APPLICATION OF RADIOACTIVE ISOTOPES IN THE CONSTRUCTION INDUSTRY

A. A. Dobrinskaya

As is well known, the production of Pu \(^{239}\) and U \(^{233}\) is closely connected with the obtaining of artificially radioactive isotopes, which at the present time are widely used for scientific research in physics, chemistry\(^{1,2,3}\), biology\(^{4}\), and medicine\(^{5}\), as well as in industry\(^{6,7,8,9,10,11,12,13,14}\) for developing new production methods, for controlling production processes, and in instrument making\(^{15,16,17}\).

In the construction industry, radioactive isotopes have so far been used insufficiently. Meanwhile, there is no doubt that here too the introduction of new methods of investigation and control using radioactive isotopes will yield substantial results and will contribute to technical progress.

The present review is devoted to presenting the most important works on the use of radioactive isotopes for the investigation of construction materials and construction machinery, the inspection of metal structures, ventilation and heating systems, and also certain other questions connected with the tasks of the construction industry.

I. INVESTIGATION OF CONSTRUCTION MATERIALS

A large number of works have been devoted to the use of radioactive isotopes for the investigation of construction materials.

The very important question of the interaction of cement and concrete with water and with various substances dissolved in it is not very accessible to investigation by the former physicochemical methods. The use of radioactive isotopes has made it possible to obtain a number of valuable results in this field.

The study of the diffusion into cement of various substances is carried out by immersing cement specimens in water in which are dissolved

salts labeled with radioactive isotopes. After holding for a long time at constant temperature, the cement specimen is removed and washed, after which its activity is measured with an end-window counter, as shown in Fig. 1. After this the surface layer is ground off to a definite depth and the activity is again measured. Such grinding, followed by measurement of the activity, is repeated several times. In this way, the dependence of the activity \(J\) on the thickness of the removed layer is obtained,

Fig. 1. Measurement of the activity of cement specimen 1 by means of end-window counter 2.

\[ J=f(x). \tag{1} \]

As is known, the integral of the equation of one-dimensional diffusion

\[ \frac{\partial C}{\partial t}=D\frac{\partial^{2}C}{\partial x^{2}} \tag{2} \]

in the case of diffusion from one layer of large thickness into another has the form

\[ \frac{C}{C_{0}}=\frac{1}{2}\left[1-\operatorname{erf}\left(\frac{x}{2\sqrt{Dt}}\right)\right]. \tag{3} \]

Here

\[ \operatorname{erf}(z)=\frac{2}{\sqrt{\pi}}\int_{0}^{z} e^{-y^{2}}\,dy. \tag{4} \]

Neglecting self-absorption in the thin layer of cement, we may put

\[ \Delta J=kC \tag{5} \]

and, consequently,

\[ \frac{\Delta J}{\Delta J_{0}}=\frac{1}{2}\left[1-\operatorname{erf}\left(\frac{x}{2\sqrt{Dt}}\right)\right]. \tag{6} \]

This equation makes it possible, from the experimentally found values of \(\Delta J\), \(x\), and \(t\), to calculate the magnitude \(D\) of the diffusion coefficient of the substance under investigation in cement.

By carrying out experiments at various temperatures, one can determine the temperature dependence of \(D\), which for cement and concrete has the form

\[ D=D_{0}e^{-\frac{Q}{RT}}. \tag{7} \]

For example, Fig. 2 gives the results of experiments by Spinks, Baldwin, and Gorbaldson1 on the penetration of the ion \(\mathrm{SO_4}\) into cement as a result of keeping a cement sample in a saturated solution of \(\mathrm{CaS^{35}O_4}\) for 4 weeks.

In Table I are given the diffusion coefficients of various anions and cations in cement and concrete, determined by the authors of the work cited above.

This table shows that the diffusion coefficient of the \(\mathrm{SO_4^{--}}\) ion has a value approximately 3 times greater than the diffusion coefficient of the \(\mathrm{Ca^{++}}\) ion. The diffusion coefficients of various ions may differ from one another by tens of times, with anions penetrating into cement and concrete considerably faster than cations.

Fig. 2. Distribution of active \(\mathrm{S^{35}O_4}\) in a cement sample after impregnation for 4 weeks.

Table I

\(T = 21^\circ\mathrm{C}\)

Diffusion coefficient \(D \cdot 10^{10}\ \mathrm{cm^2/sec}\)

Compound	Normal cement	Normal concrete (1:2)	Sulfate-resistant cement	Sulfate-resistant concrete (1:2)
\(\mathrm{Na_2S^{*}O_4}\)	1.3	8.9	1.4	9.4
\(\mathrm{CaS^{*}O_4}\)	1.5	8.5	2.6	9.5

Concrete (1:2)

Ion	Diffusion coefficient	Ion	Diffusion coefficient
\(\mathrm{Na^+}\)	3	\(\mathrm{Ca^{++}}\)	2.8
\(\mathrm{SO_4^{--}}\)	6
\(\mathrm{J^{--}}\)	130	\(\mathrm{SO_4^{--}}\)	8.5

Experiments on the study of the diffusion of the \(\mathrm{SO_4^{--}}\) ion into normal and sulfate-resistant cement and concrete showed that sulfate corrosion of concrete depends not on the rate of penetration of the sulfate ion, but on the rate of the chemical processes.

Additional data on the diffusion of various ions in concrete were obtained recently by Gewentman and Sam[^19]. They investigated penetration into concrete specimens of size \(3\times 3\times 2.5\) mm of a series of cations—\(Cs^{134}\), \(Nb^{95}\), \(Ru^{106}\), \(Ce^{144}\)—and the anion \(J^{131}\). The authors obtained a series of radioautographs that could be compared with microphotographs of concrete sections obtained by grinding the specimens to different depths. Figure 3 presents typical microphotographs and radioautographs. By comparing a series of radioautographs it is possible to study the penetration of cations and anions into the depth of the concrete. The diffusion coefficients were calculated from formulas (3)—(6). The data obtained are compared in Table II.

Table II

Diffusion coefficients in cement, lime, and concrete

Ion	Solution concentration	cement	lime	concrete
		\multicolumn{3}{c}{Diffusion coefficient \(D\cdot 10^{10}\ \mathrm{cm^2/sec}\)}
\(J^{131}\)	\(8\times 10^{-13}\ M\ KJ\)	—	—	1580
\(J^{131}\)	\(0.01\ M\ KJ\)	—	—	3020
\(J^{131}\)	\(0.15\ M\ KJ\)	—	120	—
\(Cs^{134}\)	\(3\times 10^{-9}\ M\ CsCl\)	—	—	24.5
\(Cs^{134}\)	\(0.01\ M\ CsCl\)	—	—	20.8
\(Na^{22}\)	\(0.15\ M\ Na_2SO_4\)	—	3.0	—
\(Ca^{45}\)	saturated \(CaSO_4\)	0.1	2.8	—

As is evident from the table, the principal conclusions of Spinks were confirmed in the latest work.

The stability at the point of contact with other materials depends on the chemical composition of certain building materials. Thus, processes occurring at the interface cement—iron in reinforced concrete may play a significant role.

An important task in the construction of furnaces for glass melting and of open-hearth furnaces is the selection of refractories that, at high temperatures, react only very slowly with molten glass and slags. The investigation of reactions at interfaces in all the cases listed can be readily carried out with the aid of labeled atoms[^20].

