United States
Environmental Protection
Agency
Air and Energy Engineering
Research Laboratory
Research Triangle Park, NC 27711
Research and Development
EPA/600/SR-95/020
May 1995
EPA Project Summary
Feasibility of Characterizing
Concealed Openings in the
House-Soil Interface for
Modeling Radon Gas Entry
Kirk K. Nielson and Vern C. Rogers
The report examines the feasibility
of characterizing the total effective size
of openings in the house-soil interface
that permit indoor radon entry. Since
many of these foundation openings are
concealed by the building structure or
consist of porous regions, they are
characterized indirectly by their radon
permeability rather than by direct ob-
servation.
A lumped-parameter model, based on
the detailed RAETRAD model for radon
entry, is the basis of the feasibility
study. Sensitivity analyses conducted
with the lumped-parameter model dem-
onstrate a characteristic pattern of in-
creasing indoor radon concentrations
with increasingly negative indoor air
pressures. A spike also occurs in the
radon-pressure curves near zero pres-
sure due to the very low dilution rate of
indoor radon under passive, low-venti-
lation conditions. With sensitivity analy-
ses, the lumped-parameter model indi-
cates that the dominant parameters af-
fecting indoor radon levels are the size
of the foundation openings, the pres-
sure-driven radon entry velocity, and
the ventilation parameters for the house
superstructure.
By rearranging the lumped-parameter
model, measured indoor radon levels
can be grouped with measured sub-
slab radon levels and house ventila-
tion parameters to express radon entry
rates as a linear function of indoor air
pressure. This provides a method for
least-squares linear fitting of measured
radon, pressure, and ventilation data
to identify the effective size of founda-
tion openings permitting radon entry.
The method was applied to research-
house data collected by the University
of Florida, indicating a relatively large
(2.5-m2) effective opening in the soil-
house interface. Air flow through the
hollow-block stem wall and permeable
block faces accounts for the large ef-
fective opening, which is probably also
influenced by a perimeter shrinkage
crack that usually occurs with floating-
slab construction.
The minimum data for estimating to-
tal foundation leakage, including con-
cealed leaks, include blower-door test-
ing of house ventilation rates, sub-slab
radon measurements, height measure-
ments for the indoor volume, and
steady-state indoor radon measure-
ments at two or more suction pres-
sures. Analysis of these data yields an
effective radon entry velocity, which
can be converted to a foundation leak
area using soil moisture data or an
estimate of the soil textural classifica-
tion.
This Project Summary was developed
by EPA's Air and Energy Engineering
Research Laboratory, Research Tri-
angle Park, NC, to announce key find-
ings of the research project that is fully
documented in a separate report of the
same title (see Project Report ordering
information at back).
Introduction
Radon (222Rn) gas from decay of natu-
rally occurring radium (226Ra) in soils can
move through pores and openings in a
house understructure and enter the in-
door atmosphere. If enough radon enters
a house and if it is insufficiently diluted by
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outdoor air, it can accumulate to levels
that pose significant risks of lung cancer
with chronic exposure.
Because of the complexity of radon en-
try and accumulation processes, math-
ematical models have been used to simu-
late a broader range of soil, radon, and
house conditions than could otherwise be
studied empirically. In comparing empiri-
cal data with model calculations, excess
radon entry has often been observed, de-
spite good agreement of data and models
for carefully constructed radon test cells.
Because of its pressure dependence, the
excess radon entry appears most consis-
tent with larger openings in the house-soil
interface, even though significant floor
cracks have not been observed in most of
these cases. Thus, radon entry measured
from visible slab cracks does not suffi-
ciently explain observed indoor radon lev-
els. Perimeter shrinkage cracks around
floating slabs and flow through hollow-
block stem walls may constitute most of
the concealed openings; however, open-
ings around bath tubs and other plumbing
penetrations also may be important in
some cases.
