United States Washington EPA 520/1-78-001A
Environmental Protection DC 20460
Agency
&EPA Protective Action Evaluation
Part I
The Effectiveness of
Sheltering as a
Protective Action Against
Nuclear Accidents Involving
Gaseous Releases
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LEGAL NOTICE
This report was prepared as an account of work sponsored by
the Environmental Protection Agency of the United States Govern-
ment under Contract No. 68-01-3223. Neither the United States
nor the United States Environmental Protection Agency makes any
warranty, express or implied, or assumes any legal liability or
responsibility for the accuracy, completeness or usefulness of
any information, apparatus, product or process disclosed, or
represents that its use would not infringe privately owned
rights.
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PROTECTIVE ACTION EVALUATION
PART I
THE EFFECTIVENESS OF SHELTERING AS A
PROTECTIVE ACTION AGAINST NUCLEAR
ACCIDENTS INVOLVING GASEOUS RELEASES
APRIL 1978
George H. Anno
Michael A. Dore
Prepared for
U.S. Environmental Protection Agency
Office of Radiation Programs
Washington, D.C. 20460
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Ill
FOREWORD
The Office of Radiation Programs carries out a national
program designed to evaluate the exposure of man to ionizing
and nonionizing radiation, and to promote the development of
controls necessary to protect the public health and safety
and assure environmental quality.
Office of Radiation Programs technical reports allow
comprehensive and rapid publishing of the results of intra-
mural and contract projects. The reports are distributed to
groups who have known interests in this type of information
such as the Nuclear Regulatory Commission, the Department of
Energy, and State radiation control agencies. These reports
are also provided to the National Technical Information Service
in order that they may be readily available to the scientific
community and to the public.
Comments on this report, as well as any new information,
would be welcomed; they may be sent to the Director, Environ-
mental Analysis Division (AW-461), Office of Radiation Programs,
U.S. Environmental Protection Agency, Washington, D.C. 20460.
W. D. Rowe, Ph.D.
Deputy Assistant Administrator
for Radiation Programs
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iv
PREFACE
The material contained in this report was sponsored by the
U.S. Environmental Protection Agency under the technical guidance
of Mr. J. Logsdon of the Office of Radiation Programs, Environ-
mental Analysis Division. Based on a study to assess the
application and utility of sheltering and evacuation as specific
protective measures in the event of accidental releases of gaseous
radioactive material from nuclear power plants, this report is
the first of tvio that deal specifically with the effectiveness of
public shelter structures.
The second report evaluates both sheltering and evacuation
protection measures from the standpoint of providing technical
guidance in formulating emergency planning procedures.
The purpose of this contract report is to provide a technical
basis for EPA to develop guidance with regard to actions to protect
the public from accidental airborne releases of radioactive material
from nuclear power facilities. The information in this report should
not be construed as guidance from EPA to State and local officials
in development of their radiological emergency response plans. Such
guidance will be published in the "Manual of Protective Action Guides
and Protective Actions for Nuclear Incidents," currently under de-
velopment by the EPA Office of Radiation Programs, The Environmental
Protection Agency is making this report available as a source of
technical information.
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TABLE OF CONTENTS
PREFACE ill
LIST OF FIGURES vii
LIST OF TABLES ix
I. INTRODUCTION 1
II. ANALYSIS 3
RADIONUCLIDE SOURCES 3
SHELTER STRUCTURE MODEL 5
FALLOUT GAMMA-SOURCE ATTENUATION 19
TIME-FRAME MODEL 28
DOSE REDUCTION FACTOR 32
DOSE COMPONENTS—UNSHELTERED 35
DOSE COMPONENTS—SHELTERED 37
SHELTERING AND EVACUATION 43
III. RESULTS 51
IV. CONCLUSIONS AND RECOMMENDATIONS 85
Appendix A: Fallout Gamma Source 92
Appendix B: Dose Reduction Factor 94
REFERENCES 103
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vi
TABLE OF CONTENTS
Fig. 1—Attenuation Comparisons—Infinite Water Medium 14
2—Shelter-Structure, Cloud Gamma-Attenuation Geometry ... 15
3—Attenuation for Structure Walls and Roof—Cloud Source 17
4—Finite Cloud, Gamma Dose-Correction Factors Versus
Gamma Energy 20
5—Finite Cloud, Gamma Dose-Correction Factor Versus
Effective Shelter Radius 21
6—Gamma Attenuation for Structures—Fallout Source .... 22
7—Finite Plane Source, Geometry-Correction Factor for
1 MeV Gammas 27
8~Sheltering-Model Time-Frame 29
9—Sheltering and Evacuation 45
10—Air Exchange and Infiltration Rates in Closed Passenger
Compartment When Air Conditioning is Set at a Maximum . . 47
11—WB DRF Versus T,, (T -0,T =1) 53
£• J. cl
12—Thyroid DRF Versus T , (T -0,T -1) 56
^ JL &
13—WB DRF Versus T , (T -0,T -0), L - 1 57
3. X £
14—WB DRF Versus T , Case A, (T -0,T -0), (T-0.25.T -0.5),
L - 1 a 58
15—WB DRF Versus T , Case B, (T -O.T -0), (T -0.25,T -0.5),
L - 1 a !. .2. ../. ...*.... 59
16—WB DRF Versus T , Case C, (T.-O.T -0), (T -0.25,T,-0.5),
* * <1 1 fc X fc
L - 1 60
17—WB DRF Versus L, (T -0,T -0,T -1) 62
X t, SL
18—Thyroid DRF Versus L, (T »0,T -0,T -1) 63
X £ SL
19—WB DRF Versus L, Case A, (T -0,T -0), (T-0.25,T,-0.5),
T - 1 • • • • - • • 64
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vii
Fig. 20— WB DRF Versus L, Case B, (T -O.T.-O), (T.-0.25,T9-0.5) ,
T - 1 .......... ../... .. . . . ..... 65
a
21— WB DRF Versus L, Case C, (T,-0,T,-0), (T.-O^S.T.-O.S) ,
Ta - 1 ...... ............... ..... 66
22— Thyroid DRF Versus L, (T -0,T -0), (T.-0.25.T--0.5) ,
T - 1 ......... .. 7 ....... 7 ...... 67
23— WB DRF Versus T,, Case B, LS, T - 1 ........... 69
^ £1
24— WB DRF Versus TZ, Case B, SS, T - 1 ........... 70
25— Thyroid DRF Versus T,,, Case B, T - 1 .......... 71
26— WB DRF Versus T,, Case B, SS (A-0.4,0.6,0.9,L-0.125,
1.0,2.0) . . . f ..................... 72
27— WB DRF Versus T , Case B, LS (A-0.05,0.1,0.2,L-0.125,
1.0,2.0) . . . f ..................... 73
28— WB DRF Versus T , Case B, (T -1,T,-0), SS (L-0.5,1.0,
1.5), LS (L-2) I ...... a. . f ............ 75
29— Thyroid DRF Versus T. , Case B, (T -1,T_-0), L - 0.5,
i n i <» 9 n J- & i -,
.i..w, A»J, ^..u« • • . • • . . . . . . . . . . . . . . . . /o
30— WB and Thyroid DRF Versus TI§ Case B, (Ta«l,T2-0,L-0.125) 77
31— WB and Thyroid DRF Versus T. , Case B, (T -1,T0-0.25,L-1.0) 78
X a £
32 — WB DRF Versus Iodine Ingress Fraction, Case B,
79
33 — Sheltering with Evacuation, WB, SS — Transit Time Versus
Shelter Time (T -0.5) .................. 81
cl
34 — Sheltering with Evacuation, WB, LS— Transit Time Versus
Shelter Time (T «=0.5) .................. 82
d
35 — Sheltering with Evacuation, Thyroid — Transit Time Versus
Shelter Time (T -0.5) .................. 83
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viii
LIST OF TABLES
Table 1. Radionuclide Source Data 4
2. Air Changes Taking Place Under Average Conditions in
Residences, Exclusive of Air Provided for Ventilation ... 8
3. Representative Cloud-Gamma Attenuation Factors 18
4. Representative Reduction Factors for Surface Source ... .24
5. Dose Components 34
6. Fixed Parameter Summary 52
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I. INTRODUCTION
In the event of an airborne release of radioactive material from a
nuclear power plant accident, sheltering of individuals is an important
consideration in emergency protective action planning as it may be 1)
an effective means of significantly reducing radiation dosages; 2) the
only practical option in view of possible time and logistic constraints.
Moreover, most people in urban areas, for example, spend 75 percent of
their time indoors.
This report describes an analysis to estimate the effectiveness or
benefit that might be derived from sheltering following a release of
gaseous fission products from an operating nuclear power station. The
objective of this effort is the development of sheltering effectiveness
information that could provide 'general guidance to those responsible for
formulating required emergency plans for nuclear power plant siting.
Accordingly, the approach taken here does not lend itself to the specific
evaluation of shelter structures involving detailed descriptions and
operational scenarios; but rather focuses more broadly on vhat are deemed
to be the essential parameters and their variations, and the general
characteristics of small and large categories of shelter structures
available to the public. Shelter effectiveness as referred to in this
report is the ratio of the dose that may be incurred with sheltering
conditions to that without sheltering in the open, specifically defined
as the dose reduction factor (DRF). DRF estimates for different con-
ditions of source release, shelter structure assumptions, and operational
time parameters are made for both whole-body and thyroid doses separately,
based on a single-compartment structural model of the time-varying out-
side and inside gaseous radionuclide sources of krypton, xenon, and iodine,
Design basis accident (DBA) assumptions are made for the gaseous
radionuclide release to define the proportion of rare gases and radio-
iodines. The magnitude of the release and dose estimates are based on
radionuclide data from The Reactor Safety Study (WASH-1400) [1]. How-
ever, inasmuch as the DRF, as defined above, is the key index used to
characterize the effectiveness of sheltering, it is not sensitive to the
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absolute source release magnitude insofar as an approximate proportion-
ality is maintained among the individual radionuclide sources. Source
release time and duration assumptions are related to release categories
given in Ref. 1 as PWR 1, PWR 3, and PWR 4, for which release times
range from 1.5 to 2.5 hr and the release duration ranges from 0.5 to 3 hr.
The basic shelter model characteristics considered are gamma ray
attenuation, source geometry, gaseous fission-product ingress, and air
change rate. Numerical values used for DRF calculations are based on
a literature review and some assumptions that are made where data are
sparse or lacking.
Temporal parameters considered are source release time and duration,
cloud travel time, and time spent in the shelter structure. These para-
meters are used to illustrate the sensitivity of sheltering effectiveness
to variations in parameter values. Also, the analysis of shelter effective-
ness is based on a time-frame model, which can be conveniently related
to other operational times important for emergency planning (e.g., in-
formation time-delay and reaction time) required to accomplish the pro-
tective action—in this case, sheltering. In addition to developing
shelter-effectiveness estimates parametrically, the advantage of exiting
and evacuating the vicinity of the shelter area after some initial time
in the shelter is analyzed from the standpoint of the DRF and temporal
considerations.
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II. ANALYSIS
RADIQNUCLIDE SOURCES
Table 1 gives the radionuclides and associated data used in this
study to simulate a fission-product release of the rare gases (Xe and Kr)
and the significant radioiodines. The Xe, Kr, and I radionuclide sources
and parameters shown are essentially the same as those given in WASH-
1400, Appendix VI [1], with the exception of Xe-133m and Xe-135m, which
have been added for completeness only, since they would not affect results
significantly.
Fission-product source inventory data based on ORIGEN Code calcula-
tions [2] were used to estimate the Xe-133m and Xe-135m sources listed
in Table 1, based on a 550-day irradiation period (same as Ref. 1).
Since the decay half-life of Xe-135m decaying to Xe-135 is short (15.6
min) considering the times of interest (hours) in this study, the esti-
mated shutdown zero-time Xe-135m inventory was added to the Xe-135
source on a mass basis and converted to Xe-135 on an activity basis,
which increases to 0.27 Ci instead of 0.26 Ci given for Xe-135 in Ref. 1.
The metastable decay half-life for Xe-133 is by comparison appreciable,
and no similar adjustment for the Xe-133 source inventory was made.
The average decay gamma energies listed in Table 1 for the metastable
Xe radionuclides were taken from Ref. 3 (pp. 32-33); the whole-body (WB)
cloud gamma-dose factors, from Appendix D, Ref. 1. These dose factors
for the ground-y (surface deposition source) do not take ground roughness
into effect (such as a factor of 2). The estimated effectiveness values
in terms of a dose-reduction factor would not be affected significantly
whether or not the ground roughness adjustment were included.
