CC BY
21Magazine of Civil Engineering. 2020. 96(4). Pp. 94-109
Magazine of Civil Engineering issn
2071-0305
journal homepage: http://engstroy.spbstu.ru/
DOI: 10.18720/MCE.96.8
Radiation changes of concrete aggregates under the influence of gamma radiation
A.V. Denisov
National Research Moscow State Civil Engineering University, Moscow, Russia * E-mail: [email protected]
Keywords: aggregates of concretes, radiation changes in volume and strength, influence of gamma radiation
Abstract. The work (in connection with the small study of the effects of gamma ray on concretes and their components) contains the results of calculation and analysis of radiation changes of concrete aggregates under the influence of gamma ray on the basis of analytical methods developed previously during the neutron irradiation process. The possibility of using these analytical methods in the case of exposure to gamma ray was substantiated. The relationship of the absorbed doses of gamma ray of different energies with the number of atoms displaced during irradiation was established. There is an assessment of radiation changes in the volume and strength of the main types of rocks - aggregates of concrete (igneous, sedimentary rocks and ores) under the influence of gamma ray with an average energy of 2 MeV and 5 MeV after irradiation to absorbed doses of 105 to 1011 Gy at 30 °C, 100 °C and 300 °C. For this, from the beginning, the radiation changes of the main rock-forming minerals were calculated, and on the ground of them, the radiation changes of rocks of concrete aggregates were calculated. It has been established that noticeable radiation changes of considered minerals and rock aggregates will occur only at absorbed doses of gamma ray of more than 1 • 109—1 • 1010 Gy of gamma rays with an energy of 5 MeV and of 3-109-3-1010 Gy for gamma rays with an energy of 2 MeV. The number of radiation changes grows with a rise in the absorbed dose and significantly decrease with an increase in the irradiation temperature for silicate class minerals and silicate rocks. The greatest radiation changes under the influence of gamma ray at 30 °C are observed in silicate minerals and rocks, especially olivine pyroxenes, hornblende, dunite, peridotite, pyroxenite, and gabbro. Moreover, even with an absorbed dose of gamma ray of 1011 Gy, the radiation changes are not large (increase in volume is not more than 0.36 %, decrease in strength is not more than 8.7 %). As the temperature increases, the ratio in the magnitude of radiation changes of different materials changes.
1. Introduction
Significant radiation changes in concrete could occur under the influence of ionizing radiation. In this regard, the radiation resistance of concrete used in buildings with various nuclear facilities determines the safety of operation of these buildings for both the operating staff and the environment as a whole.
The most significant radiation changes in concrete occur under the influence of neutrons of nuclear reactors. In this connection the influence of neutron radiation in concrete and their components (aggregates, minerals, cement stone) was investigated and adequately described in literature, for example in [1-22]. There are methods for the analytical determination of radiation changes in the following materials described in [8, 9, 10, 11, 12, 14, 22]:
- minerals of concrete aggregate [8, 14, 22] and cement stone [11,14] under the influence of neutrons according to the data on the fluence and neutron spectrum, irradiation temperature;
- materials of concrete aggregate according to data on radiation changes in crystals of the composing minerals them [9, 14];
- concretes according to data on radiation changes in their components (aggregates and cement stone) [10, 12, 14].
Denisov, A.V. Radiation changes of concrete aggregates under the influence of gamma radiation. Magazine of Civil Engineering. 2020. 96(4). Pp. 94-109. DOI: 10.18720/MCE.96.8
I This work is licensed under a CC BY-NC 4.0
Magazine of Civil Engineering, 96(4), 2020
At the same time, significant volumes of concrete in buildings with nuclear facilities are exposed to gamma radiation. However, the effect of gamma ray on concrete is less studied. There are only a few data on the effect of gamma radiation on concrete obtained in [1, 2, 21, 23-27], discussed in the reviews [6, 7, 13, 15, 21] and on the effect of gamma radiationon the cement stone [25, 26, 28-31], indicating that they have small radiation changes under the influence of gamma radiation.
The effect of gamma ray on concrete aggregates and the contribution of radiation-induced changes in aggregates to radiation-induced changes in concrete under the influence of gamma ray have hardly been studied. This is due to the opinion based on the results of the study of ceramic materials [32, 34] that gamma ray does not cause noticeable changes in the properties of inorganic materials. This view was confirmed in the works of [33, 35], which show that the ability to displace atoms under the influence of gamma ray is 100 to 10,000 times lower than under the influence of neutrons.
However, the studies described in the papers [1, 2, 6, 7, 13, 15, 21, 23-31] were performed after exposure to the absorbed dose of gamma radiation no more than 1.5-109 Gy. The result of a study of the effects of higher absorbed doses has not been found in literature. At higher absorbed doses, the number of displaced atoms and changes in material properties may be more significant. In addition, studies of the aggregate materials, which are more radiation-sensitive than ceramics, are not available in the literature. In this regard, studies of radiation changes in concrete aggregate materials under the influence of gamma ray are of considerable practical interest.
The purpose of this work is to assess radiation changes in the main varieties of concrete aggregates under the influence of gamma ray in a wide range of absorbed doses and radiation temperatures.
Due to the lack of data in the literature on significant radiation changes of the aggregates and their minerals under the influence of gamma ray, radiation changes of these materials were evaluated by calculation.
In achieving the goal, the following known provisions in accordance with [8, 9, 14], were taken into account:
• Changes in the basic properties of concrete aggregate materials are caused by the displacement of atoms in their minerals, leading to the accumulation of radiation defects in them.
• Changes in volume and strength are of greatest interest.
• Radiation changes in the volume and strength of concrete aggregate materials can be calculated by radiation changes in the size and volume of the minerals that compose them on the basis of the analytical method tested during neutron irradiation, described in the works [9, 14].
• Radiation changes in the volume and size of mineral crystals can be calculated on the base of the number of displaced atoms and the radiation temperature. This analytical method based on neutron radiation, is described in the works [8, 14].