Despite the difficulty of measuring the
areas of concealed openings and perme-
able regions, characterization of these ar-
eas is important to understand and mini-
mize the primary routes for radon entry. If
the size of understructure openings is
known, optimum radon control efforts can
concentrate on closing large openings and
on increasing ventilation or reducing slab
diffusion in houses with small openings.
Theoretical Basis and
Parameter Sensitivity
This feasibility study for estimating
understructure radon leakage areas used
a lumped-parameter model, which is based
in turn on the detailed RAETRAD model.
RAETRAD computes radon entry rates
into a house by integrating the total radon
transport across the floor surface area. It
also estimates indoor radon concentra-
tions from the computed entry rates by
dividing them by the house volume and its
air ventilation rate. The lumped-parameter
model explicitly includes an understructure
leakage-area factor. Since the lumped-
parameter model can be used to estimate
indoor radon concentrations using only a
few house-related parameters, it also can
be used to estimate the radon leakage
area if suitable indoor radon concentra-
tions are measured. The following analy-
sis of its theoretical basis and parametric
sensitivity demonstrates how the lumped-
parameter model can be used to estimate
understructure leakage areas.
The lumped-parameter model was de-
veloped primarily from RAETRAD sensi-
tivity analyses, which identified the most
significant house and soil parameters. The
analyses suggested simplified approxima-
tions to express average indoor radon lev-
els as a function of radon source strength
and house radon-resistance and ventila-
tion parameters. The radon source strength
was defined in terms of the sub-slab ra-
don concentration. The house radon re-
sistance was defined from floor openings,
pressure-driving forces, and slab diffusivity.
Equations for radon entry rates and
house ventilation rates were combined to
obtain the lumped-parameter expression
that was used to relate indoor radon con-
centrations and house leakage data to the
effective area of openings in the house-
soil interface. The combined expression
is:
[h (a|AP|n + b)]
(1)
where
Cnet = net indoor radon concentration
from sub-slab sources (pCi L~1)
Csub = sub-slab radon concentration
f. = area of floor openings as a frac-
tion of total floor area (dimen-
sionless)
t>dc = equivalent velocity of radon dif-
fusion through floor openings,
dependent on radon diffusion
coefficient of the soil (mm s~1)
t>ac = equivalent velocity of radon ad-
vection through floor openings,
dependent on the air perme-
ability of the soil (mm s"1)
AP = indoor air pressure relative to
outdoors (Pa)
Estimating Radon Entry Areas
Successful estimates of effective radon
entry areas, Ao, depend on a sensitive
solution for the relative area, f., in Equa-
tion 1. Although four of the parameters in
Equation 1 can be measured directly (Cnet,
Csub, AP, and h), the other seven cannot,
and must be inferred indirectly from the
empirical measurements. Two of the seven
(a and n) can be estimated from blower-
door tests of house ventilation rates, leav-
ing five unknowns in Equation 1.
The lumped-parameter expression in
Equation 1 suggests a characteristic ra-
don-pressure relation that depends on in-
door air pressures in both the radon-entry
term (numerator) and house ventilation
term (denominator). The combined effects
of indoor pressure are illustrated by esti-
mating nominal reference values for the
other parameters in Equation 1 and plot-
ting the resulting net radon levels as a
function of indoor air pressure.
Values for the measurable Csub and h
parameters, 1,000 pCi L1 and 2.44 m, re-
spectively, were assumed. The value
fc=0.002 is consistent with concealed cracks
in houses with slab-in-stem-wall founda-
tions, and the value fc=0.01 is consistent
with previous lumped-parameter analyses
of floating-slab houses. A value of 0.0143
mm s~1 for t>dc resulted from RAETRAD
calculations using typical soil radon diffu-
sion coefficients. The value for t>ac, 0.0424
mm s~1 Pa~1, is based on RAETRAD calcu-
lations for a house on sandy soil at a water
matric potential of -30 kPa. The t>s|b param-
eter, 1.58 x 10"4mm s~1, is dominated by
radon diffusion through the floor slab, but
also includes lumped-parameter terms for
house size and crack location. The value
where
= equivalent velocity of radon dif- for t>slb is for a floor slab with a radon diffu-
sion coefficient of 8 x 10~4 cm2s~1, as used
previously. The value for a, 0.3 h"1, is con-
sistent with empirical values measured for
Florida houses, and the values for b and n,
0.035 rr1 and 0.6, respectively, reflect the
age trend and pressure-dependence deter-
mined previously for the lumped-parameter
model.