An estimate of the average gamma decay energy was made for the
source nuclides to serve as a guide in 1) estimating gamma ray attenua-
tion factors for shelter structures and also in 2) making estimated
adjustments for finite source geometries of cloud-source volume and
contaminated floor-surface spaces inside the structure, since the dose
factors for cloud-y and ground-Y apply to infinite source geometries
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Table 1
RADIONUCLIDE SOURCE DATA
Nuclide
Kr-85
Kr-85m
Kr-87
Kr-88
Xe-133
Xe-133m
Xe-135
Xe-135m
1-131
1-132
1-133
1-134
1-135
Half-Life
(hr)
93,600
4.32
1.27
2.78
127
55.2
9.12
0.27
193
2.4
21
0.864
6.72
Source
(Curies * 108)
(Q)
0.006
0.26
0.52
0.76
1.7
0.04a
0.27a
0.27s
0.85
1.2
1.7
2.0
1.5
Average Gamma
Energy (MeV)
(E)
0.0
0.16
0.82
2.21
0.08
0.23b
0.26
0.52b
0.39
2.3
0.63
2.4
1.45
Dose Factors
Cloud-y
(r em/ sec)
(Ci/rn3)
0.0
0.036
0.36
0.42
0.007
0.0075C
0.06
0.0972C
0.09
0.55
0.12
0.6
0.42
Ground-Y
(rem/hr)
(Ci/m2)
0.0
2.8
17
3.7
16
12
WBD
(50-yr)
(rem/Ci)
0.0
i
2,600
130
570
40
290
Thyroid
(50-yr)
(rem/Ci)
0.0
1
1.47xl06
5.3xl04
3.96xl05
2.5xl04
1.23xl05
Based on Refs. 1 and 2.
Ref. 3.
-Ref. 4.
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(discussed below, p. 13ff.). The average gamma decay energy was estimated
to be ^1.2 MeV, based on the following simple weighting relationship:
where Q. and E, are the radionuclide source activities and gamma energies,
J J
respectively, listed in Table 1, and y (E.) is the gamma-ray linear energy
absorption coefficient as a function of energy for air given in Ref. 5.
The estimate of the average gamma ray energy was based on a summation over
all the radionuclides shown in Table 1, with the exception of Xe-135m—
again because of its short half-life for the times of interest in this
study. The gaseous radionuclide data in Table 1 are used to estimate
shelter effectiveness in dose reduction by summing each nuclide contribu-
tion (assuming single radionuclide decay) to obtain the unprotected (out-
side shelter) and protected (inside shelter) dose. Design basis assumptions
(DBA) are made for the source release—100 percent of the noble gases and
25 percent of the radioiodines available for release.
SHELTER STRUCTURE MODEL
A simplified approach rather than a detailed investigation was
adopted to account for those factors that might contribute to the bene-
fits of seeking structural shelter in the event of a gaseous, radioactive
fission-product release from a nuclear power facility accident. The
reasons for taking this approach are as follows:
1. Explicit consideration of all types of possible structures
that may be available for shelter—single-family dwellings,
apartment buildings, office buildings, subways, tunnels,
factories, and vehicles, etc.—would require an analysis.
beyond the scope of this effort because of the large varia-
bility in the parameters that determine effectiveness.
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2. In many instances, reliable parameter data are not available;
e.g., the actual chemical/physical form of the "gaseous"
constituents at some distant point from the source release
and the ingress of, in particular, radioiodine into shelter
structures.
3. The main purpose of this study is best served by providing
overall technical guidance information as to the effectiveness
of using a shelter structure based on some assumed conditions
for shielding and ventilation rates without specifically focusing
on detailed physical description and analysis of shelter structures*
After a review of the literature dealing with the key parameters of
this study's simplified model (in keeping with the above reasons),
calculations were performed using parameters selected to simulate
what this study classifies as "small" and "large" structures (SS
and LS) to illustrate the relative effectiveness of typical single-
family dwellings and of larger structures such as office buildings,
auditoriums, apartment complexes, etc. In developing the shelter model,
consideration was given to account for the following possible avenues of
exposure to shelter inhabitants:
o External WB dose from airborne radioactive material both
outside (shielded) and inside (unshielded) the shelter
structure.
o Inhalation WB and thyroid dose from airborne radioactive
material inside the shelter structure.
o External WB dose from radioactive fallout material deposited
both outside (shielded) and inside (unshielded) the shelter
structure.
In this study, beta skin dose was not considered, as it is assumed
to be of secondary importance as compared with WB and thyroid dose con-
siderations. The external WB doses (cloud-y and fallout-Y) are based
solely on radionuclide-decay gamma radiation in which both shelter-
structure attenuation and finite source geometry factors are included
in the model as discussed below.
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The entry of outside airborne radioactive cloud material is assumed
to be dependent on the shelter-structure ventilation rate (forced, natural,
or both) assuming constant homogeneous mixing based on simple one-compart-
ment outside/inside air exchange. This type of stirred-tank. mixing and
ventilation model has been applied in studies of the relationship between
indoor/outdoor pollutants (e.g., NO, NO , CO, and 0_) and has predicted
concentration versus time profiles that are similar to those measured 16].
The radioiodine fallout deposition inside the shelter is then also assumed
to be dependent on the ventilation rate as well as the fallout deposition
velocity; these aspects are also discussed below.
Shelter Structure Ventilation
A review of literature on ventilation rates of homes and buildings
indicates a wide variety of air change estimates ranging anywhere from
^0.1 to 6 per hour for single-family dwellings to *v
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Health Division of the Los Angeles City Building and Safety Department
[8] indicated internal air turnover time of from 5 to 10 min depending
on occupancy requirements, with a representative value of about 7 min—
with 15 percent outside air makeup as a comfort-level requirement—
which corresponds to 0.9 and 1.8 air changes per hour and ^1.3 air changes
per hour. Considering the above data, the rates for single-family
dwellings and large structures are generally comparable, assuming internal
forced-air systems.
In the absence of forced-air ventilation systems, home and building
air change rates would be expected to vary much more widely—as indicated
by the published data examined by Handley and Barton [7]. This conclusion
is also supported by observations of Yocom, et al. [9] who note that
particulate pollutant levels are lower in public buildings than in homes.
The AS11RAE Handbook of Fundamentals [10] points to the lack of published
data on air change rates for different buildings, exclusive of air pro-
vided for ventilation, when utilizing the air change method for estima-
ting infiltration requires experience and judgment. Table 2 gives ASHRAE
Handbook values that may be used with reasonable precision in making
infiltration estimates for residences with different room conditions.
Table 2
AIR CHANGES TAKING PLACE UNDER AVERAGE CONDITIONS IN RESIDENCES,
EXCLUSIVE OF AIR PROVIDED FOR VENTILATION
...,,-, _ ,, ,. Number of Air Changes
Kind of Room or Building Taking place per ^a
Rooms with no windows or exterior doors 1/2
Rooms with windows or exterior doors on one side 1
Rooms with windows or exterior doors on two sides 1 1/2
Rooms with windows or exterior doors on three sides 2
Entrance halls 2
o
For rooms with weathers tripped windows or with storm sash, use two-thirds
these values.
The other is the "crack method" based on measured leakage character-
istics of the building components and selected pressure differences.
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Another approach in making air change estimates due to natural
ventilation for houses is given by Coblentz and Achenbach [11], who suggest
the following empirical relationship in which the air change rate is
proportional to the outside wind speed and inside/outside temperature
differential (i.e., without inside forced ventilation):
I (changes/hr) = A + BW + CAT
where
A = air change rate for W - 0, AT - 0 (0.12 to 0.18),
B - 0.013,
C « 0.005,
W » wind speed, mph,
AT B T T ° T*1
inside outside'
Assuming the upper limit of A = 0.18 and AT = 20°F gives air change rates
of about 0.35 per hour for a 5-mph wind speed and about 0.5 for 15- to
20-mph wind speeds, which appears to be somewhat on the low side compared
with other data reviewed. This difference, however, may be due to new,
well-built houses that made up part of Coblentz and Achenbach's field
samples. In contrast, measured air change rates given by Megaw [12] for
a hut structure that were made in conjunction with radioiodine penetration
experiments were substantially higher, ranging anywhere from about 2 per
hour to 8 per hour (the latter, however, for open windows). An examina-
tion of Megaw1s data reveals an indication of air-change-rate proportionality
with outside wind speed that, roughly, was about 0.5 (changes/hr) per
(mi/hr). This figure corresponds to only an "eyeball" estimate from
Megaw's data, which are complicated by variations in wind direction.
Such variations would give rise to different pressure differential dis-
tributions due to asymmetric flow patterns, which would affect the internal
air change rate.
Based on the above review of air change rates that might be expected
for single-family dwellings (small structures) and various building
structures that could be used as temporary public shelters, values of
from 0.125 to 3 air changes per hour were assumed in performing shelter-
structure effectiveness calculations. It was felt that ^0.125 changes
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per hour might represent relatively "tight" structures (either large or
small) and that ^3 air changes per hour might represent a practical
upper limit of structural ventilation. Of course, as indicated, much
larger values of 6 to 9 air changes per hour have been measured; but it
was felt that these values would represent extreme cases (e.g., open
windows or portals), which do not represent practical cases if good
planning is assumed.
Gaseous Fission-Product Ingress
The extent to which radioiodine will penetrate a structural shield-
ing facility is dependent on the gross tightness of the structure, the
ventilation rate, filtration, and the chemical and physical properties
of the released material and the interacting species. Many of these
facets of a gaseous fission-product release from a nuclear accident
are currently unknown, particularly for radioiodine, which leads to
difficulty in accurately predicting the ingress of gaseous radioactive
material into shelter structures. For the rare gases (Xe and Kr), most
are willing to accept virtually no effective "structural filtering,"
because of their inertness and stability as gaseous forms. Accordingly,
in this study no effective filtering action has been included in esti-
mating their internal structure concentrations.
For the halogens, which are here assumed to be all radioiodines,
the case is more complicated and suffers from scarcity of experimental
work on indoor/outdoor pollutant-level relationships dealing with the
ingress of radioiodine into various potential sheltering structures.
The radioiodines are of course particularly important sources due to
their large contribution to the WB dose, as well as being totally
responsible for the thyroid dose.
Three known chemical forms of radioiodine present as airborne
gaseous species in power-station areas during and after handling defec-
tive fuel elements are elemental iodine (I2), hypoidous acid (HOI), and
organic iodides (CH.I). The ratio of the three species would depend
on the conditions under which an accidental release might take place.
Elemental iodine is thought to be the primary form released from
uranium-oxide fuel. It hydrolyzes rapidly in water, generating HOI, or
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11
it forms organic iodides through a slower reaction with organic com-
pounds, with relative stability in air increasing in the following
order [13]:
I2 < HOI < CH.I
The actual chemical/physical form of the radioiodine that would be
present at some off-site point is yet another question; however, pro-
bably very little protection would be offered by a structure against
the ingress of HOI and CH_I, both unreactive gaseous forms like Xe
and Kr [14]. The Reaator Safety Study [I] did consider other possible
forms of radioiodine that could be released (e.g., HI, Csl, and Zrl),
but concluded that these forms would not be major species as they had
not been verified experimentally. In its dose calculations, Ref. 1
assumes, primarily, elemental iodine; and, to a much lesser extent,
organic iodide (approximately a factor of 100 less). However, assuming
elemental iodine release to the atmosphere, controlled field release
tests [15] involving elemental iodine (I2-131) indicated a rapid trans-
formation in apparent particle size from the source—in that the field
e
sampling results for the released gaseous product (effective HMD * 2A)
revealed a much broader spectrum of sizes, closely resembling the normal
distribution by size, of particles in the atmosphere (with an HMD « 0.4
microns). The above would suggest some effectiveness of shelter structures
in reducing radioiodine ingress released in the elemental form, depend-
ing, of course, on overall integrity, ventilation, filtering, etc.
Estimates of radioiodine ingress into structures for this study are
primarily based on the observations and work of Megaw [12], which repre-
sents essentially the only source of published information applicable
to this study; other related, but not applicable, work [16] has been
sponsored by the Office of Civil Defense (Defense Civil Preparedness
Agency), Megaw's work originated from the accidental Wind scale
incident in which it was estimated that dose rates inside build-
ings may be from about 14 to 25 percent of those outside. Subsequent
experimental measurements were made by Megaw involving radioiodine
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12
releases and a reasonably tight wooden hut; and he concluded that the
time integral of the inside concentration (dose) may be from 20 to 80
percent of that outside, depending on wind velocity and direction.
An examination of Megaw's published data [12] does not suggest any
correlation of the inside-to-outside dose ratio with either outside wind
velocity or ventilation rate, probably because of the varying conditions
under which measurements were made; e.g., measurements were made for
unique sets of wind direction and velocity. A simple statistical
analysis of the data indicates a protection factor (ratio of inside to
outside dose) of 0.51 ± 0.12 (pooling the data from two experiments
described). From Megaw's work, however, it is not possible to identify
precisely the extent of the radioiodine filtering action or resistance
to ingress for use in a simple mixing model such as is assumed for this
study, even for the test structure used in the experiment, because of
the absence of experimental information regarding source release time
and intensity distribution and the absence of any correlation of the
inside-to-outside dose ratio with ventilation rate. The dose reduction
factors given by Megaw are therefore effective values that would include
any filtering or ingress action of the shelter structure used in the
experiment plus the specific test conditions and parameters. However,
to take into account what is felt to amount to some gross filtering
action for radioiodine—whether assumed to be due to trapping or
deposition in small cracks or openings—the above-mentioned value of
0.51 has been tacitly assumed in approximating the explicit filtering
action for shelter structures.
Radioiodine Deposition
Shelter effectiveness estimates in this study take into account
external WB dosages from outside and inside radioiodine source deposition,
using estimates for the deposition velocity, V . Values ranging from
O
0.1 to 1 cm/sec were obtained from controlled environmental radio-
Iodine tests made at the National Reactor Testing Station in Idaho [15].
