Abstract

In the complex situation in which we live, preventive measures are increasingly being taken against the threat of nuclear attack and ionizing radiation, nuclear shelters are being built for private and public purposes. The purpose of the authors is to provide a practical approach to quickly calculate the thickness of the concrete shelter wall for such cases. The shelter wall thickness is assessed on the basis of published data on radiation dose calculations, corroborated by field data from nuclear tests, and information or calculations of the dose attenuation in the shelter wall. Doses from nuclear tests or simulations are summarized in tables in relation to bomb yield and distance from the explosion point. A dose criterion is chosen as the acceptable dose behind the shield. Neutron dose transmission factors, defined as ratio of the dose criterion to the dose without shielding are calculated. The concrete wall thickness corresponding to the neutron dose transmission factor was taken from reference sources. For gamma rays, the shield thickness is calculated based on an analytical relationship between dose without shield, the dose criterion, and the shield thickness. Data tables are provided with the estimated concrete wall thickness in relation to bomb yield and distance.

Issue Section:
Review Articles
Keywords:
nuclear shelter, fission bomb yield, neutron dose, gamma ray dose, dose transmission factor, shield thickness
Topics:
Concretes, Gamma rays, Neutrons, Nuclear fission, Wall thickness, Bombs

1 Introduction

The authors' first goal was to find a reliable source for a selection of doses caused by fission neutrons, fission gamma rays, and secondary gamma rays from nuclear fission bombs. Such information was found in Ref. [1]. The second goal was to estimate the dose transmission factor (DTF) for neutrons as a ratio between the dose behind the shield and the dose without shield and to find a source where information is given on the relationship between DTF and the thickness of the shelter wall. Information was found in Ref. [2]. The third goal was to propose a formula to estimate the shelter wall thickness against gamma rays, based on the relation between the dose behind the shield, dose without shield and wall thickness. Appropriate commonly used materials such as different concrete types are proposed for both neutron and gamma ray protection. Fallout gamma radiation is taken into account to estimate the roof wall thickness. A comparison is made with the results of applying different approaches to estimate the thickness of protective walls. The most protective place for a nuclear shelter is below the ground level. In the case of underground location of the shelter, the soil shield should be taken into account in the protection of the shelter construction.

1.1 Diagram of the Shelter Wall Thickness Evaluation Process

The recommended shelter wall thickness is the highest estimated thickness value.

2 Nuclear Explosion Above Ground Level. Above Ground Shelter

2.1 Shielding Against Neutrons.

The energies of the neutrons received at some distance from nuclear explosion cover a very wide range, from several millions down to a fraction of an eV (1 eV = 1.602 × 10−19J). With spectra for the finite number of energy groups results of neutron dose calculations with a neutron transport computer codes corroborated by test data, are given in Fig. 1 developed in accordance with Fig. 8.123a from Ref. [1].

Fig. 1
Initial neutron dose per kiloton total yield as a function of slant range from fission weapon air bursts, based on defense curve of Fig. 8.123a from Ref. [1]
View largeDownload slide
Fig. 1
Initial neutron dose per kiloton total yield as a function of slant range from fission weapon air bursts, based on defense curve of Fig. 8.123a from Ref. [1]
View largeDownload slide
Close modal

2.1.1 Determination of the Initial Neutron Dose.

From Fig. 1, we read the initial neutron dose per kiloton total yield as a function of slant range from fission weapon air bursts at elevation about of 90 m, based on 0.9 normal sea-level air density, based on Ref. [1].

The doses in the figure are valid for air-burst above 90 m, 0.9 normal sea-level air density [1]. In cases of contact surface burst, the doses from Fig. 1 shall be multiplied by factor of 0.5 [1]. For bursts between the surface and 90 m an approximate value of a dose can be calculated by linear interpolation between a surface burst and one at 90 m or above [1].

2.1.2 Presentation of the Expected Neutron Doses From a Fission Bomb as a Function of Bomb Yield and Distance From the Nuclear Explosion Point.

We select the dose values from the curve in Fig. 1 and calculate for different distances ri and actual bomb yield Yj the corresponding doses
(1)

The effective dose can be calculated for fission neutrons also based on neutron fluence to effective dose conversion coefficients. Neutron fluence per kiloton energy yield can be found in Ref. [1] in Fig. 8.117a. Values of neutron fluence to effective dose conversion coefficients depending on neutron energy can be found in Ref. [3] in Fig. 5 of the cited document. The energy spectrum of neutrons leaking from a weapon is primarily a fission spectrum [4] with average energy of about 2 MeV [5]. For 2 MeV neutrons, we obtain similar doses to those shown in Table 1, but the data in Table 1 are based on more direct method.