In order to achieve this goal, the following objectives of the study were set and solved:
• To justify the possibility of using the existing analytical methods listed above, which have been tested under the influence of neutrons, to determine the results of gamma radiation exposure.
• To establish the dependence of the number of displaced atoms in minerals of concrete aggregates under the action of gamma radiation on the absorbed dose and the energy of gamma quanta.
• To calculate, using the well-known analytical method presented in [8, 14] for neutron irradiation, radiation changes in the volume and size of crystals of the main minerals of concrete aggregates after irradiation with gamma radiation to various absorbed doses.
• To calculate, using the available analytical method presented in [9, 14] for neutron irradiation, the radiation changes of the volume and strength of the main materials of concrete aggregates after irradiation with gamma radiation to various absorbed doses.
• To analyze the results obtained and establish the absorbed doses and conditions under which it is necessary to take into account the radiation changes in the materials of concrete aggregates under the influence of gamma radiation.
2. Methods
When substantiating the possibility of using the above existing analytical methods tested under the influence of neutrons, the following circumstances were taken into account for the results of exposure to gamma ray:
• In accordance with the existing method for the analytical determination of radiation changes in minerals under the influence of neutrons, radiation changes in the volume and size of minerals, although they are not the same for different minerals, are determined by the calculated number of displaced atoms and the
Magazine of Civil Engineering, 96(4), 2020
irradiation temperature. In this regard, the most important for substantiating the possibility of using this analytical method when exposed to gamma ray is the condition that the same number of displaced atoms when irradiated with neutrons and gamma ray cause approximately equal radiation changes.
• Although atom displace efficiency in gamma radiation is 100 to 10,000 times lower than that of neutrons, the number of basic radiation defects (vacancies, interstitial atoms), their distribution in the crystal lattice and the effect on the properties for equal values of number of displaced atoms and irradiation temperature should be approximately the same. For neutrons of different energies, the efficiency of atomic displacement also differs significantly from each other. However, differences in the results of irradiation of minerals with neutron fluxes with different proportions of neutrons of different energies are quite well excluded when the radiation changes are linked to the calculated number of displaced atoms in [14].
• However, there is an opinion [37], that the number and distribution of radiation defects in the space may depend on the speed of displacement of atoms, which is less under the influence of gamma ray than under the influence of neutrons. However, this was not found in existing studies when irradiating minerals with neutrons at different neutron flux densities.
• In accordance with the existing method for the analytical determination of radiation changes in concrete aggregates, radiation changes in the volume and mechanical properties are determined by changes in the size and volume of minerals, their moduli of elasticity, grain size of minerals, and the modulus of elasticity of the material. The reasons for the change in the size and volume of minerals do not play a significant role. This is shown by the results of a positive-used of this method when heating the rocks presented in [36]. In this regard, this analytical method can be used when exposed to gamma ray.
To calculate the number of displaced atoms under the influence of gamma ray, we used the cross sections for the formation of displaced atoms<5j(Eg), calculated in [33] for atoms of building materials (mainly with the atomic number 4 ^14):
- a d( Eg) = 0.1 10-24 cm 2 for gamma rays with an energy of 2 MeV;
- ad(Eg) = (0.2 - 0.5)- 10-24 cm2 for gamma rays with an energy of 5 MeV
By analogy with neutron radiation, considered in [8, 14], the number of displaced atoms nCM when irradiated by gamma ray in the minerals should be determined by the formulas:
m
nd =1 [ad (Egi )Fg (Egi) ] 0)
i-1
- when exposed to gamma rays with different energies Egi (for i = 1 - m);
nd =Vd(Eg)Fg(Eg) (2)
- when exposed to gamma rays with one energy Eg or average energy Eg ,
- where < (Egi) and &d (Eg ) are the cross sections for the formation of displaced atoms upon exposure to gamma rays with energy Egt and Eg , cm2;
- Fg (Egi) and F (E ) are fluence of y-quantum with energy Eg and Eg , y-quantum/cm2.
O O O O O O
In accordance with [39] the following coefficients kD /F (Eg) as the ratios of the dose-to-the-level
g g ®
gamma-quanta-dependent gamma-quanta energy Eg :
kD /f (Eg ) = (4.4 - 5.6)-10-12 Gy/(y-quantum/cm2) «5-10-12Gy/(y-quantum/cm2) for gamma-rays with energy Eg = 1 MeV;
kD /F (Eg) = (7.5 - 9.2)-10-12 Gy/(y-quantum/cm2) «8-10-12 Gy/(y-quantum/cm2) for gamma rays with
g g ®
energy Eg = 2 MeV;
Magazine of Civil Engineering, 96(4), 2020
kD /F (Eg) = (1.39 - 1.6)-10"11 Gy/(y-quantum/cm2) «1.5-10-11Gy/(y-quantum/cm2) for gamma rays
g g ®
with energy Eg = 5 MeV.
In accordance with [8, 14] the change in the volume of minerals under the influence of gamma ray was calculated by the formulas:
A ^ ( eb (T )nd V V JM M
a(T) —I (e (T )nd -1)
AV _
v
AY |
v V JM M
+ a(T ) • eb (T )nd
- - at a(T) * œ and J3(T) * 0 (3a)
S | (! - e~b(T)Ud ) - at a(t) = x and f (T) = 0 (3b)
v t jm .m
AV
where- is the relative increase in the volume of crystals or unit cells of the mineral, %.
V
(AV 1
I-I increase in the volume of the crystal of the mineral in a state of saturation, %
v V JM M
a(T) and b(T) are the parameters depending on the irradiation temperature, determined by the formulas:
a(T) = a(T)/ f(T) (4)
b(T) = f(T) (SV) +a(T), (5)
v V JM M
where a(T) and f (T) are the parameters depending on the irradiation temperature.
