 2 Ε and ' 4 Ε wave amplitudes over

  .2, the phases

	i 	  t	of the traces	i s	(t	)	were calculated (i numbers the traces in the radargram) with

  In(2.15), the refractive indices from Table2.2 and the refractive index of industrial water determined in this work were used.A similar estimate of the volumetric moisture can be made based on the at-

			Relation (2.15) allows one to estimate the volumetric moisture to be	w		%. 14
	tenuation coefficient of electromagnetic radiation in the rigid base, the invert and
	water:
	p		p		wp	.		(2.16)
	3		1		H	O
					2
	The attenuation coefficients necessary for the calculations with (2.16) are obtained
	by averaging the values given in Table 2.1. Relation (2.16) allows estimating the
	volumetric moisture to be	w		% 17
								54

Table 3 .

 3 2. Electrophysical parameters of sand with different moistures calculated using calibrated GPR data.

	W,%	Δm	n	p+Δp *	p	σ, S/м		σ, S/м	
	Method radargram	Eq. (3.14)	GPR	Eq. (3.15)	Eq. (3.11)	Eq. (3.10)	resonance resonance
	0,51	104	1,82 *	3,63	0,38	0,0037	3,31	0,0037	3,30
	1,78	126	2,21	4,18	0,93	0,0109	4,88	0,0056	3,46
	2,196	139	2,43	4,01	0,76	0,0098	5,90	0,0097	4,54
	4,84	157	2,75	4,08	0,83	0,0121	7,56	0,0163	6,63
	7,73	184	3,22	4,34	1,09	0,0186	10,37	0,0232	8,57
	10,01	204	3,57	4,99	1,74	0,0330	12,74	0,0265	10,56
	14,42	252	4,37	6,20	2,95	0,0684	19,09	0,0553	17,14
	16,05	255	4,46	6,33	3,08	0,0729	19,88	0,0593	18,35

Table 4 .

 4 [START_REF]American Society of Civil Engineer Standard Guideline for the Collection and Depiction of Existing Subsurface Utility Data[END_REF]. Physical characteristics of soil.

							Regulatory documents
	№	Characteristic			units	Measured value	establishing the rules and test methods
							(measurements)
	1	2			3	4		5
	1 Size Module Мк			-	1.77		GOST 8735-88
	2 True density, ρ			g/cm 3	2.60		GOST 8735-88
	3 Bulk density, ρн			g/cm 3	1.30		GOST 8735-88
	4 Clay content in lumps, Гл			%	0.00		GOST 8735-88
	5 Content of dust and clay particles, П		%	0.40		GOST 8735-88
	6 Maximal density ρdmax			g/cm 3	1.75	GOST 22733-2016
	7 Optimum moisture, Wопт			%	12.0	GOST 22733-2016
	Table 4.2. Results of determination of particle size (grain) composition in accord-
	ance with GOST 12536-2014.
	Residue	10	5	2	Sieve size, mm 1 0.5	0.25	0.1	<0.1
	Particular, %	0.0	0.0	6.5	3.1	6.3	58.3	24.9	0.9
	Total, %	0.0	0.0	6.5	9.6	15.9	74.2	99.1	100.0

Table 4 .

 4 [START_REF]British Standard: Specification for Underground Utility Detection, Verification and Location Institute of Civil Engineer[END_REF]. Results of determination of particle size (grain) composition in accordance with GOST 8735-88.

	Residue	2.5	1.25	Sieve size, mm 0.63 0.31	0.16	<0.16
	Particular, %	6.3	2.0	3.2	45.0	38.0	5.5
	Total, %	6.3	8.3	11.5	56.5	94.5	100.0

Table 4 .

 4 4. Results of determining the maximum density and optimum soil moisture.

	Compaction No	Moisture, %	Density, g/cm 3	Density of dry sand,	Optimum moisture, %	Maximum den-sity of dry sand

Density of dry sand, g/cm 3 Optimum moisture Maximal density

Table 4 .

 4 5 -Masses of salts used in the preparation of samples.

	Salt concentration	0.075% 0.100% 0.115% 0.2%	0.25% 0.3%

Table 4 .

 4 [START_REF]Subsurface radar issues[END_REF]. Specific conductivities of salts.

	Salt	Specific conductivity
		Calculated	Measured
	NaCl	1	1
	KCl	0,99	1,05
	BaCl 2	0,66	0,62

Table 4 .

 4

	8. Dielectric constants and conductivities of samples with different mois-
	ture and salinity at different temperatures.
	Sample state	Dielectric con-	Conductivity,
		stant	S/m
	W=0%, t=25 0	3.34	0.00361
	W=0%, t=-5 0	3.36	0.00315
	W=5%, t=25 0	4.80	0.00570
	W=5%, t=-5 0	4.51	0.00373
	W=5%, C NaCl =0.268%, t=25 0	4.71	0.02081
	W=5%, C NaCl =0.268%, t=-5 0	4.13	0.00711

Comparison of the data given in table

4.8

allows us to make the following conclusions:

Table 4 .

 4 9. The results of measurements of moisture at the plastic and liquid limits are given in table4.10.

Table 4 .

 4 [START_REF] Davis | Ground-penetrating radar for high resolution mapping of soil and rock stratigraphy: geophysical prospecting[END_REF]. Chemical composition of bentonite clays (in %)

	Chemical com-		Field
	pound
		Kutch [115]	Zyryanskoye	«Dash-
			[116]	Salakhinskoye»
				[116]
	SiO 2	45.16	57.37	58.60
	Al 2 O 3	15.84	19.40	13.40
	Fе 2 O 3	7.66	5.97	4.70
	FеO		0.94	0.18
	TiO 2	0.87	0.15	0.39
	CаO	2.63	1.81	2.05
	MgO	3.82	3.01	2.30
	P 2 O 5		0.040	0.11
	SO 3		0.10	0.25
	K 2 O	0.41	1.03	0.39
	Nа 2 O	4.04	0.78	2.30
	Other	19.57	9.4	15.33
	Total	100	100	100

Table 4 .