Table 1

Expected neutron doses Dij in accordance with Fig. 1 from fission bomb depending on bomb yield and distance from the nuclear explosion point

kT10203040501005001000
yd.mSvSvSvSvSvSvSvSv
1000914.430609012015030015003000
15001371.61.534.567.51575150
20001828.80.10.20.30.40.51510
250022860.010.020.030.040.050.10.51
30002743.20.0010.0020.0030.0040.0050.010.050.1
35003200.40.000090.000180.000270.000360.000450.00090.00450.009
40003857.60.000010.000020.000030.000040.000050.00010.00050.001
kT10203040501005001000
yd.mSvSvSvSvSvSvSvSv
1000914.430609012015030015003000
15001371.61.534.567.51575150
20001828.80.10.20.30.40.51510
250022860.010.020.030.040.050.10.51
30002743.20.0010.0020.0030.0040.0050.010.050.1
35003200.40.000090.000180.000270.000360.000450.00090.00450.009
40003857.60.000010.000020.000030.000040.000050.00010.00050.001
We can apply formula 2 below to use the ratio of fast neutron fluences Φi, i.e., of doses Di, for each subsequent after the first dose assessment at given distances, as shown in formula 1, taking into account that fluence to dose is a constant for a given energy
(2)
(3)

where No is the number of the emitted fast neutrons; ri is the distance from the source; L(=constant for given distance and energy) is the relaxation length; f(=constant for given energy) is the change in the relaxation length [6,7].

It can be seen that the exponent in formula 3 can be omitted only if L≫ ri as also stated in [6]. L varies between 250 m and 850 m for neutrons in air, increasing with the neutron energy [7] and is smaller than the distances in Table 1. Calculations of the inverse square of the distance are not acceptable in this case. Based on formulas 3 and 2, we have calculated results, which are similar to those given in Table 1.

2.1.3 Selection of the Dose Criterion (the Acceptable Dose Behind the Shield).

The dose criterion here is defined as DC = 0.0001 Sv dose equivalent, equal to the usual permitted daily dose from external exposure of the operator in a controlled area in nuclear facilities without special permit. Different DCs can be defined, for example, based on the accident reference levels.

2.1.4 Dose Transmission Factor (DTF) Estimation.

DTF is defined as the ratio between the personal dose equivalent of photons or neutrons behind the shield and the personal dose equivalent in front of the shield.

The DTF can express the shielding properties according to Ref. [8] as
(4)

Dij is the neutron personal dose equivalent in front of the shielding (here taken from Table 1).

The smaller the DTF, the better the shielding effect [8]. DTFij, for each actual dose value Dij from Table 1 are calculated in accordance to Eq. (4) for corresponding distances ri and bomb yield Yj.

2.1.5 Application of Appropriate Relations Between DTF and Shield Thickness.

Based on Fig. 1 in Ref. [2], calculated with the Monte Carlo N-particle transport code (MCNP code), Fig. 2 was developed, which plots the DTF curves for various materials versus shield thickness for fission neutrons. Instead of percentages of the DTF on the original figure [2] we use the corresponding numbers. It is known that the energy spectrum of neutrons leaking from a weapon is predominantly a fission spectrum [4]. The interesting material for the shelter wall is concrete. It can be seen from Fig. 2 that heavy concrete attenuates fission neutrons more effectively than concrete of lower density. From Fig. 2 we read the shelter wall thickness corresponding to the DTF of interest for the desired material, here heavy concrete with a density of 3200 kg/m3. For example, the heavy concrete shield thickness for DTF = 10−4 for fission neutrons according Fig. 2 is about 0.78 m. To achieve lower value of the DTF than those shown on the Fig. 2 (<10−5) we can multiply two or more DTFs from Fig. 2 and the resulting shield thickness will be the sum of the corresponding to every DTF wall thicknesses. (The relationship between DTF and x on the logarithmic scale in Fig. 2 is a straight line). To achieve a DTF of 10−7, we can sum 1 m, which reduces the dose with a factor 10−5, and 0.38 m, which reduces the dose with additional factor of 10−2. The resulting heavy concrete wall thickness is 1.38 m. For our purposes, we can similarly consider the curve of another material.

Fig. 2
Attenuation of fission neutron dose versus shield thickness, based on Fig. 1 of Ref. [2]
View largeDownload slide
Fig. 2
Attenuation of fission neutron dose versus shield thickness, based on Fig. 1 of Ref. [2]
View largeDownload slide
Close modal

2.1.6 Calculation of Heavy Concrete Shield Thickness.

The wall thicknesses of the heavy concrete according to Fig. 2 based on Ref. [2], as a function of the calculated DTFs in Table 2 are listed in Table 3. Table 4 is for the case if one wants to calculate from Fig. 2 shield thickness for material other than concrete, e.g. water.

