United States Air and Energy Engineering

Environmental Protection Research Laboratory

Agency Research Triangle Park, NC 27711

E AP Project Summary

Research and Development EPA/600/SR-95/020 May 1995

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 observation.

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 demonstrate a characteristic pattern of increasing indoor radon concentrations

with increasingly negative indoor air

pressures. A spike also occurs in the

radon-pressure curves near zero pressure due to the very low dilution rate of

indoor radon under passive, low-ventilation conditions. With sensitivity analyses, the lumped-parameter model indicates that the dominant parameters affecting indoor radon levels are the size

of the foundation openings, the pressure-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 subslab radon levels and house ventilation 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 foundation openings permitting radon entry.

Feasibility of Characterizing

Concealed Openings in the

House-Soil Interface for

Modeling Radon Gas Entry

Kirk K. Nielson and Vern C. Rogers

The method was applied to researchhouse data collected by the University

of Florida, indicating a relatively large

(2.5-m2) effective opening in the soilhouse interface. Air flow through the

hollow-block stem wall and permeable

block faces accounts for the large effective opening, which is probably also

influenced by a perimeter shrinkage

crack that usually occurs with floatingslab construction.

The minimum data for estimating total foundation leakage, including concealed leaks, include blower-door testing of house ventilation rates, sub-slab

radon measurements, height measurements for the indoor volume, and

steady-state indoor radon measurements at two or more suction pressures. 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 classification.

This Project Summary was developed

by EPA’s Air and Energy Engineering

Research Laboratory, Research Triangle Park, NC, to announce key findings 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 naturally occurring radium (226Ra) in soils can

move through pores and openings in a

house understructure and enter the indoor atmosphere. If enough radon enters

a house and if it is insufficiently diluted by
2

outdoor air, it can accumulate to levels

that pose significant risks of lung cancer

with chronic exposure.

Because of the complexity of radon entry and accumulation processes, mathematical models have been used to simulate a broader range of soil, radon, and

house conditions than could otherwise be

studied empirically. In comparing empirical data with model calculations, excess

radon entry has often been observed, despite good agreement of data and models

for carefully constructed radon test cells.

Because of its pressure dependence, the

excess radon entry appears most consistent 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 sufficiently explain observed indoor radon levels. Perimeter shrinkage cracks around

floating slabs and flow through hollowblock stem walls may constitute most of

the concealed openings; however, openings 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 permeable regions, characterization of these areas is important to understand and minimize 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 concentrations 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 lumpedparameter 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 concentrations are measured. The following analysis of its theoretical basis and parametric

sensitivity demonstrates how the lumpedparameter model can be used to estimate

understructure leakage areas.

The lumped-parameter model was developed primarily from RAETRAD sensitivity analyses, which identified the most

significant house and soil parameters. The

analyses suggested simplified approximations to express average indoor radon levels as a function of radon source strength

and house radon-resistance and ventilation parameters. The radon source strength

was defined in terms of the sub-slab radon concentration. The house radon resistance 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 concentrations and house leakage data to the

effective area of openings in the housesoil interface. The combined expression

is:

Cnet = 3.6 Csub [fc

 (υdc- υac∆P) + υslb] /

 [h (a|∆P|n + b)] (1)

where

Cnet = net indoor radon concentration

from sub-slab sources (pCi L-1)

Csub = sub-slab radon concentration

f

c = area of floor openings as a fraction of total floor area (dimensionless)

υdc = equivalent velocity of radon diffusion through floor openings,

dependent on radon diffusion

coefficient of the soil (mm s-1)

υac = equivalent velocity of radon advection through floor openings,

dependent on the air permeability of the soil (mm s-1)

∆P = indoor air pressure relative to

outdoors (Pa)

υslb = equivalent velocity of radon diffusion through the floor slab,

dependent on the radon diffusion coefficient of the slab concrete (mm s-1)

h = mean height of the interior volume of the house (m)

a = rate of air infiltration at a 1 Pa

pressure differential (h-1)

n = pressure exponent from blowerdoor test (dimensionless)

b = rate of air infiltration under passive conditions (h-1).

The effective area of openings in the

house-soil interface is defined from fc

 in

Equation 1 as

 Ao = fc Ah, (2)

where

Ao = effective area of openings in the

house-soil interface (m2)

Ah = house area (m2).

Estimating Radon Entry Areas

Successful estimates of effective radon

entry areas, Ao

, depend on a sensitive

solution for the relative area, fc, in Equation 1. Although four of the parameters in

Equation 1 can be measured directly (Cnet,

Csub, ∆P, 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 blowerdoor tests of house ventilation rates, leaving five unknowns in Equation 1.