Radon-pressure curves plotted for two
radon entry areas, fc=0.01 and 0.002,
showed that net indoor radon concentra-
tions decrease slowly as pressures ap-
proach passive conditions. However, at
zero pressure, the curves showed a sharp
increase in indoor radon caused by the
house's baseline ventilation rate, b. Con-
centrations for the larger radon entry area
were approximately 5 times higher than
those for the smaller area at a pressure of
-50 Pa. This difference indicates advec-
tive dominance of radon entry at this high
suction pressure. At less negative pres-
t>l
fusion through the floor slab,
dependent on the radon diffu-
sion coefficient of the slab con-
crete (mm s'1)
h = mean height of the interior vol-
ume of the house (m)
a = rate of air infiltration at a 1 Pa
pressure differential (h~1)
n = pressure exponent from blower-
door test (dimensionless)
b = rate of air infiltration under pas-
sive conditions (rr1).
The effective area of openings in the
house-soil interface is defined from f, in
Equation 1 as
= f
(2)
Ao = effective area of openings in the
house-soil interface (m2)
A = house area (m2).
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sures, however, the net indoor radon did
not increase proportionately with f.. Posi-
tive pressures were omitted because the
lumped-parameter model is based on
negative-pressure RAETRAD analyses
and does not apply to positive pressures.
When the two radon-pressure curves
were measured empirically, they provided
a potential means of estimating f., if b was
negligible compared to a|AP|n. This is il-
lustrated by rearranging Equation 1 to ob-
tain the following radon entry rate as a
linear function of AP:
Cnet h (a|AP|" + b) / (3.6 Csub)
= (fAc + uslb)-AP(fco)ac) (3)
Calculating the left-hand side of Equa-
tion 3 for each measured radon and pres-
sure point (ignoring b), the data can be
fitted by least-squares to the pressures,
AP, to plot radon entry rates as a function
of indoor air pressures. The value of f.
can then be estimated from the slope of
the resulting line as fc=slope/t>ac or from
the intercept as fc=(intercept-t>s|b)'udc to ob-
tain Ao from Equation 2.
Sensitivity Analyses
Sensitivity analyses were conducted to
evaluate which estimate of f. is preferable
and to examine the validity of ignoring b
in calculating the left-hand side of Equa-
tion 3 for empirical data fits. The sensitiv-
ity analyses used the lumped-parameter
expression in Equation 1 to demonstrate
the effects of each parameter on the ra-
don-pressure curves. In each analysis, only
one parameter was varied (the others were
held constant). This approach illustrated
the effects of a specific parameter in con-
nection with typical values of the other
parameters. The measurable parameters
(Csub and h) were not varied because they
were specified explicitly in the calcula-
tions. Only two example values, 0.01 and
0.002, were used for f, in the analyses
since it was the main parameter to be
estimated. The range of variation for the
parameters was chosen to include a real-
istic range of values that could occur in
connection with Florida housing.
The sensitivity analyses showed that
varying the equivalent diffusive radon ve-
locity through foundation openings, t>dc,
generally had little effect on the radon
pressure curves. In contrast, varying the
equivalent advective radon velocity through
foundation openings revealed that the
curves had a strong dependence on the
value of t>ac. Analyses for the equivalent
diffusive radon velocity through the con-
crete slab, t>slb, showed that varying t>slb
affected the radon-pressure curves only
slightly, with the dependence being stron-
gest in the zero-pressure spike.
Sensitivity curves plotted for different
reference (1 Pa) air infiltration rates, a,
showed a very strong dependence on a,
except in the zero-pressure spike. Like-
wise, sensitivity curves plotted for the air
pressure exponent, n, showed a strong
dependence on n, with the least depen-
dence occurring in the zero-pressure spike.