Table 2

Fission neutron DTFij to achieve the dose reduction criterion

kT10203040501005001000
yd.m
1000914.43.33 × 10−61.67 × 10−61.11 × 10−68.33 × 10−76.67 × 10−73.33 × 10−76.67 × 10−83.33 × 10−8
15001371.66.67 × 10−53.33 × 10−52.22 × 10−51.67 × 10−51.33 × 10−56.67 × 10−61.33 × 10−66.67 × 10−7
20001828.81.00 × 10−35.00 × 10−43.33 × 10−42.50 × 10−42.00 × 10−41.00 × 10−42.00 × 10−51.00 × 10−5
250022861.00 × 10−25.00 × 10−33.33 × 10−32.50 × 10−32.00 × 10−31.00 × 10−32.00 × 10−41.00 × 10−4
30002743.21.00 × 10−15.00 × 10−23.33 × 10−22.50 × 10−22.00 × 10−21.00 × 10−22.00 × 10−31.00 × 10−3
35003200.4>15.56 × 10−13.70 × 10−12.78 × 10−12.22 × 10−11.11 × 10−12.22 × 10−21.11 × 10−2
40003857.6>1>1>1>1>112.00 × 10−11.00 × 10−1
kT10203040501005001000
yd.m
1000914.43.33 × 10−61.67 × 10−61.11 × 10−68.33 × 10−76.67 × 10−73.33 × 10−76.67 × 10−83.33 × 10−8
15001371.66.67 × 10−53.33 × 10−52.22 × 10−51.67 × 10−51.33 × 10−56.67 × 10−61.33 × 10−66.67 × 10−7
20001828.81.00 × 10−35.00 × 10−43.33 × 10−42.50 × 10−42.00 × 10−41.00 × 10−42.00 × 10−51.00 × 10−5
250022861.00 × 10−25.00 × 10−33.33 × 10−32.50 × 10−32.00 × 10−31.00 × 10−32.00 × 10−41.00 × 10−4
30002743.21.00 × 10−15.00 × 10−23.33 × 10−22.50 × 10−22.00 × 10−21.00 × 10−22.00 × 10−31.00 × 10−3
35003200.4>15.56 × 10−13.70 × 10−12.78 × 10−12.22 × 10−11.11 × 10−12.22 × 10−21.11 × 10−2
40003857.6>1>1>1>1>112.00 × 10−11.00 × 10−1
Table 3

Calculated wall thickness x of heavy concrete for shielding fission neutrons at various distances from the point of explosion of a fission bomb

kT10203040501005001000
yd.Heavy concrete (density 3200 kg/m3) shield thickness x, m
1000.00914.41.061.101.161.191.211.261.411.46
1500.001371.60.830.890.920.950.991.011.151.21
2000.001828.80.580.650.680.720.750.780.931.00
2500.0022860.380.450.480.520.540.580.730.78
3000.002743.20.180.250.270.300.330.380.530.58
3500.003200.400.050.060.080.120.180.330.38
4000.003857.60000000.140.18
kT10203040501005001000
yd.Heavy concrete (density 3200 kg/m3) shield thickness x, m
1000.00914.41.061.101.161.191.211.261.411.46
1500.001371.60.830.890.920.950.991.011.151.21
2000.001828.80.580.650.680.720.750.780.931.00
2500.0022860.380.450.480.520.540.580.730.78
3000.002743.20.180.250.270.300.330.380.530.58
3500.003200.400.050.060.080.120.180.330.38
4000.003857.60000000.140.18
Table 4

Density of materials, considered in Fig. 2 

MaterialDensity, kg/m3
5% borated polyethylene1040
Water1000
MaterialDensity, kg/m3
5% borated polyethylene1040
Water1000

2.1.7 Alternative Calculations of the Concrete Shelter Wall Thickness for Neutron Releases.

We can use also the neutron DTFs from Ref. [1].

For example, to achieve DTF1=1.33 × 10−5, based on the information in Table 5, we solve the equation
(5)

i.e., to achieve DTF1 from some DTF0 shown in Table 5, we need to multiply DTF0Z times and add the corresponding wall thickness Z times. It is necessary to multiply 0.229 m with Z to calculate the required wall thickness of ordinary concrete. There is a small difference in the concrete density (2200 kg/m3) in Fig. 2 and Table 5 (2340 kg/m3) as used elsewhere in Ref. [1], but the uncertainty in reading from graphs and in the data in Table 5 is dominating. The assessed wall thicknesses from application of Fig. 2 are lower compared to the application of the DTFs from Table 5, but are more accurate, because the curves in Fig. 2 were calculated with MCNP according to Ref. [2]. For neutron shielding, we recommend the wall thickness of the shelter according to Table 3 up to 1.50 m of heavy concrete with density of 3200 kg/m3 (2.27 m for ordinary concrete with density of approximately 2200 kg/m3), calculated for fission bomb yield of 1000 kT at 914.4 m distance from the explosion point. 1.50 m concrete shelter wall thickness is also recommended in Ref. [9].

Table 5

Dose transmission factors (DTF0) for neutron releases [1]

StructureNeutrons
Concrete blockhouse shelter with density of 2340 kg/m3
0.229 m (9 in.) walls0.3–0.5
0.305 m (12 in.) walls0.2–0.4
Shelter, partly above grade
With 0.61 m (2 ft.) earth cover0.02–0.08
StructureNeutrons
Concrete blockhouse shelter with density of 2340 kg/m3
0.229 m (9 in.) walls0.3–0.5
0.305 m (12 in.) walls0.2–0.4
Shelter, partly above grade
With 0.61 m (2 ft.) earth cover0.02–0.08

2.2 Concrete Wall Thickness Estimation for Initial (Fission and Secondary) Gamma Ray Shielding.

From a 1-kiloton weapon the estimated production of fission gamma rays from 7.5 × 1022 fissions occurring in the last generation would produce a total of 6 × 1023 fission gamma rays having a spectrum of energies between about 0.01 and 10 MeV. Most of the important gamma rays are in the energy region from 1 to 4.5 MeV [4]. Secondary (nitrogen capture) gamma rays range in energy from about 1.5 MeV to about 11 MeV, with those between 4 and 7.5 MeV, together with a 10.83-MeV gamma ray, being the most prominent [4]. The fission product gamma-ray and the secondary gamma-ray contribute approximately equal dose at slant ranges up to about 2743 m (3000 yd.). For explosions of higher yield, however, hydrodynamic enhancement may cause the fission product gamma-ray dose to exceed the secondary gamma-ray dose, particularly for larger ranges [1].