Using a radioactive isotope of iron, at the Institute of Ferrous Metals A. A. Shvartsman, P. L. Gruzin, and S. A. Pechenev[^21] investigated the penetration of iron into bricks made of magnesite, chromomagnesite, and dinas. A thin layer of iron scale, into which was...

Fig. 3. Microphotographs (left) and radioautographs (right) of concrete specimens obtained as a result of the penetration into them of labeled cations. \(A, A'\)—outer surface; \(B, B'\)—after the first grinding; \(C, C'\)—after the second grinding.

radioactive iron, Fe\(^{59}\), was introduced. The specimen was then heated for 40–100 hours at temperatures of 1120–1330°.

The degree of penetration of Fe\(^{59}\) after heating was investigated by grinding layers from the surface of the specimen and measuring their activity. As a result of these experiments it was established that the rate of penetration of iron from slags, characterized by diffusion coefficients, in the three cases investigated can be expressed by the following equations:

\[ D = 224e^{-78700/RT} \quad \text{(magnesite),} \tag{8} \]

\[ D = 3.1e^{-28400/RT} \quad \text{(chrome-magnesite),} \tag{9} \]

\[ D = 0.1e^{-44800/RT} \quad \text{(dinas).} \tag{10} \]

Apparently, the resistance of refractories to chemical destruction increases in parallel with a decrease in the rate of penetration of iron oxides into the brick. Of course, without the use of radioactive tracer methods, the solution of this problem would have been greatly hampered.

One of the essential characteristics of building materials is their porosity, which depends on the methods of preparation and may change with external conditions.

G. I. Logginov, T. Yu. Lyubimova, and M. A. Shashkovskaya\(^{22}\), using radioactive isotopes, investigated the dependence of the porosity of cement stone on the number of freezing and thawing cycles. G. I. Logginov and O. M. Khusainova\(^{73}\) developed a method for determining the specific surface area of sand, cement, and other porous bodies by adsorption from aqueous and alcoholic solutions of Na\(_2\)W\(^{185}\)O\(_4\).

Fig. 4. Schematic of an apparatus for studying the permeability of porous materials. 1 — bell for supplying air with an admixture, 2 — gasket, 3 — material under investigation, 4 — counter.

The rate of penetration of air through a partition made of the material under investigation can be determined from the radioactivity recorded with a counter, as shown in Fig. 4. Another possible variant for investigating the rate of gas penetration is reduced to the use of the emanation method. For this purpose, when preparing a concrete specimen, a small amount (about 0.1%) of some uranium salt or about 0.03 milligram of radium should be added to the initial raw material. As is known, in equilibrium with uranium there are all members of the uranium family, including radon. By placing a specimen of the concrete under investigation in a vessel, one can judge the porosity of the concrete from the rate of radon release. The concentration of radon in the vessel can be determined by passing air through this

vessel and directing it into an ionization chamber or into an electrometer. By affecting this concrete in some way—for example, by freezing or heating it and repeating the above experiments—one can draw a conclusion about the change in porosity.

In studying the permeability of materials to water, either a radioactive isotope of hydrogen—tritium (\(\mathrm{H}^3\))—is introduced into the latter, or inert radioactive salts that are not adsorbed on the materials under study are dissolved in it. In this case the rate of penetration of the water is determined from the increase in radioactivity, measured by a counter.

Radioactive isotopes can be of great help in the study of physical and chemical processes connected with the production of cement, concrete, and other building materials. Labeled atoms can be used to check the homogeneity of mixing of individual cement components, to check the uniformity of distribution of small additives, and to select the most effective designs and dimensions of the corresponding machines.

B!un and Lindner \(^{23}\) used the radioactive isotope \(\mathrm{Ca}^{45}\) to determine the rate of the reaction of formation of the silicate \(\mathrm{CaSiO}_3\) at temperatures of \(1155^\circ\)—\(1295^\circ\mathrm{C}\). For this purpose, mixtures of powders \(\mathrm{SiO}_2 + 2\mathrm{Ca}^{45}\mathrm{O}\) were pressed into tablets and heated in a nitrogen atmosphere. After heating, \(\mathrm{SiO}_2\) and \(2\mathrm{CaO}\) were separated with the aid of a mixture of glycerin and alcohol in the presence of a small amount of \(\mathrm{SrCl}_2\), which accelerated the separation. Then, with the aid of a Geiger–Müller counter, the activity of the \(\mathrm{SiO}_2\) containing \(\mathrm{Ca}^{45}\mathrm{SiO}_3\) was measured. According to the authors’ data, the dependence of the rate constant of the reaction of formation of \(\mathrm{CaSiO}_3\) on temperature is described by the equation

\[ K = 2.8 \cdot 10^{-2} e^{-54000/RT}\ \mathrm{mol}\cdot \mathrm{cm}^{-2}\mathrm{sec}^{-1}. \tag{11} \]

These results can be used in studying processes occurring in the manufacture of cement clinker.

Radioactive isotopes can also provide substantial assistance in the study of the mechanism of cement setting \(^{24}\), as well as in determining the solubility of its individual components.

A. M. Smirnova and P. A. Rebinder \(^{25}\) used the isotope \(\mathrm{Ca}^{45}\) to study the kinetics of hydration of cement clinker.

Wood plays a major role in the construction industry, and its properties depend to a significant extent on treatment. To preserve wood, it is impregnated with various antiseptic mineral or organic substances. The method for studying the impregnation process differs little from the above-described method for studying diffusion in cement. It should only be noted that, because of the much higher rate of the processes in this case, the study of the distribution of the radioactive isotope as a function of distance from the surface can be carried out by the method of radiography. For this purpose, after the process is carried out

during impregnation for a certain time, the wood specimen is sawn perpendicular to the impregnation surface. A sensitive photographic film is pressed against the sawn surface, and after the appropriate exposure it is developed. The blackening of the film \(S\) depends on the concentration \(C\) of the radioactive substance in the following way:

\[ S=\gamma \lg C+\gamma_0. \tag{12} \]

Having determined the dependence of blackening on penetration depth, \(S=f(x)\), one can easily find \(C=\varphi(x)\) and calculate the diffusion coefficient by the above formula (3). As an example, Fig. 5 shows a radioautograph obtained when southern pine was impregnated with an aqueous solution of \(SrCl_2\), to which the radioactive isotope strontium \(^{26}\) had been added. In these experiments, after a certain time of impregnation the pine specimen was removed from the solution and washed. A photographic film was pressed against the impregnation surface; after exposure for 2 hours it was developed and processed by ordinary photographic methods. The radioautograph shows that the solution impregnates mainly the outer part of the wood. It almost does not penetrate into the heartwood and knots. Conducting such studies may provide valuable information for selecting the most effective antiseptic substances.

Fig. 5. Radioautograph of a transverse section of pine impregnated with a radioactive solution of \(Sr^{90}Cl_2\).

The same technique can be used in studying the corrosion of concrete, the penetration of water into building materials, filtration, etc. It should be noted, however, that the radiography method usually gives qualitative rather than quantitative results.

Radioactive isotopes can also be successfully used for the analysis of building materials. In this connection a number of diverse methods may be employed.

Apparently, the fastest method for determining boron in glass and in cement is the method of absorption of slow neutrons, developed by Martelly \(^{27}\). This method is based on the high probability of absorption of slow neutrons by boron nuclei in comparison with the nuclei of other elements present in glass and in cement.