For outside radioiodine deposition velocity, the Heaator Safety Study [1]
used a value of 0.5 cm/sec, which is also assumed in this study for
surfaces outside a shelter structure.
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13
Inside a shelter, a value of 0.025 cm/sec was assumed for the radio-
iodine deposition velocity for the floor surface, based on Megaw's
work in which he estimated the inside deposition velocity to be only
about 5 percent of the outside deposition velocity [12].
Cloud-Gamma Attenuation
The attenuation of cloud-gamma radiation that might be afforded by
building structures has been estimated by Burson and Profio [17]; the
results of their analyses served as a guide for estimating the cloud-
gamma attenuation factors used in this study. The source basis for the
attenuation calculations that were performed applies to the PWR Category
2 accident [17] ten miles from the plant, under average dry meteorological
conditions. Figure 1 shows comparison of mass-path attenuation for
different energies based on dose buildup and exponential attenuation in
water. Since, for the source energies of interest, most of the attenua-
tion will be due to Compton scattering—where Z/A remains relatively
constant at about 0.5—water data (mass-path) are suitable for applica-
tion to the usual structural materials such as wood, concrete, brick,
and even steel [17]. As shown in Fig. 1, for mass-path thicknesses
2
of interest up to ^45 gm/cm , attenuation values—particularly,
for reactor-accident spectra (ground and cloud source) and Co-60—are
all quite close. Moreover, slight variations in the spectrum are not
considered significant, since the higher-energy gamma rays would
be the most penetrating and any differences in attenuation would not
amount to any major source of uncertainty considering the other assumptions
made in this study.
Burson and Profio's attenuation factors [17] used in this study are
based on calculations assuming a simple hemispherical shell model (Fig.
2). Estimates were made of the gamma attenuation (with the dose point
at the origin) for the portion of radioactive cloud material outside the
shelter, based on numerical evaluation of the attenuation, A(x), given by a
relationship of the form
-------
1.0
0.8
0.6
s
§
0.4
0.2
0.1
14
reactor f ground source
accident (cloud source
\
1.12 hr fission
\ 6 products
'Co
\
\
\
137
Cs
10
20 30
40
50 60
70
Mass thickness, x (gm/cm )
Fig. I—Attenuation comparisons—infinite water medium
-------
15
dr.x'
(out)
air
Fig. 2—Shelter-structure, cloud gamma-attenuation geometry
-------
16
• ° V'a
dr
gamma
A(x) . energies.
R
"V
B(y r) e a dr
£L
gamma
energies
where p and p are the energy-dependent gamma-ray absorption coefficients
w
for air and water, respectively; and K and S are the energy-dependent dose-
conversion and volume-source terms, respectively; and B is the dose buildup
factor. Figure 3, a plot of the gamma ray attenuation for accident spectra •
for a = 3 m and pR = 3, is applicable for estimating gamma ray attenuation
for structures of a wide variety of enclosure sizes (effective radii, a),
since A(x) is relatively insensitive to a, because of the low density
-3 3
of air (1.293 x 10 gm/cm ) as compared to structural material. Also,
very little dose contribution would be expected from cloud sources
beyond about three mean-free paths in air; therefore, yR » 3 is a
reasonable approximation for an infinite cloud source with regard to
the gamma-radiation transport considerations in this study.
The estimates of gamma attenuation for an outside radioactive cloud
source that can be made from Fig. 3 depend on the structural assumptions.
For example, for a wooden frame house with roof and ceiling consisting
of 1/4-in. wood or asphalt shingles, 3/4 in. of wood sheathing and
rafters, and 1/2 in. of gypsum board, the mass thickness would be
1.5 (in.) x 2.54 (cm/in.) x 0.84 (gm/cm3) « 3.2 gm/cm2
where A(x) =0.9. Better protection would be afforded by a small house
with a wooden roof and masonry walls. For example, assuming half the
2rr solid angle (Fig. 2) to be subtended by the walls and the other half
by the roof, the overall attenuation factor would be
-------
17
5
o
o
•r-
*J
fl
o.i
Mass thickness, x (gm/cm )
Fig. 3--Attenuation for structure walls and roof—cloud source
-------
L8
0.5 x (0.9) + 0.5(0.38) - 0.64
where the attenuation for the walls (0.38) is based on a wall-mass thick-
ness of
4 (in.) x 2.54 (cm/in.) x 2.7 (gm/cm3) * 28 gm/cm2 ,
(assuming 8-in. concrete bricks with a 50-percent void volume).
Attenuation of cloud-gamma radiation for large structures such as
office buildings and multistory structures could be significantly more
than for simple structures such as single-family dwellings. Attenuation ol
8-in.-thick solid concrete, either exterior walls or interior walls
(e.g., fire-resistant stairwells) may be equivalent to mass thickness
2
of around 45 to 50 gm/cm , corresponding to attenuation factors of 0.2
to 0.17 (Fig. 3). Table 3 summarizes representative cloud-gamma attenua-
tion factors for the types of structures noted.
Table 3
REPRESENTATIVE CLOUD-GAMMA ATTENUATION FACTORS
Structure
Wood frame house, no basement
Masonry house, no basement
Basement of wood house
Attenuation Factor
0.9
0.6
0.6
Basement of masonry house 0.4
Large office or industrial building 0.2 or less
The above values do not suggest any substantial protection from
external cloud-gamma radiation afforded by lightly constructed, frame
single-family dwellings. In this study, however, estimates of shelter-
ing effectiveness were made assuming somewhat more substantial gamma-
attenuation protection, A(x) - 0.4 to 0.9 for small structures. For large
-------
19
structures, shelter effectiveness estimates were made for A(x) - O.OS
to 0.2; gamma attenuation could be even greater, amounting to values
much less than 0.05 for veil-protected areas within large multistory
structures.
The estimated external WB gamma-dose contribution from airborne
gaseous radioactive material that enters a shelter structure is based
on a finite cloud-source geometry correction factor, since infinite
cloud-dose conversion factors (Table 1) are used in estimating shelter
effectiveness. The source geometry correction factor is defined as
G(E,R) - D(E,R)/D(E,-)
where D(E,R) and D(E,«) are gamma doses at the origin of a hemispherical
cloud source for finite and infinite radii, respectively. Values for
G(E,R) based on point-kernel integration over a hemispherical source
volume in air, assuming Berger's expression for a dose buildup factor,
are given in Ref. 18 for various energies and source radii; values of
G(E,R) are plotted in Fig. 4. Figure 5 gives finite cloud-geometry
correction factors for a couple of gamma energies of interest in this
study, where very little difference is seen between 1 and 1.2S MeV gammas.
Simulation of small and large shelter structures in this study
assumes effective hemispherical radii of 3.4 and 10.3 m to represent
7
shelter enclosures of approximately 400 and 3600 ft of floor area,
respectively. From Fig. 5, estimated small- and large-shelter-structure-
geometry correction factors are 0.01 and 0.034, respectively. These
values are assumed in estimating the effectiveness of shelter structures.
FALLOUT GAMMA-SOURCE ATTENUATION
Considerable analytical and experimental work has been done to
determine the protection against fallout-source gamma radiation afforded
by various types of building structures, primarily for civil defense
applications. Burson and Profio [17] reviewed much of this work for
application to nuclear power plant accidents, and performed additional
calculations using the method given in Ref. 19 to estimate attenuation
factors for some simple rectangular structures (Fig. 6). Experimental
results [20-24] generally indicate protection factors (PF), often
-------
20
u
o
»J
o
,1)
c
o
-------
21
a:
10
o
*-»
o
rO
4J
O
O
0.001
Radius, R (meters)
Fig. 5--Finite cloud, gamma dose-correction factors versus effective
shelter radius
-------
22
1.0
«'
I
•••
••
-
.
0.1
0.01
2
Floor space (ft ) -
10 x 10
20 x 20
30 x 30
40 x 90
large
structures
small
struc-
tures
0
10
20
30
40
50
60
70
Mass thickness, x (gm/cm )
Fig. 6—Garana attenuation for structures—fallout source
-------
23
referred to as the reciprocal-of-attenuation factor, from 2 to 5 for a
wood frame home (without basement) and from 3 to 10 for block and brick
homes. Most attenuation-factor estimates for fallout gamma sources in-
clude the effect of ground roughness, which can vary accordingly as
tabulated below by the Defense Civil Preparedness Agency [19].
Ground Roughness Condition
Smooth plane (hypothetical)
Paved areas
Lawns
Gravelled areas
Ordinary plowed field
Deeply plowed field
Reduction Factor
1.00
1.00 to 0.85
0.85 to 0.75
0.75 to 0.65
0.65 to 0.55
0.55 to 0.47
Many other aspects affect protection against fallout sources, in-
cluding structural materials, wall-exposure areas (taking into con-
sideration basements and multilevel dwellings), topographical varia-
tions (hillside or flat ground level), mutual shielding offered by
nearby buildings and structures, and the internal location within a
shelter structure. For example, protection factors for basements may
be from 10 to 50; and material shielding of nearby buildings may offer
protection factors of from about 1.7 to 2.5 [25]. Complex structures
such as multistory office and apartment buildings offer protection
factors of 20 or more (away from doors or windows); this factor is
supported by experimental measurements [26-28]. Table 4 summarizes
recommended attenuation or reduction factors for some representative
shelter structures and also vehicles [17].
The reduction values in Table 4 are relative to 1 meter above a
hypothetical, uniform infinite plane of homogeneous source con-
centrations. The values given are only representative and not to be
taken as exact; and as indicated above, different values will result
because of wide variations in constructional details and topography.
Estimates of the external WB dose from radioiodine fallout inside
a shelter structure are based on a dose detector point 1 meter above
-------
24
Table 4
REPRESENTATIVE REDUCTION FACTORS FOR SURFACE SOURCE
Structure and/or Location
Reduction Factors
1m above a hypothetical, infinite, smooth plane
1m above ordinary ground
1m above center of 50-ft roadway half contaminated
Cars, pickups, buses, and trucks on 50-ft road:
Road fully contaminated
Road fully decontaminated
Trains
1- and 2-story wood frame homes (no basement)
1- and 2-story block or brick homes-(no basement)
Home basement—1 or 2 walls fully exposed:
1 story, less than 2 ft of basement walls exposed
2 story, less than 2 ft of basement walls exposed
2
3- or 4-story structures, 5000 to 10,000 ft per floor:
First and second floors
Basement
2
Multistory structures, >10,000 ft per floor:
Upper floors
Basement
1.00
0.70
0.55
0.5
0.25
0.4
0.4
0.2a
O.la
0.05a
0.02a
0.053
0.01a
0.013
0.005£
Away from doors and windows.
-------
25
a circular area for small and large shelter structures in which infinite-
plane dose-conversion factors were used (see Table 1, p. 4). Therefore,
a finite-plane geometry correction factor was applied in calculating
dosages, defined as
G' (R) - D(R)/D(~) ,
where D(R) and D(«) are the finite plane (radius, R) and infinite-plane
doses for d = In above the surface. G1 (R) may also be expressed as
where D(R,») is the plane-source dose for source radial dimensions from
R to », and D(») = D(0, ). The dose D(R) for a flat plane source is
given by
CO
f
ncr»> _ k o / B(pr) e dr
DQi-0 - Y sa
>/R2+d2
where
Sa = source strength per unit area,
k = dose-conversion constant,
R = distance from source plane (1 m),
= gamma-ray absorption coefficient in air,
li(ur) = 1 + Cure yr (Berger buildup factor).
Integrating the above over the appropriate source-plane upper limits
(see Appendix A) yields
and
-------
26
kS
D(-) -
(yd)
-(l-D)yd
where E.. (x) is the first-order exponential integral function, and C and
D are the Berger buildup factor coefficients for air given in Ref. 29.
Assuming 1.293 x 10~ gin/cm for air, calculations of G'(R) were made
for 0.5, 1.0, and 2.0 MeV gamma rays for various values of R using the
following data from Ref. 29.
Energy (MeV)
0.5
1.0
2.0
C
1.6001
1.1571
0.8363
D
1.0094
0.05749
0.0243
M/cm \
P\gm 1
0.088
0.063
0.046
Some results are given below for R = 10 and 30m:
Energy (MeV)
0.5
1.0
2.0
G'(R)
10m
0.413
0.414
0.419
30m
0.620
0.624
0.622
As indicated above, very little variation exists from 0.5 to 2.0
MeV; the 1-MeV values plotted in Fig. 7 are assumed to be representa-
tive for this study. Again, assuming 3.4 and 10.3 m as effective
radii applicable for small and large shelter structures, yields finite-
source geometry correction factors of 0.28 and 0.43, respectively,
which are used in the shelter model calculations.
-------
20 40
60 80 100 120
Radius, R (meters)
Fig. 7—Finite plane source, geometry-correction factor for 1 MeV gammas
-------
28
TIME-FRAME MODEL
The question of shelter protection effectiveness from airborne
radioactive material accidentally released from a nuclear power plant
is dependent upon the time required for individuals to gain entry into
a protective structure; and the length of time they remain, as compared
with the time of cloud arrival and passage. The required entry time
assumes that individuals are transferred from either unprotected or
protected locations to another location affording maximum protection,
considering logistic constraints, etc. On the other hand, individuals
could also be located in houses and buildings already providing adequate
shelter so that effectiveness would not depend on access time.