Taking into account the work [8, 14], the change in the size of the crystals of minerals along various axes under the action of gamma ray was calculated by the formula:
A AV fAV }a
+ a4 J , (6)
■ _ ai + a2--h a?
£ V
where ax - a5 are the parameters.
In this work, we used the parameters of equations (3a)-(6) obtained and presented in [8, 14].
In accordance with [9, 14], the change in the volume of rocks of concrete aggregates under the action of gamma ray was calculated by the formulas:
SVAC_(AV 1=3(A) Eo^_ 1 -Vmred - at (AV) >(SL1 (7a)
VAG v V J1 V l Jm M EM M yJdGR VM .RED V V Jl V V
avag _ fa)-fa)__3asave_-at fav^ <fav] , (7b)
Vag v V j2 v V ,
' ADM 1 + 2.2aM KjdGR 3 As AVE ) V V J1 I V
fAl \
where I — I is the maximum of the values of the radiation values of radiation-induced dimensional
V l JM M
changes in the most expanding direction of the crystals composing the material of minerals, %; aM = 3.4 10-2 % cm05 is the complex parameter of the model;
Eo is modulus of elasticity of the material at zero porosity, MPa;
Magazine of Civil Engineering, 96(4), 2020
dGR is average size of crystals composing the material of minerals, cm;
( Al )
EM m is the modulus of elasticity of crystals having an expansion I — I along the axis where
t
'M M
(Ai \
the expansion i — i takes place, MPa;
v i jm m
As ave is the average difference between the deformations of the crystals along various axes composing the material of minerals, %;
V
M .RED
is the relative volumetric content of mineral crystals with expansion,
At
, reduced to
J M M
the isotropic case, but taking into account the anisotropy of radiation deformations and the presence of crystals with expansion | M | , (differing by a value of no more= aM /^JdAVE ), rel. units;
M .i
AY )
-i is an increase in the volume of material (in %) associated with a free change in the volume
V
' AD.M
of mineral crystals composing it, determined by the formula:
A =£
v V 'ADM i=1
A
V
(8)
(AY)
where and Vi is the radiation change in volume (in %) and the relative volume content of the minerals
composing the material (in rel. units).
Values Asave and YM red by [9, 14] were determined by the formulas:
asave = si i-1j =1
A
£
1 ( AV
ij 3 v v 'adm
V
(9)
V
m .red
nm m vm m
3
+ S i=1
nM .iVM .i
( \
At
I
EM .i
M .i
(At ^ t
am m
m .m
<1
(10)
, A£ ,
where | — I is the increase in the size of the crystals of the i-th mineral along the j-th axis (j = 1 ... 3 along
i Jij
the axes a, b and c) of the crystal, %;
(Ai N
nMM and Hm i are the number of axes in the crystals along which the expansion occurs I —
'M M
(At and I —
V t.
M .i
Vm. M ; VMi ; EMM ; EMi are the relative volume content (in rel. units) and the moduli of normal
( Ai ^ ( Ai ^
elasticity (in MPa) of mineral crystals having an expansion of i — i and i — i .
v i jm M v i jm .i
The elastic moduli of mineral crystals along various axes were taken according to [39].
Magazine of Civil Engineering, 96(4), 2020
The radiation changes in the indicators of the mechanical properties of the aggregates were calculated by the formula [9, 14]:
R
AG
R
= exp
ago
ÎAVag ^ V VAG Jcr
AG
(&AG ^
V VAG Jcr
+ B
AG
(11)
where
R
AG
R
is the residual value of the mechanical property RAG after radiation exposure relative to the
AG 0
strength before irradiation RACo , rel. units;
1AG
and BAC are the complex parameters of the model, the values are given in the works [9, 14].
V VAG JCR
is an increase in the volume of material due to the formation of cracks is determined by
the formula:
V VAG Jcr
Ag ^
VAG i=1
AV V
V
+X
i=l
AV V
Viui
(12)
where is the fraction of the increase in mineral crystals due to the formation of microcracks in the crystal, taken according to the data of [9, 14].
Relative changes in strength are calculated by the formula:
ARag. = -I) .100% ,
R
AG 0
R
(13)
AG0
where
AR
AG
R
are the relative changes in strength, as the ratio of the absolute change in strength
AG0
ARag to strength before irradiation Rag0 > %.
The calculations of radiation changes were carried out for the following main rock-forming minerals:
• silicate class minerals - quartz, potassium feldspar-microcline, plagioclases (oligoclase and labrador), pyroxenes (enstatite, diopside), hornblende, olivine, serpentine;
• carbonate class minerals - calcite, dolomite;
• oxide-ore class minerals (hematite, magnetite).
• quartz glass.
The radiation changes in minerals were used to calculate the radiation changes in aggregate rocks: granite, diorite, gabbro, basalt, pyroxenite, peridotite, dunite, sandstone, limestone, and enriched hematite and magnetite ore.
When choosing the rocks, the following circumstances were taken into account:
- granites, diorites, gabbros, basalts, sandstones, limestones are the most common rocks;
- pyroxenites, peridotites, dunites, hematite and magnetite ore are examples of the most radiation-resistant rocks when irradiated with neutrons;
- sandstones and limestones were used as aggregates of concrete investigated after exposure to gamma ray in [1, 2, 24];
- hematite and magnetite ores are used for the preparation of particularly heavy concrete, effective for protection against radiation.
The characteristics of the mineral composition, the average size of the crystals of minerals and the elastic modulus of the rocks considered in the work are shown in table 1.
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Although the mineral composition, structure, and properties of these rocks can vary in a rather wide range, the use of the accepted average characteristics can be considered to estimate the values of their radiation changes under the influence of gamma ray.
Table 1. The characteristics of the mineral composition, the average size of the crystals of minerals, and the modulus of elasticity of the rocks considered in this paper.
