Libi ary, N.W. Fldg

NBS MONOGRAPH 76

An Engineering Method for Calculating

Protection Afforded by Structures

Against Fallout Radiation

/^^^^\

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
1
UNITED STATES DEPARTMENT OF COMMERCE • Luther H. Hodges, Secretary NATIONAL BUREAU OF STANDARDS • A. V. Astin, Director

An Engineering Method for Calculatin

Protection Afforded by Structures

Against Fallout Radiation

Charles Eisenhauer

National Bureau oF Standards Monograph 76

Issued July 2, 1964

For sale by the Superintendent of Documents, U.S. Government Printing Office Washington, D.C., 20402 - Price 20 cents
Library of Congress Catalog Card Number: 64-60024
Foreword

The problem of providing protection against the radiations generated by

nuclear weapons is of much concern to the Federal Government and to the people

of the United States. A great deal of effort and money is being spent currently

to analyze existing structures for shielding properties, and plans are being carried

forward to design and build shelters of many kinds.

The National Bureau of Standards has maintained a continuing research pro- gram directed toward the development of engineering data and methods basic

to the solution of these radiation shielding problems. Most of the work of the

past few years on this project has been concerned with gamma rays from radio- active fallout. This Monograph discusses the technical basis for the engineering

method currently used by the Office of Civil Defense to evaluate fallout protection in structures. Financial support for this project has come primarily from the Office of Civil Defense, the Defense Atomic Support Agency, both of the Department of Defense,

and the Bureau of Yards and Docks, Department of the Navy.

A. V. ASTIN, Director.

Ill
Contents

Page Foreword Ill

1. Introduction 1

2. Solid angle 2

3. Roof sources 3

3.1. Schematization 3

3.2. Angular distributions 5

4. Ground sources 5

4.1. Schematization 5

4.2. Barrier and geometry factors 6

4.3. Thin-walled structures 6

4.4. Thick-waUed structures 8

4.5. Walls of intermediate thickness 10

5. Skyshine. 10

6. Limited source areas 11

7. Point source 12

8. Interior partitions 12

9. Comparison with experiment 13

10. Conclusions 15

References 15

Bibliography 16

Appendix A 17

Curves from reference [1] 17

Appendix B 18

Charts from Engineering Manual 18

IV
An Engineering Method for Calculating Protection

Afforded by Structures Against Fallout Radiation

Charles Eisenhauer

This report is a discussion of the technical assumptions underlying the methods currently recom- mended by the Office of Civil Defense (OCD) for calculating protection afforded by structures against

fallout radiation. It discusses methods for calculating the contributions from radioactive sources on

the roof and on the ground surrounding a simple one-storied building. It shows in detail how each

technical chart in the OCD Professional Manual ' is derived from basic data on radiation penetration

developed by Dr. L. V. Spencer.^ Charts from the Professional ManusJ and relevant curves from

Spencer's work are included in this report in order to make it self-contained.

1. Introduction

A considerable effort has been made in the past

few years by the National Bureau of Standards and

the Office of Civil Defense to develop engineering

rules for calculating the protection afforded by

structures against fallout radiation. This effort has resulted in procedures which can be studied

at three different levels of complexity.

The primary calculations on the penetration of

fallout radiation are reported in an NBS Monograph by L. V. Spencer [1].^ It is written for the

physicist or nuclear engineer. It discusses solutions to certain ideahzed shielding configurations.

Although it indicates how protection in an actual

building might be calculated, it does not give any

detailed procedures for such calculations. Detailed procedures, based on [1], for calculation

of protection afforded by buildings have been

developed with the help of Neal FitzSimons of the

Office of Civil Defense. These procedures are reported in [2] which has been widely circulated in an Interim Edition and is due to be pubhshed

shortly. In this paper it will be referred to as the

"Engineering Manual". Due to their detailed nature these calculations are often time consuming.

It was therefore necessary to derive a simplified treatment which would be suitable for evaluating

protection in a survey of a very large number of

buildings. The procedures resulting from this simphfied treatment are reported in [3]. Although

this treatment retains the essential parameters of

the engineering method, it neglects the variation of

protection with such parameters as the height

above the floor. The protection factors predicted

by the simphfied method at a fixed height and a

central location are assumed to be representative

values for a given story of a structure.* This paper will concentrate on the procedures

described in the Engineering Manual [2]. The

purpose of the paper is to discuss the assumptions

and the reasoning by which the calculations de- scribed in the Engineering Manual were derived

' OCD Professional Manual PM 100-1: Design and Review of Structures for Protection from Fallout Gamma Radiation (in press).

^ L. V. Spencer, Structure Shielding against Fallout Radiation from Nuclear Weapons. NBS Mono. 42, June 1, 1962, U.S. Government Printing Office.

^ Figures in brackets indicate the literature references on page 15.

' Under Phase I of the National Fallout Shelter Survey, over 350,000 buildings were

evaluated by this simplified treatment [4].

from the basic data in [1]. The relevant curves from [1] are given in appendix A and the technical

charts from the Engineering Manual are given in appendix B. If the reader is interested in the

physical principles underlying the basic data he is referred to [1]; if he is interested in applying cal- culations to actual structures, he is referred to [2]. When referring to basic data, an attempt has been

made to preserve the nomenclature used by Spencer

[1]. In other cases the notation of the Engineering

Manual is used. The notation in equations involving both types of data may therefore be awkward at times.

Schematization has been a basic concept in the

development of procedures for calculating the pro- tection afforded by structures against fallout gamma

radiation. A schematized configuration is a simphfied version of an actual shielding configuration.

The configuration is simplified to make it amenable

to calculations, but the basic parameters which

determine its shielding properties are retained. In practice, the procedure is as follows: First,

calculations are made for simple, idealized struc- tures, as a function of parameters such as barrier

thickness. Rules are then given for determining

these parameters for complex structures. Finally, a complex building is treated by applying the cal- culations for the simple building having the same

set of parameters.

The schematized building considered in the de- velopment of the calculations described in this report is shown in figure 1. It is a cyHndrical

Figure 1. Schematized building.

1
pillbox, divided into horizontal layers, each of which

represents a story of the structure. Since most

buUdings of interest in shielding are several times

longer and wider than an average story height, the

radius of the cyhnder is several times greater than

the height of each layer. Each layer may contain

apertures of uniform size and location. This uni- formity is apt to be present in upper stories of actual

buildings, but not perhaps in the first story. Inter- actions of gamma rays with the air inside of the

building are neglected.

Radiation intensities in structures are calculated

in terms of a reduction factor. The reduction factor at any point is the ratio of the exposure dose

rate at that point to the exposure dose rate three

feet above an infinite plane isotropic source. The

source density is assumed to be the same in both

cases, and the detectors are assumed to be iso- tropic, that is, they respond to radiation with equal

efficiency in all directions.

A schematized version of the radiation field around a building is shown in figure 2. The radiation intensity at a detector is assumed to be the sum

of three components:

(1) Radiation which arrives at the detector from

sources on the roof.

(2) Radiation which reaches the detector from

sources on the ground outside. Of the radiation

which reaches the wall directly, without scattering

in the air, about 75 percent comes from sources which are within 100 ft of the wall. A scale of

100 ft in figure 2 has therefore been indicated as the

distance within which sources contribute significantly to the direct radiation incident on the wall.

(3) Radiation which arrives at the detector from

the upward hemisphere after scattering at least once in the air outside of the building. The contribution to this radiation from a circular annulus

of width Ap at radius p from the detector decreases

approximately exponentially as Ke^^^Ap, where K

is a constant and l/p,o is the mean free path in air.^ Since l/p,o is of the order of 500 ft, this radiation may

reach the structure after scattering at any point in

air within a hemisphere of radius of roughly 500 ft, as indicated in figure 2. This radiation is often re- ferred to as "skyshine".

''This exponential dependence has been verified for Cs-137 sources by C. E. Clifford

in Technical Memorandum No. 104 (unpublished). This work was a continuation of

the studies reported in item 17 of the bibliography.

Figure 2. Types of radiation sources.

Of course, actual buildings and their surroundings

are quite different from these schematizations.

Some of these schematizations will be justified in the course of this paper. The justification of the

others will depend on how useful they are in pre- dicting experimental results on actual buildings.

2. Solid Angle

One of the problems in relating actual buildings

to schematized buildings is how to relate buildings

of different shapes. For example, most of the cal- culations of [1] apply to circular disk sources, whereas most source areas encountered in practice

are rectangular. It is therefore necessary to decide

which circular disk calculation should be used, for example, for a given rectangular roof source. One

of the first prescriptions which may come to mind

is to equate the dose rate from roofs of equal areas. This is a poor technique when applied to gamma

radiation, however, because it weights distant source areas too heavily.