Figure 8 shows the time-frame model assumed in estimating the
effectiveness of sheltering, as well as other times of interest (to
put them in perspective). Measured from initiation of a possible
incident, (T +T ) is the estimated time-of-arrival of the assumed lead
K a
portion of a radioactive cloud. The time from source release, T_,
measured from incident initiation, may vary from about 1.5 to 9 hr for
the more severe accident categories [1]; although in one instance
(PWR 4 Category), a value of 28 hr was indicated. Source release times
of from 1.5 to 3 hr were considered to be of more interest in this
study, since protective evacuation action might very well be more
appropriate, considering the greater time that would be available.
Cloud arrival time, T , would depend completely on the location
<1
of a shelter from the point of release and the prevailing meteorological
conditions (primarily, wind speed and direction) during cloud travel
time. Assuming a given sustained average wind speed (and direction),
x/u is an estimate of T , where x is the distance from the release and
Si
u the average wind speed. For example, for an estimate of the average
low-population zone distance of around 3.4 mi based on siting data
given for 76 nuclear power plant sites [30], cloud arrival time would
be approximately 1-1/2 hr to 20 min for wind speeds of from 2 to 11 mph,
respectively. The effective time for sheltering from incident initiation
is shown in Pip. 8 as (TD+TT), where TQ is the delay time for the initiat-
ing event to the sheltering order, and T_ is the actual time spent in taking
-------
TR + V
•TD + V
(or Ts)
Time in shelter
K>
VO
Incident
initiation
TR = source release time
T, = cloud arrival time
a
T = cloud passage time
T = cloud-source release duration
(forTe>Ts, Te=Ts)
T, = shelter entrance-delay time
after cloud arrival
T2 = shelter time after cloud passage
T = evacuation time after leaving
v shelter
Tn = delay time from initiating event
to sheltering alert
TT = actual time spent taking shelter
Fig. 8--Sheltering-model time-frame
-------
30
shelter (assuming individuals are not already in a suitable shelter).
Delay time estimates (T ) have been discussed by the EPA [31] with
regard to evacuation that may be somewhat applicable to sheltering,
since the time components of T_ are similar or may in fact be one and
the same In terms of a local decision process. As assumed here, T_
represents the total delay time from initiation of an event to onset
of physical movement to a shelter. For evacuation, the EPA estimates
this delay time as being from 0.9 to 4.5 hr [31]. Also, for evacuation,
the EPA estimate for T_ is from 0.2 to 1.5 hr, which may be excessive
for sheltering on the high end. That is, reasonable sheltering times
may be anywhere from a few minutes to half an hour.
Allowance is made in the time-frame model for a shelter-entrance
delay time measured from time of cloud arrival, which would be dependent
upon T_, T , T_, and T_. The shorter T, is, the better is the shelter-
K a u i i
ing effectiveness with the maximum advantage for T. equal to zero,
(TD+TT)_< (T-+T ). Normally, T- would be expected to be either zero
or small except for relatively high sustained wind speeds and/or for loca-
tions relatively close to a release.
The cloud passage time, T , would depend on source release duration
(T ) and wind persistence time (direction and speed). T may range
s s
from 0.5 to 4 hr, depending on the accidental release events [1] that
would be of interest for seeking shelter. Estimates of wind persistence
time should be based on particular site meteorology. In terms of pro-
tective action by the public (i.e., taking shelter or evacuating), the
wind persistence time estimates made at the time of and during postincident
phases of an accident are among the most important parameters affecting
the effectiveness of the protective action. Ideally, the most useful
type of information on persistence, when making protective action
decisions, would be an estimate of the mean or expected wind-direction
persistence time—given a particular time of the day and that a particular
direction has been maintained up to that point. Such predictive ability
would have to be formulated from a detailed statistical analysis of
site meteorological data of record requiring frequent observations
(perhaps every 15 min) over an adequate period of time. A means of
-------
3)
computing source-cloud trajectory based on real-time analysis of site
and regional meterological data is described as a feature of the ARAC
program currently being developed at the Lawrence Livermore Laboratory
[32]. This kind of capability would obviously be very useful in planning
emergency public actions such as sheltering.
In this study, the persistence time is simply related to the cloud
exposure time designated in Fig. 8 as T ; such that, if T is an estimate
G
of the persistence time, then T - T for T < T, otherwise, T - T.
68 S """" G
The time-frame model for sheltering also considers the time that
individuals may have remained in a shelter after passage of the radio-
active cloud. For example, although exiting a shelter may afford
more protection and thus avoid exposure to accumulated internal con-
tamination, precise exiting with regard to cloud passage may not be
practical, and the overall time spent in a shelter could be as indica-
ted by the shaded portion of Fig. 8. This shaded portion, then, designates
an "internal receptor" with respect to radioactive gaseous fission-
product sources. That is, during T., after cloud arrival, unprotected
individuals may be exposed to airborne radioactive material by means of
direct WB gamma radiation from both airborne and ground-source fallout
material and from radioactive material entering the body via inhalation.
During the interval inside the shelter, (T_+T +T ) - (T_+T_), the inter-
K a e D T
nal receptor is exposed to WB radiation from airborne and surface-source
(fallout) material, both inside and outside the structure, and internal
radioactive material entering the body via inhalation. During T.,
after cloud passage, the internal receptor is assumed to undergo the same
type of exposure with the exception of that due to airborne gaseous
fission products outside the structure.
Finally, after TZ, the time-frame model makes allowance for the
time that may be required for leaving the area (where an individual
may be exposed to outside fallout in transit either on foot or by
vehicle). If vehicles are used for transport, simulation can include
the effect of shielding attenuation of the fallout-source gamma radia-
tion. In terms of the time-frame model, the shielding effectiveness
is defined as the ratio of the dose received under unprotected and
-------
32
protected conditions to that received under unprotected conditions over
the interval (Tg+T2+Tv) due to the exposure modes mentioned above.
The time-frame model is thus formulated to Indicate the effects of the
time parameters on shelter effectiveness. The effectiveness estimates
in this study are mainly concerned with times commencing at cloud
arrival, (TR+Ta), in which simple radioactive decay by each source
isotope is considered over (TD+T ). Note also that the time-frame
K a
model assumes an abrupt boundary at both the leading and trailing edges
of the radioactive cloud material. Of course, in reality, this is not
true, as it is well-known that turbulent diffusion in the atmosphere
gives rise, on the average, to continuously changing airborne source
boundaries—whose dimensional scales, however, are such that the above
model would be a reasonable approximation, considering the source
release intervals of interest (excluding an instantaneous puff).
DOSE REDUCTION FACTOR
The estimated measure of effectiveness afforded by a shelter
structure—based on the models and assumptions discussed above—is
referred to here as the dose reduction factor (DRF). This value is given
by the ratio of the dosage received during shelter protection to that
which would be received in the open. DRF values are estimated for both
thyroid and WB exposures. The DRF for WB gamma dose is given as
(DRF)
Y EC + 1C + FD
o o o
where
EC «* External gamma airborne source dose, sheltered,
EC » External gamma airborne source dose, unsheltered,
1C • Inhalation airborne source dose, sheltered,
1C » Inhalation airborne source dose, unsheltered,
FD = External gamma surface source dose, sheltered,
FD » External gamma surface source d
The DRF for thyroid gland dose is given as
FD » External gamma surface source dose, unsheltered.
-------
33
TV
(DRF)Thyroid " fT '
where
TC - Thyroid inhalation dose, sheltered,
TC - Thyroid inhalation dose, unsheltered.
Table 5 summarizes the dose components given above, relating the
source, receptor, and time-frame conditions that were considered in
performing DRF calculations. For example, EC and FD values include
estimates of external gamma WB dose for sources both inside and outside
a shelter structure for the exposure times (defined in Fig. 8, p. 29)
indicated. Shelter dose components (EC, FD, 1C, and TC) also include
a portion of unsheltered dose contributions accumulated over the ex-
posure period, T-, to simulate the effects of shelter-access delay times
that assume no protection during that interval. The remainder of this
section describes the development of these dose components used in the
calculation of the DRF values.
Doses downwind from an accidental release of airborne gaseous
fission products are dependent upon the concentration of the airborne
radioactive material that can be expressed as follows for continuous
source release conditions:
X(r,t) = (X(r)/Q) Q(t) (Ci/m3)
3 3
where x(r)/Q (sec/m ) is the ratio of the concentration x(O (Ci/m ),
•
at a distance r from the release to the source release rate Q (Ci/sec);
•
and Q(t-x/u) (Ci/sec) is the time-dependent source-release rate function.
In general, the dose at r is given by the integral of the concentration
over the period of exposure, T ,
e
D(r) -IK.. x(r,t) dt rem
-------
34
Table 5
DOSE COMPONENTS
Dose
Component
EC, FD
1C, 1C
EC , FD
o' o
1C , TE
0* 0
Source
In
X
X
Out
X
X
X
X
Receptor
In
X
X
X
Out
X
X
X
Exposure Times
T,, T 3
1 V
(1,-Ij) + T/
CT.-V + T2
T.
1
(Te-Tl) + T2
(T +T +T )
e 2 v
u
TV and T2 are post-outside airborne cloud times and apply to the
fallout dose (FD) only.
-------
35
where K_ is a dose conversion factor. For this study, calculations
were performed assuming x(r)/Q unity (i.e., a unit dilution factor),
since it is a common multiplier for all dose components and therefore
does not affect DRF values. Accordingly, the dose component estimates
described here are based on integrations of the time-dependent sources
both inside and outside the shelter structure. The release rate at
the source is assumed to be constant with a correction for simple radio-
active decay over a release period, T ,
8
Q(t)
-xt
(Ci/sec)
where QQ is the initial radionuclide activity inventory in the re-
actor at the time of an accident (Table 1, p. A), f is the radio-
nuclide release fraction (DBA assumptions), and X is the radioactive
decay constant. For ease of illustration, the development of the
following dose components does not use subscripts designating each
radionuclide source, and it should be understood that summations over
radionuclide sources are performed in making computations.
The calculations are obtained from differential rate equations and
integration over the time-dependent sources. Derivation of these dose
component relationships are detailed where necessary in Appendix B.
DOSE COMPONENTS—UNSHELTERED
Whole-body cloud and thyroid dose components assuming no shelter
protection are given as
Q(t) dt
"EC 1
o
1C
o
TC
** nj
"K,
1
K ,-B
2
v • R
.K3 J
-X(TR+Ta)
e
-------
36
"Kl "
_K 'B_
frQo e R *
T A
s
-AT
(1-e )
ren
where K-, K-, and K. are the dose conversion factors given for WB cloud
gamma, WB inhalation, and the thyroid inhalation dose, respectively, and
-4 3
B is the breathing rate assumed to be 3.4 x 10 (m /sec). In the above,
the source release duration, T , is assumed to be the downwind exposure
S
time, T .
e
The local fallout deposition rate outside the shelter is assumed
2
to be V v(r,t) (Ci/sec-m ), and the depletion rate to be due to only radio-
O
active decay. Expressing the airborne concentration as x(r,t)
where x includes the exp [- x(TR+T )I term, the outside ground-fallout
deposition, F(t) (Ci/ra ), is obtained from the following equation:
- AF(t)
Integrating,
F(t)
out
V x t
go
-At
(Ci/m2)
The fallout dose component is given by integration of F(t) over the
time of cloud passage, T , plus the contribution from the fallout source
after cloud passage integrated over the reference time, (T2+T ).
FD = K.
o 4
/'
0
2 v
-At ,
e dt
-AT
rem
where K, is the ground-source gamma-dose conversion factor.
-------
DOSE COMPONENTS—SHELTERED
Airborne Source—Inside
The source intake rate for a shelter structure is assumed to be
eLxo e , where e is the ingress fraction (discussed above); and
L (time) is the air change rate that is (f/v), where f is the volu-
metric air-inflow rate and v is the enclosure volume. The internal
concentration C(t) is assumed to be reduced by air outflow, radioactive
decay, and internal radioiodine surface deposition at the rates given
by (L+X) C(t) and (V'/i.) C(t). For internal surface deposition, V is
8 g
the deposition velocity inside the shelter (discussed above) and I is
the mean fall distance for iodine fallout material in the shelter
enclosure, assumed to be one-half the average floor-to-ceiling distance
or about 1.5 meters. The significance of this coefficient as compared
with (L+A) per hour can be seen from
_ 0.00025(m/sec) x 3600 (sec/hr) . , . -1
1.5 (m) " °-6 hr
where (as indicated above) a range of 0.125 to 3 hr for L was chosen
for the DRF calculations, and A can range from about 0.0036 to 0.8 hr"1
for the radioiodines. Since V - 0 for the rare gases, the (V'/A)
O £
coefficient is zero for determination of the internal noble-gas con-
centrations. Based on the above, the internal structure concentrations
are determined from the following differential equation:
where
K •= L + X + Kf , and K, - V'/£
1 f 8
Integrating,
-------
38
The dose accumulated in the shelter structure over the time interval
(T1.Te) is
D - G K^ B / C(t) dt
T,
(L+Kf)
-XT, -XT
- e
, / -KT. -KT
-Me ^e €
rem
Specific dose components are given by the above equation, depending
on the values of the dose conversion factor, K , the breathing rate, B,
and the finite cloud-geometry correction factor, G, as listed below:
EC1
IC1
TC1
KD
Kl
K2
K3
B
1
3.4 x l(f4
3.4 x 10~4
G
<1
1
1
After the cloud has passed the vicinity of the structure, the internal
concentration is
C'(t) - C(T ) e
e
-Kt
and the dose accumulated in the shelter due to the internal airborne
source is
r2
D = G KJJ B / C'(t) dt
0
G 1C B -KT,
—j^— C(Te) (1 - e *) rem
-------
39
where
ex L
-XT
-KT
-e
The dose components EC-, 1C., and 1C. are obtained in the manner given
above for EC., 1C.., and TC... Dosages due to airborne gaseous fission-
produced sources inside the structure are given by (ECj+EC-) + (IC.+IC.)
for the WB and (TC+TC for the thyroid.