2.2.1 Selection of Formulas and Parameters, Describing the Relation Between Shield Thickness and Dose (Rate).

Shield thickness x for gamma rays is calculated using Eq. (6) according to Refs. [1,9], and [10] as
(6)

D is the dose in front the shield – from Table 6 for fission gamma rays and from Table 7 for secondary gamma rays; x is the shield thickness; μ is the linear attenuation coefficient of the shielding material (Table 8), B is the build-up factor (Table 9), DC is the dose criterion.

Table 6

Fission product gamma-ray component of the initial nuclear radiation dose for different kilotons fission yield as a function of slant range from a nuclear explosion, based on 0.9 normal sea-level air density –data from Fig. 4, corrected in accordance with Fig. 3 

kT110203040501005001000
yd.mSvSvSvSvSvSvSvSvSv
1000914.40.712.62836.47010521012602100
20001828.80.010.180.450.711.8460180
30002743.20.00020.00360.0090.0160.020.0360.11.47
35003200.40.000020.00020.00040.00060.00080.0010.0020.010.02
40003857.60.00000350.0000350.000070.0001050.000140.0001750.000350.001750.0035
kT110203040501005001000
yd.mSvSvSvSvSvSvSvSvSv
1000914.40.712.62836.47010521012602100
20001828.80.010.180.450.711.8460180
30002743.20.00020.00360.0090.0160.020.0360.11.47
35003200.40.000020.00020.00040.00060.00080.0010.0020.010.02
40003857.60.00000350.0000350.000070.0001050.000140.0001750.000350.001750.0035
Table 7

Air-secondary gamma-ray component of the initial nuclear radiation dose for different kiloton yields as a function of slant range from fission weapon airbursts, based on 0.9 normal sea-level air density as per Fig. 5 

kT110203040501005001000
yd.mSvSvSvSvSvSvSvSvSv
1000914.41.717345168851708501700
15001371.60.171.73.45.16.88.51785170
20001828.80.030.30.60.91.21.531530
250022860.0040.040.080.120.160.20.424
30002743.20.00070.0070.0140.0210.0280.0350.070.350.7
35003200.40.000120.00120.00240.00360.00480.0060.0120.060.12
40003857.60.0000250.000250.00050.000750.0010.001250.00250.01250.025
kT110203040501005001000
yd.mSvSvSvSvSvSvSvSvSv
1000914.41.717345168851708501700
15001371.60.171.73.45.16.88.51785170
20001828.80.030.30.60.91.21.531530
250022860.0040.040.080.120.160.20.424
30002743.20.00070.0070.0140.0210.0280.0350.070.350.7
35003200.40.000120.00120.00240.00360.00480.0060.0120.060.12
40003857.60.0000250.000250.00050.000750.0010.001250.00250.01250.025
The shield thickness x is calculated as
(7)
The buildup factor B (E, x) is generally defined as the ratio of the total dose to the unscattered dose. Buildup factors are greater than unity and approach to unity when the absorption is dominant or when the scattering cross section vanishes [11].

The linear attenuation coefficient μ is a measure of how much the incident energy beam is weakened by the material it is passing through.

Mean-free-path (mfp) is the average distance traveled by a moving particle in a target medium between interactions with the target material [2].

Table 8

Attenuation coefficients μ for each group of energy and type of concrete based on Refs. [6] and [12]

μ,m–1
Energy, MeVPortland concrete (ρ = 2370 kg/m3) [6,12]Barite concrete (ρ = 3490 kg/m3) [6,12]
0.0023.6023.12
0.5021.6019.89
2.0012.0011.21
5.0019.3818.76
8.0018.4017.99
μ,m–1
Energy, MeVPortland concrete (ρ = 2370 kg/m3) [6,12]Barite concrete (ρ = 3490 kg/m3) [6,12]
0.0023.6023.12
0.5021.6019.89
2.0012.0011.21
5.0019.3818.76
8.0018.4017.99
Table 9

Gamma buildup factors for concrete, based on Ref. [11]

Thickness (mfp) =μ–1, m
Energy (MeV)0.0050.010.020.030.040.050.060.070.080.09
0.51.482.334.176.439.1212.41620.4125.4237.14
11.582.053.314.886.598.5410.2212.1815.4621.09
21.441.862.833.724.775.817.128.249.3611.88
41.371.772.233.013.454.164.885.566.117.32
61.311.542.042.462.893.373.814.244.875.78
81.271.521.882.232.642.923.273.764.134.63
101.221.411.732.022.382.623.113.223.544.23
Thickness (mfp) =μ–1, m
Energy (MeV)0.0050.010.020.030.040.050.060.070.080.09
0.51.482.334.176.439.1212.41620.4125.4237.14
11.582.053.314.886.598.5410.2212.1815.4621.09
21.441.862.833.724.775.817.128.249.3611.88
41.371.772.233.013.454.164.885.566.117.32
61.311.542.042.462.893.373.814.244.875.78
81.271.521.882.232.642.923.273.764.134.63
101.221.411.732.022.382.623.113.223.544.23

Gamma buildup factor for concrete depends on the material and the energy of the photons.