For analysis a neutron source is used—a mixture of \( \mathrm{Ra} + \mathrm{Re} \) (or \( \mathrm{Sb}^{124} + \mathrm{Be} \)), surrounded by paraffin to slow down the neutrons. A sample of the glass or cement under investigation is placed on the paraffin, as shown in Fig. 6. The neutrons, slowed in the paraffin, pass through the sample, after which they reach the dysprosium detector. Dysprosium atoms absorb neutrons, forming the radioactive isotope \( \mathrm{Dy}^{165} \). The higher the boron content in the sample,

Fig. 6. Diagram of the apparatus for determining boron content in glass.
\(A\)—dysprosium detector, \(B\)—glass under analysis, \(C\)—neutron source, \(D\)—paraffin, \(E\)—cadmium shield.

the more neutrons will be absorbed in it and the less active the dysprosium indicator will be. If several standards containing known amounts of boron are tested in advance, it is possible to construct a calibration curve, which will make it possible to determine the boron content in the samples under investigation. This method has found practical application for determining the boron content in concrete used to protect operating personnel from neutron flux, for example in a uranium reactor.

Another frequently used method of analysis is known as “activation analysis.” This method is used in a number of cases to determine small concentrations of elements that form radioactive isotopes upon reaction with neutrons or fast ions. As an example of the application of activation analysis, one may cite the method developed by Arlenne during the war for determining carbon in iron \(^{28}\).

When the analyzed sample is bombarded with protons or deuterons, radioactive nitrogen is formed according to the reactions:

\[ \mathrm{C}^{12}_{6} + \mathrm{H}^{1}_{1} = \mathrm{N}^{13}_{7} + \gamma, \]

\[ \mathrm{C}^{12}_{6} + \mathrm{H}^{2}_{1} = \mathrm{N}^{13}_{7} + n^{1}_{0}. \]

The isotope \( \mathrm{N}^{13} \) decays rapidly, emitting positrons. The activity of the analyzed sample after bombardment is determined with a counter and compared with the activity of a standard with known carbon content. With entirely satisfactory accuracy, analysis

together with the time spent bombarding the sample, took only 15 minutes in all. This method of analysis was recently tested and improved by I. Curie ^29.

Radioactive isotopes can be of substantial help to the analyst in all cases where a substance must be determined at very low concentrations.

Thus, the solubility of sparingly soluble substances—for example, glass, gypsum, cement—can be determined if a radioactive isotope is introduced beforehand into the materials under study, or if the samples are activated in a uranium reactor. After treating the sample with water or another solvent for a long time in order to reach equilibrium, the sample is removed, the solvent is evaporated, and the amount of remaining solid matter is determined from the activity of the deposit, often invisible to the naked eye. If the volume of solvent is known, the data obtained make it easy to calculate the solubility of the substance under investigation.

Additional information on the use of radioactive isotopes for determining solubility may be found in the article by An. N. Nesmeyanov ^30. A review devoted to the application of artificial radioactivity in analytical chemistry was published by M. B. Neiman and V. B. Miller ^31.

II. INVESTIGATION OF CONSTRUCTION MECHANISMS

Until now, the study of wear in engines and construction mechanisms has been an extremely laborious task. Usually the investigation began with disassembly of the engines and mechanisms and careful measurement of the individual moving parts and components. The engines and mechanisms were then reassembled and tested for a long time under a specified operating regime. After this the mechanisms were disassembled, and micrometric measurement of the rubbing parts made it possible to calculate the degree of wear of individual components. The laboriousness and duration of such tests made it impossible to carry out broad wear tests under different operating regimes and, in this way, continuously improve the mechanism. The use of radioactive isotopes has radically changed the state of this question ^32, ^33, ^34, ^35, ^36. The new method consists in introducing into the rubbing parts whose wear it is desired to study (piston rings, cylinder walls, bearings, journals) a suitable radioactive isotope, Fe^59, Co^60, Sn^125, Cr^51, etc. The radioactive isotope is introduced either directly into the alloy from which the parts are made, or in rods of diameter \(d = 3—4\) mm, which are press-fitted into holes drilled in the parts. In some cases the part under investigation may first be activated by irradiation in a nuclear reactor. During wear of the part in the course of tests, the radioactive isotope enters the

lubricating oil. From time to time, oil samples are examined for radioactivity with the aid of counters. It is clear that, from the increase in the radioactivity of the oil over time, the wear of the part under study can be calculated. Experience has shown that, with a suitable choice of the concentration and radioactivity of the introduced element, such a test of the wear resistance of a single part takes no more than a few hours and reduces costs many times over.

Experiments on studying the wear of engines operating on light and heavy fuel, and the wear of various mechanisms, have shown that at the beginning of the test of a new machine the wear is comparatively high; subsequently it rapidly decreases, tending toward a constant value, as shown in Fig. 7, where the results of wear tests of the piston rings of two gasoline engines of the same series are presented. The running-in period is characterized by the lapping of parts and the abrasion of incidental microprojections, burrs, etc. The constant wear in the second period depends on the design of the engine, the load regime, and the quality of the lubrication and fuel. The method considered makes it possible to study the wear of each machine part separately and, in this way, to select for each part the most suitable grade of alloys.

Fig. 7. Dependence of piston-ring wear on operating time for two gasoline engines.

This same method can be successfully applied to finding the most suitable operating regimes for engines and mechanisms, and to selecting lubricating oil and fuel. By the method of radioactive isotopes it has been shown that replacing one type of fuel with another in some cases considerably reduces wear. Thus, reducing the sulfur content in gasoline from 1.2 to 0.05% reduces the wear of engine parts by a factor of 2, as can be seen in Fig. 8, where the results of tests using the radioactive isotope \(\mathrm{Fe}^{59}\) are presented.

The introduction of certain additions of surface-active substances into lubricating oils, as well as a change in its temperature, can reduce wear severalfold. Fig. 9 presents the results of similar investigations carried out by Yu. S. Zaslavskii, G. I. Shor

and F. B. Lebedeva[^37]. In the cited work, the dependence of piston-ring wear on the temperature of the cooling water and on the quality of the lubricating oil was studied. From Fig. 9 it is evident that, when the temperature of the cooling water is lowered from 30° to 20°, wear increases by a factor of 2. The introduction into avtol of small amounts (about 3%) of the additive NAKS greatly reduces wear at low temperatures.

Similar investigations are also important in studying and selecting the operating conditions of complex construction machines, which already at the present time play a major role and will be widely used in carrying out still more grandiose construction plans in the future.

Fig. 8. Dependence of engine wear on the sulfur content in the fuel.

Fig. 9. Dependence of piston-ring wear on the temperature of the cooling water. 1 — avtol served as the lubricant; 2 — avtol with the NAKS additive.

III. CONTROL OF METAL STRUCTURES

A number of works are devoted to the application of radioactive isotopes for investigating corrosion, determining the thickness of protective coatings, and controlling the quality of welded seams.

At the present time the film theory of metal corrosion, developed by Academician V. A. Kistyakovskii[^38], is generally accepted. According to this theory, a thin oxide film forms on the surface of an oxidizing metal. Further oxidation of the metal is connected with the diffusion of reactants through this film. One may imagine two different mechanisms of further oxidation. The first mechanism is charac—

...is characterized by the diffusion of metal atoms through the oxide film. Only upon reaching the surface are they oxidized as a result of bombardment by molecular oxygen. The second mechanism assumes the diffusion of oxygen molecules through the film toward the metal surface, where oxide molecules are formed.