No. Name of the rock Mineral composition in the form of mineral Average crystal Modulus of
content in % size of minerals, cm elasticity, MPa
1 Granite Quartz - 25 %, Microcline - 40 %, Oligoclase - 20 %, Hornblende - 15 % 0.3 6-104
2 Diorite Oligoclase - 70 %, Microcline - 5 %, Hornblende - 25% 0.3 8104
3 Gabbro Enstatite, Diopside - 50 %, Labrador - 50 % 0.3 10-104
4 Basalt Enstatite, Diopside - 50 %, Labrador - 40 %, Glass - 10 % 0.01 10-104
5 Pyroxenite Enstatite, Diopside - 90 %, Olivine - 10 % 0.1 12-104
6 Peridotite Enstatite, Diopside - 40 %, Olivine - 40 %, Serpentine - 20 % 0.1 12-104
7 Dunite Enstatite, Diopside - 10 %, Olivine - 90 % 0.1 12-104
8 Sandstone Quartz - 50 %, Microcline - 25 %, Oligoclase - 25 % 0.03 6-104
9 Limestone Calcite - 75 %, Dolomite - 25 % 0.03 8104
10 Hematite ore (enriched) Hematite - 100 % 0.01 25-104
11 Magnetite ore (enriched) Magnetite - 100 % 0.01 27-104
First, using the formulas (1)-(6), the radiative changes in the volume and size of the crystals of the minerals that make up these rocks were calculated: quartz, microcline, oligoclase, hornblende, calcite and dolomite. Then, according to formulas (7)-(13), radiation changes in the volume and strength of granite, sandstone, and limestone with the accepted characteristics of the mineral composition, structure, and properties were calculated.
Considering the data of [14], the radiation changes of the considered minerals and rocks were calculated after the following exposure to gamma ray:
- gamma ray with an average energy of 2 MeV at absorbed doses from 1-105 to 1-1011 Gy for materials of radiation protection of technological equipment of nuclear power plants;
- gamma ray with an average energy of 5MeV at absorbed doses from 1-105 to 1-1011 Gy for radiation protection materials of nuclear reactors.
The radiation changes were calculated for cases of irradiation at temperatures of 30 °C, 100 °C, and 300 °C. In this case, changes in materials under the action of heating associated with irradiation (thermal changes) were not considered, since they are independent of radiation changes, they are determined and can be taken into account by other methods, for example, according to [36].
3. Results and Discussion
The dependences necessary for calculating the number of displaced atoms in concrete aggregate minerals were found based on the values of the atomic displacement cross sections ad (eg ) , calculated in
[33] for atoms of building materials and the known relations kD /F (Eg) between the absorbed dose and
g g ®
gamma-ray fluence, which depend on the energy of gamma-rays Eg .
Based on the values of ad (eg) and kD ¡f (Eg) and of formula (2) shown in the research
methodology, the following dependence of the number of displaced atoms (in fractions of a unit) in aggregate minerals when irradiated with gamma ray on the absorbed dose in Gy of gamma ray of different energy was established and accepted for calculations:
nd = 1.1-10-14 - Dg - at gamma ray energy Eg = 2 MeV; (14)
nd = 3.3. 10
14
D„
at gamma ray energy eg = 5 MeV.
Magazine of Civil Engineering, 96(4), 2020
(15)
It can be seen that the absorbed dose of gamma ray with an energy of 5 MeV corresponds to a 3 times larger number of displaced atoms than gamma ray with an energy of 2 MeV. In this connection, the absorbed dose of gamma quanta with an average energy of 2 MeV is equivalent to 1/3 of the absorbed dose of gamma quanta with an energy of 5 MeV in the efficiency of atomic displacement. This circumstance was taken into account when graphically presenting the calculation results. All calculation results are presented depending on the absorbed dose equal to the absorbed dose of gamma rays with an energy of 5 MeV or equal to 1/3 of the absorbed dose of gamma rays with an energy of 2 MeV.
The calculation results according to formulas (1) - (5) taking into account formulas (14) and (15) of radiation changes in the volume of the examined minerals from the absorbed dose of gamma ray in the range of 105-1011 Gy and the irradiation temperature from 30 to 300 °C are given on Figures 1 to 5.
Figure 1. Dependence of the calculated radiation increase in the volume of various minerals on the absorbed dose of gamma ray with an average energy of 5 MeV and 2 MeV at an irradiation temperature of 30 °C.
Figure 2. Dependence of the calculated radiation increase in the volume of various minerals on the absorbed dose of gamma ray with an average energy of 5 MeV and 2 MeV at an irradiation temperature of 100 °C.
Figure 3. Dependence of the calculated radiation increase in the volume of various minerals on the absorbed dose of gamma ray with an average energy of 5 MeV and 2 MeV at an irradiation temperature of 300 °C.
Figure 4. The dependence of the calculated radiation decrease in the volume of quartz glass on the absorbed dose of gamma ray with an average energy of 5 MeV and 2 MeV at irradiation temperatures from 30 to 300 °C.
a)
Magazine of Civil Engineering, 96(4), 2020 b)
1.E+00
^ 1.E-01 qJ'
£ 1.E-02 £
(j c
o >
1.E-I-00
1.E-05
0 100 200 Irradiation temperature, °C
300
100
200
300
Irradiation temperature, C
Quartz *— Enstatite
■x- - Ca I cite, Dolomite
— Microcline
- Horneblende
- Hematite
-□— Oligoclase
—Olivine -■- - - Magnetite
Labrador Serpentine
Figure 5. Dependence of the calculated radiation increase in the volume of various minerals on the irradiation temperature at an absorbed dose of gamma ray with an average energy of 5 MeV
11010 Gy (a) and 11011 Gy (b)
The calculation results indicate that noticeable radiation changes in the considered minerals will occur only at absorbed doses of gamma ray greater than Dgo = 1-109 - 1-1010 Gy for gamma rays with an energy
of 5 MeV and Dg o = 3-109 - 3-1010 Gy for gamma rays with an energy of 2 MeV. The radiation changes in
volume rise with an increase in the absorbed dose and decrease in silicate class minerals with an increase in the irradiation temperature.