2.2.2 Gamma-Ray Energy Range Selection.

For fission product gamma rays we chose the important energy range around 2 MeV, for secondary gamma rays is selected the energy range around 5 MeV [4].

2.2.3 Mean-Free-Path Calculation.

(8)

The thickness of the media ranges from 0.5 to 10 mfp and gamma energy ranges from 0.5 to 10 MeV. The maximum relative error is 2% [11].

2.2.4 Information About Gamma Buildup Factors for Concrete (Table 9).

2.2.5 Selection of Barite Concrete Radiological Parameters for Gamma Rays (Table 10).

2.2.6 Fission Product Gamma-Ray.

2.2.6.1 Fission Product Gamma-Ray Component of the Initial Nuclear Radiation Dose.

The necessary correction for the differences in cloud rise velocity and hydrodynamic enhancement, each of which is a function of total energy yield, is provided by the use of effective bomb yield instead of actual bomb yield [1].

Figure 3, based on Fig. 8.130b in Ref. [1], shows the effective yield as a function of actual yield. From the plots in Fig. 3, we find the effective yield for the actual yield of interest at a given distance and multiply the registered dose per kT from Fig. 4 at that distance with the effective yield.

Fig. 3
Effective yield as a function of actual yield for the fission product gamma-ray dose from a low air burst 0.9 normal sea-level air density, based on Fig. 8.130b from Ref. [1]
View largeDownload slide
Fig. 3
Effective yield as a function of actual yield for the fission product gamma-ray dose from a low air burst 0.9 normal sea-level air density, based on Fig. 8.130b from Ref. [1]
View largeDownload slide
Close modal
Fig. 4
Calculated fission product gamma-ray component of the initial nuclear radiation dose per kiloton fission yield as a function of slant range from a nuclear explosion 0.9 normal sea-level air density based on Fig. 8.130a from Ref. [1]
View largeDownload slide
Fig. 4
Calculated fission product gamma-ray component of the initial nuclear radiation dose per kiloton fission yield as a function of slant range from a nuclear explosion 0.9 normal sea-level air density based on Fig. 8.130a from Ref. [1]
View largeDownload slide
Close modal

Here we consider air burst at high above 90 m.

2.2.6.2 Evaluation of Barite Concrete Shield Thickness for Fission Product Gamma Rays.

The shield thickness is estimated by solving Eq. (7) using the parameters given in Table 10 for barite concrete (ρ = 3490 kg/m3) and fission gamma-ray energy of 2 MeV. The results are listed in Table 11.

Table 10

Barite concrete (ρ = 3490 kg/m3) radiological parameters for gamma rays

Gamma energy, MeVμ, m−1mfp = 1/μ, mBuildup factor B
518.760.0533∼4
211.210.0892∼10
Gamma energy, MeVμ, m−1mfp = 1/μ, mBuildup factor B
518.760.0533∼4
211.210.0892∼10
Table 11

Barite concrete shield thickness for fission product gamma-ray with energy 2 MeV at different distances from fission bomb explosion point and depending on bomb yield taking into account B = 10

kT110203040501005001000
yd.mx, mx, mx, mx, mx, mx, mx, mx, mx, m
1000914.40.99521.25301.32431.34771.40601.44221.50401.66391.7094
20001828.80.61620.87410.95580.99521.02701.07951.15071.39231.4903
30002743.20.26720.52510.60680.65810.67800.73050.82161.05701.2006
35003200.40.06180.26720.32910.36520.39090.41080.47260.61620.6780
40003857.600.11180.17360.20980.23540.25530.31720.46070.5226
kT110203040501005001000
yd.mx, mx, mx, mx, mx, mx, mx, mx, mx, m
1000914.40.99521.25301.32431.34771.40601.44221.50401.66391.7094
20001828.80.61620.87410.95580.99521.02701.07951.15071.39231.4903
30002743.20.26720.52510.60680.65810.67800.73050.82161.05701.2006
35003200.40.06180.26720.32910.36520.39090.41080.47260.61620.6780
40003857.600.11180.17360.20980.23540.25530.31720.46070.5226

2.2.7 Secondary Gamma-Ray

2.2.7.1 Assessment of Secondary Gamma-Ray Component of the Initial Nuclear Radiation Dose.

As pointed out in Ref. [4] in some radiation transport calculations for “free-field” radiation doses produced by predominantly fission weapons, gamma rays produced by neutron capture in the nitrogen of the atmosphere, secondary gamma rays, have been the only gamma rays considered other than fission-product gamma rays.