In order to establish which of these mechanisms is valid in the case of oxidation of copper in air, the following experiment was carried out[^39]. A very thin layer of copper containing the radioactive isotope Cu^64 was deposited electrolytically on the surface of a copper plate, as schematically shown in Fig. 10. This plate was then oxidized in air at a temperature of 1000°.

Fig. 10. Schematic of the experiment for studying the mechanism of oxidation of copper.

Fig. 11. Schematic of an apparatus for detecting corrosion of pipelines. 1 — counter, 2 — lead shield, 3 — γ-ray source.

It is clear that, in the case of oxidation by the first mechanism, the inactive oxide layer should be on the outside (Fig. 10, a), whereas in the case of oxidation by the second mechanism the active oxide layer should be on the outside (Fig. 10, b). The experiments showed that the outer layer of copper oxide is not active and, consequently, the oxidation is accompanied by diffusion through the oxide film of copper atoms, and not of oxygen.

In our country, the construction of gas pipelines and oil pipelines of enormous length is widely developed. An extremely important task is the fight against internal corrosion of these pipelines. Radioactive isotopes which emit γ-rays during decay make it possible to solve simply the problem of detecting internal corrosion of pipes and reservoirs without dismantling them[^40]. A schematic of the apparatus that makes it possible to solve this problem is shown in Fig. 11.

A radioactive isotope 3, emitting γ-rays, is placed in a lead casing with an opening through which the γ-rays are directed to the desired place on the wall of the pipeline. Passing through the wall,

γ-rays are reflected from layers of metal lying at different depths and enter the counter. Owing to the lead shield 2, only reflected γ-rays can enter the counter, which is located next to the casing containing the radioactive isotope. The counter, together with the radioactive isotope, is enclosed in a common case, which is easy to carry from place to place. By applying this instrument to various points of a pipeline or a metal wall, one can readily detect places that have undergone internal corrosion, from the sharp change in the number of pulses registered by the counter per second.

To combat corrosion of metals, the latter are often protected by coatings—layers of more noble metals, drying oil, or paint. Determining the thickness of these coatings without damaging them is an important technical problem. The most elegant solution of this problem is achieved with the aid of radioactive isotopes emitting β-particles \(^{41,42}\). Instruments manufactured for measuring the thickness of protective coatings make use of the law of reflection of β-particles. As is known, the reflection coefficient of electrons depends on the atomic number of the atoms of which the reflector consists. Therefore the reflection of electrons from the clean surface of a metal usually differs sharply from the reflection in the case when the metal surface is covered with a layer of another composition. In this case the electron reflection coefficient changes the more, the greater the difference between the atomic numbers of the substrate element and the coating element, and the thicker the latter. If the composition of the substrate and of the coating is constant, the electron reflection coefficient depends on the thickness of the coating.

Fig. 12. Diagram of an instrument for measuring coating thickness by reflection of β-particles.

The main part of an instrument for determining the thickness of protective coatings is an ionization chamber into which electrons emitted by the radioactive isotope are reflected, as shown in Fig. 12. The radioactive isotope is placed in a lead block, which eliminates the possibility of direct entry into the ionization chamber of β-particles arising during radioactive decay. The ionization current \(I\) depends on the intensity of the incident electron beam \(I_0\), on the thickness of the reflecting layer \(x\) (in \(mg/cm^2\)), and on the absorption and reflection coefficients \(\mu\) and \(\alpha\) of the β-particle beam. In the case of a monoenergetic beam one may assume that

\[ dI=\alpha I_0 e^{-2\mu x}dx \tag{13} \]

and, consequently,

\[ I=\frac{\alpha I_0}{2\mu}\left(1-e^{-2\mu x}\right). \tag{14} \]

The reflection coefficient \(\alpha\), according to Mott\(^{43}\), depends in the following way on the atomic number \(Z\) of the atoms of the reflecting layer, the electron velocity \(v=\beta c\) (\(c\) is the velocity of light in vacuum), and the angle \(\theta\), which determines the solid angle of the beam of reflected electrons entering the ionization chamber:

\[ \alpha = N\left(\frac{e^2 Z}{2mv^2}\right)(1-\beta^2)\left(1-\beta^2\sin^2\frac{\theta}{2}\right)\cosec^4\frac{\theta}{2}. \tag{15} \]

In the case of beams of \(\beta\)-particles whose velocity varies over wide limits, formulas (13), (14), and (15) satisfactorily describe the reflection and absorption of electrons, if some average value is taken for \(v\).

As follows from formula (14), for small substrate thicknesses the ionization current is proportional to \(x\):

\[ I=\alpha I_0 x. \tag{16} \]

For large values of \(x\) the ionization current reaches a limiting value

\[ I_{\mathrm{lim}}=\frac{\alpha I_0}{2\mu}. \tag{17} \]

Fig. 13. Dependence of the magnitude of the ionization current on the thickness of the substrate (curve \(A\)) and of the coating (curve \(B\)).

These relations are evident from consideration of Fig. 13, where curve \(A\) shows the dependence of the strength of the ionization current on the thickness of the substrate \(x\). The magnitude of the limiting current is proportional to the reflection coefficient \(\alpha\), which, according to formula (15), is proportional to the square of the atomic number of the substrate atoms. If the substrate is covered with a layer consisting of atoms with a large atomic number, then as the thickness of the coating increases the ionization current will increase, as shown by curve \(B\) in Fig. 13.

It is clear that, when the coating thickness is not too great, the latter can be determined from the magnitude of the ionization current.

The scale of a measuring instrument measuring the current in an ionization chamber can be graduated directly in units of coating thickness. By applying the instrument to the surface under investigation, one can immediately read off on the scale the coating thickness at that point.

In the manufacture and assembly of metal structures, welding operations are very often used. It is not possible to inspect welded seams by radiographic methods under construction-site conditions, owing to the difficulties of transporting bulky ...

with a powerful high-voltage X-ray installation. In addition, it should be noted that factory X-ray apparatuses operating at voltages of 100–150 kilovolts do not permit the radiographic inspection of products more than 1.5–2 cm thick. In recent years, γ-rays emitted by radioactive isotopes have been widely used for the radiographic inspection of metal products. Most often, for this purpose the isotope \(Co^{60}\) is used, emitting γ-rays with an energy of 1300 keV. This radiation can be used for radiographic inspection of products up to 50 cm thick.^44,45,46,47 Such a method of investigation is commonly called gamma radiography.

For radiographic inspection, a specimen of activated cobalt weighing on the order of 1–10 g is used, which is stored in a lead container.^48 The container, which weighs about 30 kg, is provided with a handle for carrying it from place to place. The external appearance of the container is shown in Fig. 14. The container has an opening closed by a lead plug.

If, with the aid of a key provided with a long handle, this plug is removed, a directed beam of γ-rays emerges from the container, which can be used for the radiographic inspection of products.

Fig. 14. Container for storage and carrying of the radioactive isotope \(Co^{60}\), used for gamma radiography.

Fig. 15. Weld seam prepared for radiographic inspection by γ-rays.

In those cases when the radiographic inspection of products can be carried out in the shop in the absence of workers, for example at night, they proceed

otherwise. The blanks to be radiographed are arranged around a circumference. Behind each blank an envelope with X-ray film is placed. On each envelope a number is put corresponding to the respective product. In the center of the circle a γ-emitter taken out of its container is placed. After a suitable exposure (usually several hours), the radioactive isotope is put back into the container, and the exposed pieces of film are developed in the laboratory. From the character of the blackening of the film it is possible to draw a conclusion as to the presence or absence of cavities, cracks, and other defects in the blanks or products subjected to radiography.