Airborne Source — Outside
During the time interval T., it is assumed that individuals are
unprotected and dose components are similar to those given for unpro-
tected exposures over the exposure interval to the cloud, T , i.e.,
fEC'l
0
ic;
TC'
u 0J
«
V
YB
-K3-B-
-X(TR+Ta)
f Q e
rxo
V
-XT
(1 - e
rem
The attenuated WB gamma-ray exposure in the shelter structure from the
outside airborne cloud source over the internal (T.,T ) is given by
j.
j_ - A(l-G) KjX0 f
T,
dt
-XT
- e
rem
where A is the cloud gamma-ray attenuation, (1-G) is the source-geometry
correction factor for the outside cloud, and x —the reference concentra-
• o
tion per unit x/Q—is
-------
40
-X(TR«)
e
T
e
Surface Source—Inside
The differential equation for the surface deposition rate for radio-
iodine in the shelter structure is
^-V'C — —1
FD1 "
;Gie*0LK4 > i
K' JA2
r -ATI
(ATj+l) e
-AT \ . / -Kl
e 1 , ! L
-IT
(AT +1) e e
\ -KT \ f
1 e\\
retn
After cloud passage, the WB dose from internal radioiodine surface de-
position that accumulated during cloud passage is given by
F(Te)in I e" dt
0
\1
;J
VeG>CXQLK4 I Te G " 1 /-U -KtW, -AT2
—_ | . ___ j e _ e J (1 - e /| rera
where F(T ), is the internal fallout level at T .
e in e
-------
41
After cloud passage, internal radioiodine fallout deposition con-
tinues to take place owing to the residual airborne source inside the
shelter structure. The rate of internal fallout deposition is
- XF(t)
Integrating the above yields the fallout deposition from the post-cloud
passage internal-airborne source in the shielding structure, which is
in turn integrated to yield the WB dose written as (see Appendix B)
FD.
V'G'ex I
g AQ
K1
-AT
-KT
- e
""
- •
) - * fr -
rem
The WB external gamma dose from internal radioiodine fallout in the shelter
structure is given by (FD +FD_+FD_).
Surface Source—Outside
During the time interval TI, the accumulated WB dose while seeking
shelter (unprotected) from outside ground fallout deposition is
FD1 = K.
o A
T.
/
F(t) ,. dt
out
V Y K.
g*o A
r
ll -
ii
H
rem
During the time interval (T1,Te), the WB gamma dose inside the
shelter structure from outside ground-fallout deposition is
-------
42
Xl
( i r -XTI -XT 1 )
- A> W«V21 <*Ti+1) e - (xvl} e ej ( rem
where A* is the shelter-structure attenuation of gamma rays from the
ground-fallout source.
The WB gamma dose accumulated inside from residual outside ground
fallout deposition is
T2
FDl - A'K. F(T ) k f e"Xt dt
2 4 e outJ
0
-XT
T e e -XT
After !», the time interval assumed during which people may continue to
be in the shelter structure after outside cloud passage, the computational
model assumes that individuals leave the vicinity of the shelter over a
time interval, T , either unprotected (e.g., on foot) or protected from
residual ground-fallout source gamma radiation while leaving the con-
taminated area in a vehicle with i
Accordingly, the WB gamma dose is
taminated area in a vehicle with a shielding attenuation factor of A1.
T+Tv
// v
-At .
e dt
AM, * Te e"^ F -XT2 -*
-------
43
The external WB dose from shielded gamma radiation emanating from
ground-fallout deposition outside the shelter structure (with the
exception FD', where the receptor is assumed outside) is FD' + FD,1 +
o o 1
FD^ + FD^. Note that for FD^, FD^, and FD' (receptor inside) a geometry
factor—i.e., (1-G1)—is not assumed, which is consistent with the attenua-
tion values, A1, for ground-source fallout deposition. That is, the
fallout source on the roof of a simple structure would approximate the
ground-fallout source deposition in terms of source geometrical effects
for the reference dose point 1 meter above an idealized ground-plane
source, (see sketch below).
Shelter
structure
Fallout with no
structure
SHELTERING AND EVACUATION
An investigation was made to determine the utility of the combined
protective action of sheltering and evacuation. That is, both from the
standpoint of time constraints and th.e DRF, the combined .protective-
action measures may offer an advantage over sheltering only. For example,
for individuals located relatively close to the point of the accidental
release in terms of either distance or cloud-arrival time, sheltering
may be the only option. Furthermore, if the duration of the source
release were to continue longer than expected because of, e.g., wind
persistence or miscalculation, exit and evacuation from the shelter
structure may be advantageous in terms of dose savings as opposed to
remaining inside over the whole cloud-passage time. The important
considerations in addressing this question are exit-time from the
-------
44
shelter structure, Tg, evacuation transport time, T,_, and cloud exposure
time, T ; and protection characteristics of the shelter structure (see
above) and any evacuation vehicle(s) that may be used from transporting
people out of a radiocontaminated area.
The analysis of the above situation is based on a simple model
(Fig. 9) assuming ideal sheltering conditions where both shelter-entrance
delay time and residence time after cloud passage are zero (T. - 0,
T_ - 0; see Fig. 8). Figure 9 is a plot of accumulated dose as a function
of shelter time up to the cloud passage time, T , where the dose is D_.
e o
Values D.. and D. are to suggest possible accumulated dosages for shelter
exit at TS and evacuation time T_. During the interval T , the model
assumes that individuals are exposed to airborne and ground-fallout
source radioactive material while in an evacuation vehicle that offers
some degree of protection discussed below. The decision is' simplified
to making a comparison of the estimated dose values. That is, for
D- < DC, exit from the shelter structure and evacuation would be a serious
consideration; whereas, for D0 > D_, it would be more advantageous to
L. &
remain inside from the standpoint of dose savings.
An equivalent means of deciding whether to effect shelter exit and
evacuation is based on DRF comparison. The actual numerical approach
taken in this analysis is based on the question of for what values of
Tg, TT, and T£ is the relationship (DRF)S/E <_ (DRF)g satisfied, where
D(T ).
(DRF)S = (Te)in (shelter only)
e out
and
. D(Vin - D(TS'Te>in * D(TS'TT>ev (shelter and
S/E D^Vout evacuation)
where
-------
D,
8
Ln
I 1
Shelter time
Fig. 9--She1tering and evacuation
-------
46
D(T ) f " dose outside shelter structure,
^i " dose inside shelter structure,
D(T_,T ). - dose inside shelter structure over interval
o e in
-------
60r 1.0
50
0.8
40
0.6
30
0.4<
20
0.2
10
no A/C me tor
Tur
ning
10 20
30 40 50 60
Vehicle speed (mph)
70 80
90
Fig. 10--Air exchange and infiltration rates in closed passenger compartment
when air conditioning is set at a maximum
-------
outside air. At higher speeds and with the same settings, Q/V (air change
rate) would be expected to approach the values obtained with the air-
conditioning unit in operation. This expectation is based on the
assumption that general leakage rather than the fan is the dominant
factor determining f/v at these speeds. A value of 0.5 min (30 hr )
was chosen for this analysis, which corresponds to ^35 mph when general
leakage is the dominant factor for f/v. Penetration of gaseous fission
products into evacuation vehicles was assumed to be 100 percent for the rare
gases and 80 percent for radioiodines, which corresponds to the upper limit
of the estimates of Megaw [12] based on simple shelter structure experiments.
For sheltering, the DRF and dose component relationships are as given
above (p. 28ff.); where, for D(Tg,T )± above, Tg - 1^ and TZ - 0. For
evacuation, the vehicle is assumed to be analogous to a shelter structure,
and dose estimates for D(TS,T_) for the exposure-evacuation time, TT,
are based on the same dose components considered for shelters—with the
exception of radioiodine deposition inside the vehicle, which is assumed
to be insignificant and, moreover, cannot be modeled accurately without
some experimental verification.
External WB cloud-dose accumulation from gamma-ray penetration of
the evacuation vehicle is
T +T
/S T -At
EC_ - A.(l-G..)KlXo J e dt
out v v
T
S
-ATS 1
' V^Wo e I (l - e * j rera
where A is the vehicle attenuation for cloud-source gamma radiation,
G the finite cloud-source geometry factor, and K., the dose conversion
factor.
Inside the evacuation vehicle, the rate of concentration change
is
-------
dC(t) T -Xt „ „, v
"It exoLve -KvC(t)
where Ky - L + A.
Integrating the above for C(0) - 0 gives
C(t) •= eX0(e~Xt - e
-K t
(Ci/m3)
for the concentration in the vehicle. The dose accumulated in the vehicle
over the period T is given as
in
T +T
S T
C(t) dt
G ex BK_ e
v Ao D
-XT.
-XT
rem
Specific dose components are obtained based on the values for the
constants as given below:
EC,
in
1C.
in
TC.
in
S
Kl
K2
K3
B
1
3.4 x 10~
3. A x 10~4
K
v
<1
1
1
-Xt
The ground-fallout deposition given above is F(t) = V Y t e
out go
The external WB dose from ground-fallout source gamma-ray penetration
of the vehicle during evacuation is
-------
50
/•
J
Ts
F(t)out dt
A'V x K, r -XT- -X(T_+T,_)-i
- VR2° 4 I (XTS+1) e S - (XTS+ TT+1) e S T I rem .
The dose accumulated during evacuation, D(T ,T ) , corresponds to
either the WB or thyroid. For the WB, the dose is (EC., +EC >IC. +FD ):
' in out in out '
for the thyroid, TC. . Note that internal exposures for EC. and 1C. are
assumed to accrue only when the evacuation vehicle is in the vicinity
of the airborne radioactive gaseous material over the period T_, which is
a very good approximation considering the large values of L . That is,
in actuality, once the vehicle leaves the vicinity of the airborne radio-
active material, x in the differential equation above is zero and the
internal vehicle concentration drops very rapidly within a few minutes—
which would not give rise to any significant dosage as compared with con-
ditions when the vehicle is assumed to be in the vicinity of the airborne
radioactive material, provided of course T_ is more than a few udnutes.
That is, the equilibrium concentration that would be reached in the
vehicle within a few minutes is given as
-Xt -Xt
e £*0 e -At
Lv
which would be approximately that outside the vehicle. Then, after leaving
the vicinity of airborne contamination, the concentration of gaseous radio-
active material in the vehicle falls off as exp[-(L +X)t], where L is
M).5 min"1 (30 hr"1).
-------
51
III. RESULTS
Estimates of shelter effectiveness have been made using the DRF
calculational model and assumptions discussed in Sec. II. It is, of
course, impossible within the scope of this effort to develop informa-
tion comprehensive enough to anticipate what might be expected for all
practical situations. Accordingly, assumptions are made regarding
input parameters and ranges of variables in order 1) to demonstrate the
degree of shelter effectiveness in a general sense, and 2) to indicate
sensitivity variations for some specific situations.
Input values used in the sheltering calculations fall under two .
categories. First, a set of fixed parameters were selected (summarized
in Table 6). These values are in part based on study ground rules
(DBA gaseous-release assumptions), review and analysis of existing data,
and an attempt to develop representative information that can also be
related to the Reactor Safety 5tu<% [1]. The notion of "fixed para-
meters" obviously applies only to this particular analysis; in reality,
there may be appreciable variations in shelter characteristics and,
for example, iodine deposition velocity. The second input category
consists of the temporal and ventilation rate variables selected to
indicate the sensitivity and degree of sheltering effectiveness over
their range of values. In some cases, extrapolation can be made (with
care) to estimate shelter effectiveness beyond the specific range limits
used in making the calculations.
Shelter effectiveness results are given in terms of the DRF in
Figs. 21 through 31. Enough data are given in Figs. 11 through 31 to
enable a fair amount of cross-plot extrapolation. All the time variables
have units of hours and are identified in Fig. 8 (p. 29). The ventila-
tion rate, L, is in units of hr ; and SS and LS designate the small and
large shelter structure categories, respectively. The plotted results
in Figs. 11 through 31 are discussed below.