Air-secondary gamma-ray component of the initial nuclear radiation dose per kiloton yield as a function of slant range from fission weapon airbursts is given in Fig. 5, developed based on Fig. 8. 127a, defense curve, from Ref. [1]. Corrections of the actual doses in this case are not necessary.

Fig. 5
Air-secondary gamma-ray component of the initial nuclear radiation dose per kiloton yield as a function of slant range from fission weapon airbursts 0.9 normal sea-level air density, based on Fig. 8.127a defense curve from Ref. [1]
View largeDownload slide
Fig. 5
Air-secondary gamma-ray component of the initial nuclear radiation dose per kiloton yield as a function of slant range from fission weapon airbursts 0.9 normal sea-level air density, based on Fig. 8.127a defense curve from Ref. [1]
View largeDownload slide
Close modal

The data from the defense curve is selected as more conservative.

In cases of contact surface burst, the doses from Table 7 shall be multiplied by factor of 0.5 [1]. Here we consider air burst at high above 90 m.

2.2.7.2 Selection of Important Energy Diapason.

For secondary gamma rays, the energy diapason around 5 MeV.

2.2.7.3 Shelter Wall Thickness Estimation for Secondary Gamma-Ray Component.

The shield thickness x is estimated by solving Eq. (7) using the parameters given in Table 10 for a secondary gamma-ray energy of 5 MeV. The results are listed in Table 12.

Table 12

Barite concrete shield thickness for secondary gamma rays with energy 5 MeV at different distances from fission bomb explosion point and depending on bomb yield taking into account buildup factor B equal to 4

kT110203040501005001000
yd.mx, mx, mx, mx, mx, mx, mx, mx, mx, m
1000914.40.59310.71590.75280.77440.78980.80170.83860.92440.9614
15001371.60.47040.59310.63010.65170.66700.67890.71590.80170.8386
20001828.80.37790.50070.53760.55920.57460.58650.62340.70920.7462
250022860.27050.39330.43020.45180.46720.47910.51600.60180.6387
30002743.20.17760.30040.33730.35890.37430.38620.42310.50890.5458
35003200.40.08360.20640.24330.26490.28030.29210.32910.41490.4518
40003857.60.000.12270.15970.18130.19660.20850.24550.33130.3682
kT110203040501005001000
yd.mx, mx, mx, mx, mx, mx, mx, mx, mx, m
1000914.40.59310.71590.75280.77440.78980.80170.83860.92440.9614
15001371.60.47040.59310.63010.65170.66700.67890.71590.80170.8386
20001828.80.37790.50070.53760.55920.57460.58650.62340.70920.7462
250022860.27050.39330.43020.45180.46720.47910.51600.60180.6387
30002743.20.17760.30040.33730.35890.37430.38620.42310.50890.5458
35003200.40.08360.20640.24330.26490.28030.29210.32910.41490.4518
40003857.60.000.12270.15970.18130.19660.20850.24550.33130.3682

To determine the effectiveness of a given shield as a protection against the initial radiation from a nuclear explosion, it is recommended to use the higher of the values for fission and secondary gamma rays [1].

2.2.8 Derivation of Shelter Wall Thickness for Different Materials, Based on Results for Concrete.

For assessment of shield thickness of different material, for example, of soil, xsoil, we can apply Eq. (6) supposing Dconcrete=Dsoil. The dose without shield D is equal for both cases
(9)

2.2.9 Alternative Calculations of the Concrete Shelter Wall Thickness for Initial Gamma Rays.

2.2.9.1 Tenth-Value Thickness.

A tenth-value thickness is defined as the thickness of the specified material which reduces the radiation dose or dose rate to one tenth of that falling upon it [1]. The effective tenth-value thickness of some materials of interest for broad beams of gamma rays emitted by the fission products in the first minute after the detonation and for secondary gamma rays are given in Ref. [1]. For example, the approximate tenth-value shield thickness for concrete (density 2340 kg/m3) is 0.2794 m (11 in.) [1]. We can compare the calculation results in Table 11 with the results from tenth-value thickness application using Eq. (5) with DTF0 equal to 0.1 and make the conclusion that both results are similar and expected given the differences in the concrete density.

2.2.9.2 Estimates of the Initial Gamma-Ray Shielding Afforded in Terms of a “Dose Transmission Factor”.

Concrete shield thickness estimates (density 2340 kg/m3) can be found using the DTF between 0.1 and 0.2 for a 0.2286 m (9-in.) shelter wall thickness [1]. For a shelter partially above grade, we use a DTF of 0.03-0.07, corresponding to a wall thickness of 0.6096 m (2 ft.) [1]. We can compare the calculation results in Table 11 with results from application of the DTF between 0.1 and 0.2 using Eq. (5). Both results are similar and expected given the differences in the concrete density. Underground shelter with an earth cover will have dose reduction factor orders of magnitude lower than the concrete blockhouse shelter.