A better prescription is to equate surfaces on

the basis of the soHd angle fi subtended at the

detector by the surface. As discussed in [1] it is more convenient to work with the sohd angle

fraction: w = a/27r.

With this normahzation, the sohd angle fraction

subtended by a plane surface approaches unity as the detector approaches the surface. The sohd

angle fraction subtended by a plane surface S of

arbitrary shape is defined by

co = ~— \ d{cos d)dip

^TT Js where 6 is the polar angle relative to a fine normal

to the plane of the surface and (p is the corresponding azimuthal angle. However, the intensity / re- corded by a detector which responds with equal

efficiency in all directions is given by

1 =

j

gicos 6, ip)d{cos d)d(p

where gicos 6, tp) is the angular distribution of radiation flux at the detector, and S is the radiating

surface. If the angular distribution at the detector were isotropic (g=V) then the intensity received

from rectangular and circular surfaces subtending

the same sohd angle fraction would be exactly

equal. Theory indicates that angular distributions

of radiation, plotted against cos 6 tend to vary from

a distribution of ~ sec d which is peaked at cos d = 0 to a distribution of ~ cot d which is extremely

peaked at cos ^=1. The former is typical of distributions of direct radiation near a plane iso- tropic source, while the latter is typical of distribu- tions of scattered radiation near a point isotropic source. Most angular distributions wiU be between

these two extremes and therefore wiU be more

2
nearly isotropic. In these cases equating responses

from rectangular areas to calculated responses from

circular disks subtending the same soUd angle frac- tion will be a fairly good approximation. The solid angle fraction subtended by the circular disk of

figure 3 is

J cos 00 dicos 6)^1- cos 00 (disk) (1)

A detector inside of a structure is surrounded in general by not one, but at least six rectangular sur- faces. It is useful to relate structures of different

shape by a minimum number of parameters. In

the engineering method the detector response in a

rectangular parallelepiped whose ceiling subtends a

solid angle fraction of (Ou and whose floor subtends a soUd angle fraction of oj; is equated to a cyhndrical

story with the same soHd angle fractions subtended

at the detector, (see fig. 4). This procedure insures

that the four walls combined subtend the same soUd

angle in both structures. Use of the solid angle fraction as a parameter has

the additional advantage that the solid angle frac- tion subtended by a rectangle can be calculated

analytically. It is given by

a» =—tan ^

, = (rectangle) (2)

where e is the ratio of the half-width of the rectangle

to the half-length, and n is the perpendicular dis- tance from the detector to the plane of the rectangle

divided by the half-length of the rectangle, (see fig. 5). This expression is plotted as a series of contour

curves in figure B3, where the definitions of n and e are equivalent to those in figure 5. This expression for the sohd angle subtended by

a rectangle appears in equivalent form in earher

work on thermal radiation [5]. In that context it appears as the angle factor for the heat exchange

between a rectangular radiator and a small spherical

radiator. It has also appeared in problems in particle detection [6]. 3. Roof Sources

3.1. Schematization

The calculation of radiation dose from roof sources involves two main assumptions. In an

actual building there may be several floors and a

roof between sources and detector, as shown in figure 6. In general, these floors will be rectangular "plates". In the schematized version the barrier is uniformly distributed between sources and

detector with the condition that the total mass

thickness between sources and detector be the same

in both cases. The rectangular source distribution

is replaced by a circular disk source subtending

the same sohd angle at the detector. These two

assumptions will now be considered in greater

detail.

Figure 3. Circular disk radiator.

Figure 4. Upper and lower solid angledfractions in a rectangular parallelepiped and a right circular cylinder.

2_

'-ir Ton

Figure 5. Solid angle fraction subtended by a rectangle.

^ 1 psf

psf

x-jpsf

(b) SCHEMATIZED

Figure 6. Relation between an actual configuration and a

configuration schematized to compute radiation from roof

sources.

3
Spencer has calculated three cases relevant to the penetration of roof radiation. The first assumes

a circular disk source separated from a detector

by a medium uniformly distributed between source and detector. The second assumes the barrier

material concentrated at the source. The third assumes the barrier material concentrated at the

detector. Since, in most cases, such as the one shown in figure 6a, the barrier is concentrated

neither at the source nor the detector, the case

of the uniformly distributed barrier was chosen as the closest approximation to cases most commonly

occurring in practice.

It is difficult to estimate the error introduced

by this approximation. It is expected, however,

that the dose rate with several discrete barriers

should he somewhere within the range of dose

rates under the three ideahzed configurations dis- cussed above. The variation in dose rate for three

values of the mass thickness Xo and the sohd angle

fraction o) are shown in each column of table 1. The values were taken from figures 28.18, 28.19,

and 28.20 of [1]. The values for Xo = Om table 1 actually apply to ^o = 0.22 pounds per square foot

(psf) of concrete which is the equivalent of 3 ft of

air. The differences among the three methods at ^0 — 0 are due to differences in scattered radiation,

and result from the infinite medium schematization which Spencer used to approximate the three

cases, (see page 30 of [1] for further details). From

table 1 it can be seen that the variation among the

three methods is greatest for thin barriers, amounting to about 40 percent. This would therefore be

expected to be the maximum error introduced by

approximating a series of discrete barriers by a uniformly distributed barrier equal to their total mass thickness.

An additional error is introduced by the approximation of replacing a rectangular source area by a

circular disk. The approximation may be written as

I

g(cos d)d{cos 6) „

5 ^TT J cos gicos d)d{cos d) (3)

where S here indicates integration over the rec- tangle. The value of cos do on the right-hand side

of the equation is determined from the condition

that the sohd angle fraction subtended by the two

surfaces be equal:

j

^ d{cos d)=\

J cos 6n J i dicose)=\ dicosO)^

S ^TT

(4)

Table I. — Comparative dose rates for three barrier configurations

0 psf X = 50 psf = 100 psf

(u = 0.05 0.1 0.5 0.05 0.1 0.5 0.05 0.1 0.5

Uniformly

distrib- uted

barrier 0.0090 0.019 0.12 0.0058 0.011 0.058 0.0026 0.004S 0.017

Barrier at source .013 .027 .16 .0050 .010 .045 .0018 .0036 .012 Barrier at detector... .011 .022 .15 .0055 .010 .050 .0022 .0040 .015

^ <

I I

Figure 7. Approximation of a rectangle by circular annuli.

or 1 — cos 00 — o>o- The value of Wo for the rectangle may be deter- mined from eq (2) of section 2. The error in dose rate due to approximating a rectangle by a circular disk therefore depends on

the form of g(cos 6). If the angular distribution is isotropic (i.e., gtcos d) ~ 1) the condition described

by eq (4) implies that eq (3) is exactly true. The

maximum error can be estimated by examining two

extreme distributions, namely

and

g (cos ff) = sec 6

g (cos 6) = cot 6. The error in each case can be estimated by suc- cessively approximating a rectangle by an increasing

number of circular sectors as shown in figure 7. As the number of circular sections increase the dose

rate calculated by the use of circular sectors should

approach the true dose rate from the rectangular

source. For details of this procedure, see [1]. Dose rates were calculated for the three circular- sector approximations shown in figure 7. The

fairly extreme case of a rectangle whose length is five times its width was considered and results were

calculated for the values n = 0.2 and « = The

results are shown in table 2.

Table 2. — Comparative dose rates due to approximating a

rectangular source by circular sectors

(e = 0.2) 1 sector 2 sectors 3 sectors

n = 0.2 g'=sec B 0.669 0.824 0.791 n = 0.2 g=coie .859 .821 .825 n=1.0 g=sec 0 .0928 .1038 .1016 n= 1.0 g = cote .411 .329 .340

4
Assuming that the values in the final column are

close to the true values, which would be obtained

by integrating over the rectangle, the possible

errors due to approximating a 1:5 rectangle by a

circular disk (one sector) could be at most 25

percent. When the detector is close to the source

(n = 0.2) the relative error is greatest for diffuse

angular distribution, g=sec 6; when the detector

is farther out, the relative error is greatest for the

peaked distribution, g= cot 6. Most cases of practical interest will generally have much smaller errors because rectangular roofs are usually less eccentric

and angular distributions he between the two

extremes. These errors, then, are inherent in the use of calculations for circular roof sources and barriers uniformly distributed between roof

and detector.

3.2. Angular Distributions

Let us now discuss the basic angular distribution

data from which the calculations were derived.

The angular distributions at a height above an

infinite plane isotropic source are given in figure Al.

