2002 International Radon Symposium Proceedings
Relationship Between the Permeability Coefficient of Concrete and LowPressure Differentials
Esam AbuIrshaid and Kevin J. Renken
University of WisconsinMilwaukee
Mechanical Engineering Department
Radon Reduction Technology Laboratory
3200 North Cramer Street
Milwaukee, Wisconsin 532 1 I
USA
ABSTRACT
This paper presents experimental results on the permeability coefficient of concrete under lowpressure
differentials. Three concrete samples have been exposed to differential pressures ranging between 1 Pa and 1
psi under controlled conditions. The laboratory tests simulate indoor radon gas entry by advection (Ap 1  20
Pa). The permeability coefficient is measured by a unique control system that employs sensitive pressure
transducers, needle control valves, thermistors, and relative humidity sensors connected to a sophisticated PCdata acquisition and control system. The concrete samples are 4" in length and 3.5" in diameter and are
maintained in aluminum holders. The concrete mixtures are standard compositions that simulate typical
Wisconsin concretes used in basement foundations. The experimental results highlight the slip effect that
produces higher values of the permeability coefficient at very lowpressure differences. Details of the
innovative experimental setup and procedures are described.

INTRODUCTION
Calculations on the indoor radon entry rate by pressuredriven flow rely on the permeability coefficient of the
concrete. The permeability coefficient is the transport coefficient for permeability, and is the proportionality
constant in Darcy's law that relates fluid flux through a porous material (e.g., concrete) to the pressure gradient.
In typical radon problems, the pressure difference across the foundation walls may range between 1  20 Pa.
However, there exists very little experimental data on the permeability coefficient of air in concrete for these
lowpressure differences. The majority of studies have documented permeability coefficients at differential
pressures beyond the scope of advective radon entry problems in residential construction (Nielson and Rogers
1991 ; Rogers and Nielson 1992; Snoddy 1994). Permeability measurements under specified high pressure
difference conditions have been found not to scale linearly to the small pressure differences of interest. This
nonlinearity for large pressure differences normally leads to an underestimate of the flow velocity at lowpressure difference conditions and hence, a large variance in the permeability value (Colic 1981). These
previous experimental investigations have neglected to account for the slip effect (or limitations of Darcy's law)
found at low pressures when extrapolating values of K. If permeability measurements are made under
conditions different from those for which they are to be applied, a correction factor has to be made. This
correction is represented by the slip effect where the superficial gas permeability (i.e., the value of K in Darcy's
law) is a linear function of the inverse mean pressure of the gas. Since the cause of this dependence is gas
slippage, it increases with increasing free path length (Sheidcgger 1974).
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2002 International Radon Symposium Proceedings
To characterize this limitation in Darcy's law, an innovative laboratory apparatus to accurately measure the
concrete air permeability at lowpressure differences that simulate indoor radon gas entry by advection was
introduced by Abraham et al. (2000). This study also compared permeability coefficients for several
experimental investigations that used pressure differences in the order of magnitude of one psi. Ferguson et al.
(2001) continued this research by reporting preliminary experimental data on the permeability coefficient of
concrete subjected to constant pressure differences between 5  15 Pa.
This paper is a continuation of the work presented by Ferguson et al. (2001). Utilizing the same automated
permeability apparatus fabricated by Abraham et al. (2000), the authors measure the permeability coefficient of
three concrete samples of different formulas over a wide range of applied pressure differences (1 Pa  1 psi).
Measurements at very low differential pressures (Ap 1  20 Pa) simulate indoor radon entry by advection and
highlight the slip effect.

PERMEABILITY COEFFICIENT
The permeability coefficient (K) is the proportionality constant in Darcy's law that relates the fluid flux through
a porous material (e.g., intact concrete) to the pressure gradient. The value of K dictates the indoor radon entry
rate by the advection transport mechanism. Darcy's law as applied to our experimental setup is expressed as:
where,
Q
K
A
Ap
p
L
volumetric flow rate of air
= permeability coefficient
= crosssectional area of the concrete sample
= applied pressure difference across the concrete
= viscosity of air
= thickness of concrete sample.