2.3 Fallout Radiation.

Radioactive fallout contaminates large areas and is an immediate and extreme biological hazard. Radioactive fallout emits alpha, beta, and gamma radiation. Estimates of attenuation of residual radiation in various structures have been made, based partly on calculations and partly on measurements with simulated fallout [1]. According to Ref. [1] blockhouse shelter wall thickness of 0.2286 m (9 in.) for protection from fallout radiation corresponds to DTF of 0.007–0.09. Total-dose contours from early fallout at 1, 6, and 18 h after a surface burst with a total yield of 2 megatons and 1-megaton fission yield (24.14 km/h (15 mph) effective wind speed) are given in Fig. 9.86b in Ref. [1]. At a distance r of about 3000–4000 m from the bomb burst according to Ref. [1] the expected total dose from fallout in the first hour is 10 Sv. To estimate the thickness of the concrete shield to protect against exposure to 10 Sv from fallout radiation, we use the dose criterion DC = 0.0001 Sv and calculate DTF1 = 0.0001/10 = 10−5. We conservatively select DTF0 = 0.09 with corresponding concrete wall thickness of 0.2286 m. According to Eq. (5) the number Z to multiply the wall thickness of 0.2286 m (9 in.) is equal to 4.78. The necessary concrete roof and wall thickness x for protection from fallout gamma-ray radiation from 1 MT fission yield is 1.093 m.

2.3.1 Rule of Thumb.

The total dose increases with time over a given distance, due to continued deposition of radioactive substances, but dose rate decreases with time due to the radioactive decay and the corresponding exposure rate is expected to decrease as well. Based on empirical measurements of fallout radiation with dose-rate meters the 7:10 Rule of thumb has been derived [13]. The 7:10 Rule of Thumb states that for every 7-fold increase in time after detonation, there is a 10-fold decrease in the exposure rate, where the rate is the same unit as the time increase; For 7 × 7 × 7 = 343 h (two weeks) the dose rate will decrease 10 × 10 × 10 = 1000 times. For 7 × 7 = 49 h the dose rate will decrease 10 × 10 = 100 times [1,9]. The rule assumes that the time of detonation is known and that fallout from only one detonation is present in relatively significant quantities. For accuracy and reliability, nothing can replace a direct instrument reading. However, depending on circumstances, it may become necessary to apply this general rule to predict when conditions may allow short trips outside a shelter [1].

3 Conclusions

This practical guideline proposes a simplified approach to estimate the required thickness of heavy concrete wall (density 3200 kg/m3) for shielding against fission neutrons and initial gamma rays. The expected neutron and initial gamma ray doses per kT yield are taken from reference source [1] at different distances and multiplied by the bomb yield. The required dose behind the shield DC is defined as 0.0001 Sv = 0.1 mSv. The required DTFs are calculated as the ratio of dose behind the shield and dose without shielding.

3.1 Neutron Shielding.

Heavy concrete shield thicknesses calculated with MCNP corresponding to a specific DTF were taken from reference source [2]. The results are tabulated in relation to the distance and bomb yield. A comparison is made based on DTFs from a reference source [1] and both methods were found to give similar results given the differences in the concrete density and accuracy of the methods. For neutron shielding is recommended a wall about 1.50 m thick made of heavier concrete with density ≥ 3200 kg/m3 is assessed for 1000 kT fission bomb yield at a distance of 914.4 m (1000 yd.).

3.2 Shielding of Initial (Fission and Secondary) Gamma Rays.

Fission product gamma ray doses are taken from the reference source [1] and they are corrected with the effective yield as a function of actual yield [1]. For secondary gamma rays no correction is necessary according to Ref. [1]. Relation between the doses in-front and behind the shield and shield thickness is used according to Eq. (6). Parameters of the function are chosen for barite concrete and the corresponding gamma energy. The results were compared with the application of tenth-value thickness and DTFs for fission and secondary gamma rays found in Ref. [1]. The results of applying the analytical function, tenth-value thickness, and empirical DTFs are similar. Based on all methods applied, a 1.70 m thick protective wall made of barite concrete (density 3420 kg/m3) assessed for 1000 kT fission bomb yield at a distance of 914.4 m (1000 yd.) is recommended for protection against fission gamma rays.

3.3 Fallout Radiation Shielding.

From the reference source [1] are taken DTFs and the corresponding concrete wall thicknesses. The calculated thickness of the walls for fallout radiation protection is about 1.10 m of ordinary concrete with density of 2340 kg/m3.

3.4 Recommended Thickness of the Wall of a Nuclear Shelter.

Based on the results of the evaluation of the shield thickness against fission neutrons, initial (fission and secondary) gamma rays, and fallout radiation, the most conservative value of 1.70 m of barite concrete with a density of 3420 kg/m3 is recommended, calculated for fission gamma rays for a 1000 kT fission bomb yield at a distance of 914.4 m (1000 yd.).

Manually operated shelter ventilation systems must be installed to protect against internal exposure from fallout radiation. Shelter wall openings must be accordingly shielded, for example, with armored doors, labyrinths, movable screens, etc. The provisions, water, air, etc. shall be ensured at least for the first two weeks for the time until the fallout radiation is reduced naturally or by organizational actions.