In figure Al, 6 is the polar angle between the

direction of the radiation and the upward normal

to the plane. The ordinate at cos 6 = 1 corresponds

to radiation reaching the detector from below,

that at cos 6 = 0 corresponds to the radiation in- tensity from the horizon, and that at cos0 = —

corresponds to the radiation intensity from the

zenith. The most significant feature of these curves

is the gradual transition from a distribution for small

heights which is sharply peaked at the horizon, to a

distribution at great heights which is peaked in the direction of the source. For cos 6 > 0.2, the

uppermost curve varies approximately as sec 6

and represents the extreme example of diffuseness

referred to earher.

The response to radiation from aU directions

by a detector at height d above an infinite plane

isotropic source is given by the integral over the

appropriate curve in figure Al. These curves are normahzed so that the integrals yield reduction

factors. The reduction factor as a function of

height in air is shown in figure A2.

Since the attenuation properties of air and concrete are very similar [1], the parameter d in figure A2 can be converted to the thickness X

of a concrete barrier by means of the relation:

Z(psf of concrete) = 0.075 c?(feet of air)

This relation is approximately vahd for other

hght construction materials but does not apply

to iron or lead. Furthermore, if X is interpreted as the depth below, rather than the height above

the source, then the new curve represents the re- duction factor beneath a roof barrier of thickness

X which is covered by an infinite plane isotropic source. This curve is given as case 1 in figure Bl.

The next problem is to calculate the dose rate from source areas of finite extent. Consider the

dose rate from a finite circular disk source. It

is well known that the dose rate beneath the center

of a circular clearing in an infinite plane isotropic source depends only on the slant distance D to the nearest source, provided the source and detector

are in an infinite homogeneous medium. If the

detector is at a depth X, then the slant radius is given by

D=Xsec 6o=Xlil-(o)

where a> is the sohd angle fraction subtended at the detector by the clearing and 6o is the angle

between the slant radius and the normal to the

plane. If L{X) is the dose rate at a depth X from

an infinite plane isotropic source, then the dose

rate beneath the center of the clearing is given by

RiX) = L[XI{l-oj)] (clearing) (5) and the dose rate beneath a circular disk source is

R{X) = L[X]-L[XI{l-w)] (disk source) (6) Contour curves of the latter function are pre- sented in figure B4, which was derived from figure

28.18 of [1]. The intersection of these contour

curves with the Xo = 0 psf axis give the reduction

factor for a roof source subtending a solid angle

fraction w with no mass thickness between source and detector. Here again "no mass thickness" means Zo = 0.22 psf (3 ft of air), so that as o) ap- proaches unity, the reduction factor approaches

unity. The curve for Xo = 0 is shown as case 1 in figure BIO.

4. Ground Sources

4.1. Schematization

The calculation of radiation from sources on the

ground surrounding a building is considerably more

complicated than the calculation of radiation from

roof sources. The basic difficulty is that the radiation from ground sources must penetrate a barrier

which is perpendicular to the plane of the source

material. Thus, there are two possible reference

directions, namely, the direction normal to the source plane and the direction normal to the barrier.

If the latter is chosen as the reference direction, and

a detector location opposite the center of a rectan- gular waU is considered, the detector may be chosen

as the origin of coordinates and the line through the

detector and perpendicular to the barrier may be

chosen as the polar axis. But, then, the angular

distribution of radiation emerging from the wall is no

longer azimuthaUy symmetric about a fine perpendicular to the wall as it was in the case of radiation

from the roof. For example, more radiation arrives

from below the detector than from above it. Fur- thermore, walls are often about 10 ft high per story,

but over 50 ft long. Thus, it is inaccurate to approx- imate these highly eccentric rectangles by circular

disks. Since there is at present no information on

responses from highly eccentric rectangles radiating

with anisotropic azimuthal angular distributions, aU

angular distributions are referred to the (vertical)

direction normal to the source plane. 5
4.2. Barrier and Geometry Factors

If a source and detector are separated by a barrier

and the detector is located some distance from the

barrier it is sometimes convenient to separate the

expression for the radiation intensity into two factors. The first factor, the barrier factor, depends only on

the mass thickness, while the second factor, the

geometry factor, depends primarily on the soUd

angle fraction subtended by the barrier and only

weakly on the mass thickness. The geometry

factor is a measure of the effect of tlie Umited sohd

angle subtended by the radiating barrier. The

concept of a geometry factor appears in other engineering disciphnes such as heat exchange between

rectangular radiation [5], particle detection [6], and

illuminating engineering [7]. The separation can be derived mathematically as

follows: Consider an angular distribution g{X, cos 6) emerging from a circular slab of thickness X and

rewrite g as

g{X, cos 0) =

I j'giX, cos e)d (cos 0)|

X i^giX, cos 6)1 j

'giX, cos d)d (cos 0)|

or

g(X, cos 6) = B{X)g'{X, cos 6)

where B and g' are condensed notations for the

first and second factors, respectively. From the

definition of g' it can be seen

\ g'iX, cos 6) dicosd)=l.

Jo The dose rate at a detector located some distance

from a circular disk may be expressed as B=\ giX, cos 6) d (cos 6)

J cos 9o = B{X) I

' g'{X, cos 0) rf(cos 61) = B(X)G{X, oj) (7) J (l-cu) where do is the maximum polar angle subtended

by the disk, as shown in figure 3. The factors

B{X) and G(X, (d) are, respectively, the barrier and

geometry factors. In discussing radiation from ground sources advantage wiU be taken of this separation because

the barrier factor has been calculated by Spencer

but the geometry factor must be estimated. In discussing radiation from roof sources this separation is not necessary since Spencer has calculated

the combined results of barrier and geometry

directly.

4.3. Thin-Walled Structures

Consider first the case of an isolated story with no walls {Xu, = 0 psf) and infinitely thick floor and

ceiling, as shown in figure 8. If the detector

Figure 8. Idealized geometry for studying non-wall-scattered

radiation. plane is defined to be the horizontal plane passing

through the detector, then the upward normal to the detector plane is the axis for the polar angle

du and the downward normal is the axis for the

polar angle 6i. The response of the detector can be calculated

in terms of the curves of figure Al. First, the curve whose c?-value corresponds to the height of the

detector, measured in feet of air, is chosen. The

du and di of figure 8 are related to the 6 of figure

Al by:

cos 01 — cos 6, 0 ^ cos 6^1

cos du = I cos 6 \ , — 1 ^ cos 6^0.

Directional responses are then obtained by inte- grating over the curve between appropriate Umits.

When Xw = 0 psf the radiation reaches the detector

without scattering in the wall. This is referred to as non-wall-scattered radiation. This awkward

terminology arises because the radiation includes some air-scattered radiation and cannot therefore

be referred to simply as "direct" radiation. The

non-wall-scattered radiation reaching the detector

from below the detector plane is given by

r cos 0^

I lid, cos d)d{cos 6)

Gd(<oi, H) = Gdd - cos di, d) =q (8)

I l(d, cos d)d{cos 6)

The notation on the right-hand side of eq (8) is that of

[1]. The integrand l{d, cos 6) is the angular distri- bution at a height of d feet of air above a plane

isotropic source. Note that the denominator is equal to unity for d = 3 ft. Gd{(oi, 3 ft)^ is shown as the top curve in figure B5.

It is a measure of radiation arriving from directions

lying between the detector plane and the Umits of

the sohd angle fraction coi. It therefore decreases

with increasing W(. Curves for Gd for other values

oi d(= H) are shown in figure B6.

In a similar manner, the non-wall-scattered radia- tion reaching the detector from above the detector

'In [2] the subscript stands for "lower" and the subscript "d" stands for "direct". 6
plane is given by

Ga' (Oiu, d) — Ga' (1 — cos du, d) Co

I l{d, cos d)d {cos 6)

(9)

J

l{d, cos d)d (cos 6)

This response can be expressed as a combination of

functions which appear explicitly in [1]:

Ga'(cJu,d}=j^[l-Sa{d,<Ou)l (10)

where r+i

Lid) =

J

l{d, cos 0)c£(cos d)

S{d) = j'^ lid, cos d)d{cos d) and

Said, OJu)

lid, COS 6)dicos 6)1 1 lid, cos d)dicos 6)

Sid) shown in figure A3 and Said, (o) shown in figure

A4 are taken from figures 28.15 and 28.3, respectively, of [1]. Lid) is shown in figure A2.

In order to account for radiation scattered from

the ceihng a term was added to Gdiio, d). This

term was estimated using the following line of

reasoning. Consider a detector as in figure 9 which

receives radiation only from^ above the detector

plane. Let the skyshine contribution be called

Gioiu)- If the detector height is 3 ft, then

GidJu) = Ga'(aj, 3 ft).