Figure 11 gives WB DRF as a function of time (T ) in the shelter
structure after passage of the airborne cloud source, assuming no delay
(T-0) in shelter access after initial cloud arrival and 1-hr cloud
-------
52
Table 6
FIXED PARAMETER SUMMARY
SOURCE TIMES
Release Time
Case TR' Hr
A 1.5
B 2.0
C 2.5
GASEOUS FISSION PRODUCTS
Release
Fraction
Kr and Xe 1.0
I 0.25
SHELTERS
Small
Structures (SS)
Cloud gamma attenuation, A 0.6 (0.4, 0.9)a
Fallout gamma attenuation, A* 0.2
Finite cloud factor, G 0.01
Finite fallout factor, G1 0.28
Release Duration
V Hr
0.5
1.0
3.0
Ingress
Fraction
1.0
0.51
Large
Structures (LS)
0.1 (0.05, 0.2)a
0.01
0.034
0.43
DEPOSITION
V (outside) - 0.005 m/sec
V(inside)
g
0.00025 m/sec
variations
-------
0.5
0.4
0.3
OL
O
53
SS L = 0.125
A
B
0.2
0.1
A & B
L = 1.0
LS L = 0.125
-L 1 1 1 L
0 0.2 0.4
0.6 0.8
(hours)
1.0 1.2
Fig. 11—WB DRF versus T?, (T.-O.T =1)
£ i
-------
54
travel time (T -1) from the point of source release. Significantly,
£L
more protection is afforded by the large shelter structure (LS) than
the small one (SS). The effect of ventilation rate is also more im-
portant for the LS than the SS, primarily because of the difference in -
cloud-gamma attenuation. That is, a larger portion of the dose in the
SS is due to gamma ray penetration of the shelter from the outside airborne
cloud source than in the LS; that portion of the dose does not depend
on the air change rate. A value of L * 1 hr may be somewhat repre-
sentative, whereas 0.125 hr~ represents a fairly low value associated
with a relatively tight structure with very little or no forced air
circulation. The relative positions of the A, B, and C categories of
release duration are also determined by the combination of cloud-gamma
attenuation and ventilation rate. For the SS, the relatively larger dose
component from outside cloud-gamma ray penetration is sufficient to
offset the dose component from internal airborne radioactive material.
For example, for T2 = 0 and L = 1, the relative positions of A, B, and
C are the same for both SS and LS; but the spread is larger for the LS
than the SS, indicating the effect of a relatively larger number of air
changes with respect to release duration (0.5, 1, and 3 for A, B, and
C, respectively) for the LS as compared with the SS. The crossover point
at T. = 0.2 for the SS is due to the increasing importance of the out-
side ground-fallout dose component, assumed to be reduced at a rate
dependent upon only radioactive decay, as compared with the dose from
inside airborne radioactive material assumed to be reduced at a rate
dependent upon radioactive decay, ventilation, and internal fallout
deposition of the radioiodines. For low air-change rates (L=0.125 hr ),
the DRF for the SS is determined largely from external sources, where
the A, B, and C curve positions primarily reflect the differences in
radioactive source decay. For the LS, the dose components from outside
sources are relatively less important than those for the SS; and a
clear separation of the A, B, and C release-duration categories is
not seen when both inside and outside dose components are relatively
more comparable.
-------
55
Figure 12 gives DRF plots for the thyroid for the same conditions
assumed for Fig. 11, which apply to both SS and LS. In general, the
DRF values indicate somewhat more protection for the thyroid than for
the WB, and are more sensitive to T_; particularly for L » 1 hr~\
since there are no competing outside-source dose components. The
relative positions for A, B, and C are due to the different number of
air changes associated with each source release duration. Since the
DRF values in Fig. 12 correspond to a radioiodine ingress fraction of
0.51, they scale accordingly.
Calculated results of the WB DRF sensitivity with cloud-source
arrival time are given in Figs. 13 through 16. The DRF variations for
the thyroid, not plotted here, are insignificant as a function of cloud
arrival time, T . In Fig. 16, the DRF decrease with T for the SS is
£1 Si
due to the relatively decreasing importance of the WB-dose component
from the outside airborne cloud source. That is, the model includes
only simple radioactive decay and predicts that the relative contribu-
tion of the noble-gas sources to the WB dose decreases more with time
than does that of the radioiodines. In reality, that decrease with T
cl
may not be quite as prevelant, particularly for times longer than a
few hours. The countereffeet, however, is indicated for the LS, since
the significance of the external gamma WB-dose component from the
outside airborne source is masked by the greater gamma-shielding
attenuation assigned to the LS as compared with the SS. The relative
positions of the A, B, and C curves are, as indicated above, due to
the increasing number of air changes, respectively, during cloud
passage.
Figure 14 shows WB DRF as a function of T for case A, assuming
Si
late shelter access (T^O.25) coupled with extended residence time
(T2«0.5) after passage of the airborne cloud. Ideal shelter timing
(T.^0, T2-0) is also shown for comparison to indicate the significant
loss of protection for non-ideal shelter-access timing. Figure 14 also
shows loss of inherent LS protection advantage (due to shielding), as
compared with the SS, because of shelter-timing considerations.
-------
56
DC
Q
0.6 0.8
(hours)
Fig. 12—Thyroid DRF versus T_, (T,»0,T -1)
L J. a
-------
57
0.5
0.4
0.3
0.2
LS
0.1
B
A
J 1 , L
-I L
Ta (hours)
•
8
Fig. 13--WB DRF versus Ta,
O), L = 1
-------
1.0
0.8
0.6
.
0.4
0.2
0
I i
J L
I I
T, = 0.25 , T9 * 0.5
/
1 s 0
- 0 , T0 = 0
T (hours)
a
ss -
LS
J I I L
8
Fig. 14--WB DRF versus Ta> case A, (Tj-O.Tg-O),
.S) , L - 1
-------
0.6
0.5
0.4
g 0.3
0.2
0.1
0
J L
59
T, « 0.25 , T9= 0.5
^ * 0
0 , T2 = 0
T, (hours)
a
LS
Fig. 15-WB DRF versus Ta§ case B, fT^O.T^O), (Tj.0.25,1 -0.5). L
-------
0.6
0.5
0.4
1 0-3
0.2
0.1
60
I . I
ss
ss
J I
23456789
T (hours)
a
Fig. 16—WB DRF versus Ta> case C, (T^O.T^O), (T^O.ZS.T^O.S), L = 1
-------
61
Figures 15 and 16 are similar plots for cases B and C, respectively,
where timing (T][ and TZ) is relatively less important, because of
longer exposure to the cloud source.
Calculated DRF results in Figs. 17 through 22 show the effects of
shelter-structure ventilation rate. Figure 17 gives the WB DRF as a
function of air change rate, L hr"1, for ideal shelter timing (T-0,
T2=0). For L less about one air change per hour, the SS DRF is based
on a relatively larger external gamma-dose contribution from the out-
side airborne cloud source; for L greater than about one air change
per hour, the DRF is based on a relatively larger dose component from
internal -airborne radioactive material. The LS DRF, on the other hand,
is based primarily on the relatively larger WB-dose component from
internal airborne gaseous radioactive sources for all values of air
change rate, L.
Figure 18 gives the thyroid DRF dependence on the ventilation rate
for ideal shelter timing. Compared with the WB DRF values in Fig. 17,
the thyroid DRF functional dependence on L is much more pronounced,
since the thyroid dose is based solely on internal airborne radioiodine.
The advantage of low air-change rates less than about one-half per hour
is quite apparent for protection against inhalation doses.
Figures 19 through 22 show the comparative effects of ideal and non-
ideal shelter timing. Figure 19 gives WB DRF values as a function of L
for case A, showing considerable overlap of SS and LS protection for
ideal (Tj-0, T2=0) and nonideal (T^O.25, T2=0.5) shelter timing,.
respectively. Figure 20 gives WB DRF for case B as a function of L when
the SS and LS overlap is much less than in case A (Fig. 19), and Fig. 21
shows no SS and LS overlap for the longer source release duration category
(C) when the inherent LS protection advantage over the SS is maintained,
even for nonideal shelter timing. Figure 22 gives plots of the thyroid
DRF, comparing the effects of nonideal and ideal shelter timing. The
inversion in the order of the A, B, and C release-duration categories for
nonideal shelter timing is primarily due to the fraction of time an
individual is assumed to remain unprotected during cloud passage for
shelter-access delay time, T^ i.e., the fraction of time an individual
is unprotected is larger for A than for C.
-------
62
0.5
0.4
0.3
0.2
0.1
LS
: :
; 1 1
i
123
i
•
i
4
L (hours'1)
Fig. 17--WB DRF versus L,
-------
0.5
63
0.4
OS
a
0.3
0.2
0.1
L (hours'1)
Fig. 18—Thyroid DRF versus L,
-------
64
1.0
I I I I
I I I I
0.8
0.6
0.4
0.2
111,1111
T .0.25 ,V
0.5
L (hours'1)
Fig. 19--WB DRF versus L, case A, (T^O.T^O), (T^O.ZS.T^O.SJ, T - 1
-------
1.0
65
0.8
0.6
0.4
0.2
= 0
= 0
= 0
LS
L (hours'1)
Fig. 20--WB DRF versus L, case B, (T^O.T^O), (T^O.25,1^0.5), Ta = 1
-------
66
0.6
0.5
0.4
u, r\ i
Q: 0.3
o
0.2
0.1
L (hours'1)
Fig. 21—WB DRF versus L, case C, (T^O.T^O), (T^O.ZS.T^O.S)
= 1
-------
67
1.0
i i i
i i i
T, « 0.25 ; T9- 0.5
0.8
0.6
0.4
0.2
L (hours' )
Fig. 22-Thyroid DRF versus L, (T^O.T^O), (T^O.25,1^0.5), Ta = 1
-------
68
Figures 23 through 25 show WB and thyroid DRF values in terms of
T^ and L in parametric perspective. WB DRF values are shown in Fig. 23
for case B and for LS. DRF values for TI - 1 (also the cloud passage
time for case B) can exceed unity for the larger values of L; this
situation corresponds to entering a shelter after cloud passage, which
gives rise to additional dose from lingering internal contamination
for T_ > 0, although the relative loss in shelter protection as a
function of T is insignificant for all values of TI and L. Also,
calculations performed during this study indicate virtually no protective
advantage in seeking shelter after unprotected exposure to a passing
radioactive cloud.
Figure 24 is essentially the same parametric perspective plot as
Fig. 23 for the SS. Figure 25 gives corresponding plots of the DRF
for thyroid, indicating considerable overlap for certain parameter
combinations of shelter-access delay time, T., and air change rate, L.
Figures 26 and 27 indicate the effects of shelter-structure attenua-
tion of gamma radiation from the outside airborne radioactive cloud for
the SS and LS, respectively. Figures 26 and 27 contain plots of the
WB DRF for independent variations of the cloud gamma attenuation, A.
In practice, such variations would not necessarily be independent of the
shelter-structure attenuation of ground-fallout gamma radiation, as
normally some correlation would be expected. The results in Fig. 26
indicate, however, that a factor-of-two increase in gamma attenuation
results in about an 80-percent increase in shelter protection for the
SS, whereas a factor-of-two reduction in the air change rate (2 to 1
air changes per hour) results in about only an 8-percent increase in
shelter protection. In the LS, the effect of cloud gamma attenuation
is not as significant. Results in Fig. 27 indicate that a factor-of-
two increase in cloud gamma attenuation results in a 50-percent increase
in shelter protection, whereas a factor-of-two reduction in air change
rate (2 to 1 air changes per hour) gives rise to a 20-percent increase
in shelter protection.
-------
69
1.2
1.0
• L
•1.0
0.125J
0.8
_3.0
-1.0
-0.5
0.125
0.75
ce.
o
0.6
-3.0
•1.0
•0.5
0.125
0.50
0.4
0.25
0.2
j L
0.125
0.2
0.4
0.6
T2 (hours)
0.8
1.0
1.2
Fig. 23—WB DRF versus TQ, case B, LS, T - 1
c. a
-------
70
1.2
1.0
0.8
g 0.6
0.4
0.2
J L
0.2
i i
i i i
0.4 0.6 0.8
T (hours)
•
3.0
1.0
;0.5
0.125
3.0
= 1.0
-0.5
0.125
1.0
0.75
J I L
1.0
1.2
Fig. 24--WB DRF versus T9, case B, SS, T = 1
c a
-------
71
3.0
1.0
0.5
3.0 0.25
0.125 0.5
1.0 0.25
0.02
0-4 0.6 0.8 1.0 1.2 1.4
Fig. 25—Thyroid DRF versus T9, case B, T = 1
f- u
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72
1.0
0.8
0.6
0.4
0.2
IT (I
I I
J L
J L
2.0 0.9
1.0 0.9
0.125 0.9
2.0 0.6
1.0 0.6
2.0 0.4
0.125 0.6
1.0 0.4
0.125 0.4
0.2
0.4
0.6
T2 (hours)
0.8
1.0
1.2
Fig. 26--WB DRF versus T2, case B, SS (A=0.4,0.6,0.9,1=0.125,1.0,2.0)
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73
0.30
0.20-
cc
a
0.10-
1.0 0.2
2.0 0.]
2.0 0.05
L.O 0.;
1.0 0.05
0.125 0.2
Fig. 27--WB DRF versus T2> case B, LS (A=0.05,0.1,0.2,1=0.125,1.0,2.0)
-------
74
Figures 28 and 29 are plots of shelter DRF as a function of shelter-
delay access time, T.., for the WB and thyroid, respectively. Figure 28
plots are given for a range of 0.5 to 1.5 air changes per hour, which
is recommended by Handley and Barton [7] as applicable to single-family
dwellings. The value of two air changes per hour for the LS is also
consistent with their recommendations for larger structures and apart-
ment buildings. For ideal shelter timing, T. - 0, and !„ •> 0, the LS
provides about twice the protection as the SS, which decreases with
increasing access delay time. Figure 29 gives thyroid DRF plots for
the same conditions as Fig. 28; since the thyroid dose is dependent
only on the ventilation rate, somewhat less protection is afforded by
the LS than by the SS, because of the difference in ventilation rate.