At 30 °C, according to the calculation results, the largest radiation increase in volume in the studied range of absorbed doses will occur in minerals of silicate class minerals.
The maximum increase in volume during irradiation at 30 °C will be observed in olivine (up to 0.3 %). A 2-2.5 times smaller increase in volume will occur in pyroxenes of diopside and enstatite (up to 0.15 %) and hornblende (up to 0.12 %). 4.6-5.5 times a smaller increase in volume will be observed in quartz (up to 0.065 %), serpentine, calcite, dolomite (up to 0.055 %). A 10-16 times smaller increase in volume will occur in the microcline minerals (up to 0.03 %) and oligoclase, labrador, hematite (up to 0.018-0.020 %). A minimal increase in volume will be observed in magnetite (up to 0.007 %). In quartz glass, regardless of the irradiation temperature, a decrease in volume will occur (up to -0.3 %).
With an increase in the irradiation temperature from 30 °C to 100 °C and 300 °C, the radiation changes in the silicates class minerals decrease, while the radiation changes of carbonate class minerals (calcite, dolomite) and iron oxides (hematite, magnetite) do not change. Moreover, the effect of temperature increases with the rise of irradiation temperature. At 100 °C the increase in the volume of silicates decreases by 11-18 times, and at 300 °C it decreases by 400-1800 times in comparison with a change in volume at 30 °C. In this regard, the ratio between radiation changes in the volume of various minerals changes, the upper and lower boundaries of the changes in volume decrease, and the increase in the volume of silicate class minerals becomes smaller than that of carbonates and iron oxides.
In the case of irradiation at 100 °C in the studied range of absorbed doses, the maximum volume increase will be observed in minerals of the carbonate class-calcite and dolomite (up to 0.055 %). An approximately twofold smaller increase in volume will occur in olivine (up to 0.027 %). A 3.7-fold smaller increase in volume will be observed in hematite (0.018 %). A 4.5-5.6 times smaller volume increase will occur in pyroxenes of enstatite, diopside (up to 0.012 %) and hornblende (up to 0.096 %). An 8-fold smaller increase in volume will be observed in magnetite (up to 0.0067 %). 10.8-13.5 times a smaller increase in volume will occur in quartz (up to 0.005 %) and serpentine (up to 0.004 %). A slight, 36-45 times smaller increase in volume will be observed in microcline, oligoclase and labrador (up to 0.0012-0.0015 %).
In the case of irradiation at 300 °C in the studied range of absorbed doses, a maximum increase in volume will also be observed in calcite and dolomite of carbonate class minerals (up to 0.055 %). A 3.7-fold smaller increase in volume will occur in hematite (0.018 %). An 8-fold smaller increase in volume will be observed in magnetite (up to 0.0067 %). For the remaining studied minerals, the increase in volume will not be significant (at 100-3000 times less) and will be 0.000018-0.00053 %.
Magazine of Civil Engineering, 96(4), 2020
The results of calculations by formulas (7)-(13) of radiation changes in the volume and compressive strength of the considered rocks - aggregates of the absorbed dose of gamma ray are shown in Figures 6-12.
The calculation results indicate that, as with minerals, noticeable radiation changes in the considered minerals will occur only at absorbed doses of gamma ray greater than Dg0 = 1-109 - 1-1010 Gy for gamma
rays with an energy of 5 MeV and Dg 0 = 3-109 - 3-109 Gy for gamma rays with an energy of 2 MeV. The
radiation changes in volume rise with an increase in the absorbed dose and decrease in rocks, consisting of silicates, with an increase in the irradiation temperature.
Figure 6. Dependence of the calculated radiation increase in the volume of various concrete aggregate rocks on the absorbed dose of gamma ray with an average energy of 5 MeV and 2 MeV at an irradiation temperature of 30 °C.
(n ra P5
£
ifl
0.00 -1.00 -2.04 -3.0« -4.00 -5.0« -6.0« -7.00 -8.00 -9.00 -10.00 1.
A * A
- Granite, Diorite -Gabbro
- Basalt
- Pyroxenite
- Peridotite
- Dunite
- Sandstone
- Limestone
- Hematite ore
- Magnetite ore
E+05
1.E+07
1.E+09
1.E+11
Absorbed dose of gamma-radiation Dg with energy of 5 MeV and 0.333Dg with energy of 2 MeV, Gy
Figure 7. Dependence of the estimated residual strength of various concrete aggregate rocks on the absorbed dose of gamma ray with an average energy of 5 MeV and 2 MeV at an irradiation temperature of 30 °C.
0,0 -OJ * -0.4
i
S -fl.s J
-1,0 -
- Granite^ Diorite -Gabbro -Basalt
■ Pyroxenite
- Peridotite
- Dunite
- Sandstone
- Limestone
- Hematite ore
■ Magnetite ore
Figure 8. Dependence of the calculated radiation increase in the volume of various concrete aggregate rocks on the absorbed dose of gamma ray with an average energy of 5 MeV and 2 MeV at an irradiation temperature of 100 °C.
qj
■o 5 -1.2 £
g -1.4 & 16 -1.8 ZO
1£4S 1I-E+C7 1JE+09 1£MI
Absorbed dose of gamma-radiation Dg with energy of 5 MeV and 0.333Dg with energy of 2 MeV, Gy
Figure 9. Dependence of the estimated residual strength of various concrete aggregate rocks on the absorbed dose of gamma ray with an average energy of 5 MeV and 2 MeV at an irradiation temperature of 100 °C.
Magazine of Civil Engineering, 96(4), 2020
a)
1.0E+00
1.0E-01
qj
S 1.0E-02 S
u
- 1.0E-03
o 1.0E-04 >
1.0E-05
1.0E-06
±±
- Granite, Diorite -Gabbro -Basait
- Pyroxenite
- Peridotite
- Dunite
- Sandstone
- Limestone
- Hematite ore
- Magnetite ore
Figure 10. Dependence of the calculated radiation increase in the volume of various concrete aggregate rocks on the absorbed dose of gamma ray with an average energy of 5 MeV and 2MeV at an irradiation temperature of 300 °C.