Remembering that geometry factors for ground

sources increase with decreasing w, it can be seen

that Gioiu) increases as the size of the aperture

(1 — (Ou) increases. We would expect that the ceil- ing albedo would also vary as G(&>u) because it too

Figure 9. Idealized geometry illustrating typical trajectories for gamma rays due to skyshine and ceiling albedo.

must enter the structure through the apertures.

However, unhke the skyshine, the ceiling albedo

must approach zero as a>u approaches zero since the

scattering slab then subtends a vanishingly small

solid angle fraction. This indicates the presence of

another factor which was assumed to be

[G(0) - G(cu„)].

Therefore the combined skyshine and ceiling albedo

are given by

Gaioiu) = G(a)„) + kGi(x>u) [G(0) - G(a>„)] = G(co„){l + ^[G(0)-G(a>„)]}

To estimate the value of k, consider the Umit of

Gaidiu) as a>«-^ 1:

G„(a>„)^G(co„)[l + ^G(0)]

since G(l) < < G(0).

Now, by graphical or numerical integration of the

uppermost curve in figure Al over negative values of cos 6 it is found that G(0) = 0.1. Since there are no

experiments or calculations to shed any light on what value of k to choose, a value of ^ = 5 was arbitrarily chosen so that the asymptotic ratio of ceihng

albedo to skyshine as cuu—* 1 was taken to be ¥2. The final expression for the combined response to skyshine and ceihng albedo,

Gaioyu)-Gio>u) {1 + 5[0.1-G(a)„)]}, (11)

is given in figure B5.

The most serious shortcoming of this expression

is that it specifies no dependence on the position of

the sources. For example, most of the skyshine

contribution comes from sources which are farther

than ~ 100 ft from the structure, while most of the

ceihng albedo probably comes from sources within ~ 100 ft of the structure. When a structure receives radiation from an infinite field it is probably

sufficient to treat ceiling albedo as a correction

factor. However, when the contamination width is less than ~ 100 ft, it may be necessary to treat the

ceihng albedo as a fourth type of source, in addition

to the three types shown in figure 2. Since the variation of the skyshine angular dis- tribution with height is very small, as shown in figure A4, this variation has been neglected. A

chart for skyshine, analogous to the height variation

of Gd shown in figure B6, has therefore been omitted.

The basic curves of lid, cos 6) of [1] can also be

used to treat a circular aperture in the roof or in a

wall, when the detector lies on the axis of the aper- ture disk. The response from skyshine through a

circular aperture in the roof is given by

R =Sid)Said, (o) (Aperture in roof) (12)

where Sid) and Said, oj) are given in figures A3 and

A4. In evaluating the response from a circular skyhght no contribution from ceihng albedo is added.

7
The response R for a detector height of = 0 is plotted as case 3 in figure BIO.

The response from radiation through a circular

aperture in the wall is given by

r 1 [217 R = <i(cos ^) p(cos <p)dip / J cos ^0 0 ri f 277

J

c?(cos ^) j/)(cos ^, <p)c?<^

where p(cos ^, ip) is the angular distribution of

radiation arriving at the detector. The various

angles are shown in figure 10. In this figure, the

detector is located at the origin and the direction

of the radiation is indicated by the arrow. The

angles and (p are the polar and azimuthal angles

relative to the direction OZ, while 6 is the polar

angle relative to the direction OY. The angle 6

is related to ^ and (p by

cos 6 = sin ^ cos ip.

Substituting the distribution / for p:

(^(cos^) /(3 ft, sin ^ cos (p)d(p n — J cosl'o £0

fl f2n

J

c?(cos ^)

J

Z(3 ft, sin ^ cos (p)d<p

(Aperture in wall). (13) The denominator guarantees a response of one-half

for a detector located in the plane of the aperture at

its center point (cos = 0). The response R for an aperture in a wall is given in case 2 of figure BIO.

Note that no ceiling albedo has been added to this contribution.

If response from an isolated aperture which is nearly square or circular in shape and which is directly opposite the detector is required, then this approach should be used. If apertures exist in a rectangular ribbon around the structure then the

Figure 10. Coordinate systems relevant to an aperture in a

vertical wall. ^ and (f are the polar and azimuthal angles relative to the direction OZ. The angle B is the polar angle relative to the direction OY.

curves in figure B5 for non-wall-scattered radiation

should be used. If an aperture is at an eccentric

position, that is, if a line from the detector, perpendicular to the wall, does not intersect the aperture,

then the curves of figure B5 should be multiplied by

the fraction of the azimuth subtended by the

aperture.

4.4. Thick-Walled Structures

Consider now, the dose rate in a structure with

very thick walls. The word "thick" as used here is relative to a mean free path for radiation. For fall- out radiation a mean free path'^ is about 40 psf.

Therefore, a "thick" wall must be at least several

times 40 psf in thickness. In the case of thick

walls, assumptions have had to be made both about

the angular distribution and the absolute magnitude

of the radiation reaching the detector since neither

has been calculated precisely.

Consider first the polar angular distribution, rela- tive to the vertical direction, of radiation from thick

walls of a structure. It has been assumed that the

angular distribution is the same as that of the air- scattered radiation in a structure with walls of zero

thickness. This assumption might be justified on

the following grounds. Much of the air-scattered

radiation arises from the sources of the order of a mean free path away. Since the intervening air can

be imagined as a barrier similar to the actual wall

barrier, the angular distributions emerging from the

two barriers might be expected to resemble each

other. It was therefore assumed that the response

to skyshine,

G{(o) =

I

" /(3 ft, cos e)(i(cos d),

' cos So = - (1 - (o)

could be used to represent wall-scattered radiation

from both above and below the detector plane. It was assumed furthermore that if the solid angle subtended by the ceiling was equal to the solid angle

subtended by the floor then the response from below

the detector plane would be equal to that from above

the detector plane. This is equivalent to assuming

that the multiple scattering in a wall wiU tend to wash out the asymmetry in intensities from above

and below, which exists in the radiation incident on

the waU. When w = 0, the maximum response G(0)

either from below or from above the detector should

be obtained. Since this maximum response should

be one-half, G(0) must be multiplied by a constant k

such that

A;G(0) = V2.

SinceG(0) =

J"

l(d, cos d)d(co% 6)^0. \,k = ^. The

response to wall-scattered radiation Gs{(d), is there- fore given by

Gs{ai) = 51 Z(3 ft, cos e)d{co& 6). (14)

J -(l-o>)

' Strictly speaking, the mean free path is not defined for a spectrum, such as that from

fallout. However, the mean free path may be considered roughly as that distance in which the intensity of the direct radiation is reduced by a factor of e.

8
(a)

Figure 11(a). Detector located in a cylinder of infinite height.

(b). Detector located between two parallel walls of

infinite length and height. The curve for Gs{(o) is shown as the scattered case of

figure B5. Like Ga, it does not include any contribution from radiation scattered from the ceiling or floor of the structure. Assuming that the geometry factor is known, the

barrier factor B{X, h, p) for a right circular cyhnder

of infinite height, (aju = 0) must stiU be determined.

This barrier factor is a function of the height h of

the detector, and the radius p and the wall thickness

X of the cyhnder (figure 11a). The only barrier

factors that have been calculated, however, give

the dose rate between two infinitely high and wide

plane walls due to a semi-infinite source on each side

(figure lib). The necessity of using the latter barrier factor in a scheme involving cyhndrical

geometry constitutes a serious logical defect in the

approach used in the engineering method. As

pointed out earher, however, if a geometry based on

the orientation of the detector with respect to each

wall had been used, equally serious defects would be

present.

The barrier factor for a plane wall of infinite height and width is illustrated in figure 28.7 of [1]. The same curves multiphed by 2 and plotted in contours are shown in figure B2. The top curve of

figure 28.7 corresponding to a detector height of 3 ft is also shown as case 2 of figure Bl.

Spencer's original curve [1] comes into a value

greater than 0.5 at X = Q. The excess over 0.5 represents backscatter from the wall behind the

detector. In order to be consistent with a normalization of unity for a detector between two walls of zero thickness, the curve was lowered near X = 0

so that it came into 0.5. The entire curve was then

multiphed by 2 to obtain the curve in figure Bl.

Some correction must now be apphed to this barrier factor to account for the shape of the structure. Although the geometry factors for ground

sources are based on circular structures, they are apphed in most cases to rectangular structures. The correction for the shape of the structure is therefore derived in terms of rectangular structures,

first. The correction for a circular structure is then discussed as a hmiting case. Consider first the ratio of dose rates inside of two

infinitely high thick-walled buildings — one with four

walls of equal length (i.e., a square tower) and the

other with two infinitely long walls separated by a distance equal to the side of the square. In order to

Figure 12(a). Azimuthal angle (p for a rectangle.

