On the Theory of Radiation Defectoscopy of Bodies with a Heterogeneous Structure Such as Concrete
Abstract Generated abstract
This paper develops theoretical criteria for radiation defectoscopy of heterogeneous materials such as concrete using betatron bremsstrahlung. It analyzes how structural inhomogeneity, especially the nonuniform distribution of coarse aggregate, produces radiation intensity and radiographic density fluctuations that limit the detectability of air cavities and other discontinuities. The authors derive detectability conditions in terms of density contrast, attenuation, buildup factor, film contrast, and measured fluctuation parameters, and describe experimental determination of these quantities from radiographs of concrete blocks. Verification with fine-grained concrete specimens showed agreement within about 20 percent between calculated and observed detectability, supporting the proposed basis for designing radiographic inspection methods for reinforced-concrete structures.
Full Text
ON THE THEORY OF RADIATION DEFECTOSCOPY OF BODIES WITH AN INHOMOGENEOUS STRUCTURE SUCH AS CONCRETE
V. A. VOROB'EV, Yu. D. GAVKALOV
(Presented by the joint scientific seminar of the DSM and MRD sectors).
Increasing the economic efficiency of construction through the use of precast reinforced-concrete structures determines the need to develop the theory and technique of nondestructive testing methods as applied to inhomogeneous materials such as concrete. One such method is the radiographic inspection of products by the bremsstrahlung radiation of a betatron. As studies [1] have shown, portable, mobile, and stationary betatrons developed at Tomsk Polytechnic Institute can be successfully used to detect discontinuities, reinforcing elements, and hidden communications in concrete products up to 2 m thick. The present article considers the basic principles of the theory of radiation defectoscopy of an inhomogeneous material such as concrete and methods for experimentally investigating the detectability of discontinuities in concrete.
The general condition for detecting a defect in direct methods of recording information when irradiating products is
\[ \Delta U = \chi \delta_U , \tag{1} \]
where \(\Delta U\) is the magnitude of the signal at the output of the recording system caused by the defect,
\(\delta_u\) is the root-mean-square noise, referred to the output, caused by various random processes of the entire system as a whole (assuming the absence of their correlations),
\(\chi\) is the probability coefficient of detection.
In contrast to a system with a homogeneous absorber, when concrete is irradiated the predominant noise components are fluctuations of the radiation intensity \(\delta J\) behind the layer of concrete, caused by the inhomogeneity of its structure.
With a random Gaussian distribution, over the volume, of small air pores and fine aggregate (sand), the fluctuations \(\delta J\) caused by the latter are of the order of the statistical fluctuations in the absorption of radiation by a layer of homogeneous material. Therefore the entire value of \(\delta J\) is determined by the nonuniform distribution of coarse aggregate (gravel, crushed stone) in a quasi-homogeneous medium (water + cement + sand) [2].
In the gamma-radiation energy interval \(E_\gamma = 0.5 \div 30\) MeV, the difference between the mass attenuation coefficients \(\mu_\rho\) of the coarse aggregate and the medium
(the chemical composition is taken from [3]) for ordinary concrete does not exceed 1.5%, i.e., \(\Delta\mu_\rho \simeq 0\), whence
\[ \Delta\mu=\mu\frac{\Delta\rho}{\rho}, \tag{2} \]
where \(\mu\) is the linear attenuation coefficient of concrete,
\(\Delta\rho\) is the difference between the density of the coarse aggregate and that of the medium,
\(\rho\) is the density of the concrete.
The value \(\dfrac{\Delta\rho}{\rho}\) reaches 30% for ordinary concrete. However, for bremsstrahlung energies \(\gg 6\) MeV and a layer of ordinary concrete \(\gg 10\) cm thick, such a change in \(\mu\) is insufficient for detecting an individual aggregate grain, and the intensity fluctuations \(\delta_I\) are caused by fluctuations in the distribution of the coarse aggregate over the entire thickness of the concrete layer.
The intensity of the radiation behind the absorber consists of the primary radiation \(I\) and the scattered radiation \(I_p\). In the general case, the change in \(I_p\) due to a defect may be neglected [3]; similarly to what was shown in [2], the fluctuations of scattered radiation \(\delta_{I_p}\) caused by the inhomogeneous structure of concrete may be neglected. Then the change in radiation intensity caused by a defect of the type of an air cavity of diameter \(\Delta x\) is
\[ \Delta I=I\mu\Delta x, \tag{3} \]
and the rms intensity fluctuations are equal to
\[ \delta_I=I\Delta\mu\delta_h=I\frac{\Delta\rho}{\rho}\mu\delta_h, \tag{4} \]
where \(\delta_h\) are the rms fluctuations of the total length \(h\) of the segments of the radiation ray through the coarse aggregate.
According to (1), from (3) and (4) we obtain the condition for detectability of an air cavity
\[ |\Delta x| \leq [\Delta x]\,\chi\frac{\Delta\rho}{\rho}\delta_h, \tag{5} \]
where \([\Delta x]\) is the detectability in a layer of homogeneous material identical to the concrete layer in thickness and with identical attenuating radiation properties.
At radiation energies when detection of an individual grain of coarse aggregate becomes possible (\(E_\gamma \leq 1\) MeV), and when scattered radiation is also recorded by the detector (for example, radiography), because of the much better detectability of defects adjacent to the detector (approximately by a factor of \(B\), where \(B\) is the buildup factor), condition (5) takes the form
\[ \Delta x=\chi\frac{\Delta\rho}{\rho}(\delta_h+h_0), \tag{6} \]
where \(h_0=h_0(E_\gamma)\) and is, in order of magnitude, the diameter of the coarse aggregate.