Especially important is the use of radioactive isotopes emitting γ-rays for checking the quality of welded seams. The places to be checked are marked with chalk and labeled. Near those places of the welded seam which it is desired to mark, iron arrows are placed, as shown in Fig. 15. The laboratory assistant applies to the indicated place a cassette with X-ray film, which in the case of welding

Fig. 16. Cassette with X-ray film for gammagraphy, pressed against a welded seam during exposure.
Fig. 17. Details of a gammagram of a welded seam at large scale.

of iron structures is drawn to the place being investigated by means of permanent magnets (Fig. 16). The radioactive isotope Co$^{60}$ is placed on the other side of the welded seam under investigation. After the exposure, the duration of which depends on the thickness of the product being checked, the activity of Co$^{60}$, and the sensitivity of the X-ray film, the latter is developed in the laboratory. The gammagram of the welded seam

with defects is shown in Fig. 17. On the negative, images of arrows are visible; from their positions it is easy to find the places in the weld seam where the defects were detected. In the lower part of Fig. 17 there is an enlarged image of the place on the gamma radiograph where lack of penetration was found.

Gamma radiography is widely used in our machine-building industry and, undoubtedly, should find broad application on construction sites.

IV. CHECKING VENTILATION AND HEATING SYSTEMS

When checking the operation of ventilation, it is necessary to determine the actual air-exchange coefficient and its conformity to the design specification. Radioactive indicators make it possible to determine the air-exchange coefficient extremely accurately and quickly. For this purpose, some harmless volatile substance is usually used, into the composition of which a radioactive isotope is introduced. One of the most commonly used substances is methyl bromide (\(\mathrm{CH_3Br}\)), which boils at a temperature of \(4^\circ\mathrm{C}\). The radioactive isotope \(\mathrm{Br}^{82}\) is introduced into this molecule. If, with the ventilation switched off, a small quantity of methyl bromide is released into the room being investigated and the activity is measured at different moments of time by means of a counting installation, it may be observed that the activity gradually decreases with time as a result of natural air exchange. If the ventilation is switched on, a more rapid fall in activity is observed, as shown in Fig. 18.

Fig. 18. Curve of the fall in activity in a room after the release into the air of a small portion of \(\mathrm{CH_3Br}^{82}\). The arrow marks the moment when the ventilation was switched on.

If the air-exchange coefficient is denoted by \(k\), then, in the case of complete mixing of the air, the activity should fall according to the equation:

\[ -\frac{dJ}{dt}=kJ. \tag{18} \]

Integration of this equation leads to the formula

\[ J=J_0 e^{-kt}. \tag{19} \]

If the experimental points are plotted in the coordinates \(\lg J\) and \(t\), they should lie on a straight line, from the slope of which the air-exchange coefficient \(k\) can be determined. The results of activity measurements for determining \(k\) are shown in Fig. 19. Before the ventilation was switched on, the coefficient of natural air exchange was equal to \(3\ \text{hour}^{-1}\); after the ventilation was switched on, its value increased to \(5\ \text{hour}^{-1}\).

Labeled atoms are expedient to use for detecting leaks in gas pipelines and heating systems. When testing gas pipelines, air with an admixture of the radioactive isotope Xe\(^{133}\) or vapors of CH\(_3\)Br\(^{82}\) is pumped into them. In the case of an above-ground gas pipeline, the place of the leak is easily detected with the aid of an ordinary counter. In the case where the gas pipeline runs underground at a depth of 1–2 meters, the radioactive gas used to find the leak must

Fig. 19. Semilogarithmic anamorphosis of the curve in Fig. 18.

Fig. 20. Change in activity with time after release of a portion of Xe\(^{133}\) under a sand layer 35 cm thick.

diffuse comparatively rapidly through the soil, but be well adsorbed in the surface layer, in order to facilitate its detection with a counter.

Special experiments carried out with the isotope Xe\(^{133}\), a small amount of which was released from a valve under a layer of compacted sand 35 cm thick, showed that the activity measured by a counter at the surface changes with time as shown in Fig. 20. The maximum activity is observed 20 min after the xenon is released, but then the activity rapidly falls to zero, which indicates weak adsorption of xenon. Therefore, for detecting leaks in pipes laid underground, the isotope Xe\(^{133}\) is of little use. For this purpose it is better to employ vapors of CH\(_3\)Br\(^{82}\), which diffuse comparatively slowly through the soil but are well retained by the surface layer.

The activity curve recorded by a counter at the surface of the ground in the case of leakage of CH\(_3\)Br\(^{82}\) from a pipeline laid at a depth of 1.8 m is shown in Fig. 21. As can be seen from the figure, the activity recorded by the counter increases over the course of 40–50 hours and then remains approximately constant. It is evident that at

in the final section the decrease in activity due to the radioactive decay of CH\(_3\)Br\({}^{82}\) and desorption of CH\(_3\)Br\({}^{82}\) is compensated by the arrival of new portions of CH\(_3\)Br\({}^{82}\), diffusing through the soil layer. It is clear that, depending on the depth at which the pipeline is laid, a survey of the route by a counter in searching for the site of a leak should be carried out 10–50 hours after the air containing an admixture of CH\(_3\)Br\({}^{82}\) has been forced in.

To locate a leak in heating systems, radioactive table salt Na\({}^{24}\)Cl is introduced into the latter. In one case

Fig. 21. Curve of the change in activity with time in the case of leakage of CH\(_3\)Br\({}^{82}\) from a pipeline laid at a depth of 1.8 meters.

during the search for a leak in a heating system\({}^{50}\), the radiators were located under the concrete floor of a large garage with an area of 1500 m\(^2\). By introducing Na\({}^{24}\)Cl into the system and surveying the field with a counter, it was possible, from the penetrating radiation, to detect the site of the leak with an accuracy of up to 15 cm and to carry out repairs without interrupting the operation of the garage.

V. INVESTIGATION OF SOIL

The development of the simplest and most accurate methods for determining the density and moisture content of soils is one of the important tasks in hydraulic engineering, road construction, and building construction. Density is the initial quantity for judging the deformations of soil and the internal stresses arising in it. Two methods for measuring soil density are described in the literature.

The first method is based on the ability of soil to absorb γ-rays. If a parallel monochromatic beam of γ-rays passes through a substance, then its intensity decreases with increasing thickness of the absorbing layer according to the law:

\[ I = I_0 e^{-\mu x}. \tag{20} \]

Here \(I_0\) is the intensity of the incident beam, \(I\) is the intensity of the transmitted beam, \(x\) is the thickness of the absorbing layer, and \(\mu\) is the linear absorption coefficient.

In practice one often uses the so-called mass absorption coefficient:

\[ \mu'=\frac{\mu}{\rho}, \tag{21} \]

In this case equation (20) is transformed into the form

\[ I=I_0 e^{-\mu'\rho d}. \tag{22} \]

It should be noted that, at \(\gamma\)-quantum energies on the order of \(1\ \mathrm{MeV}\), the attenuation of a beam of \(\gamma\)-rays is mainly due to their scattering (the Compton effect), and the mass absorption coefficient is proportional to the ratio \(Z/A\) (\(A\) is the atomic weight, and \(Z\) is the ordinal number of the element in the Mendeleev table). Therefore, for all elements whose ordinal number lies in the range from 2 to 30, the value of \(\mu'\) is practically the same. Elements with such ordinal numbers are usually found in soils. Therefore, the absorption of \(\gamma\)-rays depends not on the chemical composition of the soil, but is determined only by its density.