(b). Azimuthal angle for a many-sided polygon.

calculate this ratio, an assumption must be made

concerning the distribution of radiation in the

azimuthal direction, about the vertical axis. Evidence from calculated angular distributions at great depths from a point isotropic source indicates

that the azimuthal distribution is not isotropic but more peaked in a direction normal to the wall. The azimuthal angular distribution p{<p) emerging

from each waU was assumed to be of the form

, , , cos (pd<p p{ip)dUp =

where if is measured relative to that azimuthal plane

which is perpendicular to the wall. Then, the

response in an infinitely high, thick-waUed rec- tangular structure (fig. 12a) whose length-to-width

ratio is LjW is obtained by summing over four walls:

4 r'Pi 4

/ = 1

•' ! = 1

sin (pi 2 + - r

2 IVlFTW^ VU+W^

E = {L + miV[JTW^=il + e)lVl + e^ (15)

with e = WjL. For a square building e = 1 and

E = V2, while for an infinitely long, narrow building

e^O and £"^1. The ratio of dose rates in the

two structures is therefore V2. The expression E,

known as the eccentricity factor, is shown in figure

B8.

The response in a circular structure is obtained

from the limit of the response in a many-sided

polygon shown in figure 12b:

R

N Sin (fi 2 = hm

77 sin^y

77N

'2

If the separation of the two walls in figure lib is 2p, then the dose rate in the configuration of figure

11a would be greater than that in configuration

lib by a factor of 77/2.

It has been assumed that this eccentricity factor can also be applied when the waUs are of finite height. There have not yet been any direct ex- perimental tests of the assumption. It is confirmed

only indirectly by the general agreement of experiments with the calculations.

9
4.5. Walls of Intermediate Thickness

The vast majority of structures has walls that are neither very thick nor very thin. In view of the

lack of data it was decided merely to take a weighted

ratio of the thick-wall geometry factor (eq (14)) and

the thin-wall geometry factors (eqs (8) and (11)), with the weighting factor Sw(X) assumed to be a function only of X:

where

and

G(0), X) — SM,(X)GThick + [1 ~~ Su;(X)]GThin

GTWck = [Gs(wO + G.(a)„)]^ (17)

GThin = Gd(a>0 + Ga(a)„). (18)

Strictly speaking, the weighting factor represents

the fraction of radiation reaching the detector which

has been scattered at least once in the walls. It, therefore, probably varies somewhat with cu, but

this effect has been ignored. The values of Sw{X) were determined from data on the perpendicular

incidence of Co 60 radiation. If Bp{X) is the buildup

factor for perpendicular incidence.

Su,{X)=^

Bp(X)-l

Bp{X)

A more appropriate choice might have been the

ratio of scattered-to-total radiation for a point iso- tropic fission product source. This can be deter- mined from figure 28.6 of [1]. It differs by less than 10 percent from the curve shown in figure B7.

Furthermore, the results are not very sensitive to the curve assumed for Sw{X) because the factors

Gxhick and GThin often differ by less than 50 percent

over a large range of w. This lack of sensitivity

suggests the possibihty of using some average

G{oi) for all wall thicknesses instead of distin- guishing between Gxhick and Grhin- Such a simplification, however, must await a more accurate determination of the geometry factors as a function

of solid angle and wall thickness.

The expression for the geometry factor for thin

walls given in eq (18) should really have an eccentricity factor, analogous to that in eq (17). This

factor would be unity for a circular structure and

approximately unity for a square structure. The

factor would decrease (as does the eccentricity

factor for scattered radiation) for more elongated

buildings whose floors subtend the same solid angle. It was not calculated because it was

thought that it would only be important in areas with low protection factors since the direct geometry

factor is important only for thin walls. There are some situations where this may not be true, however. For example, in buildings with very thick

walls and small apertures, the direct radiation may

make the dominant contribution in an otherwise

weU-protected location. The eccentricity factor

for direct radiation should probably be included

in those cases. It could be obtained as a function

of //, WIH, and LIH from the work of HubbeU [8],

» /,i

'^1

ACTUAL

Figure 13(a). Actual configuration for penetration of skyshine

through a basement ceiling.

SCHEMATIZED

Figure 13(b). Schematized configuration for penetration of sky- shine through a basement ceiling.

Figure 14. Schematized geometryfor skyshine through apertures, showing the two relevant solid angle fractions. H being the detector height, W the width of the

building, and L the length of the building.

5. Skyshine

As indicated in figure 2, skyshine arises from

radiation which originates from sources on the

ground and roof and arrives from above the detector

after undergoing one or more scatterings in the

volume of air surrounding the structure. Skyshine may make an important contribution

whenever a detector is well shielded from direct

radiation. Two cases of importance are a detector

located in a basement covered by a relatively

heavy slab, but with an otherwise Hght superstructure above it (fig. 13a), and a detector located

below siU level in a structure with heavy walls and

floors (fig. 14). Consider first the penetration of skyshine through

a slab over a basement. Spencer has calculated the

intensity of radiation behind a barrier located in the negative half-space due to radiation originally

emitted into the positive half-space. This configuration is shown in figure 13b. The corresponding barrier curve is given as case 3 in figure Bl.

The situation in figure 13b differs from that in 13a in that 13b contains an infinite plane source

while 13a contains a clearing surrounded by walls. 10
Some unpublished calculations by Spencer in- dicate that the penetration of radiation to a detector

beneath a clearing without walls is similar to the

situation in 13b provided the radius of the clearing

is small compared to the mean-free-path in the backscattering medium (~ 500 ft in air). Most buildings

satisfy this criterion. However, the presence of the walls may distort the angular distribution of

radiation incident on the clearing from overhead.

In particular, the strong component at grazing

incidence which is present in configuration 13b,

and which affects the shape of the barrier curve, may be considerably suppressed in configuration

13a. For lack of any more precise data, however,

the two configurations have been assumed to be

equivalent.

Consider next the skyshine radiation through

apertures in a building with thick walls (see fig. 14). This is merely a special case of non-waUscattered radiation received from above the detector.

However, the limits of the aperture define two

solid angles which both he above the detector.

Since the geometry curves of figure B5 give the

response to radiation arriving from all directions

between the horizontal and an arbitrary hmit,

the responses must be differenced when both Umits

are above (or below) the horizon. Therefore,

R = Ga{(Ou') — Ga{(Ou),

where (Ou and Wu are the sohd angle fractions

shown in figure 14.

6. Limited Source Areas

The barrier and geometry factors developed in the preceding sections enable one to calculate the

reduction factor in an isolated structure located in an infinite field of fallout radiation sources. In many cases of practical interest, however, buildings

are surrounded by a series of finite rectangular source areas. It is therefore necessary to calculate

reduction factors for such sources. A solution for a rectangular source area can be

obtained by applying a correction to the infinite plane result or by integrating over results for point sources arranged in a rectangular array. The

former approach has been taken primarily because

barrier and geometry factors for radiation incident on a wall from point sources on the ground have

not yet been calculated. It is possible, however,

that in solutions for small areas (i.e., when the width

of the strip is equal to or less than the height of the

detector above the strip) the small areas should

eventually be treated as a collection of point sources. The basic assumption made in treating finite rectangular sources is that non-waU-scattered and

wall-scattered radiation must be treated differ- ently. Non-wall-scattered radiation in a structure such as shown in figure 15, upper left, wiU depend

on the solid angle o) subtended by the source area,

at the detector position, since it is composed

mainly of radiation which travels directly from

source to detector. In the case of waU-scattered

radiation, however, the wall acts as a secondary

source. The radiation impinging on the wall

depends on the soUd angle fraction 0)2 (figure 15,

lower right), subtended at the center of the waU

by the source area. The radiation scattered in the wall and reaching detector D depends on the

sohd angle fraction wi subtended at D by the

wall. Thus, the wall-scattered radiation depends

on two sohd angles. In calculating the barrier factor for non-waUscattered radiation from a rectangular source, case 2 of figure Bl is used just as for the infinite plane source. However, the geometry factor is obtained from figure B6 by differencing between

the response for the outer dimensions of the source

area and the response for the inner dimensions:

AG(/ = Gd{(t)i, H) — Gdicoo, H),

where w, is the sohd angle fraction subtended at the

detector by the inner dimensions of the annulus and

(tJo is the soHd angle fraction subtended by the outer dimensions. Notice that in calculating this geometry factor the source is considered as an annulus

surrounding the building. As the strip approaches

an infinite field, wo ~^ 1, Gd{(Oo, H) 0, and the dif- ference reduces to the usual single term for an

infinite source. Since the geometry factor takes

into account the variations in source geometry, the

barrier factor is assumed for convenience to be

independent of source geometry.