The lumped-parameter expression in

Equation 1 suggests a characteristic radon-pressure relation that depends on indoor air pressures in both the radon-entry

term (numerator) and house ventilation

term (denominator). The combined effects

of indoor pressure are illustrated by estimating nominal reference values for the

other parameters in Equation 1 and plotting the resulting net radon levels as a

function of indoor air pressure.

Values for the measurable Csub and h

parameters, 1,000 pCi L-1 and 2.44 m, respectively, were assumed. The value

f

c

=0.002 is consistent with concealed cracks

in houses with slab-in-stem-wall foundations, 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 υdc resulted from RAETRAD

calculations using typical soil radon diffusion coefficients. The value for υac, 0.0424

mm s-1 Pa-1, is based on RAETRAD calculations for a house on sandy soil at a water

matric potential of -30 kPa. The υslb parameter, 1.58 x 10-4 mm 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

for υslb is for a floor slab with a radon diffusion coefficient of 8 x 10-4 cm2

s-1, as used

previously. The value for a, 0.3 h-1, is consistent with empirical values measured for

Florida houses, and the values for b and n,

0.035 h-1 and 0.6, respectively, reflect the

age trend and pressure-dependence determined 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 concentrations decrease slowly as pressures approach passive conditions. However, at

zero pressure, the curves showed a sharp

increase in indoor radon caused by the

house’s baseline ventilation rate, b. Concentrations 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 advective dominance of radon entry at this high

suction pressure. At less negative pres-
3

sures, however, the net indoor radon did

not increase proportionately with fc

. Positive 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 fc

, if b was

negligible compared to a|∆P|n

. This is illustrated by rearranging Equation 1 to obtain the following radon entry rate as a

linear function of ∆P:

 Cnet h (a|∆P|n

 + b) / (3.6 Csub)

 = (fc

υdc + υslb) - ∆P (fcυac) (3)

Calculating the left-hand side of Equation 3 for each measured radon and pressure point (ignoring b), the data can be

fitted by least-squares to the pressures,

∆P, to plot radon entry rates as a function

of indoor air pressures. The value of fc

can then be estimated from the slope of

the resulting line as fc

=slope/υac or from

the intercept as fc

=(intercept-υslb)υdc to obtain Ao

 from Equation 2.

Sensitivity Analyses

Sensitivity analyses were conducted to

evaluate which estimate of fc

 is preferable

and to examine the validity of ignoring b

in calculating the left-hand side of Equation 3 for empirical data fits. The sensitivity analyses used the lumped-parameter

expression in Equation 1 to demonstrate

the effects of each parameter on the radon-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 connection with typical values of the other

parameters. The measurable parameters

(Csub and h) were not varied because they

were specified explicitly in the calculations. Only two example values, 0.01 and

0.002, were used for fc

 in the analyses

since it was the main parameter to be

estimated. The range of variation for the

parameters was chosen to include a realistic range of values that could occur in

connection with Florida housing.

The sensitivity analyses showed that

varying the equivalent diffusive radon velocity through foundation openings, υdc,

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 υac. Analyses for the equivalent

diffusive radon velocity through the concrete slab, υslb, showed that varying υslb

affected the radon-pressure curves only

slightly, with the dependence being strongest 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. Likewise, sensitivity curves plotted for the air

pressure exponent, n, showed a strong

dependence on n, with the least dependence occurring in the zero-pressure spike.

Finally, varying the value of the passivecondition 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 parameter 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 radon-pressure curves to υac indicates that

the slope of the line fitted to Equation 3 is

the preferable parameter for estimating fc

and the associated area, Ao. The minimal

sensitivity of the radon-pressure curves to

υdc and to υslb 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 research 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 sustained, “whole-house” indoor suction pressure 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 theoretical, lumped-parameter radon-pressure

curves. The measured data exhibited the

same increasingly negative slopes throughout the ∆P=-50 to -5 Pa range, and the

same large zero-pressure spike near

∆P=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 ∆P = 0

point is not directly useful for estimating

radon leakage because of the greater sensitivity 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 fc

 and υac,

which is a unique estimator of the effect

of foundation leaks on indoor radon. Even

though uncertainty in the precise value of

υac may cause uncertainty in estimating

Ao, the fc

υac product is the parameter of

greatest importance for modeling indoor

radon entry.

Because of the potential time and expense of conducting radon-pressure measurements, the feasibility of taking such

measurements for routine use in diagnosing houses may be limited. However, for

characterizing the magnitudes of typical

soil-house leakage areas for different types

of construction, measurement and analysis 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 (monolithic) floor slabs. This performance data

is vital, in turn, for defining and implementing standards for radon-protective

building construction.
4

K. K. Nielson 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

• •

BULK RATE

POSTAGE & FEES PAID

EPA

PERMIT No. G-35

EPA/600/SR-95/020

Official Business

Penalty for Private Use $300

United States

Environmental Protection Agency

Center for Environmental Research Information

Cincinnati, OH 45268