In practice, for determining soil density it is more convenient to use the logarithmic form of equation (22):

\[ \ln \frac{I}{I_0}=-\mu'\rho d. \tag{23} \]

The last expression shows that, for \(d=\mathrm{const}\), the quantity \(\ln \frac{I}{I_0}\) is proportional to the density \(\rho\). By placing various soil samples of known density in the path of the \(\gamma\)-rays and measuring the intensity of the transmitted radiation, one can obtain a series of values of \(\ln \frac{I}{I_0}\) corresponding to certain values of the density. If the result of the experiment is represented graphically in the coordinates \(\ln \frac{I}{I_0}\) and \(\rho\), a straight line is obtained, whose slope is equal to the product \(\mu'd\) and does not depend on the chemical composition of the soil. Therefore such a straight line can serve as a calibration graph when measuring the density of various soils by the absorption of \(\gamma\)-rays under the condition \(d=\mathrm{const}\). Various artificial radioactive isotopes may be used as the radiation source, for example \(\mathrm{Co}^{60}\), \(\mathrm{Cs}^{137}\), etc., emitting \(\gamma\)-rays of sufficient energy.

The layout of the apparatus, developed by K. V. Yuryev, for measuring the density of sandy soil\({}^{52}\) is shown in Fig. 22. Paral-

a parallel beam of γ-rays passes through soil of a definite thickness and is focused, by means of a lead diaphragm with a narrow opening, onto two Geiger—Müller counters arranged in series, which record the intensity of the transmitted radiation. The counters are connected “in coincidence” in order to reduce the influence of the background. A preparation of radioactive cobalt, \(^{60}\mathrm{Co}\), was used as the radiation source. The distance from the source

![Fig. 22 and Fig. 23 diagrams]

Fig. 22. Diagram of an apparatus for determining soil density by absorption of γ-rays.
1 — γ-radiation source, 2 — lead container, 3 — absorber, 4 — lead diaphragm, 5 — counter tubes.

Fig. 23. Arrangement of instruments in studying soil density under field conditions.
1 — source, 2 — ionization chamber, 3 — steel pipes.

to the lower counter was 60 cm. Under the selected conditions it was possible to detect a change in soil density with an accuracy of up to 1%. Similar results were obtained by D. E. Pol’shin and S. I. Nosal’\(^ {74}\) when measuring the density of clayey silt, kaolinite silt, and sand.

To measure soil density by absorption of γ-rays under field conditions, it is necessary to drill two parallel boreholes at some distance from each other (Fig. 23). A metal pipe is placed in one of the boreholes, in which the γ-ray source is secured, and in the other—a pipe with a counter or ionization chamber, which is connected by a cable to the measuring instrument. The magnitude of the electric current arising in the ionization chamber depends on the distance between the boreholes and on the density of the soil. It is convenient to calibrate the scale of the measuring instrument in advance in units of density. An important advantage of this method is the possibility of measuring density

soil without disturbing the structure corresponding to natural conditions of occurrence.

Another method of measuring soil density is based on the scattering of γ-rays53, 54, 55, 56.

If a beam of γ-rays emitted by a source is directed at the substance under investigation, the γ-rays will be scattered as a result of interaction with the electrons of the atoms composing the given substance. In this case the scattering will vary depending on the number of electrons in the atoms. Since, to a good approximation for soils, the number of electrons is proportional to the density, the density of the soil can be inferred from the scattering of γ-rays by the soil.

The instrument used for such measurements is shown in Fig. 24. In the lower part of a metal tube a source of γ-rays, 1, is fixed, and in the upper part a Geiger–Müller counter, 2, is connected by a cable to an amplifier and a mechanical pulse recorder (not shown in the figure). A lead shield, 3, protects the counter from the direct incidence of γ-rays immediately from the source. The metal tube with the instrument is inserted into the soil sample under investigation. The γ-rays emitted by the source pass into the soil, are scattered, and enter the counter. The intensity of the radiation falling on the counter depends on the density of the soil.

Fig. 24. Diagram of an instrument for determining soil density from γ-ray scattering. 1—source, 2—lead shielding, 3—Geiger–Müller counting tube, 4—cable to the instrument registering pulses, 5—insulator, 6—metal tube.

Figure 25 shows a calibration straight line that makes it possible, from the number of pulses registered by the counter, to determine the density of the surrounding soil. As is evident from the figure, the experimental points obtained for various soils fall quite satisfactorily on a single straight line, which proves the validity of the considerations set forth above and the possibility of using this calibration line for investigating different types of soils.

To measure soil density under field conditions, it is sufficient to drill one borehole, into which a tube \((d = 32\ \text{mm})\) with instruments is inserted. By lowering the instrument to different distances from the surface, it is possible to determine the density at different depths. According to Belcher54, such measurements give the average value of the density for the layer of surrounding soil whose radius does not exceed 23 centimeters. The accuracy of the density determinations is \(\pm 2\%\). With the aid of the considered-

method, one can quickly and reliably determine density without disturbing the soil structure.

A similar method can be successfully used for the rapid determination of the density of concrete as it hardens.

Determining the moisture content in soils is an important problem in construction, in design, and in the study of the condition of roads.

The method for determining the moisture content of soil by the scattering of fast neutrons is described in a number of works53–58. As is known, neutrons,

Fig. 25. Calibration graph for measuring soil density. The numbers denote points obtained for different soils.

entering a substance, interact with the nuclei of the atoms of that substance. In this process a nuclear reaction may occur, leading to the formation of a new nucleus. Along with this, neutron scattering is also observed59.

In elastic scattering, the mean loss of energy by a neutron is equal to:

\[ \frac{\overline{\Delta E_n}}{E_n^0} = \frac{2 m m_n}{(m + m_n)^2}. \tag{24} \]

Consequently, when a neutron collides with a proton \((m = m_p = m_n)\), its energy decreases by approximately a factor of two, whereas in collisions with heavier nuclei the neutron energy changes little.

Therefore the most effective neutron moderators are substances containing hydrogen, for example water, paraffin, and various hydrocarbons. Therefore, when neutrons enter soil, they will be better moderated and scattered by water than by substances that do not contain hydrogen. In this case the scattering will not depend on the state of aggregation of the water. An instrument for measuring moisture content by neutron scattering was constructed and tested by Belcher and Spinks\(^{54,57}\). The scheme of Belcher’s instrument is shown in Fig. 26. The source of fast neutrons 1 is placed in an aluminum tube. Near the source a detector of slow neutrons—rhodium foil 2—is fastened. The tube is immersed in the soil sample under investigation. The fast neutrons emitted by the source pass out into the surrounding soil, where they are scattered

Fig. 26. Scheme of an instrument for measuring moisture content by the scattering of fast neutrons. 1—source, 2—foil, 3—metal tube.