In calculating the contribution from waU-scattered

radiation, the Gs curve of figure B5 is used for the

geometry factor since the geometry factor for waUscattered radiation is assumed to be independent of

the source geometry. This assumption was made

because of the lack of any data in this area. The

barrier factor for waU-scattered radiation from

finite sources shown in figure B9 was based on unpubhshed calculations of Spencer, in which he

Figure 15. Solid angles related to radiation received from a

finite source of contamination. Direct radiation {upper left) and wall- scattered radiation {tower right).

11
calculated the dose rate behind a waU due to direct

radiation from semicircular sources. These semicircles were concentric about a point at the base of

the wall directly below the center of the wall as shown in the right-hand diagram of figure 16. The

results are a function of the wall thickness and the

solid angle fraction cos/2 subtended by the source. When the radius p of the semicircle is equal to or

less than the detector height, the barrier factor is extremely sensitive to the value of (Og. It was necessary to define a relationship between

the sohd angles of the semicircles for which results were calculated and the sohd angles of the rectangular sources encountered in practice (see figure 16). This relationship was set up to preserve the sohd

angle subtended at a detector point on the wall:

2 e Ws = (1 — cos 0) = - tan"' , =

+ + 1

with 6, n, e defined in figure 16. The calculation of waU-scattered radiation from

finite sources must be calculated for each wall. When the sources he on more than one side of the

building as in figure 15 there is some ambiguity in defining the strip length L indicated in figure 16. The only guiding rule that can be given is to divide

the rectangular annulus arbitrarily so that each

partial area contributes to one side orly. It is true

that, in reahty, sources lying on the comer areas may

contribute through both walls. However, this effect

is already taken into account by the eccentricity

factor. In fact, recognizing that some sources contribute through more than one wall is an alternate

way of justifying the introduction of an eccentricity

factor.^

7. Point Source

The penetration of radiation from a localized source can be approximated by penetration of

radiation from a point source if it is far enough

away so that it subtends a small sohd angle at the

^ From this viewpoint, the dose rate at the detector is regarded as a sum of contributions from each source. The shape of the structure influences the relative contribution of each source. The viewpoint taken in sec. 4.4 is that the dose rate is a sum of photons arriving at the detector. The shape of the structure influences the contribution from each direction.

Figure 16. Rectangular and semicircular sources adjoining a

vertical wall.

!

Figure 17. Localized source area A at a distance r from a

detector with intervening mass thickness X.

Source and detector are immersed in a homogeneous medium.

detector. Indeed, as was discussed in section 6, the results for point sources may eventually lead

to evaluation of radiation from small finite source

areas. The attenuation of radiation from a localized source through an absorber thickness X is given as the curve P{X) in figure 28.5b of [1]. The configuration to which the curve apphes is shown in figure

17 of this report. The curve is related to the reduction factor Rf from a plane source by the expression

Rf— ^^^ Reference [1]

where A is the area of the locahzed source and r

is the distance from source to detector. If one in- tegrated over a large number of small patches

covering a plane, the integrated dose at a detector

3 ft in air above the plane would be unity. Thus,

the above expression yields a true reduction factor. The curve has been replotted in figure Bll and

normahzed to unity. If the curve from figure Bll,

denoted by Ps{Xw) in [2], is used for a locahzed plane

patch of sources and a reduction factor is desired,

then „ QMPs(Xu,)A „ f Rf~ 2 Keierence [zj

8. Interior Partitions

Calculational procedures have now been de- veloped for building shells, with no internal structure except floors. Although the effect of interior partitions may be regarded from the standpoint of calculations as a correction factor, in practice it may well

introduce factors of two or more in protection.

Consider first the penetration of radiation from

roof sources through interior walls (see inset dia- gram of fig. B12). In the interim edition of [2] it was recommended that the barrier curves illus- trated in figure B2 be used to calculate the penetration through interior walls. The procedure was

to convert the roof thickness in psf to feet of air and

to use this value for the height above the plane

when reading values from the chart. The justifica- tion for this procedure was that the angular and

energy distribution of radiation emerging from the

underside of the ceihng was approximately equal

to that at a corresponding height in air above a plane

12
isotropic source and should therefore penetrate a

vertical waU with the same efficiency. The barrier curve Bi for an interior wall of thickness Xi was

normalized by expressing it as a ratio ^

BiXu H)

B(X, H) being obtained from figure B2. It was

found, however, that the curves for B, were not

ver\" sensitive to the value of the roof thickness

Xo. particularly for values of greater than 10

psf. Accordingly, the curve for X(j = oQ psf was

chosen as a representative value and is reproduced

in figure B12.

Consider next the penetration of radiation from

ground sources through interior partitions. When

the calculational procedures were developed there

existed \'irtually no calculations or experiments

to serve as a guide in the treatment of interior partitions. The recommended procedure was to multiply by a barrier factor equal to that for an

exterior wall of the same mass thick^iess (case 2. figure Bll. Assuming that this procedure is vahd,

it is an unambiguous recommendation for structures whose interior partitions resemble those in figure

18a. However, for the structure of figure 18b and

the fairly common one shown in figure 18c, the

reader is forced to use his own judgment. These

problems can be handled by di\ading the building

into several azimuthal sectors centered on the

detector. Although the number and thickness of

partitions lying between the detector and the source can then be specified, the appUcable barrier and

geometr>" factors remain amhiguous. The present

recommendations for treating the structure of

figure 18b are to consider the contribution wall

by wall, including the interior barrier factor only

for the w£dl on the right. The structure of figure

18c may be treated by first folding the transverse

walls into the main corridor wall and then assuming

interior partitions of effective mass thickness

iXi^kXi') surrounding the detector. As a first approximation k may be set equal to unit>', but we

do not really know how^ effective these transverse

partitions are in shielding a detector in the central

corridor. Prehminar\" experiments on model

structures by Technical Operations, Inc., [12] indi- cate that this approach is reasonable, but that k

should be set equal to 1/2. 9. Comparison with Experiment

In developing the calculations discussed in this report, an attempt was made to consider all experimental data available. Although experiments are

not without ambiguities, they have pointed out some

of the weak points in the present calculations.

Since a careful analysis of all the experimental

data has not yet been made, only those experiments

which seem to indicate the msdn areas where re- visions in the calculations are necessary' will be

quoted. Unfortunately, the experiments do not always indicate in precisely what manner the

calculations ought to be changed.

Figure 18. Three possible configurations for interior partitions.

Experiments [9, 10] on a square concrete blockhouse at the ^Army Chemical Center in Edgewood,

Md., provided, for a long time, the only experimental data with which calculations could be

compared. As shown in tables 3 and 4, agreement

between experiment and calculations is generally

about 20 percent for Co 60 radiation and 40 percent

for Cs 137 radiation. Since the geometry factors

for the blockhouse were close to unity these ex- periments did not provide a sensitive test of the

calculations.

More recent experiments by Technical Operations, Inc., [11] on a steel model of a six-story

building provide a more sensitive test of geometry

factor. In analyzing their experiments, however,

two assumptions must be made. It must be as- sumed that experimental results on a model whose

Tart f 3ei. —Reduction factors for roof sources, Co 60 source [9]

Detector height H= Q ft H= 3ft H = 6k

Roof thickness Exp. Calc. Exp. Calc. Exp. Calc.

psf

3.03

17.1 31.7

42.1

50.1

0.069

.058

.043

.032

.027

0.050

.044

.035 .030

.025

0.113

.090

.061 .044

.037

0.095

.080

.060

.050

.042

0.241

.041

.092 .064

.053

0.22

.16 .105

.080

.065

Table 3b. — Reduction factors for roof sources, Cs 137 source [9]

Detector height H = 0 ft H = 3 ft H=6h

Roof thickness Exp. Calc. Exp. Calc. Exp. Calc.

psf

3.03

17.1 31.7

42.1

50.1

0.071

.052

.032

.022

.020

0.050

.043

.034

.026

.023

0.114

.079

.046

.030

.027

0.095

.080

.056

.045

.035

0.23

.124

.065

.038

.036

0.21

.16 .090

.065 .050

13
Table /isi.— Reduction factors for ground sources, Co 60

source [10]

Detector height H = Oh // = 3 ft H = 6 ft

Wall thickness X

Exp. Calc. Exp. Calc. Exp. Calc.