=
The volumetric flow rate of air through the concrete pores is calculated from the ideal gas law and the
molecular volume of air as described by Maas and Renken (1997).
CONCRETE SAMPLES
Table 1 provides a description of the concrete test samples used in this study. The three concrete samples
The
simulate standard Wisconsin pouredconcrete for basement foundations (Hool 1918; USBR 1938).
Pea
gravel
was
used
to
obtain
a
ingredients for the concrete samples were cement, sand, stones, and water.
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2002 International Radon Symposium Proceedings
homogeneous mixture with respect to the sample size. A watertocement ratio (wh) of 0.5 was used and the
ratio of the concrete ingredients (cement:sand:pea gravel) was 1:2:4 (Sample A) and 1:2:2 (Samples Bl and
B2). As shown in Figs. 1 and 2, a cylindrical aluminum casing was employed to cast and hold the concrete
samples for testing. As per ASTM specifications (ASTM 1994), the concretes were removed from the holders
24 hours after casting and placed in a high humidity chamber for 30 days. After curing, the samples were
allowed to dry at ambient conditions for one week. The samples were then placed back into the cylindrical
holders and the circumferences of each were sealed with a cementitious epoxy,
The porosity (e) of each concrete sample was measured by using a concrete porosity measurement system first
introduced by Maas and Renken (1997). Figure 3 displays a schematic diagram of this porosity apparatus. As
expected, Sample A has a porosity that is approximately 3 1% larger than Samples B 1 and B2. The porosities of
Samples Bl and B2 differ by approximately 7%. The experimental uncertainty of these measurements is + 3%.
PERMEABILITY APPARATUS
As shown in Figs. 4 and 5, the same permeability apparatus used by Ferguson et al. (2001) is employed in this
study. More specifically, the system consists of a clean air pressure source, two pressure chambers (high and
low), the concrete samples situated between the chambers, two miniature proportional flow control valves,
pressure transducers, thermistors, humidity sensors, and a highspeed PCdata acquisition and control system
(PCDACS). An accompanying commercial programming language is employed to monitor pressure
conditions and to electronically control the operation of the needle control valves. Figure 6 presents a detailed
schematic diagram of the permeability measurement system. Complete details of the automated operation of
the system are described in Abraham et al. (2000).
DISCUSSION OF RESULTS
Figure 7 displays the experimental data generated by this study. More specifically, Fig. 7 presents a comparison
of the measured air permeability coefficients for Samples A, B l , and B2. The differential pressure applied to
the concrete samples during testing ranged between 1 Pa and 1 psi (6,895 Pa). As shown, there exists a
logarithmic increase in the value of K for all three samples as the applied pressure difference is decreased. An
approximate 100,000% increase in the average value of K is realized for all samples when Ap is decreased from
1 psi to 1 Pa. As the applied pressure difference increases beyond lo3, we start to see a levelingoff effect of the
permeability coefficients. Here, there exists an approximate 10% difference in the value of K between 5,000 Pa
and 1 psi (6,895 Pa) for all three concrete samples.
These experimental findings verify and complement the hypotheses of Abraham et al. (2000) and Ferguson et
al. (2001). These studies suggested significant increases in the permeability coefficient at very low differential
pressures could be attributed to the slip effect. Permeability measurements at highpressure differences (e.g., 1
 100 psi) have been found not to scale linearly to small pressure differences (e.g., 1  20 Pa) symbolic of
advective or pressuredriven radon entry problems (Colic 1981; Abraham et al. 2000, Ferguson et al. 2001).
Therefore, the authors conclude that Darcy's law needs to be modified with a slip effect coefficient for very
lowpressure differences across concretes. Previously published data on permeability measurements under
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2002 International Radon Symposium Proceedings
specified highpressure differences have underestimated the flow for lowpressure calculations by neglecting a
correction factor for slip. This has resulted in a significant underestimation of indoor radon entry rates
(Ferguson et al. 2001).