Fig. 27. Calibration graph for determining the moisture content in soil.

and are moderated by the nuclei of hydrogen atoms. The number of slow neutrons formed will be proportional to the water content in the soil. Some of the slow neutrons return to the location of the foil and interact with the nuclei of rhodium atoms. In this process a rhodium isotope with mass number 104 is formed, which then decays, emitting γ-rays. After exposure for a certain time, the activity of the rhodium foil was measured with a Geiger–Müller counter. In parallel, the moisture content of the soil was determined by the usual gravimetric method. From the obtained

from the data a calibration graph was constructed, shown in Fig. 27. It is evident from the figure that the activity of the radium foil depends strongly on the moisture content in the soil.

Special experiments carried out with various samples showed that, at moisture contents exceeding \(0.15\ \text{g}\cdot\text{cm}^{-3}\), increasing the diameter of the soil sample beyond \(22\ \text{cm}\) does not affect the activity of the radium foil. However, in cases of low moisture contents, when the diameter of the soil sample is increased beyond \(22\ \text{cm}\), the activity of the foil increased only slightly. Therefore, in order to determine density under field conditions, where the soil is not bounded, it is necessary to use the corrected calibration curve, shown in Fig. 28 by the dashed line.

Fig. 28. Results of parallel measurements of soil density and moisture at various depths.

According to Belcher’s data, such measurements give an average moisture value for a layer \(10\text{–}12\ \text{cm}\) thick, whose radius is \(15\ \text{cm}\) at high moisture and \(38\ \text{cm}\) at low moisture. The accuracy of the determination is about \(1\%\). The advantage of the method is that it permits measurements to be made without disturbing the structure of the soil. By placing the instrument in tubes at various distances

from the surface of the soil, it is possible to measure the moisture content of the soil at various depths.

When using a radium-beryllium neutron source, because of the intense $\gamma$-radiation of radium it was impossible to place the counter in the tube next to the foil. Therefore the foil had to be taken to the laboratory, which increased the measurement time. The authors carried out special experiments in which a Po—Be mixture was used as the neutron source. In this case $\gamma$-radiation is practically absent. Therefore the counter could be placed in the tube near the rhodium foil and continuous measurement of the moisture content in the soil could be carried out.

Shaap[^58], for measuring moisture content, used a proportional neutron counter filled with boron fluoride. The Ra—Be neutron source and the neutron counter were fastened in an aluminum tube, which was inserted into the soil under study. Part of the neutrons scattered and slowed down in the soil entered the tube and were recorded by the neutron counter. The use of a neutron counter made it possible sharply to reduce the activity of the source used, which helped to create safe working conditions and increased the sensitivity of the instrument.

If a neutron source, a $\gamma$-emitter, and neutron and $\gamma$-ray counters are combined in one instrument, then, by lowering such an instrument into a borehole, it is possible simultaneously to determine the moisture content and density of the soil. An example of results obtained in parallel measurements of the moisture content and density of soil down to a depth of 2.8 m is given in Fig. 28.

The method considered can be used for monitoring the moisture content of concrete structures and for determining moisture content in concrete mixers.

The neutron-scattering method can be successfully applied to the determination of bitumens in asphalt. For this purpose one of the instruments described above may be used. It is first necessary, using known asphalt samples, to construct calibration curves of the dependence of the activity recorded by the counter on the percentage content of bitumens in the asphalt.

When drilling deep boreholes, valuable information about the character of the occurrence of strata and about their nature can be obtained by lowering into the borehole a lead-shielded neutron source and an ionization chamber or neutron counter[^60][^61][^62]. Neutrons enter the adjacent stratum, are reflected and partially absorbed, and various radioactive isotopes are formed in the stratum. The reflected neutrons are recorded by the neutron counter, while the magnitude of the current in the ionization chamber depends on the intensity of the radioactive radiations ($\gamma$-rays and $\beta$-particles). As investigations carried out at Leningrad University[^63] have shown, the current in the ionization chamber depends on the chemical composition of the stratum near which it is located.

is lowered into the borehole. By this method it is possible to distinguish limestone, shales, clay, sand, and certain other rocks from one another.

Figure 29 shows curves (1, 2, and 3) obtained with the aid of the above-described instrument in the study of three boreholes located at distances of about 100 m from one another. The curves

а—shales; б—limestone; в—sandstone

Fig. 29. Curves recorded in neutron logging of three boreholes (curves 1, 2, and 3) and in electric logging (curve 4) at depths from 1500 to 1900 m.

almost exactly repeat one another, which indicates a horizontal arrangement of the beds at depths from 1500 to 1900 m. The results of the study using a neutron source agree well with curve 4, which shows how the electrical resistance of the beds changes at different depths.

While providing substantial assistance in the search for oil, the described method may in some cases also prove useful in studying the structure of the ground before construction work is carried out.

Radioactive isotopes can also be used in a number of investigations of the chemical or physicochemical properties of soil. Thus, for example, the question of the relative amount of free

and bound water in soil can be solved by studying the rate of exchange of this water with water labeled with tritium or deuterium. By an analogous method one can investigate the ratio of the amounts of water and ice at various temperatures in soil samples from the permafrost zone.

Radioactive isotopes can be used for “labeling” moving underground layers in those cases where it is desirable to determine the direction of movement of quicksand.

Radioactive isotopes have also been used to study the wear of asphalt roads under the action of water^64. For this purpose, a small amount of calcium chloride labeled with the isotope Ca^45 was applied to the surface of crushed stone before it was covered with asphalt. After this the asphalt was subjected to the action of water. The radioactivity of the solution thus obtained was then measured with a Geiger—Müller counter. It was found that the amount of calcium chloride which had passed into solution was proportional to the magnitude of the wear of the asphalt road.

VI. APPLICATION OF RADIOACTIVE ISOTOPES IN THE CONSTRUCTION OF HYDRAULIC STRUCTURES

Radioactive isotopes are used to determine the velocity of air motion^65. The principal part of the instrument used for this purpose consists of two electrodes located at a short distance from one another, between which a potential difference is produced.

If a layer containing a radioactive substance emitting $\alpha$-particles is applied to one of the electrodes, then the magnitude of the ionization current, measured by a galvanometer, depends on the velocity of the air jet flowing in a direction perpendicular to the gap between the electrodes, as is evident from consideration of the curve shown in Fig. 30. It is clear that, after calibration, such an instrument can be used to determine the velocity of air motion.

Fig. 30. Calibration curve for determining the velocity of an air jet from the ionization current.

To measure the velocity of water motion, a radioactive substance is introduced into it at a definite moment in time^66. The moment is noted when a counter, located downstream near the surface of the water, registers the maximum activity. Knowing the distance between the place where the radioactivity was introduced and the location of the counter, and the time required to traverse this distance,

It is easy to determine the velocity of the water flow. An instrument can be constructed that automatically measures and records the velocity of the water flow at definite time intervals. Recently a method was developed for studying turbulent water flow with the aid of radioactive isotopes.

In designing the construction of hydraulic structures, the question of the directions and rate of filtration of water through soil plays a major role. The verification of theoretical calculations of filtration is usually carried out on models. The use of radioactive isotopes in modeling can in a number of cases simplify experimentation and accelerate the obtaining of the necessary results. The distribution of radioactive isotopes at various moments of time in conducting such experiments can be investigated with the aid of a counter or by the method of radiography.

In some cases river water goes wholly or partly underground, and the direction of its flow and the place where it emerges at the surface may be difficult to determine^67. In such cases the introduction of radioactive isotopes into the water makes it possible to check the correctness of the assumption concerning the place where the water comes out onto the surface.