psf «

94

139

0.22

.071 .022

0.128(0.226)*

.051( .071)*

.019( .024)*

0.28

.10 .033

0.302

.103 .036

0.26

.096

.029

0.260

.080

.035

Table '^h.— Reduction factors for ground sources, Cs 137

source [10]

Detector height ff = Oft // = 3 ft W = 6 ft

Wall thickness X

Exp. Calc. Exp. Calc. Exp. Calc.

psf 48

94

139

0.13

.035 .0085

0.097 (0.169)* .029 ( .041)*

.0067< .0086)*

0.20

.050

.011

0.227

.059 .0128

0.18

.046 .0097

0.186

.046 .0104 'Numbers in parentheses include tlirect radiation. The amount of direct radiation included in the experimental results for // = 0 is uncertain.

dimensions are scaled down by a ratio of 12 to 1 are applicable to a fuU size structure. This is expected to be valid provided that the room dimensions in the model are at least ten times the waU

thickness in the model. This condition v\ras satis- fied by the models used in the Technical Operations, Inc., experiments. It must also be assumed

that steel and concrete have the same barrier factors for equal weights per unit area of barrier thick- ness. Spencer has shown that the barrier factors are approximately equal for perpendicular inci- dence ^ but this equality has not been demonstrated

for other angles of incidence.

The main purpose of the experiment performed

by Technical Operations, Inc., on the multistory

steel model, was to test calculations for rectangular source annuh surrounding a structure. The measurements, however, included the case of an infinite

field. Table 5 gives the reduction factors at three

heights on six stories of two different models of structures surrounded by an infinite field of contamination. The upper tabulation apphes to a

structure with floors of two inches of iron (80 psf)

and walls of V2 in. of iron (20 psf). The lower tabulation applies to a structure with floors and walls of

80 psf. The experimental values are taken from

[11] but the calculated values are those of the

author. The experimental dose rates increase more rapidly with height above the floor than pre- dicted by the calculations. This may indicate that the scattered radiation emerging from the walls is not symmetrical with respect to the horizontal, but

is more peaked in the upward direction. This in turn suggests that the geometry curve for wall- scattered radiation from the lower hemisphere

should be different from that for the upper

hemisphere.

Table ^. — Reduction factors in T/O multistory steel model [11]

Thickness of walls = 20 psf Thickness of floors = 80 psf

Detector

height H = 3h H = 6 ft H = 9 ft above noor

Stotory Exp. Calc. Exp. Calc. Exp. Calc.

1 0.36 0.38 0.36 0.38 0.35 0.35

2 .19 .26 .24 .28 .27 .28 3 .12 .194 .19 .22 .22 .22 4 .096 .154 .15 .176 .18 .179 5 .068 .124 .12 .146 .16 .145 6 .054 .102 .11 .119 .14 .117

Thickness of walls and floors = 80 psf

Detector

height H = 2.5 ft H = 5 ft ff = 7.5ft above floor

Story Exp. Calc. Exp. Calc. Exp. Calc.

1 0.098 0.072 0.107 0.075 0.098 0.067

2 .051 .048 .062 .054 .067 .049 3 .040 .037 .050 .042 .055 .039 4 .043 .030 .036 .034 .050 .032

5 .025 .024 .035 .028 .038 .026 6 .021 .020 .032 .023 .037 .022

Reduction factors for finite rectangular annuh

surrounding the Technical Operations model are shown in figures 19 and 20. Results are plotted

against the ratio of the width of the annulus to the

height of the detector above the source. Comparison of the experimental and calculated results shows good agreement for both structures, except

for the first story. It should be borne in mind, however, that for the first story, values of WJH of less than 5 are not of much practical interest. The

curve in figure 19 indicates the experimentally

observed increase in dose rate when the floors of

the model are thin. The increase is due to penetration of radiation from stories below the one at which

"1 I I M L

X ZOpst FIRST STORY

SECOND STORY

THIRD STORY FOURTH STORY

FIFTH STORY

SIXTH STORY

FIRST STORY

SECOND STORY

THIRD STORY FOURTH STORY

FIFTH STORY

SIXTH STORY

I l_

CALCULATED -

EXPERIMENTAL

' See figure 22.1 of [1]. Since the curves of fig. 22.1 are plotted against mass thick- ness, the abscissa for steel should be multiplied by 1/0.93 to obtain a comparison on

the basis of weight per unit area.

Figure 19. Reduction factors for detectors at a height H in buildings surrounded by rectangular source annuli ofwidth WcWall thickness equals 20 psf, floor thickness equals 80 psf.

14
-Ill 1

1

1 11 11 1 1 1

1

1 1 1 . 1 ^ 1 1 !_ -

-

• :

-

° m -

- -

c ° »

V X • eopsi _ o FIRST story' I

-

A SECOND STORY

THIRD STORY

* FOURTH STORY CALCULATED -

-

* * FIFTH STORY

^ V SIXTH STORY -

-

• FIRST STORY

' » SECOND STORY

a THIRD STORY

o FOURTH STORY

4 FIFTH STORY

EXPERIMENTAL -

1 1 I

. SIXTH STORY

1 1

• 1 1 1

1

Figure 20. Reduction factors for detectors at a height H in buildings surrounded by rectangular source annuli ofwidth W^.

Wall thickness equals 80 psf, floor thickness equals 80 psf.

the detector is located. Such a large contribution

from lower stories cannot be obtained from the cal- culations recommended in [2].

It should be noted that these experiments .also yield data on finite rectangular source areas which

do not run the entire length of the building. The

present calculations do not expHcitly provide rules

for handling this situation, although many ap- proaches have been suggested during the OCD

courses at Fort Belvoir and other schools. When

completed, the experiments should be analyzed to determine what rules can be inferred for handling

such source areas. An early experiment [13] performed at the Army

Chemical Center by Technical Operations indicated

that calculated dose rates may be too low by a factor

of 2 in basements with no exposed walls. This dis- crepancy may be due in part to the inaccuracy of

the schematization of figure 13, as discussed in section 5. The more recent experiments by

Technical Operations on a six-story steel model

tend to confirm this discrepancy. However, ex- perimental dose rates in basements of scaled struc- tures are compUcated by the fact that the density of earth surrounding the basement is not properly

scaled. Experiments on complex office structures have

yielded dose rates which do not agree with calculations better than a factor of 2. For example,

experiments [14] on the AEC Headquarters building

in Germantown, Md., yielded dose rates which were

a factor of two or three lower than calculations

indicate. Due to the extremely heavy walls and

floors in this building, the predominant contribution

to the dose rate came from skyshine through the

windows of the building. The situation was further

complicated by the presence of an interior partition

configuration similar to figure 18c. The expeiiment

does not, therefore, indicate precisely what modifications should be made in the calculations.

10. Conclusions

The present engineering method gives detailed

procedures for calculating the relative amount of

protection from fallout radiation associated with a wide variety of shielding situations. Comparisons

with experimental information show fairly good

agreement for simple structures surrounded by an

infinite plane source. The agreement is less satis- factory, however, for more complex structures and

for source areas whose widths are comparable to the detector height. Nevertheless, the existence

of the engineering method has suggested experiments whose results, in turn, may be expected to modify the engineering procedures.

I wish to thank L. V. Spencer of the National

Bureau of Standards for his encouragement and

advice in the development of the Engineering

Method from his basic calculations, and Neal

FitzSimons of the Office of Civil Defense, Department of Defense, for the many conversations which

helped to develop and modify the calculational

procedures. Without their help this work could

not have been accomplished.

References

[1.] L. V. Spencer, Structure shielding against fallout radiation from nuclear weapons, NBS Mono. 42, June 1962 (U.S. Government Printing Office, Washington, D.C.).

[2.] OCD Professional Manual PM 100-1; Design and review

of structures for protection from fsdlout gamma radiation.

(In press).

[3.] Fallout Shelter Surveys: Guide for architects and engineers,

OCD Report NP-10-2, Office of Civil Defense, Washington, D.C.

[4.] L. V. Spencer and C. Eisenhauer, Calculation of protection

factors for the national fallout shelter survey (unpublished).

[5.] M. Jakob, Heat Transfer, Vol. II, John Wiley & Sons (1957).

[6.] F. S. Crawford, Jr., Sohd angles subtended by a finite rectangular counter, Rev. Sci. Inst. 24, 7 (1953).

[7.] W. B. Boast, Illuminating Engineering, 1st ed, McGraw HiU

Book Co., New York (1942).

[8.] J. H. Hubbell, R. L. Bach, and J. C. Lamkin, Radiation

field from a rectangular source, J. Reseeirch, NBS, 64C,

2, Apr-June 1960.