To better illustrate this underestimation of radon entry rate prediction, we can use the simple model of Nazaroff
and Nero (1988) to approximate indoor radon concentrations due to advective flow between radonladen soil
and a typical detached house. Here, the radon gas entry rate per unit volume for a 1 Pa pressure difference
across a typical intact concrete basement wall is estimated by Darcy's law (Eqn. 1) where,
1.92 x 10' 16 m2 (based on experimental data at 1 psi for Sample A)
140 m2 (typical foundation wall surface area)
1 Pa (pressure difference across a foundation wall)
1.846 x 1o ' ~kg/msec (viscosity of air at room temperature)
= 0.10 m (4" thick concrete foundation wall).
Kavg,=
A =
Ap =
p =
L
If we assume an average radon concentration in the soil of 2,700 pCi/L (Nagda 1994), a house volume of lo3
m3, and a house ventilation rate of 0.25 ACH, we find the indoor equilibrium radon concentration level due to
advective entry through the concrete foundation wall is approximately I = 0.39 pCi/L. Now, using the same
parameters and the value of K measured at 1 Pa for Sample A, we find the indoor equilibrium radon
concentration to be approximately I = 0.94 pCi/L. A 141% increase in the indoor radon level is realized. If we
use a very tight house in the calculation ( 0 ACH), the results are even more significant. This calculation
yields indoor equilibrium radon concentrations of I = 0.01 1 and 18.6 pCi/L when the permeability coefficient is
based on experimental data at 1 psi and 1 Pa, respectively.
Figure 7 also displays the effect of concrete ingredients on the value of the permeability coefficient at low
applied differential pressures. Here, we see the overall permeability of Sample A is greater than Samples Bl
and B2 over the entire Ap test range. This is attributed to the higher porosity of Sample A. Concretes with
more pore volume are more likely to allow greater flow rate, hence greater permeability. Renken and
Rosenberg (1995) and Lambert and Renken (1999) found similar trends in the permeability coefficient for
higher porosity concretes.
Finally, Fig. 7 provides a comparison of the permeability coefficient between two nearly identical concrete
samples, B l and B2. Samples Bl and B2 were fabricated at the same time with the same batch of concrete mix.
As expected, there exists a very tight overlap in measured values of K over the entire range of applied Ap. This
data verifies the experimental method used to determine the relationship between the permeability coefficient
and the applied pressure difference. Table 2 provides the empirical relationships between K and Ap for the
three test samples. The experimental uncertainty of the measured permeability coefficient is 25% (Abraham et
al. 2000).
CONCLUSIONS AND RECOMMENDATIONS
This paper presented empirical correlations of the permeability coefficient of concrete versus applied pressure
differences. Three concrete samples of two different formulas were exposed to pressure differences in the range
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2002 International Radon Symposium Proceedings
of 1 Pa  1 psi. It was found that there exists a significant difference in the permeability coefficient when the
pressure differential across the concrete approaches real indoor radon entry conditions (Ap 1  20 Pa). When
the applied pressure difference approaches 1 psi, there is minimal difference in the value of the permeability
coefficient. This significant difference in the permeability is attributed to the slip effect and is highlighted when
applied to the estimation of indoor radon entry rates by advection. It is recommended that further tests be
conducted to fully characterize a slip effect coefficient and its dependence on applied pressure difference,
concrete composition and age, and relative humidity level.

ACKNOWLEDGEMENTS
The authors would like to thank Ms. Kimberly Jonet and Ms. Laura Ferguson for their initial work on this
project. Special thanks to Mr. George T. Abraham for his ideas and fabrication of the original control loop
system.
REFERENCES
Abraham, G. T.; Daoud, W. Z.; Renken, K. J. Experimental measurements on the permeability coefficient of a
concrete sample under low pressure differences. In: The 2000 Intcrnational Radon Symposium PrePrints. 12.1
 12.12 Milwaukee, WI: AARST; 2000.
American Society for Testing Materials (ASTM). Standard practice for making and curing concrete test
specimens in the laboratory. Annual Book of ASTM Standards. Designation C 192  90a; 1994.