Nomenclature

B =

buildup factor

Bconcr =

buildup factor for concrete

Bsoil =

buildup factor for soil

D =

dose in front of the shield, Sv

DC =

dose criterion, Sv

Dconcr =

dose behind the concrete shield, Sv

Dsoil =

dose behind the soil shield, Sv

DTF =

dose transmission factor

DTF0 =

empirical DTF

DTF1 =

requested DTF

E =

neutron or photon energy, J

f =

factor of change in the relaxation length

L =

relaxation length, m

mfp =

mean-free-path, m

N0 =

number of the emitted fast neutrons

r =

distance, m

t =

time, s

x =

shield thickness, m

xconcr =

thickness of the concrete shield, m

xsoil =

thickness of the soil shield, m

Y =

bomb yield, kg

Z =

represents the relationship between two DTfs

Greek Symbols
μ =

linear attenuation coefficient, m–1

μconcr =

linear attenuation coefficient for concrete, m–1

μsoil =

linear attenuation coefficient for soil, m–1

ρ =

density, kg/m3

Φ =

neutron fluence, Neutrons/m2 s

Subscripts
concr =

concrete shield

i =

distance index

j =

bomb yield index

soil =

soil shield

Abbreviations
concr =

concrete

DC =

dose criterion

DTF =

dose transmission factor

ft. =

feet

in. =

inch

kT =

Kiloton (1,000,000 kg TNT)

MCNP code =

Monte Carlo N-particle transport code

mfp =

mean-free-path

soil =

soil

yd. =

yard

References

1.
Glasstone
,
S.
, and
Dolan
,
P. J.
,
1977
,
The Effects of Nuclear Weapons
, 3rd ed.,
United States Department of Defense and United States Department of Energy
, p.
660
.
2.
McAlister
,
D. R.
,
2016
, “
Neutron Shielding Materials, Revision 2.1
,”
PG Research Foundation, Inc.
, Lisle, IL, p.
14
.
3.
Thomas
,
R. H.
, and
Zeman
,
G. H.
,
2001
, “
Fluence to Dose Equivalent Conversion Coefficients for Evaluation of Accelerator Radiation Environments
,”
Ernest Orlando Lawrence Berkeley National Laboratory
,
Berkeley, CA
, p.
19
.
4.
Abbott
,
L. S.
,
1973
, “
Shielding Against Initial Radiations From Nuclear Weapons
,”
Oak Ridge National Laboratory
, Oak Ridge, TN, p.
182
.
5.
Faw
,
R. E.
, and
Shultis
,
J. K.
,
2003
, “
Radiation Sources, Encyclopedia of Physical Science and Technology
,”
Chapter III.A Fission Neutrons
, 3rd ed.,
Academic Press
,
New York
, pp.
613
–
631
.
6.
Kozlov
,
V. F.
,
1999
,
Handbook on Radiation Safety
,
Energoatomizdat
,
Moscow, Russia
, p.
514
.
7.
Stapleton
,
G. B.
,
O'Brien
,
K.
, and
Thomas
,
R. H.
,
1994
, “
Accelerator Skyshine: Tyger, Tyger, Burning Bright, Gordon & Breach Science Publishers, S. A
,”
Particle Accel.
, Malaysia,
44
(
1
), pp.
1
–
15
.
8.
Gong
,
J. J.
,
Zhang
,
L.
,
Jia
,
M. C.
,
Xia
,
W. M.
, and
Chen
,
J. J.
,
2018
, “
Study on Neutron and Photon Shielding Properties of Various Concretes Using MCNP Code
,”
IOP Conf. Ser. Earth Environ. Sci.
,
199
, p.
032056
.10.1088/1755-1315/199/3/032056
Google Scholar
Crossref
Search ADS
 
9.
1983
, “
Österreichischen Verbandes Für Strahlenschutz, ÖVS - Mittailung 1
,”
Schutz der Bevölkerung vor der Strahlenwirkung von Kernwaffen
,
Austria
, p.
98
.
10.
Isman
,
M. T.
,
Supriatni
,
E.
, and
Binowo
,
T.
,
2002
, “
Build-Up Factor Calculation for Ordinary Concrete, Baryte Concrete and Blast-Furnace Slugges Concrete as γ Radiation Shielding
,” IAEA-INIS, Yogyakarta, Indonesia, Reference Number 44003630, p.
5
.
11.
Kiyani
,
A.
,
Karami
,
A. A.
,
Bahiraee
,
M.
, and
Moghadamian
,
H.
,
2013
, “
Calculation of Gamma Buildup Factors for Point Sources
,”
Adv. Mater. Res.
,
2
(
2
), pp.
93
–
98
.10.12989/amr.2013.2.2.093
Google Scholar
Crossref
Search ADS
 
12.
Al-Maliky
,
S. J.
,
2008
, “
Basic Concepts for the Design of Nuclear Shelters and the Calculation of Wall Thickness Against a Nuclear Explosion of 20 kT
,”
J. Eng. Develop.
,
12
(
2
), p.
17
.https://jeasd.uomustansiriyah.edu.iq/index.php/jeasd/article/view/1659/1319
13.
Kearny
,
C. H.
, Updated and Expanded
1987
, “
Nuclear War Survival Skills
,”
Oregon Institute of Science and Medicine Cave Junction
,
Cave Junction, OR
, p.
510
.
Copyright © 2024 by ASME