[9.] M. A. Schmoke and R. E. Rexroad, Attenuation of simulated

radiation by the roof of a concrete blockhouse, NDLTR-6, August 1961, U.S. Army Chemical Center, Edgewood, Md.

[10.] M. A. Schmoke and R. Rexroad, Attenuation of fallout radiation as a function of concrete blockhouse wall thickness, NDL-TR-43, October 1963, U.S. Army

Chemical Center, Edgewood, Md.

[11.] J. F. Batter et al., The effect of hmited strips of contamination on the dose rate in a multistory windowless building, TO-B 62-58, August 1962, Technical Operations, Inc., Burlington, Mass.

[12.] A. W. Starbird et al.. The effect of interior partitions on

the dose rate in a multistory windowless building, TO-B

63-6, January 1963, Technical Operations, Inc., Burlington, Mass.

[13.] J. F. Batter and A. W. Starbird, Attenuation of cobalt-60

radiation by a simple structure with a basement, TO—

B

61-38, July 1961, Technical Operations, Inc., Burlington, Mass.

[14.] J. F. Batter, A. Kaplan, and E. T. Clarke, An experimental

evaluation of the radiation protection afforded by a large modern concrete office building. May 1959, TO-B 59-5, Technical Operations, Inc., Burlington, Mass.

15
Bibliography

Experimental Data

1. J. F. Batter and A. W. Starbird, Attenuation of cobalt-60 by

a simple structure with a basement, TO-B 61-38, Technical

Operations, Inc., Burhngton, Mass., July 1961.

2. A. W. Starbird, J. F. Batter, and H. A. Melhorn, Modehng

techniques as apphed to fallout simulation on residential- type structures and some preliminary results, TO-B 61-35, Technical Operations, Inc., Burlington, Mass., July 1961.

3. J. F. Batter and A. W. Starbird, Attenuation of cobalt-60

radiation from a source distributed around a concrete

blockhouse, TO-B 61-34, Technical Operations, Inc., Burlington, Mass., June 1961.

4. C. W. Terrell and A. J. Jerri, Radiation streaming in shelter entranceways, ARF-1158A01-5, Armour Research Foundation of lUinois Institute of Technology, Chicago, lU., July 1961.

5. Z. Burson and H. BoreUa, Experimental evjJuation of the

radiation protection provided by the OCD region 3 demonstration shelter, CEP 60.6, Edgerton, Germeshausen, and

Grier, Santa Barbara, Cahf., April 1961.

6. Z. Burson, D. Parry, and H. BoreUa, Experimental evaluation

of the fallout radiation protection afforded by a typical southwestern residential home, Edgerton, Germeshausen,

and Grier, Inc., Santa Barbara, Calif., March 1961.

7. H. Borella, Z. Burson, and J. Jacovitch, Evaluation of the

fallout protection afforded by Brookhaven National Laboratory Medical Research Center, CEP 60.1, Edgerton,

Germeshausen, and Grier, Inc., Santa Barbara, Calif., Feb. 1961.

8. M. A. Schmoke and R. Rexroad, Attenuation of simulated

fallout radiation by the roof of a concrete blockhouse,

NDL-TR-6 Nuclear Defense Laboratory, Army Chemical

Center, Edgewood, Md., Aug. 1961.

9. M. J. Schumchyk and H. J. Tiller, Ground penetrating radiation (Lip Contribution) in a foxhole from a fallout field simulated by Cobah-60, NDL-TR-3, Nuclear Defense

Laboratory, Army Chemical Center, Edgewood, Md.,

December 1960.

10. R. E. Rexroad and M. A. Schmoke, Scattered radiation and

free field dose rates from distributed cobalt-60 and cesium137 sources, NDL-TR-2, Nuclear Defense Laboratory,

Army Chemical Center, Edgewood, Md., Sept. 1960.

11. C. Eisenhauer, Scattering of cobalt-60 gamma radiation in

air ducts, NBS Tech. Note 74, National Bureau of Standards, Washington, D.C., Oct. 1960.

12. C. Eisenhauer, Analysis of experiments on light residential structures with distributed cobalt-60 sources. (Unpublished.)

13. J. F. Batter, A. Kaplan, and E. T. Clarke, An experimental

evaluation of the radiation protection afforded by a large modern concrete office building, TO-B 59-5, Technical

Operations, Inc., Burhngton, Mass., May 1959.

14. E. T. Clarke, J. F. Batter, and A. Kaplan, Measurement of attenuation in existing structures of radiation from simulated fallout, TO-B 59-4, Technical Operations, Inc., Burhngton, Mass., April 1959.

15. J. A. Auxier et al.. Experimental evaluation of the radiation protection afforded by residential structures against dis- tributed sources, CEX-58.1, Atomic Energy Commission,

Washington, D.C., Jan. 1959.

16. F. Titus, Penetration in concrete of gamma radiation from

fallout. (Unpublished.)

17. C. E. Chfford, J. A. Carruthers, and J. R. Cunningham, Scat- tered gamma radiation from a simulated fallout field using cesium-137. Report DRCL-296, Defence Research Board, Ottawa, Canada, Jan. 1959.

18. J. R. Cunningham et al.. Protection factors for houses using

radioactive sources. Report DRCL-260, Defence Research

Board, Ottawa, Canada, Nov. 1957.

19. R. T. Graveson, Radiation protection within a standard housing structure. Report NYO-4714, Nov. 1956.

20. A. G. McDonald, The penetration of gamma radiation from a uniform contamination into houses — A first report on some

field trials. Report CD/SA-69 (Home Office), Jan. 1956.

21. N. G. Stewart et al., The shielding provided by a brick house

against the gamma radiation from a uniformly deposited

source. Experiments with cobalt-60. Report FWE-104,

- Oct. 1955. (Official Use Only.)

Calculations

22. L. V. Spencer, Structure shielding against fallout radiation from nuclear weapons, NBS Mono. 42, National Bureau of Standards, Washington, D.C., March 1962.

23. Fallout Shelter Surveys: Guide for Architects and Engineers,

NP-10-2, Office of Civil and Defense Mobilization, Washington, D.C., May 1960.

24. J. C. LeDoux and A. B. Chilton, Gamma ray streaming

through two-legged rectangular ducts, Nucl. Sci. Eng. 11, Dec. 1961.

25. R. R. Putz and E. Kuykendall, A comparison of computed

and experimentally observed intensity levels for various gamma radiation source distributions and shielding conditions in residential structures. University of Cahfornia,

Institute of Engineering Research, Feb. 1959.

26. R. R. Putz and A. Broido, A computation method for gamma

configurations. Institute of Engineering Research, University of Cahfornia, Dec. 1957.

27. A method for evaluating the protection afforded by buildings

against fallout radiation (Draft), Executive Office of the President, Office of Civil and Defense MobUization,

Sept. 1957.

28. C. W. MaUch and L. A. Beach, Radiation Protection afforded by barracks and underground shelters. Report NRL-5017,

Naval Research Laboratory, Washington, D.C., Sept. 1957.

29. C. W. Malich and L. A. Beach, Fcdlout protection afforded by standard enhsted men's bcuracks. Report NRL—4886, Naval Research Laboratory, Washington, D.C., Meu-ch

1957.

30. Bureau of Yards and Docks, Studies in atomic defense

engineering. Report NavDOCKS-P-290, Jan. 1957.

31. Home Office, Scottish Home Department, Assessment of the protection afforded by buildings against gamma radiation from faUout, May 1957. (Official Use Only.)

16
Appendix A

Curves from Reference [1]

Figure A1. Angular distribution of radiation at an isotropic detector in air above an infinite plane isotropic source.

The angle d is (he angle between the direction of the

radiation and the upward normal to the plane.

IGURE A3. Intensity of skyshine radiation as a function of

height above an infinite plane isotropic source.

d,ft 80 120 160 200 2^0

1

3000 4000

d,ft

Figure A2. Dose rate as a function of height in above an infinite plane isotropic source.

.098r

Figure A4. Detector response to skyshine as a function of the solid angle of the detector collimator and the height above an

infinite plane isotropic source.

17
Appendix B

Charts from Engineering Manual

Figure B3. Solid angle fraction, to.

18

Figure B4. Reduction factors for combined shielding

effects, roof contribution, C„.
19
MASS THICKNESS. X„ (psfl „ D 1 r\ D J • / flGURE blO. Keduction factor for passageways and shafts. Figure B9. Barrier reduction factors for wall-scattered radiation for limited strip of contamination.

U.S. GOVERNMENT PRINTING OFFICE ; 1964 OL— 725-001