The values of \(\delta_h\) can be determined by calculation, by modeling the distribution of grains in a limited volume, or experimentally,
\[ \delta_h=\delta_n\frac{\rho}{\Delta\rho}K, \tag{7} \]
where
\[ K=\frac{|\Delta x|}{\Delta D}, \qquad \text{or} \qquad K=\frac{|\Delta x|}{\Delta U}, \]
\(\Delta D, \Delta U\) are the changes in the optical density of the radiograph by the defect in radiography and in the signal at the output of the electronic circuit in the radiometric method of registration, respectively,
\(\Delta x\) is the thickness of a standard having the density of concrete,
\(\delta_D\) or \(\delta_u\), respectively, are the root-mean-square fluctuations of the optical density of the radiograph or of the signal from the radiometric circuit.
The coefficient \(K\) in (7) in the general case depends on the radiation energy and the thickness of the concrete layer.
In each section of a concrete block by a plane parallel to the plane of irradiation of the concrete, the distribution of grains in a particular case may be different, for example because of the presence of inclusions, insufficiently uniform compaction, etc. However, for a general analysis of the principal characteristics of the function \(h(z,y)\) as a function of radiation energy, the thickness of the concrete layer, and its technological composition, one may assume that \(h(\vec r)\) possesses the ergodic property, i.e., its probabilistic characteristics do not depend on the direction \(\vec r\) (\(Z, y\) is the plane of the absorber, opposite to the irradiated one).
We investigated the characteristics of fluctuations in the optical density of X-ray photographs when concrete blocks were penetrated by bremsstrahlung radiation from betatrons.
The following were determined:
- Mathematical expectation
\[ < D > \simeq \frac{1}{R}\int_0^R D(r)\,dr . \tag{8} \]
- Root-mean-square variation
\[ \delta_D = \sqrt{ \frac{1}{R}\int_0^R [D(r)-<D>]^2\,dr }. \tag{9} \]
- Correlation function
\[ K_D(r)=\frac{1}{R-r}\int_0^{R-r}[D(\xi)-<D>][D(\xi+r)-<D>]\,d\xi , \tag{10} \]
where \(D(r)\) was determined as the variation of \(D\) along an arbitrary line on the plane of the negative,
\(R\) is a segment of a straight line on the negative equal to or greater than \(10r_0\), and \(r_0\) is determined from the condition \(K(r_0)\leq 0.1K(0)\).
The exposures during radiography were chosen to be sufficient to obtain \(D=1.5\pm0.2\) units. The negative was photometered in an arbitrarily chosen direction with the area of the scanning light beam \(0.2\times0.2\ \text{mm}^2\).
It follows from the data obtained that the correlation interval \(t=2r_0\) depends on the technological composition of the concrete. In the range of layer thicknesses of ordinary concrete \(10\text{--}30\ \text{cm}\), \(t\) changes by 15% when the amount of coarse aggregate deviates by 30%. With an increase in radiation energy (from \(6\ \text{MeV}\) to \(30\ \text{MeV}\)), the correlation interval remains constant; only the root-mean-square fluctuations \(\delta_D\) change, which confirms the conclusion noted above that \(\delta_I\) is independent of the magnitude of the scattered radiation.
The design condition for the detectability of a discontinuity against a background of fluctuations in the blackening of the negative, caused by the conglomerate structure of concrete, along with (5) or (6), may be
\[ \Delta D = \chi \delta_D, \tag{11} \]
where \(\Delta D\) is the change in optical density due to the defect for a homogeneous material \((\Delta D = K^{-1}\Delta x;\ (7))\). Substituting the value of \(\Delta D\) and the coefficient \(K\) into (11), we obtain
\[ \Delta x = K\chi \delta_D = \frac{2.3B \cdot \chi \cdot \delta_D}{g \cdot \mu}, \tag{12} \]
where \(g\) is the contrast gradient of the X-ray film,
\(B\) is the buildup factor.
Thus, if \(\Delta \rho/\rho\) and \(\delta_h\), or \(\delta_D\) and \(\mu, g, B\), are known, then the detectability of an air cavity can be calculated from (5) or (12).
Experimental verification of the calculated detectability values for an air cavity, obtained by us from (12), was carried out when specimens of fine-grained concrete were irradiated with bremsstrahlung. Since \(\Delta D\) is an even function of \(\Delta x\) (on the linear portion of the characteristic curve), specially selected gravel grains with diameters of 5–20 mm were used as a standard. The radiation of the betatron was directed upward, and a thin aluminum plate was placed on the support; grains were laid on it at random, and then concrete specimens and a cassette with film were placed on them. If, from two radiographs, it proved possible to detect 9 grains out of 10, the grain was considered detected. Agreement within 20% was obtained with the calculated detectability values for an air cavity, which were 7.8 and 10 mm for 10, 20, and 40 cm of ordinary concrete, respectively. This corresponds to a detectability of 4–2.5% for the bulk of concrete structural elements produced by factories.
The data presented in the article may serve as a basis for developing a methodology and for designing radiation defectoscopy of reinforced-concrete structures under factory conditions and at construction-and-installation sites.
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V. A. Vorob'ev. Proceedings of the 4th International Conference on Betatrons. 332, Prague, 1966.
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