0.0 -0.2 4.0.4
q) m
I -0.6
u q)
-0.8 I-1.0 ^ -1.2 -1.4
1.M5 1.E+07 1.E+09 1.E+1I
Absorbe d dose of ga m ma -ra d i ati on Dg with energy of 5 MeV and 0.333Dg with energy of 2 MeV, Gy
Figure 11. Dependence of the estimated residual strength of various concrete aggregate rocks on the absorbed dose of gamma ray with an average energy of 5 MeV and 2MeV at an irradiation temperature of 300 °C.
b)
1.0E+00
g 1.0E-Ü1 qj'
m
£ 1.0E-02
<j
E 1.0E-Q3
o >
1.0E-04
1.0E-05
\N
"l -II
^¡i
0 1 00 200 irradiation temperature, °C
300
0 100 200 irradiation tem pte m pe rature, °C
300
-&— Granite, Diorite Dunite
-Gabbro - Sandstone
■ Basalt Limestone
Pyroxenite ■ Hematite ore
-Peridotite -Magnetite
Figbre 12. Dependence of the calculated radiation increase in the volume of various concrete aggregate rocks on the irradiation temperature for an absorbed dose of gamma radiation with an average energy of 5 MeV 1-1010 Gy (a) and 1-1011 Gy (b)
At 30 °C, according to the results of calculations, the greatest increase in volume and decrease in strength under the influence of gamma radiation in the studied range of absorbed doses will occur in rocks consisting of silicate class minerals.
The largest volume increase during irradiation at 30 °C will be observed in dunite (up to 0.36 %), peridotite (up to 0.31 %) and pyroxenite (up to 0.28 %). 1.4-1.7 times a smaller increase in volume will occur in granite, diorite (up to 0.22 %) and gabbro (up to 0.21 %). 4.7-7 times less a smaller increase in volume will be observed in basalt (up to 0.059 %), sandstone (up to 0.050 %), limestone and dolomite (up to 0.051 %). The smallest increase in volume will occur in hematite ore (up to 0.018 %) and magnetite ore (up to 0.0066 %).
The greatest decrease in strength during irradiation at 30 °C will be observed for granite (up to -8.7 %). Almost two times lesser decrease in strength will occur in dunite (up to -5.8 %), peridotite (up to -5.4 %), pyroxenite (up to -4.2 %) and gabbro (-4.3 %). In other rocks, the decrease in strength is not significant and amounts to -1.3 % or less, but decreases in the direction: limestone (up to -1.3 %) ^ basalt (up to -0.6 %) ^ hematite and magnetite ore (up to - 0.1 %).
Magazine of Civil Engineering, 96(4), 2020
With an increase in the irradiation temperature from 30 °C to 100 °C and 300 °C, the radiation changes of silicate aggregate rocks decrease, but the radiation changes of carbonate and ore aggregate rocks do not change. Moreover, the effect of temperature increases with increasing irradiation temperature. At 100 °C, an increase in the volume of silicate rocks except for basalt decreases by 13-31 times, and at 300 °C it decreases by 300-970 times compared with a change in volume at 30 °C. In basalt, the decrease is «2 times at 100 °C and «80 times at 300 °C. In this regard, the ratio between radiation changes in the volume of various silicate and carbonate, ore rocks varies, the upper and lower boundaries of volume changes decrease, and the increase in the volume of silicate rocks becomes less than that of carbonate and ore rocks.
In the case of irradiation at 100 °C in the studied range of absorbed doses, the maximum increase in volume will be observed in limestone (up to 0.051 %). An approximately twofold smaller increase in volume will occur in basalt (up to 0.028 %) and dunite (up to 0.026 %). 2.8-3.7 times a smaller increase in volume will be observed in hematite ore (0.018 %). peridotite (up to 0.017 %) and pyroxenitis (up to 0.014 %). In 6.2-7.3, a smaller increase in volume will occur in granite and diorite (up to 0.008 %), gabbro (up to 0.007 %) and magnetite ore (up to 0.007 %). A minimal and insignificant increase in volume will be observed in sandstone (up to 0.0032 %).
The decrease in strength during irradiation at 100 °C will be insignificant in all rocks, since it does not exceed -1.8 %. However, it decreases in the direction: basalt (up to -1.8 %) ^ limestone (up to -1.3 %) ^ dunite (up to 0.3 %) ^ other rocks (up to -0.2 %).
In the case of irradiation at 300 °C in the studied range of absorbed doses, the maximum increase in volume will be observed in limestone (up to 0.051 %). A 2.8 times smaller increase in volume will occur in hematite ore (up to 0.018 %). A 7.3-fold smaller increase in volume will be observed in magnetite ore. In other rocks, the increase in volume is not significant and does not exceed 0.0007 %.
The decrease in strength during irradiation at 300 °C will be even less significant than during irradiation at 100 °C. The greatest decrease in strength will be -1.3 % for limestone and -1.2 % for basalt. In other rocks, the decrease in strength will not be significant (no more than -0.1 %).
Thus, the radiation changes of aggregates of concrete and their minerals under the influence of gamma ray at the considered absorbed doses can be significant only at absorbed doses of more than 109 Gy. Radiation changes increase with the absorbed dose. However, even with an absorbed dose of 1011 Gy, the radiation changes are not large (an increase in volume of not more than 0.36 %, a decrease in strength of not more than 8.7 %). Since, in accordance with the existing analytical methods [10, 12, 14] the changes in concrete are close to changes in aggregates, the radiation changes in concrete under the influence of gamma ray at the considered absorbed doses will not be large either.
Since the available experimental data on concretes were obtained in [1, 2, 6, 7, 13, 15, 21, 23-27] at absorbed doses of less than 1.5-109 Gy, the radiation-induced changes in concrete found in these works are mainly caused by changes in their cement stone.