Figures 30 and 31 illustrate the difference in shelter protection
afforded for the WB and thyroid under ideal and less-than-ideal con-
ditions. In Fig. 30, DRF values are given as a function of T. for a
low air-change rate (0.125 hr"1) and TZ - 0. For T = 0, the SS pro-
vides a factor of about 2.8 for WB-dose protection; whereas the LS
provides a factor of about 12.5—a relative protective advantage of
4.5—for the LS over the SS. In Fig. 31, for less-than-ideal shelter-
ing conditions (T2=0.25 and L=l hr"1), the SS provides a factor of
about 2.2 protection for the WB dose; whereas the LS provides a WB
protective factor of ^6.7—a relative protective advantage of about
3—for the LS over the SS. The change in the protection for the
thyroid dose between ideal and less-than-ideal sheltering conditions
is about eight-fold; the shelter protection factor of the thyroid dose
is about 40 for ideal conditions and about 5 for less-than-ideal
conditions.
Figure 32 shows the estimated effect of the iodine ingress fraction
on the WB DRF. The rise in WB DRF is linear with the iodine ingress
fraction, with the slope primarily dependent on the ventilation air-
change rate. The increase is most apparent for the LS, for repre-
sentative air change rates, and least apparent for the SS, for low air-
change rates. Again, this difference is due to the relative contribution of
the dose components from radioactive sources outside and inside the
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75
1.0
Release Time, TR » 2 hr
Exposure Time, T - 1 hr
01—L
J , L
'
J L
0.2 0.4 0.6 0.8
T (hours)
1.0
1.2
Fig. 28--WB DRF versus TI? case B, (Ta=l,T2=0), SS (1=0.5,1.0,1.5), LS (L=2)
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76
—1-71—I 1 1
0
0.2
0.4
0.6 0.8
(hours)
1.0
1.2
Fig. 29—Thyroid DRF versus T^ case B, (Ta=l,T2=0), L = 0.5, 1.0, 1.5, 2.0
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77
at
o
0.02
0.2 0.4
0.6 0.8
(hours)
1.0 1.2 1.4
Fig. 30--WB and thyroid DRF versus TI§ case B, (T =1,T2=0,L=0.125)
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78
2.0
1.0
0.1
0.02
J I L
0 0.2 0.4
0.6 0.8
T (hours)
J L
1.0 1.2 1.4
Fig. 31--WB and thyroid DRF versus Tj, case B, (T »1,T2=0.25,L»1.0)
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79
0.1 - •
0.2 0.4 0.6 0.8 1.0
Iodine ingress fraction
1.2
Fig. 32--WB DRF versus iodine ingress fraction, case B, (T,=O.T9=0,T =1)
icct
-------
.80
shelter. As indicated above, a value of 0.51 was used in the calcula-
tions for estimating the DRF. If iodine ingress were 100 percent, the
DRF may be from about 1.4- to 14-percent higher for SS and from about
16- to 46-percent higher for LS. Of course, for the thyroid dose, the
DRF could be nearly double (assuming ideal shelter-access timing).
Figures 33 through 35 are based on calculations for the combined
protective action of sheltering and evacuation. The results shown are
for the shelter time, Tg, and the evacuation transport time, TT, which
together would provide protection equal to that of sheltering alone
during the period of cloud exposure, T . The conditions of sheltering
are consistent with ideal timing; i.e., individuals are assumed to be
in the shelter at the time of cloud arrival (T =0) and exit immediately
after cloud exposure (T2=0). The combined protective actions of shelter-
ing and evacuation assume that individuals exit the shelter after a
period, TS, and evacuate during the period TT, while exposed to the
airborne radioactive cloud material during its transit away from the
shelter area. Accordingly, if the structure were exited after a
shelter period, Tg, evacuation out of the vicinity of cloud exposure
should not exceed the time period, TT» to effect a dose protection at
least equal to that provided by staying in the shelter. Therefore,
time combinations (Tg,TT) that lie between the curves and the axes
would give rise to greater dose protection from sheltering plus evacua-
tion than from sheltering only. For example, considering WB-dose pro-
tection in the SS shelter for low air-change rate conditions and a
cloud exposure period, Tg = 3 hr, evacuation from the shelter vicinity
should be accomplished in no more than about 0.75 hr if the shelter is
abandoned after 1 hr of cloud exposure; if exit takes place after 2 hr
of sheltering, the evacuation time that should not be exceeded is
shortened to about 0.4 hr. Under the higher representative air change
rate of L = 1 hr , the maximum allowable evacuation times increase
somewhat to about 1 and 0.5 hr for respective shelter-exit times of
1 and 2 hr, assuming a 3-hr cloud exposure period. The increase in
allowable transit time, TT> is primarily due to a larger dose incurred
in the shelter structure with the higher air change rate.
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81
10
1-
3
O
1.0
c
«J
0.1
L =
0.125 hr
1.0 hr"1
-1
\
0.1
\
\
1.0
Shelter time, TS (hours)
10
Fig. 33—Sheltering with evacuation, WB, SS--transit time versus shelter time
(Ta=0.5)
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82
10
1.0
-
-
.
0.1
0.01
L i 042$ hi
L » i.o hi
T • t
, , .
* *
4-
0.1
1.0
10
Shelter time, T«. (hours)
Fig. 34--Sheltering with evacuation, MB, LS--transit time versus shelter
time (T =0.5)
3
-------
83
10
1.0
-
'
0.1
0.01
: .
• '
» •
i ;
, .
[ilm-_
L »• OJ125 Hr;
L f 1.0 hr. .
1 '.
0.1
1.0
10
Shelter time, TS (hours)
Fig. SB—Sheltering with evacuation, thyroid—transit time versus shelter
time (T =0.5)
Q
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84
Figure 34 gives shelter evacuation break-even times for the LS
shelter. For low air-change rate conditions, much less time is allowed
for evacuation from the LS shelter area than from the SS for a given
shelter-exit time, Tg, because of the significantly greater margin of
protection (lower DRF) offered by the LS. For the higher representative
air change rate of L - hr~ , the allowable transit time from the LS
shelter again is less than that for the SS shelter; but the time
difference is not as great as compared with that for the low air-change
rate situation.
Figure 35 gives the shelter evacuation break-even time points for
thyroid dose protection. The lower maximum allowable evacuation transit
times for the lower air change rate as compared with the higher representa-
tive air change rate are due to the larger margin of protection provided
when air change rates are low and accordingly less time is required for
the accumulation of the break-even dose during evacuation from the
shelter.
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85
IV. CONCLUSIONS AND RECOMMENDATIONS
Shelter protection provided by a large variety of public structures
can provide a significant reduction in WB and thyroid dose from ex-
posure to radioactive gaseous fission products that might be released
during a nuclear power plant accident. Protective sheltering is
attractive if shelter-access timing is ideal, but its effectiveness
diminishes almost linearly with access delay time after cloud arrival.
Sheltering protection against inhalation exposures that result in
thyroid dose depends on the number of air changes taking place over
the period of exposure to airborne radioactive cloud material. Shelter-
ing protection for WB exposures depends on the attenuation of gamma
radiation originating from the airborne cloud source, the number of
air changes during cloud exposure, and (to a lesser extent) the
attenuation of gamma radiation originating from the ground fallout
about the shelter structure. Accordingly, optimum ventilation control
(low air-change rates during cloud passage) is more effective for
reducing thyroid dose than WB dose. Albeit, ventilation control is
relatively more effective for reducing WB dose in LS than in SS.
Large structures such as office buildings, multistory apartment
complexes, department stores, etc., generally would provide significantly
more sheltering for WB exposures than smaller structures such as single-
family dwellings—a factor of about 4.5 more during low air-change rate
conditions and 3 more for nominal air change rates. That is, WB doses
would be reduced by a factor of 2.5 to 3 for SS sheltering; whereas
for LS sheltering, WB doses would be reduced by a factor of about 12
during low air-change rate conditions. For representative air change
rate conditions, WB dose would be reduced by about 2.3 for SS and from
6 to 9 for LS. Wli dose can be further reduced in a shelter structure
through use of expedient filtration; e.g., by stuffing cracks and open-
ings with cloth or paper materials, which would reduce radioactive material
ingress (discussed above, p. 10 ff.) and/or the natural ventilation rate.
Similarly, another means of respiratory protection is to cover the nose
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86
and mouth area with such common items as towels, handkerchiefs, or toilet
paper: e.g., a crumpled handkerchief (or one with eight or more folded
layers), a towel of three or more folded layers, or toilet paper of three
or more folded layers can reduce inhaled radioactive material (particulate
iodine in this study) by a factor of about 10 [35]. The reduction of
WB dose in a SS, however, is not appreciable—about 2.5 percent for low
ventilation rates and about 15 percent for representative ventilation rates.
The reduction in WB dose in a LS would be more appreciable—about 13
percent for low ventilation rates and about 70 percent for representative
ventilation rates.
The difference in thyroid dose protection between SS and LS shelters
is not as apparent as for WB dose, because of the more nebulous correla-
tion of building air change rate than gamma radiation-attenuation pro-
perties with the general type of structure. The degree of variability
in the air change rate—an important parameter affecting the thyroid
exposure—prevents meaningful estimates of the thyroid DRF for SS as
opposed to LS shelters. Accordingly, LS may not necessarily have any
protective advantage for thyroid dose reduction over SS or vice versa,
due to any number of factors—open portals, filtering action, air con-
ditioning, structural integrity, etc. Sheltering protection for either
SS or LS, however, can result in thyroid dose reduction by a factor of
from about 20 to 70 for low air-change rates, and from 4 to 10 for repre-
sentative air change rates. These ranges are primarily due to the
corresponding range of cloud-exposure periods of from 0.5 to 3 hr, where
the DRF increases, although not linearly with the air change rate (or
number of air changes). Another important parameter affecting the thyroid
DRF value (also the WB DRF to a lesser extent) is the ingress fraction,
which is treated like an effective filtering action in this study. For
that parameter, a value of 0.51 was assumed for the radioiodines, based
on review of limited experimental work discussed above (p. 10 ff.). The
thyroid DRF values given would then scale linearly with whatever value
is assumed. The use of expedient filtration discussed above for WB dose
can be even more effective in reducing thyroid dose (i.e., reducing radio-
iodine ingress and/or ventilation by stuffing openings and cracks or
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87
usini; such common items as handkerchiefs and towels for respiratory pro-
tection). Such expedient filtration could reduce thyroid dose by a
factor of about 10 [35].
The protection against WB dose decreases linearly with the amount
of radioiodine penetrating to the occupied spaces of a shelter structure.
The decrease is more apparent for LS than SS, because of the relative
differences in the gamma ray attenuation from sources outside the shelter,
and is also related to the number of air changes that take place during
the cloud-exposure period. For this analysis, an ingress fraction of
0.51 is assumed for making DRF calculational estimates. This assumption
implies that radioiodine sources collect at certain locations in the
shelter structures. Therefore, insofar as these locations could repre-
sent "hot spots," local exposure of individuals who may be adjacent to
these collection points could result in dose increase. No attempt has
been made here, however, to deal with that problem other than to make
note of it. In view of current uncertainty regarding penetration of
radioiodine into structures that could be used as shelters, the need
for more experimental results must be emphasized.
The degree of WB dose protection afforded by shelter structures
as a function of cloud-exposure time depends largely on the relative
contributions of the exposure modes. The larger the relative external
dose contribution from penetration of gamma radiation into the shelter
as compared with WB-inhalation dose, the less the effect of cloud-exposure
time on shelter effectiveness. For example, for the SS where gamma ray
penetration is relatively more important, the DRF would remain relatively
constant for cloud-exposure periods up to several hours. For low ventila-
tion rates, the sheltering protection may even increase somewhat—only
about 15 percent or so—because of changes in the radioisotope source
mix as a result of decay.
For LS shelters, where the WB dose component from gamma ray pene-
tration is relatively less important than in SS shelters, the degree of
protection still remains nearly constant for cloud-exposure periods up
to several hours for low ventilation rates; but for representative
ventilation rates, the relative protection for sheltering diminishes
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88
significantly—e.g., a factor of about 1.7 for a 3-hr cloud-exposure
period as compared with a 0.5-hr period. The utility of ventilation-
rate control in minimizing the number of air changes during sheltering,
especially for LS, is strongly supported by the results of this analysis.
Maintaining low ventilation rates is even more important from the stand-
point of thyroid dose reduction for either LS or SS, as the loss in
protection for the same cloud-exposure periods mentioned above would
amount to a factor of about 2.5 for a representative ventilation rate
of one air change per hour during sheltering.
Small-structure shelter protection for WB doses tends to increase
somewhat with cloud arrival time because of radioisotope decay and
corresponding changes in radionuclide proportions. For LS shelters,
protection remains nearly constant with cloud arrival time, because
of the relatively larger inhalation dose component; this holds true
even more so for thyroid dose protection.