Finally, varying the value of the passive-
condition air infiltration rate, b, showed
very little dependence on b throughout
the negative pressure range, but a very
strong dependence in the zero-pressure
spike.
The sensitivity analyses for the b pa-
rameter indicated that it can reasonably
be ignored in computing the radon entry
fitting parameter on the left-hand side of
Equation 3. The strong sensitivity of ra-
don-pressure curves to t>ac indicates that
the slope of the line fitted to Equation 3 is
the preferable parameter for estimating f.
and the associated area, Ao. The minimal
sensitivity of the radon-pressure curves to
t>dc and to t>s|b indicates that the intercept
of the line fitted to Equation 3 is not a
good parameter for estimating fc.
Radon-Pressure Analysis of the
University of Florida Research
House
In addition to its use in the sensitivity
analyses, the lumped-parameter equation
(Equation 1) was applied to empirical data
measured at a University of Florida re-
search house. The empirical data were
measured by the university as part of its
Florida Radon Research Program study
of radon dynamics in a house dedicated
for research in Gainesville, FL. The data
included radon-pressure curves obtained
by using a blower door to induce a sus-
tained, "whole-house" indoor suction pres-
sure while monitoring indoor radon levels
until they reached steady-state values.
The radon concentration and building
air pressure measurements taken in the
research house analysis showed overall
consistency with the shapes of the theo-
retical, lumped-parameter radon-pressure
curves. The measured data exhibited the
same increasingly negative slopes through-
out the AP=-50 to -5 Pa range, and the
same large zero-pressure spike near
AP=0. The results of this analysis confirm
that the slope of the line fitted to Equation
3 is a much more sensitive parameter
than the line's intercept for determining fc
and the associated area, Ao. However, the
analysis also determined that the AP = 0
point is not directly useful for estimating
radon leakage because of the greater sen-
sitivity of data points at more negative
pressures.
Conclusions
Fitting measured radon-pressure data
to the parameters in Equation 3 proved to
be the most direct and sensitive approach
for estimating the product of f, and t>ac,
which is a unique estimator of the effect
of foundation leaks on indoor radon. Even
though uncertainty in the precise value of
t>ac may cause uncertainty in estimating
Ao, the fct>ac product is the parameter of
greatest importance for modeling indoor
radon entry.
Because of the potential time and ex-
pense of conducting radon-pressure mea-
surements, the feasibility of taking such
measurements for routine use in diagnos-
ing houses may be limited. However, for
characterizing the magnitudes of typical
soil-house leakage areas for different types
of construction, measurement and analy-
sis of radon-pressure data may be very
useful. In fact, this approach is probably
the only method presently available for
empirically characterizing the magnitudes
of concealed leaks or high-permeability
regions in the foundations of houses with
different types of foundation construction.
Such characterization is vital to estimating
the true performance of passive barriers
such as conventional and improved (mono-
lithic) floor slabs. This performance data
is vital, in turn, for defining and imple-
menting standards for radon-protective
building construction.
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K. K. Me/son and V. C. Rogers are with Rogers and Associates Engineering Corp.,
Salt Lake City, UT 84110-0330.
David C. Sanchez is the EPA Project Officer (see below).
The complete report, entitled "Feasibility of Characterizing Concealed Openings in
the House-Soil Interface for Modeling Radon Gas Entry," (Order No. PB95-
178414; Cost: $17.50, subject to change) will be available only from:
National Technical Information Service
5285 Port Royal Road
Springfield, VA 22161
Telephone: 703-487-4650
The EPA Project Officer can be contacted at:
Air and Energy Engineering Research Laboratory
U.S. Environmental Protection Agency
Research Triangle Park, NC 27711
United States
Environmental Protection Agency
Center for Environmental Research Information
Cincinnati, OH 45268
Official Business
Penalty for Private Use $300
BULK RATE
POSTAGE & FEES PAID
EPA
PERMIT No. G-35
EPA/600/SR-95/020
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