It is important that the calculated radiation changes of minerals and aggregate rocks under the influence of gamma ray are much less than the maximum changes established by neutron radiation (increase in volume to 18-23 %, decrease in strength to 100 % in silicate materials, increase in volume to 3 % in carbonate and oxide materials). In this regard, it is of interest to evaluate what absorbed doses of gamma ray are necessary to achieve the same effects as under the influence of neutrons.
According to [14], the indicated maximum radiation changes in the aggregate rocks are observed at the following approximate values of the damaging neutron fluences (with an energy of more than 10 KeV):
- 1-1020 neutron/cm 2 for silicate materials at 30 oC;
- 3-1020 neutron/cm 2 for silicate materials at 100 oC;
- 10-1020 neutron/cm 2 for silicate materials at 300 oC;
- (1-10)-1020 neutron/cm2 for carbonate materials and materials based on iron oxides.
For the neutron spectra of the main reactors used in these studies, the fluences of 1-1020 -10-1020neutron/cm2 correspond to the fraction of displaced atoms nCM = 0.14-1.4, since the average cross
section for atomic displacement is aCM (En ) = 1400-10-24 cm2. Then, to obtain under the action of gamma ray
the same maximum effects as under the action of neutrons in accordance with formulas (14) and (15), the following absorbed to gamma ray are necessary:
Dg = nCM/1.1 10-14 = (0.14 - 1.4)/1.1-10-14 = 1.3-1013 - 1.3-1014 Gy - at gamma ray energy Eg = 2 MeV;
Dg = nCM /3.3 • 10-14 = (0.14 - 1.4)/3.3-10-14 = 4.2-1012 -4.2-1013 Gy - at gamma ray energy Eg = 5 MeV.
Magazine of Civil Engineering, 96(4), 2020
Such high absorbed doses of gamma ray to radiation protection concrete in modern nuclear facilities are not achievable. Therefore, radiation changes under the influence of gamma ray, commensurate with the maximum radiation changes under the influence of neutrons, are practically impossible at currently operating nuclear facilities.
It is also of interest to evaluate the contribution of radiation changes due to gamma ray to radiation changes in the radiation protection materials of nuclear reactors, which are simultaneously affected by neutrons and gamma ray.
It can be made in the following way:
According to [40], the ratio (pn / pg of the density of the damaging neutron flux (with an energy of more than 10 KeV) pn (neutron/(cm2-s)) to the energy flux density of gamma ray q>g (MeV/(cm2-s)) behind the nuclear reactor vessel is:
- cpn /p « 0.05 MeV -1 - for uranium-graphite and water-cooled thermal neutron reactors;
- pn / pg «3 MeV -1 - for fast neutron reactors.
Then the ratio nd g / ndn of the number of displaced atoms under the action of gamma ray nd g with gamma ray energy Eg = 5 MeV (average energy behind the reactor vessel) to the number of displaced atoms under the action of neutrons nd n with the cross sections for the formation of displaced atoms ad (E ) = 0.5-10-24 cm2 and ad (En) = 1400-10-24 cm2 will be:
a d(E ) 0 5 -10-24 -6 nd g/nd n =pn/ pg---— = 0. 05 - —-= 3. 6 -10 6 - for uranium-graphite and water-
d.s d.n Tg Egad(En) 5 -1400
cooled thermal neutron reactors;
, , ad(Eg) . 0.5-10-24 4 , , .
nd g/nd n =pn/ pg---— = 3--= 2.1-10 - for fast-neutron reactors.
d.g d.n Tn Tg Eg-ad(En) 5 -1400
Since nd.g / nd.n is much less than 1, the effect of gamma ray on the radiation changes of minerals
and rock-aggregates of concrete, and hence concrete, radiation protection of nuclear reactors under the simultaneous exposure to neutrons and gamma ray can be neglected. In this regard, the radiation changes under the influence of gamma ray must be taken into account when gamma ray only is exposed to materials with absorbed doses of more than 109 Gy.
It is characteristic that the results of evaluating the gamma ray effect on minerals and rocks do not correspond to the opinion that silicate minerals and rocks receive the largest and smallest radiation changes upon exposure based on the results of irradiation of minerals and rocks with high neutron fluences. When irradiated with neutrons with the formation of a large number of displaced atoms, the largest radiation changes are obtained by quartz, feldspars and including them granites, diorites (with coarser grains especially), sandstones, and much smaller changes - by serpentine, pyroxenes, hornblende, olivine and including them gabbro, basalts , diabases, pyroxenites, peridotites and dunits. Under the gamma ray influence of the considered absorbed dose values, the maximum changes from silicate materials will occur in olivine, pyroxenes and including them dunite, peridotite, pyroxenite, and the minimum changes will occur in quartz, serpentine, feldspars (microcline, oligoclase, labrador) and including them sandstone and basalt. The intermediate radiation changes will be observed in granites, diorites and gabbro, to the compositional features of which the influence of their coarse-grained structure is added.
Further computational research should be devoted to:
- assessment of radiation changes in cement stone based on existing experimental data on concrete irradiation;
- assessment of radiation changes in concrete with various aggregates under the influence of gamma ray in a wide range of absorbed doses and radiation temperatures based on the results of the assessment of radiation changes in aggregates and cement stone.
Such an assessment can also be performed on the basis of the above considered methods for the analytical determination of radiation changes in concrete and its components.
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4. Conclusion
1. The paper assesses the radiation changes of concrete aggregates under the influence of gamma ray based on analytical methods developed previously during the study of neutron radiation influence. The possibility of using these analytical methods in the case of exposure to gamma ray is discussed and justified in this paper.
2. For practical use of these analytical methods, the relationship between the absorbed dose of gamma radiation of different energies and the number of atoms displaced during irradiation has been established. It was found that the absorbed dose of gamma radiation with an energy of 5 MeV corresponds to 3 times more displaced atoms than the absorbed dose of gamma radiation with an energy of 2 MeV.