Colle, R; Rubin, R. J.; Knab, L. I.; Hutchinson, J. M. R. Radon transport through and exhalation from building
materials: a review and assessment. National Bureau of Standards, Technical Note 1139. Washington, DC;
1981.
Ferguson, L. J.; Daoud, W. Z.; Renken, K. J. Further measurements on the permeability coefficient of a
concrete sample under low pressure differences. In: The 2001 International Radon Symposium PrePrints. 78 86 Daytona Beach, Florida: AARST; 2001.
Hool, G.A. Concrete Engineer's Handbook. New York: McGrawHill; 1918.
Lambert, T. L,; Rcnkcn, K. J. Experiments on industrial byproduct utilization as a concrete admixture to reduce
radon gas transport properties. In: The 1999 International Radon Symposium Preprints. 13.013.10 Las Vegas,
NV: AARST; 1999.
Maas, J .I.; Rcnken, K. J. Laboratory assessment of cementitious coatings as a barrier to radon gas entry. In:
The 1997 International Radon Symposium PrePrints. 1.1  1.13 Cincinnati, OH: AARST; 1997.
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2002 International Radon Symposium Proceedings
Nagda, N. L. Radon: prevalence, measurements, health risks and control. ASTM Manual Series, Philadelphia,
PA: ASTM; 1994.
Nazaroff, W. W.; Nero, A. V. Radon and its decay products in indoor air. New York: John Wiley & Son; 1988.
Nielson, K.K.;Rogers, V.C. Radon entry into dwellings through concrete floors. In: The 1991 International
Symposium on Radon and Radon Reduction Technology. Vol. 3: US EPA; 1991.
Rcnkcn, K. J.; Rosenberg, T. Laboratory measurements of the transport of radon gas through concrete samples.
Health Physics. 68:800808; June 1995.
Rogers, V.C.; Nielson, K.K. Data and models for radon transport through concrete. In: The 1992 International
Symposium on Radon and Radon Reduction Technology. Vol. 3: US EPA; 1992.
Shcidegger, A.E. The Physics of Flow Through Porous Media. Toronto, Canada: University of Toronto Press;
1974.
Snoddy, R. Laboratory assessment of the permeability and diffusion characteristics of Florida concretes, phase
I, methods development and testing. EPA600/R94053. US EPA, Research Triangle Park, NC; April 1994.
United States Bureau of Reclamation (USBR). Concrete manual: a manual for the control of concrete
construction. Denver, CO: USBR; 1938.
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2002 International Radon Symposium Proceedings
Fig. 1. Photo of concrete sample in an aluminum holder.
Fig. 2. Schematic of concrete sample and aluminum holder.
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2002 International Radon Symposium Proceedings
Secondary Chamber,
Sample Chamber,
\
Panicle and Humidity Filter
@
0
On 1 OffValve
Pressure Transducer
TOData Acauisition:
Pressure, Pa, Pb; Temperature,
Ta, Tb,Relative Humidity, RHa
Fig. 3. Schematic diagram of porosity apparatus (Maas and Renken 1997).
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2002 International Radon Symposium Proceedings
Fig. 4. Photo of experimental apparatus to measure the air permeability o f concrete.
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2002 International Radon Symposium Proceedings
Concrete
Sample
LowPressurc
Chamber
Fig. 5. Schematic of permeability apparatus.
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2002 International Radon Symposium Proceedings
Dilta Acquisition and Control Syslcm
Control Signal
Fig. 6. Schematic diagram o f system to measure the air permeability coefficient of concrete.
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2002 International Radon Symposium Proceedings

+ Sample A
Sample B 1
*
Sample B2
Sample A
Fig.7. Measured air permeability coefficients for Samples A, B l , and B2.
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2002 International Radon Symposium Proceedings
Sample
Table 1. Description of concrete test samples.
L (in.)
Porosity, e (96)
Cement:Sand:Pea Gravel
wlc
D (in.)
Table 2. Empirical relationships between permeability coefficient and applied pressure difference for concrete
test samples.
Sample
K vs. Ap
A
K = 3.0 x lo^ ~
p
~
.
~
~
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~