 4 [START_REF] Daniels | Ground Penetrating Radar[END_REF] Moisture of the materials used at plastic and liquid limitsThe results presented in Table4.8 show that sodium is the predominant cation in the Kutch bentonite, which makes it possible to attribute it to the alkaline type (the predominance of sodium, calcium and magnesium ions). The larger size of Na ions explains the high liquid level (according to data from [115], 459%).

	Clay	Moisture at plastic limit	Moisture at liquid limit
		W p , %	W I , %
	Bentonite "Dusch"	39.41	163.24
	Bentonite "Kutch"	47.69	335.72
	Bentonite "Zir"	35.92	158.38
	Kaolinite "KZhV"	27.4	46.1

  .11.

	Таблица 4.11. Результаты измерения диэлектрической проницаемости и
	удельной проводимости при разных влажностях и температурах.
	Sample state	Dielectric constant ε	Specific conductivity σ
	W=0%, t=25 0	4.13	0.01159
	W=50%, t=25 0	8.15	0.03981
	W=50%, t=-5 0	4.28	0.01097

  3.1.1 and 4.3.1.2. The measurement results are presented in Figures 4.15 and 4.16.

		28 32	W p						W l
		24
		20
	ε	16
		12
		8
		4
		0	50	100	150	200	250	300	350	400
						W,%

  .1.1 and 4.3.1.2. The measurements results are presented in Figures 4.21 and 4.22.

To estimate the ratio of refractive indices, the values of the refractive indices of materials are used from "Recommendations for quality control of road construction works using the GPR method" published on the basis of the instruction of the Federal Road Agency dated 10.06.2016 No. 1025-p, and from the study of [START_REF] Makeeva | Dielectric properties of composite materials 129 based on cement of different genesis[END_REF].

The values of mass concentrations are taken from the standard "GOST 27006-86 Concrete. Rules for the selection of composition". The values of refractive indices and mass concentrations used in the calculation may well vary depending on the frequencies of GPR surveys, materials used, and required density of concrete mixes. In this regard, the evaluation of the refractive indices ratio with (2.17) should be considered rather approximate. The calculation showed that the grade B15 concrete can have a refractive index 10% less than the B25 concrete, which is consistent with the ratio of 1.10 obtained with formula (2.16) using the data given in Table 2. [START_REF]Standard Guide for Using the Surface Ground Penetrating Radar Method for Subsurface Investigation[END_REF].

The proximity of the electrical characteristics of concretes grades B15 and B25 allows explaining the low contrast of the interface between the rigid base and the leveling layer equation (2.8). It can be seen from Fig. 2.6 that the interface between these structural layers is formed from fragments of the GPR irregularity patterns in a rigid base.

At the same time, the interface between the leveling layer and the invert is represented by a contrast line in the GPR section shown in Fig. 2.6; this can be explained by a noticeable difference in the refractive indices (eq. 2.10) caused by water saturation of the invert. The measurements of the electrophysical properties of samples with a NaCl concentration of 10% were only possible at samples moisture less than 50% since a further increase in moisture at such salinity leads to the pushing the field out of the sample, which makes it difficult to interpret the results of the experiment.

At salinities of 1 and 2%, the behavior of the electrophysical quantities against moisture qualitatively coincides with their behavior in the "Dusch" bentonite.

In figures 4.15 and 4.16, the vertical lines show the moisture values at the plastic and liquid limits of the Kutch bentonite given in Table 4. [START_REF] Daniels | Ground Penetrating Radar[END_REF]. As in the case of Dusch bentonite, the moisture at the plastic limit is characterized by a value less than 50%. At this moisure, local maxima of the dielectric constant (Figure 4.15) and conductivity (Figure 4.16) are formed.

The liquid limit moisture value of the "Kutch" bentonite turned out to be almost two times higher (335.7%) than that of the bentonite "Duch" (163.2). In the vicinity of this moisure value (300%) special points are seen in the dielectric constant and conductivity graphs.

Electrophysical properties of bentonite "Zir"

To assess the effect of additional salinity of the "Kutch" bentonite on dielectric constant and conductivity, we used the samples of various moistures, prepared according to the technology described in sections 4. The measurement results are presented in Figures 4.17 The measurement of electrophysical properties of samples with a NaCl concentration of 10% was performed only at moistures less than 60% since a further increase in moisture at such salinity leads to the pushing the field out of the sample, which makes it difficult to interpret the results of the experiment.

At salinities of 1 and 2%, the behavior of the electrophysical quantities against humidity qualitatively coincides with their behavior in the bentonite "Duch" and "Kutch".

General conclusions

The methods for determining the electrophysical properties of ground materials considered in Chapter 1 significantly expand the capabilities of the method for diagnosing structural layers of artificial structures, which will allow the transformaion of an indicative GPR method into a method for geophysical measurement.

In this context, in this study, the problem of the development of the GPR method for determining the electrophysical properties of soils on the basis of integration with optical and resonant methods has been solved. Traditionally, the density and moisture of soils are determined by destructive methods, for example, by drilling and sampling. These methods are characterized by high accuracy of measurements, however, they are relatively expensive and time consuming, they also require a stopping of the traffic on the surveyed site for the duration of the measurements. To overcome these difficulties, it is increasingly recommended to use a non-destructive GPR method, which allows one to obtain continuous information about the state of soil layers, both in the detailed diagnostics mode and as part of specialized diagnostic mobile tools (railway cars, matrices and automobiles). For its effective use in solving problems of quantitative diagnos-