3. As a result of the calculations, the radiation changes of the main types of rocks - concrete aggregates (igneous, sedimentary rocks and ores) under the influence of gamma radiation with an average energy of 2 MeV and 5 MeV after irradiation to absorbed doses from 105 to 1011 Gy at 30 °C, 100 °C and 300 °C were estimated. For this purpose, the radiation changes of the main rock-forming minerals were calculated, and the radiation changes of rocks of concrete aggregates were calculated from them.
4. It has been established that the noticeable radiation changes in the examined minerals and aggregate rocks will occur only at absorbed doses of gamma ray greater than Dgo = 1-109 - 1-1010 Gy for
gamma rays with an energy of 5 MeV and Dg o = 3-109 - 3-1010 Gy for 2 MeV gamma rays. The radiation
changes in the volume of minerals increase with a rise in the absorbed dose and decrease in silicate class minerals and silicate rocks with an increase in the irradiation temperature.
5. At 30 °C, the largest increase in volume under the influence of gamma radiation in the studied range of absorbed doses will occur in minerals of the silicate class. The maximum increase in volume during irradiation at 30 °C will occur in olivine (up to 0.3 %). A minimal and insignificant increase in volume will be observed in magnetite (up to 0.007 %). The radiation change in the volume of minerals decreases in the direction: olivine-pyroxenes (diopside, enstatite) ^hornblende^quartz, serpentine, calcite, dolomite^microcline, oligoclase, labrador, hematite^magnetite.
6. With an increase in the irradiation temperature from 30 °C to 100 °C and 300 °C, the radiation changes of silicate class minerals decrease, while the radiation changes of carbonate class minerals (calcite, dolomite) and iron oxides (hematite, magnetite) do not change. Moreover, the effect of temperature increases with the rise of irradiation temperature. At 100 °C, the radiation increase in the volume of silicates decreases by 11-18 times and becomes insignificant and at 300 °C it decreases by 400-1800 times compared with the change in volume at 30 °C and becomes insignificant. In this regard, the ratio between radiation changes in the volume of various minerals changes, the upper and lower boundaries of the changes in volume decrease, and the increase in the volume of silicate class minerals becomes smaller than that of carbonates and iron oxides.
7. In quartz glass, regardless of the irradiation temperature, there will be a decrease in volume (up to -0.3%).
8. Radiation changes in the volume of rocks of concrete aggregates increase with an increase in the absorbed dose and decrease in rocks consisting of minerals of the silicate class with an increase in the irradiation temperature.
9. At 30 °C, according to the results of calculations, the greatest increase in volume and decrease in strength under the influence of gamma radiation in the studied range of absorbed doses will occur in rocks consisting of silicate class minerals.
10. The largest increase in volume under the influence of gamma radiation during irradiation at 30 °C will be observed in dunite (up to 0.36 %), peridotite (up to 0.31 %) and pyroxenite (up to 0.28 %). The smallest, insignificant increase in volume will occur in magnetite ore (up to 0.0066 %). The radiation change in the volume of rocks decreases in the direction of: dunite, peridotite and pyroxenite^granite, diorite and gabbro (up to 0.22 %)^basalt, sandstone, limestone and dolomite (up to 0.059%)^magnetite ore (up to 0.018 %)^hematite ore.
11. The greatest decrease in strength during irradiation at 30 oC will be observed in granite (up to -8.7 %). Almost half less reduction of strength will occur in dunite (up to -5.8 %), peridotite (up to -5.4 %), pyroxenite (up to -4.2 %) and gabbro (-4.3 %). In other rocks, the reduction of strength is not significant and is -1.3 % or less, but it decreases in the direction of: limestone (to -1.3 %)^basalt (to -0.6 %)^hematite and magnetite ore (to -0.1 %).
12.With an increase in the irradiation temperature from 30 °C to 100 °C and 300 °C, the radiation changes of silicate aggregate rocks decrease, while the radiation changes of carbonate and ore aggregate
Magazine of Civil Engineering, 96(4), 2020
rocks do not change. At 100 °C, the increase in the volume of silicate rocks in addition to basalt decreases by 13-31 times, and at 300 °C decreases by 300-970 times compared to the change in volume at 30 °C. In basalt, the decrease is about 2 times at 100 °C and about 80 times at 300 °C. In this regard, the ratio between the radiation changes in the volume of various silicate and carbonate, ore rocks changes, the upper and lower limits of volume changes are reduced, and the increase in the volume of silicate rocks become less than of carbonate and ore rocks. Radiation changes in strength with increasing irradiation temperature change similarly to changes in volume.
13.In general, it can be noted that even with the absorbed dose of 1011 Gy gamma ray the changes of rocks-concrete aggregates are not great (an increase in volume is no more than 0.36 %, a decrease in strength is no more than 8.7 %). In this regard, the changes in concrete under the influence of gamma ray at the considered absorbed doses will not be significant.
14.The calculated radiation changes of minerals and rock aggregates of concrete under the action of gamma radiation are much smaller than the maximum changes established during neutron irradiation (an increase in volume is to 18-23 %, a decrease in strength is to 100 % in silicate materials, an increase in volume is to 3 % in carbonate and oxide materials). According to the results of calculations, the radiation changes under the action of gamma ray, commensurate with the maximum radiation changes under the action of neutrons in nuclear facilities operating at the present time are practically impossible.
15.The calculations have shown that the influence of gamma ray on the radiation changes of minerals and rock aggregates of concrete, and therefore concrete, the radiation protection of nuclear reactors with the simultaneous exposure to neutrons and gamma ray can be neglected. In this regard, the radiation changes under the influence of gamma radiation must be taken into account when only gamma ray is applied to materials and when absorbed doses are greater than 109 Gy.
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Contacts:
Aleksandr Denisov, [email protected]
© Denisov, A.V., 2020