Fig. 31. Diagram of an instrument for measuring the percentage content of soil in pulp. 1—source of γ-rays, 2—pipe, 3—ionization chamber, 4—current amplifier and measuring instrument.

In hydraulic engineering construction, which is being carried out in the USSR on a large scale, dredges have found wide application. To monitor the operation and increase the productivity of a dredge, it is necessary to know the soil content in the water-soil mixture in the pulp passing through the pipeline. The task arose of developing a rapid and reliable method for determining the concentration of soil in the pulp. This problem was successfully solved by E. G. Kardash^68 in the Research Laboratory of Kotlonadzor and independently by S. V. Starodubtsev and co-workers^69 at the Leningrad Physico-Technical Institute.

Figure 31 shows the diagram of an instrument for determining the density of pulp. A γ-ray source 1—Co^60 in a lead container—is placed on one side, and an ionization chamber 2 on the other side of the pipeline. The γ-rays pass through the walls of the pipe, a layer of pulp of thickness \(x\), and enter the ionization chamber. The electric current arising—

... entering the ionization chamber is amplified by a special amplifier 3 and measured by a pointer measuring instrument 4, whose scale is graduated in percentages of the soil content in the pulp.

The intensity of the γ-rays entering the ionization chamber depends on the intensity of the rays incident on the pipe, on absorption by the pipe walls and by the pulp, and on the distance \(x\). As is known, the energy of a parallel monochromatic beam is attenuated according to an exponential law. Therefore the intensity of the γ-rays that have passed through the pulp is determined by the equation

\[ I = I_0 e^{-\left(\delta \mu'_0 x+\mu_1 d\right)} . \tag{25} \]

Here \(I\) is the intensity of the beam that has passed through the pulp, \(I_0\) is the intensity of the beam incident on the pulp, \(\mu'_0\) and \(\mu_1\) are the absorption coefficients of water and of the wall material, \(\delta\) is the density of the pulp, and \(d\) is the thickness of the pipe walls.

In the case where the pipe is filled with pure water, the intensity \(I_1\) of the beam entering the ionization chamber is equal to

\[ I_1 = I_0 e^{-\left(\mu_0 x+\mu_1 d\right)} . \tag{26} \]

Substituting the value of \(I_1\) into equation (25), we obtain the following expression:

\[ I = I_1 e^{-\left[(\delta-1)\mu_0 x\right]} . \tag{27} \]

It follows from formula (27) that the intensity of the γ-rays entering the ionization chamber decreases as the density of the pulp increases. The instrument makes it possible to measure the density of the pulp from 1.5 to 1.9 with a relative error of about 3%.

The weight of the instrument could be reduced if it were possible to lower the activity of the γ-ray source, which at the same time would facilitate compliance with safety requirements. S. V. Starodubtsev constructed a portable instrument whose weight has been considerably reduced. The source of γ-radiation in this instrument is radioactive cobalt. A counter with an integrating circuit and a microammeter is used for recording the γ-rays. This instrument is intended for locating plugs formed by soil in a pipeline.

A similar method has recently been applied to determine the concentration of silt at the bottom of rivers and lakes \(^{70}\). Since the concentration of silt is relatively low, soft γ-rays with an energy of about 50 kev must be used for its measurement. The radioactive isotopes ordinarily used emit high-energy γ-rays, while those isotopes that emit low-energy γ-rays decay too rapidly. In this connection, the use of the latter for solving the given problem is excluded. Therefore, in instruments for determining the concentration of silt, the radioactive isotope \(\mathrm{Sr}^{90}\) is used with a comparatively thin lead screen. The β-particles emitted by the isotope enter the lead-

nium and cause the formation in the latter of bremsstrahlung X-rays with an energy of about 50 keV. These rays are also used to determine the concentration of silt in an installation, the diagram of which is shown in Fig. 32. The instrument is lowered into the water from a vessel that moves slowly in a specified direction. The measuring instrument located on the vessel makes it possible to determine the concentration of silt along the vessel’s path at various depths.

When designing reservoirs, canals, basins for water purification, and other hydraulic-engineering structures, it is important to know how the outlines of the banks, the method of supplying and removing water, and other characteristics of the structure affect the distribution of water-flow velocities at various depths and in various directions. To solve this problem it is expedient to use radioactive isotopes characterized by a short half-life, for example bromine (\(\mathrm{Br}^{82}\)).

Fig. 32. Diagram of an instrument for determining the concentration of silt on the bottoms of rivers and lakes. 1—source of \(\beta\)-rays, 2—lead plate, 3—counter.

By this method\(^{71}\) the distribution of water flows in a settling basin was studied. Polluted water entered through a pipe into the center of the basin and slowly moved along the radii, overflowing over the settling wall. Solid particles suspended in the water slowly settled to the bottom of the basin. Geiger–Müller counters were placed at various points in the basin at various depths. A small amount of sodium bromide solution (\(\mathrm{NaBr}^{82}\)) was introduced into the pipe through which the water entered. The change with time of the activity recorded by the counters was then recorded. From the curves thus obtained for the dependence of activity on time at various points of the basin, the pattern of distribution of the water flows was determined. The jets of water moved from the center to the periphery along the bottom of the basin, while in the upper layers eddies were observed, which did not promote normal settling of contaminants. Changing the profile of the bottom and the shape of the pipe supplying the water led to elimination of the eddies. Investigation, by means of counters, of the change of activity with time around the circumference of the basin made it possible to prove that the velocities of water motion along different radii differed from one another. In another settling basin, as was determined by experiments using radioactive bromine, the water flows were uniformly distributed around the entire circumference.

Recently a method has been developed for determining the profile of the front of a flowing liquid by means of radioactive isotopes\(^{72}\), without taking samples. The procedure consists in filling part of a pipe with liquid,

...in which a small amount of a substance containing a radioactive isotope emitting γ-rays is dissolved. The other part of the tube is filled with an unlabeled solution. As is known, when a liquid moves, its velocity \(v\) depends on the distance \(y\) from the wall. In the case of laminar flow in a tube with a circular cross section, this velocity is determined by the formula

\[ \frac{v}{v_0}=4\left[\frac{y}{d}-\left(\frac{y}{d}\right)^2\right], \tag{28} \]

where \(v_0\) is the maximum velocity at the center of the tube, and \(d\) is the diameter of the tube.

A scintillation counter is installed next to the tube, shielded with lead in such a way that it records only pulses emitted from a comparatively thin layer of liquid. It can be shown that the counting rate \(I\) at the time \(t\) and the counting rate \(I_0\) before the beginning of the motion of the liquid, when the entire cross section of the tube is filled with the labeled solution, are related by the formula

\[ \frac{I}{I_0}=4\left[\frac{y}{d}-\left(\frac{y}{d}\right)^2\right]. \tag{29} \]

By measuring the counting rate at various moments of time, one can, with the aid of equations (28) and (29), calculate the distribution of liquid velocities in the tube. For such measurements, it is convenient to use \(Na^{24}\) as the radioactive isotope.

There can be no doubt that radioactive isotopes will also find application in solving a number of other important problems in hydraulic engineering construction.

In the brief survey given above of the application of radioactive isotopes in the construction industry, a number of results obtained in the USSR and abroad have been described. These results already make it possible at present to improve control and reduce the cost of carrying out construction work. However, work in this field began only a few years ago. The further development of these methods and the introduction of radioactive isotopes into the practice of research and production work in the construction industry will undoubtedly yield many new results.

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1. Reference number as printed on the page. ↩