Shelter protection for WB dose diminishes for LS to a greater
extent than for SS with increasing ventilation rates. For a low
ventilation rate (L=0.125 hr"1) as compared with a high ventilation
rate (L«=4 hr ), SS shelter protection diminishes by a factor of
^1.32, whereas LS shelter protection diminishes by a factor of ^2.7;
thyroid dose protection decreases by a factor of ^6.
The attenuation of gamma radiation from airborne radioactive material
outside the shelter structure is more important to the WB DRF than that
of ground fallout about the shelter. Also, the effect of gamma ray
attenuation on the DRF from sources outside the shelter .is more signifi-
cant for the SS than the LS, whereas the converse holds for the ventila-
tion rate. That is, a factor-of-two increase in gamma attenuation
results in about an 80-percent increase in shelter protection for the
SS, whereas a factor-of-two reduction in the air change rate results in
only about an 8-percent increase in shelter protection for WB dose.
For the LS, a factor-of-two increase in cloud-gamma attenuation results
in a 50-percent increase in shelter protection, whereas a factor-of-two
reduction in the air change rate gives rise to a 20-percent increase
in shelter protection.
-------
The penalty in shelter protection for remaining in the shelter
after the cloud-exposure period depends on the number of air changes
taking place during cloud passage coupled with the relative contribution
to the dose from inhalation. When air change rates are low, no signi-
ficant loss of protection for the WB dose in either the SS or LS occurs,
regardless of how long individuals remain in the shelter after cloud
passage. WB-dose sheltering protection is not affected very much when
remaining in a SS after cloud passage; for a LS, shelter effectiveness
may be reduced from 10 to 20 percent by remaining in the shelter for a
period up to about an hour after cloud passage. The sheltering pro-
tection penalty is much more pronounced for the thyroid dose, which can
amount to a factor of about a 1.2 to 3 increase in the DRF, as compared with
ideal shelter-timing conditions, should individuals remain in the shelter
for a period up to about one hour after cloud passage.
The extent to which sheltering is attractive depends on the ratio
of the projected dose to the protective action guide (PAG). Generally
speaking, when that ratio is comparable to the reciprocal of the DRF,
sheltering is effective as an emergency protective action. Also, for
conditions where the projected dose is so large as to cause acute
injury, and the predicted time of cloud arrival prevents effective
evacuation, a reduction in dose by even a factor of 2 to 3 may be
quite important.
The combined protective actions of sheltering followed by evacua-
tion during cloud exposure (as opposed to only sheltering) can be an
attractive option from the standpoint of total dose reduction. The
advantage becomes increasingly more attractive as the degree of pro-
tection offered by a shelter structure decreases and/or the cloud-
exposure period increases. That is, for WB DRF considerations, the
shelter/evacuation option is generally more attractive for SS than LS
and also for high air-change rate conditions than low ones. The air-
rate change considerations are more important for the LS than the SS
as far as the option advantage is concerned, and most important for
thyroid dose protection. Logistically, the option can be attractive
for cloud-time arrival conditions that would preclude effective evacua-
tion coupled with increasing periods of cloud exposure.
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90
The extent to which the results for shelter effectiveness developed
in this study can be applied to the release of particulate airborne
radioactive material from a nuclear incident can not be quantitatively
estimated here for two reasons: 1) the relative contribution that
radioactive particulates make to the total dose depends on the extent
of their release; 2) the ingress of particulate fission-product material
into shelter structures may be different from that assumed here for
gaseous radionuclides. Overall, however, shelters would tend to offer
more protection in varying degrees than that indicated here for the
gaseous fission product. Therefore, application of the DRF values to
particulate release material would be conservative. Further mention
should be made for some specific considerations.
Shelter structures would be increasingly more effective in reducing
dosages from inhalation exposures, for increasing proportions of partic-
ulate release, simply because of effective filtering action. For WB
dosages, shelter structures would tend also to be somewhat more effective;
however, the extent to which that may be the case is complicated by varia-
tions in the dose component contributions. In general, however, when the
WB dose for nonshelter conditions (unprotected) becomes progressively
more attributable to particulates, the more effective sheltering becomes.
Also, LS shelters would offer more protection than SS shelters for equi-
valent particulate release situations.
Both experimental and analytical work is needed to more accurately
and specifically assess the protective advantage of sheltering.
In the experimental area, the extent of radioactive ingress into
potential shelter structures still remains uncertain. Therefore, some
effort using representative structures (or models) under controlled
shelter-structure conditions and a variety of correlated meteorological
conditions should be undertaken to obtain reliable measurements. If
possible, the experiment should also address representative particulate
ingress.
Another experiment that could yield useful information for shelter-
ing protection prediction is the measurement of WB external gamma dose
from airborne cloud material for shelter structures on an inside/outside
dose basis. Of course, such an undertaking may be difficult in view of
the intentional controlled release of radioactive airborne material.
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91
Such measurements, however, could possibly be obtained in conjunction
with experimental programs carried out for verification of computer
codes used to predict off-site doses (e.g., the ERDA Health and Safety
Laboratory programs).
In the analytical area, it would be useful to make additional esti-
mates of shelter protection for specific cases based on more definitive
shelter characteristics that might correspond to specific locations.
The principal specific parameters would be gamma ray attenuation, finite-
source geometry-correction factors, air change rate, fallout deposition,
and cloud arrival time. Also needed is model improvement regarding
radionuclide source components. To that end, it would be useful to
assess the effect on the shelter DRF when parent-daughter decay is
considered along with specific attenuation and finite source-geometry
correction actions for each radionuclide. Finally, additional analytical
attention should be given to include estimates of sheltering pro-
tection for radioactive airborne releases that contain particulate
material. Such a research effort would focus on the extent and nature
of the particulates and their ingress into shelter structures. DRF
estimates would also be made using the type of model for the gaseous
fission-product release addressed in this study.
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92
Appendix A
FALLOUT GAMMA SOURCE
FINITE GEOMETRY CORRECTION
Consider the following sketch for the dose calculated at a vertical
distance d from a plane source of isotropic gamma-emitting material of
2
source strength S (gammas/cm /sec):
3.
R2, is
The dose rate at P from an annular source, radially bounded from R to
4irr
(1)
where k is a dose conversion constant, B(ur) is a gamma-ray dose buildup
factor, and jj is the gamma-ray absorption coefficient. The ratio of the
dose D(0,R) to D(0,°°) is defined here as the finite plane-source geometry
correction factor given as
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93
D(R>°°)
(2)
222
Assuming the Berger buildup factor form, and since r » p + d ,
m
/
kS f -yr
D(R,«0 = -~ I (1+Cyr eUwr) ^ dr
kS
f ^
J r
VR^?
dr + Cy
+d
(3)
Substituting u = yr for the first integral, and evaluating:
kS
V
fe-»
J ~
du -
Cy e
-(l-D)yr
(l-D)y
7 7
+ _C e-(l-D)y
fR2-,d2l
(4)
where E^x) is the first-order exponential integral function.
since D(0,«>) = DU,"),
lim
R -> 0
Then,
ks
0(0,00) . -a. Ei(yd) + _£_ e-(i-D)ud
(5)
-------
Appendix B
DOSE REDUCTION FACTOR
DOSE COMPONENTS --UN SHELTERED
WB Fallout Gamma Source
The outside-fallout deposition rate is assumed to be
e"xt - AF(t> • CD
Multiplying (1) by the integrating factor eAt,
which can be written as the total differential,
(2)
O **
Then, integrating
t
f d [eXt1F(t')] = \XQfdt' .
we have
F(t) = V x
go
and then
F(t>n,,r - V X t e'U Ci/in2
Terms used in this appendix are listed on p. 102.
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95
The fallout dose during cloud passage where x 1* 0» over the interval
(0,Te), is
K, / F(t) dt - V K,x f
A J ^ 'out g 4Ao./
-Xt .
t e dt
(4)
Integrating by parts,
/•e \f 0~xt
/ t e dt - -(Xt+1) -S-y-
- * [*•
-XT
e w (XTe+l)|
(5)
After cloud passage, the residual ground fallout is
F' (t) = F(T ) e
'out v e'out
-Xt
The WB gamma dose accumulated over the period (T-+T ) after cloud passage
from residual fallout is
K, / F'(t) ^ dt « K.F(T ) /"
4 J out 4 e out y
0 0
-Xt .
e dt
^outlL1-'
(6)
The outside reference fallout WB gamma dose (unprotected) due to ground-
fallout deposition as given by Eqs. (5) and (6) above is
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96
-AT
FD = V
o
- (AT +1) e
-XT
T e
e
1 - e
rem
(7)
DOSE COMPONENTS—SHELTERED
Airborne Source—Inside
The rate of change of the airborne concentration in the shelter
structure during cloud passage is
- IC(t)
(8)
Kt
Choosing e as the integrating factor and rewriting as the total
differential,
d Ktp, .,
te C(t)l
(R-A)t
v
(9)
where K = L+A+Kf and K-A * L+K-. Integrating over the interval (0,t)
where C(0) = 0,
C(t)
dt'
e
and the concentration is
_, . CXOL , -At -Kt.
C(t) - -r- (e - e }
Ci/ra
(10)
The dose in the shelter structure is given by integrating the con-
centration (10) over the interval (T ,T ) and multiplying by the appropriate
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97
dose conversion and finite-source correction factors designated here
by K:
T
•2
r
D - K / C(t) dt
T,
1
L
(11)
After cloud passage, the concentration in the shelter structure as a
function of time is
ex L / -XT -KT \
ol o e\ -Kt T
1 -" J , (12)
and the dose accumulated in the shelter structure over the period T
after cloud passage is
*2
D = < J C'(t) dt
0
(L+Kf
Surface Source — Inside
In the shelter structure, the rate of change of surface-fallout
deposition (assumed on the floor space) is
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98
Again, choosing the integrating factor e and rewriting as the
total differential,
d , At
dF [e
(L+Kf)
(15)
where K1 = (L+Kf).
Then, integrating where F(0) = 0,
Vlex L r
V'eX L
8 °
(L+Kf)
['-* a-.*',]
giving the inside fallout deposition as
WM ,- SCX° rf-a~Xt x ^ ~At -Kt,
F(t)in T&HCj te -F" (e ' e ^
Ci/m
(16)
The WB external gamma dose accumulated over (T,,T ) is
1 e
FD,
G'V'ex LK,
e o A
(L+Kf)
dt
1 f& . -At -Kt, .
~ K7" 7 ^6 ~ 6 ^
.(17)
Integrating Eq. (17) above (first integral by parts) gives
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99
FD
1 (L+Kf)
-XT -AT
e x - (ATe+l) e
-KT
- e
rem . (18)
After cloud passage, the accumulated fallout level at T is given by
Eq. (16) evaluated at I& O^Vin^ which diminishes by radioactive decay.
The WB external gamma dose accumulated over interval T. after cloud
passage is
FD
dt
V'G'ex LK.
g Ao 4
(L+Kf)
-AT
T e e ,
e 1
A K'A
, -At -Ktv
(e - e )
X
1
- e | rem
(19)
After cloud passage, the continuing fallout rate in the shelter
structure due to residual airborne radioiodine is
- V'C'(t) - XF(t) .,
(20)
where C'(t) is given by Eq. (12). Choosing eU as the integrating
factor and rewriting as the total differential,
At
^
V
-AT
dt
(21)
Integrating, where F(0) - 0,
-------
100
it
V>X L / -AT -KT.
(L+K,
- e
dt
Vex L
go
-------
101
Integrating by parts,
FD'
o
r -A*ii
1 - ( Ij+iy e *
rem
(24)
Similarly, the WB external gamma dose inside the shelter structure
accumulated over interval (TlfT ) from outside-fallout deposition is
T
FD'
^'v X K, T
S2° (ATj+1)
-XT
-XT 1
- (XTe+l) e
rem . (25)
SHELTERING AND EVACUATION—VEHICLE AIRBORNE CONCENTRATION
The rate of concentration change in the vehicle is
- Kvc(t) ,
(26)
where K = L + X.
K t
v
Choosing e as the integrating factor and rewriting,
_
dt
r K t i
U V C(t)
= CX L
o v
L t
v
Integrating where C(0) = 0,
(27)
K t
e V C(t)
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102
and the concentration is
/ _U -K t\ 1
C(O - ex I e - e V ) Ci/mJ . (28)
DEFINITION OF TERMS
F(t) = fallout (per unit area)
C(t) = inside airborne concentration (per unit volume)
X = outside airborne concentration (per unit volume)
V = deposition velocity outside
c»
V = deposition velocity inside
O
X = radioactive decay constant (per unit time)
K, = fallout dose conversion constant
K = dose conversion constant
T = cloud exposure period
T = shelter entrance delay period
T = shelter period after cloud passage
T a evacuation period away from shelter
L = ventilation turnover rate (per unit time)
Kf = V'/£ (per unit time)
1 8
SL « mean fall distance for iodine inside
K = L + A + K,
e = ingross fraction
G1 = finite-source correction factor for fallout
LV » ventilation turnover rate for vehicle (per unit time).
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103
REFERENCES
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104
16. Bigger, M. M., R. J. Crew, and R. K. Fuller, Non-Ingested Dose
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105
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* U.S. GOVERNMENTPDmniKOFFICE Mn-720-335/6098
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